A Pharmacology Primer
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A Pharmacology Primer, 6e
Terry Kenakin, Author
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ACADEMIC
PRESS
A Pharmacology Primer
Techniques for More Effective and Strategic
Drug Discovery
Sixth Edition
Terry P. Kenakin
Professor of Pharmacology
The University of North Carolina School of Medicine
Chapel Hill, NC, United States
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Notices
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Dedication
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Contents
Preface to sixth edition
xiii
2.6.3
2.6.4
1. What is pharmacology?
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
1.10
1.11
1.12
1.13
1.14
About this book
What is pharmacology?
The receptor concept
Pharmacological test systems
The nature of drug receptors
From the snapshot to the movie
Pharmacological intervention and the
therapeutic landscape
System-independent drug parameters:
affinity and efficacy
What is affinity?
The Langmuir adsorption isotherm
What is efficacy?
Doseeresponse curves
1.12.1
Potency and maximal response
1.12.2
P-scales and the representation
of potency
Chapter summary and conclusions
Derivations: conformational selection
as a mechanism of efficacy
References
2.7
1
1
3
4
7
7
2.8
2.9
2.10
8
11
13
14
15
17
18
2.11
2.12
18
20
20
21
2. How different tissues process drug
response
2.1
2.2
2.3
2.4
2.5
2.6
The ‘eyes to see’: pharmacologic assays
The biochemical nature of stimuluse
response cascades
The mathematical approximation of
stimuluseresponse mechanisms
Influence of stimuluseresponse
cascades on doseeresponse curve
slopes
System effects on agonist response:
full and partial agonists
Differential cellular response to
receptor stimulus
2.6.1
Choice of response pathway
2.6.2
Augmentation or modulation of
stimulus pathway
23
25
27
29
30
33
33
34
Differences in receptor density
Target-mediated trafficking of
stimulus
Receptor desensitization and
tachyphylaxis
The measurement of drug activity
Advantages and disadvantages of
different assay formats
Drug concentration as an independent
variable
2.10.1
Dissimulation in drug
concentration
2.10.2
Free concentration of drug
Chapter summary and conclusions
Derivations
2.12.1
Series hyperbolae can be
modeled by a single
hyperbolic function
2.12.2
Successive rectangular hyperbolic equations necessarily
lead to amplification
2.12.3
Saturation of any step in a
stimulus cascade by two
agonists leads to identical
maximal final responses for
the two agonists
2.12.4
Procedure to measure free
drug concentration in the
receptor compartment
References
35
37
37
40
40
41
41
43
43
43
44
44
44
45
45
3. Drugereceptor theory
3.1
3.2
3.3
3.4
3.5
3.6
3.7
About this chapter
Drugereceptor theory
The use of mathematical models in
pharmacology
Some specific uses of models in
pharmacology
Mass action building blocks
Classical model of receptor
function
The operational model of receptor
function
47
47
48
49
55
56
57
vii
viii
Contents
3.8
3.9
3.10
3.11
3.12
3.13
3.14
3.15
Two-state theory
The ternary complex model
The extended ternary complex model
Constitutive receptor activity and
inverse agonism
The cubic ternary complex model
Multistate receptor models and
probabilistic theory
Chapter summary and conclusions
Derivations
3.15.1
Radioligand binding to
receptor dimers demonstrating
cooperative behavior
3.15.2
Effect of variation in an HIV-1
binding model
3.15.3
Derivation of the operational
model
3.15.4
Operational model forcing
function for variable slope
3.15.5
Derivation of two-state theory
3.15.6
Derivation of the extended
ternary complex model
3.15.7
Dependence of constitutive
activity on receptor density
3.15.8
Derivation of the cubic ternary
complex model
References
4.7.3
Displacement of a radioligand
by an allosteric antagonist
4.7.4
Relationship between IC50 and
KI for competitive antagonists
4.7.5
Maximal inhibition of binding
by an allosteric antagonist
4.7.6
Relationship between IC50 and
KI for allosteric antagonists
4.7.7
Two-stage binding reactions
4.7.8
Effect of G-Protein coupling on
observed agonist affinity
4.7.9
Effect of excess receptor in
binding experiments: saturation
binding curve
4.7.10
Effect of excess receptor in
binding experiments: displacement experiments
4.7.11
Derivation of an allosteric binding model
References
58
59
59
60
62
63
65
65
65
66
67
67
68
68
69
69
69
4.3
4.4
4.5
4.6
4.7
The structure of this chapter
Binding theory and experiment
4.2.1
Saturation binding
4.2.2
Displacement binding
4.2.3
Kinetic binding studies
Complex binding phenomena: agonist
affinity from binding curves
Experimental prerequisites for correct
application of binding techniques
4.4.1
The effect of protein concentration on binding curves
4.4.2
The importance of equilibration
time for equilibrium between
two ligands
Binding in allosteric systems
Chapter summary and conclusions
Derivations
4.7.1
Displacement binding:
competitive interaction
4.7.2
Displacement binding:
noncompetitive interaction
71
71
74
76
79
5.1
5.2
5.3
5.4
80
84
84
85
87
91
92
92
92
93
94
94
94
94
94
95
95
96
5. Drug targets and drug-target
molecules
4. Pharmacological assay formats:
binding
4.1
4.2
92
5.5
Defining biological targets
Specific types of drug targets
5.2.1
G-protein-coupled receptors
5.2.2
Ion channels
5.2.3
Enzymes
5.2.4
Nuclear receptors
5.2.5
Nucleotide-based drug targets
Small drug-like molecules
5.3.1
Hybrid molecules
5.3.2
Chemical sources for potential
drugs
Biologics
5.4.1
Replacement proteins
5.4.2
Eliminating ‘undruggable’ proteins through PROTACs
5.4.3
Peptides
5.4.4
Antibodies
5.4.5
Immunotherapy
5.4.6
Vaccines
5.4.7
Nucleic acidebased drug species
Summary and conclusions
References
Further reading
97
100
100
102
103
111
112
114
116
121
126
127
130
131
135
141
141
142
147
147
149
6. Agonists: the measurement of affinity
and efficacy in functional assays
6.1
Functional pharmacological
experiments
151
Contents
6.2
6.3
6.4
6.5
6.6
6.7
6.8
6.9
6.10
6.11
The choice of functional assays
Recombinant functional systems
Functional experiments: dissimulation
in time
Experiments in real time versus
stop-time
Quantifying agonism: the BlackeLeff
operational model of agonism
6.6.1
Affinity-dependent versus
efficacy-dependent agonist
potency
6.6.2
Secondary and tertiary testing
of agonists
Biased signaling
6.7.1
Receptor selectivity
Null analyses of agonism
6.8.1
Partial agonists
6.8.2
Full agonists
Comparing full and partial agonist
activities: Log(max/EC50)
Chapter summary and conclusions
Derivations
6.11.1
Relationship between the EC50
and affinity of agonists
6.11.2
Method of Barlow, Scott, and
Stephenson for affinity of
partial agonists
6.11.3
Maximal response of a partial
agonist is dependent on
efficacy
6.11.4
System independence of full
agonist potency ratios
6.11.5
Measurement of agonist
affinity: method of Furchgott
6.11.6
Agonism as a positive
allosteric modulation of
receptoresignaling protein
interaction to derive
DLog(max/EC50) ratios
References
159
160
Introduction
Kinetics of drugereceptor interaction
Surmountable competitive antagonism
7.3.1
Schild analysis
7.3.2
Patterns of DoseeResponse
curves that preclude schild
analysis
7.3.3
Best practice for the use of
schild analysis
7.3.4
Analyses for inverse agonists in
constitutively active receptor
systems
7.4
7.5
7.6
7.7
162
166
168
169
175
175
175
179
182
183
183
183
184
184
184
184
185
187
7. Orthosteric drug antagonism
7.1
7.2
7.3
7.3.5
7.3.6
152
156
189
189
192
192
197
198
199
7.8
7.9
7.10
7.11
7.12
Analyses for partial agonists
The method of Lew and Angus:
nonlinear regression analysis
Noncompetitive antagonism
Agonisteantagonist hemiequilibria
Resultant analysis
Antagonism in vivo
7.7.1
Antagonists with efficacy in
vivo
7.7.2
Kinetics of target coverage
7.7.3
Kinetics of dissociation
7.7.4
Estimating antagonist
dissociation with hemiequilibria
Blockade of indirectly acting agonists
Irreversible antagonism
Chemical antagonism
Chapter summary and conclusions
Derivations
7.12.1
Derivation of the Gaddum
equation for competitive
antagonism
7.12.2
Derivation of the Gaddum
equation for noncompetitive
antagonism
7.12.3
Derivation of the schild
equation
7.12.4
Functional effects of an
inverse agonist with the
operational model
7.12.5
pA2 measurement for inverse
agonists
7.12.6
Functional effects of a partial
agonist with the operational
model
7.12.7
pA2 measurements for partial
agonists
7.12.8
Method of Stephenson for
partial agonist affinity
measurement
7.12.9
Derivation of the Method of
Gaddum for noncompetitive
antagonism
7.12.10
Relationship of pA2 and pKB
for insurmountable
orthosteric antagonism
7.12.11
Resultant analysis
7.12.12
Blockade of indirectly acting
agonists
7.12.13
Chemical antagonism:
abstraction of agonist
concentration
7.12.14
Chemical antagonism:
abstraction of antagonist
concentration
References
ix
201
203
204
208
210
210
212
214
216
219
219
220
222
226
227
227
227
228
228
228
229
229
229
230
230
230
231
231
231
232
x Contents
8. Allosteric modulation
8.1
8.2
8.3
8.4
8.5
8.6
8.7
8.8
8.9
Introduction
The nature of receptor allosterism
Unique effects of allosteric modulators
Functional study of allosteric modulators
8.4.1
Phenotypic allosteric modulation
profiles
8.4.2
Allosteric agonism
8.4.3
Affinity of allosteric modulators
8.4.4
Negative allosteric modulators
8.4.5
Positive allosteric modulators
8.4.6
Quantifying PAM activity in vivo
8.4.7
NAM/PAM induced agonist bias
8.4.8
Optimal assays for allosteric
function
Functional allosteric model with
constitutive activity
Internal checks for adherence to the
allosteric model
Methods for detecting allosterism
Chapter summary and conclusions
Derivations
8.9.1
Allosteric model of receptor
activity
8.9.2
Effects of allosteric ligands on
response: changing efficacy
8.9.3
Schild analysis for allosteric
antagonists
8.9.4
Application of Log(Max/R50)
values from R50 curves to
quantify the effects of PAMs
8.9.5
Quantifying allosterically
mediated induced bias in
agonism
8.9.6
Functional allosteric model with
constitutive receptor activity
References
233
233
235
240
242
243
243
246
250
254
255
255
256
257
260
262
262
9.3
9.4
9.5
Introduction
The optimal design of pharmacological
experiments
9.2.1
Drug efficacy
9.2.2
Affinity
9.2.3
Orthosteric versus allosteric
mechanisms
Null experiments and fitting data to
models
Interpretation of experimental data
Predicting therapeutic activity in all
systems
10.1
10.2
10.3
10.4
263
263
264
264
265
266
10.5
10.6
10.7
10.8
10.9
10.10
269
269
270
283
292
293
296
299
299
301
302
303
304
304
304
305
305
10. Pharmacokinetics
262
9. The optimal design of
pharmacological experiments
9.1
9.2
9.6
9.7
9.5.1
Predicting agonism
9.5.2
Predicting binding
9.5.3
Drug combinations in vivo
Summary and conclusions
Derivations
9.7.1
IC50 Correction Factors:
competitive antagonists
9.7.2
Relationship of pA2 and pKB for
Insurmountable Orthosteric
antagonism
9.7.3
Relationship of pA2 and pKB for
Insurmountable Allosteric
Antagonism
References
10.11
Introduction
Biopharmaceutics
The chemistry of “drug-like”
character
Pharmacokinetics
10.4.1
Drug absorption
10.4.2
Route of drug
administration
10.4.3
General pharmacokinetics
10.4.4
Metabolism
10.4.5
Clearance
10.4.6
Volume of distribution and
half-life
10.4.7
Renal clearance
10.4.8
Bioavailability
Nonlinear pharmacokinetics
Multiple dosing
Modifying pharmacokinetics through
medicinal chemistry
Practical pharmacokinetics
10.8.1
Allometric scaling
Placement of pharmacokinetic assays
in discovery and development
The pharmacokinetics of biologics
10.10.1
Absorption
10.10.2
Duration of action
10.10.3
Antibody PK
10.10.4
mRNA PK
Summary and conclusions
References
307
307
308
313
313
319
322
325
330
332
338
340
342
343
345
347
349
350
352
353
354
355
355
355
356
11. Safety pharmacology
11.1
11.2
Safety pharmacology
Hepatotoxicity
11.2.1
Drugedrug interactions
11.2.2
Direct hepatotoxicity
359
365
365
370
Contents
11.2.3
11.3
11.4
11.5
11.6
11.7
11.8
11.9
Hepatotoxicity in context in
vivo
Cytotoxicity
Mutagenicity
hERG activity and Torsades de
Pointes
Autonomic receptor profiling and
off-target effects
General pharmacology
Clinical testing and drug toxicity
Summary and conclusions
References
13.2.3
372
372
374
376
13.2.5
376
377
379
381
381
12.2
12.3
12.4
12.5
12.6
12.7
12.8
Some challenges for modern drug
discovery
The drug-discovery process
Target-based drug discovery
12.3.1
Target validation and the
use of chemical tools
12.3.2
Recombinant systems
Systems-based drug discovery
High-throughput screening
12.5.1
Structure-based drug design
and virtual screening
12.5.2
Phenotypic screening
The lead optimization process
Drug effectiveness
12.7.1
Clinical testing
12.7.2
Determining detailed profiles
of candidate efficacy
12.7.3
Assays in context
12.7.4
Characterization of candidate
efficacies
Summary and conclusions
References
Further reading
13.2.6
13.2.7
12. The drug-discovery process
12.1
13.2.4
383
384
384
385
388
390
393
404
405
409
413
414
416
417
418
419
420
422
13.2.8
13.2.9
13.2.10
13.2.11
13.2.12
13.2.13
13.2.14
13. Selected pharmacological methods
13.1
13.2
Binding experiments
13.1.1
Saturation binding
13.1.2
Displacement binding
Functional assays
13.2.1
Determination of equiactive
concentrations on Dosee
Response curves
13.2.2
Method of Barlow, Scott,
and Stephenson for
measurement of the affinity
of a partial agonist
423
423
423
426
13.2.15
Reference
Method of Furchgott for the
measurement of the affinity
of a full agonist
Schild analysis for the
measurement of competitive
antagonist affinity
Method of Stephenson for
measurement of partial
agonist affinity
Method of Gaddum for
measurement of noncompetitive antagonist affinity
Method for estimating affinity of insurmountable antagonist (dextral displacement
observed)
Resultant analysis for
measurement of affinity of
competitive antagonists
with multiple properties
Measurement of the affinity
and maximal allosteric
constant for allosteric modulators producing surmountable effects
Method for estimating
affinity of insurmountable
antagonist (no dextral
displacement observed):
detection of allosteric effect
Measurement of pKB for
competitive antagonists
from a pIC50
Statistical assessment of
selectivity
Measurement of surmountable allosteric antagonism
Measurement of
insurmountable allosteric
antagonism (second
method)
Measurement of PAM
activity
xi
428
429
431
433
434
436
436
438
441
442
447
448
450
451
426
Appendix 1: Statistics
Index
427
453
483
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Preface to sixth edition
Pharmacologists almost always are working in systems
they do not fully understand. This has engendered a unique
“null system” of comparisons (before and after drug) that
has sustained the field. Our view of what is actually
happening in our experiment is obtained through our assay,
and as the Nobel Laureate Sir James Black wrote “.The
prismatic qualities of the assay distort our view in obscure
ways and degrees.” (1993; Nobel Lectures: Physiology
and Medicine). What this means to the discipline is that it is
uniquely dependent upon technology unveiling what we do
not understand about physiology and as technology advances the frontier of understanding, so too does the
perception of pharmacological mechanisms and the effect
of drugs on physiology. In essence, as the acuity of the
pharmacological prism improves, so too does our understanding of drug mechanisms. The practical outcome of this
is that a book on pharmacology must be updated every few
years to keep up with the new understanding gained from
technologies “new eyes to see.” This volume has been
updated and has added major chapters on biologics and the
drug discovery process that reflects the changing landscape
of drug therapy as well as views of historical findings
modified by new knowledge.
Terry P. Kenakin Ph.D.
Professor of Pharmacology,
The University of North Carolina School of Medicine,
Chapel Hill, NC, United States
xiii
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Chapter 1
What is pharmacology?
I would in particular draw the attention to physiologists to
this type of physiological analysis of organic systems which
can be done with the aid of toxic agents ..
dClaude Bernard (1813e78).
1.1 About this book
Essentially this is a book about the methods and tools used in
pharmacology to quantify drug activity. Receptor pharmacology is based on the comparison of experimental data and
simple mathematical models, with a resulting inference of
drug behavior to the molecular properties of drugs. From this
standpoint, a certain level of understanding of the mathematics involved in the models is useful but not imperative.
This book is structured such that each chapter begins with the
basic concepts and then moves on to the techniques used to
estimate drug parameters, and, finally, for those so inclined,
the mathematical derivations of the models used. Understanding the derivation is not a prerequisite for understanding
the application of the methods or the resulting conclusion;
these are included for completeness and are for readers who
wish to pursue exploration of the models. In general, facility
with mathematical equations is definitely not required for
pharmacology; the derivations can be ignored without any
detriment to the use of this book.
Second, the symbols used in the models and derivations, on occasion, duplicate each other (i.e., a is an
extremely popular symbol). However, the use of these
multiple symbols has been retained, since this preserves the
context of where these models were first described and
utilized. Also, changing these to make them unique would
cause confusion if these methods were to be used beyond
the framework of this book. Therefore, care should be taken
to consider the actual nomenclature of each chapter.
Third, an effort has been made to minimize the need to
cross-reference different parts of the book (i.e., when a
particular model is described, the basics are reiterated
somewhat to minimize the need to read the relevant but
different part of the book in which the model is initially
described). While this leads to a small amount of repeated
description, it is felt that this will allow for a more uninterrupted flow of reading and use of the book.
A Pharmacology Primer. https://doi.org/10.1016/B978-0-323-99289-3.00015-4
Copyright © 2022 Elsevier Inc. All rights reserved.
1.2 What is pharmacology?
Pharmacology (an amalgam of the Greek pharmakos,
medicine or drug, and logos, study) is a broad discipline
describing the use of chemicals to treat and cure diseases.
The Latin term pharmacologia was used in the late 1600s,
but the term pharmacum was used as early as the 4th
century to denote the term drug or medicine. In the Greek
translations “Pharmakeia” refers to Sorcery/Witchcraft
which no doubt was evident when particular herbal treatments were effective. There are subdisciplines within
pharmacology representing specialty areas. Pharmacokinetics deals with the disposition of drugs in the human
body. To be useful, drugs must be absorbed and transported
to their site of therapeutic action. Drugs will be ineffective
in therapy if they do not reach the organs(s) to exert their
activity; this will be discussed specifically in Chapter 9,
Pharmacokinetics, of this book. Pharmaceutics is the study
of the chemical formulation of drugs to optimize absorption
and distribution within the body. Pharmacognosy is the
study of plant natural products and their use in the treatment of disease. A very important discipline in the drugdiscovery process is medicinal chemistry, the study of the
production of molecules for therapeutic use. This couples
synthetic organic chemistry with an understanding of how
biological information can be quantified and used to guide
the synthetic chemistry to enhance therapeutic activity.
Pharmacodynamics is the study of the interaction of the
drug molecule with the biological target (referred to
generically as the “receptor,” vide infra). This discipline
lays the foundation of pharmacology since all therapeutic
application of drugs has a common root in pharmacodynamics (i.e., as a prerequisite to exerting an effect, all drug
molecules must bind to and interact with receptors).
The history of pharmacology is tied to the history of
drug discoverydsee Chapter 9, The Optimal Design of
Pharmacological Experiments. As put by the Canadian
physician Sir William Osler (1849e919; the “father of
modern medicine”), “. the desire to take medicine is
perhaps the greatest feature which distinguishes man from
animals ..” Pharmacology as a separate science is
approximately 120e140 years old. The relationship between chemical structure and biological activity began to be
studied systematically in the 1860s [1]. It began when
1
2
A Pharmacology Primer
physiologists, using chemicals to probe physiological systems, became more interested in the chemical probes than
the systems they were probing. By the early 1800s, physiologists were performing physiological studies with
chemicals that became pharmacological studies more aimed
at the definition of the biological activity of chemicals. The
first formalized chair of pharmacology, indicating a formal
university department, was founded in Estonia by Rudolf
Bucchiem in 1847. In North America, the first chair was
founded by John Jacob Abel at Johns Hopkins University
in 1890. A differentiation of physiology and pharmacology
was given by the pharmacologist Sir William Paton [2]:
If physiology is concerned with the function, anatomy with
the structure, and biochemistry with the chemistry of the
living body, then pharmacology is concerned with the
changes in function, structure, and chemical properties of
the body brought about by chemical substances
dW.D.M. Paton (1986).
Many works about pharmacology essentially deal in
therapeutics associated with different organ systems in the
body. Thus, in many pharmacology texts, chapters are
entitled drugs in the cardiovascular system, the effect of
drugs on the gastrointestinal (GI) system, the central nervous system (CNS), and so on. However, the underlying
principles for all of these is the same, namely, the pharmacodynamic interaction between the drug and the biological recognition system for that drug. Therefore, a
prerequisite to all of pharmacology is an understanding of
the basic concepts of doseeresponse and how living cells
process pharmacological information. This generally is
given the term pharmacodynamics or receptor pharmacology, where receptor is a term referring to any biological
recognition unit for drugs (membrane receptors, enzymes,
DNA, and so on). With such knowledge in hand, readers
will be able to apply these principles to any branch of
therapeutics effectively. This book treats doseeresponse data
generically and demonstrates methods by which drug activity can be quantified across all biological systems irrespective of the nature of the biological target.
A great strength of pharmacology as a discipline is that
it contains the tools and methods to convert “descriptive
data,” i.e., data that serve to characterize the activity of a
given drug in a particular system, to “predictive data.” This
latter information can be used to predict that drug’s activity
in all organ systems, including the therapeutic one. This
defines the drug-discovery process which is the testing of
new potential drug molecules in surrogate systems (where a
potentially toxic chemical can do no lasting harm) before
progression to the next step, namely, testing in human
therapeutic systems. The models and tools contained in
pharmacology to convert drug behaviors in particular
organs to molecular properties (see Chapter 2: How
Different Tissues Process Drug Response) are the main
subject of this book, and the step-by-step design of pharmacologic experiments to do this are described in detail in
Chapter 8, The Optimal Design of Pharmacological Experiments (after the meaning of the particular parameters
and terms is described in previous chapters).
The human genome is now widely available for drugdiscovery research. Far from being a simple blueprint of
how drugs should be targeted, it has shown biologists that
receptor genotypes (i.e., properties of proteins resulting
from genetic transcription to their amino acid sequence) are
secondary to receptor phenotypes (how the protein interacts
with the myriad of cellular components and how cells tailor
the makeup and functions of these proteins to their individual needs). Since the arrival of the human genome, receptor pharmacology as a science is more relevant than ever
in drug discovery. Current drug therapy is based on less
than 500 molecular targets, yet estimates utilizing the
number of genes involved in multifactorial diseases suggest
that the number of potential drug targets ranges from 2000
to 5000 [3]. Thus, current therapy is using only 5%e10%
of the potential trove of targets available in the human
genome.
A meaningful dialog between chemists and pharmacologists is the single most important element of the drugdiscovery process. The necessary link between medicinal
chemistry and pharmacology has been elucidated by
Paton [2]:
For pharmacology there results a particularly close relationship with chemistry, and the work may lead quite
naturally, with no special stress on practicality, to therapeutic application, or (in the case of adverse reactions) to
toxicology.
dW.D.M. Paton (1986).
Chemists and biologists reside in different worlds from
the standpoint of the type of data they deal with. Chemistry
is an exact science with physical scales that are not subject
to system variance. Thus, the scales of measurement are
transferable. Biology deals with the vagaries of complex
systems that are not completely understood. Within this
scenario, scales of measurement are much less constant and
much more subject to system conditions. Given this, a gap
can exist between chemists and biologists in terms of understanding and also in terms of the best method to progress
forward. In the worst circumstance, it is a gap of credibility
emanating from a failure of the biologist to make the
chemist understand the limits of the data. Usually, however,
credibility is not the issue, and the gap exists due to a lack
of common experience. This book was written in an
attempt to limit or, hopefully, eliminate this gap.
What is pharmacology? Chapter | 1
1.3 The receptor concept
One of the most important concepts emerging from early
pharmacological studies is the concept of the receptor.
Pharmacologists knew that minute amounts of certain
chemicals had profound effects on physiological systems.
They also knew that very small changes in the chemical
composition of these substances could lead to huge differences in activity. This led to the notion that something
on or in the cell must specifically read the chemical information contained in these substances and translate it into a
physiological effect. This something was conceptually
referred to as the “receptor” for that substance. Pioneers
such as Paul Ehrlich (1854e915, Fig. 1.1A) proposed the
existence of “chemoreceptors” (actually he proposed a
collection of amboreceptors, triceptors, and polyceptors) on
cells for dyes. He also postulated that the chemoreceptors
on parasites, cancer cells, and microorganisms were
different from healthy host and thus could be exploited
therapeutically. The physiologist turned pharmacologist
John Newport Langley (1852e926, Fig. 1.1B), during his
studies with the drugs jaborandi (which contains the alkaloid pilocarpine) and atropine, introduced the concept that
receptors were switches that received and generated signals
and that these switches could be activated or blocked by
specific molecules. The originator of quantitative receptor
theory, the Edinburgh pharmacologist Alfred Joseph Clark
(1885e941, Fig. 1.1C), was the first to suggest that the
data, compiled from his studies of the interactions of
acetylcholine and atropine, resulted from the unimolecular
3
interaction of the drug and a substance on the cell surface.
He articulated these ideas in the classic work The Mode of
Action of Drugs on Cells [4], later revised as the Handbook
of Experimental Pharmacology [5]. As put by Clark
It appears to the writer that the most important fact shown
by a study of drug antagonisms is that it is impossible to
explain the remarkable effects observed except by assuming
that drugs unite with receptors of a highly specific pattern
.. No other explanation will, however, explain a tithe of
the facts observed.
dA.J. Clark (1937).
Clark’s next step formed the basis of receptor theory by
applying chemical laws to systems of “infinitely greater
complexity” [4]. It is interesting to note the scientific atmosphere in which Clark published these ideas. The
dominant ideas between 1895 and 1930 were based on
theories such as the law of phasic variation essentially
stating that “certain phenomena occur frequently.” Homeopathic theories like the ArndteSchulz law and
WebereFechner law were based on loose ideas around
surface tension of the cell membrane, but there was little
physicochemical basis for these ideas [6]. In this vein,
prominent pharmacologists of the day, such as Walter
Straub (1874e944), suggested that a general theory of
chemical binding between drugs and cells utilizing receptors was “. going too far . and . not admissible”
[6]. The impact of Clark’s thinking against these concepts
cannot be overemphasized to modern pharmacology.
FIGURE 1.1 Pioneers of pharmacology. (A) Paul Ehrlich (1854e915). Born in Silesia, Ehrlich graduated from Leipzig University to go on to a
distinguished career as head of institutes in Berlin and Frankfurt. His studies with dyes and bacteria formed the basis of early ideas regarding recognition
of biological substances by chemicals. (B) John Newport Langley (1852e926). Though he began reading mathematics and history in Cambridge in 1871,
Langley soon took to physiology. He succeeded the great physiologist M. Foster to the chair of physiology in Cambridge in 1903 and branched out into
pharmacological studies of the autonomic nervous system. These pursuits led to germinal theories of receptors. (C) Alfred J. Clark (1885e941). Beginning
as a demonstrator in pharmacology in King’s College (London), Clark went on to become Professor of pharmacology at University College London. From
there he took the chair of pharmacology in Edinburgh. Known as the originator of modern receptor theory, Clark applied chemical laws to biological
phenomena. His books on receptor theory formed the basis of modern pharmacology.
4
A Pharmacology Primer
It is possible to underestimate the enormous significance of the receptor concept in pharmacology until it is
realized how relatively chaotic the study of drug effect
was before it was introduced. Specifically, consider the
myriad of physiological and pharmacological effects of
the hormone epinephrine in the body. As shown in
Fig. 1.2, a host of responses are obtained from the CNS,
cardiovascular system, smooth muscle, and other organs.
It is impossible to see a thread which relates these very
different responses until it is realized that all of these are
mediated by the activation of a single protein receptor,
namely, in this case, the b-adrenoceptor. When this is
understood, a much better idea can be gained as to how to
manipulate these heterogeneous responses for therapeutic
benefit; the receptor concept introduced order into physiology and pharmacology.
Drug receptors can exist in many forms, including cell
surface proteins, enzymes, ion channels, membrane transporters, DNA, and cytosolic proteins (see Fig. 1.3). There
are examples of important drugs for all of these. This book
deals with general concepts which can be applied to a range
of receptor types, but most of the principles are illustrated
with the most tractable receptor class known in the human
genome, namely, seven transmembrane (7TM) receptors
(7TMRs). These receptors are named for their characteristic
structure that consists of a single protein chain that traverses the cell membrane seven times to produce extracellular and intracellular loops. These receptors activate
G-proteins to elicit response, thus they are also
commonly referred to as G-protein-coupled receptors
(GPCRs); this should now be considered a limiting moniker
as these proteins signal to a wide variety of signaling
molecules in the cell and are not confined to G-protein
effects. There are between 800 and 1000 [7] of these in
the genome [the genome sequence predicts 650 GPCR
genes, of which approximately 190 (on the order of 1% of
the genome of superior organisms) are categorized as
known 7TMRs [8] activated by some 70 ligands]. In the
United States, in 2000, nearly half of all prescription drugs
were targeted toward 7TM receptors [3]. These receptors,
comprising between 1% and 5% of the total cell protein,
control a myriad of physiological activities. They are
tractable for drug discovery because they are on the cell
surface, and therefore drugs do not need to penetrate the
cell to produce effect. In the study of biological targets such
as 7TMRs and other receptors, a “system” must be
employed that accepts chemical input and returns biological
output. It is worth discussing such receptor systems in
general terms before their specific uses are considered.
1.4 Pharmacological test systems
Molecular biology has transformed pharmacology and the
drug-discovery process. As little as 20 years ago, screening
for new drug entities was carried out in surrogate animal
tissues. This necessitated a rather large extrapolation to
span the differences in genotype and phenotype. The belief
that the gap could be bridged came from the notion that the
chemicals recognized by these receptors in both humans
and animals were the same (vide infra). Receptors are
unique proteins with characteristic amino acid sequences.
While polymorphisms (spontaneous alterations in amino
acid sequence, vide infra) of receptors exist in the same
species, in general the amino acid sequence of a natural
ligand-binding domain for a given receptor type largely
may be conserved. There are obvious pitfalls of using
FIGURE 1.2 A sampling of the heterogeneous physiological and pharmacological response to the hormone epinephrine. The concept of receptors links
these diverse effects to a single control point, namely, the b-adrenoceptor.
What is pharmacology? Chapter | 1
5
FIGURE 1.3 Schematic diagram of potential drug targets. Molecules can affect the function of numerous cellular components both in the cytosol and on
the membrane surface. There are many families of receptors that traverse the cellular membrane and allow chemicals to communicate with the interior of
the cell.
surrogate species receptors for predicting human drug activity, and it never can be known for certain whether
agreement for estimates of activity for a given set of drugs
ensures accurate prediction for all drugs. The agreement is
very much drug and receptor dependent. For example, the
human and mouse a2-adrenoceptors are 89% homologous
and thus considered very similar from the standpoint of
amino acid sequence. Furthermore, the affinities of the a2adrenoceptor antagonists atipamezole and yohimbine are
nearly indistinguishable (atipamezole human a2-C10
Ki ¼ 2.9 0.4 nM, mouse a2-4H Ki ¼ 1.6 0.2 nM;
yohimbine human a2-C10 Ki ¼ 3.4 0.1 nM, mouse a24H Ki ¼ 3.8 0.8 nM). However, there is a 20.9-fold
difference for the antagonist prazosin (human a2-C10
Ki ¼ 2034 350 nM, mouse a2-4H Ki ¼ 97.3 0.7 nM)
[9]. Such data highlight a general theme in pharmacological
research, namely, that a hypothesis, such as one proposing
that two receptors which are identical with respect to their
sensitivity to drugs are the same, cannot be proven, only
disproven. While a considerable number of drugs could be
tested on the two receptors (thus supporting the hypothesis
that their sensitivity to all drugs is the same), this hypothesis is immediately disproven by the first drug that shows
differential potency on the two receptors. The fact that a
series of drugs tested show identical potencies may mean
only that the wrong sample of drugs has been chosen to
unveil the difference. Thus, no general statements can be
made that any one surrogate system is completely predictive of activity on the target human receptor. This will always be a drug-specific phenomenon.
The link between animal and human receptors is the fact
that both proteins recognize the endogenous transmitter
(e.g., acetylcholine, norepinephrine), and therefore the hope
is that this link will carry over into other drugs that
recognize the animal receptor. This imperfect system
formed the basis of drug discovery until human cDNA for
human receptors could be used to make cells express human receptors. These engineered (recombinant) systems are
now used as surrogate human-receptor systems, and the
leap of faith from animal receptor sequences to humanreceptor sequences is not required (i.e., the problem of
differences in genotype has been overcome). However,
cellular signaling is an extremely complex process and cells
tailor their receipt of chemical signals in numerous ways.
Therefore, the way a given receptor gene behaves in a
particular cell can differ in response to the surroundings in
which that receptor finds itself. These differences in
phenotype (i.e., properties of a receptor produced by
interaction with its environment) can result in differences in
both the quantity and quality of a signal produced by a
concentration of a given drug in different cells. Therefore,
there is still a certain, although somewhat lesser, leap of
faith taken in predicting therapeutic effects in human tissues under pathological control from surrogate recombinant
or even surrogate natural human-receptor systems. For this
reason, it is a primary requisite of pharmacology to derive
system-independent estimates of drug activity that can be
used to predict therapeutic effect in other systems.
A schematic diagram of the various systems used in
drug discovery, in order of how appropriate they are to
therapeutic drug treatment, is shown in Fig. 1.4. As discussed previously, early functional experiments in animal
tissue have now largely given way to testing in recombinant
cell systems engineered with human-receptor material. This
huge technological step greatly improved the predictability
of drug activity in humans, but it should be noted that there
6
A Pharmacology Primer
FIGURE 1.4 A history of the drug-discovery process. Originally, the only biological material available for drug research was animal tissue. With the
advent of molecular biological techniques to clone and express human receptors in cells, recombinant systems supplanted animal-isolated tissue work. It
should be noted that these recombinant systems still fall short of yielding drug response in the target human tissue under the influence of pathological
processes.
still are many factors that intervene between the genetically
engineered drug-testing system and the pathology of human
disease.
A frequently used strategy in drug discovery is to express human receptors (through transfection with human
cDNA) in convenient surrogate host cells (referred to as
“target-based” drug discovery; see Chapter 10: Safety
Pharmacology for further discussion). These host cells are
chosen mainly for their technical properties (i.e., robustness, growth rate, stability) and not with any knowledge of
verisimilitude to the therapeutically targeted human cell
type. There are various factors relevant to the choice of
surrogate host cell, such as a very low-background activity
(i.e., a cell cannot be used that already contains a related
animal receptor for fear of cross-reactivity to molecules
targeted for the human receptor). Human receptors are often
expressed in animal surrogate cells. The main idea here is
that the cell is a receptacle for the receptor, allowing it to
produce physiological responses, and that activity can be
monitored in pharmacological experiments. In this sense,
human receptors expressed in animal cells are still a theoretical step distanced from the human receptor in a human
cell type. However, even if a human surrogate is used (and
there are such cells available), there is no definitive evidence that a surrogate human cell is any more predictive of
a natural receptor activity than an animal cell when
compared to the complex receptor behavior in its natural
host cell type expressed under pathological conditions.
Receptor phenotype dominates in the end organ, and the
exact differences between the genotypic behavior of the
receptor (resulting from the genetic makeup of the receptor)
and the phenotypic behavior of the receptor (due to the
interaction of the genetic product with the rest of the cell)
may be cell specific. Therefore, there is still a possible gap
between the surrogate systems used in the drug-discovery
process and the therapeutic application. Moreover, most
drug-discovery systems utilize receptors as switching
mechanisms and quantify whether drugs turn on or turn off
the switch. The pathological processes that we strive to
modify may be more subtle. As put by pharmacologist Sir
James Black [10]:
. angiogenesis, apoptosis, inflammation, commitment of
marrow stem cells, and immune responses. The cellular
reactions subsumed in these processes are switch like in
their behavior . biochemically we are learning that in all
these processes many chemical regulators seem to be
involved. From the literature on synergistic interactions, a
control model can be built in which no single agent is
effective. If a number of chemical messengers each bring
information from a different source and each deliver only a
subthreshold stimulus but together mutually potentiate each
other, then the desired information-rich switching can be
achieved with minimum risk of miscuing.
dJ.W. Black (1986).
Such complex end points are difficult to predict from
any one of the component processes leading to yet another
leap of faith in the drug-discovery process. For these reasons, an emerging strategy for drug discovery is the use of
natural cellular systems. This approach is discussed in some
detail in Chapter 11, The Drug Discovery Process.
Even when an active drug molecule is found and activity is verified in the therapeutic arena, there are factors
that can lead to gaps in its therapeutic profile. When drugs
are exposed to huge populations, genetic variations in this
population can lead to discovery of alleles that code for
mutations of the target (isogenes), and these can lead to
variation in drug response. Such polymorphisms can lead to
What is pharmacology? Chapter | 1
resistant populations (i.e., resistance of some asthmatics to
the b-adrenoceptor bronchodilators [11]). In the absence of
genetic knowledge, these therapeutic failures for a drug
could not easily be averted since they in essence occurred
because of the presence of new biological targets not
originally considered in the drug-discovery process. However, as new epidemiological information becomes available, these polymorphisms can now be incorporated into
the drug-discovery process.
There are two theoretical and practical scales that can
be used to make system-independent measures of drug
activity on biological systems. The first is a measure of the
attraction of a drug for a biological target, namely, its
affinity for a receptor. Drugs must interact with receptors
to produce an effect, and the affinity is a chemical term
used to quantify the strength of that interaction. The second is much less straightforward and is used to quantify
the degree of effect imparted to the biological system after
the drug binds to the receptor. This is termed efficacy. This
property was named by Stephenson [12] within classical
receptor theory as a proportionality factor for the tissue
response produced by a drug. There is no absolute scale
for efficacy, but rather it is dealt with in relative terms
(i.e., the ratio of the efficacy of two different drugs on a
particular biological system can be estimated and, under
ideal circumstances, will transcend the system and be
applicable to other systems as well). It is the foremost task
of pharmacology to use the translations of drug effect
obtained from cells to provide system-independent estimates of affinity and efficacy. Before specific discussion
of affinity and efficacy, it is worth considering the molecular nature of biological targets.
1.5 The nature of drug receptors
While some biological targets such as DNA are not protein
in nature, most receptors are. It is useful to consider the
properties of receptor proteins to provide a context for the
interaction of small molecule drugs with them. An important property of receptors is that they have a 3D structure.
Proteins are usually composed of one or more peptide
chains; the composition of these chains makes up the primary and secondary structure of the protein. Proteins also
are described in terms of a tertiary structure, which defines
their shape in 3D space, and a quaternary structure, which
defines the molecular interactions between the various
components of the protein chains (Fig. 1.5). It is this 3D
structure which allows the protein to function as a recognition site and effector for drugs and other components of
the cell; in essence, the ability of the protein to function as a
messenger, shuttling information from the outside world to
the cytosol of the cell. For 7TMRs, the 3D nature of the
receptor forms binding domains for other proteins such as
7
G-proteins (these are activated by the receptor and then go
on to activate enzymes and ion channels within the cell; see
Chapter 2: How Different Tissues Process Drug Response)
and endogenous chemicals such as neurotransmitters, hormones, and autacoids that carry physiological messages.
This important class of drug target is named for a characteristic structure consisting of 7TM domains looping into
the extracellular and intracellular spacedsee Fig. 1.6.
These molecules are the main transfer points of information
from the outside to the inside of the cell, and such transfers
occur through changes in the conformation of the receptor
protein (vide infra). For other receptors, such as ion channels and single transmembrane enzyme receptors, the
conformational change per se leads to a response, either
through an opening of a channel to allow the flow of ionic
current or the initiation of enzymatic activity. Therapeutic
advantage can be taken by designing small molecules to
utilize these binding domains or other 3D binding domains
on the receptor protein in order to modify physiological and
pathological processes.
1.6 From the snapshot to the movie
Drugs interact with living physiology and the outcome of
the interaction is controlled by a combination of the
intrinsic properties of the drug and the sensitivity of the
system to intervention. This being the case, drugs can have
different profiles of activity in different tissues depending
on the tissue sensitivity and setpoint of physiology.
Through the mechanics of mathematical models of drug
activity and the system-independent scales of drug activity
(i.e., affinity, efficacy), pharmacological procedures are
uniquely able to convert a single observation of drug activity in a test system (the ‘snapshot’) to a prediction of the
complete realm of activities for that same drug in a range of
tissues of varying setpoints of physiology (the ‘movie’).
This is an essential property of pharmacology in drug discovery as all initial evaluations of new drug activity are
made in isolated systems and assessments of what the new
molecule will do in other systems must be made. In
essence, the cellular host system completely controls what
the experimenter observes regarding the events taking place
at the drug receptor. Drug activity is thus revealed through
a “cellular veil” that can, in many cases, obscure or substantially modify drugereceptor activity (Fig. 1.7). Minute
signals, initiated either at the cell surface or within the
cytoplasm of the cell, are interpreted, transformed, amplified, and otherwise altered by the cell to tailor that signal to
its own particular needs. The application of pharmacological principles and modeling enable ‘snapshots’ of drug
activity obtained is experiments to guide the progress of
molecules toward drug candidate statusdsee Chapter 3 for
further details.
8
A Pharmacology Primer
FIGURE 1.5 Increasing levels of protein structure. A protein has a given amino acid sequence to make peptide chains. These adopt a 3D structure
according to the free energy of the system. Receptor function can change with changes in tertiary or quaternary structure.
1.7 Pharmacological intervention and
the therapeutic landscape
It is useful to consider the therapeutic landscape with
respect to the aims of pharmacology. As stated by Sir
William Ossler (1849e919) “. the prime distinction between man and other creatures is man’s yearning to take
medicine.” The notion that drugs can be used to cure disease is as old as history. One of the first written records of
actual “prescriptions” can be found in the Ebers Papyrus
(c.1550 BCE): “. for night blindness in the eyes . liver
of ox, roasted and crushed out . really excellent!“dsee
Fig. 1.8. Now it is known that liver is an excellent source of
vitamin A, a prime treatment for night blindness, but that
chemical detail was not known to the ancient Egyptians.
Disease can be considered under two broad categories:
those caused by invaders such as pathogens and those
caused by intrinsic breakdown of normal physiological
function. The first generally is approached through the
invader (i.e., the pathogen is destroyed, neutralized, or
removed from the body). The one exception of where the
host is treated when an invader is present is the treatment of
HIV-1 infection leading to AIDS. In this case, while there
are treatments to neutralize the pathogen, such as antiretrovirals to block viral replication, a major new approach
is the blockade of the interaction of the virus with the
protein that mediates viral entry into healthy cells, the
chemokine receptor CCR5. In this case, CCR5 antagonists
are used to prevent HIV fusion and subsequent infection.
The second approach to disease requires an understanding
of the pathological process and repair of the damage to
return to normal function.
The therapeutic landscape onto which drug discovery
and pharmacology in general combat disease can generally be described in terms of the major organ systems of
the body and how they may go awry. A healthy cardiovascular system consists of a heart able to pump deoxygenated blood through the lungs and to pump oxygenated
blood throughout a circulatory system that does not
unduly resist blood flow. Since the heart requires a high
What is pharmacology? Chapter | 1
FIGURE 1.6 Depiction of the structure of seven transmembrane domain
receptors, one of the most if not the most important therapeutic targets
available in the human genome. Chemicals access the receptor through the
extracellular space by binding to the extracellular domains of the protein.
This causes a conformational change in the protein that alters the interaction of signaling proteins in the cell cytosol. This latter process results in
the initiation of cellular signaling.
degree of oxygen itself to function, myocardial ischemia
can be devastating to its function. Similarly, an inability to
maintain rhythm (arrhythmia) or loss in strength with
concomitant inability to empty (congestive heart failure)
can be fatal. The latter disease is exacerbated by elevated
arterial resistance (hypertension). A wide range of drugs
are used to treat the cardiovascular system, including
coronary vasodilators (nitrates), diuretics, renine
angiotensin inhibitors, vasodilators, cardiac glycosides,
calcium antagonists, beta and alpha blockers, antiarrhythmics, and drugs for dyslipidemia. The lungs must
extract oxygen from the air, deliver it to the blood, and
release carbon dioxide from the blood into exhaled air.
Asthma, chronic obstructive pulmonary disease (COPD),
and emphysema are serious disorders of the lungs and
airways. Bronchodilators (beta agonists), antiinflammatory drugs, inhaled glucocorticoids, anticholinergics, and theophylline analogs are used for treatment of
these diseases. The CNS controls all conscious thought
and many unconscious body functions. Numerous diseases of the brain can occur, including depression, anxiety, epilepsy, mania, degeneration, obsessive disorders,
and schizophrenia. Brain functions such as those
9
controlling sedation and pain also may require treatment.
A wide range of drugs is used for CNS disorders,
including serotonin partial agonists and uptake inhibitors,
dopamine agonists, benzodiazepines, barbiturates, opioids, tricyclics, neuroleptics, and hydantoins. The GI tract
receives and processes food to extract nutrients and
removes waste from the body. Diseases such as stomach
ulcers, colitis, diarrhea, nausea, and irritable bowel syndrome can affect this system. Histamine antagonists,
proton pump blockers, opioid agonists, antacids, and serotonin uptake blockers are used to treat diseases of the GI
tract.
The inflammatory system is designed to recognize self
from nonself, and to destroy nonself to protect the body. In
diseases of the inflammatory system, the self-recognition
can break down, leading to conditions in which the body
destroys healthy tissue in a misguided attempt at protection.
This can lead to rheumatoid arthritis, allergies, pain, COPD,
asthma, fever, gout, graft rejection, and problems with
chemotherapy. Nonsteroidal antiinflammatory drugs,
aspirin and salicylates, leukotriene antagonists, and histamine receptor antagonists are used to treat inflammatory
disorders. The endocrine system produces and secretes
hormones crucial to the body for growth and function.
Diseases of this class of organs can lead to growth and
pituitary defectsddiabetes; abnormality in thyroid, pituitary, adrenal cortex, and androgen function; osteoporosis;
and alterations in estrogeneprogesterone balance. The
general approach to treatment is through replacement or
augmentation of secretion. Drugs used are replacement
hormones, insulin, sulfonylureas, adrenocortical steroids,
and oxytocin. In addition to the major organ and physiological systems, diseases involving neurotransmission and
neuromuscular function, ophthalmology, hemopoiesis and
hematology, dermatology, immunosuppression, and drug
addiction and abuse are amenable to pharmacological
intervention.
Cancer is a serious malfunction of normal cell growth.
In the years from 1950 to 1970, the major approach to
treating this disease was to target DNA and DNA precursors according to the hypothesis that rapidly dividing
cells (cancer cells) are more susceptible to DNA toxicity
than normal cells. Since that time, a wide range of new
therapies based on manipulation of the immune system,
induction of differentiation, inhibition of angiogenesis, and
increased killer T-lymphocytes to decrease cell proliferation has greatly augmented the armamentarium against
neoplastic disease. Previously, lethal malignancies such as
testicular cancer, some lymphomas, and leukemia are now
curable.
Three general treatments of disease are surgery, genetic
engineering (still an emerging discipline), and pharmacological intervention. While early medicine was subject to
the theories of Hippocrates (460e357 BCE), who saw
10
A Pharmacology Primer
FIGURE 1.7 The cellular veil. Drugs act on biological receptors in cells to change cellular activity. The initial receptor stimulus usually alters a
complicated system of interconnected metabolic biochemical reactions, and the outcome of the drug effect is modified by the extent of these interconnections, the basal state of the cell, and the threshold sensitivity of the various processes involved. This can lead to a variety of apparently different
effects for the same drug in different cells. Receptor pharmacology strives to identify the basic mechanism initiating these complex events.
FIGURE 1.8 The Ebers Papyrus is a 110-page scroll (20 m long) thought to have been written in 1550 BCE but containing information dating from
3400 BCE. It is a record of Egyptian medicine and contains numerous “prescriptions” some of which, though empirical, are valid therapeutic approaches
to diseases.
health and disease as a balance of four humors (i.e., black
and yellow bile, phlegm, and blood), by the 16th century
pharmacological concepts were being formulated. These
could be stated concisely as the following [13]:
l
l
Every disease has a cause for which there is a specific
remedy.
Each remedy has a unique essence that can be obtained
from nature by extraction (“doctrine of signatures”).
l
The administration of the remedy is subject to a dosee
response relationship.
The basis for believing that pharmacological intervention can be a major approach to the treatment of disease is
the fact that the body generally functions in response to
chemicals. Table 1.1 shows partial lists of hormones and
neurotransmitters in the body. Many more endogenous
chemicals are involved in normal physiological function.
What is pharmacology? Chapter | 1
11
TABLE 1.1 Some endogenous chemicals controlling normal physiological function.
Neurotransmitters
Acetylcholine
2-Arachidonylglycerol
Anandamide
ATP
Corticotropin-releasing hormone
Dopamine
Epinephrine
Aspartate
Gamma-aminobutyric acid
Galanin
Glutamate
Glycine
Histamine
Norepinephrine
Serotonin
Thyroid-stimulating hormone
Follicle-stimulating hormone
Luteinizing hormone
Prolactin
Adrenocorticotropin
Antidiuretic hormone
Thyrotropin-releasing hormone
Oxytocin
Gonadotropin-releasing hormone
Hormones
Growth-hormone-releasing hormone
Corticotropin-releasing hormone
Somatostatin
Melatonin
Thyroxin
Calcitonin
Parathyroid hormone
Glucocorticoid(s)
Mineralocorticoid(s)
Estrogen(s)
Progesterone
Chorionic gonadotropin
Androgens
Insulin
Glucagon
Amylin
Erythropoietin
Calcitriol
Calciferol
Atrial-natriuretic peptide
Gastrin
Secretin
Cholecystokinin
Neuropeptide Y
Insulin-like growth factor
Angiotensinogen
Ghrelin
Leptin
ATP, adenosine triphosphate.
The fact that so many physiological processes are
controlled by chemicals provides the opportunity for
chemical intervention. Thus, physiological signals mediated by chemicals can be initiated, negated, augmented, or
modulated. The nature of this modification can take the
form of changes in the type, strength, duration, or location
of signal.
1.8 System-independent drug
parameters: affinity and efficacy
The process of drug discovery relies on the testing of molecules in systems to yield estimates of biological activity in
an iterative process of changing the structure of the molecule
until optimal activity is achieved. It will be seen in this book
that there are numerous systems available to do this, and that
each system may interpret the activity of molecules in
different ways. Some of these interpretations can appear to
be in conflict with each other, leading to apparent capricious
patterns. For this reason, the way forward in the drug
development process is to use only system-independent information. Ideally, scales of biological activity should be
used that transcend the actual biological system in which the
drug is tested. This is essential to avoid confusion and also
because it is quite rare to have access to the exact human
system under the control of the appropriate pathology
available for in vitro testing. Therefore, the drug-discovery
process necessarily relies on the testing of molecules in
surrogate systems and the extrapolation of the observed activity to all systems. The only means to do this is to obtain
system-independent measures of drug activity, namely, affinity and efficacy.
If a molecule in solution associates closely with a receptor protein, it has affinity for that protein. The area where
it is bound is the binding domain or locus. If the same
molecule interferes with the binding of a physiologically
active molecule such as a hormone or a neurotransmitter
(i.e., if the binding of the molecule precludes activity of the
physiologically active hormone or neurotransmitter), the
molecule is referred to as an antagonist. Therefore, a pharmacologically active molecule that blocks physiological effect is an antagonist. Similarly, if a molecule binds to a
receptor and produces its own effect, it is termed an agonist.
It also is assumed to have the property of efficacy. Efficacy is
12
A Pharmacology Primer
detected by observation of pharmacological response.
Therefore, agonists have both affinity and efficacy.
Classically, agonist response is described in two stages,
the first being the initial signal imparted to the immediate
biological target, namely, the receptor. This first stage is
composed of the formation, either through interaction with
an agonist or spontaneously, of an active state receptor
conformation. This initial signal is termed the stimulus
(Fig. 1.9). This stimulus is perceived by the cell and processed in various ways through successions of biochemical
reactions to the end point, namely, the response. The sum
total of the subsequent reactions is referred to as the
stimuluseresponse mechanism or cascade (see Fig. 1.10).
Efficacy is a molecule-related property (i.e., different
molecules have different capabilities to induce a physiological response). The actual term for the molecular aspect
of response-inducing capacity of a molecule is intrinsic
efficacy (see Chapter 3: DrugeReceptor Theory for how
this term evolved). Thus, every molecule has a unique
value for its intrinsic efficacy (in cases of antagonists this
could be zero). The different abilities of molecules to
induce response are illustrated in Fig. 1.10. This figure
shows doseeresponse curves for four 5-HT (hydroxytryptamine) (serotonin) agonists in rat jugular vein. It can be
seen that if response is plotted as a function of the percent
receptor occupancy, different receptor occupancies for
the different agonists lead to different levels of response.
For example, while 0.6 g force can be generated by
5-HT by occupying 30% of the receptors, the agonist 5cyanotryptamine requires twice the receptor occupancy to
generate the same response (i.e., the capability of 5cyanotryptamine to induce response is half that of 5-HT
[14]). These agonists are then said to possess different
magnitudes of intrinsic efficacy.
FIGURE 1.9 Schematic diagram of response production by an agonist. An initial stimulus is produced at the receptor as a result of agonistereceptor
interaction. This stimulus is processed by the stimuluseresponse apparatus of the cell into observable cellular response.
FIGURE 1.10 Differences between agonists producing contraction of rat jugular vein through activation of 5-HT receptors. (A) Doseeresponse curves
to 5-HT receptor agonists, 5-HT (filled circles), 5-cyanotryptamine (filled squares), N,N-dimethyltryptamine (open circles), and N-benzyl-5methoxytryptamine (filled triangles). Abscissae: logarithms of molar concentrations of agonist. (B) Occupancy response curves for curves shown in
panel A. Abscissae: percent receptor occupancy by the agonist as calculated by mass action and the equilibrium dissociation constant of the agoniste
receptor complex. Ordinates: force of contraction in g. Data drawn from P. Leff, G.R. Martin, J.M. Morse, Differences in agonist dissociation constant
estimates for 5-HT at 5-HT2-receptors: a problem of acute desensitization? Br. J. Pharmacol. 89 (1986) 493e499.
What is pharmacology? Chapter | 1
It is important to consider affinity and efficacy as
separately manipulatable properties. Thus, there are chemical features of agonists that pertain especially to affinity
and other features that pertain to efficacy. Fig. 1.11 shows a
series of key chemical compounds made en route to the
histamine H2 receptor antagonist cimetidine (used for
healing gastric ulcers). The starting point for this discovery
program was the knowledge that histamine, a naturally
occurring autacoid, activates histamine H2 receptors in the
stomach to cause acid secretion. This constant acid secretion is what prevents the healing of lesions and ulcers. The
task was then to design a molecule that would antagonize
the histamine receptors mediating acid secretion and prevent histamine H2 receptor activation to allow the ulcers to
heal. This task was approached with the knowledge that
molecules, theoretically, could be made that retained or
even enhanced affinity but decreased the efficacy of histamine (i.e., these were separate properties). As can be seen
in Fig. 1.11, molecules were consecutively synthesized
with reduced values of efficacy and enhanced affinity until
the target histamine H2 antagonist cimetidine was made.
This was a clear demonstration of the power of medicinal
chemistry to separately manipulate affinity and efficacy for
which, in part, the Nobel Prize in Medicine was awarded in
1988.
1.9 What is affinity?
The affinity of a drug for a receptor defines the strength of
interaction between the two species. The forces controlling the affinity of a drug for the receptor are thermodynamic (enthalpy as changes in heat and entropy as changes
13
in the state of disorder). The chemical forces between the
components of the drug and the receptor vary in importance in relation to the distance of the drug from the receptor’s binding surface. Thus, the strength of
electrostatic forces (attraction due to positive and negative
charges and/or complex interactions between polar
groups) varies as a function of the reciprocal of the distance between the drug and the receptor. Hydrogen
bonding (the sharing of a hydrogen atom between an
acidic and basic group) varies in strength as a function of
the fourth power of the reciprocal of the distance. Also
involved are van der Waals’ forces (weak attraction between polar and nonpolar molecules) and hydrophobic
bonds (interaction of nonpolar surfaces to avoid interaction with water). The combination of all of these forces
causes the drug to reside in a certain position within the
protein-binding pocket. This is a position of minimal free
energy. It is important to note that drugs do not statically
reside in one uniform position. As thermal energy varies
in the system, drugs approach and dissociate from the
protein surface. This is an important concept in pharmacology as it sets the stage for competition between two
drugs for a single binding domain on the receptor protein.
The probability that a given molecule will be at the point
of minimal free energy within the protein-binding pocket
thus depends on the concentration of the drug available to
fuel the binding process and also the strength of the interactions for the complementary regions in the binding
pocket (affinity). Affinity can be thought of as a force of
attraction and can be quantified with a very simple tool,
first used to study the adsorption of molecules onto a
surface, namely, the Langmuir adsorption isotherm.
FIGURE 1.11 Key compounds synthesized to eliminate the efficacy (burgundy red) and enhance the affinity (green) of histamine for histamine H2
receptors to make cimetidine, one of the first histamine H2 antagonists of use in the treatment of peptic ulcers. Quotation from J.W. Black, A personal view
of pharmacology, Ann. Rev. Pharmacol. Toxicol. 36 (1996) 1e33.
14
A Pharmacology Primer
1.10 The Langmuir adsorption isotherm
Defined by the chemist Irving Langmuir (1881e957,
Fig. 1.12), the model for affinity is referred to as the
Langmuir adsorption isotherm. Langmuir, a chemist at
General Electric, was interested in the adsorption of molecules onto metal surfaces for the improvement of lighting
filaments. He reasoned that molecules had a characteristic
rate of diffusion toward a surface (referred to as condensation and denoted a in his nomenclature) and also a
characteristic rate of dissociation (referred to as evaporation and denoted as V1; see Fig. 1.12). He assumed that the
amount of surface that already has a molecule bound is not
available to bind another molecule. The surface area bound
by molecule is denoted q1, expressed as a fraction of
the total area. The amount of free area open for the binding
of molecule, expressed as a fraction of the total area, is
denoted as 1 q1. The rate of adsorption toward the surface therefore is controlled by the concentration of drug in
the medium (denoted m in Langmuir’s nomenclature)
multiplied by the rate of condensation on the surface and
the amount of free area available for binding:
Rate of diffusion toward surface ¼ amð1 q1 Þ. (1.1)
The rate of evaporation is given by the intrinsic rate of
dissociation of bound molecules from the surface multiplied by the amount already bound:
Rate of evaporation ¼ V1 q1 .
(1.2)
Once equilibrium has been reached, the rate of
adsorption equals the rate of evaporation. Equating (1.1)
and (1.2) and rearranging yields
q1 ¼
am
.
am þ V1
(1.3)
This is the Langmuir adsorption isotherm in its original
form. In pharmacological nomenclature, it is rewritten according to the convention
r¼
½AR
½A
¼
;
½Rt ½A þ KA
(1.4)
where [AR] is the amount of complex formed between the
ligand and the receptor, and [Rt] is the total number of receptor sites. The ratio r refers to the fraction of maximal
binding by a molar concentration of drug [A] with an equilibrium dissociation constant of KA. This latter term is the
ratio of the rate of offset (in Langmuir’s terms V1 and
referred to as k2 in receptor pharmacology) divided by
the rate of onset (in Langmuir’s terms a denoted k1 in receptor pharmacology).
It is amazing to note that complex processes such as
drugs binding to protein, activation of cells, and observation of syncytial cellular response should apparently so
closely follow a model based on these simple concepts.
This was not lost on A.J. Clark in his treatise on druge
receptor theory The Mode of Action of Drugs on Cells [4]:
It is an interesting and significant fact that the author in
1926 found that the quantitative relations between the concentration of acetylcholine and its action on muscle cells, an
action the nature of which is wholly unknown, could be most
accurately expressed by the formulae devised by Langmuir
to express the adsorption of gases on metal filaments.
dA.J. Clark (1937).
FIGURE 1.12 The Langmuir adsorption isotherm representing the binding of a molecule to a surface. Photo shows Irving Langmuir (1881e957), a
chemist interested in the adsorption of molecules to metal filaments for the production of light. Langmuir devised the simple equation still in use today for
quantifying the binding of molecules to surfaces. The equilibrium is described by condensation and evaporation to yield the fraction of surface bound (q1)
by a concentration m.
What is pharmacology? Chapter | 1
The term KA is a concentration, and it quantifies affinity. Specifically, it is the concentration that binds to 50%
of the total receptor population [see Eq. (1.4) when [A] ¼
KA]. Therefore, the smaller is the KA, the higher is the
affinity. Affinity is the reciprocal of KA. For example, if
KA ¼ 108 M, then 108 M binds to 50% of the receptors.
If KA ¼ 104 M, a 10,000-fold higher concentration of the
drug is needed to bind to 50% of the receptors (i.e., it is of
lower affinity).
It is instructive to discuss affinity in terms of the
adsorption isotherm in the context of measuring the amount
of receptor bound for given concentrations of drug. Assume
that values of fractional receptor occupancy can be visualized for various drug concentrations. The kinetics of such
binding is shown in Fig. 1.13. It can be seen that initially
the binding is rapid, in accordance with the fact that there
are many unbound sites for the drug to choose. As the sites
become occupied, there is a temporal reduction in binding
until a maximal value for that concentration is attained.
Fig. 1.13 also shows that the binding of higher concentrations of drug is correspondingly increased. In keeping with
the fact that this is first-order binding kinetics (where the
rate is dependent on a rate constant multiplied by the
concentration of reactant), the time to equilibrium is shorter
for higher concentrations than for lower concentrations.
The various values for receptor occupancy at different
concentrations constitute a concentration binding curve
(shown in Fig. 1.14A). There are two areas in this curve of
particular interest to pharmacologists. The first is the
maximal asymptote for binding. This defines the maximal
number of receptive binding sites in the preparation. The
binding isotherm [Eq. (1.4)] defines the ordinate axis as the
fraction of the maximal binding. Thus, by definition, the
maximal value is unity. However, in experimental studies,
real values of capacity are used since the maximum is not
15
known. When the complete curve is defined, the maximal
value of binding can be used to define fractional binding at
various concentrations and thus define the concentration at
which half-maximal binding (binding to 50% of the receptor population) occurs. This is the equilibrium dissociation constant of the drugereceptor complex (KA), the
important measure of drug affinity. This comes from the
other important region of the curve, namely, the midpoint.
It can be seen from Fig. 1.14A that graphical estimation of
both the maximal asymptote and the midpoint is difficult to
perform with the graph in the form shown. A much easier
format to present binding, or any concentrationeresponse
data, is a semilogarithmic form of the isotherm. This allows
better estimation of the maximal asymptote and places the
midpoint in a linear portion of the graph where intrapolation can be done (see Fig. 1.14B). Doseeresponse
curves for binding are not often visualized, as they require a
means to detect bound (over unbound) drug. However, for
drugs that produce a pharmacological response (i.e., agonists), a signal proportional to bound drug can be observed.
The true definition of a doseeresponse curve is the
observed in vivo effect of a drug given as a dose to a whole
animal or human. However, it has entered into the common
pharmacological jargon as a general depiction of drug and
effect. Thus, a doseeresponse curve for binding is actually
a binding concentration curve, and an in vitro effect of an
agonist in a receptor system is a concentrationeresponse
curve.
1.11 What is efficacy?
The property that gives a molecule the ability to change a
receptor, such that it produces a cellular response, is termed
efficacy. Early concepts of receptors likened them to locks
and keys. As stated by Paul Ehrlich,
FIGURE 1.13 Time course for increasing concentrations of a ligand with a KA of 2 nM. Initially, the binding is rapid but slows as the sites become
occupied. The maximal binding increases with increasing concentrations as does the rate of binding.
16
A Pharmacology Primer
FIGURE 1.14 Doseeresponse relationship for ligand binding according to the Langmuir adsorption isotherm. (A) Fraction of maximal binding as a
function of concentration of agonist. (B) Semilogarithmic form of curve shown in panel A.
Substances can only be anchored at any particular part of
the organism if they fit into the molecule of the recipient
complex like a piece of mosaic finds its place in a pattern.
This historically useful but inaccurate view of receptor
function has in some ways hindered development models of
efficacy. Specifically, the lock-and-key model implies a
static system with no moving parts. However, one feature
of proteins is their malleability. While they have structure,
they do not have a single structure but rather many potential
shapes referred to as conformations. A protein stays in a
particular conformation because it is energetically favorable
to do so (i.e., there is minimal free energy for that
conformation). If thermal energy enters the system, the
protein may adopt another shape in response. Stated by
Linderstrom-Lang and Schellman [15]:
. a protein cannot be said to have “a” secondary structure but exists mainly as a group of structures not too
different from one another in free energy .. In fact, the
molecule must be conceived as trying every possible
structure ..
dLindstrom and Schellman (1959).
Not only are a number of conformations for a given
protein possible, but the protein samples these various
conformations constantly. It is a dynamic and not a static
entity. Receptor proteins can spontaneously change
conformation in response to variations in the energy of the
system. An important concept here is that small molecules, by interacting with the receptor protein, can bias the
conformations that are sampled. It is in this way that drugs
can produce active effects on receptor proteins (i.e.,
demonstrate efficacy). A thermodynamic mechanism by
which this can occur is through what is known as
conformational selection [16]. A simple illustration can be
made by reducing the possible conformations of a given
receptor protein to just two. These will be referred to as
the “active” (denoted [Ra]) and “inactive” (denoted [Ri])
conformations.
Thermodynamically it would be expected that a ligand
may not have identical affinity for both receptor conformations. This was an assumption in early formulations of
conformational selection. For example, differential affinity
for protein conformations was proposed for oxygen binding
to hemoglobin [17] and for choline derivatives and nicotinic receptors [18]. Furthermore, assume that these conformations exist in an equilibrium defined by an allosteric
constant L (defined as [Ra]/[Ri]) and that a ligand [A] has
affinity for both conformations defined by equilibrium association constants Ka and aKa, respectively, for the inactive and active states.
It can be shown that the ratio of the active species Ra in
the presence of a saturating concentration (rN) of the
ligand versus in the absence of the ligand (r0) is given by
the following (see Section 1.14):
rN að1 þ LÞ
¼
.
r0
ð1 þ aLÞ
(1.5)
It can be seen that if the factor a is unity (i.e., the affinity of the ligand for Ra and Ri is equal [Ka ¼ aKa]), then
there will be no change in the amount of Ra when the ligand
is present. However, if a is not unity (i.e., if the affinity of
the ligand differs for the two species), then the ratio
necessarily will change when the ligand is present. Therefore, its differential affinity for the two protein species will
alter their relative amounts. If the affinity of the ligand is
higher for Ra, then the ratio will be >1 and the ligand will
enrich the Ra species. If the affinity for the ligand for Ra is
less than for Ri, then the ligand (by its presence in the
system) will reduce the amount of Ra. For example, if the
affinity of the ligand is 30-fold greater for the Ra state, then
in a system where 16.7% of the receptors are spontaneously
in the Ra state, the saturation of the receptors with this
agonist will increase the amount of Ra by a factor of 5.14
(16.7%e85%).
This concept is demonstrated schematically in Fig. 1.15.
It can be seen that the initial bias in a system of proteins
containing two conformations (square and spherical) lies
What is pharmacology? Chapter | 1
17
FIGURE 1.15 Conformational selection as a thermodynamic process to bias mixtures of protein conformations. (A) The two forms of the protein are
depicted as circular and square shapes. The system initially is predominantly square. Gaussian curves to the right show the relative frequency of
occurrence of the two conformations. (B) As a ligand (blue dots) enters the system and prefers the circular conformations, these are selectively removed
from the equilibrium between the two protein states. The distributions show the enrichment of the circular conformation at the expense of the square one.
(C) A new equilibrium is attained in the presence of the ligand favoring the circular conformation because of the selective pressure of affinity between the
ligand and this conformation. The distribution reflects the presence of the ligand and the enrichment of the circular conformation.
far toward the square conformation. When a ligand (filled
circles) enters the system and selectively binds to the circular conformations, this binding process removes the circles driving the backward reaction from circles back to
squares. In the absence of this backward pressure, more
square conformations flow into the circular state to fill the
gap. Overall, there is an enrichment of the circular conformations when unbound and ligand-bound circular conformations are totaled.
This also can be described in terms of the Gibbs free
energy of the receptoreligand system. Receptor conformations are adopted as a result of attainment of minimal
free energy. Therefore, if the free energy of the collection
of receptors changes, so too will the conformational
makeup of the system. The free energy of a system
composed of two conformations ai and ao is given by the
following [19]:
X
P
DGi ¼
DG0i RT
X
lnð1 þ Ka;i ½AÞ=lnð1 þ Ka;0 ½AÞ;
(1.6)
where Ka,i and Ka,0 are the respective affinities of the ligand
for states i and o. It can be seen that unless Ka,i ¼ Ka,0, the
logarithmic term will not equal zero and the free energy of
P
P
the system will change
DGi s DG0i . Thus, if a
ligand has differential affinity for either state, then the
free energy of the system will change in the presence of
the ligand. Under these circumstances, a different conformational bias will be formed by the differential affinity of
the ligand. From these models comes the concept that binding is not a passive process, whereby a ligand simply adheres to a protein without changing it. The act of binding
can itself bias the behavior of the protein. This is the thermodynamic basis of efficacy.
1.12 Doseeresponse curves
The concept of “doseeresponse” in pharmacology has been
known and discussed for some time. A prescription written
in 1562 for hyoscyamus and opium for sleep clearly states,
“If you want him to sleep less, give him less” [13]. It was
recognized by one of the earliest physicians, Paracelsus
(1493e1541), that it is only the dose that makes something
beneficial or harmful: “All things are poison, and nothing is
without poison. The dose [sic] alone makes a thing not
poison.”
Doseeresponse curves depict the response to an agonist
in a cellular or subcellular system as a function of the
agonist concentration. Specifically, they plot response as a
function of the logarithm of the concentration. They can be
defined completely by three parameters, namely, location
along the concentration axis, slope, and maximal asymptote
(Fig. 1.16). At first glance, the shapes of doseeresponse
curves appear to closely mimic the line predicted by the
Langmuir adsorption isotherm, and it is tempting to assume
18
A Pharmacology Primer
1.12.1 Potency and maximal response
FIGURE 1.16 Doseeresponse curves. Any doseeresponse curve can be
defined by the threshold (where response begins along the concentration
axis), the slope (the rise in response with changes in concentration), and
the maximal asymptote (the maximal response).
that doseeresponse curves reflect the first-order binding
and activation of receptors on the cell surface. However, in
most cases, this resemblance is happenstance, and dosee
response curves reflect a far more complex amalgam of
binding, activation, and recruitment of cellular elements of
response. In the end, these may yield a sigmoidal curve, but
in reality they are far removed from the initial binding of
drug and receptor. For example, in a cell culture with a
collection of cells with varying thresholds for depolarization, the single-cell response to an agonist may be complete
depolarization (in an all-or-none fashion). Taken as a
complete collection, the depolarization profile of the culture
where the cells all have differing thresholds for depolarization would have a Gaussian distribution of depolarization
thresholdsdsome cells being more sensitive than others
(Fig. 1.17A). The relationship of depolarization of the
complete culture to the concentration of a depolarizing
agonist is the area under the Gaussian curve. This yields a
sigmoidal doseeresponse curve (Fig. 1.17B) that resembles
the Langmuirian binding curve for drugereceptor binding.
The slope of the latter curve reflects the molecularity of the
drugereceptor interaction (i.e., one ligand binding to one
receptor yields a slope of unity for the curve). In the case of
the sequential depolarization of a collection of cells, it can
be seen that a narrower range of depolarization thresholds
yields a steeper doseeresponse curve, indicating that the
actual numerical value of the slope for a doseeresponse
curve cannot be equated to the molecularity of the binding
between agonist and receptor. In general, shapes of
doseeresponse curves are completely controlled by cellular
factors and cannot be used to discern drugereceptor
mechanisms. These must be determined indirectly by null
methods.
There are certain features of agonist doseeresponse curves
that are generally true for all agonists. The first is that the
magnitude of the maximal asymptote is totally dependent
on the efficacy of the agonist and the efficiency of the
biological system to convert receptor stimulus into tissue
response (Fig. 1.18A). This can be an extremely useful
observation in the drug-discovery process when attempting
to affect the efficacy of a molecule. Changes in chemical
structure that affect only the affinity of the agonist will have
no effect on the maximal asymptote of the doseeresponse
curve for that agonist. Therefore, if chemists wish to optimize or minimize efficacy in a molecule, they can track the
maximal response to do so. Second, the location, along
the concentration axis of doseeresponse curves, quantifies
the potency of the agonist (Fig. 1.18B). The potency is the
molar concentration required to produce a given response.
Potencies vary with the type of cellular system used to
make the measurement and the level of response at which
the measurement is made. A common measurement used to
quantify potency is the EC50, namely, the molar concentration of an agonist required to produce 50% of the
maximal response to the agonist. Thus, an EC50 value of
1 mM indicates that 50% of the maximal response to the
agonist is produced by a concentration of 1 mM of the
agonist (Fig. 1.19). If the agonist produces a maximal
response of 80% of the system maximal response, then
40% of the system maximal response will be produced by
1 mM of this agonist (Fig. 1.19). Similarly, an EC25 will be
produced by a lower concentration of this same agonist; in
this case, the EC25 is 0.5 mM.
1.12.2 P-scales and the representation of
potency
Agonist potency is an extremely important parameter in
drugereceptor pharmacology. Invariably it is determined
from log-doseeresponse curves. It should be noted that
since these curves are generated from semilogarithmic
plots, the location parameter of these curves is log normally distributed. This means that the logarithms of the
sensitivities (EC50) and not the EC50 values themselves
are normally distributed (Fig. 1.20A). Since all statistical
parametric tests must be done on data that come from
normal distributions, all statistics (including comparisons
of potency and estimates of errors of potency) must come
from logarithmically expressed potency data. When log
normally distributed EC50 data (Fig. 1.20B) are converted to EC50 data, the resulting distribution is seriously
skewed (Fig. 1.20C). It can be seen that error limits on
the mean of such a distribution are not equal [i.e., one
standard error of the mean unit (see Chapter 12: Statistics
and Experimental Design) either side of the mean gives
What is pharmacology? Chapter | 1
19
FIGURE 1.17 Factors affecting the
slope of doseeresponse curves. (A)
Gaussian distributions of the thresholds
for depolarization of cells to an agonist
in a cell culture. Solid line shows a
narrow range of threshold, and the
lighter line a wider range. (B) Area
under the curve of the Gaussian distributions shown in panel A. These would
represent the relative depolarization of
the entire cell culture as a function of
the concentration of agonist. The more
narrow range of threshold values corresponds to the doseeresponse curve of
steeper slope.
FIGURE 1.18 Major attributes of
agonist doseeresponse curves.
Maximal responses solely reflect
efficacy (left), while the potency
(location along the concentration
axis) reflects a complex function of
both efficacy and affinity (right).
FIGURE 1.19 Doseeresponse curves. Doseeresponse curve to an
agonist that produces 80% of the system maximal response. The EC50
(concentration producing 40% response) is 1 mM, the EC25 (20%) is
0.5 mM, and the EC80 (64%) is 5 mM.
different values on the skewed distribution (Fig. 1.20C)].
This is not true of the symmetrical normal distribution
(Fig. 1.20B).
One representation of numbers such as potency estimates
is with the P-scale. The P-scale is the negative logarithm of
number. For example, the pH is the negative logarithm of a
hydrogen ion concentration (105 M ¼ pH ¼ 5). It is essential
to express doseeresponse parameters as P-values (log of
the value, as in the pEC50) since these are log normal.
However, it sometimes is useful on an intuitive level to
express potency as a concentration (i.e., the antilog value).
One way this can be done and still preserve the error estimate is to make the calculation as P-values and then convert
to concentration as the last step. For example, Table 1.2
shows five pEC50 values, giving a mean pEC50 of 8.46 and a
standard error of 0.21. It can be seen that the calculation of
the mean as a converted concentration (EC50 value) leads to
an apparently reasonable mean value of 3.8 nM, with a
standard error of 1.81 nM. However, the 95% confidence
limits (range of values that will include the true value) of the
concentration value is meaningless, in that one of them (the
lower limit) is a negative number. The true value of the EC50
lies within the 95% confidence limits given by the mean þ 2.57 the standard error, which leads to the values 8.4
and 0.85 nM. However, when pEC50 values are used for
the calculations, this does not occur. Specifically, the mean
of 8.46 yields a mean EC50 of 3.47 nM. The 95% confidence
limits on the pEC50 are 7.8e9.0. Conversion of these limits
to EC50 values yields 95% confidence limits of 1e11.8 nM.
Thus, the true potency lies between the values of 1 and
11.8 nM 95% of the time.
20
A Pharmacology Primer
FIGURE 1.20 Log normal distributions of sensitivity of a pharmacological preparation to an agonist. (A) Doseeresponse curve showing the distribution
of the EC50 values along the log concentration axis. This distribution is normal only on a log scale. (B) Log normal distribution of pEC50 values (log
EC50 values). (C) Skewed distribution of EC50 values converted from the pEC50 values shown in panel B.
TABLE 1.2 Expressing mean agonist potencies with
error.
pEC50a
EC50 (nM)b
8.5
3.16
8.7
2
8.3
5.01
8.2
6.31
8.6
2.51
Mean ¼ 8.46
Mean ¼ 3.8
SE ¼ 0.21
SE ¼ 1.81
a
Replicate values of 1/N log EC50’s.
Replicate EC50 values in nM.
l
l
l
l
l
b
1.13 Chapter summary and conclusions
l
l
l
l
Some ideas on the origins and relevance of pharmacology and the concept of biological “receptors” are
discussed.
Currently, there are drugs for only a fraction of the
druggable targets present in the human genome.
While recombinant systems have greatly improved the
drug-discovery process, pathological phenotypes still
are a step away from these drug-testing systems.
Because of the fact that drugs are tested in experimental,
not therapeutic, systems, system-independent measures
of drug activity (namely, affinity and efficacy) must
be measured in drug discovery.
l
System-independent measures of drug activity coupled
with pharmacological models of drug mechanisms can
combine to convert a single ‘snapshot’ of activity in
one system into the complete ‘film’ of what the drug
will do in vivo.
Affinity is the strength of binding of a drug to a receptor.
It is quantified by an equilibrium dissociation constant.
Affinity can be depicted and quantified with the Langmuir adsorption isotherm.
Efficacy is measured in relative terms (having no absolute scale) and quantifies the ability of a molecule to
produce a change in the receptor (most often leading
to a physiological response).
Doseeresponse curves quantify drug activity. The
maximal asymptote is totally dependent on efficacy,
while potency is due to an amalgam of affinity and
efficacy.
Measures of potency are log normally distributed. Only
P-scale values (i.e., pEC50) should be used for statistical
tests.
1.14 Derivations: conformational
selection as a mechanism of
efficacy
Consider a system containing two receptor conformations
Ri and Ra that coexist in the system according to an allosteric constant denoted L.
Assume that ligand A binds to Ri with an equilibrium
association constant Ka, and Ra by an equilibrium association constant aKa. The factor a denotes the differential
What is pharmacology? Chapter | 1
affinity of the agonist for Ra (i.e., a ¼ 10 denotes a 10-fold
greater affinity of the ligand for the Ra state). The effect of
a on the ability of the ligand to alter the equilibrium between Ri and Ra can be calculated by examining the amount
of Ra species (both as Ra and ARa) present in the system in
the absence of ligand and in the presence of ligand. The
equilibrium expression for ([Ra]þ[ARa])/[Rtot], where
[Rtot] is the total receptor concentration given by the conservation equation [Rtot] ¼ [Ri]þ[ARi]þ[Ra]þ[ARa], is
r¼
Lð1 þ a½A=KA Þ
;
½A=KA ð1 þ aLÞ þ 1 þ L
(1.7)
where L is the allosteric constant, [A] is the concentration
of ligand, KA is the equilibrium dissociation constant of
the agonistereceptor complex (KA ¼ 1/Ka), and a is the
differential affinity of the ligand for the Ra state. It can
be seen that in the absence of agonist ([A] ¼ 0), r0 ¼ L/
(1 þ L), and in the presence of a maximal concentration
of ligand (saturating the receptors; [A]/N),
rN¼(a(1 þ L))/(1 þ aL). The effect of the ligand on
changing the proportion of the Ra state is given by the ratio
r/r0. This ratio is given by
rN að1 þ LÞ
.
¼
r0
ð1 þ aLÞ
(1.8)
Eq. (1.8) indicates that if the ligand has an equal affinity
for both the Ri and Ra states (a ¼ 1), then rN/r0 will equal
unity, and no change in the proportion of Ra will result
from maximal ligand binding. However, if a > 1, then the
presence of the conformationally selective ligand will cause
the ratio rN/r0 to be > 1, and the Ra state will be enriched
by presence of the ligand.
References
[1] A.-H. Maehle, C.-R. Prull, R.F. Halliwell, The emergence of the
drug-receptor theory, Nat. Rev. Drug Discov. 1 (2002) 1637e1642.
[2] W.D.M. Paton, On becoming a pharmacologist, Annu. Rev. Pharmacol. Toxicol. 26 (1986) 1e22.
21
[3] J. Drews, Drug discovery: a historical perspective, Science 287
(2000) 1960e1964.
[4] A.J. Clark, The Mode of Action of Drugs on Cells, Edward Arnold,
London, 1933.
[5] A.J. Clark, A. Heffter, General Pharmacology Handbuch der Experimentellen Pharmakologie, Springer, Berlin, 1937, pp. 165e176, 4.
[6] B. Holmstedt, G. Liljestrand, Readings in Pharmacology, Raven
Press, New York, NY, 1981.
[7] A. Marchese, S.R. George, L.F. Kolakowski, K.R. Lynch,
B.F. O’Dowd, Novel GPCRs and their endogenous ligands:
expanding the boundaries of physiology and pharmacology, Trends
Pharmacol. Sci. 20 (1999) 370e375.
[8] J.C. Venter, M.D. Adams, E.W. Myers, P.W. Li, R.J. Mural,
G.G. Sutton, The sequence of the human genome, Science 291
(2001) 1304e1351.
[9] R. Link, D. Daunt, G. Barsh, A. Chruscinski, B. Kobilka, Cloning of
two mouse genes encoding a2-adrenergic receptor subtypes and
identification of a single amino acid in the mouse a2-C10 homolog
responsible for an interspecies variation in antagonist binding, Mol.
Pharmacol. 42 (1992) 16e17.
[10] J.W. Black, A personal view of pharmacology, Annu. Rev. Pharmacol. Toxicol. 36 (1996) 1e33.
[11] R. Buscher, V. Hermann, P.A. Insel, Human adrenoceptor polymorphisms: evolving recognition of clinical importance, Trends
Pharmacol. Sci. 20 (1999) 94e99.
[12] R.P. Stephenson, A modification of receptor theory, Br. J. Pharmacol. 11 (1956) 379e393.
[13] S. Norton, Origins of pharmacology, Mol. Interv. 5 (2005) 144e149.
[14] P. Leff, G.R. Martin, J.M. Morse, Differences in agonist dissociation
constant estimates for 5-HT at 5-HT2-receptors: a problem of acute
desensitization? Br. J. Pharmacol. 89 (1986) 493e499.
[15] A. Linderstrom-Lang, P. Schellman, Protein conformation, Enzymes
1 (1959) 443e471.
[16] A.S.V. Burgen, Conformational changes and drug action, Fed. Proc.
40 (1966) 2723e2728.
[17] J.J. Wyman, D.W. Allen, The problem of the haem interaction in
haemoglobin and the basis for the Bohr effect, J. Polym. Sci. 7
(1951) 499e518.
[18] J. Del Castillo, B. Katz, Interaction at end-plate receptors between
different choline derivatives, Proc. Roy. Soc. Lond. B. 146 (1957)
369e381.
[19] E. Freire, Can allosteric regulation be predicted from structure? Proc.
Natl. Acad. Sci. U.S.A. 97 (2000) 11680e11682.
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Chapter 2
How different tissues process drug
response
[Nature] can refuse to speak but she cannot give a wrong
answer.
d Dr. Charles Brenton Hugins (1966).
We have to remember that what we observe is not nature in
itself, but nature exposed to our method of questioning .
dWerner Heisenberg (1901e76).
2.1 The ‘eyes to see’: pharmacologic
assays
If a drug possesses the molecular property of efficacy, then
it produces a change in the receptor that may be detected by
the cell. However, this can occur only if the stimulus is of
sufficient strength and the cell has the amplification machinery necessary to convert the stimulus into an observable response. In keeping with the mandatory partnership of
the sensitivity of the cell system and the intrinsic power of
the agonist to produce a response, the cellular assay becomes a key component that controls the amount of information that can be gained from the experiment, in
essence, the assay becomes the ‘eyes to see’ the change
imparted to the cell by the drug. Cellular assays can be
natural (and thus the sensitivity and components are set by
Nature) or recombinant whereby the experimenter can
manipulate the levels of response components and thus the
sensitivity of the system. Fig. 2.1 shows some of the factors
that play into the design of a pharmacologic assay whether
as applied to binding studies (Chapter 4) or functional
studies (Chapter 6). When building recombinant systems,
the first option is the type of cell to be used. Different cells
have different components and some of these may be
critical to the response of a given agonist. A case in point is
the response to the hormone amylin which interacts with a
receptor formed by a dimer of the calcitonin receptor and
the membrane protein RAMP3 (Receptor Activity modifying Protein 3). Thus, if a cell is not used that contains
RAMP3, then transfection of calcitonin receptors will not
constitute receptors for amylin and the assay will yield
erroneous results (for further details see Fig. 5.3). Similarly,
the relative stoichiometry of signaling components in a cell
A Pharmacology Primer. https://doi.org/10.1016/B978-0-323-99289-3.00013-0
Copyright © 2022 Elsevier Inc. All rights reserved.
may affect observed bias of agonist response (for further
details see Chapter 6). For complex binding curves
whereby the binding complex is an amalgam of the receptor
with other components (i.e., G-protein), differences in the
complimentary protein can lead to differences in binding
profiles. For instance, overexpression of receptor to the
point where the G-protein components in a cell are insufficient to produce adequate levels of ternary complex, then
complex binding curves will be produced (for further details see Fig. 4.19). If cell response is measured, then
various cells reflect changes in function in different ways
thus ‘business rules’ for the definition of what will be
considered drug response must be determined and adhered
to throughout the experiment. A major determinant of the
sensitivity of cells for agonists acting on receptors is the
level of receptor density expressed in the cell, i.e., a high
receptor density produces a sensitive tissue whereas a low
density an insensitive tissue. The impact of functional assay
composition will be considered repeatedly in this book as it
is of paramount importance for the discernment of drug
activity in in vitro systems.
Fig. 2.2A shows a functional doseeresponse curve for
human calcitonin in human embryonic kidney (HEK) cells
transfected with cDNA for human calcitonin receptor type
2 [1]. The response being measured here is the hydrogen
ion release by the cells, a sensitive measure of cellular
metabolism. Also shown (dotted line) is a curve for calcitonin binding to the receptors (as measured with radioligand binding). A striking feature of these curves is that the
curve for function is shifted considerably to the left of the
binding curve. Calculation of the receptor occupancy
required for 50% maximal tissue response indicates that
less than 50% occupancy, namely, more on the order of
3%e4%, is needed. In fact, a regression of tissue response
upon the receptor occupancy is hyperbolic in nature
(Fig. 2.2B), showing a skewed relationship between receptor occupancy and cellular response. This skewed
relationship indicates that the stimulation of the receptor
initiated by binding is amplified by the cell in the process of
response production.
The ability of a given agonist to produce a maximal
system response can be quantified as a receptor reserve.
23
24
A Pharmacology Primer
FIGURE 2.1 Main options available for the design of recombinant assay systems are the type of cell to be used and the level of receptors available to
response to agonists.
FIGURE 2.2 Binding and doseeresponse curves for human calcitonin on human calcitonin receptors type 2. (A) Doseeresponse curves for microphysiometry responses to human calcitonin in HEK cells (open circles) and binding in membranes from HEK cells (displacement of [125I]-human
calcitonin). (B) Regression of microphysiometry responses to human calcitonin (ordinates) upon human calcitonin fractional receptor occupancy
(abscissae). Dotted line shows a direct correlation between receptor occupancy and cellular response. HEK, human embryonic kidney. (A) Data from W.-J.
Chen, S. Armour, J. Way, G.C. Chen, C. Watson, P.E. Irving, Expression cloning and receptor pharmacology of human calcitonin receptors from MCF-7
cells and their relationship to amylin receptors, Mol. Pharmacol. 52 (1997) 1164e1175.
The reserve refers to the percentage of receptors not
required for production of maximal response (sometimes
referred to as spare receptors). For example, a receptor
reserve of 80% for an agonist means that the system
maximal response is produced by activation of 20% of the
receptor population by that agonist. Receptor reserves can
be quite striking. Fig. 2.3 shows guinea pig ileal smooth
muscle contractions to the agonist histamine before and
after irreversible inactivation of a large fraction of the receptors with the protein alkylating agent phenoxybenzamine [2]. The fact that the depressed maximum
doseeresponse curve is observed so far to the right of the
control doseeresponse curve indicates a receptor reserve of
98% [i.e., only 2% of the receptors must be activated by
histamine to produce the tissue’s maximal response
(Fig. 2.3B)]. In teleological terms, this may be useful, since
it allows neurotransmitters to produce rapid activation of
organs with minimal receptor occupancy leading to optimal
and rapid control of function.
Receptor reserve is a property of the tissue (i.e., the
strength of amplification of receptor stimulus inherent to the
cells) and it is a property of the agonist (i.e., how much
stimulus is imparted to the system by a given agonist receptor
occupancy). This latter factor is quantified as the efficacy of
the agonist. A high-efficacy agonist need occupy a smaller
fraction of the receptor population than a lower efficacy
agonist to produce a comparable stimulus. Therefore, it is
incorrect to ascribe a given tissue or cellular response system
with a characteristic receptor reserve. The actual value of the
receptor reserve will be unique to each agonist in that system.
For example, Fig. 2.4 shows the different amplification hyperbolae of Chinese hamster ovary (CHO) cells transfected
with b-adrenoceptors in producing cyclic adenosine monophosphate (AMP) responses to three different b-adrenoceptor
How different tissues process drug response Chapter | 2
25
FIGURE 2.3 Guinea pig ileal responses to histamine. (A) Contraction of guinea pig ileal longitudinal smooth muscle (ordinates as a percentage of
maximum) to histamine (abscissae, logarithmic scale). Responses obtained before ( filled circles) and after treatment with the irreversible histamine
receptor antagonist phenoxybenzamine (50 mM for 3 minutes; open circles). (B) Occupancyeresponse curve for data shown in (A). Ordinates are percentage of maximal response. Abscissae are calculated receptor occupancy values from an estimated affinity of 20 mM for histamine. Note that maximal
response is essentially observed after only 2% receptor occupancy by the agonist (i.e., a 98% receptor reserve for this agonist in this system). Data
redrawn from T.P. Kenakin, D.A. Cook, Blockade of histamine-induced contractions of intestinal smooth muscle by irreversibly acting agents, Can. J.
Physiol. Pharmacol. 54 (1976) 386e392.
FIGURE 2.4 Occupancyeresponse curves for b-adrenoceptor agonists in
transfected CHO cells. Occupancy (abscissae) calculated from binding affinity measured by displacement of [125I]-iodocyanopindolol. Response
measured as increases in cyclic AMP. Drawn from S. Wilson, J.K. Chambers, J.E. Park, A. Ladurner, D.W. Cronk, C.G. Chapman, Agonist potency
at the cloned human beta-3 adrenoceptor depends on receptor expression
level and nature of assay, J. Pharmacol. Exp. Ther. 279 (1996) 214e221.
agonists [3]. It can be seen that isoproterenol requires many
times less receptors to produce 50% response than do both
the agonists BRL 37344 and CGP 12177. This underscores
the idea that the magnitude of receptor reserves is very much
dependent on the efficacy of the agonist (i.e., one agonist’s
spare receptor is another agonist’s essential one).
2.2 The biochemical nature of
stimuluseresponse cascades
Cellular amplification of receptor signals occurs through a
succession of saturable biochemical reactions. Different
receptors are coupled to different stimuluseresponse
mechanisms in the cell. Each has its own function and
operates on its own timescale. For example, receptor
tyrosine kinases (activated by growth factors) phosphorylate target proteins on tyrosine residues to activate protein
phosphorylation cascades such as mitogen-activated protein
(MAP) kinase pathways. This process, on a timescale on
the order of seconds to days, leads to protein synthesis from
gene transcription with resulting cell differentiation and/or
cell proliferation. Nuclear receptors, activated by steroids,
operate on a timescale of minutes to days and mediate gene
transcription and protein synthesis. This leads to homeostatic, metabolic, and immunosuppression effects. Ligandgated ion channels, activated by neurotransmitters, operate
on the order of milliseconds to increase the permeability of
plasma membranes to ions. This leads to increases in
cytosolic Ca2þ, depolarization, or hyperpolarization of
cells. This in turn results in muscle contraction, release of
neurotransmitters, or inhibition of these processes.
G-protein-coupled receptors (GPCRs) react with a wide
variety of molecules, from small ones such as acetylcholine
to some as large as the protein SDF-1a. Operating on a
timescale of minutes to hours, these receptors mediate a
plethora of cellular processes. A common reaction in the
activation cascade for GPCRs is the binding of the activated
receptor to a trimeric complex of proteins called G-proteins
(Fig. 2.5). These proteinsdcomposed of three subunits
named a, b, and gdact as molecular switches for a number
of other effectors in the cell. The binding of activated receptors to the G-protein initiates the dissociation of GDP
from the a-subunit of the G-protein complex, the binding of
guanosine monophosphate (GTP), and the dissociation of the
complex into a- and bg-subunits. The separated subunits of
the G-protein can activate effectors in the cell such as adenylate cyclase and ion channels. Amplification can occur at
these early stages if one receptor activates more than one
26
A Pharmacology Primer
FIGURE 2.5 Activation of trimeric G-proteins by activated receptors. An agonist produces a receptor active state that goes on to interact with the Gprotein. A conformational change in the G-protein causes bound GDP to exchange with GTP. This triggers dissociation of the G-protein complex into aand bg-subunits. These go on to interact with effectors such as adenylate cyclase and calcium channels. The intrinsic GTPase activity of the a-subunit
hydrolyzes bound GTP back to GDP, and the inactivated a-subunit reassociates with the bg-subunits to repeat the cycle.
FIGURE 2.6 Production of cyclic AMP from ATP by the enzyme adenylate cyclase. Cyclic AMP is a ubiquitous second messenger in cells activating
numerous cellular pathways. The adenylate cyclase is activated by the a-subunit of Gs-protein and inhibited by the a-subunit of Gi-protein. Cyclic AMP is
degraded by phosphodiesterases in the cell.
G-protein. The a-subunit also is a GTPase, which hydrolyzes
the bound GTP to produce its own deactivation. This terminates the action of the a-subunit on the effector. It can be
seen that the length of time for which the a-subunit is active
can control the amount of stimulus given to the effector, and
that this also can be a means of amplification (i.e., one asubunit could activate many effectors). The a- and bg-subunits then reassociate to complete the regulatory cycle
(Fig. 2.5). Such receptor-mediated reactions generate cellular
molecules called second messengers. These molecules go on
to activate or inhibit other components of the cellular machinery to change cellular metabolism and state of activation.
For example, the second messenger (cyclic AMP) is generated
by the enzyme adenylate cyclase from ATP. This second
messenger furnishes fuel, through protein kinases, for the
phosphorylation of serine and threonine residues on a number
of proteins such as other protein kinases, receptors, metabolic
enzymes, ion channels, and transcription factors (see Fig. 2.6).
Activation of other G-proteins leads to the activation of
phospholipase C. These enzymes catalyze the hydrolysis of
How different tissues process drug response Chapter | 2
27
FIGURE 2.7 Production of second messengers IP3 and DAG through activation of the enzyme phospholipase C. This enzyme is activated by the asubunit of Gq-protein and also by bg-subunits of Gi-protein. IP3 stimulates the release of Ca2 from intracellular stores, while DAG is a potent activator of
protein kinase C. DAG, diacylglycerol; IP3, inositol 1,4,5-triphosphate.
phosphatidylinositol 4,5-bisphosphate to 1,2-diacylglycerol
(DAG) and inositol 1,4,5-triphosphate (see Fig. 2.7). This
latter second messenger interacts with receptors on intracellular calcium stores, resulting in the release of calcium into the
cytosol. This calcium binds to calcium sensor proteins such as
calmodulin or troponin C, which then go on to regulate the
activity of proteins such as protein kinases, phosphatases,
phosphodiesterase, nitric oxide synthase, ion channels, and
adenylate cyclase. The second messenger DAG diffuses in the
plane of the membrane to activate protein kinase C isoforms,
which phosphorylate protein kinases, transcription factors, ion
channels, and receptors. DAG also functions as a source of
arachidonic acid, which goes on to be the source of eicosanoid
mediators such as prostanoids and leukotrienes. In general, all
these processes can lead to a case where a relatively small
amount of receptor stimulation can result in a large
biochemical signal. An example of a complete stimuluse
response cascade for the b-adrenoceptor production of blood
glucose is shown in Fig. 2.8 [4].
There are numerous second messenger systems such as
those utilizing cyclic AMP and cyclic guanosine monophosphate (GMP), calcium and calmodulin, phosphoinositides,
and DAG with accompanying modulatory mechanisms. Each
receptor is coupled to these in a variety of ways in different cell
types. Therefore, it can be seen that it is impractical to attempt
to quantitatively define each stimuluseresponse mechanism
for each receptor system. Fortunately, this is not an important
prerequisite in the pharmacological process of classifying agonists, since these complex mechanisms can be approximated
by simple mathematical functions.
2.3 The mathematical approximation of
stimuluseresponse mechanisms
Each of the processes shown in Fig. 2.8 can be described by
a MichaeliseMenten type of biochemical reaction, a standard generalized mathematical equation describing the
interaction of a substrate with an enzyme. Michaelis and
Menten realized in 1913 that the kinetics of enzyme reactions differed from those of conventional chemical reactions. They visualized the reaction of substrate and an
enzyme yielding enzyme plus product as a form of this
equation: reaction velocity ¼ (maximal velocity of the
reaction substrate concentration)/(concentration of substrate þ a fitting constant Km). The constant Km (referred to
as the MichaeliseMenten constant) characterizes the
tightness of the binding of the reaction between substrate
and enzyme, essentially a quantification of the coupling
efficiency of the reaction. Km is the concentration at which
the reaction is half the maximal value or, in terms of kinetics, the concentration at which the reaction runs at half
its maximal rate. This model forms the basis of enzymatic
biochemical reactions and can be used as a mathematical
approximation of such functions.
As with the Langmuir adsorption isotherm, which in
shape closely resembles MichaeliseMenten type
biochemical kinetics, the two notable features of such reactions are the location parameter of the curve along the
concentration axis (the value of Km or the magnitude of the
coupling efficiency factor) and the maximal rate of the reaction (Vmax). In generic terms, MichaeliseMenten reactions can be written in the form
Velocity ¼
½substract$Vmax
½input$MAX
¼
½input þ b
½substract þ Km
(2.1)
where b is a generic coupling efficiency factor. It can be
seen that the velocity of the reaction is inversely proportional to the magnitude of b (i.e., the lower the value of
b, the more efficiently is the reaction coupled). If it is
assumed that the stimuluseresponse cascade of any given
cell is a series succession of such reactions, there are two
general features of the resultant that can be predicted mathematically. The first is that the resultant of the total series of
reactions will itself be of the form of the same hyperbolic
28
A Pharmacology Primer
FIGURE 2.8 Stimuluseresponse cascade for the production of blood glucose by activation of b-adrenoceptors. Redrawn from N.D. Goldberg, G.
Weissman, R. Claiborne, Cyclic nucleotides and cell function, in: G. Weissman, R. Claiborne (Eds.), Cell Membranes Biochemistry, Cell Biology, and
Pathology, H. P. Publishing, New York, NY, 1975, pp. 185e202.
shape (see Section 2.12.1). The second is that the location
parameter along the input axis (magnitude of the coupling
efficiency parameter) will reflect a general amplification
of any single reaction within the cascade (i.e., the magnitude of the coupling parameter for the complete series
will be lower than the coupling parameter of any single reaction; see Fig. 2.9). The magnitude of btotal for the series
sum of two reactions (characterized by b1 and b2) is given
by (see Section 2.12.2):
btotal ¼
b1 b2
.
1 þ b2
(2.2)
It can be seen from Eq. (2.2) that for positive nonzero
values of b2, btotal < b1. Therefore, the location parameter
of the rectangular hyperbola of the composite set of reactions in series is shifted to the left (increased potency) of
that for the first reaction in the sequence (i.e., there is
amplification inherent in the series of reactions).
The fact that the total stimuluseresponse chain can be
approximated by a single rectangular hyperbola furnishes the
basis of using an end-organ response to quantify an agonist
effect in a nonsystem-dependent manner. An important
feature of such a relationship is that it is monotonic (i.e.,
there is only one value of y for each value of x). Therefore,
FIGURE 2.9 Amplification of stimulus through successive rectangular
hyperbolae. The output from the first function (b ¼ 0.3) becomes the input
of a second function with the same coupling efficiency (b ¼ 0.3) to yield a
more efficiently coupled overall function (b ¼ 0.069). Arrows indicate the
potency for input to yield 50% maximal output for the first function and
the series functions.
the relationship between the strength of signal imparted
to the receptor between two agonists is accurately reflected
by the end-organ response (Fig. 2.10). This is the primary
reason that pharmacologists can circumvent the effects of the
cellular veil and discern system-independent receptor events
from translated cellular events.
How different tissues process drug response Chapter | 2
29
FIGURE 2.10 The monotonic nature of stimuluseresponse mechanisms. (A) Receptor stimulus generated by two agonists designated 1 and 2 as a
function of agonist concentration. (B) Rectangular hyperbola characterizing the transformation of receptor stimulus (abscissae) into cellular response
(ordinates) for the tissue. (C) The resulting relationship between tissue responses to the agonists as a function of agonist concentration. The general rank
order of activity (2 > 1) is preserved in the response as a reflection of the monotonic nature of the stimuluseresponse hyperbola.
FIGURE 2.11 Agonist-stimulated phosphorylation process with unsaturable dephosphorylation. Panel A shows dephosphorylation (solid ascending
line) as a linear unsaturable process and phosphorylation (descending dotted lines) for a range of agonist concentrations. Rates decrease as the substrate is
depleted. Where these curves intersect denotes a steady-state response (open circles). Panel B: Steady-state responses (ordinates) as a function of agonist
concentration. A sigmoidal curve of slope ¼ 1 describes steady-state responses. Redrawn from J.J. Tyson, K.C. Chen, B. Novak, Sniffers, buzzers, toggles
and blinkers: dynamics of regulatory and signaling pathways in the cell, Curr. Opin. Cell Biol. 15 (2003) 221e231.
2.4 Influence of stimuluseresponse
cascades on doseeresponse curve
slopes
For standard mass action kinetics whereby a single molecule
binds to a single receptor, the resulting binding curves have
Hill coefficient slopes of unity (providing cooperativity is
not present in the binding reactions). However, for agonists
with such simple Langmuirian binding kinetics (slope ¼ 1),
the cellular response curves for that agonist in functional
systems often will have slopes different from unity; this is
not due to cooperativity of binding but rather through signal
processing by the stimuluseresponse cascades in the cell
cytosol [5]. For example, a simple cytosolic biochemical
reaction such as the phosphorylation and dephosphorylation
of an enzyme can change the slope of concentrationeresponse
curve of agonists affecting the reaction. Fig. 2.11 shows
a concentrationeresponse curve for an agonist promoting the
phosphorylation of an enzyme. Fig. 2.11A shows an
ascending solid line depicting the rate of enzyme dephosphorylation and multiple descending dotted lines depicting
rates of phosphorylation for different concentrations of
agonist. The open circles represent steady states where the rate
of phosphorylation equals the rate of dephosphorylation; these
are the observed response points for the agonist and are
shown, as a function of agonist concentration, in Fig. 2.11B.
30
A Pharmacology Primer
FIGURE 2.12 Agonist-stimulated phosphorylation process with saturable dephosphorylation process described by MichaeliseMenten kinetics. Curve
descriptions as for Fig. 2.11. Panel B shows that the relationship between steady-state responses and agonist concentration is described by a sigmoid
function of slope ¼ 3. Redrawn from J.J. Tyson, K.C. Chen, B. Novak, Sniffers, buzzers, toggles and blinkers: dynamics of regulatory and signaling
pathways in the cell, Curr. Opin. Cell Biol. 15 (2003) 221e231.
This figure shows a case where the dephosphorylation is
nonsaturable; the slope of the resulting concentratione
response curve has a slope of unity consistent with mass action binding kinetics. However, if the dephosphorylation
process is saturable and described by MichaeliseMenten kinetics (as might be expected in a cellular biochemical
reaction), then a different pattern emerges. Specifically, the
resulting concentrationeresponse curve (obtained from
the steady-state intersections of the phosphorylation and
dephosphorylation rates) has a slope of 3, considerably steeper
than that mediating agonist binding to the receptor. Thus, it
can be seen that the processing of receptor stimulus by the cell
can control the slopes of concentrationeresponse curves
making inferences about cooperativity fruitless in functional
systems. Depending on the nature of the feedback loops found
in cellular stimuluseresponse cascades, a wide variety of
response outcomes can result from varying concentratione
response curve slope, to transient and phasic activity [5]
(Fig. 2.12).
2.5 System effects on agonist response:
full and partial agonists
For any given receptor type, different cellular hosts should
have characteristic efficiencies of coupling, and these
should characterize all agonists for that same receptor
irrespective of the magnitude of the efficacy of the agonists.
Different cellular backgrounds have different capabilities
FIGURE 2.13 Receptor occupancy curves for activation of human
calcitonin type 2 receptors by the agonist human calcitonin. Ordinates:
response as a fraction of the maximal response to human calcitonin.
Abscissae: fractional receptor occupancy by human calcitonin. Curves
shown for receptors transfected into three cell types: HEK cells, CHO
cells, and Xenopus laevis melanophores. It can be seen that the different
cell types lead to differing amplification factors for the conversion from
agonist receptor occupancy to tissue response. CHO, Chinese hamster
ovary; HEK, human embryonic kidney.
for amplification of receptor stimuli. This is illustrated by
the strikingly different magnitudes of the receptor reserves
for calcitonin and histamine receptors shown in Figs. 2.2
and 2.3. Fig. 2.13 shows the response produced by human
calcitonin activation of the human calcitonin receptor type
How different tissues process drug response Chapter | 2
31
FIGURE 2.14 Depiction of agonist efficacy as a weight placed on a balance to produce displacement of the arm (stimulus) and the observation of the
displacement of the other end of the arm as tissue response. The vantage point determines the amplitude of the displacement. Where no displacement is
observed, no agonism is seen. Where the displacement is between the limits of travel of the arm (threshold and maximum), partial agonism is seen. Where
displacement goes beyond the maximal limit of travel of the arm, uniform full agonism is observed.
2 when it is expressed in three different cell formats (HEK
293 cells, CHO cells, and Xenopus laevis melanophores).
From this figure it can be seen that while only 3% receptor
activation by this agonist is required for 50% response in
melanophores, this same occupancy in CHO cells produces
only 10% response and even less in HEK cells.
One operational view of differing efficiencies of receptor coupling is to consider the efficacy of a given
agonist as a certain mass characteristic of the agonist. If this
mass were to be placed on one end of a balance, it would
depress that end by an amount dependent on the weight.
The amount that the end is depressed would be the stimulus
(see Fig. 2.14). Consider the other end of the scale as
reflecting the placement of the weight on the scale (i.e., the
displacement of the other end is the response of the cell).
The point along the arm at which this displacement is
viewed reflects the relative amplification of the original
stimulus (i.e., the closer to the fulcrum, the less the
amplification). Therefore, different vantage points along the
displaced end of the balance arm reflect different tissues
with different amplification factors (different magnitudes of
coupling parameters). The response features of cells have
limits (i.e., a threshold for detecting the response and a
maximal response characteristic of the tissue). Depending
on the efficiency of stimuluseresponse coupling apparatus
of the cell, a given agonist could produce no response, a
partially maximal response, or the system maximal
response (see Fig. 2.14). The observed response to a given
drug gives a label to the drug in that system. Thus, a drug
that binds to the receptor but produces no response is an
antagonist, a drug that produces a submaximal response is
FIGURE 2.15 The expression of different types of drug activities in
cells. A drug that produces the full maximal response of the biological
system is termed a full agonist. A drug that produces a submaximal
response is a partial agonist. Drugs also may produce no overt response or
may actively reduce basal response. This latter class of drug is known as an
inverse agonist. These ligands have negative efficacy. This is discussed
specifically in Chapter 3, DrugeReceptor Theory.
a partial agonist, and a drug that produces the tissue
maximal response is termed a full agonist (see Fig. 2.15).
The term ‘full agonist’ should be qualified since it really is
defined by the test system in which the agonist is studied.
Specifically, ‘full’ agonists simply exceed the maximal
response window provided by the cellular assay and in this
sense the cellular assay truncates further information about
the true power of the agonist to provide response. Fig. 2.16
shows the relationship between the actual stimulation given
to the cell by the agonist and what we, as experimenters, are
allowed to see.
32
A Pharmacology Primer
FIGURE 2.17 Doseeresponse curves to the b-adrenoceptor low-efficacy
agonist prenalterol in three different tissues from guinea pigs. Responses
all mediated by b1-adrenoceptors. Depending on the tissue, this drug can
function as nearly a full agonist, a partial agonist, or a full antagonist.
Redrawn from T.P. Kenakin, D. Beek, Is prenalterol (H 133/80) really a
selective beta-1 adrenoceptor agonist? Tissue selectivity resulting from
differences in stimuluseresponse relationships, J. Pharmacol. Exp. Ther.
213 (1980) 406e413.
FIGURE 2.16 Physiological response systems such as membrane receptors produce cell stimulus upon activation; the magnitude of that
activation will be proportional to the magnitude of initiating stimulus but
the limits to this stimulation will depend upon the relative stoichiometry of
the components. Cells, however, have a maximal window of response that
they can report and this still limit the response produced by agonists. Once
the window of activation has been exceeded by an agonist, then a uniform
‘maximal response’ will be observed that gives no further information
about the actual maximal strength of signal imparted to the cell. All ligands
that exceed this window show a uniform maximal response and are
referred to as ‘full’ agonists.
It should be noted that while these labels often are given
to a drug and used across different systems as identifying
labels for the drug, they are in fact dependent on the system. Therefore, the magnitude of the response can
completely change with changes in the coupling efficiency
of the system. For example, the low-efficacy b-adrenoceptor agonist prenalterol can be an antagonist in guinea
pig extensor digitorum longus muscle, a partial agonist in
guinea pig left atria, and nearly a full agonist in right atria
from thyroxine-treated guinea pigs (Fig. 2.17) [6].
As noted previously, the efficacy of the agonist determines the magnitude of the initial stimulus given to the
receptor, and therefore the starting point for the input into
the stimuluseresponse cascade. As agonists are tested in
systems of varying coupling efficiency, it will be seen that
the point at which system saturation of the stimuluse
response cascade is reached differs for different agonists.
Fig. 2.18 shows two agonists, one of higher efficacy than
the other. It can be seen that both are partial agonists in
tissue A, but that agonist 2 saturates the maximal response
producing capabilities of tissue B and is a full agonist. The
same is not true for agonist 1. In a yet more efficiently
coupled system (tissue C), both agonists are full agonists.
This illustrates the obvious error in assuming that all agonists that produce the system maximal response have equal
efficacy. All full agonists in a given system may not have
equal efficacy.
The more efficiently coupled is a given system, the
more likely that agonists will produce the system maximum
response (i.e., be full agonists). It can also be shown that if
an agonist saturates any biochemical reaction within the
stimuluseresponse cascade, it will produce full agonism
(see Section 2.12.3). This also means that there will be an
increasing tendency for an agonist to produce the full
maximal response as the response is measured further down
the stimuluseresponse cascade the response is measured.
Fig. 2.19 shows three agonists, all producing different
amounts of initial receptor stimulus. These stimuli are then
passed through three successive rectangular hyperbolae
simulating the stimuluseresponse cascade. As can be seen
from the figure, by the last step, all the agonists are full
How different tissues process drug response Chapter | 2
33
FIGURE 2.18 Depiction of agonist efficacy as a weight placed on a balance to produce displacement of the arm (stimulus) and the observation of the
displacement of the other end of the arm as tissue response for two agonists, one of higher efficacy (Efficacy2) than the other (Efficacy1). The vantage point
determines the amplitude of the displacement. In system A, both agonists are partial agonists. In system B, agonist 2 is a full agonist and agonist 1 a partial
agonist. In system C, both are full agonists. It can be seen that the tissue determines the extent of agonism observed for both agonists, and that system C
does not differentiate the two agonists on the basis of efficacy.
agonists. Viewing the response at this point gives no
indication of differences in efficacy.
2.6 Differential cellular response to
receptor stimulus
As noted in the previous discussion, different tissues have
varying efficiencies of stimuluseresponse coupling. However, within a given tissue, there may be the capability of
choosing or altering the responsiveness of the system to
agonists. This can be a useful technique in the study of
agonists. Specifically, the ability to observe full agonists as
partial agonists enables the experimenter to compare relative efficacies (see previous material). Also, if stimuluse
response capability can be reduced, weak partial agonists
can be studied as antagonists to gain measures of affinity.
There are three general approaches to add texture to agonism: (1) choice of response pathway, (2) augmentation or
modulation of pathway stimulus, and (3) manipulation of
receptor density. This latter technique is operable only in
recombinant systems where receptors are actively
expressed in surrogate systems.
2.6.1 Choice of response pathway
The production of second messengers in cells by receptor
stimulation leads to a wide range of biochemical reactions.
As noted in the previous discussion, these can be approximately described by MichaeliseMenten type reaction
curves, and each will have unique values of maximal rates
of reaction and sensitivities to substrate. There are occasions where experimenters have access to different end
points of these cascades, and with them different amplification factors for agonist response. One such case is the
stimulation of cardiac b-adrenoceptors. In general, this
leads to a general excitation of cardiac response composed
of an increase in heart rate (for right atria), an increased
force of contraction (inotropy), and an increase in the rate
of muscle relaxation (lusitropy). These latter two cardiac
functions can be accessed simultaneously through measurement of isometric cardiac contraction, and each has its
own sensitivity to b-adrenoceptor excitation (lusitropic responses being more efficiently coupled to elevation of cyclic AMP than inotropic responses). Fig. 2.20 shows the
relative sensitivity of cardiac lusitropy and inotropy to elevations in cyclic AMP in guinea pig left atria [7]. It can be
seen that the coupling of lusitropic response is fourfold
more efficiently coupled to cyclic AMP elevation than is
inotropic response. Such differential efficiency of coupling
can be used to dissect agonist response. For example, the
inotropic and lusitropic responses of the b-adrenoceptor
agonists isoproterenol and prenalterol can be divided into
different degrees of full and partial agonisms (Fig. 2.21). It
can be seen from Fig. 2.21A that there are concentrations of
34
A Pharmacology Primer
FIGURE 2.19 Effects of successive rectangular hyperbolae on receptor stimulus. (A) Stimulus to three agonists. (B) Three rectangular hyperbolic
stimuluseresponse functions in series. Function 1 (b ¼ 0.1) feeds function 2 (b ¼ 0.03), which in turn feeds function 3 (b ¼ 0.1). (C) Output from
function 1. (D) Output from function 2 (functions 1 and 2 in series). (E) Final response: output from function 3 (all three functions in series). Note how all
three are full agonists when observed as final response.
isoproterenol that increase the rate of myocardial relaxation
(i.e., 0.3 nM) without changing inotropic state. As the
concentration of isoproterenol increases, the inotropic
response appears (Fig. 2.21B and C). Thus, the dosee
response curve for myocardial relaxation for this full
agonist is shifted to the left of the doseeresponse curve for
inotropy in this preparation (Fig. 2.21D). For a partial
agonist such as prenalterol, there is nearly a complete
dissociation between cardiac lusitropy and inotropy
(Fig. 2.21E). Theoretically, an agonist of low efficacy can
be used as an antagonist of isoproterenol response in the
more poorly coupled system (inotropy) and then compared
with respect to efficacy (observation of visible response) in
the more highly coupled system.
2.6.2 Augmentation or modulation of stimulus
pathway
The biochemical pathways making up the cellular
stimuluseresponse cascade are complex systems with
feedback and modulation mechanisms. Many of these are
mechanisms to protect against overstimulation. For
example, cells contain phosphodiesterase enzymes to
degrade cyclic AMP to provide a fine control of stimulus
strength and duration. Inhibition of phosphodiesterase
therefore can remove this control and increase cellular
levels of cyclic AMP. Fig. 2.22A shows the effect of
phosphodiesterase inhibition on the inotropic response of
guinea pig papillary muscle [8]. It can be seen from this
How different tissues process drug response Chapter | 2
35
phosphodiesterase degradation of intracellular cyclic AMP.
This technique can be used to modulate responses as well.
Smooth muscle contraction requires extracellular calcium
ion (calcium entry mediates contraction). Therefore,
reduction of the calcium concentration in the extracellular
space causes a modulation of the contractile responses (see
example for the muscarinic contractile agonist carbachol,
Fig. 2.22B). In general, the sensitivity of functional systems
can be manipulated by antagonism of modulating mechanisms and control of cofactors needed for cellular response.
2.6.3 Differences in receptor density
FIGURE 2.20 Differential efficiency of receptor coupling for cardiac
function. Guinea pig left atrial force of contraction (inotropy, open circles)
and rate of relaxation (lusitropy, filled circles) as a function (ordinates) of
elevated intracellular cyclic AMP concentration (abscissae). Redrawn from
T.P. Kenakin, J.R. Ambrose, P.E. Irving, The relative efficiency of betaadrenoceptor coupling to myocardial inotropy and diastolic relaxation:
organ-selective treatment of diastolic dysfunction, J. Pharmacol. Exp.
Ther. 257 (1991) 1189e1197.
figure that although 4.5% receptor stimulation by isoproterenol is required for 50% inotropic response in the natural
system (where phosphodiesterase-modulated intracellular
cyclic AMP response), this is reduced to only 0.2%
required receptor stimulation after inhibition of
The number of functioning receptors controls the magnitude of the initial stimulus given to the cell by an agonist.
Number of receptors on the cell surface is one means by
which the cell can control its stimulatory environment.
Thus, it is not surprising that receptor density varies with
different cell types. Potentially, this can be used to control
the responses to agonists since low receptor densities will
produce less response than higher densities. Experimental
control of this factor can be achieved in recombinant
systems. The methods of doing this are discussed more
fully in Chapter 5, Agonists: The Measurement of Affinity
and Efficacy in Functional Assays. Fig. 2.23 shows the
cyclic AMP and calcium responses to human calcitonin
activating calcitonin receptors in HEK cells [9].
FIGURE 2.21 Inotropic and lusitropic responses of guinea pig left atria to b-adrenoceptor stimulation. Panels AeC: isometric tension waveforms of
cardiac contraction (ordinates are mg tension; abscissae are ms). (A) Effect of 0.3 nM isoproterenol on the waveform. The wave is shortened due to an
increase in the rate of diastolic relaxation, whereas no inotropic response (change in peak tension) is observed at this concentration. (B) A further
shortening of waveform duration (lusitropic response) is observed with 3 nM isoproterenol. This is concomitant with positive inotropic response (increase
maximal tension). (C) This trend continues with 100 nM isoproterenol. (D) Doseeresponse curves for inotropy (filled circles) and lusitropy (open circles)
in guinea pig atria for isoproterenol. (E) Doseeresponse curves for inotropy (filled circles) and lusitropy (open circles) in guinea pig atria for the badrenoceptor partial agonist prenalterol. Data redrawn from T.P. Kenakin, J.R. Ambrose, P.E. Irving, The relative efficiency of beta-adrenoceptor
coupling to myocardial inotropy and diastolic relaxation: organ-selective treatment of diastolic dysfunction, J. Pharmacol. Exp. Ther. 257 (1991)
1189e1197.
36
A Pharmacology Primer
FIGURE 2.22 Potentiation and modulation of response through control of cellular processes. (A) Potentiation of inotropic response to isoproterenol in
guinea pig papillary muscle by the phosphodiesterase inhibitor IBMX. Ordinates: percent of maximal response to isoproterenol. Abscissa: percent receptor
occupancy by isoproterenol (log scale). Responses shown in absence (open circles) and presence (filled circles) of IBMX. (B) Effect of reduction in
calcium ion concentration on carbachol contraction of guinea pig ileum. Responses in the presence of 2.5 mM (filled circles) and 1.5 mM (open circles)
calcium ion in physiological media bathing the tissue. IBMX, isobutylmethylxanthine. Data redrawn from (A) T.P. Kenakin, J.R. Ambrose, P.E. Irving,
The relative efficiency of beta-adrenoceptor coupling to myocardial inotropy and diastolic relaxation: organ-selective treatment of diastolic dysfunction,
J. Pharmacol. Exp. Ther. 257 (1991) 1189e1197 and (B) A.S.V. Burgen, L. Spero, The action of acetylcholine and other drugs on the efflux of potassium
and rubidium from smooth muscle of the guinea-pig intestine, Br. J. Pharmacol. 34 (1968) 99e115.
FIGURE 2.23 Effect of receptor expression level on responses of human calcitonin receptor type 2 to human calcitonin. (A) Cyclic AMP and calcium
responses for human calcitonin activation of the receptor. Abscissae: logarithm of receptor density in fmol/mg protein. Ordinates: pmol cyclic AMP (lefthand axis) or calcium entry as a percentage of maximum response to human calcitonin. Two receptor expression levels are shown: At 65 fmol/mg, there is
sufficient receptor to produce only a cyclic AMP response. At 30,000 fmol/mg receptor, more cyclic AMP is produced, but there is also sufficient receptor
to couple to Gq-protein and produce a calcium response. (B and C) Doseeresponse curves to human calcitonin for the two responses in cell lines
expressing the two different levels of receptor. Effects on cyclic AMP levels (open circles; left-hand ordinal axes) and calcium entry (filled squares; righthand ordinal axes) for HEK cells expressing calcitonin receptors at 65 fmol/mg (panel B) and 30,000 fmol/mg (panel C). HEK, human embryonic kidney.
Data redrawn from T.P. Kenakin, Differences between natural and recombinant G-protein coupled receptor systems with varying receptor G-protein
stoichiometry, Trends Pharmacol. Sci. 18 (1997) 456e464.
How different tissues process drug response Chapter | 2
Responses from two different recombinant cell lines of
differing receptor density are shown. It can be seen that
not only does the quantity of response change with
increasing receptor number response (note ordinate scales
for cyclic AMP production in Fig. 2.23B and C) but also
the quality of the response changes. Specifically, calcitonin is a pleiotropic receptor with respect to the Gproteins with which it interacts (this receptor can couple
to Gs-, Gi-, and Gq-proteins). In cells containing a low
number of receptors, there is an insufficient density to
activate Gq-proteins, and thus no Gq response (calcium
signaling) is observed (see Fig. 2.23B). However, in
cells with a higher receptor density, both a cyclic AMP
and a calcium response (indicative of concomitant Gs- and
Gq-protein activation) are observed (Fig. 2.23C). In this
way, the receptor density controls the overall composition
of the cellular response to the agonist.
2.6.4 Target-mediated trafficking of stimulus
The foregoing discussion is based on the assumption that
the activation of the receptor by an agonist leads to uniform stimulation of all cellular pathways connected to that
target. Over the past 15 years, incontrovertible evidence
has emerged that for some agonists this is not the case, and
that, in fact, some agonists can bias or preferentially
activate some pathways linked to the receptor over others
[10]. This is in contrast to the previous view of efficacy in
pharmacology, which assumed a linear property for agonism, that is, activation of the receptor brought with it all
the physiological functions mediated by that receptor. A
concomitant view for seven transmembrane receptors was
that these primarily couple to G-proteins to elicit response;
it is now known that non-G-protein-linked cellular pathways are also a very important means for these receptors
to alter cellular metabolism and function [11e14]. A very
important major signaling pathway for seven transmembrane receptors comprises the binding of a group of
intracellular proteins called arrestins. These proteins were
thought to only mediate the desensitization and internalization of receptors until it was discovered that they also
can function as scaffolds to bind diverse, catalytically
active, intracellular proteins to form “signalosomes” [11],
which produce a wide range of cellular signals. Thus, the
recruitment of various protein and lipid kinases, phosphatases, phosphodiesterases, and ubiquitin ligase into
signalosomes leads to the regulation of members of the
Src family of nonreceptor tyrosine kinases, mitogenactivated protein kinases, protein kinase B (Akt),
glycogen synthase kinase 3, protein phosphatase 2 A,
nuclear factor-kB, and other proteinsdsee Fig. 2.24. The
activation of these non-G-protein pathways causes a lowlevel but prolonged response in the cell [referred to as
extracellular receptor-mediated kinase (ERK) activation,
37
external receptor kinase signal] as opposed to the rapid
but transient G-protein-mediated response (see Fig. 2.25).
It requires different assays to detect this b-arrestinmediated response; thus, in the absence of such an
assay, a molecule may be an undetected b-arrestin agonist.
For example, one of the most extensively studied drugs in
the world, the b-blocker propranolol (discovered in 1964),
was not classified as a b-arrestin ERK agonist until nearly
40 years after its initial discovery [15]; this new activity
was detected when ERK assays became available. This
underscores the importance of defining agonism in the
context of the assay. Thus, propranolol is an inverse
agonist for cyclic AMP and a positive agonist for ERK
activation. In fact, new vantage points to view agonist
activity can lead to reclassification of ligands. For
example, Fig. 2.26 shows a collection of b-blockers
reclassified in terms of their activity on b-adrenoceptors as
activators of G-proteins and ERK via b-arrestin binding
[16,17]. This polyfunctional view of receptors extends
beyond cellular signaling, as it is now known that modification of receptor behavior does not require activation of
conventional signaling pathways. For example, the internalization (absorption of the receptor into the cytoplasm
either to be recycled to the cell surface or degraded) had
been thought to be a direct function of activation, yet
antagonists that do not activate the receptor are now
known to cause active internalization of receptors [18].
The detection of these dichotomous activities is the direct
result of having new assays to observe cellular function, in
this case, the internalization of receptors. Fig. 2.27 shows
a number of receptor behaviors that now can be separately
monitored with different assays.
2.7 Receptor desensitization and
tachyphylaxis
There is a temporal effect that must be considered in
functional experiments, namely, the desensitization of the
system through sustained or repeated stimulation. Receptor
response is regulated by processes of phosphorylation and
internalization, which can prevent overstimulation of
physiological function in cells. This desensitization can be
specific for a receptor, in which case it is referred to as
homologous desensitization, or it can be related to modulation of a pathway common to more than one receptor and
thus is heterologous desensitization. In this latter case,
repeated stimulation of one receptor may cause the reduction in responsiveness of a number of receptors. The effects
of desensitization on agonist doseeresponse curves are not
uniform. Thus, for powerful, highly efficacious agonists,
desensitization can cause a dextral displacement of the
doseeresponse with no diminution of maximal response
(see Fig. 2.28A). In contrast, desensitization can cause a
38
A Pharmacology Primer
FIGURE 2.24 Seven transmembrane receptor signaling through two major networks. Receptors can interact with G-proteins (Gs) to activate AC and
PKA, Gq to activate PLCb and PKC, through Ga and Gbg G-protein subunits to interact with GIRK channels and small GTP-ases (Rho-GEF). Receptors
also can be phosphorylated by G-protein-coupled receptor kinase (GRK) to subsequently bind arrestins; this process uncouples G-protein signaling but
also can form scaffolds for the assembly of signalosomes and internalization of receptors. Arrestin-mediated signaling involves the Src family of tyrosine
kinases (Src), E3 ubiquitin ligases (Mdm2), ERK1/2 mitogen-activated protein kinase cascades (Raf-MEK-ERK1/2), cyclic AMP phosphodiesterases
(PDE4D), Ral-GDS, DAGK, regulators of nuclear factor-kB signaling (IkBa-IkKa), glycogen synthase kinase 3 regulatory complex PP2A-Akt-GSK3,
and the actin filament-severing complex cofilin-chronofilin-LIMK. AC, adenylate cyclase; DAGK, diacylglycerol kinases; GIRK, gated inwardly rectifying
Kþ; PKA, protein kinase A; PKC, protein kinase C; PLCb, phospholipase Cb; Ral-GDS, Ral-GDP dissociation stimulator; Rho-GEF, rho-guanine
nucleotide exchange factor. Redrawn from D. Gesty-Palmer, L.M. Luttrell, Refining efficacy: exploiting functional selectivity for drug discovery, Adv.
Pharmacol. 62 (2011) 79e107.
FIGURE 2.25 Schematic diagram of two major cellular signaling pathways mediated by seven transmembrane receptors. A rapid response is generated
through the activation of G-proteins (see Fig. 2.5), while a more persistent response is mediated by a receptor/b-arrestin complex of kinases intracellularly.
Natural endogenous agonists usually activate both of these, while synthetic agonists may be made, in some cases, to selectively activate one pathway or
the other.
How different tissues process drug response Chapter | 2
39
FIGURE 2.26 Venn diagram showing classifications of b-blocking drugs. A uniform property of these drugs is blockade of the b-adrenoceptor.
However, within this class of drugs, subclasses exist relating to G-protein function, which can weakly stimulate adenylate cyclase (partial agonists), have a
negative effect on elevated basal response (inverse agonists), or have no positive or negative stimulatory effect (neutral antagonists). Another subclass
exists relating to ERK activity where some of these are positive and others inverse agonists. ERK, extracellular receptoremediated kinase. Redrawn from
T.P. Kenakin, Pharmacological onomastics: what’s in a name? Br. J. Pharmacol. 153 (2008) 432e438.
FIGURE 2.27 Schematic showing some of the properties of seven transmembrane receptors. While many of these behaviors are interdependent upon
each other, others are not, and receptors can be made to demonstrate partial panels of these behaviors selectively through binding of different ligands.
Separate assays can be used to detect these various behaviors.
depression of the maximal response to weak partial agonists (see Fig. 2.28B). The overall effects of desensitization
on doseeresponse curves relate to the effective receptor
reserve for the agonist in a particular system. If the
desensitization process eliminates receptor responsiveness
where it is essentially irreversible in terms of the timescale
of response (i.e., response occurs in seconds whereas
reversal from desensitization may require hours), then the
desensitization process will mimic the removal of active
receptors from the tissue. Therefore, for an agonist with a
high receptor reserve (i.e., only a small portion of the receptors are required for production of maximal tissue
response), desensitization will not depress the maximal
response until a proportion greater than the reserve is
affected. In contrast, for an agonist with no receptor
reserve, desensitization will produce an immediate decrease
in the maximal response. These factors can be relevant to
the choice of agonists for therapeutic application. This is
discussed more fully in Chapter 5, Agonists: The Measurement of Affinity and Efficacy in Functional Assays.
40
A Pharmacology Primer
FIGURE 2.28 Effects of desensitization on inotropic responses of guinea pig atria to isoproterenol (panel A) and prenalterol (panel B). Ordinates:
response as a percent of the maximal response to isoproterenol. Abscissae: logarithms of molar concentrations of agonist (log scale). Responses shown
after peak response attained (within 5 minutes, filled circles) and after 90 minutes of incubation with the agonist (open squares). Data redrawn from T.P.
Kenakin, J.R. Ambrose, P.E. Irving, The relative efficiency of beta-adrenoceptor coupling to myocardial inotropy and diastolic relaxation: organ-selective
treatment of diastolic dysfunction, J. Pharmacol. Exp. Ther. 257 (1991) 1189e1197.
2.8 The measurement of drug activity
In general, there are two major formats for pharmacological
experiments: cellular function and biochemical binding.
Historically, function has been by far the more prevalent
form of experiment. Since the turn of the century, isolated
tissues have been used to detect and quantify drug activity.
Pioneers such as Rudolph Magnus (1873e927) devised
methods of preserving the physiological function of isolated tissues (i.e., isolated intestine) to allow the observation of drug-induced response. Such preparations formed
the backbone of all in vitro pharmacological experimental
observation and furnished the data to develop druge
receptor theory. Isolated tissues were the workhorses of
pharmacology, and various laboratories had their favorite.
As put by Paton [19]:
The guinea pig longitudinal muscle is a great gift to the
pharmacologist. It has low spontaneous activity; nicely
graded responses (not too many tight junctions); is highly
sensitive to a very wide range of stimulants; is tough, if
properly handled, and capable of hours of reproducible
behavior.
dW.D.M. Paton (1986).
All drug discoveries relied upon such functional assays
until the introduction of binding techniques. Aside from the
obvious shortcoming of using animal tissue to predict human responsiveness to drugs, isolated tissue formats did not
allow for high-throughput screening of compounds (i.e., the
experiments were labor intensive). Therefore, the numbers
of compounds that could be tested for potential activity
were limited by the assay format. In the mid-1970s, a new
technology (in the form of biochemical binding) was
introduced, and this quickly became a major approach to
the study of drugs. Both binding and function are valuable
and have unique application, and it is worth considering the
strengths and shortcomings of both approaches in the
context of the study of drugereceptor interaction.
2.9 Advantages and disadvantages of
different assay formats
High-throughput volume was the major reason for the
dominance of binding in the 1970 and 1980s. However,
technology has now progressed to the point where the
numbers of compounds tested in functional assays can
equal or even exceed the volume that can be tested in
binding studies. Therefore, this is an obsolete reason for
choosing binding over function, and the relative scientific
merits of both assay formats can now be used to make the
choice of assay for drug discovery. There are advantages
and disadvantages to both formats. In general, binding assays allow the isolation of receptor systems by the use of
membrane preparations and selective radioligand (or other
traceable ligands; see material following) probes. The
interference with the binding of such a probe can be used as
direct evidence of an interaction of the molecules with the
receptor. In contrast, functional studies in cellular formats
can be much more complex, in that the interactions may not
be confined to the receptor but rather extend further into the
complexities of cellular functions. Since these may be celltype dependent, some of this information may not be
transferable across systems and therefore will not be useful
for prediction of therapeutic effects. However, selectivity
can be achieved in functional assays through the use of
selective agonists. Thus, even in the presence of mixtures
of functional receptors, a judicious choice of agonist can be
used to select the receptor of interest and reduce nonspecific
signals.
In binding, the molecules detected are only those that
interfere with the specific probe chosen to monitor receptor
activity. There is a potential shortcoming of binding assays in
How different tissues process drug response Chapter | 2
which often the pharmacological probes used to monitor
receptor binding are not the same probes that are relevant to
receptor function in the cell. For example, there are molecules that may interfere with the physiologically relevant
receptor probe (the G-proteins that interact with the receptor
and control cellular response to activation of that receptor)
but not with the probe used for monitoring receptor binding.
This is true for a number of interactions generally classified
as allosteric (vide infra; see Chapters 4 and 7 for details)
interactions. Specifically, allosteric ligands do not necessarily interact with the same binding site as the endogenous
ligand (or the radioligand probe in binding), and therefore
binding studies may not detect them.
Receptor levels in a given preparation may be insufficient to return a significant binding signal (i.e., functional
responses are highly amplified and may reveal receptor
presence in a more sensitive manner than binding). For
example, CHO cells show a powerful 5-HT1B receptormediated agonist response to 5-HT that is blocked in
nanomolar concentrations by the antagonist ()-cyanopindolol [20]. However, no significant binding of the
radioligand [125I]-iodocyanopindolol is observed. Therefore, in this case, the functional assay is a much more
sensitive indicator of 5-HT responses. The physiological
relevant probe (one that affects the cellular metabolism) can
be monitored by observing cellular function. Therefore, it
can be argued that functional studies offer a broader scope
for the study of receptors than do binding studies. Another
major advantage of function over binding is the ability of
the former, and not the latter, to directly observe ligand
efficacy. Binding registers only the presence of the ligand
bound to the receptor but does not return the amount of
stimulation that the bound agonist imparts to the system.
In general, there are advantages and disadvantages to
both assay formats, and both are widely employed in
pharmacological research. The specific strengths and
weaknesses inherent in both approaches are discussed in
more detail in Chapters 4 and 5. As a preface to the
consideration of these two major formats, a potential issue
with both of them should be considered, namely, dissimulations between the concentrations of drugs added to the
experimentally accessible receptor compartment and the
actual concentration producing the effect.
2.10 Drug concentration as an
independent variable
In pharmacological experiments, the independent variable
is drug concentration, and the dependent (observed) variable is tissue response. Therefore, all measures of drug
activity, potency, and efficacy are totally dependent on
accurate knowledge of the concentration of drug at the
receptor producing the observed effect. With no knowledge
41
to the contrary, it is assumed that the concentration added to
the receptor system by the experimenter is equal to the
concentration acting at the receptor (i.e., there is no difference in the magnitude of the independent variable).
However, there are potential factors in pharmacological
experiments that can negate this assumption and thus lead
to serious error in the measurement of drug activity. One is
error in the concentration of the drug that is able to reach
the receptor.
2.10.1 Dissimulation in drug concentration
The receptor compartment is defined as the aqueous volume containing the receptor and cellular system. It is
assumed that free diffusion leads to ready access to this
compartment (i.e., that the concentration within this
compartment is the free concentration of drug at the receptor). However, there are factors that can cause differences between the experimentally accessible liquid
compartment and the actual receptor compartment. One
obvious potential problem is limited solubility of the drug
being added to the medium. The assumption is made tacitly
that the dissolved drug in the stock solution, when added to
the medium bathing the pharmacological preparation, will
stay in solution. There are cases where this may not be a
valid assumption.
Many drug-like molecules have aromatic substituents
and thus have limited aqueous solubility. A routine practice
is to dissolve stock drugs in a solvent known to dissolve
many types of molecular structures. One such solvent is
dimethylsulfoxide (DMSO). This solvent is extremely
useful because physiological preparations such as cells in
culture or isolated tissues can tolerate relatively high concentrations of DMSO (i.e., 0.5%e2%) with no change in
function. When substances dissolved in one solvent are
diluted into another solvent where the substance has
different (lower) solubility, local concentration gradients
may exceed the solubility of the substance in the mixture.
When this occurs, the substance may begin to come out of
solution in these areas of limited solubility (i.e., microcrystals may form). This may in turn lead to a phenomenon
known as nucleation, whereby the microcrystals form the
seeds required for crystallization of the substance from the
solution. The result of this process can be the complete
crystallization of the substance from the entire mixture. For
this reason, the dilution into the solution of questionable
solubility (usually the aqueous physiological salt solution)
should be done at the lowest concentration possible to
ensure against nucleation and potential loss of solubility of
the drug in the pharmacological medium. All dilutions of
the stock drug solution should be carried out in the solution
of maximal solubility, usually pure DMSO, and the solution for pharmacological testing must be taken directly
42
A Pharmacology Primer
from these stocks. Even under these circumstances, the
drug may precipitate out of the medium when added to the
aqueous medium. Fig. 2.29 shows the effects of limited
solubility on a doseeresponse curve to an agonist. Solubility limits are absolute. Thus, once the limit is reached,
no further addition of stock solution will result in an
increased soluble drug concentration. Therefore, the
response at that solubility limit defines the maximal
response for that preparation. If the solubility is below that
required for the true maximal response to be observed
FIGURE 2.29 Theoretical effects of agonist insolubility on dosee
response curves. Sigmoidal curve partially in dotted lines shows the
theoretically ideal curve obtained when the agonist remains in solution
throughout the course of the experiment determining the doseeresponse
relationship. If a limit to the solubility is reached, then the responses will
not increase beyond the point at which maximal solubility of the agonist is
attained (labeled limited solubility). If the precipitation of the agonist in
solution causes nucleation that subsequently causes precipitation of the
amount already dissolved in solution, then a diminution of the previous
response may be observed.
(dotted line, Fig. 2.28), then an erroneously truncated
response to the drug will be observed. A further effect on
the doseeresponse curve can be observed if the drug,
upon entering the aqueous physiological solution, precipitates because of local supersaturated concentration
gradients. This could lead to nucleation and subsequent
crystallization of the drug which had previously dissolved
in the medium. This would reduce the concentration
below the previously dissolved concentration and lead to a
decrease in the maximal response (bell-shaped dosee
response curve, Fig. 2.29).
Another potential problem causing differences in the
concentration of drug added to the solution (and that
reaching the receptors) is the sequestration of drug in regions other than the receptor compartment (Fig. 2.30).
Some of these effects can be due to active uptake or
enzymatic degradation processes inherent in the biological
preparation. These are primarily encountered in isolated
whole tissues and are not a factor in in vitro assays
composed of cellular monolayers. However, another factor
that is common to nearly all in vitro systems is the potential
adsorption of drug molecules onto the surface of the vessel
containing the biological system (i.e., well of a cell culture
plate). The impact of these mechanisms depends on the
drug and the nature of the surface, being more pronounced
for some chemical structures and also more pronounced for
some surfaces (i.e., nonsilanized glass). Table 2.1 shows
the striking differences in adsorption of [3H]-endorphin
with pretreatment of the surface with various agents. It
can be seen that a difference of over 99.9% can be observed
when the surface is treated with a substance that prevents
adsorption such as myelin basic protein.
FIGURE 2.30 Schematic diagram showing the routes of possible removal of drug from the receptor compartment. Upon diffusion into the compartment,
the drug may be removed by passive adsorption en route. This will cause a constant decrease in the steady-state concentration of the drug at the site of the
receptor until the adsorption process is saturated.
How different tissues process drug response Chapter | 2
TABLE 2.1 Effect of pretreatment of surface on
adsorption of [3H]-endorphin.
Treatment
fmole
adsorbed
% reduction over
lysine treatment
Lysine
615
0
Arginine
511
16.9
Bovine serum albumin
383
38
Choline chloride
19.3
97
Polylysine
1.7
99.5
Myelin basic protein
1.5
99.9
completely derailed by processes causing differences in
what is thought to be the concentration of drug at the
receptor and the actual concentration producing the effect.
Insofar as experiments can be done to indicate that these
effects are not operative in a given experiment, they
should be.
2.11 Chapter summary and conclusions
l
Data from P. Ferrar, C.H. Li, b-Endorphin: radioreceptor binding assay,
Int. J. Pept. Protein Res. 16 (1980) 66e69.
l
2.10.2 Free concentration of drug
If the adsorption process is not saturable within the concentration range of the experiment, it becomes a sink claiming a
portion of the drug added to the medium, the magnitude of
which is dependent on the maximal capacity of the sink (U) and
the affinity of the ligand for the site of adsorption (1/Kad, where
Kad is the equilibrium dissociation constant of the ligande
adsorption site complex). The receptor then interacts with the
remaining free concentration of drug in the compartment. The
free concentration of drug, in the presence of an adsorption
process, is given as follows (see Section 2.12.4):
1
Afree ¼ ½AT ½AT þ Kad
2
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ffi
2
AT þ Kad þ U 4½AT U
þU
43
l
l
l
l
(2.3)
The free concentration of a drug [Afree] in a system
containing an adsorption process with maximal capacity
ranging from 0.01 to 10 mM and for which the ligand has an
affinity (1/Kd) is shown in Fig. 2.31A. It can be seen that
there is a constant ratio depletion of free ligand in the
medium at low concentrations until the site of adsorption
begins to be saturated. When this occurs, there is a curvilinear portion of the line reflecting the increase in the free
concentration of ligand in the receptor compartment due to
cancellation of adsorption-mediated depletion (adsorption
sites are fully bound and can no longer deplete the ligand).
It is useful to observe the effects such processes can have
on doseeresponse curves of drugs. Fig. 2.31B shows the
effect of an adsorption process on the observed effects of an
agonist in a system where an adsorption process becomes
saturated at the higher concentrations of agonist. It can be
seen that there is a change in shape of the doseeresponse
curve (increase in Hill coefficient with increasing concentration). This is characteristic of the presence of an agonist
removal process that is saturated at some point within the
concentration range of agonist used in the experiment.
In general, it should be recognized that the most
carefully designed experimental procedure can be
l
l
l
l
It is emphasized that drug activity is observed through a
translation process controlled by cells. The aim of pharmacology is to derive system-independent constants
characterizing drug activity from the indirect product
of cellular response.
Different drugs have different inherent capacities to
induce response (intrinsic efficacy). Thus, equal cellular
responses can be achieved by different fractional receptor occupancies of these drugs.
Some cellular stimuluseresponse pathways and second
messengers are briefly described. The overall efficiency
of receptor coupling to these processes is defined as the
stimuluseresponse capability of the cell.
While individual stimuluseresponse pathways are
extremely complicated, they all can be mathematically
described by hyperbolic functions.
The ability to reduce stimuluseresponse mechanisms to
single monotonic functions allows relative cellular
response to yield receptor-specific drug parameters.
When the maximal stimuluseresponse capability of a
given system is saturated by agonist stimulus, the
agonist will be a full agonist (produce a full system
response). Not all full agonists are of equal efficacy;
they only all saturate the system.
In some cases, the stimuluseresponse characteristics of
a system can be manipulated to provide a means to
compare maximal responses of agonists (efficacy).
Receptor desensitization can have differing overall effects on high- and low-efficacy agonists.
All drug parameters are predicated on an accurate
knowledge of the concentration of drug acting at the receptor. Errors in this independent variable negate all
measures of dependent variables in the system.
Adsorption and precipitation are two commonly
encountered sources of error in drug concentration.
2.12 Derivations
l
l
l
l
Series hyperbolae can be modeled by a single hyperbolic function (2.12.1).
Successive rectangular hyperbolic equations necessarily
lead to amplification (2.12.2).
Saturation of any step in a stimulus cascade by two agonists leads to identical maximal final responses for the
two agonists (2.12.3).
Procedure to measure drug concentration in the receptor
compartment (2.12.4).
44
A Pharmacology Primer
FIGURE 2.31 Effects of a saturable adsorption process on concentrations of agonist (panel A) and doseeresponse curves to agonists (panel B). (A)
Concentrations of drug added to system (abscissae, log scale) versus free concentration in solution (ordinates, log scale). Numbers next to curves indicate
the capacity of the adsorption process in mM. The equilibrium dissociation constant of the agonist adsorption site is 10 nM. Dotted line indicates no
difference between added concentrations and free concentration in solution. (B) Effect of a saturable adsorption process on agonist doseeresponse curves.
Numbers next to curves refer to the maximal capability of the adsorption process. The equilibrium dissociation constant of the agonist adsorption site is
0.1 mM. Curve farthest to the left is the curve with no adsorption taking place.
2.12.1 Series hyperbolae can be modeled by a
single hyperbolic function
Rectangular hyperbolae are of the general form:
y¼
Ax
xþB
(2.4)
x
x þ b2
(2.5)
Assume a function
y1 ¼
where the output y1 becomes the input for a second function of the form
y1
y2 ¼
.
(2.6)
y1 þ b 2
concentration axis (the potency). Assume also a second
rectangular hyperbola where the input function is defined
by Eq. (2.8):
r2 ¼
½A=ð½A þ KA Þ
.
ð½A=ð½A þ KA ÞÞ þ b
(2.9)
The term b is the coupling efficiency constant for the
second function. The location parameter (potency) of the
second function (denoted Kobs) is given by
Kobs ¼
KA b
.
1þb
(2.10)
It can be seen that for nonzero and positive values of b,
Kobs < KA (i.e., the potency of the overall process will be
greater than the potency for the initial process).
It can be shown that a series of such functions can be
generalized to the form
2.12.3 Saturation of any step in a stimulus
x
cascade by two agonists leads to identical
yn ¼
xð1 þ bn ð1 þ bn1 ð1 þ bn2 ð1 þ bn3 Þ:Þ:Þ.Þ þ ðbn $b1 Þ maximal final responses for the two agonists
(2.7)
For a given agonist [A], the product of any one reaction in
which can be rewritten in the form of Eq. (2.4), where A ¼
the stimuluseresponse cascade is given by
ð1 þ bn ð1 þ bn1 ð1 þ bn2 ð1 þ bn3 Þ:Þ.Þ:Þ1 and B ¼
½A$M1
ðbn.: b1 Þ=ð1 þbn ð1 þbn1 ð1 þbn2 ð1 þbn3 Þ:Þ.Þ:Þ.
(2.11)
Output1 ¼
½A þ b1
Thus, it can be seen that the product of a succession of rectangular hyperbolae is itself a hyperbola.
where M1 is the maximal output of the reaction and b1 is the
coupling constant for the reaction. When this product becomes the substrate for the next reaction, the output becomes
2.12.2 Successive rectangular hyperbolic
equations necessarily lead to amplification
Output2 ¼
Assume a rectangular hyperbola of the form
r1 ¼
½A
;
½A þ KA
(2.8)
where [A] is the molar concentration of drug and KA is the
location parameter of the doseeresponse curve along the
½A$M1 M2
½AðM1 þ b2 Þ þ b1 b2
(2.12)
The maximal output from this second reaction (i.e., as
[A]/N) is
Max2 ¼
M1 M2
.
M1 b2
(2.13)
How different tissues process drug response Chapter | 2
By analogy, the maximal output from the second reaction for another agonist [A0 ] is
Max02 ¼
M01 M2
M01 þ b2
(2.14)
The relative maximal responses for the two agonists are
therefore
Relative Maxima ¼
Max2
1 þ b2 =M01
.
0 ¼
Max2
1 þ b2 =M1
(2.15)
It can be seen from this equation that if M1 ¼ M0 1
(i.e., if the maximal response to two agonists in any previous reaction in the cascade is equal), the relative maxima
of the two agonists in subsequent reactions will be equal
(Max2/Max0 2 ¼ 1).
2.12.4 Procedure to measure free drug
concentration in the receptor compartment
Assume that the total drug concentration [A1] is the sum of
the free concentration [Afree] and the concentration bound
to a site of adsorption [AD] (therefore, [Afree] ¼ [AT] [AD]). The mass action equation for adsorption is
½AD ¼
ð½AT ½ADÞU
½AT ½AD þ Kad
(2.16)
where the maximal number of adsorption sites is U and
the equilibrium dissociation constant of the drug site of
adsorption is Kad. Eq. (2.16) results in the quadratic equation:
½AD ½ADðU þ ½AT þ Kad Þ þ ½AT U ¼ 0;
2
(2.17)
one solution for which is
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ffi
2
1
AT þ Kad þ U 4½AT U .
½AT þ Kad þ U 2
(2.18)
Since [Afree] ¼ [AT] [AD], then
1
Afree ¼ ½AT ½AT 2
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ffi
2
AT þ Kad þ U 4½AT U
þ Kad þ U (2.19)
References
[1] W.-J. Chen, S. Armour, J. Way, G.C. Chen, C. Watson, P.E. Irving,
Expression cloning and receptor pharmacology of human calcitonin
receptors from MCF-7 cells and their relationship to amylin receptors, Mol. Pharmacol. 52 (1997) 1164e1175.
[2] T.P. Kenakin, D.A. Cook, Blockade of histamine-induced contractions of intestinal smooth muscle by irreversibly acting agents, Can.
J. Physiol. Pharmacol. 54 (1976) 386e392.
45
[3] S. Wilson, J.K. Chambers, J.E. Park, A. Ladurner, D.W. Cronk,
C.G. Chapman, Agonist potency at the cloned human beta-3 adrenoceptor depends on receptor expression level and nature of assay,
J. Pharmacol. Exp. Therapeut. 279 (1996) 214e221.
[4] N.D. Goldberg, G. Weissman, R. Claiborne, Cyclic nucleotides and
cell function, in: G. Weissman, R. Claiborne (Eds.), Cell Membranes, Biochemistry, Cell Biology, and Pathology, H. P. Publishing,
New York, NY, 1975, pp. 185e202.
[5] J.J. Tyson, K.C. Chen, B. Novak, Sniffers, buzzers, toggles and
blinkers: dynamics of regulatory and signaling pathways in the cell,
Curr. Opin. Cell Biol. 15 (2003) 221e231.
[6] T.P. Kenakin, D. Beek, Is prenalterol (H 133/80) really a selective
beta-1 adrenoceptor agonist? Tissue selectivity resulting from differences in stimuluseresponse relationships, J. Pharmacol. Exp.
Therapeut. 213 (1980) 406e413.
[7] T.P. Kenakin, J.R. Ambrose, P.E. Irving, The relative efficiency of
beta-adrenoceptor coupling to myocardial inotropy and diastolic
relaxation: organ-selective treatment of diastolic dysfunction,
J. Pharmacol. Exp. Therapeut. 257 (1991) 1189e1197.
[8] A.S.V. Burgen, L. Spero, The action of acetylcholine and other
drugs on the efflux of potassium and rubidium from smooth
muscle of the Guinea-pig intestine, Br. J. Pharmacol. 34 (1968)
99e115.
[9] T.P. Kenakin, Differences between natural and recombinant Gprotein coupled receptor systems with varying receptor G-protein
stoichiometry, Trends Pharmacol. Sci. 18 (1997) 456e464.
[10] T.P. Kenakin, Collateral efficacy as pharmacological problem
applied to new drug discovery, Expet Opin. Drug Discov. 1 (2006)
635e652.
[11] L.M. Luttrell, S.S.G. Ferguson, Y. Daaka, W.E. Miller,
S. Maudsley, G.J. Della Rocca, b-Arrestin-dependent formation of
b2 adrenergic-Src protein kinase complexes, Science 283 (1999)
655e661.
[12] D. Gesty-Palmer, L.M. Luttrell, Refining efficacy: exploiting functional selectivity for drug discovery, Adv. Pharmacol. 62 (2011)
79e107.
[13] R.J. Lefkowitz, S.K. Shenoy, Transduction of receptor signals by barrestins, Science 308 (2005) 512e517.
[14] L.M. Luttrell, Composition and function of G-protein-coupled receptor signalsomes controlling mitogen-activated protein kinase activity, J. Mol. Neurosci. 26 (2005) 253e263.
[15] M. Azzi, P.G. Charest, S. Angers, G. Rousseau, T. Kohout, barrestin-mediated activation of MAPK by inverse agonists reveals
distinct active conformations for G-protein-coupled receptors, Proc.
Natl. Acad. Sci. U.S.A. 100 (2003) 11406e11411.
[16] T.P. Kenakin, Pharmacological onomastics: what’s in a name? Br. J.
Pharmacol. 153 (2008) 432e438.
[17] S. Galandrin, M. Bouvier, Distinct signaling profiles of b1 and b2
adrenergic receptor ligands toward adenylyl cyclase and mitogenactivated protein kinase reveals the pluridimensionality of efficacy,
Mol. Pharmacol. 70 (2006) 1575e1584.
[18] J.A. Gray, B.L. Roth, Paradoxical trafficking and regulation of 5HT2A receptors by agonists and antagonists, Brain Res. Bull. 56
(2001) 441e451.
[19] W.D.M. Paton, On becoming a pharmacologist, Annu. Rev. Pharmacol. Toxicol. 26 (1986) 1e22.
[20] P. Ferrar, C.H. Li, b-Endorphin: radioreceptor binding assay, Int. J.
Pept. Protein Res. 16 (1980) 66e69.
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Chapter 3
Drugereceptor theory
What is it that breathes fire into the equations and makes a
universe for them to describe?
Stephen W. Hawking (1991).
An equation is something for eternity .
Albert Einstein (1879e1955).
Casual observation made in the course of a purely theoretical research has had the most important results in
practical medicine . Saul was not the last who, going forth
to see his father’s asses, found a kingdom.
Arthur Robertson Cushny (1866e1926).
3.1 About this chapter
This chapter discusses the various mathematical models
that have been put forward to link the experimental observations (relating to drugereceptor interactions) and the
events taking place on a molecular level between the drug
and protein recognition sites. A major link between the data
and the biological understanding of drugereceptor activity
is the model. In general, experimental data are a sampling
of a population of observations emanating from a system.
The specific drug concentrations tested control the sample
size, and the resulting dependent variables reflect what is
happening at the biological target. A model defines the
complete relationship for the whole population (i.e., for an
infinite number of concentrations). The choice of model,
and how it fits into the biology of what is thought to be
occurring, is critical to the assessment of the experiment.
For example, Fig. 3.1A shows a set of doseeresponse data
which have been fitted to two mathematical functions. It
can be seen that both equations appear to adequately fit the
data. The first curve is defined by
0:75
y ¼ 78 1 eð0:76ð½A ÞÞ 2:
(3.1)
This is simply a collection of constants in an exponential function format. The constants cannot be related to
the interactions at a molecular level. In contrast, the refit of
the data to the Langmuir adsorption isotherm:
y¼
80$½A
½A þ EC50
A Pharmacology Primer. https://doi.org/10.1016/B978-0-323-99289-3.00003-8
Copyright © 2022 Elsevier Inc. All rights reserved.
(3.2)
allows some measure of interpretation (i.e., the location
parameter along the concentration axis may reflect affinity
and efficacy, while the maximal asymptote may reflect efficacy; Fig. 3.1B). In this case, the model built on chemical
concepts allows interpretation of the data in molecular
terms. The fitting of experimental data to equations derived
from models of receptor function is at least consistent with
the testing and refinement of these models with the resulting further insight into biological behavior. An early proponent of using such models and laws to describe the very
complex behavior of physiological systems was A. J. Clark,
known as the originator of receptor pharmacology. As put
by Clark in his monograph The Mode of Action of Drugs
on Cells [1]:
The general aim of this author in this monograph has been
to determine the extent to which the effects produced by
drugs on cells can be interpreted as processes following
known laws of physical chemistry.
A. J. Clark (1937).
A classic example of where definitive experimental
data necessitated refinement and extension of a model of
drugereceptor interaction involved the discovery of
constitutive receptor activity in GPCR systems. The stateof-the-art model before this finding was the ternary
complex model for G-protein-coupled receptors (GPCRs),
a model that cannot accommodate ligand-independent
(constitutive) receptor activity. With the experimental
observation of constitutive activity for GPCRs by Costa
and Herz [2], a modification was needed. Subsequently,
Samama et al. [3] presented the extended ternary complex
model to fill the void. This chapter discusses relevant
mathematical models and generally offers a linkage between empirical measures of activity and molecular
mechanisms.
3.2 Drugereceptor theory
The various equations used to describe the quantitative
activity of drugs and the interaction of those drugs with
receptors are generally given the name drugereceptor
theory. The models used within this theory originated from
those used to describe enzyme kinetics. A. J. Clark is
credited with applying quantitative models to drug action.
47
48
A Pharmacology Primer
FIGURE 3.1 Data set fit to two functions of the same general shape. (A) Function fit to the exponential Eq. (3.1). (B) Function fit to rectangular
hyperbola of the form 80*[A]/([A]þ1).
His classic books The Mode of Action of Drugs on Cells [1]
and Handbook of Experimental Pharmacology [4] served
as the standard texts for quantitative receptor pharmacology
for many years.
A consideration of the more striking examples of specific
drug antagonisms shows that these in many cases follow
recognizable laws, both in the case of enzymes and cells.
A. J. Clark (1937).
With increasing experimental sophistication has come
new knowledge of receptor function, and insights into the
ways in which drugs can affect that function. In this
chapter, drugereceptor theory is described in terms of what
is referred to as “classical theory”; namely, the use and
extension of concepts described by Clark and other researchers such as Stephenson [5], Ariens [6,7], MacKay
[8], and Furchgott [9,10]. In this sense, classical theory is
an amalgam of ideas linked chronologically. These theories
were originated to describe the functional effects of drugs
on isolated tissues and thus naturally involved functional
physiological outputs. Another model used to describe
functional drug activity, derived by Black and Leff [11], is
termed the operational model. Unlike classical theory, this
model makes no assumptions about the intrinsic ability of
drugs to produce a response. The operational model is a
very important new tool in receptor pharmacology and is
used throughout this book to illustrate receptor methods
and concepts. Another model used primarily to describe the
function of ion channels is termed two-state theory. This
model contributed ideas essential to modern receptor theory, specifically in the description of drug efficacy in terms
of the selective affinity for protein conformation. Finally,
the idea that proteins translocate within cell membranes
[12] and the observation that seven transmembrane receptors couple to separate G-proteins in the membrane led
to the ternary complex model. This scheme was first
described by DeLean et al. [13] and later modified to the
extended ternary complex model by Samama et al. [3].
These are described separately as a background to discussion of drugereceptor activity and as context for the
description of the quantitative tools and methods used in
receptor pharmacology to quantify drug effect.
3.3 The use of mathematical models in
pharmacology
Mathematical models are the link between what is observed
experimentally and what is thought to occur at the molecular level. In physical sciences, such as chemistry, there is a
direct correspondence between the experimental observation and the molecular world (i.e., a nuclear magnetic
resonance spectrum directly reflects the interaction of
hydrogen atoms in a molecule). In pharmacology, the observations are much more indirect, leaving a much wider
gap between the physical chemistry involved in druge
receptor interaction and what the cell does in response to
those interactions (through the “cellular veil”; see Fig. 2.1).
Hence, models become uniquely important.
There are different kinds of mathematical models, and
they can be classified in two ways: by their complexity and
by the number of estimable parameters they use. The
simplest models are cartoons with very few parameters.
Thesedsuch as the black box that was the receptor at the
turn of the centurydusually are simple inputeoutput
functions with no mechanistic description (i.e., the drug
interacts with the receptor and a response ensues). Another
type, termed the Parsimonious model, is also simple but has
a greater number of estimable parameters. These do not
completely characterize the experimental situation but do
offer insights into mechanism. Models can be more complex as well. For example, complex models with a large
number of estimable parameters can be used to simulate
behavior under a variety of conditions (simulation models).
Similarly, complex models for which the number of
Drugereceptor theory Chapter | 3
independently verifiable parameters is low (termed heuristic models) can still be used to describe complex behaviors not apparent by simple inspection of the system.
In general, a model will express a relationship between
an independent variable (input by the operator) and one or
more dependent variables (output, produced by the model).
A ubiquitous form of equation for such inputeoutput functions is curves of the rectangular hyperbolic form. It is worth
illustrating some general points about models with such an
example. Assume that a model takes on the general form:
Output ¼
½Input$A
.
B$½Input þ C
(3.3)
The form of that function is shown in Fig. 3.2. There are
two specific parameters that can be immediately observed
from this function. The first is that the maximal asymptote of
the function is given solely by the magnitude of A/B. The
second is that the location parameter of the function (where it
lies along the input axis) is given by C/B. It can be seen that
when [Input] equals C/B the output necessarily will be 0.5.
Therefore, whatever the function be, the midpoint of the
curve will lie on a point at [Input] ¼ C/B. These ideas are
useful since they describe two essential behaviors of any
drugereceptor model; namely, the maximal response (A/B)
and the potency (concentration of input required for effect;
C/B). Many of the complex equations used to describe
drugereceptor interaction can be reduced to these general
forms, and the maxima and midpoint values can be used to
furnish general expressions for the dependence of efficacy
and potency on the parameters of the mechanistic model
used to furnish the equations.
3.4 Some specific uses of models in
pharmacology
Models are critical to pharmacology and are used in a variety of settings. As pointed out in Chapter 1, What Is
FIGURE 3.2 General curve for an inputeoutput function of the rectangular hyperbolic form (y ¼ 50x/(10xþ100)). The maximal asymptote is
given by A/B and the location parameter (along the x axis) is given by C/B
(see text).
49
Pharmacology, models furnish scales to bridge physiology
and chemistry to allow predictions to be made about drug
activity in therapeutic systems from data obtained in test
systems. Arguably the first pharmacological model was the
conception of a “receptor” for drug action in physiological
systems. Since that time, models have grown increasingly
complex and explicit as new knowledge about physiology
emerges. The two main functions of models in the pharmacology of drug discovery is to furnish systemindependent scales of drug activity (i.e., affinity,
efficacydvide infra) and to create a logical molecular
mechanism for drug action. In this regard, models can take
descriptive data (what we see in a given experiment) and
transform it into “predictive” data (allowing prediction of
activity in all systems). For example, the measurement and
determination of a concentrationeresponse curve in an
in vitro functional system can describe potency and
maximal effect in that system. However, usually this
experiment is done to gain insight into more important
questions such as:
l
l
l
l
What will be the potency and maximal effect in other
tissues?
Will this produce response in my therapeutic system?
How will this drug behave in vivo with the endogenous
agonist?
Will the observed response be relevant to therapeutic
activity?
The predictive aspect of models is critical, in that it can
be used to modify our understanding of the physiological
system we are dealing with. This is done by constructing a
model from data we have in hand, using that model to
predict a new behavior, to allow us to design a new
experiment to test whether the system produces that
behavior. The method employed to do this identifies what a
behavior of the system that the model currently used to
describe it cannot account for. For example, as will be
described in Chapter 6, Agonists: The Measurement of
Affinity and Efficacy in Functional Assays, the concept of
agonist potency ratios predicts that ratios will be constant
throughout a range of testing in tissues of varying sensitivity. However, the assumption upon which this prediction
is based is that the cellular function linking receptor stimulus and cell response is monotonic, i.e., there is only one
value of y for every value of x. Based on this assumption,
the model of efficacy proposed by Stephenson (vide infra)
predicts that any pair of agonists must have a constant ratio
of potencies for all responses controlled by a receptor.
With the advent of recombinant systems in pharmacology,
it was observed that two analogs of pituitary adenylate
cyclase-activating polypeptide (PACAP) (PACAP1e27 and
PACAP1e38) activating the PACAP receptor produce
opposite potency ratios when the receptor mediates cyclic
adenosine monophosphate (AMP) versus inositol phosphate
50
A Pharmacology Primer
metabolism [14]; this behavior cannot be accommodated by
the single active state model proposed by Stephenson and led
the way to the description of new agonist models to describe
biased signaling (see Chapter 6: Agonists: The Measurement
of Affinity and Efficacy in Functional Assays).
The optimal application of model prediction increases
the opportunity to observe such definitive behavior (i.e.,
showing a system behavior the model simply cannot
explain). For example, allosteric modulators have a
fundamentally different mode of interaction with receptors
than do standard (orthosteric) ligands; specifically, while
standard ligands bind to the natural agonist binding site,
allosteric modulators bind to another site on the receptor
protein (see Chapter 8: Allosteric Modulation). In spite of
this very different mode of action, many allosteric modulators can produce drug effects that are identical to standard
orthosteric drugs except when, under certain circumstances,
differences emerge. The ability to discern these differences
increases if the system is explored under as many experimental circumstances as possible, i.e., the pattern of drug
effect in a range of concentrations is explored. For example,
Fig. 3.3 shows a pattern of response for a full agonist in the
absence and presence of a partial agonist; based on a single
concentration the pattern is consistent with an orthosteric or
allosteric model of action for the partial agonist. However,
be testing a wide range of concentrations of the partial
agonist, a pattern emerges that is only consistent only with
an allosteric model of action (see Fig. 3.3)dthe extended
testing unveils a behavior that an orthosteric mode of action
cannot accommodate. While this is a better application of
model testing, it still is a “one-way” experiment, i.e., if the
behavior is uncovered, it is successful; if no unique
behavior is uncovered, then it might be that the wrong
experimental design was used to do so. The scientific
philosopher Karl Popper (1902e94) exemplified this idea
by stating that “nothing can be proven correct . only
FIGURE 3.3 Patterns of doseeresponse can identify drug mechanisms. Partial agonists produce elevated baselines and antagonism of full agonist
concentrationeresponse curves but a single concentration of a given partial agonist provides an effect that could either be orthosteric blockade of the
agonist binding site or allosteric alteration of receptor conformation through binding at a site separate from the agonist. However, testing of a range of
concentrations of the partial agonist differentiates these two mechanisms in that orthosteric blockade produces limitless dextral displacement of the full
agonist concentration response (panel A) with a resulting linear Schild regression (described in Chapter 7: Orthosteric Drug Antagonism) while an
allosteric mechanism demonstrates saturation of effect (which occurs when the allosteric binding site is fully occupied) leading to a limited dextral
displacement of full agonist concentration response curves and a curvilinear Schild regression (panel B).
Drugereceptor theory Chapter | 3
incorrect.” This is because, if something has not been
proven incorrect, it may be that the experiment was simply
insufficient to do so. That is why, all experiments are
designed from the point of view of disproving the “null
hypothesis,” i.e., two models are compared and the initial
assumption is that there is no difference between them and
that they describe the data equally well. When the data
cannot fit this assumption, it is disproven and one of the
models emerges as being incorrect and progress is made.
An ideal model also has internal checks that allow the
researcher to determine whether the calculation is or is not
following the predicted patterns set out by the model. A
classic example of an internal check for a model is the
linearity and slope of a Schild regression for simple
competitive antagonism (see Chapter 7: Orthosteric Drug
Antagonism). In this case, the calculations must predict a
linear regression of linear slope or the model of simple
competitive antagonism is not operable. The internal check
determines the applicability of the model. Useful pharmacological models will create a mechanism that will have
rules that allow predictions to be made. Adherence to those
rules is a good internal check to see if the model actually
does describe the system adequately. For example, the
51
blockade of a full agonist response by a partial agonist
predicts that the basal response will be elevated when the
partial agonist is present (due to the intrinsic efficacy of the
partial agonist) and also that the concentration response
curves to the full agonist will be shifted to the right along
the concentration axis due to the blockade of responsedsee
Fig. 3.4A for curves to isoproterenol in the absence and
presence of the partial agonist chloropractolol [15]. However, for simple competitive antagonism to be the only drug
activity displayed, the points of intersection of the full
agonist in the presence and absence of the partial agonist
should coincide; as seen in Fig. 3.4A, this is not the case
(see broken line circle). In this case the lack of verisimilitude of the experimental data to model predictions revealed
a second property of chloropractolol, namely blockade of
the catecholamine metabolizing enzyme catechol o-methyl
transferase (COMT). This produces sensitization of the
tissue to isoproterenol after chloropractolol treatment to
cause the disparity in the curve intersection. After COMT
blockade, the intersection of the curves complies with the
prediction of the model for simple competitive antagonism
(see Fig. 3.4C). Another internal check for this model is
that the midpoint for partial agonist direct effect (in this
FIGURE 3.4 Using internal checks to determine internal consistencies with models. (A) Effect of the b-adrenoceptor partial agonist chloropractolol on
heart rate responses to isoproterenol in rat atria. Curves in absence (filled circles) and presence of chloropractolol 1 nM (open circles), 10 nM (filled
triangles), and 100 nM (open triangles). Circled area shows nonconcordance of intersections for the curves. (B) Direct heart rate effects of chloropractolol
(pEC50 ¼ 7.8, 95% c.l. ¼ 7.6e8.0). (C) Effects chloropractolol on isoproterenol responses after blockade of COMT; concentrations as for panel A. (D)
Schild regressions for chloropractolol in the absence (open circles) and presence of COMT blockade. COMT, catechol o-methyl transferase. Data redrawn
from T.P. Kenakin, J.W. Black, The pharmacological classification of practolol and chloropractolol, Mol. Pharmacol. 14 (1978) 607e623.
52
A Pharmacology Primer
case increased heart rate) should equal the affinity of the
partial agonist (as depicted in a Schild regression described
in Chapter 7: Orthosteric Drug Antagonism). Fig. 3.4D
shows two Schild regressions; one is obtained after COMT
blockade, is linear, and yields an affinity that is not
significantly different from the EC50 for chloropractolol
direct activation of receptors (shown in Fig. 3.4B). An
aberrant nonlinear Schild regression is obtained before
COMT blockade yielding an incorrect measure for chloropractolol affinity (Fig. 3.4D). Thus, the internal check
within the model reveals a drug property for chloropractolol
that, when negated by prior blockade of the enzyme, enables classification of this molecule as an orthosteric
competitive partial agonist of the b-adrenoceptor.
Models can be very useful in designing experiments,
predicting drug effect, and describing complex systems.
Ideally, models should be composed of species that can be
independently quantified. Also, the characteristics of the
processes that produce changes in the amounts of these
species should be independently verifiable.
Models have been defined to describe the binding of
ligands to receptor proteins (discussed in Chapter 4: Pharmacological Assay Formats: Binding). These range from
simple (with verifiable constants) to extremely complex;
these latter models often have many parameters some of
which are not verifiable. For example, Fig. 3.5 shows a
binding model that theoretically accounts for receptor
activation states and binding to signaling proteins [16]. This
model is heuristic in that, though it is comprehensive, it
also is not useful for data fitting since there are too many
unverifiable constants.
It also is important to input the correct data into a model
to assure its maximal effectiveness. For example, Fig. 3.6
shows a hypothetical structure activity profile of four
molecules made for bronchodilation in asthma. Fig. 3.6A
shows the potencies of these molecules in a functional
assay as pEC50 (Log EC50 where EC50 refers to the
concentration of agonist producing 50% maximal response)
values of the four molecules. It can be seen that very little
texture is observed, i.e., there appears to be no structure
activity relationship with these changes in molecular
structure. However, potency is a complex factor of affinity
of the molecule for the receptor and the efficacy of
the molecule in producing response [EC50 ¼ Affinity/
(1þefficacy) where affinity is the equilibrium dissociation
constant of the agonistereceptor complex and efficacy is
given by s from the operational model (vide infra)]. When
the activity of these molecules is expressed in these more
molecular scales (affinity and efficacy), it can be seen that
there is a striking structureeactivity relationship in a progressive increase in affinity and concomitant decrease in
efficacy is produced by the changes in structure (Fig. 3.6B).
FIGURE 3.5 The quaternary complex model of allosteric interactions at GPCRs; a thermodynamically complete, extended model taking into account the
concomitant binding of orthosteric ligand, A, allosteric ligand, B, and G protein, G, on a receptor that can exist in two conformational states (R and R*).
The model parameters are defined in the insert Table of the Figure redrawn from A. Christopoulos, T. Kenakin, G protein-coupled receptor allosterism and
complexing, Pharmacol. Rev. 54 (2002) 323e374.
Drugereceptor theory Chapter | 3
53
FIGURE 3.6 Hypothetical structureeactivity relationship for four badrenoceptor agonist bronchodilators. (A) When the observed potency of these
compounds as bronchodilators is compared as pEC50 values, it appears that the changes in structure did nothing to change activity. (B) However, potency
is affinity divided by efficacy and when these particular components are examined it can be seen that dramatic but opposing effects were seen with these
indices with changes in structure.
These latter scales make the changes in structure much
more valuable to medicinal chemists, in that they denote the
changes in structure that control the separate affinities and
efficacies of the chemical scaffold.
The main tool that can be used to assess model fit is
goodness of fit and statistical hypothesis testing; these
techniques are described in detail in the Appendix: Statistics
and Experimental Design. It will be seen that a fallacy of this
general approach is that a “better fit” indicates adherence to a
model. This, again, is a one-way solution since many models
can fit a given set of data and often no unique solution results. The more complex the model (i.e., the more parameters
used to fit nuances in data), the better will be the fit but Ftests in the hypothesis testing procedure determine whether
one is entitled to use a complex model (see Appendix:
Statistics and Experimental Design for further discussion).
An important type of mathematical model yields a
linear relationship between two variables. Linear models
are beneficial in that they are simple, lead to predictable
dependent outputs, and have straightforward tests of
properties (i.e., slope and location along the independent
variable axisdsee Appendix: Statistics and Experimental
Design). Historically, pharmacological models were
modified to yield linear outputs because the techniques
available for data fitting and parameter derivation at the
time could not adequately accommodate nonlinear functions (i.e., in lieu of computers, rulers were used to derive
parameters). For example, a well-known linear transform is
the LineweavereBurke equation for enzyme catalysis. As
shown in Fig. 3.7A, the increased rate of enzyme activity
with substrate concentration forms a hyperbolic type
function. This can be made into a linear function through
the transform of expressing substrate concentration [S] and
resulting enzyme velocities as reciprocal valuesdsee
Fig. 3.7B. Linear transforms have these advantages but
they also can skew data, cause heteroscedasticity of errors,
and be misleading. For example, the Scatchard transform
for binding data (see Chapter 4: Pharmacological Assay
Formats: Binding) can lead to grossly miscalculated binding parameters as shown in Fig. 4.5. Therefore, if raw
nonlinear data can be utilized, it generally is in modern
analyses with the advent of computers that are able to use
complex nonlinear relationships. However, this very
weakness can also be used to advantage as linear transforms can amplify deviations from ideal behavior as well.
For instance, deviation from simple mass action binding
can be greatly amplified through reexpression of the data in
a linear Scatchard analysis; Fig. 4.6A shows the nearly
undetectable effect of excessive protein in a binding assay
in a raw saturation binding curve which is clearly amplified
to detectable levels upon linear transformation with the
Scatchard equation (Fig. 4.6B).
Models can also predict apparently aberrant behaviors
in systems that may appear to be artifactual (and therefore
54
A Pharmacology Primer
FIGURE 3.7 The nonlinear MichaeliseMenten function (panel A) can be transformed into a straight line function through the LineweavereBurke
transformation (panel B).
appear to denote experimental problems) but are in fact
perfectly correct behaviors according to a given complex
system. Simulation with modeling allows the researcher to
determine whether the data are erroneous or indicative of a
correct system activity. For example, consider a system in
which the receptors can form dimers, and where the affinity
of a radioligand (radioactive molecule with affinity for the
receptor allowing measurement of ligandereceptor complex binding to be measured) differs between the single
receptor and the dimer. It is not intuitively obvious how the
system will behave when a nonradioactive ligand that also
binds to the receptor is added. In a standard single receptor
system, preincubation with a radioligand followed by
addition of a nonradioactive ligand will produce displacement of the radioligand. This will cause a decrease in the
bound radioactive signal. The result usually is a sigmoidal
doseeresponse curve for displacement of the radioligand
by the nonradioactive ligand (see Fig. 3.8). This is discussed in some detail in Chapter 4, Pharmacological Assay
Formats: Binding. The point here is that addition of the
same nonradioactive ligand to a system of prebound radioligand would be expected to produce a decrease in signal.
However, in the case of dimerization, if the combination of
two receptors forms a “new” receptor of higher affinity for
the radioligand, addition of a nonradioligand may actually
increase the amount of radioligand bound before decreases
are observed [17]. This is an apparent paradox (addition of
a nonradioactive species actually increasing the binding of
a radioactive species to a receptor). The equation for the
amount of radioactive ligand [A*] bound (signal denoted
by u) in the presence of a range of concentrations of
nonradioactive ligand [A] is (Section 3.15.1):
½A=Kd þ a½A½A=K2d þ 2að½A=Kd Þ
u¼
2
ð1 þ ½A=Kd þ að½A=Kd Þ2
ð1 þ ½A=Kd þ ½A=Kd þ a ½A½A=K2d þ að½A=Kd Þ
það½A=Kd Þ ð½A=Kd þ 2að½A=Kd Þ
2
2
(3.4)
FIGURE 3.8 Displacement of prebound radioligand [A*] by nonradioactive concentrations of [A]. Curve for a ¼ 1 denotes no cooperativity in
binding (i.e., formation of the receptor dimer does not lead to a change in
the affinity of the receptor for either [A] or [A*]). The curve a ¼ 10 indicates a system whereby formation of the receptor dimer leads to a 10fold increase in the affinity for both [A*] and [A]. In this case, it can be
seen that addition of the nonradioactive ligand [A] actually leads to an
increase in the amount of radioligand [A*] bound before a decrease at
higher concentrations of [A]. For this simulation [A*]/Kd ¼ 0.1.
2
Drugereceptor theory Chapter | 3
As shown in Fig. 3.8, addition of the nonradioactive
ligand to the system can increase the amount of bound
radioactivity in a system where the affinity of the ligand is
higher for the dimer than it is for the single receptor. The
prediction of this effect by the model changes the interpretation of a counterintuitive finding to one that conforms
to the experimental system. Without the benefit of the
modeling, observation of increased binding of radioligand
with the addition of a nonradioactive ligand might have
been interpreted erroneously.
Models also can assist in experimental design and the
determination of the limits of experimental systems. For
example, it is known that three proteins mediate the
interaction of HIV with cells; namely, the chemokine receptor CCR5, the cellular protein CD4, and the viral coat
protein gp120. An extremely useful experimental system
to study this interaction is one in which radioactive CD4,
prebound to soluble gp120, is allowed to bind to cellular
receptor CCR5. This system can be used to screen for HIV
entry inhibitors. One of the problems with this approach is
the availability and expense of purified gp120. This reagent can readily be prepared in crude broths but very
pure samples are difficult to obtain. A practical question,
then, is to what extent would uncertainty in the concentration of gp120 affect an assay that examines the binding
of a complex of radioactive CD4 and gp120 with the
CCR5 receptor in the presence of potential drugs that
block the complex? It can be shown in this case that the
model of interaction predicts the following equation for
the relationship between the concentrations of radioactive
CD4 [CD], crude gp120 [gp], [CCR5], and the ratio of the
observed potency of a displacing ligand [B] to its true
potency (i.e., to what extent errors in the potency estimation will be made with errors in the true concentration
of gp120; see Section 3.15.2):
K4 ¼
½IC50 ð½CD=K1 Þð½gp=K2 Þ þ 1
(3.5)
where K4, K1, and K2 are the equilibrium dissociation constants of the ligand [B], CD4, and gp120 and the site of
interaction with CCR5/CD4/gp120, respectively. The relationship between the concentration of radioligand used in
the assay and the ratio of the observed potency of the ligand
in blocking the binding to the true potency is shown in
Fig. 3.9. The gray lines indicate this ratio with a 50% error
in the concentration of gp120 (crude gp120 preparation). It
can be seen from this figure that as long as the concentration of radioligand is kept below [CD4]/K1 ¼ 0.1, differences between the assumed concentration of gp120 in the
assay and true concentrations make little difference to the
estimation of ligand potency. In this case, the model delineates experimental parameters for the optimal performance
of the assay.
55
FIGURE 3.9 Errors in the estimation of ligand potency for displacement
of radioactive CD4egp120 complex (surrogate for HIV binding) as a
function of the concentration of radioactive CD4 (expressed as a fraction
of the equilibrium dissociation constant of the CD4 for its binding site).
Gray lines indicate a 50% error in the concentration of gp120. It can be
seen that very little error in the potency estimation of a displacing ligand is
incurred at low concentrations of radioligand but that this error increases as
the concentration of CD4 is increased.
3.5 Mass action building blocks
All linkage pharmacological models find their root source
in the mass action law [18,19]:
A þ B#A0 þ B0
(3.6)
as presented by Guldberg and Waade. This statement is
deceptively simple as all it appears to say is reactants A
and B are converted to two other products A0 and B0 . However, the enormous implication of this statement is that matter is neither created nor destroyed and must be accounted
for in the reaction as an interconversion. The mass action
equation predicts a sigmoidal relationship between the
amount of drugereceptor complex and the logarithm of
the concentration of drug. This type of relationship forms
the basis of all physiological binding and catalysis (i.e., enzymes) [20] and, in fact, versions of this law form the
building blocks for the major pharmacologic models
defining the action of receptors, proteins, and enzymes.
Fig. 3.10 shows how variants of the mass action law
describe agonism and efficacy for receptors (‘series’ mass
action equations). In these cases the affinity of the receptor
R for some ligand A is modified by a second reaction of the
mass action form, i.e., a conversion of the receptor species
to another form. When this occurs, the observed affinity of
the ligand A for the receptor will depend on both the concentration of the cobinding allosteric ligand and its nature.
Another arrangement of the mass action motif describes
parallel mass action expressions; these describe allostery
and ion channel functiondsee Fig. 3.10.
56
A Pharmacology Primer
FIGURE 3.10 The mass action equations as a building block component of standard pharmacologic receptor, enzyme, and ion channel models. The
mass action scheme can be in series where the product of the first step becomes the reactant for a second step or in parallel where two mass actions that can
communicate with each other run concurrently. Redrawn from T.P. Kenakin, The mass action equation in Pharmacology Br. J Clin Pharmacol (2015)
https://doi.org/10.1111/bcp.12810
3.6 Classical model of receptor
function
The binding of a ligand [A] to a receptor R is assumed to
follow mass action according to the Langmuir adsorption
isotherm (see Eq. 1.4), as defined by Clark [1,4]. No provision for different drugs of differing propensities to stimulate receptors was made until E. J. Ariens [6,7] introduced
a proportionality factor (termed intrinsic activity and
denoted by a in his terminology) to the binding function
[7]. Intrinsic activity is the maximal response to an agonist
expressed as a fraction of the maximal response for the
entire system (i.e., a ¼ 1 indicates that the agonist produces
the maximal response, a ¼ 0.5 indicates half the maximal
response, and so on). An intrinsic activity of zero indicates
no agonism. Within this framework, the equation for
response is thus
Response ¼
½Aa
½A þ KA
(3.7)
where KA is the equilibrium dissociation of the agoniste
receptor complex. Note how in this scheme, response is
assumed to be a direct linear function of receptor occupancy multiplied by a constant. This latter requirement
was seen to be a shortcoming of this approach since it
was known that many nonlinear relationships between receptor occupancy and tissue response existed. This was
rectified by Stephenson [5], who revolutionized receptor
theory by introducing the abstract concept of stimulus.
This is the amount of activation given to the receptor
upon agonist binding. Stimulus is processed by the tissue
to yield response. The magnitude of the stimulus is a function [denoted by f in Eq. (3.8)] of another abstract quantity,
referred to as efficacy [denoted by e in Eq. (3.8)]. Stephenson also assumed that the tissue response was some function (not direct) of stimulus. Thus, tissue response was
given by
½Ae
Response ¼ fðStimulusÞ ¼ f
.
(3.8)
½A þ KA
It can be seen that efficacy in this model is both an
agonist and a tissue-specific term. Furchgott [9] separated
the tissue and agonist components of efficacy by defining a
term intrinsic efficacy (denoted by ε), which is a strictly
agonist-specific term (i.e., this term defines the quantum
stimulus given to a single receptor by the agonist). The
product of receptor number ([Rt]) and intrinsic efficacy is
then considered to be the agonist- and tissue-dependent
element of agonism:
½A$ε$½Rt Response ¼ f
.
(3.9)
½A þ KA
The function f is usually hyperbolic, which introduces
the nonlinearity between receptor occupancy and response.
A common experimentally observed relationship between
receptor stimulus and response is a rectangular hyperbola
Drugereceptor theory Chapter | 3
57
(see Chapter 2: How Different Tissues Process Drug
Response). Thus, response can be thought of as a hyperbolic function of stimulus:
Response ¼
Stimulus
;
Stimulus þ b
(3.10)
where b is a fitting factor representing the efficiency of
coupling between stimulus and response. Substituting for
stimulus from Eq. (3.8) and rearranging response in classical theory is given as
½A½Rt ε=b
Response ¼ f
.
(3.11)
½Aðð½Rt ε=bÞ þ Þ þ KA
The various components of classical theory relating
receptor occupancy to tissue response are shown schematically in Fig. 3.11. It will be seen that this formally is
identical to the equation for response derived in the operational model (see material following), where s ¼ [Rt]ε/b.
It is worth exploring the effects of the various parameters on agonist response in terms of classical receptor
theory. Fig. 3.12 shows the effect of changing efficacy. It
can be seen that increasing efficacy causes an increased
maximal response with little shift to the left of the dosee
response curves until the system maximal response is
achieved. Once this occurs (i.e., the agonist is a full agonist
in the system), increasing efficacy has no further effect on
the maximal response, but rather causes shifts to the left of
the doseeresponse curves (Fig. 3.12A). In contrast,
changing KA, the equilibrium dissociation constant of the
agonistereceptor complex, has no effect on maximal
response but only shifts the curves along the concentration
axis (Fig. 3.12B).
FIGURE 3.12 Classical model of agonism. Ordinates: response as a
fraction of the system maximal response. Abscissae: logarithms of molar
concentrations of agonist. (A) Effect of changing efficacy as defined by
Stephenson [5]. Stimuluseresponse coupling defined by hyperbolic
function Response ¼ stimulus/(stimulusþ0.1). (B) Doseeresponse curves
for agonist of e ¼ 1 and various values for KA.
3.7 The operational model of receptor
function
Black and Leff [11] presented a model, termed the operational model, which avoids the inclusion of ad hoc terms
for efficacy. Since its publication in 1983, the operational
model has become the preeminent model for describing and
quantifying agonism. This model is based on the experimental observation that the relationship between agonist
concentration and tissue response is most often hyperbolic.
This allows for response to be expressed in terms of receptor and tissue parameters (see Section 3.15.3):
Response ¼
FIGURE 3.11 Major components of classical receptor theory. Stimulus
is the product of intrinsic efficacy (ε), receptor number [R], and fractional
occupancy as given by the Langmuir adsorption isotherm. A stimuluse
response transduction function f translates this stimulus into tissue
response. The curves defining receptor occupancy and response are
translocated from each other by the stimuluseresponse function and
intrinsic efficacy.
½A$s$Emax
;
½Aðs þ 1Þ þ KA
(3.12)
where the maximal response of the system is Emax, the
equilibrium dissociation constant of the agonistereceptor
complex is KA, and s is the term that quantifies the power
of the agonist to produce response (efficacy) and the ability
of the system to process receptor stimulus into response.
Specifically, s is the ratio [Rt]/KE, which is the receptor
density divided by a transducer function expressing the
ability of the system to convert agonistereceptor complex
58
A Pharmacology Primer
to response and the efficacy of the agonist. In this sense, KE
resembles Stephenson’s efficacy term, except that it emanates from an experimental and pharmacological rationale
(see Section 3.15.3). The essential elements of the operational model can be summarized graphically. In Fig. 3.13,
the relationship between agonist concentration and receptor
binding (plane 1), the amount of agonistereceptor complex
and response (plane 2), and agonist concentration and
response (plane 3) can be seen. Early iterations of the operational model were, in fact, referred to as the “shoe-box”
model, and the three planes were depicted as a box to
show the interrelationship of response, transduction, and
occupancy. The operational model furnishes a unified
view of receptor occupancy, stimulation, and production
of response through cellular processing. Fig. 3.14A shows
the effects of changing s on doseeresponse curves. It can
be seen that the effects are identical to changes in efficacy
in the classical model, namely, an increased maximal
response of partial agonism until the system maximal
response is attained followed by sinistral displacements of
the curves. As with the classical model, changes in KA
cause only changes in the location parameter of the curve
along the concentration axis (Fig. 3.14B).
The operational model, as presented, shows dosee
response curves with slopes of unity. This pertains specifically only to stimuluseresponse cascades where there is no
cooperativity and the relationship between stimulus ([AR]
complex), and overall response is controlled by a hyperbolic function with slope ¼ 1. In practice, it is known that
there are experimental doseeresponse curves with slopes
that are not equal to unity, and there is no a priori reason for
there not to be cooperativity in the stimuluseresponse
process. To accommodate the fitting of real data (with
slopes not equal to unity) and the occurrence of
FIGURE 3.14 Operational model of agonism. Ordinates: response as a
fraction of the system maximal response. Abscissae: logarithms of molar
concentrations of agonist. (A) Effect of changing s values. (B) Effect of
changing KA.
stimuluseresponse cooperativity, a form of the operational
model equation can be used with a variable slope (see
Section 3.15.4):
E¼
Emax sn ½An
n
n.
ð½A þ KA Þ þ sn ½A
(3.13)
The operational model is used throughout this book for
the determination of drug parameters in functional systems.
3.8 Two-state theory
Two-state theory was originally formulated for ion channels. The earliest form, proposed by Del Castillo and Katz
[21], was composed of a channel that when bound to an
agonist changed from a closed to an open state. In the
absence of agonist, all the channels are closed:
FIGURE 3.13 Principal components of the operational model. The 3D
array defines processes of receptor occupation (plane 1), the transduction
of the agonist occupancy into response (plane 2) in defining the relationship between agonist concentration, and tissue response (plane 3). The
term a refers to the intrinsic activity of the agonist.
A þ R%ARclosed %ARopen .
(3.14)
From theories on cooperative enzymes proposed by
Monod et al. [22] came the idea that channels could coexist
in both open and closed states.
Drugereceptor theory Chapter | 3
59
The number of channels open, as a fraction of the total
number of channels, in the presence of a ligand [A] is given
as (see Section 3.15.5):
ropen ¼
aL½A=KA þ L
.
½A=KA ð1 þ aLÞ þ L þ 1
(3.15)
There are some features of this type of system of note.
First, it can be seen that there can be a fraction of the
channels open in the absence of agonist. Specifically, Eq.
(3.15) predicts that in the absence of agonist ([A] ¼ 0) the
fraction of channels open is equal to ropen ¼ L/(1 þ L). For
nonzero values of L, this indicates that ropen will be > 1.
Second, ligands with preferred affinity for the open channel
(a > 1) will cause opening of the channel (they will be
agonists). This can be seen from the ratio of channels open
in the absence and presence of a saturating concentration of
ligand [rN/r0 ¼ a(1 þ L)/(1 þ aL)]. This equation reduces to
rN
1þL
.
¼
ð1=aÞ þ L
r0
(3.16)
It can be seen that for values a > 1, the value (1/a)<1,
and the denominator in Eq. (3.16) will be less than the
numerator. The ratio with the result that rN/r0 will be > 1
(increased channel opening; i.e., agonism). Also, the potency of the agonist will be greater as the spontaneous
channel opening is greater. This is because the observed
EC50 of the agonist is
EC50 ¼
KA ð1 þ LÞ
.
ð1 þ aLÞ
(3.17)
This equation shows that the numerator will always be
less than the denominator for a > 1 (therefore, the EC50<
KA, indicating increased potency over affinity), and that
this differential gets larger with increasing values of L
(increased spontaneous channel opening). The effects of an
agonist with a 10-fold greater affinity for the open channel,
in systems of different ratios of spontaneously open channels, are shown in Fig. 3.15. It can be seen that the maximal
agonist activity, the elevated basal activity, and the agonist
potency are increased with increasing values of L. Twostate theory has been applied to receptors [23e25] and
was required to explain the experimental findings relating
to constitutive activity in the late 1980s. Specifically, the
ability of channels to spontaneously open with no ligand
present was adapted for the model of receptors that could
spontaneously form an activated state (in the absence of an
agonist vide infra).
3.9 The ternary complex model
Numerous lines of evidence in the study of GPCRs indicate
that these receptors become activated, translocate in the cell
FIGURE 3.15 Doseeresponse curves to an agonist in a two-state ionchannel system. Ordinates: fraction of open channels. Abscissae: logarithms of molar concentrations of agonist. Numbers next to the curves refer
to values of L (ratio of spontaneously open channels to closed channels).
Curve calculated for an agonist with a 10-fold higher affinity for the open
channel (a ¼ 10). Open circles show EC50 values for the doseeresponse
curves showing the increased potency to the agonist with increasing
spontaneously open channels (increasing values of L).
membrane, and subsequently bind with other membranebound proteins. It was first realized that guanine nucleotides could affect the affinity of agonists but not
antagonists, suggesting the two-stage binding of ligand to
receptor and subsequently the complex to a G-protein
[26e28]. The model describing such a system, first
described by DeLean et al. [13], is termed the ternary
complex model. Schematically, the process is
A þ R%AR þ G%ARG;
(3.18)
where the ligand is A, the receptor R, and the G-protein G.
For a number of years, this model was used to describe
pharmacological receptor effects until a new experimental
evidence forced the modification of the original concept.
Specifically, the fact that recombinant GPCR systems
demonstrate constitutive activity shows that receptors spontaneously form activated states capable of producing
response through G-proteins in the absence of agonists.
This necessitated modification of the ternary complex
model.
3.10 The extended ternary complex
model
The resulting modification is called the extended ternary
complex model [3], which describes the spontaneous formation of active state receptor ([Ra]) from an inactive state
receptor ([Ri]) according to an allosteric constant (L ¼ [Ra]/
[Ri]). The active state receptor can form a complex with
G-protein ([G]) spontaneously to form RaG, or agonist
activation can induce formation of a ternary complex
ARaG.
As described in Section 3.15.6, the fraction r of Gprotein-activating species (producing response)dnamely,
60
A Pharmacology Primer
[RaG] and [ARaG]das a fraction of the total number of
receptor species [Rtot] is given by
high G-protein concentration, high-affinity receptor/Gprotein coupling (low value of KG), and/or a natural tendency for the receptor to spontaneously form the active
L½G=KG ð1 þ ag½A=KA Þ
; state. This latter property is described by the magnitude of
r¼
½A=KA ð1 þ aLð1 þ g½G=KG ÞÞ þ Lð1 þ ½G=KG Þ þ 1 L, a thermodynamic constant unique for every receptor.
(3.19)
Constitutive receptor activity is extremely important
because
it allows the discovery of ligands with negative
where the ligand is [A] and KA and KG are the equilibrium
efficacy.
Before the discovery of constitutive GPCR acdissociation constants of the ligandereceptor and G-protein
tivity,
efficacy
was considered only as a positive vector
receptor complexes, respectively. The term a refers to the
(i.e.,
producing
an increased receptor activity, and only
multiple differences in affinity of the ligand for Ra over
ligand-mediated
activation of receptors was thought to
Ri (i.e., for a ¼ 10 the ligand has a 10-fold greater affinity
induce
G-protein
activity). With the discovery of spontafor Ra over Ri). Similarly, the term g defines the multiple
neous
activation
of G-proteins by unliganded receptors
difference in affinity of the receptor for G-protein when
came
the
prospect
of ligands that selectively inhibit this
the receptor is bound to the ligand. Thus, g ¼ 10 means
spontaneous
activation,
specifically inverse agonism.
that the ligand-bound receptor has a 10-fold greater affinity
Constitutive
activity
can be produced in a recombinant
for the G-protein than the ligand-unbound receptor.
system
by
increasing
the
level of receptors expressed on the
It can be seen that the constants a and g, insofar as they
cell
membrane.
quantify the ability of the ligand to selectively cause the
The dependence of constitutive activity on [Ri] is given
receptor to couple to G-proteins, become the manifestation
by
(see
Section 3.15.7):
of efficacy. Therefore, if a ligand produces a bias of the
system toward more active receptor species (positive a)
½Ra G
½Ri and/or enables the ligand-occupied receptor to bind to G;
(3.21)
¼
½G
½R
þ
ðKG =LÞ
tot
i
proteins with a higher affinity (positive g), then it will be
an agonist with positive efficacy. In addition, if a ligand where [R ] is the receptor density, L is the allosteric coni
selectively stabilizes the inactive state of the receptor stant describing the propensity of the receptor to spontane(a < 1) or reduces the affinity of the receptor for G-proteins ously adopt the active state, and K is the equilibrium
G
(g < 1), then it will have negative efficacy and subse- dissociation constant for the activated receptor/G-protein
quently will reverse elevated basal receptor activity. This complex. It can be seen from Eq. (3.21) that a hyperbolic
will be observed as inverse agonism, but only in systems relationship is predicted between constitutive activity and
that demonstrate constitutive receptor activity.
receptor concentration. Constitutive activity is favored by
3.11 Constitutive receptor activity and
inverse agonism
The extended ternary complex model can take into account
the phenomenon of constitutive receptor activity. In
genetically engineered systems where receptors can be
expressed in high density, Costa and Herz [2] noted that
high levels of receptor expression uncovered the existence
of a population of spontaneously active receptors and that
these receptors produce an elevated basal response in the
system. The relevant factor is the ratio of receptors and Gproteins (i.e., elevated levels of receptor cannot yield
constitutive activity in the absence of adequate amounts of
G-protein, and vice versa). Constitutive activity (due to the
[RaG] species) in the absence of ligand ([A] ¼ 0) is
expressed as:
Constitutive Activity ¼
L½G=KG
.
Lð1 þ ½G=KG Þ þ 1
(3.20)
From this equation, it can be seen that for a given receptor density systems can spontaneously produce physiological response and that this response is facilitated by
a large value of L (low-energy barrier to spontaneous formation of the active state) and/or a tight coupling between
the receptor and the G-protein (low value for KG). This provides a practical method of engineering constitutively
active receptor systems, namely, through the induction of
high levels of receptor expression. For example, in a system
containing 1000 receptors with a native KG/L value of
105 M, 0.9% of the G-proteins (i.e., nine G-proteins) will
be activated. If this same system were to be subjected to
an engineered receptor expression (through genetic means)
of 100,000 receptors, then the number of activated Gproteins would rise to 50% (50,000 G-proteins). At some
point, the threshold for observation of visibly elevated basal
response in the cell will be exceeded, and the increased Gprotein activation will result in an observable constitutive
receptor activity.
Constitutive receptor systems are valuable, in that they
are capable of detecting inverse agonism and negative efficacy. Ligands that destabilize the spontaneous formation
of activated receptor/G-protein complexes will reduce
constitutive activity and function as inverse agonists in
constitutively active receptor systems. The therapeutic
relevance of inverse agonism is still unknown, but it is clear
Drugereceptor theory Chapter | 3
that inverse agonists differ from conventional competitive
antagonists. As more therapeutic experience is gained with
these two types of antagonists, the importance of negative
efficacy in the therapeutic arena will become clear. At this
point, it is important to note if a given antagonist possesses
a property for retrospective evaluation of its effects.
The most probable mechanism for inverse agonism is
the same one operable for positive agonism, namely, selective receptor state affinity. However, unlike agonists that
have a selectively higher affinity for the receptor active
state (to induce G-protein activation and subsequent physiological response), inverse agonists have a selectively
higher affinity for the inactive receptor state and thus uncouple already spontaneously coupled [RaG] species in the
system.
It can also be seen from Eq. (3.21) that the magnitude of
the allosteric constant L and/or the magnitude of the receptor/G-protein ratio determines the amount of constitutive activity in any receptor system. In binding studies, low
levels of [RaG] complex (with concomitant activation of Gprotein) may be insignificant in comparison to the levels of
total ligand-bound receptor species (i.e., [ARaG] and [AR]).
However, in highly coupled functional receptor systems a
low level of spontaneous receptor interaction may result in
a considerable observable response (due to stimuluse
response amplification of stimulus; see Chapter 2: How
Different Tissues Process Drug Response). Thus, the
observed constitutive activity in a functional system (due to
high receptor density) can be much greater than expected
from the amounts of active receptor species generated (see
Fig. 3.16). This suggests that for optimal observation of
constitutive receptor activity and detection of inverse
61
agonism, functional, rather than radioligand binding, systems should be used.
A practical approach to constructing constitutively
active receptor systems, as defined by Eq. (3.21), is through
receptor overexpression. Thus, exposure of surrogate cells
to high concentrations of cDNA for receptors yields
increasing cellular expression of receptors. This, in turn,
can lead to elevated basal response due to spontaneous
receptor activation. Fig. 3.17 shows the development of
constitutive receptor activity in melanophore cells transfected with cDNA for human calcitonin receptor. Melanophores are especially well suited for experiments with
constitutive activity, as the effects can be seen in real time
with visible light. Fig. 3.17A and B show the difference in
the dispersion of melanin (response to Gs-protein activation
due to constitutive calcitonin receptor activity) upon
transfection with cDNA for the receptor. Fig. 3.17C shows
the doseeresponse relationship between the cDNA added
and the constitutive activity as predicted by Eq. (3.21).
As described by the extended ternary complex model,
the extent of constitutive activity observed will vary with
the receptor according to the magnitude of L for each receptor. This is shown in Fig. 3.18, where the constitutive
activity as a function of cDNA concentration is shown for a
number of receptors. It can be seen from this figure that
increasing receptor expression (assumed to result from the
exposure to increasing concentrations of receptor cDNA)
causes elevation of basal cellular response. It can also be
seen that the threshold and maximal asymptotic value for
this effect varies with receptor type, thereby reflecting the
different propensity of receptors to spontaneously form the
active state (varying magnitudes of L).
FIGURE 3.16 Constitutive activity due to receptor overexpression: visualization through binding and function. (A) Constitutive activity observed as
receptor species ([RaG]/[Rtot]) and cellular function ([RaG]/([RaG]þb)), where b ¼ 0.03. Stimuluseresponse function ([RaG]/([RaG]þb)) shown in inset.
The output of the [RaG] function becomes the input for the response function. Dotted line shows relative amounts of elevated receptor species and
functional response at [R]/KG ¼ 1. (B) Effects of an inverse agonist in a system with [R]/KG ¼ 1 (see panel A) as observed through receptor binding and
cellular function.
62
A Pharmacology Primer
FIGURE 3.17 Constitutive activity in melanophores expressing hCTR2 receptor. (A) Basal melanophore activity. (B) Effect of transfection with human
cDNA for human calcitonin receptors (16 mg/mL). (C) Concentrationeresponse curve for cDNA for human calcitonin receptors (abscissae as log scale)
and constitutive activity. Data redrawn from G. Chen, J. Way, S. Armour, C. Watson, K. Queen, C. Jayawrickreme, Use of constitutive G-protein-coupled
receptor activity for drug discovery, Mol. Pharmacol. 57 (1999) 125e134.
The term “inverse agonist” is in some ways a misnomer,
as these ligands really are simply antagonists with an added
feature that allows them to reduce elevated basal activity.
Thus, in the absence of constitutive activity, inverse agonists function like competitive antagonists. However, the
fact that reversal of elevated basal activity produces a
concentrationeresponse curve indicative of a type of agonism leads to behaviors for these molecules that parallel
some behaviors of normal positive agonists. Inverse agonism can be modeled with the BlackeLeff operational
model by utilizing the expression for active receptor species
given by the extended ternary complex model (Eq. 3.19),
multiplying this by receptor density [Rtot] and inserting the
result into the base expression for the BlackeLeff model to
yield
Response ¼
L½G=KG ð1 þ ag½A=KA ÞsR
½A=KA ð1 þ aLð1 þ g½G=KG ð1 þ sR ÞÞÞ
þL½G=KG ð1 þ sR ÞL þ 1
(3.22)
The efficacy term sR is the efficacy of the spontaneously
formed active state of the receptor. Fig. 3.19 shows the effect
of increasing receptor density on the concentrationeresponse
curve to an inverse agonist (a ¼ 0.03, g ¼ 0.1). Thus, as
there is a greater receptor reserve in the system (increasing
sR), concentrationeresponse curves shift to the right and the
maximal inverse effect decreases. Thus, in a very sensitive
system, partial inverse agonism can result.
3.12 The cubic ternary complex model
While the extended ternary complex model accounts for the
presence of constitutive receptor activity in the absence of
ligands, it is thermodynamically incomplete from the
standpoint of the interaction of receptor and G-protein
FIGURE 3.18 Dependence of constitutive receptor activity as ordinates
(expressed as a percent of the maximal response to a full agonist for each
receptor) versus magnitude of receptor expression (expressed as the
amount of human cDNA used for transient transfection, logarithmic scale)
in Xenopus laevis melanophores. Data shown for human chemokine CCR5
receptors (open circles), chemokine CXCR receptors (filled triangles),
neuropeptide Y type 1 receptors (filled diamonds), neuropeptide Y type 2
receptors (open squares), and neuropeptide Y type 4 receptors (open
inverted triangles). Data recalculated and redrawn from G. Chen, J. Way,
S. Armour, C. Watson, K. Queen, C. Jayawrickreme, Use of constitutive Gprotein-coupled receptor activity for drug discovery, Mol. Pharmacol. 57
(1999) 125e134.
FIGURE 3.19 Inverse agonism as calculated by Eq. (3.22). Shown are
curves for sR ¼ 100, 300, 1000, 3000, and 10,000 in a system of
L ¼ 100[G]/KG ¼ 10. The inverse agonist has a ¼ 0.03 and g ¼ 0.1.
Drugereceptor theory Chapter | 3
species. Specifically, it must be possible from a thermodynamic point of view for the inactive state receptor (ligand
bound and unbound) to interact with G-proteins. The cubic
ternary complex model accommodates this possibility
[29e31]. From a practical point of view, it allows for the
potential of receptors (whether unbound or bound by inverse agonists) to sequester G-proteins into a nonsignaling
state.
A schematic representation of receptor systems in terms
of the cubic ternary complex model is shown in Fig. 3.20.
The amount of signaling species (as a fraction of total receptor) as defined by the cubic ternary complex model (see
Section 3.15.8) predicts that the constitutive activity of
receptor systems can reach a maximal asymptote which is
below the system maximum (partial constitutive activity).
This is because the cubic ternary complex model predicts
the maximal constitutive activity, as given by the following
equation:
r¼
bL½G=KG ð1 þ agd½A=KA Þ
½A=KA ð1 þ aL þ g½G=KG ð1 þ agbdLÞÞ
þ½G=KG ð1 þ bLÞ þ L þ 1
(3.23)
There are some specific differences between the cubic
and extended ternary complex models in terms of their
predictions of system and drug behavior. The first is that
the receptor, either ligand bound or not bound, can form a
complex with the G-protein and that this complex need not
signal (i.e., [ARiG] and [RiG]). Under these circumstances,
an inverse agonist (one that stabilizes the inactive state of
the receptor) theoretically can form inactive ternary complexes and thus sequester G-proteins away from signaling
pathways. There is evidence that this can occur with
63
cannabinoid receptors [32]. The cubic ternary complex
model also where [A] ¼ 0 and [G]/N predicts:
Maximal Constitutive Activity ¼ bL=ð1 þ bLÞ.
(3.24)
It can be seen from this equation that maximal constitutive activity need not reach a maximal asymptote of unity.
Submaximal constitutive activity has been observed with
some receptors with maximal receptor expression [31].
While there is scattered evidence that the cubic ternary
complex is operative in some receptor systems, and while it
is thermodynamically more complete, it also is heuristic in
that it includes more individually nonverifiable constants
than other models. This makes this model limited in practical application.
3.13 Multistate receptor models and
probabilistic theory
The previously discussed models fall under the category of
“linkage models,” in that the protein species are all identified and linked together with the energies for their formation controlling their relative prevalence. These models
work well as approximations but fall short for descriptions
of true protein thermodynamics where multiple conformations of unknown identity can coexist. Linkage model approximations can be used to define the relationship between
general protein species (i.e., ligand bound and unbound)
but cannot accommodate complex multistate receptor systems. However, sometimes such multistate models are
required to describe nuances of receptor signaling and
ligand functional selectivity. While multistate models do
not define actual receptor species, they can estimate the
probability of their formation. To describe a multistate
model quantitatively, it is simplest to arbitrarily begin with
one receptor state (referred to as [Ro]e) and define the affinity of a ligand [A] and a G-protein [G] for that state as
[33,34]
Ko ¼ ½ARo =½Ro ½A
(3.25)
K o ¼ ½GRo =½Ro ½G;
(3.26)
A
and
G
FIGURE 3.20 Major components of the cubic ternary complex model
[26e28]. The major difference between this model and the extended
ternary complex model is the potential for formation of the [ARiG]
complex and the [RiG] complex, both receptor/G-protein complexes that
do not induce dissociation of G-protein subunits and subsequent response.
Efficacy terms in this model are a, g, and d.
respectively. It is useful to define a series of probabilities en
route to the presentation of Eq. (3.27)e(3.30). The probability of the receptor being in that form is denoted by po while
the probability of the receptor forming another conformation
[R1] is defined as p1. The ratio of the probabilities for forming state R1 versus Ro is given as j1 where j1 ¼ p1/po; the
value j controls the energy of transition between the states.
The relative probability of forming state [R1] with ligand
binding is denoted by Aj1 ¼ Ap1/Apo and with G-protein
binding as Gj1 ¼ Gp1/Gpo. An important vector operating
on this system is defined as b, where b refers to the fractional
64
A Pharmacology Primer
stabilization of a state with binding of either ligand (defined
A
b1 ¼ Aj1/ji) or G-protein (Gb1 ¼ Gj1/ji). Every ligand and Gprotein has characteristic values of b for each receptor state
and it is these b vectors that constitute ligand affinity and efficacy. With these probabilities and vectors, the following
operators are defined:
U ¼ 1 þ Sji
(3.27)
UA ¼ 1 þ USA bi pi
(3.28)
UG ¼ 1 þ USG bi pi
(3.29)
UAG ¼ 1 þ USA bGi bi pi ;
(3.30)
where i refers to the specific conformational state and the
superscripts G and A refer to the G-protein and ligandbound forms, respectively. With these functions defined,
it can be shown that macroaffinity is given by
1
MacroaffinityðKÞ¼A k0 UA ðUÞ ;
(3.31)
where k0 is related to the interaction free energy between
ligand and a reference microstate of the receptor. A measure of efficacy is given by
EfficacyðaÞ ¼ ðUUAG ÞðUA UG Þ
1
(3.32)
With this model, the effects of ligand binding on collections
of receptor conformations (ensembles) can be simulated
(see Fig. 3.21). The unique feature of this model is that it
allows the simulation of collections of conformations that
may have differing pharmacological effects. This is
extremely useful in the description of agonist functional
selectivity where different agonists activate different portions of stimuluseresponse cascades through activation of
the same receptor (see Ref. [32]). In fact, a major advantage
of such molecular dynamic approaches to receptor conformation is that no linearity is assumed. When considering
traditional linkage models, an order of formation is
imposed on the system; for example, the ARaG complex
can only be formed after prior formation of either the
RaG or the ARa complex. It will be seen in Chapter 6, Agonists: The Measurement of Affinity and Efficacy in Functional Assays, than the advent of experimental data to show
that receptors can bias signaling through formation of multiple active states, such imposed order is a barrier to understanding the effects of biased ligands. Molecular dynamics
views changes in receptor conformation as the receptor rolling on what is termed an “energy landscape” with various
wells representing favored receptor statesdsee Fig. 3.22.
This has the advantage of having no imposed order on
the formation of receptor states (i.e., the receptor may travel
in any direction on the landscape, not just one directiond
see Fig. 3.22) by ligands and allows biased collateral efficacy to be describeddsee Chapter 5, Agonists: The Measurement of Affinity and Efficacy in Functional Assays,
for further discussion.
FIGURE 3.21 Relative abundance of different receptor conformations shown as histograms. Left panel shows receptor at rest and right panel the
ensemble of conformations when bound by a ligand. In the right panel, the conformations for which the ligand has high affinity are stabilized and enriched
at the expense of other conformations. The composition of the new collection of conformations depends upon the molecular structure of the agonist
allowing for ligand-specific pharmacological effect.
Drugereceptor theory Chapter | 3
l
65
namely, the concept of negative efficacy and inverse
agonism.
The cubic ternary complex model considers receptors
and G-proteins as a synoptic system with some interactions that do not lead to visible activation.
3.15 Derivations
l
l
l
l
l
l
FIGURE 3.22 Depiction of an energy landscape consisting of energy
wells representing preferred energy states; as the receptor rolls on the
landscape it may fall into an energy well and this would represent a
preferred conformation of the receptor. Some of of these preferred conformations could be linked to function (i.e. cellular signaling).
3.14 Chapter summary and conclusions
l
l
l
l
l
l
l
l
l
Models are constructed from samples of data and can be
used to predict the behavior of the system for all conditions (the population of data).
Preferred models have parameters that have some physiological or pharmacological rationale. In general, the
behavior of these parameters can be likened to changes
in potency and/or efficacy of drugs.
Models can resolve apparent conflicts in observed data
and be used to optimally design experiments.
The prime building block for exiting pharmacologic
models (except probability models) is the Mass Action
Law.
From the time of A. J. Clark until the late 1970s, receptor models have been refined to describe drug affinity
and efficacy. These ideas are collectively referred to
as “classical” receptor theory.
A major modification in the description of drug function
is termed the operational model. This model is theoretically more sound than classical theory and extremely
versatile for estimating drug parameters in functional
systems.
The observation that receptors can demonstrate spontaneous activity necessitated elements of ion two-state
theory to be incorporated into receptor theory.
The ternary complex model followed by the extended
ternary complex model was devised to describe the action of drugs on GPCRs.
The discovery of constitutive receptor activity uncovered a major new idea in receptor pharmacology,
l
l
Radioligand binding to receptor dimers demonstrating
cooperative behavior (Section 3.15.1).
Effect of variation in an HIV-1 binding model (Section
3.15.2).
Derivation of the operational model (Section 3.15.3).
Operational model forcing function for variable slope
(Section 3.15.4).
Derivation of two-state theory (Section 3.15.5).
Derivation of the extended ternary complex model (Section 3.15.6).
Dependence of constitutive activity on receptor density
(Section 3.15.7).
Derivation of the cubic ternary complex model (Section
3.15.8).
3.15.1 Radioligand binding to receptor dimers
demonstrating cooperative behavior
It is assumed that receptor dimers can form in the cell
membrane (two [R] species to form one [R-R] species).
Radioligand [A*] can bind to the receptor [R] to form
radioactive complexes [A*R], [A*RAR], and [A*RA*R].
It is also assumed that there is an allosteric interaction between the receptors when they dimerize. Therefore, the affinity of the receptor(s) changes with dimerization:
The conservation equation for the total receptor species
is given as
½Rtot ¼ ½R þ ½AR þ ½A R þ ½A R AR
þ½AR AR þ ½A R A R.
(3.33)
The radioactive signal (denoted by r) is produced from
the receptor species bound to radioligand [A*]:
r¼
½A R þ ½A R AR þ 2½A R A R
(3.34)
½Rtot Using the equilibrium equations for the system, this
equation becomes
½AK þ a½A½AK2 þ 2a½A K2
2
r¼
1 þ ½AK þ ½AK þ a½A½AK2 þ a½A K2 þ a½A K2
(3.35)
2
2
where K is the association constant. Assume that a fixed
concentration of radioligand [A*] is bound to the receptor,
;
66
A Pharmacology Primer
yielding a fixed radioactive signal. In the presence of a
range of concentrations of a nonradioactive version of
ligand [A], the signal from a fixed concentration of radioactive ligand ([A*]) (denoted by u) can be calculated from
the ratio of Eq. (3.35) with [A] ¼ 0 and [A*] fixed over
the equations evaluated with [A*] fixed:
ð½A=Kd Þ þ a½AK2d þ 2að½A=Kd Þ2
ð1 þ ½A=Kd Þ þ að½A=Kd Þ
2
ð1 þ ½A=Kd þ ½A=Kd þ a ½A½A=K2d þ að½A=Kd Þ
2
u¼
það½A=Kd Þ2 ð½A=Kd Þ þ 2að½A=Kd Þ2
(3.36)
r¼
ð½CD=K1 Þð½gpK2 Þ þ ½CD=K5
½CDK1 ð½gp=K2 þ K1 =K5 Þ þ ½gp=K3 þ ½B=K4 þ 1
(3.39)
where the equilibrium dissociation constants are denoted by
K1 (gp/CD4), K2 (gp-CD4 complex/receptor), K3 (gp/receptor), K4 (ligand B/receptor), and K5 (CD4/receptor).
The observed affinity of the radiolabel CD4 is given by
the expression:
Kobs ¼
K1 ðð½gp=K3 Þ þ ½B=K4 þ 1Þ
.
½gp=K2 þ K1 =K5
(3.40)
where Kd ¼ 1/K. Using Eq. (3.36), displacement curves
for this system can be calculated. If the binding of one
ligand is positively cooperative with respect to the binding
of the other (a > 1) (binding of one [A] and subsequent
dimerization with another receptor increases the affinity
for the second [A]), then an apparently paradoxical increase in the radioactive signal is observed from addition
of nonradioactive ligand if low concentrations of radioligand are used.
Solving Eq. (3.40) for [B] ¼ 0 and variable [B] yields
the equation defining the IC50 of a nonradioactive ligand
inhibitor (defined as the molar concentration of ligand
[B] that blocks the radioactive binding signal by 50%).
This yields the equation for the concentration of
[B] that produces 50% inhibition of radioactive CD4
binding:
3.15.2 Effect of variation in an HIV-1 binding
model
From Eq. (3.41), it can be seen that the systemindependent measure of affinity (K4) is given by:
Assuming that all interactions of the species are possible,
the system consists of the receptor CCR5 [R], radioligand
CD4 [CD], viral coat protein gp120 [gp], and potential
displacing ligand [B].
The CCR5 receptor conservation equation is given as
½Rtotal ¼ ½R þ ½CDR þ ½gpCDR þ ½gpR þ ½BR;
(3.37)
where the concentration of the complex between viral coat
protein gp120 and receptor is [gpR], concentration of complex between the receptor and complex between gp120 and
CD4 is [gpCDR], membrane protein CD4 receptor complex
density is [CDR], and foreign ligand B receptor complex is
[BR]. The signal is generated by radioactive CD4 resulting
from the two receptor-bound species [gpCDR] and [CDR].
It is assumed that [gp]>[CD]>[R] (as is common in experimental systems). The signal, as a fraction of the total receptor concentration, is given by
Fractional signal ¼ r ¼
½gpCDR þ ½CDR
.
½Rtotal (3.38)
From the equilibrium equations, expressions for the
various receptor species can be derived and substituted into
Eq. (3.38). With conversion of all equilibrium association
constants to equilibrium dissociation constants, a general
binding expression results for radioactive CD4 binding to
CCR5 with gp120 as a cofactor [14]:
IC50 ¼ K4 ð½CD = K1 ð½gp = K2 þ K1 = K5 Þ þ ½gp = K3 þ 1Þ.
(3.41)
K4 ¼
½IC50 .
ð½CD=K1 ð½gp=K2 þ K1 =K5 Þ þ ½gp=K3 þ 1Þ
(3.42)
The assay returns the IC50, the concentration of [B] that
blocks the binding by 50%. The desired estimate is K4, the
system-independent estimate of the affinity of [B] for
the interactants of the system. This model addresses the
following question: What is the effect of variation in
[gp120] on the IC50 and hence the estimate of K4? At this
point it is useful to define two ratios. The first is the ratio of
the differential affinity of the gp/CD4 complex versus the
affinity of gp120 for the receptor alone. This is defined as
q ¼ K3/K2. Large values of q indicate that the preformed
complex gp/CD4 is the principal binding species to the
receptor and that the affinity of gp for the receptor is
relatively unimportant. In experimental systems, this is
found to be true. The second useful ratio is the differential
affinity of CD4 for gp120 over the receptor. This is defined
as j ¼ K5/K1. High values of j indicate that CD4 prefers
to form the CD4/gp120 complex over binding to the receptor, and this agrees with the known physiology of HIV
entry into cells via this mechanism:
K4 ¼
½IC50 :
ð½CD=K1 ð½gp=K2 þ 1=jÞ þ ½gp=qK2 þ 1Þ
(3.43)
Drugereceptor theory Chapter | 3
Consistent with the known physiology, the values of
both q and j are high. Therefore, 1/q and 1/j/0 and Eq.
(3.43) lead to a relation of the form:
K4 ¼
½IC50 .
ð½CD=K1 Þð½gp=K2 Þ þ 1
(3.44)
It can be seen from Eq. (3.44) that unknown variation in
gp120 levels can lead to differences in the correction factor
between the experimentally observed IC50 and the desired
quantity K4. However, this variation is minimal if low
levels of control signal are used for screening (i.e., minimal
concentration of CD4 is used to gain an acceptable signalto-noise ratio).
3.15.3 Derivation of the operational model
The basis of this model is the experimental fact that most
agonist doseeresponse curves are hyperbolic in nature. The
reasoning for making this assumption is as follows. If
agonist binding is governed by mass action, then the relationship between the agonistereceptor complex and
response must be either linear or hyperbolic as well.
Response is thus defined as
Response ¼
½A$Emax
½A þ v
(3.45)
where the concentration of agonist is [A], Emax is the
maximal response of the system, and v is a fitting parameter
determining the sensitivity of the system to [A]. This expresses the agonist concentration as
Response$n
½A ¼
Emax Response
(3.46)
Also, mass action defines the concentration of
agonistereceptor complex as
½AR ¼
½A$½Rt ½A þ KA
½AR$KA
½Rt ½AR
(3.48)
Equating Eq. (3.46) and (3.48) and rearranging yields
Response ¼
½AR$Emax $KA
½ARðKA vÞ þ ½Rt v
few if any cases of truly linear relationships between
agonist concentration and tissue response. Therefore, the
default for the relationship is a hyperbolic one.
Assuming a hyperbolic relationship between response
and the amount of agonistereceptor complex, response is
defined as
Response
½AR
¼
;
Emax
½AR þ KE
(3.50)
where KE is the fitting parameter for the hyperbolic
response. However, KE also has a pharmacological meaning, in that it is the concentration of [AR] complex that produces half the maximal response. It also defines the ease
with which the agonist produces response (i.e., it is a transduction constant). The more efficient the process from production to [AR] to response, the smaller is KE. Combining
Eq. (3.48) and (3.49) yields the quintessential equation for
the operational model:
Response ¼
½A$½Rt $Emax
½Að½Rt þ KE Þ þ KA $KE
(3.51)
A very useful constant used to characterize the propensity of a given system and a given agonist to yield
response is the ratio [Rt]/KE. This is denoted by s.
Substituting for s yields the working equation for the
operational model:
Response ¼
½A$s$Emax
½Aðs þ 1Þ þ KA
(3.52)
This model also can accommodate a doseeresponse
curve having Hill coefficients different from unity (see the
next section). This can occur if the stimuluseresponse
coupling mechanism has inherent cooperativity. A general
procedure can be used to change any receptor model into a
variable slope operational function. This is done by passing
the receptor stimulus through a forcing function.
(3.47)
where [Rt] is the receptor density and KA is the equilibrium
dissociation constant of the agonistereceptor complex.
This yields a function for [A] as well:
½A ¼
67
(3.49)
It can be seen that if KA < v, then negative and/or
infinite values for response are allowed. No physiological
counterpart to such behavior exists. This leaves a linear
relationship between agonist concentration and response
(where KA ¼ v) or a hyperbolic one (KA > v). There are
3.15.4 Operational model forcing function for
variable slope
The operational model allows the simulation of cellular
response from receptor activation. In some cases, there may
be cooperative effects in the stimuluseresponse cascades
translating activation of receptor-to-tissue response. This
can cause the resulting concentrationeresponse curve to
have a Hill coefficient different from unity. In general, there
is a standard method for doing this, namely, reexpressing
the receptor occupancy and/or activation expression
(defined by the particular molecular model of receptor
function) in terms of the operational model with Hill coefficient not equal to unity. The operational model utilizes
the concentration of response-producing receptor as the
substrate for a MichaeliseMenten type of reaction, given as
68
A Pharmacology Primer
Response ¼
½Activated ReceptorEmax
;
½Activated Receptor þ KE
and
where KE is the concentration of activated receptor species
that produces half maximal response in the cell and Emax is
the maximal capability of response production by the cell.
If the system exhibits cooperativity at the cellular level,
then Eq. (3.53) can be rewritten as
½Activated Receptor Emax
;
½Activated Receptorn þ KEa
n
Response ¼
(3.54)
where n is the slope of the concentrationeresponse curve.
The quantity of activated receptor is given by rAR [Rt],
where rAR is the fraction of total receptor in the activated
form and [Rt] is the total receptor density of the preparation. Substituting into Eq. (3.54) and defining s ¼ [Rt]/KE
yields
Response ¼
rARn sn Emax
.
rARn sn þ 1
(3.55)
The fractional receptor species rAR is generally given
by
rARn ¼
½Active Receptor Speciesn
;
½Total Receptor Speciesn
(3.56)
where the active receptor species are the ones producing
response and the total receptor species given by the receptor conservation equation for the particular system
(rAR ¼ numerator/denominator). It follows that
ðActive ReceptorÞ sn Emax
n
n
ðActive ReceptorÞ sn þ ðTotal ReceptorÞ
(3.57)
n
Response ¼
sn $½A $Emax
n
n
ð½A þ KA Þ þ sn ½A
(3.62)
The amount of open channel, expressed as a fraction of
total channel ropen¼([ARopen]þ[Ropen]/([Rtotal])), is
ropen ¼
aL½A=KA þ L
;
½A=KA ð1 þ aLÞ þ L þ 1
3.15.6 Derivation of the extended ternary
complex model
The extended ternary complex model [3] was conceived
after it was clear that receptors could spontaneously activate G-proteins in the absence of agonist. It is an amalgam
of the ternary complex model [13] and two-state theory
which allows proteins to spontaneously exist in two conformations, each having different properties with respect to
other proteins and to ligands. Thus, two receptor species are
described: [Ra] (active state receptor able to activate Gproteins) and [Ri] (inactive state receptors). These coexist
according to an allosteric constant (L ¼ [Ra]/[Ri]).
The equilibrium equations for the various species are
½ARi ¼
½ARa G
agL½GKg
(3.64)
½ARa G
g½GKg
(3.65)
½ARa ¼
½ARa G
ag½GKg ½AKa
(3.66)
½ARa G
;
agL½GKg ½AKa
(3.67)
½Ra ¼
(3.58)
½Ri ¼
A channel exists in two states: open (Ropen) and closed
(Rclosed). A ligand [A] binds to both with an equilibrium
association constant K for the closed channel and aK for
the open channel.
The equilibrium equations for the various species are
ARopen
½ARclosed ¼
;
(3.59)
aL
ARopen
;
(3.60)
½Rclosed ¼
aL½AK
(3.63)
where KA is the equilibrium dissociation constant of the
ligandechannel complex.
n
3.15.5 Derivation of two-state theory
(3.61)
The conservation equation for channel species is
½Rtotal ¼ ARopen þ ½ARclosed þ Ropen þ ½Rclosed .
Therefore, the operational model for agonism can be
rewritten for variable slope by passing the stimulus equation through the forcing function (Eq. 3.57) to yield
Response ¼
ARopen
.
½Rclosed ¼
a½AK
(3.53)
and
½Ra G ¼
½ARa G
ag½AKa
(3.68)
The conservation equation for receptor species is
½Rtot ¼ ½ARa G þ ½Ra G þ ½ARa þ ½ARi þ ½Ra þ ½Ri .
(3.69)
It is assumed that the receptor species leading to Gprotein activation (and therefore physiological response)
are complexes between the activated receptor ([Ra]) and the
Drugereceptor theory Chapter | 3
G-protein, namely, [ARaG]þ[RaG]. The fraction of the
response-producing species of the total receptor species
(([ARaG]þ[RaG])/Rtot) is denoted by r and given by
r¼
½Ri ¼
L½G=KG ð1 þ ag½A=KA Þ
.
½A=KA ð1 þ aLð1 þ g½G=KG ÞÞ þ Lð1 þ ½G=KG Þ þ 1
(3.70)
½ARa G
;
agdbL½GKg ½AKa
(3.77)
½ARa G
;
agd½AKa
(3.78)
½ARa G
;
agdbL½AKa
(3.79)
½Ra G ¼
½Ri G ¼
69
and
3.15.7 Dependence of constitutive activity on
receptor density
Considering the extended ternary complex model:
The equilibrium equations are
½Ra L¼
½Ri ½ARi G ¼
½ARa G
.
adbL
The conservation equation for receptor species is
½Rtot (3.71)
¼ ½ARa G þ ½ARi G þ ½Ri G
þ½Ra G þ ½ARa þ ½ARi þ ½Ra þ ½Ri .
and
KG ¼
½Ra G
.
½Ra ½G
(3.72)
The conservation equation for G-protein is [Gtot] ¼
[G]þ[RaG]. The amount of receptor-activated G-protein
expressed as a fraction of total G-protein ([RaG]/[Gtot]) is
½Ra G
½Ri ;
¼
½Gtot ½Ri þ ðKG =LÞ
(3.73)
where L is the allosteric constant and [Ri] is the amount of
transfected receptor in the inactive state.
3.15.8 Derivation of the cubic ternary
complex model
½ARa G
;
agdbL½GKg
(3.74)
½ARa G
;
gbd½GKg
(3.75)
½ARa ¼
½Ra ¼
½ARa G
;
agdb½GKg ½AKa
(3.81)
It is assumed that the receptor species leading to Gprotein activation (and therefore physiological response)
are complexes between the activated receptor ([Ra]) and the
G-protein, namely, [ARaG]þ[RaG]. The fraction of the
response-producing species of the total receptor
speciesd([ARaG]þ[RaG])/Rtotdis denoted by r and is
given by
r¼
bL½G=KG ð1 þ agd½A=KA Þ
½A=KA ð1 þ aL þ g½G=KG ð1 þ agbLÞÞ
þ½G=KG ð1 þ bLÞ þ L þ 1 .
(3.82)
References
The cubic ternary complex model takes into account the
fact that both the active and inactive receptor species must
have a finite affinity for G-proteins [26e28]. The two receptor species are denoted by [Ra] (active state receptor
able to activate G-proteins) and [Ri] (inactive state receptors). These can form species [RiG] and [RaG] spontaneously, and species [ARiG] and [ARaG] in the presence of
ligand.
This forms eight vertices of a cube (see Fig. 3.14). The
equilibrium equations for the various species are
½ARi ¼
(3.80)
(3.76)
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A Pharmacology Primer
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(Eds.), Advances in Drug Research, Academic Press, New York,
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R.F. Furchgott, The Classification of Adrenoceptors (Adrenergic
Receptors): An Evaluation from the Standpoint of Receptor Theory,
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J.W. Black, P. Leff, Operational models of pharmacological agonist,
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P. Cuatrecasas, Membrane receptors, Annu. Rev. Biochem. 43
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A. DeLean, J.M. Stadel, R.J. Lefkowitz, A ternary complex model
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D. Spengler, C. Waeber, C. Pantaloni, F. Holsboer, J. Bockaert,
P.H. Seeburg, et al., Differential signal transduction by five splice
variants of the PACAP receptor, Nature 365 (1993) 170e175.
T.P. Kenakin, J.W. Black, The pharmacological classification of
practolol and chloropractolol, Mol. Pharmacol. 14 (1978) 607e623.
A. Christopoulos, T. Kenakin, G protein-coupled receptor allosterism
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modeling synoptic receptor systems, in: A. Christopoulos (Ed.),
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C.M. Guldberg, P. Waage, Studies concerning affinity, C. M. Forhandlinger: Videnskabs-Selskabet i Christiana 35 (1864).
C.M. Guldberg, P. Waage, Concerning chemical affinity, Erdmann’s
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T.P. Kenakin, The mass action equation in Pharmacology, Br. J.
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J. Del Castillo, B. Katz, Interaction at end-plate receptors between
different choline derivatives, Proc. Roy. Soc. Lond. B. 146 (1957)
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J. Monod, J. Wyman, J.P. Changeux, On the nature of allosteric
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cooperative models for drug action, in: H.P. Rang (Ed.),
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MD, 1973, pp. 149e182.
[24] A. Karlin, On the application of ‘a plausible model’ of allosteric
proteins to the receptor for acetylcholine, J. Theor. Biol. 16 (1967)
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terms of an allosteric receptor model, Mol. Pharmacol. 9 (1973) 1e9.
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of antagonists to brain muscarinic receptors, Mol. Pharmacol. 14
(1978) 737e750.
[27] R.J. Lefkowitz, D. Mullikin, M.G. Caron, Regulation of b-adrenergic
receptors by guanyl-5’-yl imidodiphosphate and other purine nucleotides, J. Biol. Chem. 251 (1976) 4686e4692.
[28] M.E. MaGuire, P.M. Van Arsdale, A.G. Gilman, An agonist-specific
effect of guanine nucleotides on the binding of the beta adrenergic
receptor, Mol. Pharmacol. 12 (1976) 335e339.
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[30] J.M. Weiss, P.H. Morgan, M.W. Lutz, T.P. Kenakin, The cubic
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Chapter 4
Pharmacological assay formats: binding
The author produced a series of interactive quizzes to test your understanding of the contents of this chapter. Click on the
link to access it: https://www.elsevier.com/books-and-journals/book-companion/9780323992893.
The yeoman work in any science . is done by the experimentalist who must keep the theoreticians honest.
dMichio Kaku (1995).
4.1 The structure of this chapter
This chapter discusses the application of binding techniques to the study of drugereceptor interaction. It will be
seen that the theory of binding and the methods used to
quantify drug effect are discussed before the experimental
prerequisites for good binding experiments are given. This
may appear to be placing the cart before the horse in
concept. However, the methods used to detect and rectify
nonequilibrium experimental conditions utilize the very
methods used to quantify drug effect. Therefore, they must
be understood before their application to optimize experimental conditions can be discussed. This chapter first presents what the experiments strive to achieve and then
explores the possible pitfalls of experimental design that
may cause the execution to fall short of the intent.
4.2 Binding theory and experiment
A direct measure of the binding of a molecule to a protein
target can be made if there is some means to distinguish the
bound molecule from the unbound and a means to quantify
the amount bound. Historically, the first widely used
technique to do this was radioligand binding. Radioactive
molecules can be detected by observation of radioactive
decay, and their amount quantified through calibration
curves relating the amount of molecule to the amount of
radioactivity detected. An essential part of this process is
the ability to separate the bound from the unbound molecule. This can be done by taking advantage of the size of
the protein versus the soluble small molecule. The protein
can be separated by centrifugation, equilibrium dialysis, or
filtration. Alternatively, the physical proximity of the
molecule to the protein can be used. For example, in
scintillation proximity assays, the receptor protein adheres
A Pharmacology Primer. https://doi.org/10.1016/B978-0-323-99289-3.00016-6
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to a bead containing scintillant, a chemical that produces
light when close to radioactivity. Thus, when radioactive
molecules are bound to the receptor (and therefore are near
the scintillant), a light signal is produced, heralding the
binding of the molecule. Other methods of detecting molecules such as fluorescence are increasingly being utilized in
binding experiments. For example, molecules that produce
different qualities of fluorescence, depending on their
proximity to protein, can be used to quantify binding.
Similarly, in fluorescence polarization experiments, fluorescent ligands (when not bound to protein) reduce the degree
of light polarization of light passing through the medium
through free rotation. When these same ligands are bound,
their rotation is reduced, thereby concomitantly reducing the
effect on polarization. Thus, binding can be quantified in
terms of the degree of light polarization in the medium.
In general, there are emerging technologies available to
discern bound from unbound molecules, and many of these
can be applied to receptor studies. It will be assumed from
this point that the technological problems associated with
determining bound species are not an experimental factor,
and subsequent discussions will focus on the interpretation
of the resulting binding data. Several excellent sources of
information on the technology and practical aspects of
binding are available [1e3].
It is important to note that pharmacological binding
versus functional studies measure different protein species
in the assay. Binding measures the amount of protein bound
to a radioactive tracer while function measures the effects
of an activated receptor species as sensed by the cell (see
Fig. 4.1). Therefore, there are numerous cases where
binding versus functional studies yield different data (see
Fig. 8.25 for an example) and in terms of therapeutic drug
activity, functional data are preferred. However, binding
may give insights not obvious from functional studies and
thus it can still be a useful endeavor. In addition, orthosteric
binding experiments that depend on the presence of the
radioligand on the receptor being disrupted by other ligands
(i.e., through binding to the same binding site) may not
detect allosteric receptor actions, i.e., those where the
ligand and the radioligand bind to separate sites on the
71
72
A Pharmacology Primer
FIGURE 4.1 Model depicting receptor that can exist in an active
(Ra) and inactive (Ri) state formed
by binding of agonist A and allosteric ligand B. When the radioligand is agonist A, binding
experiments detect the species in
red (panel labeled binding). In
functional
experiments
(panel
labeled function), the cellular
response is produced by agonist
bound species and any constitutively active receptor species (in the
form of Ra or BRa) shown in red.
FIGURE 4.2 Blockade of glutamate responses by the allosteric
antagonist
CPCCOEt
(7hydroxyiminocyclopropan[b]chromen-1a-carboxylic acid ethyl ester
(panel A) and lack of displacement
of radioactive glutamate binding by
the same antagonist (panel B).
allosteric Redrawn from S. Litschig,
F. Gasparini, D. Rueegg, N. Stoehr,
P.J. Flor, I. Vranesic, L. Pre’zeau,
J.P. Pin, C. Thomsen, R. Kuhn,
CPCCOEt,
a
noncompetitive
metabotropic glutamate receptor 1
antagonist,
inhibits
receptor
signaling without affecting glutamate binding. Mol. Pharmacol. 55
(1999) 453e461.
receptor protein. Fig. 4.2A shows the noncompetitive
allosteric antagonism of glutamate responses by an antagonist ligand CPCCOEt (7-hydroxyiminocyclopropan[b]
chromen-1a-carboxylic acid ethyl ester) that produces this
effect through an allosteric interaction. However, as seen in
Fig. 4.2B this same antagonist does not interfere in any way
with the binding of the radioligand and thus a binding
experiment would not have detected this antagonism [4].
Binding experiments can be done in three modes: saturation, displacement, and kinetic. Saturation binding directly
observes the binding of a tracer ligand (radioactive, fluorescent, or otherwise detectable) to the receptor. The method
quantifies the maximal number of binding sites and the affinity of the ligand for the site (equilibrium dissociation
constant of the ligandereceptor complex). This is a direct
measure of binding using the Langmuir adsorption isotherm
model. A major limitation of this technique is the obvious
need for the ligand to be traceable (i.e., it can be done only
for radioactive or fluorescent molecules). Displacement
studies overcome this limitation by allowing measurement of
the affinity of nontraceable ligands through their interference
with the binding of tracer ligands. Thus, molecules are used
to displace or otherwise prevent the binding of tracer ligands
and the reduction in signal is used to quantify the affinity of
the displacing ligands. Finally, kinetic studies follow the
binding of a tracer ligand with time. This can yield first-order
rate constants for the onset and offset of binding, which can
be used to calculate equilibrium binding constants to assess
the temporal approach to equilibrium or to determine binding reversibility or to detect allosteric interactions. Each of
these is considered separately. The first step is to discuss
some methodological points common to all these types of
binding experiments.
The aim of a binding experiment is to define and
quantify the relationship between the concentration of
ligand in the receptor compartment and the portion of the
concentration that is bound to the receptor at any one
instant. A first prerequisite is to know that the amount of
Pharmacological assay formats: binding Chapter | 4
bound ligand that is measured is bound only to the receptor
and not to other sites in the sample tube or well (i.e., cell
membrane, wall of the vessel containing the experimental
solution, and so on). The amount of ligand bound to these
auxiliary sites but not specifically to the target is referred to
as nonspecific binding (denoted nsb). The amount bound
only to the pharmacological target of interest is termed the
specific binding. The amount of specific binding is defined
operationally as the bound ligand that can be displaced by
an excess concentration of a specific antagonist for the
receptor that is not radioactive (or otherwise does not
interfere with the signals). Therefore, another prerequisite
of binding experiments is the availability of a nontracer
ligand (for the specific target defined as one that does not
interfere with the signal, whether it be radioactivity, fluorescence, or polarized light). Optimally, the chemical
structure of the ligand used to define nsb should be different
from the binding tracer ligand. This is because the tracer
may bind to nonreceptor sites (i.e., adsorption sites, other
nonspecific proteins), and if a nonradioactive version of the
same molecular structure is used to define specific binding,
it may protect those very same nonspecific sites (which
erroneously define specific binding). A ligand with
different chemical structure may not bind to the same
nonspecific sites and thus lessen the potential of defining
nsb sites as biologically relevant receptors.
The nsb of low concentrations of biologically active
ligands is essentially linear and nonsaturable within the
ranges used in pharmacological binding experiments. For a
traceable ligand (radioactive, fluorescent, and so on), nsb is
given as
nsb ¼ k$½A (4.1)
where k is a constant defining the concentration relationship for nsb and [A*] is the concentration of the traceable
molecule. The specific binding is saturable and defined
by the Langmuir adsorption isotherm:
Specific binding ¼
½A
½A þ Kd
(4.2)
73
where Kd is the equilibrium dissociation constant of the
ligandereceptor complex. The total binding is the sum of
these and is given as
Total binding ¼
½A$Bmax
þ k$½A ½A þ Kd
(4.3)
The two experimentally derived variables are nsb and
total binding. These can be obtained by measuring the
relationship between the ligand concentration and the
amount of ligand bound (total binding) and the amount
bound in the presence of a protecting concentration of
receptor-specific antagonist. This latter procedure defines
the nsb. Theoretically, specific binding can be obtained by
subtracting these values for each concentration of ligand,
but a more powerful method is to fit the two data sets (total
binding and nsb) to Eqs. (4.1) and (4.3) simultaneously.
One reason that this is preferable is that more data points
are used to define specific binding. A second reason is that
a better estimate of the maximal binding (Bmax) can be
made by simultaneously fitting two functions. Since Bmax is
defined at theoretically infinite ligand concentrations, it is
difficult to obtain data in this concentration region. When
there is a paucity of data points, nonlinear fitting procedures
tend to overestimate the maximal asymptote. The additional
experimental data (total plus nsb) reduce this effect and
yield more accurate Bmax estimates.
In binding, a good first experiment is to determine the
time required for the binding reaction to come to equilibrium with the receptor. This is essential to know, since most
binding reactions are made in stop-time mode, and realtime observation of the approach to equilibrium is not
possible (this is not true of more recent fluorescent techniques where visualization of binding in real time can be
achieved). A useful experiment is to observe the approach
to equilibrium of a given concentration of tracer ligand and
then to observe reversal of binding by addition of a
competitive antagonist of the receptor. An example of this
experiment is shown in Fig. 4.3. Valuable data are obtained
with this approach, since it indicates the time needed to
reach equilibrium and confirms the fact that the binding is
FIGURE 4.3 Time course for the onset of a
radioligand onto the receptor and the reversal of
radioligand binding upon addition of a high concentration of a nonradioactive antagonist ligand.
The object of the experiment is to determine the
times required for steady-state receptor occupation
by the radioligand and confirmation of reversibility
of binding. The radioligand is added at point A, and
an excess competitive antagonist of the receptor at
point B.
74
A Pharmacology Primer
reversible. Reversibility is essential to the attainment of
steady states and equilibria (i.e., irreversible binding reactions do not come to equilibrium).
which yields a straight line with the transforms
4.2.1 Saturation binding
referred to alternatively as a Scatchard, Eadie, or Eadiee
Hofstee plot. From this linear plot, Kd ¼ 1/slope and
the x intercept equals Bmax.
Alternatively, another method of linearizing the data
points is by using
A saturation binding experiment consists of the equilibration of the receptor with a range of concentrations of
traceable ligand in the absence (total binding) and presence
of a high concentration (approximately 100 Kd) of
antagonist to protect the receptors (and thus determine the
nsb). Simultaneous fitting of the total binding curve [Eq.
(4.3)] and nsb line [Eq. (4.1)] yields the specific binding
with parameters of maximal number of binding sites (Bmax)
and equilibrium dissociation constant of the ligande
receptor complex (Kd) [see Eq. (4.2)]. An example of this
procedure for the human calcitonin receptor is shown in
Fig. 4.4 [5]. Before the widespread use of nonlinear fitting
programs, the Langmuir equation was linearized for ease of
fitting graphically. Thus, specific binding ([A * R]) according to mass action is represented as
½A R
½A
¼
Bmax
½A þ Kd
FIGURE 4.4 Saturation binding.
Left panel: Curves showing total
binding (filled circles), nonspecific
binding (filled squares), and
specific binding (open circles) of the
calcitonin
receptor
antagonist
radiolabel 125I AC512 (Bmax ¼ 6.63
pM; Kd ¼ 26.8 pM). Panels to the
right show linear variants of the
specific binding curve: Scatchard
[Eq. (4.5)], double reciprocal [Eq.
(4.6)], and Hanes plots [Eq. (4.7)]
cause distortion and compression of
data. Nonlinear curve-fitting techniques are preferred. Left panel:
Data redrawn from W.-J. Chen, S.
Armour, J. Way, G. Chen, C. Watson, P. Irving, et al., Expression
cloning and receptor pharmacology
of human calcitonin receptors from
MCF-7 cells and their relationship
to amylin receptors, Mol. Pharmacol. 52 (1997) 1164e1175.
(4.4)
½A R Bmax ½A R
¼
½A
Kd
Kd
1
1 Kd
1
¼
$
þ
½A R ½A Bmax Bmax
(4.5)
(4.6)
This is referred to as a double reciprocal or
LineweavereBurk plot. From this linear plot, Kd ¼ slope/
intercept and the 1/intercept ¼ Bmax. Finally, a linear plot
can be achieved with
½A
½A
Kd
¼
þ
½A R Bmax Bmax
(4.7)
This is referred to as a Hanes, HildebrandeBenesi, or
Scott plot. From this linear plot, Kd ¼ intercept/slope and
1/slope ¼ Bmax.
Pharmacological assay formats: binding Chapter | 4
Examples of these are shown for the saturation data in
Fig. 4.4. At first glance, these transformations may seem
like ideal methods for analyzing saturation data. However,
transformation of binding data is not generally recommended. This is because transformed plots can distort
experimental uncertainty, produce compression of data, and
cause large differences in data placement. Also, these
transformations violate the assumptions of linear regression
and can be curvilinear simply because of statistical factors
(e.g., Scatchard plots combine dependent and independent
variables). These transformations are valid only for ideal
data and are extremely sensitive to different types of
experimental errors. They should not be used for estimation
of binding parameters. Scatchard plots compress data to the
point where a linear plot can be obtained. Fig. 4.5 shows a
curve with an estimate of Bmax that falls far short of being
able to furnish an experimental estimate of the Bmax, yet the
Scatchard plot is linear with an apparently valid estimate
from the abscissa intercept.
In general, nonlinear fitting of the data is essential for
parameter estimation. Linear transformations, however, are
useful for visualization of trends in data. Variances from a
straight edge are more discernible to the human eye than
are differences from curvilinear shapes, so linear transformations can be a useful diagnostic tool. An example of
where the Scatchard transformation shows significant
75
deviation from a rectangular hyperbola is shown in Fig. 4.6.
The direct presentation of the data shows little deviation
from the saturation binding curve as defined by the Langmuir adsorption isotherm. The data at 10 and 30 nM yield
slightly underestimated levels of binding, a common
finding if slightly too much protein is used in the binding
assay (see Section 4.4.1). While this difference is nearly
undetectable when the data are presented as a direct binding
curve, it does produce a deviation from linearity in the
Scatchard curve (see Fig. 4.6B).
Estimating the Bmax value is technically difficult since it
basically is an exercise in estimating an effect at infinite
drug concentration. Therefore, the accuracy of the estimate
of Bmax is proportional to the maximal levels of radioligand
that can be used in the experiment. The attainment of
saturable binding can be deceiving when the ordinates are
plotted on a linear scale, as they are in Fig. 4.43. Fig. 4.7
shows a saturation curve for calcitonin binding that appears
to reach a maximal asymptote on a linear scale. However,
replotting the graph on a semilogarithmic scale illustrates
the illusion of maximal binding on the linear scale and, in
this case, how far short of true maxima a linear scale can
present a saturation binding curve. An example of how to
measure the affinity of a radioligand and obtain an estimate
of Bmax (maximal number of binding sites for that radioligand) is given in Section 13.1.1.
FIGURE 4.5 Erroneous estimation of maximal binding with
Scatchard plots. The saturation
binding curve shown to the left has
no data points available to estimate
the true Bmax. The Scatchard transformation to the right linearizes the
existing points, allowing an estimate
of the maximum to be made from
the x-axis intercept. However, this
intercept in no way estimates the
true Bmax since there are no data to
define this parameter.
FIGURE 4.6 Saturation binding
expressed directly and with a
Scatchard plot. (A) Direct representation of a saturation binding plot
(Bmax ¼ 25 pmol/mg, Kd ¼ 50 nM).
Data points are slightly deviated
from ideal behavior (lower two
concentrations yield slightly lower
values for binding, as is common
when slightly too much receptor
protein is used in the assay, vide
infra). (B) Scatchard plot of the data
shown in panel (A). It can be seen
that the slight deviations in the data
lead to considerable deviations from
linearity on the Scatchard plot (B).
76
A Pharmacology Primer
4.2.2 Displacement binding
In practice, there will be a limited number of ligands
available that are chemically traceable (i.e., radioactive,
fluorescent). Therefore, the bulk of radioligand experiments
designed to quantify ligand affinity are done in a
displacement mode whereby a ligand is used to displace or
otherwise affect the binding of a traceable ligand. In general, an inverse sigmoidal curve is obtained with reduction
in radioligand binding upon addition of nonradioactive
antagonist. An example of how to measure the affinity of a
displacing ligand is given in Section 13.1.2.
The equations describing the amount of bound radioligand observed in the presence of a range of concentrations
of nontraceable ligand vary with the model used for the
molecular antagonism. These are provided in material
following, with brief descriptions. More detailed discussions of these mechanisms can be found in Chapter 6,
Orthosteric Drug Antagonism. If the binding is competitive
(both ligands compete for the same binding domain on the
receptor), the amount of tracer ligandereceptor complex
(r*) is given as (see Section 4.7.1)
r ¼
½A=Kd
½A=Kd þ ½B=KB þ 1
(4.8)
where the concentration of tracer ligand is [A*], the nontraceable displacing ligand is [B], and Kd and KB are
respective equilibrium dissociation constants. If the binding
is noncompetitive (binding of the antagonist precludes the
binding of the tracer ligand), the signal is given by (see
Section 4.7.2)
FIGURE 4.7 Saturation binding of the
radioligand human 125I-human calcitonin to human calcitonin receptors in a
recombinant cell system in human embryonic kidney cells. Left-hand panel
shows total binding (open circles),
nonspecific binding (open squares), and
specific receptor binding (open triangles). The specific binding appears to
reach a maximal asymptotic value. The
specific binding is plotted on a semilogarithmic scale (shown in the righthand panel). The solid line on this
curve indicates an estimate of the
maximal receptor binding. The data
points (open circles) on this curve show
that the data define less than half the
computer-estimated total saturation
curve. Data redrawn from W.-J. Chen,
S. Armour, J. Way, G. Chen, C. Watson,
P. Irving, et al. Expression cloning and
receptor pharmacology of human
calcitonin receptors from MCF-7 cells
and their relationship to amylin receptors, Mol. Pharmacol. 52 (1997)
1164e1175.
r ¼
½A=Kd
½A=Kd ð½B=KB þ 1Þ þ ½B=KB þ 1
(4.9)
If the ligand allosterically affects the affinity of the receptor (antagonist binds to a site separate from that for the
tracer ligand) to produce a change in receptor conformation
to affect the affinity of the tracer (vide infra) for the tracer
ligand (see Chapter 7: Allosteric Modulation for more
detail), the displacement curve is given by (see
Section 4.7.3)
r ¼
½A=Kd ð1 þ a½B=KB Þ
½A=Kd ð1 þ a½B=KB Þ þ ½B=KB þ 1
(4.10)
where a is the multiple factor by which the nontracer ligand
affects the affinity of the tracer ligand (i.e., a ¼ 0.1 indicates that the allosteric displacing ligand produces a 10fold decrease in the affinity of the receptor for the tracer
ligand).
As noted previously, in all cases these various functions
describe an inverse sigmoidal curve between the displacing
ligand and the signal. Therefore, the mechanism of interaction cannot be determined from a single displacement curve.
However, observation of a pattern of such curves obtained at
different tracer ligand concentrations (range of [A*] values)
may indicate whether the displacements are due to a
competitive, noncompetitive, or allosteric mechanism.
Competitive displacement for a range of [A*] values
[Eq. (4.8)] yields the pattern of curves shown in Fig. 4.8A.
A useful way to quantify the displacement is to determine
the concentration of displacing ligand that produces a
Pharmacological assay formats: binding Chapter | 4
crease in observed IC50
77
FIGURE 4.8 Displacement of a
radioligand by a competitive nonradioactive ligand. (A) Displacement
of radioactivity (ordinate scale) as
curves shown for a range of concentrations of displacing ligand
(abscissae as log scale). Curves
shown for a range of radioligand
concentrations denoted on the graph
in units of [A*]/Kd. Curved line
shows the path of the IC50 for the
displacement curves along the
antagonist concentration axis. (B)
Multiple values of the Ki for the
competitive displacing ligand (ordinate scale) as a function of the concentration of radioligand being
displaced (abscissae as linear scale).
Linear relationship shows the inof the antagonist with increasing concentrations of radioligand to be displaced [according to Eq. (4.11)].
diminution of the signal to 50% of the original value. This
concentration of displacing ligand will be referred to as the
IC50 (inhibitory concentration for 50% decrease). For
competitive antagonists, it can be shown that the IC50 is
related to the concentration of tracer ligand [A*] by (see
Section 4.7.4)
IC50 ¼ KB $ð½A = Kd þ 1Þ
(4.11)
This is a linear relation often referred to as the
ChengePrusoff relationship [6]. It is characteristic of
competitive ligandereceptor interactions. An example is
shown in Fig. 4.8B.
In most conventional biochemical binding studies, the
concentration of receptor protein is well below that of the
ligands and thus the binding process does not significantly
deplete the ligands. However, there are certain procedures
such as fluorescent binding assays which require high
concentrations of receptor to maximize the window for
observing a response. Under these circumstances, the
fluorescent probe concentration is kept below the Kd value
(where Kd is the equilibrium dissociation constant of the
fluorescent probeereceptor complex) and the receptor
concentration is maximized (above the Kd value) [7]. In
these types of assays, the standard correction for IC50 to Ki
values is not valid and a revised procedure utilizing the
following equation must be used [7]:
Ki ¼
½I50
½A50 =Kd þ ½R0 =Kd þ 1
(4.12)
where [I]50 is the free antagonist concentration at 50% inhibition, Kd is the equilibrium dissociation constant of the
fluorescent probeereceptor complex, [A*]50 is the free concentration of fluorescent probe at 50% inhibition, and [R]0
is the free concentration of receptor at 0% inhibition. The
practical application of this equation is discussed in detail
in Section 4.7.4.
FIGURE 4.9 Displacement curves for a noncompetitive antagonist.
Displacement curve according to Eq. (4.9) for values of radioligand [A*]/
Kd ¼ 0.3 (curve with lowest ordinate scale beginning at 0.25), 1, 3, 10, 30,
and 100. While the ordinate scale on these curves increases with increasing
[A*]/Kd values, the location parameter along the x-axis does not change.
The displacement of a tracer ligand, for a range of tracer
ligand concentrations, by a noncompetitive antagonist is
shown in Fig. 4.9. In contrast to the pattern shown for
competitive antagonists, the IC50 for inhibition of tracer
binding does not change with increasing tracer ligand
concentrations. In fact, it can be shown that the IC50 for
inhibition is equal to the equilibrium dissociation constant
of the noncompetitive antagonistereceptor complex (see
Section 4.7.2).
Allosteric antagonist effects can be an amalgam of
competitive and noncompetitive profiles in terms of the
relationship between IC50 and [A*]. This relates to the
magnitude of the term a, specifically the multiple ratio of
the affinity of the receptor for [A*] imposed by the binding
of the allosteric antagonist. A hallmark of allosteric inhibition is that it is saturable (i.e., the antagonism maximizes
upon saturation of the allosteric binding site). Therefore, if
78
A Pharmacology Primer
FIGURE
4.10 Displacement
curves according to Eq. (4.10) for
an allosteric antagonist with
different cooperativity factors [panel
(A), a ¼ 0.01; panel (B), a ¼ 0.1].
Curves shown for varying values of
radioligand ([A*]/Kd). It can be
seen that the curves do not reach nsb
values for high values of radioligand and that this effect occurs at
lower concentrations of radioligand
for antagonists of higher values of
a. nsb, nonspecific binding.
a given antagonist has a value of a of 0.1, this means that
the saturation binding curve will shift to the right by a
factor of 10 in the presence of an infinite concentration of
allosteric antagonist. Depending on the initial concentration
of radioligand, this may cause the displacement binding
curve to fail to reach nsb levels. This effect is illustrated in
Fig. 4.10. Therefore, in contrast to competitive antagonists,
where displacement curves all take binding of the radioligand to nsb values, an allosteric ligand will displace only
to a maximum value determined by the initial concentration
of radioligand and the value of a for the allosteric antagonist. In fact, if a displacement curve is observed where the
radioligand binding is not displaced to nsb values, this is
presumptive evidence that the antagonist is operating
through an allosteric mechanism. The maximum displacement of a given concentration of radioligand [A*] by
an allosteric antagonist with given values of a is (see
Section 4.7.5)
Maximal Fractional Inhibition ¼
½AKd þ 1
(4.13)
½A=Kd þ 1=a
where Kd is the equilibrium dissociation constant of the
radioligandereceptor complex (obtained from saturation
binding studies). The observed displacement for a range
of allosteric antagonists for two concentrations of radioligands is shown in Fig. 4.11. The effects shown in
Fig. 4.11 indicate a practical test for the detection of allosteric versus competitive antagonism in displacement
FIGURE 4.11 Displacement curves
for allosteric antagonists with varying
values of a (shown on figure).
Ordinates: bound radioligand. (A)
Concentration of radioligand [A*]/
Kd ¼ 0.1. (B) Displacement of higher
concentration of radioligand [A*]/
Kd ¼ 3.
binding studies. If the value of the maximal displacement
varies with different concentrations of radioligand, this
would suggest that an allosteric mechanism is operative.
Fig. 4.12 shows the displacement of the radioactive peptide
ligand 125I-MIP-1a from chemokine CCR1 receptors by
nonradioactive peptide MIP-1a and by the allosteric small
molecule modulator UCB35625. Clearly, the nonpeptide
ligand does not reduce binding to nsb levels, indicating
an allosteric mechanism for this effect [8].
Another, more rigorous, method to detect allosteric
mechanisms (and one that may furnish a value of a for the
antagonist) is to formally observe the relationship between
the concentration of radioligand and the observed antagonism by displacement with the IC50 of the antagonist. As
shown with Eq. (4.11), for a competitive antagonist, this
relationship is linear (ChengePrusoff correction). For an
allosteric antagonist, the relationship is hyperbolic and
given by (see Section 4.7.6)
IC50 ¼ KB
ð1 þ ð½A=Kd ÞÞ
ð1 þ að½A=Kd ÞÞ
(4.14)
It can be seen from this equation that the maximum of
the hyperbola defined by a given antagonist (with ordinate
values expressed as the ratio of IC50 to KB) will have a
maximum asymptote of 1/a. Therefore, observation of a
range of IC50 values needed to block a range of radioligand concentrations can be used to estimate the value of
a for a given allosteric antagonist. Fig. 4.13 shows the
Pharmacological assay formats: binding Chapter | 4
FIGURE 4.12 Displacement of bound 125I-MIP-1a from chemokine
CCR1 by MIP-1a (filled circles) and the allosteric ligand UCB35625
(open circles). Note how the displacement by the allosteric ligand is
incomplete. CCR1, C receptors type 1. Data redrawn from I. Sabroe, M.J.
Peck, B.J. Van Keulen, A. Jorritsma, G. Simmons, P.R. Clapham, A small
molecule antagonist of chemokine receptors CCR1 and CCR3, J. Biol.
Chem. 275 (2000) 25985e25992.
FIGURE 4.13 Relationship between the observed IC50 for allosteric
antagonists and the amount of radioligand present in the assay according to
Eq. (4.14). Dotted line shows relationship for a competitive antagonist.
relationship between the IC50 for allosteric antagonism
and the concentration of radioligand used in the assay, as a
function of a. It can be seen that unlike the linear
relationship predicted by Eq. (4.11) (see Fig. 4.8B), the
curves are hyperbolic in nature. This is another hallmark
of allosteric versus simple competitive antagonist
behavior.
An allosteric ligand changes the shape of the receptor,
and in so doing will necessarily alter the rate of association
and dissociation of some trace ligands. This means that
allosterism is tracer dependent (i.e., an allosteric change
detected by one radioligand may not be detected in the
same way, or even detected at all, by another).
For example, Fig. 4.14 shows the displacement binding of
two radioligand antagonists, [3H]-methyl-quinuclidinyl
79
FIGURE 4.14 Effect of alcuronium on the binding of [3H]-methyl-QNB
(filled circles) and [3H]-atropine (open circles) on muscarinic receptors.
Ordinates are percentage of initial radioligand binding. Alcuronium decreases the binding of [3H]-methyl-QNB and increases the binding of [3H]atropine. Data redrawn from L. Hejnova, S. Tucek, E.E. El-Fakahany,
Positive and negative allosteric interactions on muscarinic receptors, Eur.
J. Pharmacol. 291 (1995) 427e430.
benzilate (QNB) and [3H]-atropine, on muscarinic receptors
by the allosteric ligand alcuronium. It can be seen that quite
different effects are observed. In the case of [3H]-methylQNB, the allosteric ligand displaces the radioligand and
reduces binding to the nsb level. In the case of [3H]atropine, the allosteric ligand actually enhances binding
of the radioligand [9]. There are numerous cases of probe
dependence for allosteric effects. For example, the allosteric ligand strychnine has little effect on the affinity of the
agonist methylfurmethide (twofold enhanced binding) but a
much greater effect on the agonist bethanechol (49-fold
enhancement of binding [10]). An example of the striking
variation of allosteric effects on different probes by the
allosteric modulator alcuronium is shown in Table 4.1
[9,11,12].
4.2.3 Kinetic binding studies
A more sensitive and rigorous method of detecting and
quantifying allosteric effects is through observation of the
kinetics of binding. In general, the kinetics of most allosteric modulators has been shown to be faster than the kinetics of binding of the tracer ligand. This is an initial
assumption for this experimental approach. Under these
circumstances, the rate of dissociation of the tracer ligand
(rA*t) in the presence of the allosteric ligand is given by
[13,14]
rAt ¼ rA $ekoffobs $t
(4.15)
where rA* is the tracer ligand receptor occupancy at equilibrium and koff-obs is given by
80
A Pharmacology Primer
TABLE 4.1 Differential effects of the allosteric
modulator alcuronium on various probes for the m2
muscarinic receptor.
Agonistsa
(1/a)
Arecoline
1.7
Acetylcholine
10
Bethanechol
10
Carbachol
9.5
Furmethide
8.4
Methylfurmethide
7.3
Antagonists
Atropineb
0.26
Methyl-N-piperidinyl benzilateb
0.54
c
Methyl-N-quinuclidinyl benzilate
63
Methyl-N-scopolamine
0.24
a
From Ref. [10].
From Ref. [11].
c
From Ref. [8].
b
koffobs ¼
a½BkoffAB =KB þ koffA
1 þ a½B=KB
(4.16)
Therefore, the rate of offset of the tracer ligand in the
presence of various concentrations of allosteric ligand can
be used to detect allosterism (change in rates with allosteric
ligand presence) and to quantify both the affinity (1/KB)
and a value for the allosteric ligand. Allosteric modulators
(antagonists) will generally decrease the rate of association
and/or increase the rate of dissociation of the tracer ligand.
Fig. 4.15 shows the effect of the allosteric ligand 5-(Nethyl-N-isopropyl)-amyloride (EPA) on the kinetics of
binding (rate of offset) of the tracer ligand [3H]-yohimbine
to a2-adrenoceptors [15]. It can be seen from this figure that
EPA produces a concentration-dependent increase in the
rate of offset of the tracer ligand, thereby indicating an
allosteric effect on the receptor.
4.3 Complex binding phenomena:
agonist affinity from binding curves
The foregoing discussion has been restricted to the simple
Langmuirian system of the binding of a ligand to a receptor. The assumption is that this process produces no change
in the receptor (i.e., analogous to Langmuir’s binding of
molecules to an inert surface). The conclusions drawn from
a system where the binding of the ligand changes the receptor are different. One such process is agonist binding, in
which, due to the molecular property of efficacy, the
agonist produces a change in the receptor upon binding to
elicit a response. Under these circumstances, the simple
schemes for binding discussed for antagonists may not
apply.
If the ligand changes the receptor then the observed
affinity of the ligand for the receptor will not be described
by KA (where KA ¼ 1/Ka) but rather by that microaffinity
modified by a term describing the avidity of the isomerization reaction. The observed affinity will be given by (see
Section 4.7.7)
Kobs ¼
KA $c=s
1 þ c=s
(4.17)
One target type for which the molecular mechanism of
efficacy has been partly elucidated is the G-protein-coupled
receptor (GPCR). It is known that activation of GPCRs
leads to an interaction of the receptor with separate membrane G-proteins to cause dissociation of the G-protein
subunits and subsequent activation of effectors (see
Chapter 2: How Different Tissues Process Drug Response).
For the purposes of binding, this process can lead to an
aberration in the binding reaction as perceived in experimental binding studies. Specifically, the activation of the
FIGURE 4.15 Effect of the allosteric modulator EPA on the kinetics
dissociation of [3H] yohimbine from
a2-adrenoceptors. (A) Receptor occupancy of [3H] yohimbine with
time in the absence (filled circles)
and presence (open circles) of EPA
0.03, 0.1 (filled triangles), 0.3 (open
squares), 1 (filled squares), and
3 mM (open triangles). (B) Regression of observed rate constant for
offset of concentration of [3H]
yohimbine in the presence of various
concentrations of EPA on concentrations of EPA (abscissae in mM on
a logarithmic scale). EPA, 5-(N-ethyl-N-isopropyl)-amyloride. Data redrawn from R.A. Leppick, S. Lazareno, A. Mynett, N.J. Birdsall, Characterization of
the allosteric interactions between antagonists and amiloride at the human a2A-adrenergic receptor, Mol. Pharmacol. 53 (1998) 916e925.
Pharmacological assay formats: binding Chapter | 4
receptor with subsequent binding of that receptor to another
protein (to form a ternary complex of receptor, ligand, and
G-protein) can lead to the apparent observation of a “highaffinity” siteda ghost site that has no physical counterpart
but appears to be a separate binding site on the receptor.
This is caused by two-stage binding reactions.
In the absence of two-stage binding, the relative quantities of [AR] and [R] are controlled by the magnitude of Ka
in the presence of ligand [A]. This, in turn, defines the
affinity of the ligand for R (affinity ¼ [AR]/([A] [R])).
Therefore, if an outside influence alters the quantity of
[AR], the observed affinity of the ligand for the receptor R
will change. If a ligand predisposes the receptor to bind to
G-protein, then the presence of G-protein will drive the
binding reaction to the right (i.e., [AR] complex will be
removed from the equilibrium defined by Ka). Under these
circumstances, more [AR] complex will be produced than
that governed by Ka. The observed affinity will be higher
than it would be in the absence of G-protein. Therefore, the
property of the ligand that causes the formation of the
ternary ligand/receptor/G-protein complex (in this case,
efficacy) will cause the ligand to have a higher affinity than
it would have if the receptor were present in isolation (no
G-protein present). Fig. 4.16 shows the effect of adding a
G-protein to a receptor system on the affinity of an agonist
[16]. As shown in this figure, the muscarinic agonist oxotremorine has a receptor equilibrium dissociation constant
of 6 mM in a reconstituted phospholipid vesicle devoid of
G-proteins. However, upon addition of G0 protein, the affinity increases by a factor of 600 (10 nM).
This effect can actually be used to estimate the efficacy
of an agonist (i.e., the propensity of a ligand to demonstrate
high affinity in the presence of G-protein, vide infra).
The observed affinity of such a ligand is given by (see
Section 4.7.8)
Kobs ¼
FIGURE 4.16 Effects of G-protein on the displacement of the muscarinic antagonist radioligand [3H]-l-quinuclidinyl benzilate by the agonist
oxotremorine. Displacement in reconstituted phospholipid vesicles (devoid
of G-protein subunits) shown in open circles. Addition of G-protein (G0
5.9 nM bg-subunit/3.4 nM a0-IDP subunit) shifts the displacement curve
to the left (higher affinity; see filled circles) by a factor of 600. Data
redrawn from V.A. Florio, P.C. Sternweis, Mechanism of muscarinic receptor action on go in reconstituted phospholipid vesicles, J. Biol. Chem.
264 (1989) 3909e3915.
81
KA
1 þ ½G=KG
(4.18)
where KG is the equilibrium dissociation constant of the receptor/G-protein complex. A low value for KG indicates
tight binding between receptors and G-proteins (i.e., high
efficacy). It can be seen that the observed affinity of the
ligand will be increased (decrease in the equilibrium dissociation constant of the ligandereceptor complex) with
increasing quantities of G-protein [G] and/or very efficient
binding of the ligand-bound receptor to the G-protein (low
value of KG, the equilibrium dissociation constant for the
ternary complex of ligand/receptor/G-protein). The effects
of various concentrations of G-protein on the binding saturation curve to an agonist ligand are shown in Fig. 4.17A. It
can be seen from this figure that increasing concentrations
of G-protein in this system cause a progressive shift to the
left of the saturation doseeresponse curve. Similarly, the
FIGURE 4.17 Complex binding
curves for agonists in G-protein
unlimited receptor systems. (A)
Saturation binding curves for an
agonist where there is high-affinity
binding due to G-protein complexation. Numbers next to curves refer
to the amount of G-protein in the
system. (B) Displacement of antagonist radioligand by same agonist in
G-protein unlimited system.
82
A Pharmacology Primer
same effect is observed in displacement experiments.
Fig. 4.17B shows the effect of different concentrations of
G-protein on the displacement of a radioligand by a nonradioactive agonist.
The previous discussion assumes that there is no limitation on the stoichiometry relating receptors and Gproteins. In recombinant systems, where receptors are
expressed in surrogate cells (often in large quantities), it is
possible that there may be limited quantities of G-proteins
available for complexation with receptors. Under these
circumstances, complex saturation and/or displacement
curves can be observed in binding studies. Fig. 4.18A
shows the effect of different submaximal effects of
G-protein on the saturation binding curve to an agonist
radioligand. It can be seen that clear two-phase curves can
be obtained. Similarly, two-phase displacement curves also
can be seen with agonist ligands displacing a radioligand in
binding experiments with subsaturating quantities of Gprotein (Fig. 4.18B). Fig. 4.19 shows an experimental
displacement curve of the antagonist radioligand for human
calcitonin receptors [125I]-AC512 by the agonist amylin in
a recombinant system where the number of receptors exceeds the amount of G-protein available for complexation
FIGURE 4.18 Complex binding
curves for agonists in G-protein
limited receptor systems. (A) Saturation binding curves for an agonist
where the high-affinity binding due to
G-protein complexation ¼ 100 Kd
(i.e., Kobs ¼ Kd/100). Numbers next
to curves refer to ratio of G-protein to
receptor. (B) Displacement of antagonist radioligand by same agonist in
G-protein limited system.
FIGURE 4.19 Displacement of antagonist radioligand 125IAC512 by the agonist amylin. Ordinates: percentage of
initial binding value for AC512. Abscissae: logarithms of
molar concentrations of rat amylin. Open circles are data
points, solid line fits to two-site model for binding. Dotted line
indicates a single phase displacement binding curve with a
slope of unity. Data redrawn from W.-J. Chen, S. Armour, J.
Way, G. Chen, C. Watson, P. Irving, et al., Expression cloning
and receptor pharmacology of human calcitonin receptors
from MCF-7 cells and their relationship to amylin receptors,
Mol. Pharmacol. 52 (1997) 1164e1175.
to the ternary complex state. It can be seen that the
displacement curve has two distinct phases: a high-affinity
(presumably due to coupling to G-protein) binding process
followed by a lower affinity binding (no benefit of
G-protein coupling).
While high-affinity binding due to ternary complex
formation (ligand binding to the receptor followed by
binding to a G-protein) can be observed in isolated systems
where the ternary complex can accumulate and be quantified, this effect is canceled in systems where the ternary
complex is not allowed to accumulate. Specifically, in the
presence of high concentrations of GTP (or a chemically
stable analog of GTP such as GTPgS), the formation of the
ternary complex [ARG] is followed immediately by hydrolysis of GTP and the G-protein and dissociation of the
G-protein into a- and gb-subunits (see Chapter 2: How
Different Tissues Process Drug Response for further details). This causes subsequent dissolution of the ternary
complex. Under these conditions, the G-protein complex
does not accumulate, and the coupling reaction promoted
by agonists is essentially nullified (with respect to the
observable radioactive species in the binding reaction).
When this occurs, the high-affinity state is not observed in
Pharmacological assay formats: binding Chapter | 4
the binding experiment. This has a practical consequence in
binding experiments. In broken-cell preparations for binding, the concentration of GTP can be depleted and thus the
two-stage binding reaction is observed (i.e., the ternary
complex accumulates). However, in whole-cell experiments, the intracellular concentration of GTP is high and
the ternary complex [ARG] species does not accumulate.
Under these circumstances, the high-affinity binding of
agonists is not observed, only the so-called low-affinity
state of agonist binding to the receptor. Fig. 4.20 shows
the binding (by displacement experiments) of a series of
adenosine receptor agonists to a broken-cell membrane
preparation (where high-affinity binding can be observed)
and the same agonists in a whole-cell preparation (where
the results of G-protein coupling are not observed) [17]. It
can be seen from this figure that a phase shift for the affinity of the agonists under these two binding experiment
conditions is observed. The broken-cell preparation reveals the effects of the ability of the agonists to promote
83
G-protein coupling of the receptor. This latter property, in
effect, is the efficacy of the agonist. Thus, ligands that
have a high observed affinity in broken-cell systems often
have a high efficacy. A measure of this efficacy can be
obtained by observing the magnitude of the phase shift of
the affinities measured in broken-cell and whole-cell
systems.
A more controlled experiment to measure the ability of
agonists to induce the high-affinity state, in effect a measure of efficacy, can be done in broken-cell preparations in
the presence and absence of saturating concentrations of
GTP (or GTPgS). Thus, the ratio of the affinity in the
absence and presence of GTP (ratio of the high-affinity and
low-affinity states) yields an estimate of the efficacy of the
agonist. This type of experiment is termed the “GTP shift”
after the shift to the right of the displacement curve for
agonist ligands after cancellation of G-protein coupling.
Fig. 4.21 shows the effects of saturating concentrations of
GTPgS on the affinity of b-adrenoceptor agonists in turkey
FIGURE 4.20 Affinity of adenosine receptor agonists in
whole cells (red bars) and membranes (blue bars,
high-affinity binding site). Data shown for (1) 2phenylaminoadenosine, (2) 2-chloroadenosine, (3) 50 -Nethylcarboxamidoadenosine, (4) N6-cyclohexyladenosine,
(5) ()-(R)-N6-phenylisopropyladenosine, and (6) N6cyclopentyladenosine. Data redrawn from P. Gerwins, C.
Nordstedt, B.B. Fredholm, Characterization of adenosine
A1 receptors in intact DDT1 MF-2 smooth muscle cells,
Mol. Pharmacol. 38 (1990) 660e666.
FIGURE 4.21 Correlation of the GTP shift for b-adrenoceptor agonists in turkey erythrocytes (ordinates) and
intrinsic activity of the agonists in functional studies
(abscissae). Data redrawn from R.J. Lefkowitz, M.G.
Caron, T. Michel, J.M. Stadel, Mechanisms of hormoneeffector coupling: the b-adrenergic receptor and adenylate cyclase, Fed. Proc. 41 (1982) 2664e2670.
84
A Pharmacology Primer
TABLE 4.2 Minimal criteria and optimal conditions for binding experiments.
l
l
l
l
l
l
l
l
Minimal criteria and optimal conditions for binding experiments: The means of making the ligand chemically detectable (i.e.,
addition of radioisotope label, fluorescent probe) does not significantly alter the receptor biology of the molecule. The binding
is saturable
The binding is reversible and able to be displaced by other ligands
There is a ligand available to determine nonspecific binding
There is sufficient biological binding material to yield a good signal-to-noise ratio but not too much so as to cause depletion of the
tracer ligand
For optimum binding experiments, the following conditions should be met: There is a high degree of specific binding and a
concomitantly low degree of nonspecific binding
Agonist and antagonist tracer ligands are available
The kinetics of binding are rapid
The ligand used for determination of nonspecific binding has a different molecular structure from the tracer ligand
erythrocytes [18]. As can be seen from this figure, a
correlation of the magnitude of GTP shifts for a series of
agonists and their intrinsic activities as measured in functional studies (a more direct measure of agonist efficacy;
see Chapter 5: Agonists: The Measurement of Affinity and
Efficacy in Functional Assays). The GTP shift experiment
is a method to estimate the efficacy of an agonist in binding
studies.
The previous discussions indicate how binding experiments can be useful in characterizing and quantifying the
activity of drugs (provided the effects are detectable as
changes in ligand affinity). As for any experimental procedure, there are certain prerequisite conditions that must
be attained for the correct application of this technique to
the study of drugs and receptors. A short list of required
and optimal experimental conditions for successful binding
experiments is given in Table 4.2. Some special experimental procedures for determining equilibrium conditions
involve the adjustment of biological material (i.e., membrane or cells) for maximal signal-to-noise ratios and/or
temporal approach to equilibrium. These are outlined in the
material following.
4.4 Experimental prerequisites for
correct application of binding
techniques
4.4.1 The effect of protein concentration on
binding curves
In the quest for optimal conditions for binding experiments,
there are two mutually exclusive factors with regard to
the amount of receptor used for the binding reaction. On the
one hand, increasing receptor (Bmax) also increases the
signal strength and usually the signal-to-noise ratio. This is
a useful variable to manipulate. On the other hand, a very
important prerequisite to the use of the Langmuirian type
kinetics for binding curves is that the binding reaction does
not change the concentration of tracer ligand being bound.
If this is violated (i.e., if the binding is high enough to
deplete the ligand), then distortion of the binding curves
will result. The amount of tracer ligandereceptor complex
as a function of the amount of receptor protein present is
given as (see Section 4.7.9)
½A R
1 AT þ Kd þ Bmax
¼
2
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2
AT þ Kd þ Bmax 4 AT Bmax
(4.19)
where
the radioligandereceptor complex is [A * R] and
AT is the total concentration of radioligand. Ideally, the
amount of receptor (magnitude of Bmax) should not limit
the amount of [A * R] complex formed and there should
be a linear relationship between [A * R] and Bmax. However,
Eq. (4.19) indicates that the amount of [A * R] complex
formed for a given [A*] indeed can be limited by the amount
of receptor present (magnitude of Bmax) as Bmax values
exceed Kd. A graph of [A*R] for a concentration of
[A*] ¼ 3 Kd as a function of Bmax is shown in
Fig. 4.22. It can be seen that as Bmax increases, the relationship changes from linear to curvilinear as the receptor begins
to deplete the tracer ligand. The degree of curvature varies
with the initial amount of [A*] present. Lower concentrations are affected at lower Bmax values than are higher concentrations. The relationship between [AR] and Bmax for a
range of concentrations of [A*] is shown in Fig. 4.23A.
When Bmax levels are exceeded (beyond the linear range),
saturation curves shift to the right and do not come to an
observable maximal asymptotic value. The effect of excess
receptor concentrations on a saturation curve is shown in
Fig. 4.23B.
For displacement curves, a similar error occurs with
excess protein concentrations. The concentration of [A * R]
in the presence of a nontracer-displacing ligand [B] as a
function of Bmax is given by (see Section 4.7.10)
Pharmacological assay formats: binding Chapter | 4
½A R
1 ¼
AT þ Kd ð1 þ ½B=KB Þ þ Bmax
2
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2
ffi
AT þ Kd þ ð1 þ ½B=KB Þ þ Bmax 4 AT Bmax
(4.20)
85
where the concentration of the displacing ligand is [B] and
KB is the equilibrium dissociation constant of the displacing ligandereceptor complex. A shift to the right of
displacement curves, with a resulting error in the IC50
values, occurs with excess protein concentration (see
Fig. 4.24).
4.4.2 The importance of equilibration time for
equilibrium between two ligands
FIGURE 4.22 Effect of increasing protein concentration on the binding
of a tracer ligand present at a concentration of 3 Kd. Ordinates: [A * R]
in moles/L calculated with Eq. (4.19). Abscissae: Bmax in moles/L 109.
Values of Bmax greater than the vertical solid line indicate region where the
relationship between Bmax and [A * R] begins to be nonlinear and where
aberrations in the binding curves will be expected to occur.
In terms of ensuring that adequate time is allowed for the
attainment of equilibrium between a single ligand and receptors, the experiment shown in Fig. 4.3 is useful. However, in displacement experiments, there are two ligands
(tracer and nontraceable ligand) present and they must
compete for the receptor. This competition can take
considerably longer than the time required for just a single
ligand. This is because the free ligands can bind only to free
unbound receptors (except in the case of allosteric mechanisms, vide infra). Therefore, the likelihood of a receptor
being free to accept a ligand depends on the reversibility of
the other ligand, and vice versa. Assuming mass action
kinetics describes the binding of the radioligand [A*] and
competitive antagonist [B]:
FIGURE 4.23 Effects of excess protein on saturation curves. (A) Bound ligand for a range of concentrations of radioligand, as a function of pM of
receptor (Fig. 4.22 is one example of these types of curves). The binding of the range of concentrations of radioligands is taken at two values of Bmax
(shown by the dotted lines, namely, 130 pM and 60 nM) and plotted as saturation curves for both Bmax values on the top panels (note the difference in the
ordinate scales). (B) The saturation curves shown on the top panels are replotted as a percentage of the maximal binding for each level of Bmax. These
comparable scales allow comparison of the saturation curves and show the dextral displacement of the curves with increasing protein concentration.
86
A Pharmacology Primer
FIGURE 4.24 Effect of excess protein concentration on
displacement curves [as predicted by Eq. (4.22)]. As the
Bmax increases (log Bmax values shown next to curves),
the displacement curves shift to the right.
where [A] is the radioligand and k1 and k2 the respsective rates of onset and offset from the receptor.
where [B] is the competitor and k3 and k4 the respective
rates of onset and offset from the receptor. As described
by Motulsky and Mahan [19], the following differential
equations describe the binding of the radioligand and
competitor with time:
d½A R
¼ ½A ½Rk1 ½ARk2
dt
(4.21)
d½BR
¼ ½B½Rk3 ½BRk4
dt
(4.22)
The solution to the differential equations leads to an
expression that describes the amount of radioligand
bound to receptors with time in the presence of the
competitor [19]:
rAt ¼
k1 ½A k4 ðU JÞ ðk4 UÞ Ut ðk4 JÞ Jt
þ
e e
Uj
UJ
U
J
(4.23)
longer to reach equilibrium for the radioligand in the
presence of the competitor. This should be considered
when designing binding experiments, i.e., measurement of
radioligand kinetics to determine when the experiment
should be terminated and measurements taken by observation of radioligand binding alone may underestimate the
time needed for attainment of equilibrium.
Radioligand binding experiments are usually initiated
by addition of the membrane to a premade mixture of
radioactive and nonradioactive ligand. After a period of
time thought adequate to achieve equilibrium (guided by
experiments like that shown in Fig. 4.3), the binding reaction is halted and the amount of bound radioligand is
quantified. Fig. 4.26 shows the potential hazard of using
kinetics observed for a single ligand (i.e., the radioligand)
as being indicative of a two-ligand system. In the absence
of another ligand, Fig. 4.26A shows that the radioligand
comes to equilibrium binding within 30 minutes. However,
in the presence of a receptor antagonist (at two concentrations [B]/KB ¼ 10 and 30), a clearly biphasic receptor
where
U
¼
1
½k3 ½B þ k4 þ k1 ½A þ k2
2
þðk3 ½B þ k4 k1 ½A k2 Þ þ 4k3 k1 ½A½B
2
1=2 (4.24)
and
J
¼
1
½k3 ½B þ k4 þ k1 ½A þ k2
2
ðk3 ½B þ k4 k1 ½A k2 Þ2 þ 4k3 k1 ½A½B1=2
(4.25)
Fig. 4.25 shows the kinetics of binding of a radioligand
in the absence and presence of a competitor with comparatively rapid binding kinetics; it can be seen that it takes
FIGURE
4.25 Binding
kinetics
of
a
radioligand
with:
k1 ¼ 3.0 105 min1/mol, k2 ¼ 3.0 103 min1, [A]/KA ¼ 3.0 in the
absence (solid line) and presence (dotted line) of a competitor for receptor
binding (k3 ¼ 106 min1/mol, k4 ¼ 0.03 min1, [B]/KB ¼ 10).
Pharmacological assay formats: binding Chapter | 4
87
FIGURE 4.26 Time course for
equilibration of two ligands for a
single receptor. (A) Time course for
displacement of a radioligand present
at a concentration of [A*]/Kd ¼ 1.
Kinetic parameter for the radioligand
k1 ¼ 105 s1/mol, k2 ¼ 0.05 s1. Equilibrium is attained within 30 minutes in the absence of a second
ligand ([B]/KB ¼ 0). Addition of an
antagonist (kinetic parameters ¼ k1 ¼ 106 s1/mol, k2 ¼ 0.001 s1)
at concentrations of [B]/KB ¼ 10
and 30, as shown in panel (A). (B)
Displacement of radioligand [A*] by the antagonist B measured at 30 and 240 minutes. It can be seen that a 10-fold error in the potency of the
displacing ligand [B] is introduced into the experiment by inadequate equilibration time.
FIGURE 4.27 FRET signal for a labeled antibody for
colony-stimulating factor 1 receptors and small molecule kinase inhibitor tracer conjugated to a label.
Antibody, tracer, and antagonist were added simultaneously and the FRET signal monitored in real time;
data shown for Ki20227 (316 nM, t1/2 ¼ 330 minutes)
and sunitinib (316 nM, t1/2 ¼ 1 minutes). FRET, fluorescence resonance energy transfer. Data redrawn from
C.M. Uitdhaag, C.M. Sunnen, A.M. van Doornmalen,
N. de Rouw, A. Oubrie, R. Azevedo, Multidimensional
profiling of CSF1R screening hits and inhibitors:
assessing cellular activity, target residence time, and
selectivity in a higher throughput way, J. Biomol.
Screen. 16 (2011) 1007e1017.
occupancy pattern by the radioligand can be observed, in
which the radioligand binds to free receptors quickly
(before occupancy by the slower acting antagonist) and
then a reequilibration occurs as the radioligand and antagonist redistribute according to the rate constants for receptor occupancy of each. The equilibrium for the two
ligands does not occur until >240 minutes. Fig. 4.26B
shows the difference in the measured affinity of the
antagonist at times of 30 and 240 minutes. Fig. 4.27 shows
this effect with fluorescence resonance energy transfer
(FRET) binding where the tracer and antagonist are added
simultaneously and the FRET signal is monitored in real
time. This figure shows that a biphasic binding curve is
seen for the slowly dissociating antagonist Ki20227 and not
for the rapidly dissociating antagonist sunitinib [20]. It can
also be seen from these data that the times thought adequate
from the observation of a single ligand to the receptor (as
that shown in Fig. 4.3) may be quite inadequate compared
to the time needed for two ligands to come to temporal
equilibrium with the receptor. Therefore, in the case of
displacement experiments utilizing more than one ligand,
temporal experiments should be carried out to ensure that
adequate times are allowed for complete equilibrium to be
achieved for two ligands.
4.5 Binding in allosteric systems
As noted earlier in this chapter, there can be dissimulations
between the protein species binding ligands and those
producing pharmacological response (see Figs. 4.1 and
4.2). While pharmacological function is the main activity
monitored in drug discovery, it can sometimes also be
useful to know the receptor species binding allosteric and
orthosteric ligands. There are various models that have
been published to represent the receptor species present in
allosteric systems; one of the first is the Hall model [20,21]
which represents active-state and inactive-state receptors
bound to agonist [A] and allosteric modulator [B]dsee
Fig. 4.28A. This model can be extended to include binding
of signaling protein (such as a G protein)dsee Fig. 4.28B.
88
A Pharmacology Primer
FIGURE 4.28 Allosteric models
showing receptor species present in
system through formation of an
active receptor state (R*)dpanel
(A), Hall Allosteric model [20], or
through formation of an active state
and allowing the receptor to couple
to G-proteins [panel (B)] [21].
Agonist is A, allosteric modulator is
B, receptor is R, and G-protein is G.
A practical problem with extended models to account for
all protein species and activation states is that they become
heuristic, i.e., they require many parameters that cannot be
independently verifieddsee Fig. 3.5 for an example.
However, allosteric binding models can be useful to account for unique behaviors.
A minimal model to account for the protein binding
species in an allosteric system is shown in Fig. 4.29. The
radioligand binding species are [AR], [ARG], [ARBG], and
[ABR]. The factors a, b, g, and s denote the influence of
the various ligands on the receptor (R) and signaling protein species (i.e., G-protein, G) to associate. Specifically, a
is the cooperativity of B imposed on binding of A, g the
cooperativity of G-protein binding imposed by A (efficacy
of A), s the cooperativity of B to G-protein interaction
(efficacy of B), and b the dual cooperativity of G protein
rA ¼
½B=KB ða½A=KA ð1 þ gbs½G=KG ÞÞ þ ½A=KA ð1 þ g½G=KG Þ
½B=KB ða½A=KA ð1 þ gbs½G=KG Þ þ s½G=KG þ 1Þ þ ½A=KA ð1 þ g½G=KG Þ þ ½G=KG þ 1
imposed by binding of A and B (quaternary complex formation). This model can be used to determine the effects of
a modulator on the binding of an orthosteric radioligand
with the following equation (derived in Section 4.7.11):
rB ¼
Binding can provide models of drug effects in receptor
systems and ligand properties. For example, Fig. 4.30
shows the effect of the allosteric modulator Sch527123
(a ¼ 0.1, b ¼ 0.05, g ¼ 30, s ¼ 0.05) on [125I]-CXCL8
binding to CXCR1 receptors [23]; the 125I-CXCL8 binds to
form the [ARG] species, and the data show an incomplete
blockade which the model shows to be residual [ARBG],
[ABR], and [ARG] receptors species binding 125I-CXCL8.
The same allosteric parameters for Sch527123 can be
used to describe the displacement of radioactive Sch527123
by nonradioactive CXCL8. In this case, a modified equation from Eq. (4.26) is used to denote the allosteric molecule as the radioligand ([B*]) and the orthosteric ligand as
the nonradioactive species ([A]) (see Section 4.7.11). Thus,
the fraction of receptor bound to the radioactive allosteric
modulator (rB) is
(4.26)
Fig. 4.31 shows experimental data indicating incomplete blockade by CXCL8 fit to the binding model [23].
The incomplete blockade is caused by the fact that CXCL8
forms a large proportion of [ARBG] which, because
a½A=KA ½B=KB ð1 þ bgs½G=KG Þ þ s½B=KB ½G=KG þ ½B=KB
½A=KA ð1 þ a½B=KB þ g½G=KG ð1 þ abs½B=KB ÞÞ þ ½B=KB ð1 þ s½G=KG Þ þ ½G=KG þ 1
(4.27)
Pharmacological assay formats: binding Chapter | 4
Sch527123 is an allosteric ligand that can bind to the receptor when CXCL8 is also bound, the [ARBG] species
registers as bound radioligand and the blockade is
“incomplete.” Fitting to the binding model enables a conceptual scheme for the antagonist activity of Sch527123 to
emerge as a negative allosteric modulator (NAM) for
CXCR1 effects of the agonist CXCL8. Binding studies
reveal that SCH527123 decreases the binding affinity of the
receptor for CXCL8 but actually promotes receptor
coupling to G-proteins by CXCL8. However, the resulting
CXCL8 ternary complex becomes devoid of signaling
properties, i.e., the resulting ternary complex is sterile from
the standpoint of signaling.
FIGURE 4.29 Simple allosteric binding model showing the relationship
between (R), radioligand (A), allosteric modulator (B), and G-protein (G).
89
Binding can yield insight into allosteric ligand behaviors that may not otherwise be evident. For example, the
NAM for the CXCR2 receptors SB265610 blocks the
binding of the orthosteric CXCR2 agonist 125I-IL-8 [22].
However, binding studies with nonradioactive IL-8 show
that IL-8 is unable to displace radioactive 3H-SB265610
(see Fig. 4.32A); this effect was shown not to be due to
pseudoirreversible binding of SB265610. Experimental
data have shown that in general, SB265610 does not
interfere with orthosteric agonist binding but blocks
response either through negative effects on agonist-receptor
signaling protein coupling or simply by shutting off the
ability of the agonist-bound receptor to signal. Thus,
binding in a low G-protein experimental system would still
allow 3H-SB265610 binding to the receptor even in the
presence of SB265610 (formation of the [ABR] complex);
this would not change the bound radioactivity ([BR]
complex)dsee Fig. 4.32B. In a high G-protein system,
IL-8 would have the power to create the alternative
[ARG] species thus reducing the radioactivity due to
bound 3H-SB265610, i.e., IL-8 will block the binding of
3
H-SB265610 in a high G-protein systemdsee Fig. 4.32.
This is important in the light of the fact that SB265610
blocks the response to chemokines in functional systems.
However, this is also problematic in that there is a disparity
in the potency of SB265610 as a blocker of chemokine
binding versus function; specifically, SB265610 is
considerably more potent in reversing chemokine binding
than it is in reversing chemokine function. This question
can be addressed with the allosteric binding model as well.
Fig. 4.32 shows the effect of SB265610 displacement of
FIGURE 4.30 Interaction of a nonradioactive allosteric modulator Sch527123 (right) and bound radioactive 125I-CXCL8 (left) with CXCR2 receptors
according to Eq. (4.26). Model shown in Fig. 4.30 used to fit data from Ref. [22]. Parameters are a ¼ 0.1, b ¼ 0.05, s ¼ 0.1, g ¼ 50, [A]/KA ¼ 1, [G]/
KG ¼ 3, and KB ¼ 50 pM. In the absence of Sch527123, 97% of the receptor is in the ARG form; in the presence of Sch527123, the receptor species
distribute to BR (33%), BRG (52%) with small amounts of ABR (3%), ABRG (7%), and ARG (3%). The fact that these small amounts of radioligand
binding species (containing A) exist is indicated by the failure of Sch527123 to completely suppress the 125I-CXCL8 signal in the assay (see red arrow).
90
A Pharmacology Primer
FIGURE 4.31 Interaction of nonradioactive CXCL8 (A) and bound radioactive allosteric modulator Sch527123 (B) with CXCR2 receptors according to
Eq. (4.27). Model parameters (Fig. 4.29) are a ¼ 0.17, b ¼ 0.1, s ¼ 300, g ¼ 1, [B]/KB ¼ 1, KA ¼ 1 nM to fit data from Ref. [23]. In the absence of
CXCL8, 100% of the radioactive species is in the BRG form. CXCL8 is an agonist which promotes complexation of the receptor with G-protein. In the
presence of CXCL8, the radioactive species formed are ARG (31%), AR (10%), and ARBG (58%). This latter species contains radioactive Sch527123;
therefore, there is a large residual radioactive signal in the assay (note arrow in red).
FIGURE 4.32 Blockade of allosteric [3H]-SB265610 binding by nonradioactive orthosteric ligand IL-8 on CXCR2 receptors. Panel (A): Experimental
data from Ref. [22] showing the inability of IL-8 to affect binding of [3H]-SB265610 in a low G-protein system. Nonradioactive SB265610 affects binding
of [3H]-SB265610 eliminating the possibility of irreversible [3H]-SB-265610 binding. Panel (B): Model shown in Fig. 4.29 used to fit data from Ref. [22];
parameters are a ¼ 1, b ¼ 1, s ¼ 0.001, g ¼ 10, [B]/KB ¼ 1, KA ¼ 1 nM. The agonist IL-8 promotes receptor coupling to G-protein for a high-affinity
binding. In the presence of low concentrations of G-protein ([G]/KG ¼ 0.01), IL-8 is unable to affect the binding of [3H]-SB265610 because there is
insufficient G-protein to create the high-affinity species ARG; the receptor species are AR (35%), ARG (28%), and R (36%) [panel (C)]. In the presence of
SB265610, the species revert to BR (88%) and ABR (12%); the affinity of SB265610 for this conversion is high [dotted line curve panel (B)]. Panel (D):
In the presence of high amounts of G protein ([G]/KG ¼ 1), IL-8 promotes a high level of ARG (91%) and can affect the binding of [3H]-SB265610 [solid
line curve in panel (B)].
125
I-IL-8 binding in a low G-protein and high G-protein
system. In a low G protein system (as was utilized in the
binding study [22]), SB265610 readily forms the [BR]
complex thereby reducing the bound radioactivity ([AR]
and [ARG] complex). However, in a high G-protein containing system, bound 125I-IL-8 is in the form of a ternary
Pharmacological assay formats: binding Chapter | 4
91
FIGURE 4.33 Interaction of allosteric modulator SB265610 (B) receptor bound to orthosteric radioligand 125I-IL-8 (A) with CXCR2 receptors. Model
shown in Fig. 4.29 used to fit data from Ref. [22]; parameters are a ¼ 0.1, b ¼ 0.1, s ¼ 0.001, g ¼ 10, [A]/KA ¼ 1, KB ¼ 1 nM. The agonist IL-8
promotes receptor coupling to G-protein for a high-affinity binding. In the presence of low concentrations of G-protein ([G]/KG ¼ 0.1), the affinity of
125
I-IL-8 for the receptor is low and the receptor species are AR (35%), ARG (28%), and R (36%) [panel A]. In the presence of SB265610, the species
revert to BR (88%) and ABR (12%); the affinity of SB265610 for this conversion is high (dotted line curve). In the presence of high amounts of G-protein
([G]/KG ¼ 10), 125I-IL-8 promotes a high level of ARG (91%) [panel (B)]. SB265610 must overcome this G-protein complexation to reverse radioligand
binding; thus, there is fall in the observed affinity of SB265610 (solid line curve).
complex ([ARG]) which now requires SB265610 to uncouple the receptor from the G-protein to form the [BR]
complex. This causes a 30- to 100-fold decrease in
SB265610 potency as observed in binding and functional
studiesdsee Fig. 4.33.
4.6 Chapter summary and conclusions
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If there is a means to detect (i.e., radioactivity, fluorescence) and differentiate between protein-bound and free
ligand in solution, then binding can directly quantify the
interaction between ligands and receptors.
Binding experiments are done in three general modes:
saturation, displacement, and kinetic binding.
Saturation binding requires a traceable ligand but directly
measures the interaction between a ligand and a receptor.
Displacement binding can be done with any molecule
and measures the interference of the molecule with a
bound tracer.
Displacement experiments yield an inverse sigmoidal
curve for nearly all modes of antagonism. Competitive,
noncompetitive, and allosteric antagonism can be discerned from the pattern of multiple displacement curves.
l
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Allosteric antagonism is characterized by the fact that it
attains a maximal value. A sensitive method for the
detection of allosteric effects is through studying the kinetics of binding.
Kinetic experiments are also useful to determine the
time needed for attainment of equilibria and to confirm
reversibility of binding.
Agonists can produce complex binding profiles due to
the formation of different protein species (i.e., ternary
complexes with G-proteins). The extent of this phenomenon is related to the magnitude of agonist efficacy and
can be used to quantify efficacy.
While the signal-to-noise ratio can be improved with
increasing the amount of membrane used in binding
studies, too much membrane can lead to depletion of
radioligand with a concomitant introduction of errors
in the estimates of ligand affinity.
The time to reach equilibrium for two ligands and a receptor can be much greater than that required for a single receptor and a single ligand.
Allosteric binding models can be more complex
because allosteric ligands may still allow binding of
radioligand (if the allosteric ligand is a radioligand);
92
l
A Pharmacology Primer
thus, the presence of radioligand does not necessarily
indicate ligand-free receptor.
Allosteric binding models also can be extremely useful
to determine mode of action of modulators and identify
receptor species with varying functions.
4.7 Derivations
l
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Displacement binding: competitive interaction (Section
4.7.1).
Displacement binding: noncompetitive interaction
(Section 4.7.2).
Displacement of a radioligand by an allosteric antagonist (Section 4.7.3).
Relationship between IC50 and KI for competitive antagonists (Section 4.7.4).
Maximal inhibition of binding by an allosteric antagonist (Section 4.7.5).
Relationship between IC50 and KI for allosteric antagonists (Section 4.7.6).
Two-stage binding reactions (Section 4.7.7).
Effect of G-protein coupling on observed agonist affinity (Section 4.7.8).
Effect of excess receptor in binding experiments: saturation binding curve (Section 4.7.9).
Effect of excess receptor in binding experiments:
displacement experiments (Section 4.7.10).
4.7.1 Displacement binding: competitive
interaction
Converting to equilibrium dissociation constants
(i.e., Kd ¼ 1/Ka) leads to the following equation:
r ¼
½AKd
½AKd þ ½B=KB þ 1
(4.32)
4.7.2 Displacement binding: noncompetitive
interaction
It is assumed that mass action defines the binding of the
radioligand to the receptor and that the nonradioactive
ligand precludes binding of the radioligand [A*] to receptor. There is no interaction between the radioligand and
displacing ligand. Therefore, the receptor occupancy by the
radioligand is defined by mass action times the fraction q of
receptor not occupied by noncompetitive antagonist:
r ¼
½A=Kd
$q
½A=Kd þ 1
(4.33)
where Kd is the equilibrium dissociation constant of the
radioligandereceptor complex. The fraction of receptor
bound by the noncompetitive antagonist is given as
(1 q). This yields the following expression for q:
1
q ¼ ð1 þ ½B=KB Þ
(4.34)
Combining Eq. (4.33) and Eq. (4.34) and rearranging
yield the following expression for radioligand bound in the
presence of a noncompetitive antagonist:
r ¼
½A=Kd
½A=Kd ð½B=KB þ 1Þ þ ½B=KB þ 1
(4.35)
The effect of a nonradioactive ligand [B] displacing a
radioligand [A*] by a competitive interaction is shown
schematically as
The concentration that reduces binding by 50% is
denoted as the IC50. The following relation can be defined:
where Ka and Kb are the respective ligandereceptor association constants for radioligand and nonradioactive
ligand. The following equilibrium constants are defined:
½A=Kd
0:5½A=Kd
¼
½A=Kd ðIC50 =KB þ 1Þ þ IC50 =KB þ 1 ½A=Kd þ 1
(4.36)
½R ¼
½A R
½AKa
½BR ¼ Kb ½B½R ¼
Kb ½B½A R
½AKa
(4.28)
(4.29)
Total receptor concentration ½Rtot ¼ ½R þ ½A R þ ½BR
(4.30)
This leads to the expression for the radioactive species
[A * R]/[Rtot] (denoted as r*):
r ¼
½AKa
½AKa þ ½BKb þ 1
(4.31)
It can be seen that the equality defined in Eq. (4.36) is
true only when IC50 ¼ KB (i.e., the concentration of a
noncompetitive antagonist that reduces the binding of a
tracer ligand by 50% is equal to the equilibrium dissociation constant of the antagonistereceptor complex).
4.7.3 Displacement of a radioligand by an
allosteric antagonist
It is assumed that the radioligand [A*] binds to a site separate
from the one binding an allosteric antagonist [B]. Both ligands
have equilibrium association constants for receptor complexes
of Ka and Kb, respectively. The binding of either ligand to the
receptor modifies the affinity of the receptor for the other
Pharmacological assay formats: binding Chapter | 4
ligand by a factor a. There can be three ligand-bound receptor
species, namely, [A * R], [BR], and [BA * R]:
The resulting equilibrium equations are
Ka ¼
½A R
½A½R
(4.37)
Kb ¼
½BR
½B½R
(4.38)
aKa ¼
½A RB
½BR½A
(4.39)
aKb ¼
½A RB
½A R½B
(4.40)
Solving for the radioligand-bound receptor species [A * R]
and [A * RB] as a function of the total receptor species:
ð½Rtot ¼ ½R þ ½A R þ ½BR þ ½A RBÞ yields (4.41)
¼
ðð1=a½BKb Þ þ 1Þ
ðð1=a½BKb Þ þ ð1=aKa Þ þ ð1=a½AKa Kb Þ þ 1Þ
(4.42)
Simplifying and changing association to dissociation
constants (i.e., Kd ¼ 1/Ka) yield (as defined by Ehlert [20]):
r ¼
½A=Kd ð1 þ a½B=KB Þ
½A=Kd ð1 þ a½B=KB Þ þ ½B=KB þ 1
(4.43)
4.7.4 Relationship between IC50 and KI for
competitive antagonists
A concentration of displacing ligand that produces a 50%
decrease in r* is defined as the IC50. The following relation
can be defined:
½A=Kd
0:5½A=Kd
¼
½A=Kd þ 1 ½A=Kd þ IC50 =KB þ 1
(4.44)
From this, the relationship between the IC50 and the
amount of tracer ligand [A*] is defined as [2]
IC50 ¼ KB $ð½A = Kd þ 1Þ
(4.45)
If it cannot be assumed that the free concentration of
binding probe molecule (in most cases a fluorescent) and/or
competing ligand does not change with receptor binding,
then the calculation of Ki values from IC50 values requires a
different procedure [6]. The base equation for the conversion is
Ki ¼
where [I]50 is the free antagonist concentration at 50% inhibition, Kd is the equilibrium dissociation constant of the
fluorescent probeereceptor complex, [A*]50 is the free concentration of fluorescent probe at 50% inhibition, and [R]0
is the free concentration of receptor at 0% inhibition. The
value for [R]0 is obtained from calculating the positive
root of
½R0 þ ½R0 ðKd þ ½AT Þ ½RT ¼ 0
2
½I50
½A50 =kd þ ½R0 =Kd þ 1
(4.46)
(4.47)
where [A*]T and [R]T are the total concentration of fluorescent probe and receptor, respectively. The positive root of
Eq. (4.47) is
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2
½R0 ¼ 0:5 ðKd þ ½AT Þ þ 4½RT Kd ½AT
(4.48)
The conservation equation for total receptor in the
absence of antagonist [B] is
½RT ¼ ½R0 þ ½A R0
½A R þ ½A RB
½Rtot 93
(4.49)
A value for [A * R]0 can be calculated. For the total
fluorescent probe concentration, the following relation
holds:
½AT ¼ ½A0 þ ½A R0
(4.50)
From Eq. (4.50) and obtaining [A * R]0 from Eq. (4.49),
a value for [A*]0 is obtained. A value of [A * R]50 is
then defined as the concentration of tracerereceptor
complex present at 50% inhibition of binding
([A * R]50 ¼ [A * R]0/2). By analogy to Eq. (4.50),
[A*]50 ¼ [A * R]T[A * R]50 ¼ [A*]T[A * R]0/2. The
conservation equation for receptor in the presence of a
concentration of antagonist that produces 50% reduction in
binding is
½RT ½R50 þ ½A R50 þ ½BR50
(4.51)
The value for free receptor at the 50% inhibition
point (defined as [R]50) is given by the mass action
equation for free tracer ligand concentration at 50%
inhibition:
Kd ¼
½R50 ½A50
½A50
(4.52)
By analogy to Eq. (4.50),
I50 ¼ IC50 ½BR50
(4.53)
where IC50 is the concentration of antagonist found to
reduce the binding by 50% under experimental conditions.
Substituting for [BR]50 from Eq. (4.51) with [A * R]50 as
[A * R]0/2 from Eq. (4.52) yields
½I50 ¼ IC50 ½RT þ
Kd ½A R50
þ ½A R50
½A50
(4.54)
94
A Pharmacology Primer
Thus the procedure begins with the determination of
[R]0 [Eq. (4.51)], then [A * R]0 [Eq. (4.52)], and obtaining
[A*]0 [Eq. (4.48)]. This is followed by dividing [A * R]0 by
2 to yield [A * R]50, calculating [R]50 [Eq. (4.52)] which
then allows calculation of [BR]50 [Eq. (4.51)]. The I50 value
then is calculated [Eq. (4.53)]. Substituting for I50, [A*]50,
and [R]0 into Eq. (4.46) allows calculation of the true Ki
value for the antagonist.
The ratio of bound radioligand [A*] in the absence and
presence of an allosteric antagonist [B], denoted by rA*/
rA*B, is given by
(4.55)
The fractional inhibition is the reciprocal, namely, rA*/
rA*B. The maximal fractional inhibition occurs as [B]/
KB/N. Under these circumstances, maximal inhibition is
given by
Maximal Inhibition ¼
½A=Kd þ 1
½A=Kd þ 1=a
(4.56)
(4.57)
This equation reduces to
IC50
(4.62)
KA $c=s
1 þ c=s
Kobs ¼
(4.63)
It can be seen that for nonzero positive values of c/s
(binding promotes formation of R*), Kobs < KA.
4.7.8 Effect of G-Protein coupling on observed
agonist affinity
Receptor [R] binds to agonist [A] and goes on to form a
ternary complex with G-protein [G]:
The equilibrium equations are
½A½R
½AR
(4.64)
½AR½G
½AR
(4.65)
Ka ¼
½Rtot ¼ ½R þ ½AR þ ½ARG
(4.66)
Converting association to dissociation constants (i.e.,
1/Ka ¼ KA):
½ARG
ð½A=KA Þð½G=KG Þ
¼
½Rtot ½A=KA ð1 þ ½G=KG Þ þ 1
(4.67)
The observed affinity according to Eq. (4.67) is
(4.58)
4.7.7 Two-stage binding reactions
Assume that the ligand [A] binds to receptor [R] to produce
a complex [AR], and by that, reaction changes the receptor
from [R] to [R*].
The equilibrium equations are
½A½R
½AR
(4.59)
c
½AR
¼
s ½AR
(4.60)
Ka ¼
½AR
½A=KA
¼
½Rtot ½A=KA ð1 þ c=sÞ þ c=s
The receptor conservation equation is
The concentration of allosteric antagonist [B] that reduces a
signal from a bound amount [A*] of radioligand by 50% is
defined as the IC50:
ð1 þ ð½A=Kd ÞÞ
¼ KB
ð1 þ að½A=Kd ÞÞ
(4.61)
Therefore, the quantity of end product [AR*] formed for
various concentrations of [A] is given as
Kg ¼
4.7.6 Relationship between IC50 and KI for
allosteric antagonists
ð1 þ ½A=Kd Þ
¼ 0:5
½A=Kd ð1 þ aIC50 =KB Þ þ IC50 =KB þ 1
½Rtot ¼ ½R þ ½AR þ ½AR where KA ¼ 1/Ka. The observed equilibrium dissociation
constant (Kobs) of the complete two-stage process is given as
4.7.5 Maximal inhibition of binding by an
allosteric antagonist
rAB ½A=Kd ð1 þ a½B=KB Þ þ ½B=KB þ 1
¼
ð½A=Kd þ 1Þ$ð1 þ a½B=KB Þ
rA
The receptor conservation equation is
Kobs ¼
KA
1 þ ð½G=KG Þ
(4.68)
4.7.9 Effect of excess receptor in binding
experiments: saturation binding curve
The Langmuir adsorption isotherm for radioligand binding
[A*] to a receptor to form a radioligandereceptor complex
[A * R] can be rewritten in terms of one where it is not
assumed that receptor binding produces a negligible effect
on the free concentration of ligand:
AT ½A R Bmax
½A R ¼ (4.69)
AT ½A R þ Kd
Pharmacological assay formats: binding Chapter | 4
where Bmax reflects the maximal binding (in this case, the
maximal amount of radioligandereceptor complex). Under
these circumstances, analogous to the derivation shown in
Section 2.11.4, the concentration of radioligand bound is
½A R2 ½A RðBmax þ ½AT þ Kd Þ þ ½AT Bmax ¼ 0
(4.70)
4.7.11 Derivation of an allosteric binding
model
Referring to Fig. 4.28, the following receptor species can be
identified:
½ARG ¼
One solution to Eq. (4.70) is
1 ½A R ¼
AT þ Kd þ Bmax
2 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
(4.71)
q
2
AT þ Kd þ Bmax 4 AT Bmax
4.7.10 Effect of excess receptor in binding
experiments: displacement experiments
The equation for the displacement of a radioligand [A*] by
a nonradioactive ligand [B] can be rewritten in terms of one
where binding does depleteh the iamount of radioligand in
Afree
the medium (no change in
):
AT ½A R Bmax
½A R ¼ AT ½A R þ Kd þ ½B=KB
(4.72)
where Bmax reflects the maximal formation of radioligande
receptor complex. Under these circumstances, the concentration of radioligand bound in the presence of a nonradioactive ligand displacement is
2
½A R ½A R Bmax þ AT þ Kd ð1 þ ½B=KBÞ
þ AT Bmax ¼ 0:
(4.73)
1 AT þ Kd ð1 þ ½B=KB Þ þ Bmax
¼
2
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2
ffi
AT þ Kd ð1 þ ½BKB Þ þ Bmax 4 AT Bmax
(4.74)
rA ¼
½R ¼
½ARBG
abd½BKb
½ARBG
abgs½BKb ½AKa ½GKg
(4.75)
(4.76)
½RG ¼
½ARBG
abgs½BKb ½AKa
(4.77)
½AR ¼
½ARBG
abgs½BKb ½GKg
(4.78)
½BR ¼
½ARBG
abgs½AKa ½GKg
(4.79)
½ABR ¼
½ARBG
bgs½GKg
(4.80)
½BRG ¼
½ARBG
abg½AKa
(4.81)
The receptor conservation equation is
½Rtot ¼ ½ARBG þ ½ARG þ ½AR þ ½ABR þ ½RG
þ ½BRG þ ½BR þ ½R
(4.82)
Converting equilibrium association constants to equilibrium dissociation constants (i.e., Ka ¼ KA), the receptor
conservation equation can be reexpressed as
½Rtot ¼ ½B=KBð1 þ 1 s½G = KG þ a½A = KAð1
One solution to Eq. (4.73) is
½A R
95
þbgs½G = KGÞÞ þ ½A=KAð1 þ g½G = KGÞ þ 1 (4.83)
When the radioligand is [A], then the radioligand bound
species are [ARBG], [ARG], [ABR], and [AR]. The fraction of receptors bound by radioligand (rA*) is this sum
divided by [Rtot] which is
½B=KB ða½A=KA ð1 þ gbs½G=KG ÞÞ þ ½A=KA ð1 þ g½G=KG Þ
½B=KB ða½A=KA ð1 þ gbs½G=KG Þ þ s½G=KG þ 1Þ þ ½A=KA ð1 þ g½G=KG Þ þ ½G=KG þ 1
(4.84)
96
A Pharmacology Primer
This equation calculates the effect of a nonradioactive
allosteric modulator on the binding of a radioactive orthosteric ligand. If the radioactive species is the allosteric
rB ¼
modulator ([ARBG], [ABR], [BRG], [BR]), then Eq. (4.84)
can be rewritten to yield (rB*) as
a½A=KA ½B=KB ð1 þ bgs½G=KG Þ þ s½B=KB ½G=KG þ ½B=KB
½A=KA ð1 þ a½B=KB þ g½G=KG ð1 þ abs½B=KB ÞÞ þ ½B=KB ð1 þ s½G=KG Þ þ ½G=KG þ 1
References
[1] E.C. Hulme, Receptor Biochemistry: A Practical Approach, Oxford
University Press, Oxford, 1990.
[2] I.M. Klotz, Ligand-Receptor Energetics: A Guide for the Perplexed,
John Wiley and Sons, New York, NY, 1997.
[3] L.E. Limbird, Cell Surface Receptors: A Short Course on Theory and
Methods, Martinus Nijhoff, Boston, MA, 1995.
[4] S. Litschig, F. Gasparini, D. Rueegg, N. Stoehr, P.J. Flor,
I. Vranesic, L. Prezeau, J.P. Pin, C. Thomsen, R. Kuhn, CPCCOEt, a
noncompetitive metabotropic glutamate receptor 1 antagonist, inhibits receptor signaling without affecting gluta mate binding, Mol.
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[5] W.-J. Chen, S. Armour, J. Way, G. Chen, C. Watson, P. Irving, et al.,
Expression cloning and receptor pharmacology of human calcitonin
receptors from MCF-7 cells and their relationship to amylin receptors, Mol. Pharmacol. 52 (1997) 1164e1175.
[6] Y.C. Cheng, W.H. Prusoff, Relationship between the inhibition
constant (Ki) and the concentration of inhibitor which causes 50
percent inhibition (I50) of an enzymatic reaction, Biochem. Pharmacol. 22 (1973) 3099e3108.
[7] Z. Nikolovska-Coleska, R. Wang, X. Fang, H. Pan, Y. Tomita,
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XIAP BIR3 domain using fluorescence polarization, Anal. Biochem. 332 (2004) 261e273.
[8] I. Sabroe, M.J. Peck, B.J. Van Keulen, A. Jorritsma, G. Simmons,
P.R. Clapham, A small molecule antagonist of chemokine receptors
CCR1 and CCR3, J. Biol. Chem. 275 (2000) 25985e25992.
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allosteric interactions on muscarinic receptors, Eur. J. Pharmacol.
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[10] J. Jakubic, E.E. El-Fakahany, Allosteric modulation of muscarinic
acetylcholine receptors, Pharmaceuticals (Basel) 3 (9) (2010)
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[11] J. Jakubic, L. Bacakova, E.E. El-Fakahany, S. Tucek, Positive
cooperativity of acetylcholine and other agonists with allosteric ligands on muscarinic acetylcholine receptors, Mol. Pharmacol. 52
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[12] J. Proska, S. Tucek, Mechanisms of steric and cooperative interactions of alcuronium on cardiac muscarinic acetylcholine receptors, Mol. Pharmacol. 45 (1994) 709e717.
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at G-protein coupled receptors using radioligand assays, in: S.J. Enna
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York, NY, 2000, pp. 1.22.21e1.22.40.
[14] S. Lazareno, N.J.M. Birdsall, Detection, quantitation, and verification of allosteric interactions of agents with labeled and unlabeled
ligands at G protein-coupled receptors: interactions of strychnine and
acetylcholine at muscarinic receptors, Mol. Pharmacol. 48 (1995)
362e378.
[15] R.A. Leppick, S. Lazareno, A. Mynett, N.J. Birdsall, Characterization of the allosteric interactions between antagonists and amiloride
at the human a2A-adrenergic receptor, Mol. Pharmacol. 53 (1998)
916e925.
[16] V.A. Florio, P.C. Sternweis, Mechanism of muscarinic receptor action on Go in reconstituted phospholipid vesicles, J. Biol. Chem. 264
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[17] P. Gerwins, C. Nordstedt, B.B. Fredholm, Characterization of
adenosine A1 receptors in intact DDT1 MF-2 smooth muscle cells,
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Chapter 5
Drug targets and drug-target molecules
A very interesting set of compounds that were waiting for
the right disease.
Jerome Horwitz.
AZT stood up and said, ’Stop your pessimism. Stop your
sense of futility. Go back to the lab. Go back to development. Go back to clinical trials. Things will work.’
Samuel Broder.
Remember the Three Princes of Serendip who went out
looking for treasure? They didn’t find what they were
looking for, but they kept finding things just as valuable.
That’s serendipity, and our business [drugs] is full of it.
George W(ilhelm) Merck.
5.1 Defining biological targets
In a target-based system, the chemical end point is clearly
defined, that is, a molecule with a desired (agonism, antagonism) activity on the biological target. In some cases, the target
may be clearly defineddas for the BCReABL kinase inhibitor Gleevec, which inhibits a constitutively active kinase
known to be present only in patients with chronic myelogenous leukemia. In other cases, the endogenous players for a
biological target may not be known, yet a synthetic molecule
with activity on the target still may be thought to be of value
(orphan receptors). Also, there are combinations of biological
targets that could themselves become new phenotypic targets
(i.e., homodimers, heterodimers) and combinations of targets
and accessory proteins that could constitute a new target. It is
worth considering all these ideas in the context of the definition of a therapeutically relevant biological target.
Targets that have no known endogenous ligands are
known as “orphan” receptors, and there are still many such
receptors in the genome. A process of “deorphanization,”
either with techniques such as reverse pharmacology (in
silico searches of databases to match sequences with known
receptors) or with ligand fishing with compound collections
and tissue extracts, has been implemented over the past 20
years, yielding a list of newly discovered pairings of ligands and receptors (see Table 5.1; [1]). As chemical tools
for such receptors are discovered, they can be used in a
chemical genomic context to associate these receptors with
A Pharmacology Primer. https://doi.org/10.1016/B978-0-323-99289-3.00011-7
Copyright © 2022 Elsevier Inc. All rights reserved.
diseases. A variety of tools have been employed in recent
years to “deorphanize” an increasing number of orphan
receptors; Fig. 5.1 shows how orphan receptors are forming
a considerable portion of published data on receptor drug
targets [2].
Once an endogenous ligand for a target is known, there
may still be physiological mechanisms that create texture
with that target which may not be captured in a recombinant system. Biological phenotype overrides genotype, as
a single gene can be expressed in different host cells and
take on different functions and sensitivities to molecules.
One such mechanism is homo- or heterodimerization of
receptors.
For proteins such as tyrosine kinase receptors, dimerization (the association of two receptors to form a new
species in the membrane) is a well-known mechanism of
action [3]. Increasingly, this has also been shown for
GPCRs, and evidence suggests that this phenomenon may
be relevant to drug discovery [4]. The relevance comes from
the acquisition of new drug-sensitive phenotypes for existing
receptors upon dimerization. These new phenotypes can take
the form of increased sensitivity to agonists. For example,
recombinant systems containing transfected angiotensin II
receptors can be insensitive to angiotensin (subthreshold
level of receptor expression) until bradykinin receptors are
cotransfected into the system. When this occurs, the angiotensin response appears (angiotensin sensitivity increases
through the formation of an angiotensinebradykinin receptor heterodimer); see Fig. 5.2A [5]. Such heterodimerization
may have relevance to the observation that an increased
number of bradykinin receptors and angiotensinebradykinin
receptor heterodimers are present in women with preeclampsia (a malady associated with abnormal vasoconstriction) [6]. Similarly, chemokines show a 10- to 100-fold
increased potency on a heterodimer of CCR2 and CCR5
receptors than with either receptor alone [7]. Oligomerization can be especially prevalent among some receptor types
such as chemokine or opioid receptors. A historical mystery
in the opioid field had been the question of how only three
genes for opioid receptors could foster so many opioid receptor phenotypes in tissues (defined as m1, m2, d1, d2, k1,
k2, k3), until it became clear that opioid receptor heterodimerization accounted for the diversity. This latter receptor
family illustrates another possible therapeutic application of
97
98
A Pharmacology Primer
TABLE 5.1 Deorphanized receptors for cardiovascular function.
Orphan receptor
Ligand
Cardiovascular effect
UT (GPR14, SENR)
Urotensin II
Vasoconstriction, cardiac inotropy
Mas
Angiotensin (1e7)
Antidiureses, vasorelaxation
GPR66 (TGR1, FM3)
Neuromedin U
Regional vasoconstriction, inotropy
APJ
Apelin
Vasoconstriction, cardiac inotropy
PTH2
TIP-39
Renal vasodilatation
GPR10 (GE3, UHR-1)
Prolactin rel. peptide
Regulation of BP
OXR (HFGAN72)
Orexin A, B
Regulation of BP
GPR103 (HLWAR77)
RF-amides
Regulation of BP
TA
Trace amines (tyramine)
Vasoconstriction
GPR38
Motilin
Vasodilatation
GHS-R
Ghrelin
Vasodilatation
LGR7,8
Relaxin
Cardiac inotropy, vasodilatation
CRF1/2
Urocortin
Vasodilatation
Edg-1 (LPB1)
Sphingosine-1-phosphate
PLC, MAPK activation
Edg-2,4,7 (LPA1e3)
Lysophosphatidic acid
DNA synthesis
G2A
Lysophosphatidylcholine
Macrophage function
P2Y12 (SP1999)
ADP
Platelet aggregation
HM74/-A
Nicotinic acid
Lipid lowering, antilipolytic
GOR40
Medium chain fatty acids
Insulin regulation
AdipoR1,R2
Adiponectin
Fatty acid metabolism
From S.A. Douglas, E.H. Ohlstein, D.G. Johns. Techniques: cardiovascular pharmacology and drug discovery in the 21st century. Trends
Pharmacol. Sci. 25 (2004) 225e233.
FIGURE 5.1 There is a growing number of publications on orphan receptors as potential drug targets.
Redrawn from A.S. Hauser, M.M. Attwood, M. RaskAndersen, H.B. Schiöth, D.E. Gloriam, Trends in
GPCR drug discovery: new agents, targets and indications, Nat. Rev. Drug Discov. 16 (2017) 829e842.
dimerization, namely, the acquisition of new drug sensitivity. For example, the agonist 60 -guanidinoaltrindole (60 GNTI) produces no agonist response at d-opioid receptors
and very little at k-opioid receptors. However, this agonist
produces powerful responses on the heterodimer of d- and kopioid receptors (see Fig. 5.2B) [8]. Interestingly, the
responses to 60 -GNTI are blocked by antagonists for either
d- or k-opioid receptors. Moreover, 60 -GNTI produces
analgesia only when administered into the spinal cord,
demonstrating that the dimerization is organ specific and that
reductions in side effects of agonists (and antagonists) may
be achieved through targeting receptor dimers. In the case of
Drug targets and drug-target molecules Chapter | 5
99
FIGURE 5.2 Acquisition of drug phenotype with receptor heterodimerization. (A) Cells transfected with a subthreshold level of angiotensin I receptor
(no response to angiotensin; open circles) demonstrate response to the same concentrations of angiotensin upon cotransfection of bradykinin 1 receptors
(filled circles). (B) The opioid agonist 60 -GNTI produces no response in human embryonic kidney cells transfected with d-opioid receptors (open squares)
and little response on cells transfected with k-opioid receptors (open circles). However, cotransfection of d- and k-opioid receptors produces a system
responsive to 60 -GNTI (filled circles). 60 -GNTI, 60 -guanidinonaltrindole. Redrawn from S. AbdAlla, H. Lother, U. Quitterer, At1-receptor heterodimers
show enhanced G-protein activation and altered receptor sequestration, Nature 407 (2000) 94e98; (B) Redrawn from M. Wildoer, J. Fong, R.M. Jones,
M.M. Lunzer, S.K. Sharma, E. Kostensis, A heterodimer-selective agonist shows in vivo relevance of G-protein coupled receptor dimers, Proc. Natl. Acad.
Sci. U.S.A. 102 (2005) 9050e9055.
60 -GNTI, reduced side effects with spinal analgesia are the
projected drug phenotype.
The systematic study of drug profiles on receptor dimers
is difficult, although controlled expression of receptor
levels through technologies such as the baculovirus
expression system provides a practical means to begin to do
so (vide infra). The study of receptor association also is
facilitated by technologies such as bioluminescence resonance energy transfer (BRET) and fluorescence resonance
energy transfer (FRET) [9]. BRET monitors energy transfer
between a bioluminescent donor and a fluorescent acceptor
(each on a C-terminal tail of a GPCR) as the two are
brought together through dimerization. This technique requires no excitation light source and is ideal for monitoring
the real-time interaction of GPCR interaction in cells.
FRET enables observation of energy transfer between two
fluorophores bound in close proximity to each other. The
change in energy is dependent upon the distance between
the donor and acceptor fluorophores to the sixth power,
making the method sensitive to very small changes in
distance. When the fluorophores are placed on the
C-terminal end of GPCRs, interaction between receptors
can be detected. As homo- and heterodimerization is
studied, the list of receptors observed to utilize this mechanism is growing; Table 5.2 shows a partial list of the receptors known to form dimers with themselves
(Table 5.2A) or other receptors (Table 5.2B). The list of
phenotypes associated with these dimerization processes is
also increasing. With the emergence of receptor dimers as
possible therapeutic targets have developed parallel ideas
about dimerized ligands.
Drug targets can be complexes made up of more than
one gene product (i.e., integrins, nicotinic acetylcholine ion
channels). Thus, each combination of targets could be
considered a target in itself [10]. Some of these phenotypes
may be the result of proteineprotein receptor interactions
[11e13]. For example, the human calcitonin receptor has a
distinct profile of sensitivity to and selectivity for various
agonists. Fig. 5.3A shows the relative potency of the human
calcitonin receptor to the agonists human calcitonin and rat
amylin; it can be seen that human calcitonin is a 20-fold
more potent agonist for this receptor than is rat amylin
[11]. When the antagonist AC66 is used to block responses,
both agonists are uniformly sensitive to blockade
(pKB ¼ 9.7; Fig. 5.3B). However, when the protein
RAMP3 (receptor activity modifying protein type 3) is
coexpressed with the receptor in this cell, the sensitivity to
agonists and antagonists completely changes. As seen in
Fig. 5.3C, the rank order of potency of human calcitonin
and rat amylin reverses, such that rat amylin is now
threefold more potent than human calcitonin. Similarly, the
sensitivity of responses to AC66 is reduced by a factor of
seven when amylin is used as the agonist (pKB ¼ 8.85;
Fig. 5.3D). It can be seen from these data that the phenotype of the receptor changes when the cellular milieu into
which the receptor is expressed changes. RAMP3 is one of
100
A Pharmacology Primer
TABLE 5.2 Homo- and heterodimeric receptors.
(A) Homooligomers
Histamine H2
Somatostatin SSTR1B
AT1 angiotensin II
Luteinizing horm./hCG
Somatostatin SSTR1C
b2-adrenoceptor
Melatonin MT1
Somatostatin SSTR2A
Bradykinin B2
Melatonin MT2
Thyrotropin
Chemokine CCR2
Muscarinic Ach M2
Vasopressin V2
Adenosine A1
Chemokine CCR5
Muscarinic Ach M3
IgG hepta
Chemokine CXCR4
m-Opioid
Gonadotropin rel. Horm.
Dopamine D1
m-Opioid
Metabotropic mGluR1
Dopamine D2
k-Opioid
Metabotropic mGluR2
Dopamine D3
Serotonin 5-HT1B
Ca2þ sensing
Histamine H1
Serotonin 5-HT1D
GABAB(2)
GABAB(1)
Somatostatin SSTR1A
(B) Heterooligomers
5-HT1B
Plus
5-HT1D
SSTR2A
Plus
SSTR1B
Adenosine A1
Plus
Dopamine D1
SSTR1A
Plus
m-Opioid
Adenosine A1
Plus
mGluR1
SSTR1A
Plus
SSTR1C
Adenosine A1
Plus
Purinergic P2Y1
SSTR1B
Plus
Dopamine D2
Adenosine A2
Plus
Dopamine D2
T1R1 a.a. taste
Plus
T1R3 a.a. taste
Angiotensin AT1
Plus
Angiotensin AT2
T1R2 a.a. taste
Plus
T1R3 a.a. taste
CCR2
Plus
CCR5
-Opioid
Plus
k-Opioid
Dopamine D2
Plus
Dopamine D3
m-Opioid
Plus
m-Opioid
GABAB(1)
Plus
GABAB(2)
-Opioid
Plus
b2-Adrenoceptor
Muscarinic M2
Plus
Muscarinic M3
k-Opioid
Plus
b2-adrenoceptor
Melatonin MT1
Plus
Melatonin MT2
From S.R. George, B.F. O’Dowd, S.P. Lee. G-protein-coupled receptor oligomerization and its potential for drug discovery. Nat. Rev. Drug Discov. 1 (2002)
808e820.
a family of proteins that affect the transport, export,
and drug sensitivity of receptors in different cells.
The important question for the drug development process
is this: If a given receptor target is thought to be therapeutically relevant, what is the correct phenotype for
screening? As can be seen from the example with the human calcitonin receptor, if an RAMP3 phenotype for the
receptor is the therapeutically relevant phenotype, then
screening in a system without RAMP3 coexpression would
not be useful.
5.2 Specific types of drug targets
It is worth discussing the differences between the most
common drug targets employed in the drug discovery
process.
5.2.1 G-protein-coupled receptors
Approximately 35% of all known approved drugs target Gprotein-coupled receptors (GPCRs) since these are pharmacologically tractable (conveniently residing on the cell
membrane) and control a myriad of cell processes. In terms
of clinical success rates on GPCRs, 78% of drugs are
successful in Phase I, 39% in Phase II, and 29% in Phase
III, somewhat higher than the same totals for other target
classes. Historically these receptors were named after their
most prominent signaling partners, namely G proteins but
studies in recent years have shown that these receptors
interact with other important signaling systems in the cell
including b-arrestin. Therefore, perhaps a more inclusive
name for this target would be based on their structure,
specifically seven transmembrane domains spanning the
Drug targets and drug-target molecules Chapter | 5
101
FIGURE 5.3 Assumption of a new
receptor phenotype for the human
calcitonin receptor upon coexpression
with the protein RAMP3. (A) Melanophores transfected with cDNA for
human calcitonin receptor type 2 show
a distinct sensitivity pattern to human
calcitonin and rat amylin; hCAL is 20fold more potent than rat amylin. (B) A
distinct pattern of sensitivity to the
antagonist AC66 also is observed;
both agonists yield a pKB for AC66 of
9.7. (C) Coexpression of the protein
RAMP3 (receptor activity modifying
protein type 3) completely changes the
sensitivity of the receptor to the agonists. The rank order is now changed
such that amylin has a threefold greater
potency than human calcitonin. (D)
This change in phenotype is carried
over into the sensitivity to the antagonist. With coexpression of RAMP3,
the pKB for AC66 changes to 8.85
when rat amylin is used as the agonist.
Data redrawn from S.L. Armour, S.
Foord, T. Kenakin, W.-J. Chen,
Pharmacological characterization of
receptor activity modifying proteins
(RAMPs) and the human calcitonin
receptor, J. Pharmacol. Toxicol.
Methods 42 (1999) 217e224.
cell membrane (7 transmembrane receptors (7TMRs)). The
activation of G proteins by GPCRs is discussed in other
portions of this book (i.e., see Fig. 2.8). In general, GPCRs
are the largest family of human membrane proteins (z800
receptors of which approximately half being olfactory receptors) activated by a wide range of stimuli (ions, small
molecules, lipids, peptides, proteins, and even light).
GPCRs are Nature’s prototype allosteric protein since they
bind a ligand in the intracellular space to alter the protein as
it interacts with another species in the cytoplasm of the cell.
As discussed in Chapter 8, allosteric mechanisms have
unique properties and these translate to the general mode of
action of GPCRs. Specifically, these are (1) pleiotropic
interaction with multiple cytosolic signaling partners and
(2) the ability to selectively channel the ligand signal to
some of these at the expense of others, i.e., this is allosteric
probe dependence also referred to as ‘biased signaling.’
This makes GPCRs an extremely versatile drug target with
the ability to control a wide range of cell functions selectively. GPCRs are classified in many ways, one being the
nature of the signaling mechanisms they mediate. There are
a number of these receptors where these mechanisms are
not yet known or at least the natural agonist for the receptor
controlling the signaling is not known (orphan receptors).
Currently some examples of orphan receptors prosecuted
for therapeutic activity are GPR119 for the treatment of
diabetes, leucine-rich repeat-containing GPCR 4 (LGR4)
and LGR5 for the treatment of gastrointestinal disease,
GPR35 for the treatment of an allergic inflammatory
condition, GPR55 as an antispasmodic target, the protooncogene Mas (MAS) for the treatment of thrombocytopenia, and GPR84 for the treatment of ulcerative colitis. Of
the GPCR established families, most drugs are found for
opioid, acetylcholine, 5-hydroxytryptamine, histamine, and
adrenoceptors. However, there are large families of GPCRs
with as yet untapped potential for drug activity including
protein chemokine receptors, lipid receptors, Class B1
peptide receptors, adhesion receptors, amino acid receptors,
and sensory receptors. While historically GPCR drugs have
targeted established diseases such as hypertension, allergy,
analgesics, schizophrenia, and depression, this class has
now expanded into new areas such as Alzheimer’s disease,
obesity, multiple sclerosis, smoking cessation, short bowel
syndrome, and hypocalcemia. Since GPCRs mediate
102
A Pharmacology Primer
several neurotransmitter pathways (glutamatergic, serotoninergic, adrenergic, and peptidergic) they are key targets
for central nervous system diseases; however, more indications for metabolic diseases such as diabetes and
treatment of cancer are being pursued.
5.2.2 Ion channels
Of the estimated 400 ion channels in the human genome,
few have been therapeutically exploited. However, the
widespread tissue distribution of ion channels and the huge
number of physiological effects mediated by this protein
complex make ion channels an important drug target in
discovery. Ion channels are transmembrane proteins that
have a gated water-filled pore (controlling the active flow of
ions) that, in turn, controls the voltage potential across cell
membranes. Channels are classified as either voltage or
ligand gated depending on the primary stimulus that leads
to channel opening and closing. A wide range of ligands
from capsaicin (TRP vanilloid 1 channel, TRPV1), menthol
(TRP melastatin 8 channel, TRPM8) to the benzodiazepine
diazepam (g-aminobutyric acid class A (GABAA)) are
active on ion channels but there are a large number of ion
channels for which there is no operable ligand thus opening
therapeutic possibilities.
In general most ion channels are composed of four or
five helices that fit together to form a barrellike structure to
create the water-filled pore through the membrane. This
responds to chemical stimuli, temperature changes, or
mechanical forces to cause ions to flow in or out of cells.
Many ion channels possess a selectivity filter to control
which ions utilize the channel as well as a gating mechanism that controls the opening and closure of the pore
through conformational changes of the channel protein; this
is combined with a sensor mechanism that responds to
stimuli. Other modules bind ligands and accessory proteins
to produce complex controldsee Fig. 5.4. Ion transfer
through channels is extremely fast being on the order of
100 million ions per second yet with a fidelity for ion type
of 10,000 to 1. There are a number of ‘channelopathies’
that indicate how important ion channels are to normal
physiology and many diseases are known to originate from
channel malfunction. Some of these are Cav channels for
retinal disease, Nav channels for epilepsy, cardiac arrhythmias and pain, Kv channels for seizures, voltage-gated
potassium channel subfamily Q (KCNQ) channels for
deafness and epilepsy, TRP polycystic (TRPP) channels
for renal cysts, inward rectifier potassium (Kir) channels for
kidney transport and hypoglycemia, and TRP mucolipin
(TRPML) channels for NiemannPick disease.
In terms of drug discovery, screening for drugs on ion
channels utilizes ligand binding, ion flux assays, fluorescence readouts, flash luminescence assays, and automated
electrophysiological assays (i.e., ionWorks). At present
many of the drugs active on ion channels are relatively
unselective and/or state-independent modulators thereby
implying that these compounds bind to somewhat
conserved regions of the channel pore domainsdsee
Table 5.3. This being the case, there have been efforts to
target more selective agents, i.e., nonpore domain binding
FIGURE 5.4 Basic structural components of an ion channel showing the pore region, filter, and gate (left). Panel on right shows an example of a single
ion channel recording showing a cycle of opening and closing in response to a repeated current gating trigger.
Drug targets and drug-target molecules Chapter | 5
TABLE 5.3 Drugs target ion channels.
Channel
Drug
Indication
L-type Cav
Verapamil, Diltiazem,
Amlodipine, Nifedipine
Hypertension
Gabapentin, Pregabalin
Pain
hERG
Sotalol
Arrhythmia
Nav
Flecainaide
Arrhythmia
Cav
Ziconotide
Severe pain
Nav
Lidocaine, Bupivacaine
Local
Anesthetic
Nav
Lamotrigine
Epilepsy,
Bipolar
Nav
Riluzole
Amyotrophic
Lateral
sclerosis
Nav
Phenytoin, Lacosamide,
Carbamazepine
Epilepsy
KCNQ2/3
Flupirtine, Retigabine,
Epilepsy
GABAA
Diazepam
Depression
nAChR
Varenicline
Smoking
cessation
compounds (for example, through binding to the subunits
of voltage-gated calcium channels or even through targeting a particular channel state), for possible greater
selectivity.
103
Enzyme inhibitors change an ongoing physiological
process; therefore their effect is contingent upon how active
that process is. For example, the phosphodiesterase inhibitor III fenoximone produces positive inotropy in vivo
when the heart is activated by adrenergic agonists producing cyclic AMP. Normally cyclic AMP is rapidly
degraded by the enzyme but an inhibitor increases cyclic
AMP levels in the heart which then promotes the inotropy.
However, in vitro fenoximone does nothing to an isolated
heart muscle because that pathway is not activated.
Enzyme inhibitors are a rich source of drugs. Historically, one of the earliest enzyme inhibitors was described
by Hippocrates (460e377 BCE) in the form of a pack of
willow leaves for gout (now known to contain salicin, an
analog of aspirin), an inhibitor of cyclooxygenase.
Although there are allosteric enzyme activators (vide infra),
most drugs related to enzymes are inhibitors; a partial list of
enzyme inhibitor drugs is shown in Table 5.4.
The activity of enzymes is described by a kinetic model
culminating in the MichaeliseMenten equation. Derived by
Leonore Michaelis and Maude Menten and published in
1912, this is one of the most important equations in pharmacology and biochemistry. It is useful to derive this
relationship as it forms the basis of how we utilize enzyme
inhibitors in therapy. The enzyme (E) binds substrate (S) to
form an enzymeesubstrate complex (ES) with reversible
rates of onset (k1) and offset (k1). This complex then goes
on to regenerate the enzyme and form a product (P) with a
rate constant k2. Enzyme inhibitors (I) can bind either to the
enzyme with an association rate constant of ki1 or to the
enzymeesubstrate complex with an association rate constant of ki2; the scheme is shown below.
5.2.3 Enzymes
Biology and physiology is based on chemical and
biochemical reactions of the form reactants interacting with
an operator to form products; enzymes are some of Nature’s
most efficient operators. For example, the spontaneous
transformation of adenosine to inosine with no operator is
nearly nonexistent and has a rate constant of 120 years.
However, in the presence of the enzyme adenosine deaminase, the rate constant becomes 370 s; this is a 2.1
quintillion-fold (2,100,000,000,000) enhancement. Enzymes do this through one of three ways:
1. Create an environment that stabilizes the transition state
(straining the substrate)dto provide distorted to energy
needed for complete transition
2. Providing alternative pathway for substrate (temporary
reaction with substrate to form enzymeesubstrate complex that would be impossible in absence of enzyme).
3. Reduce reaction entropy by bringing substrates together
in the correct orientation to react.
(5.1)
An equilibrium condition is defined whereby the rate of
ES formation equals the rate of ES degradation.
Rate of ES formation ¼ k1 ½S½E
(5.2)
Rate of ES dissociation ¼ k1 ½ES þ k2 ½ES
(5.3)
At equilibrium k1 ½S½E ¼ k1 ½ES þ k2 ½ES
(5.4)
The enzyme conservation equation is:
½Etotal ¼ ½E þ ½ES þ ½EI þ ½ESI
(5.5)
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A Pharmacology Primer
TABLE 5.4 Enzyme inhibitor drugs.
Drug
Target enzyme
Disease indication
Acetazolamide
Carbonic anhydrase
Glaucoma
Acyclovir
Viral DNA polymerase
Herpes
Agenerase
Viral protease
AIDS
Amprenavir
HIV protease
AIDS
Allopurinol
Xanthine Oxidase
Gout
Argatroban
Thrombin
Cardiovascular disease
Aspirin
Cyclooxygenase
Inflammation/pain/fever
Amoxicillin
Penicillin binding proteins
Bacterial infection
Carbidopa
Dopa decarboxylase
Parkinson’s disease
Celebrex
Cyclooxygenase-2
Inflammation/pain/fever
Clavulanate
b-lactamase
Bacterial resistance
Combivir
Viral reverse transcriptase
AIDS
Digoxin
Naþ/K þ ATPase
Heart failure
Dutasteride
5-A reductase
Benign prostate hyperplasia
Efavirenz
HIV reverse transcriptase
AIDS
Etoposide
Topoisomerase II
Cancer
Episteride
Steroid 5a-reductase
Benign prostate hyperplasia
Fluorouracil
Thymidylate synthase
Cancer
Leflunomide
Dihydroorotate dehydrogenase
Inflammation/pain/fever
Levitra
Phosphodiesterase V
Erectile dysfunction
Lisinopril
Angiotensin converting enzyme
Hypertension
Lovastatin
HMG-CoA reductase
Cardiovascular disease
Methotrexate
Dihydrofolate reductase
Cancer, immunosuppression
Nitecapone
Catechol-o-methyl transferase
Parkinson’s disease
Norfloxacin
DNA gyrase
Urinary tract infection
Omeprazole
Hþ/K þ ATPase
Peptic ulcer
PALA
Aspartate transcarbamoylase
Cancer
Raltegravir
Viral integrase
AIDS
Relenza
Viral neuraminidase
Influenza
Sorbitol
Aldose reductase
Diabetic retinopathy
Tacrine
Acetylcholinesterase
Alzheimer’s disease
Trazodone
Adenosine deaminase
Depression
Trimethoprim
Bacterial dihydrofolate reductase
Bacterial infection
Tykerb
Erb-2/EGFR
Breast cancer
Equilibrium equations are defined for the enzyme inhibitor complexes [EI] and [ESI]. Substitution into the
enzyme conservation equation defines all species in terms
of [E], [ES], and total enzyme [Etotal]. The association
constants for enzymeeinhibitor complexes are converted to
dissociation constants (KI1 ¼ 1/ki1 and KI2 ¼ 1/ki2). The
equilibrium equations for the inhibited species are:
K1
I1 ¼ ½EI=ð½E½IÞ
(5.6)
½EI ¼ ½E½I=KI1
(5.7)
Drug targets and drug-target molecules Chapter | 5
K1
I2 ¼ ½ES=ð½ES½IÞ
(5.8)
½ESI ¼ ½ES½I=KI2
(5.9)
The enzyme conservation equation can be rewritten as:
½E ¼ ½Etotal ½ES ½E½I=KI1 ½ES½I=KI2
(5.10)
The equation for [E] is then:
½E ¼ ½Etotal ½ESð1 þ ½I = KI2 Þ=ð1 þ ½I = KI1 Þ
(5.11)
Defining the MichaeliseMenten constant Km as
(k-1 þ k2)/k1 and isolating [ES]:
½ES $ Km ¼ ðð½S½Etotal Þ = ð1 þ ½I = KI1 ÞÞ ðð½S½ESÞ
ð1 þ ½I = KI2 Þ = ð1 þ ½I = KI1 ÞÞ
(5.12)
An enzyme velocity for the rate of reaction at time zero
is defined (V0) which essentially is the complete conversion
of [ES] species to produce product (there is no time for the
back reaction to take place to regenerate [ES]) as V0 ¼ k2
[ES]. Defining [ES] as V0/k2 and substituting for [ES]
yields:
V0 ¼ ðk2 ð½S = ð1 þ ½I = KI1 ÞÞ½Etotal Þ=ð½Sð1 þ ½I=KI2 Þ =
ð1 þ ½I=KI1 ÞÞ þ Km Þ
(5.13)
Defining Vmax as the maximal rate of reaction when all
of the enzyme [ET] is generating product according to k2
(Vmax ¼ k2 [ET]) and rearranging gives the equation for the
rate of reaction for an enzyme with a substrate S in the
105
presence of an inhibitor that either interacts with the bare
enzyme or the enzymeesubstrate complex [14]:
Vo ¼ ðVmax = ð1 þ ½I = KI1 Þ½SÞ=ð½S þ Km ðð1 þ ½I = KI1 Þ =
ð1 þ ½I=KI2 ÞÞÞ
(5.14)
There are a number of ways in which a molecule can
antagonize enzyme function, but there is a simple molecular scheme that organizes these effects; a molecule can
block enzyme function either through interaction with the
enzyme itself (with no substrate present), or the enzymee
substrate complex, or both. The relative affinity of the
molecule for the bare enzyme versus the enzymeesubstrate
complex determines the pattern of inhibition and also the
relationship between the concentration of inhibitor and the
sensitivity of the enzyme reaction for that inhibition. As
shown in Fig. 5.5, there are basically four schemes for
enzyme inhibition.
The MichaeliseMenten equation defines a hyperbolic
relationship between enzyme velocity and substrate
concentration; this is shown in Fig. 5.6A. Specifically it
shows the increase in enzyme velocity with increasing
substrate concentration until the enzyme is saturated (and
the velocity attains an asymptotic value at Vmax). A
convenient manipulation of this relationship (developed
before computer programs for fitting nonlinear curves were
widely available) is the LineweavereBurke transform of
Eq. (5.14). This yields a linear relationship:
1=Vo ¼ ð1 = ½SÞðKm = Vmax Þ ð1 = Vmax Þ
(5.15)
FIGURE 5.5 Mechanisms of enzyme inhibition. The substrate S is converted to a product P through interaction with the enzyme E. The enzymee
substrate complex is denoted ES. The enzyme inhibitor I can interact with E with equilibrium dissociation constant K1 or ES with constant K2. To the right
of the arrow is a general equation relating enzyme velocity to substrate and inhibitor concentration. Lower panel shows various kinetic extremes leading to
characteristic patterns of enzyme inhibition as discussed in the text.
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A Pharmacology Primer
This is shown in Fig. 5.6B, a double reciprocal plot of
1/V as a function of 1/[S] yields a straight line with a slope
of (Km/Vmax) and an x intercept of (Km)1.
Different patterns of enzyme activity with a substrate
will be observed with enzyme inhibitors depending
on whether they inhibit the bare enzyme, or the enzymee
substrate complex, or both. For example, simple competitive blockade occurs when the inhibitor can only bind to
the enzyme, usually through binding to the substrate
binding site to preclude substrate binding. The specific
equation describing this condition can be derived from Eq.
(5.14) by setting KI2 to infinity such that the expression
(1 þ [I]/KI2) /1. Under these circumstances enzyme velocity is given as:
Vo ¼ ðVmax = ð1 þ ½I = KI1 Þ½SÞ=ð½S þ Km ðð1 þ ½I = KI1 ÞÞ
(5.16)
The effects on the enzyme function curve and
LineweavereBurke plot are shown in Fig. 5.7. In
competitive inhibition, very high concentrations of substrate can overcome the competitive inhibition; therefore
the Vmax is not affected (much like simple competitive
antagonism for receptors; see Fig. 7.6A). The immutability
of Vmax is shown by the common y-axis intercept of the
FIGURE 5.6 Enzyme reactions according to the MichaeliseMenten equation (Eq. 5.13). (A) Graphical representation of the rate of the enzyme reaction
as a function of the substrate concentration. (B) Linear transformation of the equation to a format referred to as the LineweavereBurke plot.
FIGURE 5.7 Competitive enzyme inhibition. (A) Competitive inhibition is characterized by a constant Vmax and an increase in Km. (B) The
LineweavereBurke plots increase in slope with inhibition but the y-axis intercept remains constant. The inhibitor has a very low affinity for ES since the
substrate occupies the binding site.
Drug targets and drug-target molecules Chapter | 5
LineweavereBurke plot (no change in the intercept which
is V1
max). An example of such competition is the reversal of
lethal hypoxia and acidosis produced with ingestion of
methyl alcohol. In this condition, the enzyme alcohol dehydrogenase converts the methyl alcohol substrate to
formaldehyde, a very toxic substance. Therapeutically, this
can be reversed by giving the patient an alternative substrate such as ethanol or fomepizole to compete with
methanol as these two substrates do not produce toxic
producesdsee Fig. 5.8.
107
Another mechanism of enzyme inhibition involves
binding of the inhibitor to both the bare enzyme and
enzymeesubstrate complex. If the affinity of the inhibitor
for both protein species is the same, then the inhibition is
labeled noncompetitive. Eq. (5.14) can be formatted for this
type of antagonism by setting KI1 ¼ KI2. The patterns for
this noncompetitive inhibition are shown in Fig. 5.9. It can
be seen that while Vmax is diminished, the location parameters of the substrateeactivation curves do not change;
this is similar to noncompetitive antagonism of receptors as
FIGURE 5.8 Example of competitive inhibition through cosubstrate binding for alcohol dehydrogenase. For patients who ingest methanol, this enzyme
produces a lethal metabolite as formate. To treat this acutely, ethanol or fomepizole is administered to compete for the methanol substrate to prevent the
formation of the toxic product.
FIGURE 5.9 Noncompetitive enzyme inhibition. (A) Noncompetitive inhibition is characterized by no change in Km and a decreasing Vmax. (B) In this
case the enzyme inhibitor has equal affinity for E and ES.
108
A Pharmacology Primer
shown in Fig. 7.16. Fig. 5.9B shows the distinctive pattern
of the LineweavereBurke plots, namely a common x-axis
intercept and varying intercepts of the y-axis. If the inhibitor interacts with both the enzyme and enzymeesubstrate
complex to varying degrees (KI1sKI2), then a mixed type
of inhibition involving a mixture of depression of Vmax and
dextral displacement of the curves (increasing Km) is
observed (see Fig. 5.10). This pattern is similar to the
noncompetitive antagonism of receptors in a system with a
receptor reserve e see Fig. 7.16B. An example of this type
of inhibition in shown in Fig. 5.11 for the enzyme P38.
Finally, if the inhibitor only interacts with the
enzymeesubstrate complex, this is termed uncompetitive
inhibition. This results in a depression of Vmax and a
decrease in the Km value; i.e., the enzyme becomes more
sensitive to the antagonism but operates with a lower Vmax
value e see Fig. 5.12. This is similar to some allosteric
receptor antagonists (see Fig. 8.21B) as shown for the
uncompetitive inhibition of glutathione hydrolysis by
human g-glutamyl transpeptidase (Fig. 5.13). In this
figure, the data from the LineweavereBurke plot for the
enzyme inhibition (Fig. 5.12A) can be reformatted as a
standard doseeresponse curve (Fig. 5.13B) to illustrate
the hallmarks of uncompetitive antagonism, namely
depression of maximal response and sensitization to
substrate.
FIGURE 5.10 Mixed enzyme inhibition. (A) Mixed inhibitors increase the Km and decrease Vmax. (B) In this case, the inhibitor has affinities for both E
and ES but they are not equal.
FIGURE 5.11 Mixed inhibition of
P38 MAPKinase by 3-benzoyl-2,4dihydroxyphenyl-phenylmethanone.
KI1 ¼ 47.34,
KI2 ¼ 75.7 nM,
Km ¼ 85 mM. Data redrawn from
B.A.P. Wilson, M.S. Alam, T.
Guszczynski, M. Jakob, R. Shilpa,
S.R. Shenoy, C.A. Mitchell, E.I.
Goncharova1, R. Jason, J.R. Evans,
P. Peter Wipf, G. Liu, J.D. Ashwell,
B.R. O’Keefe BR. Discovery and
characterization of a biologically
active noneATP-competitive p38
MAP kinase inhibitor. J. Biomol.
Screen. 21 (2016) 277e289.
Drug targets and drug-target molecules Chapter | 5
109
FIGURE 5.12 Uncompetitive enzyme inhibition. (A) Uncompetitive inhibition is characterized by a decrease in Km and a decreasing Vmax. (B) In this
case the enzyme inhibitor binds only to the ES complex.
FIGURE 5.13 (Panel A) An example of uncompetitive enzyme inhibition whereby the antagonist blocks glutathione hydrolysis by human g-glutamyl
transpeptidase. (Panel B) shows the same data plotted as a substrate doseeresponse curve to show elements of the cooperative allosteric effect of the
substrate and inhibitor. Redrawn from Wickham et al. Biochem. J. 450 (2013) 547.
It is more than academically interesting to know the
mode of enzyme inhibition because this can dictate the
quantitative relationship between how much inhibitor is in
the target compartment and how much enzyme inhibition is
produced. The molecular quantitative parameter that determines the potency of the enzyme inhibition is the equilibrium dissociation constant of the inhibitoreenzyme
complex (KI), but the observed inhibition may be modified
by the concentration of substrate present in the form of the
IC50 (concentration of inhibitor producing 50% inhibition
of a given rate of enzyme reaction for a given substrate
concentration). Fig. 5.14 shows the relationship between
the observed potency of inhibition (IC50) and the molecular
KI for enzyme inhibitors with different mechanisms of
action. It can be seen that the potency of a competitive
inhibitor decreases with increasing substrate concentration
as expected (similar to IC50 values of competitive antagonists e see Fig. 5.14). This linear relationship becomes
curvilinear with mixed enzyme inhibition and nonexistent
for noncompetitive inhibitors. Thus, the potency of
noncompetitive enzyme inhibitors is constant in the face of
a range of substrate concentrations (similar to noncompetitive receptor antagonists e see Fig. 5.14B).
An interesting profile is seen with uncompetitive antagonists, where there is an inverse relationship between the
substrate concentration and the potency of the enzyme inhibitor. This is because the substrate must be bound to the
enzyme for inhibition to occur, i.e., the substrate creates the
110
A Pharmacology Primer
FIGURE 5.14 Relationship between the observed inhibition of enzymes (IC50) and the molecular equilibrium dissociation constant of enzyme inhibitors
as a function of substrate concentration. For drugedrug interactions, this deflects the potency of an enzyme inhibitor producing an interaction as a function
of the concentration of the second drug used in therapy. For competitive interactions, as the dosage of the second drug increases, the effect of the drug
causing a DDI through enzyme inhibition diminishes. To a lesser extent this is true of mixed enzyme inhibitors up to a limiting value. For noncompetitive
enzyme inhibitors, the concentration of the second drug is immaterial. For uncompetitive enzyme antagonists, as the concentration of the second drug
increases, the effect of the enzyme inhibitor actually increases.
protein species sensitive to the inhibition. Therefore for an
uncompetitive type of interaction, increasing the dosage of
one of the drugs might actually increase the drugedrug
interaction effect for the other. The relationship between
substrate concentration and competitive and uncompetitive
enzyme inhibitors is shown in Fig. 5.15. This example
depicts the effects of kinase inhibitors in vitro (where
substrate concentrations are traditionally kept low) and then
in tumors where substrate concentrations may be extremely
high. As shown in Fig. 5.15, a competitive inhibitor will
show favorable potency in the in vitro assay but lose potency in vivo whereas this would not be the case with the
uncompetitive inhibitor.
In general, enzyme inhibition is measured by subjecting
a steady-state ongoing enzyme reaction (operating at a
substrate concentration near the Km value) to a range of
concentrations of the putative enzyme inhibitor and determining an IC50 much like the antagonism of a functional
receptor assay. A high-throughput approach to identifying
specific types of enzyme inhibitors can be gained through
measurement of IC50 values for compounds at two substrate
concentrations e see Fig. 5.16. In this scheme, competitive,
mixed, noncompetitive, and uncompetitive compounds can
rapidly be identified.
As well as enzyme inhibition, under some conditions
enzyme activation can be a viable therapeutic activity.
Enzyme activators must be allosteric (i.e., not bind to the
substrate binding site) so that the enzyme can still interact
with its substrate. One example of such a molecule is
FIGURE 5.15 Relationship between substrate concentration (abscissae)
and potency of enzyme inhibitors (multiples of KI as ordinates). For a
competitive enzyme inhibitor, the potency of the inhibitor decrease with
increasing substrate concentration. For an uncompetitive inhibitor, the
opposite is true as the potency increases with increasing substrate concentration to a limiting value of KI.
Drug targets and drug-target molecules Chapter | 5
111
FIGURE 5.16 Screening scheme to detect enzyme inhibition. The difference in antagonist potency with changes in substrate concentration can
be used to identify competitive, mixed, noncompetitive, and uncompetitive
enzyme inhibition.
the compound Ro281675 which acts on glucokinase
to increase the sensitivity to glucose which in turn
increases insulin release and reduces liver glucose output in
diabetes [15].
5.2.4 Nuclear receptors
Steroid and thyroid hormones act on nuclear receptors to
regulate gene expression to control development, homeostasis, and metabolism cells. These receptors bind DNA
and after interacting with ligands, which produce a
conformational change, the conformationally altered receptors regulate the expression of adjacent genes thereby
functioning as transcription factors to either upregulate or
downregulate gene expression. Nuclear receptors (molecular masses 50e100 K Da) are modular in structure and
contain different domains as shown in Fig. 5.17. While the
N-terminal, DNA-binding, and ligand-binding domains are
structurally stable and folded, the hinge region and optional
C-terminal domains are conformationally flexible and
disordered.
Nuclear receptors may be subdivided into mechanistic
classes:
(1) Type I: These exist in the cell cytosol and ligand binding causes dissociation of heat shock proteins, homodimerization, and translocation (i.e., active transport)
from the cytoplasm into the cell nucleus to cause binding to hormone response elements. The nuclear
receptoreDNA complex then recruits other proteins
that transcribe DNA into messenger RNA and eventually to protein. Some examples of Type I NRs are
androgen receptors, estrogen receptors, glucocorticoid
receptors, and progesterone receptors.
(2) Type II: These are retained in the nucleus and usually
bind with RXR, as heterodimers to DNA. In the absence
FIGURE 5.17 Cartoon of the principle binding modules for nuclear
receptors.
of ligand they are complexed with corepressor proteins;
ligand binding causes dissociation of corepressor and
recruitment of coactivator proteins. Subsequently, other
proteins including RNA polymerase are then recruited
to the NReDNA complex that transcribes DNA into
messenger RNA. Some examples of Type II NRs are
the retinoic acid receptor, retinoid X receptor, and thyroid hormone receptor.
(3) Type III: These are similar to Type I NRs but bind to
direct repeat instead of inverted repeat hormone
response elements.
(4) Type IV: These bind either as monomers or dimers; examples of type IV receptors are found in most of the NR
subfamilies.
A list of human nuclear receptors is given in Table 5.5.
There are certain cofactors and behaviors unique to
nuclear receptors that are worthy of note. For instance,
nuclear receptors are capable of dimerizing (homotypic
dimerization) with specificity. In addition, hormone
response elements bound to ligands mediate recruitment of
other proteins (transcription coregulators) that facilitate or
inhibit the transcription of the associated target gene into
mRNA. These coregulators vary in function from chromatin remodeling (the target gene will be either more or
less accessible to transcription) to a bridging function to
stabilize the binding of other coregulatory proteins.
Agonist binding (i.e., estradiol and testosterone)
generally induces a conformation of the receptor to cause
binding of coactivator proteins to upregulate gene expression. Specifically, agonists have an intrinsic histone acetyltransferase (HAT) activity which weakens the
association of histones to DNA to promote gene
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A Pharmacology Primer
TABLE 5.5 Human nuclear receptors.
Group
Receptor
Ligands
Thyroid hormone Receptor
TRa, TRb
Thyroid hormone
Retinoic acid Receptor
RARa, RARb, RARg
Vitamin A, related compounds
Peroxisome proliferator activator receptor
PPAR-a, PPARb/d, PPARg
Fatty acids, prostaglandins
Rev-ErbA
Rev-ErbAa, Rev-ErbAb
heme
RAR-related orphan receptor
RORa, RORb, RORg
Cholesterol, ATRA
Liver X receptorelike
LXRb, LXRa, FXR
Oxysterols
Vitamin D receptorelike
VDR, PXR, CAR
Vitamin D, xenobiotics, androstane
Hepatocyte nuclear Factor-4
HNF4-a, HNF4-g
Fatty acids
Retinoid X receptor
RXRa, RXRb, RXRg
Retinoids
Testicular receptor
TR2, TR4
TLX/PNR
TLX, PNR
COUP/EAR
COUP-TFI, COUP-TFII, EAR-2
Retinoic acid
Estrogen receptor
ERa, ERb
Estrogens
Estrogen-related receptor
ERRa, ERRb, ERRg
3-Ketosteroid receptors
GR, MR, PR, AR
Nerve growth factor IBelike
NGF1B, NURR1, NOR1
Steroidogenic factorelike
SF1, LRH-1
Germ Cell nuclear factorelike
GCNF
DAX/SHP
DAX1, SHP
transcription. This can be accomplished by some synthetic
ligands such as the glucocorticoid receptor antiinflammatory drug dexamethasone. In contrast, the binding of
an antagonist ligand (which blocks the effect of agonist
through competitive binding) induces a conformation of the
receptor that preferentially binds corepressor proteins
which, in turn, recruits histone deacetylases (HDACs) to
strengthen the association of histones to DNA to repress
gene transcription. An example of antagonistic nuclear receptor drug is mifepristone, a ligand that binds to the
glucocorticoid and progesterone receptors and blocks the
activity of the endogenous hormones cortisol and progesterone. Just as with GPCRs, some antagonists can
demonstrate inverse agonist activity (i.e., inverse agonists).
For nuclear receptors these promote constitutive activity,
namely a low level of gene transcription in the absence of
agonists.
In accordance with allosteric probe dependence (discussed in Chapter 8 as the differences in protein function
produced by ligands depending on what the protein interacts with), drugs for nuclear receptors can produce
complex profiles of agonism and antagonism. For NRs,
drugs with this mixed agonist/antagonist profile of action
are referred to as selective receptor modulators (SRMs);
Cortisol, aldosterone, progesterone, testosterone
Phosphatidylinositols
some examples are Selective Androgen Receptor Modulators (SARMs), Selective Estrogen Receptor Modulators
(SERMs), and Selective Progesterone Receptor Modulators
(SPRMs). It is thought that the relative levels of coactivators and corepressors in cells may determine whether
agonism or antagonism will result from these ligand interactions. Another unique property of nuclear receptors is
the demonstration of transactivation (receptor binds directly
to DNA) and transrepression where the receptor binds to
DNA and other proteins resulting in the deactivation of a
second transcription factor. This can result in the separation
of effects such as in interaction of Selective Glucocorticoid
Receptor Agonists (SGRAs) with glucocorticoid receptors.
Some of these molecules more strongly transrepress than
transactivate and this increases the separation between the
desired antiinflammatory effects and undesired metabolic
side effects of these selective glucocorticoids.
5.2.5 Nucleotide-based drug targets
5.2.5.1 DNA targets
DNA can also function as a drug target. A well-known drug
acting on DNA is the anticancer agent (carcinomas, germ
cell tumors, lymphomas, sarcomas) cisplatin. It is proposed
Drug targets and drug-target molecules Chapter | 5
113
FIGURE 5.18 Schematic of cisplatin anticancer activity. Cross-linking DNA causes
mismatch in DNA repair, P53, and C-Abl kinase
activation to cause eventual apoptosis.
FIGURE 5.19 Binding of the antibiotic and antiviral drug netropsin to
minor groove of DNA.
that cisplatin can cross-link with the purine bases on the
DNA to interfere with DNA repair mechanisms and cause
DNA damage, and subsequently inducing apoptosis in
cancer cellsdsee Fig. 5.18). The fact that DNA forms a
highly structured and detailed double helical complex
makes specific binding possible and there are many drugs
that do this. For example, the polyamide antibiotic and
antiviral drug netropsin (also known as congocidine or
sinanomycin) binds to the minor groove of AT-rich sequences of double-stranded DNA to the minor groove of
DNA (Fig. 5.19). There are other mechanisms whereby
small molecules can modify the function of DNA. Fig. 5.20
shows another involvement of DNA in drug mechanisms
with the binding of UNC4976, a positive allosteric modulator of the polycomb repressive complex 1 chromodomain
protein CBX7. Although DNA is not the direct binding
partner for UNC4976, it cooperatively binds to CBX7 and
DNA to form a tight complex that antagonizes the
recruitment of CBX7 to target genes by increasing
nonspecific binding to DNA. In general, polycomb group
proteins (PcGs) are important for maintaining cellular
identity and normal differentiation by repressing polycomb
target genes. Mutation or deregulation of PcG proteins have
been implicated in several cancers and other diseases.
Under these circumstances, positive allosteric modulation
of PcGs could serve to relocate chromatin-templated processes and reduce tumor growth. Fig. 5.20 shows the
binding scheme for UNC4976 to CBX7 as an allosteric
system [16,17] whereby the affinity of CBX7 for DNA is
increased by a factor a; in these experiments binding was
increased by a factor of 4.2 [18].
5.2.5.2 RNA targets
Historically, RNA has been viewed strictly as a carrier of
genetic information existing solely to transmit information
for protein coding. These molecules were considered to be
highly flexible species devoid of structure and thus
appeared not to be qualified to be discrete drug receptors.
However, now it is known that RNA exists as a dynamic
ensemble of conformations with well-defined tertiary
structures thus enabling specific molecular interactions with
drugs. It is known that the majority of RNA is noncoding (it
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A Pharmacology Primer
FIGURE 5.20 Schematic for binding of UNC4976 to CBX7 and DNA. Allosteric system showing CBX7 binding to DNA with and without UNC4976
bound to show a cooperativity for binding of 4.2-fold when UNC4976 is bound. Equations show equilibrium expressions for the protein species. Redrawn
from K.N. Lamb, D. Bsteh, S.N. Dishman, H.F. Moussa, H. Fan, J.I. Stuckey et al. Discovery and characterization of a cellular potent positive allosteric
modulator of the polycomb repressive complex 1 chromodomain, CBX7. Cell Chem Biol 6 (2019) 1e15.
is estimated that 70% of the human genome encodes noncoding RNA) and many of these species are associated with
diseases such as cancer and nontumorigenic diseases;
humans produce on the order of 15,000 long noncoding
RNAs. Coding and noncoding RNAs often fold into complex conformations (through processes such as Watsone
Crick base pairing) which, when targeted by drug molecules, can affect numerous cellular processes. These are
often mediated by ‘undruggable proteins’dsee Section
5.4.2, i.e., these proteins lack distinctive cleftlike motifs
where small molecules can bind. Thus RNA structures
feature structural elements such as bulges, loops, junctions,
pseudoknots, and higher order structures. However, targeting such structures could be problematic in that they
produce many polar binding pockets exposed to solvent to
a greater extent than those encountered on proteins. At
present there is a paucity of small molecule structures
known to specifically target RNA. There are some examples as the linezolid antibiotics (Fig. 5.21) and drugs like
ribocil and branaplam and this active area of research is
expanding into new chemical diversity [19]. An example of
where this could be a viable therapeutic approach is the
demonstration of the interaction of the benzimidazole
Compound 1 with miR-96 (Fig. 5.22). This molecule inhibits the processing of pri-miR-96 causing the upregulation of its target FOXO1 and subsequent induction of
apoptosis in MCF7 breast cancer cells [20].
In general, there are three requirements for RNA-based
drug target utilization: (1) identification of a valuable RNAtarget, (2) development of a screening effort to identify
drug-like molecules interacting with RNA, and (3) identification of RNA motifs that can accommodate ligand
binding with specificity and high affinity.
5.3 Small drug-like molecules
In addition to diversity in biological targets, there is
emerging diversity in the types of chemicals that can be
used therapeutically to interact with these targets. Before
the advent of widespread functional HTS, the majority of
new therapeutic entities could be classed as full agonists,
partial agonists, or antagonists. Since the screening mode
used to discover these often was orthosterically based (i.e.,
displacement of a radioligand in binding), the resulting
leads usually were correspondingly orthosteric. With HTS
in functional mode, there is the potential to cast a wider
screening net to include allosteric modulators. With the use
of the cellular functional machinery in detecting biologically active molecules comes the potential to detect allosteric antagonists (modulators) or potentiators. As
discussed in Chapter 8, Allosteric Modulation, there are
fundamental differences between orthosteric and allosteric
ligands that result in different profiles of activity and
different therapeutic capability (see Section 8.3). As more
Drug targets and drug-target molecules Chapter | 5
115
FIGURE 5.21 Small molecules
known to target RNA.
FIGURE 5.22 High information
content structure of noncoding RNA
complex interacting with linezolid
and rifampin.
allosteric ligands are detected by functional HTS, the
ligand-target validation issues may become more prominent. In general, the requirement of target presence in the
system to demonstrate an effect is the first, and most
important, criterion to be met. In cases where sensitivity of
the effect to known target antagonists is not straightforward, demonstration of the target effect, when the target is
transfected into a range of host cells, is a useful
confirmation.
Another variation on a theme for biological targets involves a concept known as polypharmacology, namely,
ligands with activity at more than one target within the
same concentration range. The unique therapeutic profiles
of such molecules rely upon the interplay of activities at
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A Pharmacology Primer
multiple biological targets. Polypharmacological ligands
make positive use of the generally observed phenomenon
that many drugs, although designed to be selective, often
have numerous other activities. Thus, drugs should be
considered to be selective but not specific (where specific
means the molecule possesses only one single activity at all
concentration ranges). For example, Fig. 5.23 shows the
numerous activities found for the a2-adrenoceptor antagonist yohimbine and the antidepressant amitriptyline.
There are increasing numbers of examples of clinically
active drugs in psychiatry that have multiple target activities. For example, olanzapine, a useful neuroleptic, has
highly unspecific antagonist activity at 10 different neurotransmitter receptors. Similarly, there are numerous antidepressant drugs where multiple inhibitory effects on
transport processes (norepinephrine, serotonin, dopamine)
may be of therapeutic utility; see Fig. 5.24. Additionally
some antipsychotic drugs have numerous activities; for
example, the atypical antipsychotic clozapine has activity at
histamine H4, dopamine D2, dopamine D4, 5-HT2A, 5HT2C, and 5-HT6 receptors. In addition, its major metabolite, desmethylclozapine, is an allosteric modulator of
muscarinic receptors. This phenomenon is not restricted to
the CNS; there is evidence that multiple activities may be
an important aspect of kinase inhibitors in oncology as
FIGURE 5.23
well. The unique value of the antiarrhythmic drug amiodarone is its activity on multiple cardiac ion channels [21].
5.3.1 Hybrid molecules
Introducing multiple activities into molecules can be a
means of maximizing possible therapeutic utility. Fig. 5.25
shows the theoretical application for activity at two types of
receptors, namely, a- and b-adrenoceptors. Depending on
the dominant activities, molecules from a program designed
to yield dual a- and b-adrenoceptor ligands could be
directed toward a range of therapeutic applications.
Chemical strategies can introduce multiple activities into a
single molecule through dimerization of structures known
to possess a single activity to form structures which possess
multiple activities. The linkage of known active chemical
structures for multiple activities has been described as a
strategy, but an even more obvious amalgam of structures,
joined with a linker, can be used to target receptor homoand heterodimers [22]. The conscious incorporation of two
activities into molecules through hybridization is a known
therapeutic strategy. For instance, dopastatin (BIM23A760) is a hybrid of a somatostatin receptor agonist
linked to a dopamine agonist, designed for beneficial effects of neuroendocrine tumor disease pathology [23].
Multiple receptor effects (ordinates denote pK values for antagonism or receptor occupancy) of (A) yohimbine and (B) amitriptyline.
FIGURE 5.24 Mixture of activities of known antidepressants as
inhibitors of amine transport processes (norepinephrine, serotonin,
and dopamine).
FIGURE 5.25 Venn diagram consisting of the various possible activities (agonism and antagonism) on two receptor subtypes (a- and b-adrenoceptors).
Letters label the areas of intersection denoting joint activity; the table shows possible therapeutic application of such joint activity.
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A Pharmacology Primer
Dimeric ligands can show increased potency. For example,
a dimer of the 5-HT1B receptor ligand sumatriptan, used for
the treatment of migraine, shows a 100-fold increase in
potency over monomeric sumatriptan [24]. Dimerization of
ligands is a way to introduce mixtures of activity. One
example of this is a dimeric linking of a d-opioid antagonist
(naltrindole) and k1-opioid agonist (ICI-199,441) to yield a
molecule of greater potency and mixed activity [25]; see
Fig. 5.26. Dimeric ligands need not be obvious amalgams
of active structures. For example, in view of clinical data
suggesting that a mixture of histamine and leukotriene
antagonism was superior to either single agent in asthma,
and the finding that the antihistamine cyproheptadine was a
weak antagonist of LTD4, a molecule based on cyproheptadine that was modified with features from the endogenous
leukotriene agonist LTD4 yielded a molecule with better
activity in asthma [26]; see Fig. 5.27. Dual activity also has
been designed from knowledge of similar substrates. The
treatment of hypertension with the ACE inhibitor captopril
is established. The enzyme neutral endopeptidase (NEP) is
a metalloprotease that degrades atrial natriuretic factor, a
peptide known to cause vasodilatation and oppose the action of angiotensin. These activities led to the postulate that
a combined ACEeNEP inhibitor would be efficacious in
hypertension, and one approach to this utilizes the notion
that these two enzymes cleave similar dipeptide fragments.
From this, a constrained antiphenylalanine dipeptide
mimetic designed to mimic a low-energy conformation of
the His-Leu portion of angiotensin bound to ACE and the
Phe-Leu portion of leu-enkephalin bound to NEP were used
to produce a dual inhibitor of both ACE and NEP
(Fig. 5.27). This formed the basis for the synthesis of a
potent ACEeNEP inhibitor of nanomolar potency
(Fig. 5.27).
While combined activities can yield useful overall
properties, the combination of an agonist and a structurally
related antagonist into one molecule can yield a graded
effect that may lead to designed efficacy. Aside from the
size of the linker, the main variable is the relative affinities
of the agonist (termed the ‘agonist warhead’) and antagonist (termed the ‘antagonist warhead’) moieties. If the
antagonist warhead is a competitive antagonist of the receptor, then the affinity of this part of the molecule simply
determines the maximal response of the agonist warhead;
this effect is shown in Fig. 5.28A. The value of s denotes
the ratio of the affinities of the agonist and antagonist parts
of the molecule, i.e., s ¼ 0.1 means that the affinity of the
antagonist moiety is 10-fold greater than the affinity of
the agonist moiety. It can be seen that as the affinity of the
antagonist increases, the maximal response of the overall
hybrid is diminished [26]. If the antagonist moiety is a
noncompetitive antagonist then the effect is more complicated. In systems with no receptor reserve (i.e., 100% of the
receptor are required for maximal response), then linking
the noncompetitive antagonist depresses the maximal
response of the agonist warhead and produces a bell-shaped
curve for overall response (see Fig. 5.28B). As with all
noncompetitive antagonists, if there is a receptor reserve
(not all of the receptors need be activated to produce the
maximal response), then the depression of maximum and
bell shape still is observed but at a much greater antagonist
affinity and with a broadened bell shape that shows
depressed maxima at higher levels of agonism (see
Fig. 5.28C).
Hybrid molecules also may have more complex kinetics
of onset due to the dual nature of the receptor effects.
Specifically, if the rates of onset and offset of the agonist
warhead and the antagonist modulator are different, then a
deviation from single species first-order kinetics may be
seen. Fig. 5.29 shows the equations and a schematic of the
system for a hybrid molecule. The kinetics are similar to
those of coaddition of a radioligand and antagonist [27]
with the difference that the concentration of both moieties
is the same.
One of the practical problems associated with ligands
yielding polypharmacology is that their therapeutic profiles
FIGURE 5.26 Dimeric antagonist formed by oligoglycyl-based linkage of two opioid receptor subtype antagonists naltrindole and ICI-199,441. From
D.J. Daniels, A. Kulkarni, Z. Xie, R.G. Bhushan, A bivalent ligand (KDAN-18) containing d-antagonist and k-agonist pharmacophores bridges d2 and k1
opioid receptor phenotypes, J. Med. Chem. 48 (2005) 1713e1716.
Drug targets and drug-target molecules Chapter | 5
119
FIGURE 5.27 Design of multiple ligand activity. (A) Dual histamine H1 receptor and leukotriene receptor antagonist incorporating known antihistaminic properties of cyproheptadine and LTD4. (B) Joint ACEeNEP inhibitor formed from incorporating similarities in substrate structures for both
enzymes. ACE, angiotensin converting enzyme; NEP, neutral endopeptidase. Data from T.P. Kenakin, Drug and Organ Selectivity: Similarities and
Differences, Academic Press, New York, NY, 1985, pp. 71e109; From R. Morphy, Z. RankDesigned multiple ligands: an emerging drug discovery
paradigm, J. Med. Chem. 48 (2005) 6523e6543.
FIGURE 5.28 Doseeresponse curves to hybrid molecules of an agonist and competitive antagonist (panel A), an agonist and a noncompetitive antagonist
in a system with low receptor reserve (panel B), and an agonist and a noncompetitive antagonist in a system with a high receptor reserve (panel C).
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A Pharmacology Primer
FIGURE 5.29 Real-time kinetics
of a hybrid agonisteantagonist
molecule. Whereas a single phase
agonist yields a single phase hyperbolic onset curve (magenta), a flattened hyperbola is seen when the
rate of onset of the agonist is greater
than the antagonist moiety. This
flattened profile is attenuated as the
rates of onset of the agonist and
antagonist approach each other.
FIGURE 5.30 Changes in heart rate (ordinates) for agonist-induced changes in cardiac inotropy (changes in rate of ventricular pressure) in anesthetized
cats. Responses shown to isoproterenol (blue circles) and dobutamine (red circles). (A) Response in normal cats shows inotropic selectivity (less
tachycardia for given changes in inotropy) for dobutamine over isoproterenol. (B) The inotropic selectivity of dobutamine is reduced by previous aadrenoceptor blockade by phentolamine. From T.P. Kenakin, S.F. Johnson, The importance of a-adrenoceptor agonist activity of dobutamine to inotropic
selectivity in the anesthetized cat, Eur. J. Pharmacol. 111 (1985) 347e354.
of action often can only be tested effectively in vivo. For
example, debilitating concomitant tachycardia seen with
beneficial increases in cardiac performance is a common
finding for standard b-adrenoceptor agonist catecholamines
such as isoproterenol (see Fig. 5.30A). However, the badrenoceptor agonist dobutamine produces much less
tachycardia for the same increased cardiac performance.
This interesting differentiation has been shown to be due to
a low-level pressor effect of dobutamine (which opposes
tachycardia through a reflex vagal stimulation) caused by
weak a-adrenoceptor agonism [28]; blockade of a-adrenoceptors in vivo greatly reduces the difference between
isoproterenol and dobutamine (see Fig. 5.30B). This
inotropic (over chronotropic selectivity) cannot be seen in
Drug targets and drug-target molecules Chapter | 5
isolated organs, only in the in vivo system. In this case, the
whole animal is needed to detect the beneficial properties of
dobutamine polypharmacology (aþb-agonism).
5.3.2 Chemical sources for potential drugs
A starting point to this process is the definition of what the
therapeutic end point of the drug-discovery process will be,
namely, a drug. There are certain properties that molecules
must have to qualify as therapeutically useful chemicals.
While, in theory, any molecule possessing activity that can
be introduced into the body compartment containing the
therapeutic target could be a possible drug, in practice,
therapeutically useful molecules must be absorbed into the
body (usually by the oral route), distribute to the biological
target in the body, be stable for a period of time in the body,
be reversible with time (excreted or degraded in the body
after a reasonable amount of time), and be nontoxic.
Ideally, drugs must be low-molecular-weight bioavailable
molecules. Collectively, these desired properties of molecules are often referred to as “drug-like” properties. A
useful set of four rules for such molecules has been proposed by Lipinski et al. [29]. Molecules that fulfill these
criteria generally can be considered possible therapeutically
useful drugs, providing they possess target activity and few
toxic side effects. Specifically, these rules state that “druglike” molecules should have less than five hydrogen-bond
donor atoms, a molecular mass of <500Da, and high lipophilicity (C log P > 5) and that the sum of the nitrogen
and oxygen atoms should be <10. Therefore, when estimating the potential therapeutic drug targets, these properties should be taken into consideration.
There are numerous chemical starting points for drugs.
Historically, natural products have been a rich source of
molecules. As discussed in Chapter 1, What Is Pharmacology?, the Ebers Papyrus is one of the earliest documents
recording ancient medicine. Similarly, the Chinese Materia
Medica (100 BCE), the Shennong Herbal (100 BCE), the
Tang Herbal (659 AD), the Indian Ayurvedic system (1000
BCE), and books of Tibetan medicine Gyu-zhi (800 AD) all
document herbal remedies for illness. Some medicinal
substances have their origins in geographical exploration.
For example, tribes indigenous to the Amazon River had
long been known to use the bark of the Cinchona officinalis
to treat fever. In 1820, Caventou and Pelletier extracted the
active antimalarial quinine from the bark, which provided
the starting point for the synthetic antimalarials chloroquine
and mefloquine. Traditional Chinese herbal medicine has
yielded compounds such as artemisinin and derivatives for
the treatment of fever from the Artemisia annua. The
anticancer vinca alkaloids were isolated from the
Madagascar periwinkle Catharanthus roseus. Opium is an
ancient medicinal substance described by Theophrastus in
the 3rd century BCE, which was used for many years by
121
Arabian physicians for the treatment of dysentery and
“relief of suffering” (as described by Sydenham in 1680) in
the Middle Ages. Known to be a mixture of alkaloids,
opium furnished therapeutically useful pure alkaloids when
Serturner isolated morphine in 1806, Robiquet isolated
codeine in 1832, and Merck isolated papaverine in 1848. At
present, only 5%e15% of the 25,000 species of higher
plants have been studied for possible therapeutic activity.
Of prescriptions in the United States written between 1959
and 1980, 25% contained plant extracts or active principals.
Marine life can also be a rich source of medicinal material. For example, the C-nucleosides spongouridine and
spongothymidine isolated from the Caribbean sponge
Cryptotheca crypta possess antiviral activity. Synthetic
analogs led to the development of cytosine arabinoside, a
useful anticancer drug. Microbes also provide extremely
useful medicines, the most famous case being penicillin
from Penicillium chrysogenum. Other extremely useful
bacterially derived products include the fungal metabolites,
the cephalosporins (from Cephalosporium cryptosporidium), aminoglycosides, and tetracyclines from Actinomycetales, immunosuppressives such as the cyclosporins
and rapamycin (from Streptomyces), cholesterol-lowering
agents mevastatin and lovastatin (from Penicillium), and
anthelmintics and antiparasitics such as the ivermectins
(from Streptomyces). As with plants, less than 1% of potential bacterial and less than 5% of fungal sources have
been explored for their medicinal value. In general, the
World Health Organization estimates that 80% of the
world’s population relies on traditional medicine with
natural products.
Yet another source of drugs is the very soil where plants
grow. Thus the bacteria Streptomyces peucetius from the
soil found around the castle del Monte in Apulia, Italy,
produces a red pigment active against mouse tumors and
subsequently found to contain doxorubicin. This drug intercalates DNA to cause DNA damage and cell death in
breast, bladder cancers, lymphomas, and leukemias. Similarly, soil from Easter Island yields a soil bacteria Streptomyces hygroscopicus which, in turn, yields the immune
suppressant drug rapamycin. This name originates from the
indigenous name of the Easter Island source, namely Rapa
Nui. Rapamycin inhibits the kinase mTOR1 to decrease cell
proliferation making it useful for transplant patients and in
the treatment of certain cancers.
From this perspective, natural products appear to be a
great future source of drugs. However, teleologically, there
may be evolutionary pressure against biological activity of
natural products. Thus, while millions of years of selective
pressure has evolved molecules that specifically interact
with physiological receptors (i.e., neurotransmitters, hormones) with little “cross talk” to other targets, it can be
argued that those same years exerted a selective evolutionary pressure to evolve receptors that interact only with
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A Pharmacology Primer
those molecules and not the myriad of natural products to
which the organism has been exposed. In practical terms,
natural products as drugs or starting points for drugs have
certain inherent disadvantages as well. Specifically, these
tend to be expensive, not chemically tractable (structurally
complex and difficult to derivatize), and involve difficult
and expensive scale-up procedures (active species tend to
be minor components of samples). Natural products also
often contain a larger number of ring structures and more
chiral centers and have sp3 hybridization bridgehead atoms
present. Natural products are often high in steric
complexity, and containing few nitrogen, halogen, and
sulfur atoms and being oxygen rich with many hydrogen
donors, these often are very prone to enzymatic reactions.
In addition, a practical problem in utilizing such pharmacophores is the unpredictable novelty and intellectual
property that may result. In spite of these shortcomings,
between the years 1981 and 2002, of the 67% of 877
synthetic new chemical entities, 16.4% utilized pharmacophores derived directly from natural products.
Another approach to the discovery of drugs is “rational
design.” The basis for this strategy is the belief that detailed
structural knowledge of the active site to which the drug
binds will yield corresponding information that can guide
the design of molecules to interact with it. One of the bestknown examples, yielding rich dividends, is the synthesis
of the ACE inhibitor captopril from a detailed analysis of
the enzyme’s active site. Similar design of small molecules
to fit specific binding loci of enzymes was accomplished for
HIV protease (nelfinavir) and Relenza for the prevention of
influenza. Other rational design approaches utilize dual
pharmacophores from other active drugs to combine useful
therapeutic activities. This approach offers the advantage
that the dual biological activity will be absorbed, metabolized, and excreted in a uniform manner, that is, the activity
profile of the drug will not change through the varying
ratios of two simultaneously dosed drugs. This also gives
medicinal chemists a place to start. For example, ICS
205e903, a novel and potent antagonist of some neural
effects of serotonin in migraine, was made by utilizing the
structure of cocaine, a substance known to have seriously
debilitating central effects but also known to block some of
the neural effects of serotonin with the serotonin structure
[30]. The result was a selective serotonin antagonist devoid
of the disadvantages of cocaine (Fig. 5.31A). Similarly, a
b-adrenoceptor blocker with vasodilating properties has
been made by combining the structure of the b-blocker
propranolol with that of a vasodilator (Fig. 5.31B) [31].
There are numerous natural substances that have useful
therapeutic properties as well as other undesirable properties. From these starting points, medicinal chemists have
improved on nature. For example, while extremely useful
in the treatment of infection, penicillin is not available by
the oral route; this shortcoming is overcome in the analog
ampicillin (Fig. 5.32A). Similarly, the obvious deleterious
effects of cocaine have been eliminated in the local anesthetic procaine (Fig. 5.32B). The short activity and weak
steroid progesterone is converted to a stronger, long-acting
analog (þ)-norgestrel through synthetic modification
(Fig. 5.32C). Catecholamines are extremely important for
sustaining life and have a myriad of biological activities.
For example, norepinephrine produces a useful bronchodilation that has utility in the treatment of asthma. However, it also has a short duration of action, is a chemically
unstable catechol, and produces debilitating tachycardia,
vasoconstriction, and digital tremor. Synthetic modification
to salbutamol eliminated all but the tremorogenic side effects to produce a very useful bronchodilator for the treatment of asthma (Fig. 5.32D).
It can be argued that drugs themselves can be extremely
valuable starting points for other drugs in that by virtue of
the fact that they are tolerated in humans, they allow the
observation of their other effects. Some of those effects
(“side effects”) may lead to useful therapeutic indications.
For example, the observed antiedemal effects of the antibacterial sulfanilamide in patients with congestive heart
failure led to the discovery of its carbonic anhydrase inhibitor activity and the subsequent development of the
diuretic furosemide (Fig. 5.33A). Similarly, the antidiabetic
effects of the antibiotic carbutamide led to the development
of the antidiabetic tolbutamide (Fig. 5.33B). Some of the
early antihistamines were found to exert antidepressant and
antipsychotic properties; these led to modern psychopharmaceuticals. The immunosuppressant activity of the
fungal agent ciclosporin also was exploited for therapeutic
utility.
Endogenous substances such as serotonin, amino acids,
purines, and pyrimidines all have biological activity and
also are tolerated in the human body. Therefore, in some
cases these can be used as starting points for synthetic
drugs. For example, the amino acid tryptophan and
neurotransmitter serotonin were used to produce selective
ligands for 5-HT5A receptors and a selective somatostatin3
antagonist, adenosine A2b receptor antagonists from
adenine, and a selective adenosine 2A receptor agonist
from adenosine itself (Fig. 5.34).
Major pharmaceutical efforts revolve around the testing
of large chemical libraries for biological activity. Assuming
that most drugs must have a molecular weight of less than
600 (due to desired pharmacokinetic properties, as discussed in Chapter 10, Pharmacokinetics), there are wide
ranges in the estimates of the number of molecules that
exist in “chemical space,” that is, how many different
molecules can be made within this size limit? The estimates
range from 1040 to 10100 molecules, although the need for
activated carbon centers for the construction of carbone
carbon bonds in synthetic procedures reduces the possible
candidates for synthetic congeners. In spite of this fact, the
Drug targets and drug-target molecules Chapter | 5
123
FIGURE 5.31 Examples of drug design through
hybridization: combination of two structural types
to produce a unique chemical entity. (A) Design of
ICS 205e903 [2]. (B) Compound with vasodilating
and b-blocking properties.
number of possibilities is staggering. For example, in the
placement of 150 substituents on mono to 14-substituted
hexanes there are 1029 possible derivatives. Considering a
median value of 1064, possible structures in chemical space
clearly indicate that the number of possible structures
available is far too large for complete coverage by chemical
synthesis and biological screening. It has been estimated
that a library of 24 million compounds would be required to
furnish a randomly screened molecule with biological activity in the nanomolar potency range. While combinatorial
libraries have greatly increased the productivity of medicinal chemists (i.e., a single chemist might have produced 50
novel chemical structures in a year 10 years ago, but with
the availability of solid and liquid phase synthesis and other
combinatorial techniques, a single chemist can produce
thousands of compounds in a single month at a fraction of
the cost of previous techniques), 24 million compounds per
lead is still considerably larger than the practical capability
of industry.
One proposed reason for the failure of many HTS
campaigns is the lack of attention to “drug-like” (namely,
the ability to be absorbed into the human body and having a
lack of toxicity) properties in the chemical library. The
nondrug-like properties of molecules lead to biological
activity that cannot be exploited therapeutically. This is
leading to improved drug design in chemical libraries
incorporating features to improve drug-like properties. One
difficulty with this approach is the multifaceted nature of
the molecular properties of drug-like molecules, that is,
while drug-like chemical space is simpler than biological
target space, the screens for drug-like activity are multimechanism based and difficult to predict. Thus, incorporating favorable drug-like properties into chemical libraries
can be problematic. Also, different approaches can be
counterintuitive to the incorporation of drug-like properties.
Thus, the rational design of drugs tends to increase molecular weight and lead to molecules with high hydrogen
bonding and unchanged lipophilicity; this generally can
lead to reduced permeability. A target permeability for
drug-like molecules (which should have aqueous solubility
minimum of >52 mg/mL) should achieve oral absorption
from a dose of >1 mg/kg. HTS approaches tend to increase
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A Pharmacology Primer
FIGURE 5.32 Examples of chemical modification of active drugs that have either unwanted
effects (cocaine, norepinephrine) or suboptimal
effects (penicillin, progesterone) to molecules
with useful therapeutic profiles. (A) Oral activity conferred on penicillin. (B) Destructive effects of cocaine eliminated to produce useful
local anaesthesia by procaine. (C) Oral activity
for progesterone produced by discovery of
norgeatrel. (D) Elimination of problematic
effects of norepinephrine to produce important
drug for asthma, salbutamol.
molecular weight, leave hydrogen bonding unchanged from
the initial hit, and increase lipophilicity; this can lead to
decreases in aqueous solubility with concomitant decrease
in drug-like properties. Ideas centered on the concept of
drug-like properties have caused a change in the types of
molecules made for screening libraries. It has been seen
that drugs often resemble their screening hit molecular origins (see zofenopril, Fig. 5.35). For this reason, candidates
for new drug libraries are preselected to have drug-like
properties in anticipation of better pharmacokinetics.
Thus, physiochemical rules for library candidates have
been reported in the literature (see Ref. [31]; Fig. 5.35).
The assumption made in estimations of the number of
molecules that would be required to yield biologically
active molecules is that potential drugs are randomly and
uniformly distributed throughout chemical space. Analysis
of known drugs and biologically active structures indicates
that this latter assumption probably is not valid. Instead,
drugs tend to cluster in chemical space, that is, there may be
as little as 10,000 drug-like compounds in pharmacological
space [32]. The clustering of drug-like molecules in
chemical space has led to the concept of “privileged
structures” from which medicinal chemists may choose for
starting points for new drugs. A privileged structure is
defined as a molecular scaffold with a range of binding
properties that yield potent and selective ligands for a range
of targets through modification of functional groups. Privileged structures can be a part of already known drugs, such
as the dihydropyridines (known as calcium channel
blockers). In this case, inhibitors of platelet aggregation
(platelet activating factor inhibitors) and neuropeptide Y
type 1 receptor ligands have been made from the dihydropyridine backbone (Fig. 5.36). Privileged structures also
can simply be recurring chemical motifs such as the indole
motif shown in Fig. 5.37 and shared by marketed drugs and
investigational ligands. Similarly, the 2-tetrazole-biphenyl
motif is found in the angiotensin2 receptor antagonist losartan and glycinyl-histidinyl-serine (GHS) receptor ligand
L-692,429 (Fig. 5.38A) and a wide range of biologically
active structures is based in spiropiperidines (Fig. 5.38B).
Drug targets and drug-target molecules Chapter | 5
125
FIGURE 5.33 Examples of case where the
side effects of drugs used for another indication
led to the discovery and development of a new
therapeutic entity for another disease. (A)
Diuresis seen with patients on sulfanilamide led
to the discovery of a useful diuretic in furosemide. (B) Diabetic patient patient improvement
in symptoms on the antibacterial carbutamide
led to the development of the important antidiabetic drug tolbutamide.
FIGURE 5.34 Examples of natural substances
(shown in red) that have been chemically modified
to yield therapeutically useful selective drugs.
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A Pharmacology Primer
FIGURE 5.35 Relationship of the chemical structure of the ACE inhibitor antihypertensive drug zofenopril to the molecule
found in a high-throughput screen that led to
its discovery and development. In panel on
right are physicochemical rules for candidate library molecules to retain drug-like
activity. ACE, angiotensin converting
enzyme. Data from M.M. Hann, T.I. Oprea,
Pursuing lead likeness concept in pharmaceutical research, Curr. Opin. Chem. Biol. 8
(2004) 255e263.
FIGURE 5.36 Example of a preferred structure, in this case the dihydropyridine scaffold.
5.4 Biologics
A biologic is manufactured in a living system such as a
microorganism, or plant or animal cells. Most biologics are
very large, complex molecules or mixtures of molecules
and are produced using recombinant DNA technology.
Therapeutic biologics can be replacement proteins, peptides, antibodies, vaccines, and nucleic acidebased drug
species. It is worth considering these separately are they
constitute a diverse array of therapeutics.
Drug targets and drug-target molecules Chapter | 5
127
FIGURE 5.37 The preferred indole structure forms the basis of a number of selective ligands for receptors.
5.4.1 Replacement proteins
In general, protein replacement is a strategy to replace a
protein that is deficient or abnormal, adding one to augment
an existing pathway, introduce a novel function, or interfere
with a molecule or organism. Historically, early protein
replacement therapy has involved the use of anticoagulants,
blood factors, hormones, bone morphogenetic proteins,
engineered protein scaffolds, enzymes, growth factors, interferons, interleukins, and thrombolytics. Protein replacement had long been dominated by plasma-derived products
but now recombinant engineered proteins, which are more
stable, are becoming the standard. In addition, they are
more potent and have higher purity. One of the earliest
interventions with replacement therapy was in the realm of
hemophilia. Thus the absence of coagulation factor VIII
(FVIII) leads to hemophilia A and a lack of coagulation
factor XI (FXI) leads to hemophilia B; replacement of both
of these proteins was a staple of therapy. The introduction
of PEGylated Factors, Fc-fusion proteins, and Albuminfusion proteins greatly prolonged half-life to reduce frequency of dosing of these factors and has revolutionized
therapy. Current new proteins for hemophilia include
Alprolix (recombinant factor IX Fc-fusion for hemophilia),
Beloctate (recombinant factor VIII-Gc fusion for hemophilia A), Adynovate (recombinant factor VIII PEGylated
for hemophilia A), and Idelvion (recombinant factor IX
albumin fusion for hemophilia B).
Engineered proteins can be an effective therapy in diseases such as the activity of adnectins in lipid lowering
therapy. The proprotein convertase subtilisin kexin-9
(PCSK9) is a target for reducing low-density lipoprotein
(LDL) but it is resistant to small molecule drug approaches.
Adnectins are a protein family derived from human fibronectin engineered for high affinity that bind tightly to
PCSK9; BMS-962476. These 11 kDa polypeptides, conjugated with polyethylene glycol to improve pharmacokinetics, bind with subnanomolar affinity to human PCSK9 to
cause reduction in PCSK9 levels and lower cholesterol
[33]. Another important class of therapeutics are cytokine
immunomodulatory biologics that mimic, replace, or
augment endogenous cytokines. Some examples of these
are recombinant IL2 (for metastatic renal cell carcinoma,
melanoma), interferon-alpha (for chronic hepatitis), interferon beta-1a (for multiple sclerosis), granulocyte colonystimulating factor (G-CSF) (for bone marrow transplant),
128
A Pharmacology Primer
FIGURE 5.38 Examples of preferred structures [2-tetrazole-biphenyls, panel (A); and spiropiperidines, panel (B)] yielding selective ligands for
receptors.
interferon beta-1b (for multiple sclerosis), and interferon
gamma (for chronic malignant osteoporosis). A possible
drawback to any immunomodulatory biologic is the
possibility of serious infection, malignancy, cytokinerelease syndrome, anaphylaxis, and hypersensitivity.
Other examples of protein therapeutics are aflibercept
(VEGF Fc-fusion for macular degeneration), tbo-filgrastim
(G-CSF growth factor for neutropenia), peginterferon
beta-1a (PEGylated IFNb-1b for multiple sclerosis),
etanercept-szzs (TNFR-Fc-fusion for arthritis), glucarpidase (enzyme for kidney failure), taliglucerase alfa
(b-glucocerebrosidase for Gauchet Syndrome), ocriplasmin
(enzyme for symptomatic vitreomacular adhesion), and
sebelipase alfa (lysosomal acid lipase for lysosomal acid
lipase deficiency).
An important issue with the application of replacement
protein in therapy is the cost of production (and quality
control of purity). Biomanufacturing biologics involves
engineering a cell to produce a specific protein. In this
endeavor, genes encoding proteins usually employ
Escherichia coli bacterial cells or CHO cells and manufacturers establish a master cell bank (transferred to a
bioreactor) to supply genetically identical cells for future
products. The first biologic drug, insulin, was produced
Drug targets and drug-target molecules Chapter | 5
with E. coli and this was followed by human growth hormone, interferon, and parathyroid hormone. As work
continued it was realized that E. coli couldn’t produce a
wide range therapeutic proteins (specifically, highly complex proteins, such as monoclonal antibodies and certain
enzymes) due to two main obstacles: (1) bacterial cells
cannot correctly fold complex proteins and (2) they cannot
confer required posttranslational modifications, specifically
phosphorylation (addition of a negatively charged phosphate group to a protein by a kinase which changes its
conformation) and glycosylation (addition of a carbohydrate to a protein by a glycolase to ensure proper folding
and increase stability). Glycosylation is important to shape,
stability, and function of monoclonal antibodies. For
example, monoclonal antibodies (mAbs) in cancer therapy
recognize protein on the surface of a tumor cell to attract
white blood cells (i.e., macrophages); these attach to the
mAb and destroy the antibodyetumor cell complex. White
blood cells recognize mAbs based on their glycosylation
pattern; thus changes to the glycosylation pattern may increase or decrease mAb efficacy.
Production cells can be modified to produce improved biologics, i.e., SMARTag cells that overexpress formylglycinegenerating enzyme (FGE) which converts the amino acid
cysteine to the amino acid formylglycine a substance not found
in proteins naturally. Formylglycine contains an aldehyde
group which is attached to the entity to be delivered to the target
cell. The specificity of this reaction ensures that attachment
occurs only at the formylglycine sites, creating a uniform,
stable product. Production can have tangible effects on biologic
efficacy as in the case of the drug for leukemia Gazyva which is
produced in genetically engineered mammalian cell lines
overexpressing two alternative glycosylation enzymes
(different sugars on mAb). Gazyva has better clinical efficacy
than Roche’s earlier drug Rituxan (though both drugs use same
target) as Gazyva has a different glycosylation pattern that
makes the antibodyetumor complex more recognizable to
macrophages.
If the replacement protein can be administered directly to
the target organ and before permanent organ damage has
occurred, it can be an effective therapy. An important issue
for replacement proteins is the need for injection and/or
infusion administration. Another possible issue is immunogenicity. Specifically, the production of antibodies against
the replacement protein can pose problems. For example,
after administration of recombinant interferons for multiple
sclerosis, a reduction in clinical efficacy of the treatment was
noted due to antibody formation [34]. In fact, replacement
proteins such as IL-2, IL-1, IL-12, and interferon gamma can
be used as immunostimulatory agents in therapy.
Stability and purity of protein biologics are important
considerations in their therapeutic application. The
contamination of biological substances with viruses and the
possibility of protein conformational changes during
129
production serve as a caveat to the blanket production of
replacement proteins for therapy. In general, the chemical
and physical stability of proteins can be affected by factors
such as pH, temperature, surface interactions, and contaminants from excipients. For example, heterogeneity in
mAbs such as incomplete disulfide bond formation,
glycosylation, N-terminal pyroglutamine cyclization,
C-terminal lysine processing, deamidation, isomerization,
oxidation, amidation of the C-terminal amino acid, or
modification of the N-terminal acids by maleuric acid can
lead to heterogeneity in mAb-mediated treatment.
Protein therapeutics cannot solely be chemically synthesized but rather must be manufactured in living cells;
this can lead to variability in product due to differences in
cell lines, species origin, culture conditions, and variation
in posttranslational modification. Therefore, heterogeneity
in biologic composition is an issue and methods to detect
heterogeneity are important; one of the most important
methods to do this is the bioassay whereby the biological
activity of the protein is monitored for purity. An important
tool in this endeavor is the kinetics of interaction of drug
entities as this can be used to determine biologic purity.
The kinetics of interaction of a system can be used to
assess the homogeneity of the reactants. Specifically the
onset of effect of a single drug entity is governed by firstorder kinetics whereby a single entity (i.e., agonist) binds to
a receptor to produce a signal. If a second entity is present
in the milieu, and if it should be an antagonist, then a
complex onset of action of the action will result. It is not
inconceivable that an antagonist moiety may be produced
as modification through degradation of a biologic or antibody could alter the efficacy of that species but not its affinity. The observation of real-time kinetic effect in such a
system can be a powerful tool to discern the production of
an antagonist species. This is because, while the relative
affinities of the agonist and antagonist species will determine the overall equilibrium effect, the rate at which a
steady-state is attained by these two species could reveal
their presence. Thus, the rate of agonist response with time
(Respt) in a single entity system is given by:
Respt ¼ Respequil eðk1 ½A þ k2 Þt
(5.17)
where Respequil is the equilibrium steady-state response after complete onset, agonist concentration is [A], k1 and k2
are the respective rates of onset and offset. If, however,
there is another species in the system that blocks response
(antagonist [B]) then the receptor occupancy by A is given
by:
k1 ½Að1 lÞ k4 ðU jÞ k4 U Ut
þ
e
rA ¼
Uj
Uj
U
k4 j jt
e
(5.18)
j
130
A Pharmacology Primer
KA ¼ k1 ½Að1 lÞ þ k2
(5.19)
perturbations in the signaling end of the molecule would
leave a peptide that still binds and may function as an
(5.20) antagonist. For this simulation this system has been
KB ¼ k3 l½A þ k4
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi designed to model the most common scenario in these
2
U ¼ 0.5 KA þ KB þ ðKA KB Þ þ 4k1 k3 l½A½Að1 lÞ cases, i.e., the production of slow offset antagonist from a
(5.21) fast onset agonist. As seen in Fig. 5.39B, the expected
single-phase onset of agonism is converted to a biphasic
q
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2
j ¼ 0.5 KA þ KB ðKA KB Þ þ 4k1 k3 l½A½Að1 lÞ curve whereby the response increases and then wanes as the
antagonist species binds.
(5.22)
where l is the fraction of agonist converted to an antagonist. Thus, if the relative rates of onset and offset of the
agonist and antagonist species are different, then the observation of response in real time could reveal the heterogeneity of the system and show the presence of the antagonist
species.
Fig. 5.39A shows a system where an agonist (i.e.,
agonist biologic) degrades to an antagonist species to produce a mixture of agonist and antagonist in the receptor
compartment. This might be a scenario seen with bioactive
peptides that partly degrade to a fragment that still binds to
the receptor but does not signal. For instance, dynorphin-A
is a peptide with structure Tyr-Gly-Gly-Phe-Leu-Arg-ArgIle-Arg-Pro-Lys-Leu-Lys where the ‘message’ (signaling
moiety) is Tyr-Gly-Gly-Phe and the rest of the molecule is
the ‘address.’ In fact it has been proposed that Class B
GPCRs bind peptides through a two domain model. Specifically, the C terminus of the peptide interacts with the
receptor extracellular N-terminal domain promoting an
“affinity trap” that enables the engagement of the Nterminus of the peptide with the receptor transmembrane
domain required for receptor activation [35]. Thus,
5.4.2 Eliminating ‘undruggable’ proteins
through PROTACs
Nearly 650,000 ‘undruggable’ proteineprotein interactions
(PPIs) in the human interactome can be potentially
considered as novel therapeutic targets and only 2% of
these had been targeted with drugs by 2011. PPIs are
considered to be undruggable because they don’t have welldefined binding pockets. Undruggable proteins have contact surfaces that are usually flat, featureless, and relatively
large, interacting through electrostatic and hydrophobic
interactions, hydrogen bonds, and Van der Waals forces
over less well-defined, larger areas. Specifically these proteins have a multitude of polar and hydrophobic regions
and these surfaces can be very large and contain many
functional groups able to assume different orientations to
achieve free energy minima. In this energetic context, a
small molecule usually fails to compete with natural partners, mainly due to its size and the limited number of
interactions.
PPIs imply conformational changes in protein regions
with bonding groups and the associated structural
FIGURE 5.39 Schematic of a cellular response system where an agonist (red) activates a membrane-bound receptor to produce a signal. A portion of the
agonist forms an antagonist in solution (green) which can then bind to the receptor with possibly different kinetics. (B) The normally monophasic onset of
response in real time of a pure agonist will be converted to a biphasic response depending on the relative rates of onset and offset of the two species. The
amount of agonist degraded to antagonist determines the extent of the biphasic response.
Drug targets and drug-target molecules Chapter | 5
fluctuations can be reversible or irreversible. PPIs can be
divided on the basis of being “obligate” or “nonobligate”
complexes. Obligate PPIs: proteins are unstructured in
isolation but can achieve stability with binding interactions
colocalized in cellular compartments whereas nonobligate
proteins are compactly structured. In addition, PPIs can
yield homo- and hetero-oligomeric complexes with very
different lifetimes. Undruggable proteins can be selectively
removed with PROTAC technology. Proteolysis Targeting
Chimeras (Protacs) are unique hybrid molecules consisting
of three domains: (1) ligand binding domain (‘warhead’)
for a target protein, (2) ligand binding domain for E3
ubiquitin ligase, and (3) a linker joining the two domains.
These molecules produce a knockdown of the targeted
protein by directing the protein to the ubiquitin-proteosome
system (see Fig. 5.40). This has proven to be a useful
strategy for the degradation of various types of target
proteins related to a number of diseases including cancers,
viral infections, immune disorders, and neurodegeneration.
An advantage of PROTACs is the lack of requirement
for an efficacious (i.e., a catalytic) interaction between the
PROTAC probe and the target protein. An example of
the successful application of PROTAC technology is with
the molecule MZ1 (Fig. 5.41A). This is a chimera consisting of JQ1, a BET protein bromodomain inhibitor and
an E3 ubiquitin ligase. When such a ‘warhead’ is used (i.e.,
a molecule like JQ1 binding to the cancer-active protein
BDR4) the requisite activity of the molecule is an interaction that produces a change in the state of the target protein
(i.e., efficacy). With PROTACs, the only requirement of
this ‘warhead’ is the ability to bind to the target protein.
This has expanded the realm of interactions of affinity-
131
warhead molecules for target proteins; evidence for the
advantage of this strategy is seen in Fig. 5.41B and C where
it can be seen that the relative inability of the anticancer
molecule JQ1 to reduce BRD4 levels and tumor size is
considerably enhanced by the linking of JQ1 to the ubiquitin E3 moiety (Fig. 5.41C). Similarly, the androgen receptor PROTAC ARD-69 used in prostate cancer therapy is
100-times more potent than the potent androgen receptor
warhead [37]. In addition, PROTACs not only eliminate the
catalytic functions of enzymes such as kinases in cancer,
the destruction of the kinase also eliminates the noncatalytic scaffolding functions of these enzymes (i.e., focal
adhesion kinases, FAKs); conventional kinase inhibitors do
not inhibit all FAK functions. PROTACs also can be used
for so-called ‘undruggable’ targets that have no catalytic
activity. For example, the lack of a druggable site on the
surface of Signal Transducer and Activator of Transcription
3 (STAT3) has limited the exploitation of this target in
therapy but the development of PROTAC for STAT3 has
demonstrated tumor regression [36].
5.4.3 Peptides
Biologic peptides are an important drug class with a host of
therapeutic applications. Historically, the first successful
biologic peptide drug was insulin for Type 1 diabetes. The
discovery began in 1889 when Minkowski and von Mering
linked diabetes to the pancreas and then in 1910 when
Sharpey-Shafer identified insulin as key missing factor. In
1921 Banting removed insulin from islets to treat diabetes.
Shortly thereafter Banting, Collip, and MacLeod developed
insulin from cattle pancreas. The first large-scale
FIGURE 5.40 Schematic diagram of the mechanism of action of PROTAC molecules. The aim is to associate a target protein with the E3 ubiquitin
ligase which will then make the protein a target for proteolysis. The PROTAC molecule binds to both the target molecule and the E3 ligase causing the
ligase to place ubiquitin onto the target protein. This then signals the proteosome mechanisms of the cell to degrade the target protein.
132
A Pharmacology Primer
FIGURE 5.41 (A) The PROTAC MZ1 links a molecule known to bind to the cancer active protein BRD4 through JQ1 (a known ligand for BRD4
binding) to the ubiquitin system through an E3 ubiquitin ligase ligand. (B) The levels of BRD4 are more efficiently reduced by the PROTAC in JQ1
resistant-derived tumors than just the JQ1 molecule. (C) The improved reduction of BRD4 is shown to result in the MDA-MB-231R-derived tumors. Data
redrawn from del Mar Noblejas-López M, Nieto-Jimenez C, Burgos M, Gómez-Juárez M, Montero JC,Esparís-Ogando A, Galán-Moya EM, Ocaña1 A.
Activity of BET-proteolysis targeting chimeric (PROTAC) compounds in triple negative breast cancer J Exp Clin Cancer Res 38 (2019) 383.
FIGURE 5.42 Structure of insulin with various
modifications.
production of insulin was done by Eli Lilly from cattle and
pigs but allergic reactions were common. The first genetically engineered synthetic “human” insulin using E. coli
bacteria was made in 1978 and by 1982 Eli Lilly produced
biosynthetic human insulin under the brand name Humulin.
Insulin is a 51 amino acid peptide arranged in two
chains (A and B) linked with disulfide bonds (see
Fig. 5.42). It is made in the b-cells of the pancreas and
regulates blood sugar. Type 1 diabetes is caused by an
autoimmune destruction of normal b-cells causing the
Drug targets and drug-target molecules Chapter | 5
inability to regulate blood levels of sugar; if left untreated it
leads to a 2 to 4 times risk of heart disease and stroke,
blindness, and diabetic neuropathy (loss of sensation in
extremities leading to amputation). Due to the loss of bcells, the current treatment for type 1 diabetes is replacement with exogenous insulin. Analogs and modifications of
insulin have been made mainly to modify subcutaneous
administration pharmacokinetics through substitutions between B26 and B30, residues not critical for insulin affinity
for the receptor. The structures of two rapid-acting insulin
analogs (insulin aspart, insulin lispro) and the structures of
two long-acting insulin analogs (insulin glargine, detemir
insulin) are shown in Fig. 5.42. The onset, peak, and
duration of effect of various insulins are shown in Fig. 5.43.
Insulin Lispro and Aspart are ultrarapid; short-acting insulins allow administration just before meal to decrease
postmeal hypoglycemia. Regula insulin has a rapid onset
and can be used i.v. in emergencies or subcutaneously:
Before insulin lispro it was used for rapid onset but 1 h
before meal. Intermediate onset insulins (NPH, Lente) are
furnished in fine crystals suspensions not suitable for i.v.
administration but given subcutaneously. Ultralente Insulin
(long acting) is given in morning or morning and evening
and covers periods of 12e24 h. Supplemental doses of
regular insulin can be given with meals if needed. Insulin
glargine is an ultralong acting insulin with a peakless effect
lasting over 24 h. There are numerous devices used for the
absorption of insulin given i.v. (injection pens), subcutaneously (pumps), and through inhalation.
Thirty-two percent of the most ubiquitous class of drug
receptor, namely GPCRs, bind endogenous peptides. Specifically, over 85 endogenous peptides target 51 proteins
over half of which are GPCRs. Historically, after the
introduction of the first therapeutic peptide (insulin) four decades passed before the first synthetically produced
peptide hormones, namely oxytocin and vasopressin,
became therapeutic entities. However, the remarkable potency, low toxicity, and high selectivity of peptides favor
their entrance into therapeutic pharmacology and
133
replacement peptides and pharmacologically improved
peptides have now become important therapeutic agents.
There are generally three designations for types of therapeutic peptides: (1) natural peptides which are identical to
endogenous peptides although made synthetically, (2)
analog peptides that have substitutions from natural peptides to improve their activity, and (3) heterologous peptides obtained independently in screening efforts with no
relation to endogenous peptides (i.e., LY-2510924 for
CXCR4 [37]). Therapeutic peptides are being used to treat
many diseases including diabetes (insulin, dulaglutide,
semaglutide, exenatide), cancer (leuproline, octreotide,
goserelin), multiple sclerosis (glatiramer, actar), osteoporosis (teriparatide), acromegaly (lanreotide), irritable bowel
syndrome (linaclotide), and multiple myeloma (carfilzomib). Therapeutic peptides can be recombinantly made
natural peptides (calcitonin for inhibition of bone resorption
in osteoporosis) and parathyroid hormone (enhances release
of calcium from stores in bone for osteoporosis). Therapeutic peptides also can be natural products from fungi,
plants, and animals (i.e., cyclosporine from fungi and
bivalirudin from leeches). In addition, there are a large
number of neurologically active venoms from spiders,
scorpions, snails, and reptiles that furnish peptides for
therapeutic exploitation. For example, the incretin GLP1(7e37) elevates insulin secretion after food ingestion but
is rapidly destroyed by the enzyme dipeptidyl peptidase 4
(DPP4). One strategy to reduce this metabolism is through
engineering an a-aminobutyric acid residue into semiglutide to make semaglutide and a C18 fatty diacid at
Lys26; these modifications also increase binding to serum
albumin which, in turn, reduces renal elimination. Ultimately, the problem for GLP-1 was solved through the
discovery of a venom from the Gila monster, exendin-4,
which was used as the basis for the development of the
analog drug exenatide which is resistant to DPP4 for diabetes e see Fig. 5.44. In addition to being GPCR-targeted
drugs, venoms are also active as ion channel inhibitors (i.e.,
m-conotoxin from the venomous cone snail).
FIGURE 5.43 Time course of action of various insulins.
Ordinate axes are glucose infusion rates (mg/kg/min)
required to maintain constant glucose concentrations
(surrogate of duration and intensity of insulin action).
134
A Pharmacology Primer
FIGURE 5.44 Amino acid sequences of the incretin
GLP-1 showing the cleavage region by the enzyme
DPP4 and the sequence of exenatide, a peptide from the
saliva of the Gila monster with 53% homology with
GLP-1 (orange regions are unique to exenatide).
While some peptides act as receptor antagonists (i.e.,
atosiban is a blocker of the oxytocin receptor as a treatment
for preterm labor), most therapeutic peptides are agonists
targeting receptors such as the m and k opioid receptors for
pain, oxytocin, and vasopressin for induction of labor and
apelin and angiotensin receptors for cardiovascular disease.
As agonists, peptides have high affinity (pKi ¼ 8.4) and
potency (pEC50 ¼ 8.5). Peptide analogs of known natural
agonist peptides are a fruitful therapeutic avenue and recent
evidence indicates that peptide signaling is complex (due to
pleiotropic signaling mediated by peptide receptors); this
can be a positive in that more selective signaling may
result, but also a negative since synthetic peptide agonists
may have different signaling profiles from the natural
peptide. This is a direct result of the standard allosteric
phenomenon for GPCRs known as ‘biased signaling’
whereby the peptide agonist stabilizes a unique conformation of the peptide receptor to traffic agonist stimulus to
some signaling pathways in the cell at the expense of
othersdsee Chapter 6. This is a well-known ‘fine-tuning’
of receptor responses to targets with multiple natural agonists. For instance, within the chemokine system for control
of leukocyte migration in homeostatic and inflammatory
physiological processes there is apparent redundancy with
19 receptors that are activated by 47 chemokines. However,
this apparent redundancy may in fact be fine-tuning of
textured response. For example, while the chemokine
receptor CCR7 has two natural agonists, namely CCL19
and CCL21, these produce fundamentally different (biased)
cellular responses from activation of the same receptor.
Both agonists activate G-proteins but only CCL19 (not
CCL21) terminates the G-protein stimulation through receptor agonist-dependent phosphorylation and recruitment
of b-arrestin [38]. The corollary to this is that there would
no guarantee that a synthetic peptide for the CCR7 would
accurately mimic the natural CCR7 agonist(s) in terms of
signaling. Biased agonism has been explored to produce
improved therapeutic signaling and reduced toxic side effects for a number of receptor systems and peptide receptors are prominent in this area. For instance, the effects
of ghrelin on growth hormone release may be distinguished
from the food intake effects through biased ghrelin receptor
agonism [39]. Peptide receptor antagonists also can produce biased signaling therapeutically as in the case of
atosiban as it directs signaling of the receptor away from
Gaq-mediated calcium response toward the inhibitory cell
proliferation activity of Gai [40]; such a bias in signaling is
beneficial in treating cancer where oxytocin receptors are
known to be overexpressed.
Peptides can produce cellular signaling but also have
other efficacies that can be therapeutically useful. For
example, chemokines activate receptors such as CCR5 and
cause them to internalize into the cytoplasm thereby
removing them from the cell surface (Fig. 5.45A). In the
FIGURE 5.45 (A) Utilization of the cell surface receptor CCR5 by HIV-1 to cause infection. (B) Removal of cell surface CCR5 through internalization
by the chemokine RANTES; the chemokine dissociates from the receptor in the acidic environment of the cytoplasm allowing the receptor to recycle back
to the surface. (C) Internalization by the chemokine AOP-RANTES which does not dissociate in the cytoplasm thereby causing the lysosomal destruction
of the receptor and preventing recyclization back to the cell surface.
Drug targets and drug-target molecules Chapter | 5
135
FIGURE 5.46 Lethal radioactive payload is
attached to a somatostatin ligand which then binds
to the receptor. The tumor cell then internalizes the
complex to cause the radioactive moiety to produce
cell death. The inordinately high somatostatin receptor expression on tumor cells facilitates selectivity as a greater somatostatin receptor density
promotes greater lethal payload binding to tumors.
case of CCR5 (the point of infection for the virus HIV-1
causing AIDS) a viable strategy for AIDS treatment and
prevention is to suppress cell surface CCR5 receptors to
prevent infection. However, biased efficacy is operative in
this mechanism as well since different peptides stabilize
differently altered conformation of CCR5 to initiate internalization. Thus a chemokine such as RANTES (Regulated
on Activation, Normal T Expressed, and Secreted) internalizes CCR5 but dissociates in the slightly acidic
environment of the cell to allow the receptor to recycle back
the surface (and allow infection)dFig. 5.45B. Another
chemokine,
AOP-RANTES
(AminooxypentaneRANTES), stays bound to the receptor when it is internalized and causes it to be destroyed thus preventing
reinfectiondFig. 5.45C [41]. Another approach for therapeutic peptides is the incorporation of multiple activity
through incorporation of multiple peptide domains in the
molecule as in the case of the ‘twincretins’ which act on
GLP-1 and GIP receptors [42]. In addition to internalization, peptides can be used as tumor killing agents by virtue
of binding to tumor receptors with lethal payloads. For
example, many tumors overexpress somatostatin receptors
and somatostatin analogs carrying lethal nuclides like 111In,
90
Y, 68Ga, or 99mTor attached via chelating groups have
been used in the treatment of cancer e see Fig. 5.46 [43].
5.4.4 Antibodies
Antibodies (Abs) are large heterodimeric (molecular weight
z150 kDa) proteins within the immune globulin family
produced by B-cell lymphocytes; monoclonal antibodies
are produced by a single clone of B-cells. They consist of
two identical light chains and two identical heavy chains
(composed of different domains) held together by disulfide
bondsdsee Fig. 5.47. Antibodies have extraordinary
powers of recognition that can discern R versus S enantiomers of the same proteins or identify whether or not
proteins are phosphorylated. They bind to antigen proteins
with an extraordinarily high affinity (on the order of 1010
to 1011 M) through a region referred to as the antigenbinding fragment (Fab). Binding to antigen (often demonstrated in Western blots as a stained single band) is
extremely tight even withstanding repeated washes in
staining procedures. There are an estimated 375,000
proteineprotein interactions within the human interactome
and antibodies discern many that are resistant to modification by small molecules, i.e., Abs have been cited as
useful for so-called ‘undruggable’ proteins.
The main requirements of therapeutic antibodies are that
they have high antigen binding activity, high stability, and
low immunogenicity. Early antibodies that were produced
in mice led to antimurine antibodies causing an immunogenic response. Over the subsequent years this problem has
been greatly alleviated through successive production of
chimeric antibodies (mouse-human so-called ‘humanized’
antibodies) and then the production of fully human antibodies. Some examples of decreasing immunogenicity
range from muromab (mouse Ab for CD3 receptors),
infliximab (mouse-human chimeric Ab for TNF-a), palivizumab (humanized Ab for RSV-F protein), and panitumubab (fully human Ab for epidermal growth factor
receptor (EGFR)) [44]. In vitro libraries such as phage
display allow the selection of high affinity fully human
antibodies. The first fully human Ab, against antitumor
necrosis factor a (TNF-a) for rheumatoid arthritis adalimumab, was approved in 2002. Immunogenic reactions can
still occur in some cases with fully human antibodies [45];
for example, production of anti-TNF-a Abs can unmask
and reactivate latent tuberculosis [46].
Antibodies have a number of therapeutic advantages
including fewer off-target effects and drugedrug interactions, high specificity, and potentially high efficacy
through targeted therapy. Therapeutic monoclonal antibodies must reach high enough levels of serum titers to be
effective with sufficient half-life to provide protection.
Antibodies have a better dosing frequency (better serum t1/
136
A Pharmacology Primer
FIGURE 5.47 Antibodies are Y-shaped structures consisting of four
polypeptidesdtwo heavy chains and two light chains. The Fab fragment is
a region on an antibody that binds to antigens and it is composed of one
constant and one variable domain of each of the heavy and the light chain.
2), restricted CNS penetration, and less interpatient variability in terms of pharmacokinetics. In addition, the
combination of mRNA technology and Ab therapy has
advantages. The half-life of mRNA is controlled by the t1/2
of the Ab and the t1/2 of the mRNA and this can be an
advantage for Abs with intrinsically short t1/2s. The application of mRNA is also an advantage since, unlike utilization of DNA where there is the potential of integration of
the foreign DNA into the host and subsequent production
of anti-DNA antibodies, mRNA can deliver the genetic
information to produce the Ab in the cell itself without risk
of posttranslational modification. Sequences can be
designed rapidly and produced in high quantities during
outbreaks of disease. In addition, the therapeutic application of Abs has been extended through engineering of
antibodyedrug conjugates and bispecific binding modes.
There are numerous modes of action for Abs to produce
physiologically relevant effects. These are:
Ab blockade of receptors: Abs can be made to
antagonize receptors for therapeutic benefit. For example,
denosumab binds tightly to the human receptor (RANK) for
the activator of nuclear factor kappa-B ligand. The natural
agonist for this receptor is RANKL which when bound
induces osteoclast formation, function, and survival; this, in
turn, causes bone resorption, a problem in osteoporosis.
Denosumab binds to RANK to prevent activation by
RANKL and thus reduces bone resorption [47]. Another
receptoreAb interaction is seen with the PTH receptor.
Fig. 5.48 shows the effect of an ECD-scFvhFc Ab; the a1
helix of the ECD partially overlaps with the known binding
site in the PTH (1e34) receptor; therefore this Ab inhibits
b-arrestin-2 recruitment after PTH (1e34)-driven receptor
activation; this represents a pathway-selective monoclonal
antibody to inhibit distinct PTH1R signaling pathways
[48]. Direct blockade of cell surface receptors is also a
useful strategy for the treatment of cancer as tumors often
overexpress proteins such as EGFRs and HER2 which can
go on to become drug targets. Ab blockade of these receptors by drugs such as trastuzumab decreases tumor
growth rate, induces apoptosis, and sensitizes tumors to
chemotherapy in HER2-positive breast cancer [49]. Antibodies have been shown to block many GPCRs and have
even differentiated specific conformations of GPCRs [50].
In addition, they have been shown to block enzymes such
as the allosteric blockade of trypsin-like serine protease
hepatocyte growth factor activator (HGFA) [51].
Ab production of Receptor Response: Antibodies also
can induce receptor conformational changes to produce
agonist responses such as receptor downregulation and cell
signaling either through producing ligand binding or allosteric modulation mediated by binding to sites distinct from
the orthosteric binding site [52]. Ab-agonists have been
made to activate receptors for natural agonists such as
FIGURE 5.48 Blockade of PTH receptors by an antibody. (A) Schematic of activation of receptoreb-arrestin interaction by PTH1-34 and interference
of PTH1-34 binding to the receptor and failure to activate b-arrestin in the presence of the antibody. (B) Concentration-dependent inhibition of b-arrestin
recruitment by PTH1-34 activated receptors by the antibody. Data redrawn from K. Sarkar, L. Joedicke, M. Westwood, R. Burnley, M. Wright, D.
McMillan, B. Byrne. Modulation of PTH1R signaling by an ECD binding antibody results in inhibition of b-arrestin 2 coupling Sci Rep. 9 (2019) 14432.
Drug targets and drug-target molecules Chapter | 5
cytokines, hormones, and growth factors while others, such
as anti-CD20 antibodies, promote apoptosis. Some Abagonists promote dimerization to produce response while
others mimic natural signaling, i.e., stimulation of FGF21
for diabetes and obesity [53]. An example of Ab-agonism is
shown in Fig. 5.49 showing the internalization of mGlu7
receptor dimers on the cell surface by the Ab MAB1/28; the
doseeresponse curve shows the inhibition of cyclic AMP
blockade by the antibody as it internalizes the receptors.
Some antibodies produce direct response in cancer to
produce cell death. For example, rituximab kills tumor cells
through direct binding to tumor CD20 receptors to trigger
apoptosis. Similar direct tumor toxicity effects have been
targeted to other receptors such as CD38 (daratumubab),
EGFR (cetuximab, panitumab, necitumubab), GD2
(dinuximab), HER2 (trasuzumab, pertuzumab), PDGFRa
(orlaratumab), and SLAMF7 (elotuzumab) [54].
Ab scavenging of endogenous ligands: Another mode
of antibody action in cell systems is the scavenging of
biologically active molecules. In this scenario, antibodies
are present in the receptor compartment and tightly bind
released or circulating mediators to inactivate them and
prevent signaling. For example, a common approach to
autoimmune diseases is the blockade of pro-inflammatory
cytokines such as TNF-a, a mediator causing vasodilation
and inflammation [55]. There are direct therapeutic applications of this scavenging strategy in the treatment
of migraine headache. Specifically, it is postulated that
the peptide CGRP is released from trigeminal nerves
to produce cranial artery vasodilation to cause pain; antibodies for CGRP can be administered to bind to the
released CGRP and prevent it from activating receptors as
is seen with the mAbs erenumab, fremanezumab, and
137
galcanezumab [56]dsee Fig. 5.50. The pseudoirreversible
binding of the Ab is an important aspect of this mechanism;
the application to CGRP can be modeled in that same way
as a time-dependent enzyme inhibition. Fig. 5.51A shows
the first-order rate of reaction between CGRP and the Ab as
a function of Ab concentration; this translates to
concentration-dependent kinetic binding as shown in
Fig. 5.51B. The result of such scavenging is shown schematically in Fig. 5.51C. Thus, while a wave of CGRP is
released to cause vasodilatation (solid line), the concentration of CGRP is reduced in a concentration-dependent
manner by the Ab as shown by the broken lines.
While Ab interactions with natural ligands can be an
advantageous therapeutic strategy, the unexpected production of antidrug antibodies (ADAs) due to immune reactions to biologic drugs can be a serious problem leading
to reduced efficacy of drugs, rashes, and systemic inflammatory responses [57].
Antibody-dependent Cell-mediated Cytotoxicity
(ADCC): Antibodies can bind to two specific domains
where the Fab fragment binds to the antigen on the cancer
cell and the Fc (Fragment crystallizable) domain binds to
immunocompetent cells to cause antibody-dependent
cell-mediated cytotoxicity and Ab-dependent cell phagocytosis by macrophages. Fc receptors are found on B
lymphocytes, follicular dendritic cells, natural killer cells,
macrophages, neutrophils, eosinophils, basophils, human
platelets, and mast cells; these are involved in the protective
functions of the immune system. Abs also can be used to
interfere with autoimmune diseases whereby activated CD4
lymphocytes in peripheral lymph nodes interact with
antigen-presenting cells and B-cells. Specifically, they can
block and deplete T cells and/or B cells, inhibit the
FIGURE 5.49 Activation of mGlu7 receptor dimer by the agonist L-AP4 to produce reductions in cytosolic cyclic AMP. (A) Binding of the Ab Mab1/
28 causes internalization of the receptor to block the L-AP4 receptor inhibition of cAMP. (B) Cyclic AMP levels in cells were elevated by addition of
forskolin and then reduced to a level of 30% maximum by the addition of L-AP4. Further addition of Mab1/28 internalizes the receptor to block the L-AP4
agonism and allow forskolin elevation to be visualized. Data redrawn from C. Ullmer, S. Zoffmann, B. Bohrmann, H. Matile, L. Lindemann, P.J. Flor, P.
Malherbe. Functional monoclonal antibody acts as a biased agonist by inducing internalization of metabotropic glutamate receptor 7. Br. J. Pharmacol.
167 (2012) 1448e1466.
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A Pharmacology Primer
interaction of T cells and antigen-presenting cells, block Tand B-cell recruitment, block T-cell differentiation and
recruitment, and block pro-inflammatory cytokines. The
activation and migration of these cells to disease-targeted
parenchyma leads to the production of cytokines and proinflammatory molecules leading to cell damage and disease progression.
Ab-induced cell fusion can be a powerful mechanism
for the treatment of autoimmune disease in that therapeutic
antibodies can induce cell fusion through dual binding of
antigens on the cell surface and binding to other species.
For example, a fusion with natural killer cells in the immune system results in release of inflammatory cytokines
and chemokines to kill the antigen containing cell (i.e.,
perhaps a cancer cell)dsee Fig. 5.52. The scheme is shown
below yielding an explicit equation for the production of
the cell fusion initiating species (in this case a dimer of Ab
and antigen)
(5.23)
The equilibrium equations for the system are:
FIGURE 5.50 Scavenging trigeminal neuronally released CGRP by
antibodies as a method of preventing CGRP-mediated vasodilatation in
migraine.
FIGURE 5.51 First-order chemical reaction between antibodies and endogenous
mediators. (A) The concentration-dependent
interaction between the Ab and substrate.
(B) At each concentration of Ab, the rate of
depletion continues with time. Three
different concentrations of Ab are shown
with first-order rates increasing with
increasing Ab concentration. (C) A real-time
trace of released endogenous mediator, in
this case CGRP in migraine, under control
conditions (solid line curve) and three concentrations of scavenging Ab as shown in
panel B (broken line curves).
½Ag ¼ ½Ab Ag=½AbKa
(5.24)
Drug targets and drug-target molecules Chapter | 5
139
FIGURE 5.52 Ab-mediated cell fusion for elimination of a cancer cell by a natural killer cell. Antibodies for complexes with antigens on the cancer cell
surface (process 1) leading to fusion with FcgRIIIA on the natural killer cell (process 2) and subsequent release of active cytokines for cell death (process 3).
Series processes lead to amplification of signals as shown in the doseeresponse curves for each process.
½Ab Ag ¼ ½Ab Ag Ab=a½AgKa
curves for production of fusion species (process 1), cell
fusion (process 2), and release of cytokine (process 3) are
where the concentration of antibody is [Ab], of antigen is
shown in Fig. 5.52.
[Ag], the AbeAg complex is [Ab-Ag] and the dimer speSome Abs kill tumor cells by multiple mechanisms;
cies of two antibodies to the antigen complex as [AbeAge
for example, daratumumab binds CD38 and its Fc fragment
Ab]. The binding association constant of Ab and Ag is Ka
is bound by C1q, initiating a complement cascade
and a the effect of the binding of a single Ab to the Ag on
and resulting in a membrane-attack complex (MAC) leadthe affinity of the complex with the second Ab. The receping to cell lysis and death. Specifically, an MAC is
tor conservation equation is:
a complex of proteins formed on the surface of pathogen
½Agtotal ¼ ½Ag þ ½Ab Ag þ ½Ab Ag Ab (5.26) cell membranes (due to activation of the host’s complement
system) forming pores that disrupt the cell to cause
where [Agtotal] is the total complement of antigen on the
cell lysis e Fig. 5.53A. In addition, daratumumab can
cell. This yields an equation for the fusion initiating species
bind CD38 allowing its Fc fragment to bind an FcR-bearing
(defined as f) as:
effector cell, such as a natural killer cell, leading to
activation
of
antibody-dependent
cell-mediated
f ¼ ½Ab Ag Ab=½Agtotal cytotoxicitydFig. 5.53B. Additionally, once bound
¼ ða½Ab = KA ½Ag = KA Þ=ð½Ab = KA ð1 þ a½Ag = KA Þ þ 1Þ
to CD38, the daratumumab Fc fragment binds to an
(5.27) FcR-bearing macrophage to induce antibody-dependent
where KA is the dissociation constant for the AbeAg com- cellular phagocytosisdFig. 5.53C or the FcR-mediated
cross-linking can cause direct apoptosis to cell death e
plex (KA ¼ 1/Ka).
The creation of the fusion species leads to cell fusion Fig. 5.53D [58].
Bispecific Antibodies: Improved efficacy and selecand the equation defining this interaction if given by:
tivity can be achieved with antibodies that bind dual targets.
Fusion ¼ h ¼ f½FcgRIIIA= f½FcgRIIIA þ Kfusion
These can be bivalent, multivalent, or Fc-receptor engi(5.28) neered (enhanced Fc receptor function) antibodies that bind
to more than one target with increased potency. The dual
where the binding species on the killer cell is [FcgRIIIA]
binding allows simultaneous binding of cytotoxic T cells
and the dissociation constant of the f-[FcgRIIIA] complex
and antigen-expressing tumor cells for enhanced cytotoxis Kfusion. Once fusion takes place, the amount of inflammaicity and higher binding specificity. This immunotheratory cytokines (r[cytokine] as a fraction of the maximal pool
peutic approach to cancer therapy causes the body’s own
of cytokine) released is given by the forcing function
immune system to eliminate or control cancer. For
r½cytokine ¼ h=ðh þ bÞ
(5.29) example, obinutuzumab, an anti-CD20 Ab with enhanced
FcgR binding, has improved efficacy over the firstwhere b is the sensitivity of the killer cell for release of generation Ab rituximab [59]. Multivalent antibodies such
cytokine to cell fusion.
as catumaxomab bind to CD3 on cytotoxic T cells and
As with any multiple series biochemical functions, there EpCAM on human adenocarcinomas e see Fig. 5.54. In
is an amplification step with each increment process; the addition to enhanced potency, Ab specificity can be
(5.25)
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A Pharmacology Primer
FIGURE 5.53 Four ways in which the therapeutic Ab daratumumab kills tumor cells. (A) Daratumumab jointly binds to CD38 and C1q via the Fc
fragment to induce a complement cascade resulting in production of a membrane-attack complex (MAC) which causes cell lysis and death. (B) Daratumumab binds CD38 while its Fc fragment binds an FcR-bearing effector cell, such as a natural killer cell. (C) Daratumumab jointly binds CD38 and an
FcR-bearing macrophage to induce antibody-dependent cellular phagocytosis. (D) Daratumubab FcR-mediated cross-linking causes apoptosis. Redrawn
from L. Sanchez, Y. Wang, D.S. Siegel, L. Michael, M.L. Wang. Daratumumab: a first-in-class CD38 monoclonal antibody for the treatment of multiple
myeloma J. Hematol. Oncol. 9 (2016) 51e59.
FIGURE 5.54 Bispecific antibody binding brings T cells, tumor cells,
and macrophages together to promote tumor death.
improved by engineering dual targeting for two antigens
(bispecific Abs) thereby sparing cells that contain only one
of the antigens and thus reducing side effects. For example,
bispecific IgG antibodies targeting both HER2 and EGFR
eliminate tumors containing both antigens but not cells
containing only one of the targets [60].
AntibodyeDrug Complexes: Another application of
antibodies is the delivery of toxic payloads to pathogenic
cells in so-called ‘antibodyedrug complexes’ (ADCs).
Specifically, these are humanized or human monoclonal
antibody conjugates with highly cytotoxic small molecules
(payloads) joined to the antibody for an antigen on the
target cell (i.e., cancer cell) with various linkers. This
technology enables the selective delivery of the cytotoxin
to the target cancer cell to favorably bias the pharmacokinetics of cancer therapy and reduce the possibility of systemic side effects. Thus the high affinity binding of the
antibody to an antigen on the target cell produces a complex that is internalized by endocytosis. This results in the
proteosomic destruction of the complex and release of the
cytotoxic payload which then kills the cell e see Fig. 5.55.
There are four factors involved in the successful
implementation of this approach: blood flow to the tumor,
Drug targets and drug-target molecules Chapter | 5
141
FIGURE 5.55 The delivery of a cytotoxic
payload to a cancer cell by an antibody
ADC (antibodyedrug complex). The ADC
selectively binds to the antigen on the cell
surface of the target cell and the resulting
complex is internalized via endocytosis.
Once internalized, the complex is degraded
by the proteosomic mechanism of the cell
and the cytotoxin is released to cause cell
death.
transport across the capillary wall (extravasation), diffusion
through the tissue, and, finally, binding and internalization
at the cell surface. The introduction of smaller format drug
conjugates (from 80 to 1 kDa) has greatly increased the
effectiveness of this strategy [61]. An example of this type
of strategic deliver of a potent cytotoxic drug for cancer
treatment is the use of the mAb for HER2 trastuzumab
linked to the cytotoxin emtansine [62]. Another variant on
ADC technology utilizes immunoliposomes (liposomes
containing cytotoxic drug) guided to the tumor through
Ab binding [63]. This technology has been applied to
the delivery of several kinds of toxic drugs to tumors
including DNA damaging agents such as duocarmycins
and camptothecin analog topoisomerase inhibitors. In
addition to toxic molecules used as a payload for these
complexes, lethal radioactivity can be introduced into the
tumor cell through radioimmunoconjugates such as CD20
targeted 90Y-ibritumobab tiuxetan and 131I-tositumobab.
The application of various linker chemistries to the payload
and antibody is the currently active area of research in this
field [64].
5.4.5 Immunotherapy
2. Immune checkpoint inhibitors: These block immune
checkpoints, a part of the immune system that limits
inappropriate immune responses; blocking these results
in a powerful immune response against cancer. Immune
checkpoints are a normal part of the immune system
and prevent an immune response from destroying
healthy cells. These checkpoints engage when proteins
on T cells recognize and bind to antigens on cancer
cells. When such ‘checkpoint proteins’ and their partners engage this turns off the T cells: in cancer this prevents T cells from destroying tumors. Two checkpoint
proteins are PD-1 and its partner protein PD-L1 and
some tumors turn down the T cell response by producing elevated PD-L1. Anti-PD-1 or Anti-PD-L1 molecules prevent the tumor protective response against
T cells to thus increase T cell killing of cancer cellsd
see Fig. 5.56.
3. T-cell transfer therapy: Also called adoptive cell therapy, adoptive immunotherapy, or immune cell therapy.
In this technique, immune cells are taken from the tumor and modified to attack cancer cells. T cells from
a patient’s blood are transfected to express a chimeric
antigen receptor (CAR) that seeks and binds to protein
on tumor cell.
4. Vaccines: These boost the immune system’s response to
cancer cells.
In addition to the application of antibodies to produce lethal
signals to tumor cells and marking tumor cells for
destruction, there are other approaches to mobilizing the
immune system to destroy cancer cells.
5.4.6 Vaccines
1. Immune system modulators: These enhance the immune
response against cancer and can be aimed at specific
areas or be general to the immune system.
Vaccines form a large category of therapeutically important
biologics. After a person has received a vaccine and
responded to it they develop immunity, i.e., their immune
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A Pharmacology Primer
FIGURE 5.56 Checkpoint protein
inhibitors as anticancer drugs.
T cells sense foreign cells (i.e., tumor cells) through binding of T-cell
receptors to tumor cell antigens.
However, a natural protective
mechanism to prevent T-cell
destruction of normal cells exists in
the form of checkpoint proteins.
Specifically, when the PD-1 probe of
the T-cell encounters a PD-L1 moiety on the foreign cell, T-cell
destruction is blocked. To cancel
this protection of tumor cells, antiPD-L1 or anti-PD-1 ligands can
block the inhibition of checkpoints
and allow tumor cell destruction.
system is prepared for an infection. Thus when a vaccinated
person is exposed to a virus (for example, hepatitis B) or
bacteria (for example, diphtheria), his or her body is able to
destroy the virus or bacteria and prevent the disease. It is
important for everyone to get the vaccine to give the
community “herd” immunity to prevent severe outbreaks of
diseases. Vaccines are used for the prevention of a number
of diseases including diphtheria, hepatitis A and B, human
papillomavirus, influenza, measles, meningococcal disease,
mumps, pertussis, pneumococcal disease, polio, rubella,
tetanus, and varicella.
Normally the body fights infection with white cells
(macrophages, B-lymphocytes, and T-lymphocytes). Macrophages digest dead cells and disease matter leaving
behind fragments (antigens) which then stimulate the production of antibodies through B-lymphocytes. Tlymphocytes attack infected cells and some of these
remain as ‘memory cells’ to fight future infections. Vaccines imitate infections to trigger production of Tlymphocytes and antibodies. There are numerous sources
of vaccines ranging from live attenuated vaccines (live
weakened virus or bacteria such as those used for rubella
and chickenpox), inactivated vaccines (killed infective
component such as those used for polio), toxoid vaccines
for bacteria that produce toxins (producing weakened
toxins called toxoids), subunit vaccines containing only
parts of the virus or bacteria (essential antigens such as
DTaP vaccines for pertussis), and conjugate vaccines
containing antigens on a carbohydrate outer coating to
disguise the antigen (treatment of Haemophilus influenzae
Type B). A useful method of delivering instructions to cells
to produce viral or bacterial proteins is through mRNA and
this can be an advantageous approach to vaccine therapy.
This is because mRNA vaccines only carry the information
to make a small part of a pathogen, thus preventing cells
from producing live pathogen. The mRNA molecules
contain the genetic material to instruct cells to make a viral
protein that triggers an immune response. The first successful and approved mRNA vaccine was made for treatment of COVID-19 a disease caused by the coronavirus
(named for the crownlike spikes on their surface) known as
SARS-CoV-2. The mRNA produces the unique spike
protein to act as an antigen for the production of the protecting antibodies.
5.4.7 Nucleic acidebased drug species
Deoxyribonucleic acid (DNA) and ribonucleic acid (RNA),
linear polymers of nucleic acids, have now entered the
realm of stand-alone therapies but delivery of these two
cells is still problematic. Historically, nanoparticles have
been the main technology used for delivery of nucleosides
to cells and in vivo. While viral vectors also have been
employed, the ease of synthesis, low toxicity, and limited
immune response of nonviral delivery systems (liposomes,
bacteriophages) make these superior. Specifically, liposomes protect the nucleotides from nuclease, penetrate the
cell membrane, and deliver material to target cells.
5.4.7.1 DNA (gene therapy)
Gene therapy uses genetic material with the aim of
changing the course of a disease. These can be single-gene
diseases where there is a change in only one gene as in the
case of cystic fibrosis, an inherited disease characterized by
accumulated thick mucous that causes respiratory and
digestive problems. Other examples include Huntington’s
disease which is a progressive brain disorder that causes
uncontrolled movements and emotional changes with loss
of cognition, and sickle cell disease, a progressive genetic
disease caused by sickle hemoglobin leading to anemia,
Drug targets and drug-target molecules Chapter | 5
blood vessel disease, and blood vessel damage. Yet other
types of diseases are chromosomal diseases where parts of
chromosomes are altered or missing and complex genetic
diseases where changes occur in two or more genes.
Gene therapy can be defined as something that contains a recombinant nucleic acid used to regulate, repair,
replace, add to, or delete a genetic sequence in the host
cell. This can be achieved by transcription and/or translation of transferred genetic material that is integrated into
the host genome. This can be done in generally two ways:
germ line genetic therapy or somatic gene therapy. The
latter strives to insert new genetic material into target cells
without passing the change on to the next generation. In
germ line therapy, the change is passed on to future generations. Current therapies are centered on somatic gene
therapy.
One way gene therapy can be achieved is by adding
new genes which then give the cell new instructions to treat
the disease at the genetic level. Another approach is
through editing genes either through gene disruption or
inactivation which creates targeted breaks in the DNA
without instructions on how the cell can repair those breaks.
This approach, utilized for cancer, infectious diseases, and
neurodegenerative diseases, disrupts and/or inactivates the
gene. Yet another strategy is to produce gene correction or
insertion whereby targeted breaks in the DNA are made but
with instructions to the cell how to repair those breaks. This
strategy, used for treatment of genetic diseases and
immuno-oncology, corrects the function of the gene or
inserts functioning genetic material. One example of this
approach is CAR T-cell immunotherapy involving
Chimeric Antigen Receptor T-cells (CAR T-cells) which
143
are a person’s own harvested T cells to which genetic
material has been added to cause these T cells to attack
cancer cells. The genetic material, which can be introduced
via a lentiviral vector, instructs the T cell to express an
artificial chimeric antigen receptor which will enable the
T cell to recognize and attack cancer cellsdsee Fig. 5.57.
Some examples of approved gene therapies to date are
adeno-associated virus vector delivered in vivo for inherited retinal dystrophy and another for spinal muscular atrophy and ex vivo delivery (lentivirus) for acute
lymphoblastic anemia and retroviral vector delivery for
refractory large B-cell lymphoma.
A main focus of these techniques is the optimization of
delivery vectors which could be plasmids, nanostructures,
or viruses, and current research is aimed at providing more
specific and efficient gene transfer vectors. There has been
more experience with viruses as these are excellent for cell
invasion and insertion of genetic material. The most widely
used viral vectors are modified human immunodeficiency
virus, lentivirus, adenovirus, adeno-associated virus, and
herpes simplex virus. The desired gene is delivered with a
therapeutic gene expression cassette composed of a promoter that drives gene transcription, the transgene of interest, and a termination signal to end gene transcription.
However, there are concerns for possible latent immune
responses from these strategies. While retroviruses predominate as a preferred method, there is a risk with this
approach in the form of integration of the transgene into the
host genome (insertional mutagenesis) leading to possible
new cancers. Nonviral approaches utilize layer-by-layer
based nanoparticles, liposomes, and cell-penetrating
peptides.
FIGURE 5.57 Schematic of gene delivery to cells to enable Chimeric Antigen Receptor T-cells (CAR T-cells) destruction of foreign tumor cells. A gene for
an antibody targeting a tumor cell antigen is inserted into a T cell which then expresses the antibody to allow the T cell to seek and destroy the tumor cell.
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A Pharmacology Primer
Currently gene therapy is aimed at recessive gene disorders (cystic fibrosis, hemophilia, muscular dystrophy,
sickle cell anemia), acquired genetic diseases such as cancer, and certain viral infections (i.e., AIDS). Specifically,
some examples of gene therapy treatments are genetic
disorders such as adenosine deaminase deficiency, a-1antitrypsin deficiency, cystic fibrosis, familial hypercholesterolemia, Gaucher’s disease, and hemophilia B. As with
any therapy, there are inherent risks. For gene therapy this
includes harmful immune reactions, complications from the
inserted genetic material (i.e., insertional oncogenesis
involving DNA mutations), adverse events associated with
off-target editing, and unexpected gene activation or
inactivation.
In addition to the introduction of new genes into cells,
DNA-based oligonucleotides also can be used therapeutically. These are short single-stranded DNA-based oligonucleotides that are complimentary to a target mRNA to
form at DNAeRNA hybrids that modulate protein
expression through the RNAi pathway (vide infra). They
can inhibit translation or even increase translation efficiency by blocking an upstream open reading frame. For
example, the oligonucleotide-based drug mipomersen silences mRNA through antisense for the treatment of high
cholesterol.
5.4.7.2 CRISPR
Another approach to modifying DNA for research and
therapy is through Clustered Regularly Interspaced Short
Palindromic Repeats (CRISPR) technology. This utilizes a
family of DNA sequences found in the genomes of prokaryotic organisms such as bacteria and archaea. Bacteria
utilize such sequences from DNA fragments to detect and
destroy DNA during infections and play a role in antiviral
(i.e., antiphage) defense thus providing a form of acquired
FIGURE 5.58 Schematic of a CRISPR procedure
whereby a sequence of DNA linked to a Cas-9
enzyme seeks a corresponding sequence on a
cellular intrinsic DNA. This allows the Cas-9 to
sever the DNA strand. At this point, a number of
possibilities from DNA destruction, repair, or
insertion can take place to alter the genetic makeup
of the cell.
immunity. CRISPR is a gene-editing technology based on
this natural defense mechanism in bacteria against viral
DNA. When foreign DNA is detected by the bacteria it
produces two types of short RNA one of which contains the
sequence of the invading DNA (known as the ‘guide’
RNA). These two RNAs form a complex with a DNA
cutting enzyme CAS9. The guide RNA finds the corresponding sequence in the host DNA and the CAS9
sequence binds to the region to allow CAS to cut the DNA.
The cell then fixes the break which can result in (1)
disabling a gene, (2) repair it to fix a mistake, or (3) insert a
new genedsee Fig. 5.58. Therapeutically, CRISPR can be
used to edit a patient’s T cells to convert them to cells that
will seek and destroy cancer cells. One such approach
utilizes four genetic modifications made to T cells one of
which allows T cells to identify NY-ESO-1, a molecule on
cancer cells. CRISPR is used to remove three genes: two
that can interfere with the NY-ESO-1 receptor and another
that limits the cells’ cancer-killing abilities. The finished
product, dubbed NYCE T cells are grown in large numbers
and then infused into patients. CRISPR also has applications to research such as exploring origin of the power
promoting domain movement for initiating cleavage.
5.4.7.3 Messenger RNA
Another nucleotide-based therapy utilizes messenger RNA
(mRNA). mRNA is single-stranded synthetic RNA, structurally resembling natural mRNA, that transiently expresses
proteins by utilizing the natural machinery of the cell to
translate an in vivo message for a particular protein, i.e., a
designed mRNA can produce a protein of choice to alter a
disease state. For example, mRNA in lipid nanoparticles
has been used to replace Factor IX (FIX)-deficient mouse
model of hemophilia; the levels of FIX remain consistent
over repeated administration [65]. A useful property of
Drug targets and drug-target molecules Chapter | 5
synthetic mRNA is that it does not need to enter the cell
nucleus. Another advantage inherent in this technology is
that the mRNA is transiently active and is completely
degraded by natural metabolic pathways; therefore in
addition, it does not integrate into the natural cell genome
(avoiding a threat of insertional mutagenesis). Structural
changes can be made to natural mRNA to modify the
synthetic mRNA for specific purpose.
There are two approaches to the introduction of synthetic
mRNA for therapeutic advantage. One transfers mRNA into
patient’s cell ex vivo and then adoptively transfects back
those cells to the patient. The other is through direct delivery
of mRNA in vivo. The challenge of in vitro delivered mRNA
is to achieve as high net level of encoded protein and also to
transfect as many cells as possible. Technology has advanced
to reduce the impact of problems with this technology such as
short half-life and unfavorable immunogenicity. In vitro
administered negatively charged mRNA must cross the cell
membrane and passive diffusion is minimal. Once in the
145
cytoplasm, highly active ubiquitous cytoplasmic RNases
degrade the mRNA; complexation of mRNA (i.e., protamine
and nanoparticle carriers) can be used to facilitate cell uptake
and retard RNase degradationdsee Fig. 5.59. Specifically,
introducing structural elements into the mRNA that modulate
translation and RNA metabolism can greatly increase mRNA
halftime in the cytoplasm. The translated protein product in
the cell undergoes posttranslational modification and guided
by signal peptides (either intrinsic to the cell or recombinantly engineered) to the appropriate cellular compartment
or secreted by the cell. Standard single-stranded mRNA has
50 cap and 30 poly(A) tail and an open reading frame encoding
the protein of interest marked by start and stop codons
flanked by untranslated regions (see Fig. 5.60) and advances
have been made to modify these regions to produce more
therapeutically advantageous mRNAs. For example the
poly-tail and cap structure control the efficiency of translation and stabilization of mRNA from decay and the UTR’s
control translation and half-life.
FIGURE 5.59 Schematic of the delivery of
mRNA to cells (liposome or naked mRNA) to cause
translation of the encoded protein for a variety of
outcomes (production of secreted protein, cell protein, membrane protein, antigen, or cytokine).
FIGURE 5.60 Modifications of mRNA to optimize delivery and function for control of protein
production in cells.
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A Pharmacology Primer
In general mRNA is an effective method of inducing
protein production in cells. This can have a range of useful
applications such as, for example, increased regeneration of
myocardial tissue after myocardial infarction [66],
replacement of Factor IX in hemophilia [65], and various
hepatic diseases [67]. Therapeutically mRNA is used to
treat a variety of problems ranging from cancer, infectious
and autoimmune diseases, and diseases requiring protein
replacement. A major consideration in the application of
mRNA for therapy is pharmacokineticsdsee Chapter 10.
The RNA Interference (RNAi)-based Therapy: It is
now appreciated that RNA does not only transfer information from DNA to protein processing systems but also
plays significant structural, enzymatic, and informationdecoding roles during protein synthesis. Within this system the RNAi pathway can be used therapeutically. The
natural function of RNAi is protection against invasion by
genetic material (i.e., viruses) producing aberrant RNA;
therefore RNAi can be a powerful defense. RNAi is a
process whereby RNA molecules with sequences complementary to a gene’s coding sequence to induce degradation
of the corresponding mRNAs to block the translation of
mRNA into protein. RNA interference takes place in the
cytoplasm (access to the nucleus is not necessary); therefore it has great therapeutic potential in treatment of cancers, viral infection, and genetic disorders. RNAi can be
used to suppress the expression of disease-related genes
and also to induce posttranslational gene silencing. In the
cell, the endoribonuclease Dicer cleaves endogenous or
exogenous double-stranded RNA into 21- to 23-nucleotide
siRNA which then unzips to a passenger strand (that is then
degraded) and a guide strand. This guide strand is incorporated into the RNA-induced silencing complex (RISC is
an Argonaute protein with an inserted RNA guide strand
and other proteins) which then recognizes and performs
sequence-specific cleavage of the target mRNA.
A possible concern with these approaches is whether it is
completely safe to highjack the RNAi pathway as there can
be adverse effects from a competition between endogenous
miRNA and therapeutic miRNA. In addition, there may be
unwanted activation of the system of innate immunity.
Exploitation of the RNAi pathway has come of age with the
production of patisiran, a treatment for hereditary
transythretin-mediated amyloidosis (build-up of amyloid in
peripheral nerves). Other molecules being developed include
QP1-1002 (P53 based treatment for delayed graft function),
tivanisitran (TRPV1 based treatment for dry eye), fitusiran
(antithrombin for hemophilia A, B), and inclisiran (PCSK9based treatment for acute hepatic porphyrias). Synthetic
RNAi triggers are usually between 15 and 30 basepairs in
length; smaller double-stranded RNAs cannot engage with
RNAi machinery while RNA longer than 30 bp can induce
cytotoxicity. There are various types of small RNA that can
be applied to therapy with this system:
Short interfering RNAs [siRNAs]: siRNAs are basepaired duplexes that are completely complimentary to
target mRNA and facilitate silence of the target gene.
siRNAs are ‘short’ stable double-stranded molecules
(21e23 nucleotides long) which can be synthesized
chemically. Chemical modifications to siRNA can affect
sensitivity to ribonucleases, recognition by the RNAi system, hydrophobicity, toxicity, duplex melting temperature,
and conformation of the RNA helix. A single siRNA
molecule can inactivate several mRNA molecules in a
sequence-specific manner. Two issues with siRNA are offtarget effects (suppression of genes other than target gene)
and delivery into the cell. Short-interfering RNAs (siRNAs)
are used for sequence-specific knockdown of diseasecausing genes in a variety of diseases including cancers,
genetic disorders, and macular degeneration.
Short hairpin RNA (shRNA): shRNA has the advantage
of possessing a prolonged expression of the RNAi effect.
miRNA can mediate gene silencing posttranscriptionally.
MicroRNAs: MicroRNAs (miRNAs) are short (15e22
nucleotides) single-stranded noncoding RNA molecules
which function as negative regulators of posttranscriptional
modulation in almost all biological processes. Dysregulation of miRNA has been associated with many diseases
processes. One of the advantages of exploiting microRNA
is that these target more than a single gene. miRNAs have
been identified for several cancers and there are many
diseases (diabetes, obesity, Alzheimer’s, Parkinson’s disease, cardiovascular, and autoimmune disorder) where it
has been shown that there is significantly greater expression
of miRNA in diseased tissue over normal tissue. Therapeutic approaches include miRNA antagonists and miRNA
mimics (also called ‘miRNA replacement therapy’). For
cancer miRNA therapy oligonucleotides or virus-based
constructs are used to block their expression or introduce
a tumor suppressor miRNA lost due to the disease process.
Other approaches involve modulating miRNA expression
by targeting transcription and processing.
RNA aptamers and RNA decoys: Some small RNAs
fold into three-dimensional structures which can then bind
to proteins and block protein function. For example,
pegaptanib an aptamer against vascular endothelial growth
factor (VEGF) is used in treatment of age-related macular
degeneration [68].
Ribozymes: A subset of (catalytic) RNAs called ribozymes
can function as enzymes in the complete absence of protein. In
general, ribozymes have either a hairpin or hammerheadshaped active center and a unique secondary structure that
allows them to cleave other RNA molecules at specific
sequences. Therapeutically, ribozymes may cleave pathological RNA (i.e., for HIV) with high specificity to suppress gene
function. An early example of this approach is the ribozyme
ANGIOZYMETM, an anti-Flt-1 ribozyme designed specifically to cleave the mRNAs for primary VEGF [69].
Drug targets and drug-target molecules Chapter | 5
Circular RNAs: Circular RNAs (circRNAs) have a
covalent bond between the ends thereby closing the
sequence; this makes them stable by conferring resistance
to degradation by exonucleases. CircRNAs bind to RNAbinding proteins or ribonucleoprotein complexes thereby
competing with endogenous RNAs and play an important
role in some human diseases. For example, ciRS-7 is a
circRNA functions as a miRNA sponge to adsorb and
quench normal miRNA-7 known to be relevant in Parkinson’s disease, Alzheimer’s disease, colorectal cancer, and
pancreatic ductal adenocarcinoma.
5.5 Summary and conclusions
l
l
l
l
l
l
l
l
l
l
Any structure where three-dimensional organization of
entities is involved can function as a drug receptor. Receptors include proteins (receptors, enzymes, ion channels, nuclear receptors) and nucleic acid structures
(DNA, RNA).
Receptors constitute the largest family of drug targets
and largely function as allosteric proteins binding ligands and cellular signaling components to initiate
cell response.
Biological targets may consist of single entity proteins,
complexes of receptors (dimers), or receptors plus
accessory proteins. Mixtures of gene products can produce unique phenotypic biological targets.
Potential chemical structures for drug testing can originate from natural products, design from modeling the
active site of the biological target, modification of natural substances, hybridization of known drugs, or
random screening of chemical diversity.
There is evidence to suggest that drug-like structures
exist in clusters in chemical space (privileged structures); identification of these can greatly enhance success in screening.
Large-scale sampling of chemical space can be
achieved with HTS. This process involves the design
of robust but sensitive biological test systems and the
statistical sifting of biological signals from noise. The
Z0 statistic can be useful in this latter process.
Surrogate screening (utilizing similar but not exact therapeutically relevant targets) can lead to dissimulation in
screening data, especially for allosteric molecules. For
this reason, frequent reality testing with a therapeutically relevant assay is essential.
Biologics are becoming a very important class of therapeutic drug entity; these involve replacement proteins,
peptides, antibodies, DNA, and mRNA.
Biologics have unique capabilities not shared by small
molecule therapeutics including interactive activity
with the human immune system.
An important consideration for biologics is delivery to
therapeutic systems due to their size.
147
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Chapter 6
Agonists: the measurement of affinity
and efficacy in functional assays
The author produced a series of interactive quizzes to test your understanding of the contents of this chapter. Click on the
link to access it: https://www.elsevier.com/books-and-journals/book-companion/9780323992893.
Cells let us walk, talk, think, make love, and realize the bath
water is cold.
d Lorraine Lee Cudmore, “The Center of Life” (1977).
6.1 Functional pharmacological
experiments
Another major approach to the testing of drug activity is the
use of functional assays. These are composed of any biological system that yields a biochemical product or physiological response to drug stimulation. Such assays detect
molecules which produce a biological response or those
that block the production of a physiological response.
These can be whole tissues, cells in culture, or membrane
preparations. Like biochemical binding studies, the pharmacological output can be tailored by using selective
stimulation, whereas in binding studies the output can be
selected by the choice of radioligand or other traceable
probe; in functional studies the output can be selected by
choice of agonist. When necessary, selective antagonists
can be used to obviate unwanted functional responses and
isolate the receptor of interest. This practice was more
prevalent in isolated tissue studies, where the tissue was
chosen for the presence of the target receptor, and in some
cases this came with concomitant presence of other related
and obfuscating receptor responses. In recombinant systems, a surrogate host cell line with a blank cellular background can often be chosen. This results in much more
selective systems and less need for selective agonist probes.
There are two main differences between binding and
functional experiments. The first is that functional responses
are usually highly amplified translations of receptor stimulus
(see Chapter 2: How Different Tissues Process Drug
Response). Therefore, while binding signals emanate from
complete receptor populations, functional readouts often utilize only a small fraction of the receptor population in the
preparation. This can lead to a greatly increased sensitivity to
A Pharmacology Primer. https://doi.org/10.1016/B978-0-323-99289-3.00005-1
Copyright © 2022 Elsevier Inc. All rights reserved.
drugs that possess efficacy. No differences should be seen for
antagonists. This amplification can be especially important for
the detection of agonism, since potency may be more a
function of ligand efficacy than affinity. Thus, a highly efficacious agonist may produce detectable responses at
100e1000 times lower concentrations than those that produce
measurable amounts of displacement of a tracer in binding
studies. The complex interplay between affinity and efficacy
can be misleading in structureeactivity studies for agonists.
For example, Fig. 6.1 shows the lack of correlation of relative
agonist potency for two dopamine-receptor subtypes and the
binding affinity on those receptor subtypes for a series of
dopamine agonists [1]. These data show that, for these molecules, changes in chemical structure lead to changes in
relative efficacy that are not reflected in the affinity measurement. The relevant activity is relative agonist potency.
Therefore, the affinity data are misleading. In this case, a
functional assay is the correct approach for optimization of
these molecules.
Functional assays give flexibility in terms of the
biochemical functional response which can be monitored
FIGURE 6.1 Ratio of affinity (open circles) and agonist potency (filled
circles) for dopamine agonists on dopamine D2 versus D3 receptors.
Abscissae: numbers referring to agonist key on right. Data calculated from
C.L. Chio, M.E. Lajiness, R.M. Huff, Activation of heterologously
expressed D3 dopamine receptors: comparison with D2 dopamine receptors, Mol. Pharmacol. 45 (1994) 51e60.
151
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A Pharmacology Primer
such traceable probe or it is too expensive to be a viable
approach. Functional studies require only that an endogenous
agonist be available. As with binding studies, dissimulations
in the value of the independent variable (namely, drug concentration) lead to corresponding errors in the observed value
of the dependent variable (in the case of functional experiments, cellular response). The factors involved (namely, drug
solubility and adsorption; see Chapter 2: How Different Tissues Process Drug Response) are equally important in functional experiments. However, there are some additional
factors unique to functional studies that should be considered.
These are dealt with in Section 6.4.
FIGURE 6.2 Different types of functional readouts of agonism. Receptors
need not mediate cellular response but may demonstrate behaviors such as
internalization into the cytoplasm of the cell (mechanism 1). Receptors can
also interact with membrane proteins such as G-proteins (mechanism 2) and
produce cytosolic messenger molecules (mechanism 3), which can go on to
mediate gene expression (mechanism 4). Receptors can also mediate
changes in cellular metabolism (mechanism 5).
for drug activity. Fig. 6.2 shows some of the possibilities.
In some cases, the immediate receptor stimulus can be
observed, such as the activation of G-proteins by agonistactivated receptor. Specifically, this is in the observation
of an increased rate of exchange of guanosine diphosphate
(GDP) to guanosine triphosphate (GTP) on the G-protein asubunit. Following G-protein activation comes initiation of
effector mechanisms. For example, this can include activation of the enzyme adenylyl cyclase to produce the second messenger cyclic adenosine monophosphate (AMP).
This and other second messengers go on to activate enzymatic biochemical cascades within the cell. A second layer
of response observation is the measurement of the quantity
of these second messengers. Yet another layer of response
is the observation of the effects of the second messengers.
Thus, activation of enzymes such as mitogen-activated
protein (MAP) kinase can be used to monitor drug activity.
A second difference between binding and function is the
quality of drug effect that can be observed. Specifically,
functional studies reveal interactions between receptors and
cellular components which may not be observed in binding
studies, such as some allosteric effects or other responses in
a receptor’s pharmacological repertoire (i.e., receptor
internalization). For example, the cholecystokinin (CCK)
receptor antagonist d-Tyr-Gly-[(Nle28,31,d-Trp30)CCK26e32]-phenethyl ester is a receptor antagonist and does
not produce receptor stimulation. While ostensibly this may
appear to indicate a lack of efficacy, this ligand does produce profound receptor internalization [2]. Therefore, a
different kind of efficacy is revealed in functional studies,
which would not have been evident in binding.
A practical consideration is the need for a radioactive
ligand in binding studies. There are instances where there is no
6.2 The choice of functional assays
There are a number of assay formats that are available to
test drugs in a functional mode. As discussed in Chapter 2,
How Different Tissues Process Drug Response, a main
theme throughout the various stimuluseresponse cascades
found in cells is the amplification of receptor stimulus
occurring as a function of the distance, in biochemical steps
and reactions, away from the initial receptor event. Specifically, the farther down the stimuluseresponse pathway
the agonism is observed, the more amplified the signal.
Fig. 6.3 illustrates the effects of three agonists at different
points along the stimuluseresponse cascade of a hypothetical cell. At the initial step (i.e., G-protein activation,
ion channel opening), all are partial agonists, and it can be
seen that the order of potency is 2 > 1>3 and the order of
efficacy is 3 > 2>1. If the effects of these agonists were to
be observed at a step further in the stimuluseresponse
cascade (i.e., production of second messenger), it can be
seen that agonists 2 and 3 are full agonists, while agonist 1
is a partial agonist. Their rank order of potency does not
change but now there is no distinction between the relative
efficacies of agonists 2 and 3. At yet another step in the
cascade (namely, end organ response), all are full agonists
with the same rank order of potency. The point of this
simulation is to note the differences, in terms of the characterization of the agonists (full vs. partial agonists, relative
orders of efficacy), which occur by simply viewing their
effects at different points along the stimuluseresponse
pathway.
Due to the complex nature of cell signaling networks,
the functional response of cells to agonists may be complex
necessitating business rules for what will be considered as
response. One of the most complex signals is that for calcium transients as measured with fluorescence since this is
a hemiequilibrium assay capturing only the first few seconds of cell response [3]. Fig. 6.4 shows a range of calcium
transient responses to histamine illustrating the dilemma of
whether peak response, area under the curve, or sustained
response would be the appropriate measure for histamine
agonism.
Agonists: the measurement of affinity and efficacy in functional assays Chapter | 6
153
FIGURE 6.3 Amplification inherent in different vantage points along the stimuluseresponse pathway in cells. Agonists have a rank order of efficacy of
3 > 2 > 1 and a rank order of potency of 2 > 1 > 3. Assays proximal to the agonistereceptor interaction have the least amplification. The product of the
initial interaction goes on to activate other processes in the cell. The signal is generally amplified. As this continues, texture with respect to differences in
efficacy is lost and the agonists all demonstrate full agonism.
FIGURE 6.4 Calcium transient responses to histamine in HeLa S3
subclone cells. Redrawn from T.R. Miller, D.G. Witte, L.M. Ireland, C.H.
Kang, J.M. Roch, J.N. Masters, T.A. Esbenshade, A.R. Hancock, Analysis
of apparent noncompetitive responses to competitive H1-histamine receptor antagonists in fluorescent imaging plate reader-based calcium
based assays, J. Biomol. Screen 4 (1999) 249e258.
Historically, isolated tissues have been used as the primary form of functional assay, but since these usually come
from animals, the species differences, coupled with the fact
that human recombinant systems can now be used, have made
this approach obsolete. Functional assays in whole-cell formats, where end organ response is observed (these will be
referred to as group I assays), can be found as specialized cells
such as melanophores, yeast cells, or microphysiometry assays. Group II assays record the product of a pharmacological
stimulation (e.g., an induction of a gene that goes on to produce a traceable product such as a light-sensitive protein).
Second messengers (such as cyclic AMP, calcium, and
inositol triphosphate) can also be monitored directly either in
whole-cell or broken-cell formats (group III assays). Finally,
membrane assays such as the observation of binding of
GTPgS to G-proteins can be used. While this is an assay
carried out in binding mode, it measures the ability of agonists
to induce a response and thus may also be considered a
functional assay. It is worth considering the strengths and
shortcomings of all these approaches.
Group I assays (end organ response) are the most highly
amplified and therefore most sensitive assays. This is an
advantage in screening for weakly efficacious agonists but
has the disadvantage of showing all agonists above a given
level of efficacy to be full agonists. Under these circumstances, information about efficacy cannot be discerned from
154
A Pharmacology Primer
the assay, since at least for all the agonists that produce
maximal system response, no information regarding relative
efficacy can be obtained. There are cell culture group I assays.
One such approach uses microphysiometry. All cells respond
to changes in metabolism by adjusting the internal hydrogen
ion concentration. This process is tightly controlled by
hydrogen ion pumps that extrude hydrogen ions into the
medium surrounding the cell. Therefore, with extremely
sensitive monitoring of the pH surrounding cells in culture, a
sensitive indicator of cellular function can be obtained.
Microphysiometry measures the hydrogen ion extrusion of
cells to yield a generic readout of cellular function. Agonists
can perturb this control of hydrogen ion output. One of the
major advantages of this format is that it is generic (i.e., the
observed pH does not depend on the nature of the biochemical
coupling mechanisms in the cytosol of the cell). For example,
the success of cell transfection experiments can be monitored
with microphysiometry. Unless receptors are biochemically
tagged, it may be difficult to determine whether the transfection of cDNA for a receptor into a cell actually results in
membrane expression of the receptor. On occasion, the cell is
unable to process the cDNA to form the complete receptor and
it is not expressed on the cell surface. Fig. 6.5A shows
microphysiometry responses to calcitonin (an agonist for the
human calcitonin receptor) before and after transfection of the
cells with cDNA for the human calcitonin receptor. The
appearance of the calcitonin response indicates that successful membrane expression of the receptor occurred. Another
positive feature of this format is the fact that responses can be
observed in real time. This allows the observation of steady
states and the possibility of obtaining cumulative dosee
response curves to agonists (see Fig. 6.5B and C).
A specialized cell type that is extremely valuable in drug
discovery is the Xenopus laevis melanophore. This is a cell
derived from the skin of frogs that controls the dispersion of
pigment in response to receptor stimulation. Thus, activation of Gi protein causes the formation of small granules of
pigment in the cell, rendering them transparent to visible
light. In contrast, activation of Gs and Gq protein causes
dispersion of the melanin, resulting in an opaque cell (loss
FIGURE 6.5 Microphysiometry responses of HEK293 cells transfected with human calcitonin receptor. (A) Use of microphysiometry to detect receptor
expression. Before transfection with human calcitonin receptor cDNA, HEK cells do not respond to human calcitonin. After transfection, calcitonin
produces a metabolic response, thereby indicating successful membrane expression of receptors. (B) Cumulative concentrationeresponse curve to human
calcitonin shown in real time. Calcitonin added at the arrows in concentrations of 0.01, 0.1, 1.10, and 100 nM. (C) Doseeresponse curve for the effects
seen in panel (B).
Agonists: the measurement of affinity and efficacy in functional assays Chapter | 6
of transmittance of visible light). Therefore, the activation
of receptors can be observed in real time through changes in
the transmittance of visible light through a cell monolayer.
Fig. 6.6 shows the activation of human b-adrenoceptors in
melanophores by b-adrenoceptor agonists. It can be seen
that activation of Gs protein by the activated b-adrenoceptor
leads to an increase in pigmentation of the melanophore.
This, in turn, is quantified as a reduced transmittance of
visible light to yield graded responses to the agonists. One
of the key features of this format is that the responses can be
observed in real time. Fig. 6.7A shows the reduced transmittance to visible light of melanophores transfected with
human calcitonin receptors activated with the agonist
human calcitonin. Another feature of this format is that
the transfected receptors are very efficiently coupled
(i.e., agonists are extremely potent in these systems).
Fig. 6.7B shows the doseeresponse curve for human
calcitonin in transfected melanophores compared to the less
efficiently coupled calcium fluorescence assay in human
embryonic kidney cells for this same receptor.
FIGURE 6.6 Melanophores, transfected with human b-adrenoceptors,
disperse melanin to become opaque when stimulated with b-adrenoceptor
agonists such as albuterol and terbutaline. Inset shows light transmission
through a melanophore cell monolayer with increasing concentration of
agonist. Light transmission is quantified and can be used to calculate
graded responses to the agonists.
155
Another specialized cell line that has been utilized for
functional drug screening is derived from yeast cells. A major
advantage of this format is that there are few endogenous
receptors and G-proteins, leading to a very low background
signal (i.e., the major signal is the transfected receptor of
interest). Yeast can be genetically altered to fail to grow in a
medium lacking histidine unless a previously transfected
receptor is present. Coupled with the low maintenance and
high growth rate, yeast cells are a viable system of highthroughput screening and secondary testing of drugs.
Group II assays consist of those which monitor cellular
second messengers. Thus, activation of receptors to cause
Gs protein activation of adenylate cyclase will lead to
elevation of cytosolic or extracellularly secreted cyclic
AMP. This second messenger phosphorylates numerous
cyclic AMP-dependent protein kinases, which go on to
phosphorylate metabolic enzymes, and transport and regulatory proteins (see Chapter 2: How Different Tissues
Process Drug Response). Cyclic AMP can be detected
either radiometrically or by fluorescent probe technology.
Another major second messenger in cells is the calcium
ion. Virtually, any mammalian cell line can be used to
measure transient calcium currents by fluorescence assays
when cells are preloaded with an indicator dye that allows
monitoring of changes in cytosolic calcium concentration.
These responses can be observed in real time, but one of their
characteristic is that they are transient. This may lead to
problems with hemiequilibria in antagonist studies, whereby
the maximal responses to agonists may be depressed in the
presence of antagonists. These effects are discussed more
fully in Chapter 7, Orthosteric Drug Antagonism.
Another approach to the measurement of functional
cellular responses is through the use of reporter assays
(group III). Reporter assays yield the amount of cellular
product made in response to stimulation of the cell. For
example, elevation of cyclic AMP causes activation of
protein kinase A. The activated subunits resulting from
protein kinase A activation bind to cyclic AMP response
FIGURE 6.7 Calcitonin receptor responses. (A) Real-time melanin dispersion (reduced light transmittance) caused by agonist activation (with human
calcitonin) of transfected human calcitonin receptors type II in melanophores. Responses to 0.1 nM (filled circles) and 10 nM (open circles) human
calcitonin. (B) Doseeresponse curves to calcitonin in melanophores (open circles) and HEK293 cells, indicating calcium transient responses (filled
circles).
156
A Pharmacology Primer
element binding protein, which then binds to a promoter
region of cyclic AMP-inducible genes. If the cell is previously stably transfected with genes for the transcription of
luciferase in the nucleus of the cell, elevation of cyclic
AMP will induce the transcription of this protein. Luciferase produces visible light when brought into contact with
the substrate LucLite, and the amount of light produced is
proportional to the amount of cyclic AMP produced.
Therefore, the cyclic AMP produced through receptor
stimulation leads to a measurable increase in the observed
light produced upon lysis of the cell. There are numerous
other reporter systems for cyclic AMP and inositol
triphosphate, which are two prevalent second messengers in
cells (see Chapter 2: How Different Tissues Process Drug
Response). It can be seen that such a transcription system
has the potential for great sensitivity, since the time of
exposure can be somewhat tailored to amplify the observed
response. However, this very advantage can also be a
disadvantage, since the time of exposure to possible toxic
effects of drugs is also increased. One advantage of realtime assays such as melanophores and microphysiometry
is their ability to obtain responses in a short period of time
and thereby possibly reduce toxic effects that require longer
periods of time to become manifested. Reporter responses
are routinely measured after a 24-hour incubation (to give
sufficient time for gene transcription). Therefore, the
exposure time to drug is increased with a concomitant
possible increase in toxic effects.
Finally, receptor stimulus can be measured through
membrane assays directly monitoring G-protein activation
(group IV assays). In these assays, radiolabeled GTP (in a
stable form; e.g., GTPgS) is present in the medium. As
receptor activation takes place, the GDP previously bound
to the inactive state of the G-protein is released and the
radiolabeled GTPgS binds to the G-protein. This is quantified to yield a measure of the rate of GDP/GTPgS exchange, and hence receptor stimulus.
The majority of functional assays involve primary
signaling. In the case of G-protein-coupled receptors
(GPCRs), this involves activation of G-proteins. However,
receptors have other behaviorsdsome of which can be
monitored to detect ligand activity. For example, upon
stimulation, many receptors are desensitized through
phosphorylation and subsequently taken into the cell and
either recycled back to the cell surface or digested. This
process can be monitored by observing ligand-mediated
receptor internalization. For many receptors, this involves
the migration of a cytosolic protein called b-arrestin.
Therefore, the transfection of fluorescent b-arrestin to cells
furnishes a method for tracking the movement of the
fluorescent b-arrestin from the cytosol to the inner membrane surface as receptors are activated (Fig. 6.8). Alternative approaches to detecting internalization of GPCRs
involve pH-sensitive cyanine dyes such as CypHer-5,
which fluoresce when irradiated with red laser light, but
only in an acidic environment. Therefore, epitope tagging
of GPCRs allows binding of antibodies labeled with
CypHer-5 to allow detection of internalized receptors
(those that are in the acidic internal environment of the cell
and thus fluoresce in laser light) [4]. A general list of
minimal and optimal conditions for functional assays is
given in Table 6.1.
6.3 Recombinant functional systems
The advent of molecular biology and the ability to express
transfected genes (through transfection with cDNA) into
surrogate cells to create functional recombinant systems
have brought a revolution in pharmacology. Previously,
pharmacologists were constrained to the prewired sensitivity of isolated tissues for the study of agonists. As discussed in Chapter 2, How Different Tissues Process Drug
Response, different tissues possess different densities of
receptors, different receptor coproteins in the membranes,
and different efficiencies of stimuluseresponse mechanisms. Judicious choice of tissue type could yield uniquely
useful pharmacologic systems (i.e., sensitive screening
tissues). However, before the availability of recombinant
systems, these choices were limited. With the ability to
express different densities of human, target proteins such as
receptors has come a transformation in drug discovery.
Recombinant cellular systems can now be made with a
range of sensitivities to agonists. The techniques involved
in the construction of recombinant receptor systems are
beyond the scope of this chapter, but some general ideas are
useful in that they can be used for the creation of optimal
systems for drug discovery.
The first idea to consider is the effect of receptor density
on the sensitivity of a functional system to agonists.
Clearly, if quanta of stimulus are delivered to the
stimuluseresponse mechanism of a cell per activated receptor, the amount of the total stimulus will be directly
proportional to the number of receptors activated. Fig. 6.9
shows Gi-protein-mediated responses of melanophores
transiently transfected with cDNA for human neuropeptide
Y-1 receptors [5]. As can be seen from this figure,
increasing receptor expression (transfection with increasing
concentrations of receptor cDNA) causes an increased potency and maximal response to the neuropeptide Y agonist
peptide YY (PYY).
Receptor density has disparate effects on the potency
and maximal responses to agonists. The operational model
predicts that the EC50 of an agonist will vary with receptor
density according to the following relationship (see Section
6.11.1):
EC50 ¼
KA $KE
;
½Rt þ KE
(6.1)
Agonists: the measurement of affinity and efficacy in functional assays Chapter | 6
157
FIGURE 6.8 Internalization of GPCRs. (A) Receptors adopt an active conformation either spontaneously or through interaction with a ligand and
become phosphorylated. This promotes b-arrestin binding, which precedes internalization of the receptor into clathrin pits. Receptors then are either
degraded in endosomes or recycled to the cell surface. (B) A fluorescent analog of b-arrestin can be visualized and tracked according to location either at
the cell membrane (receptors not internalized) or near the cell nucleus (internalized receptors). This enables detection of changes in GPCRs. GPCRs,
G-protein-coupled receptors.
TABLE 6.1 Minimal and optimal criteria for
experiments utilizing cellular function.
Minimal
l
l
An agonist and antagonist to define the response on the
target are available
The agonist is reversible (after washing with drug-free
medium)
Optimal
l
l
l
l
l
The response should be sustained and not transient. No
significant desensitization of the response occurs within
the time span of the experiment
The response production should be rapid
The responses can be visualized in real time
There are independent methods to either modulate or
potentiate functional responses
There is a capability to alter the receptor density (or cells
available with a range of receptor densities)
FIGURE 6.9 Doseeresponse curves to peptide PYY (YPAKPEAPGEDASPEELSRYYASLRHYLNLVTRQRYNH2) in melanophores. Ordinates: minus values for 1 Tf/Ti reflecting increases in light transmission.
Abscissae: logarithms of molar concentrations of PYY. Cells transiently
transfected with cDNA for the human NPY1 receptor. Levels of
cDNA ¼ 10 (filled circles), 20 (open circles), 40 (filled triangles), and
80 mg (open squares). PYY, peptide YY. Data redrawn from G. Chen, J.
Way, S. Armour, C. Watson, K. Queen, C. Jayawrickreme, Use of
constitutive G protein-coupled receptor activity for drug discovery, Mol.
Pharmacol. 57 (1999) 125e134.
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A Pharmacology Primer
where [Rt] is the receptor density, KA is the equilibrium
dissociation constant of the agonistereceptor complex,
and KE is the concentration of activated receptor that produces half-maximal response (a measure of the efficiency
of the stimuluseresponse mechanism of the system) (see
Section 6.11.1 for further details). Similarly, the agonist
maximal response is given by
Maximal Response ¼
½Rt $Emax
;
½Rt þ KE
(6.2)
where Emax is the maximal response capability of the system. It can be seen that increases in receptor density will
cause an increase in agonist maximal response, to the limit
of the system maximum (i.e., until the agonist is a full
agonist). Thereafter, increases in receptor density will
have no further effect on the maximal response to the
agonist. In contrast, Eq. (6.1) predicts that increases in receptor density will produce concomitant increases in the
potency of a full agonist with no limit. These effects are
shown in Fig. 6.10. It can be seen from this figure that at
receptor density levels where the maximal response reaches
an asymptote, agonist potency increases linearly with increases in receptor density. Fig. 6.10B shows the relationship between the pEC50 for the b2-adrenoceptor agonist
isoproterenol and b2-adrenoceptor density in rat C6 glioma
cells. It can be seen that while no further increases in
maximal response are obtained, the agonist potency increases with increasing receptor density [6].
Recombinant systems can also be engineered to produce
receptor-mediated responses by introducing adjunct proteins. For example, it has been shown that the Ga16 Gprotein subunit couples universally to nearly all receptors
[7]. In recombinant systems, where expression of the receptor does not produce a robust agonist response, cotransfection of the Ga16 subunit can substantially enhance
observed responses. Fig. 6.11 shows that both the maximal
response and potency of the neuropeptide Y peptide agonist
PYY are enhanced when neuropeptide Y-4 receptors are
cotransfected with cDNA for receptor and Ga16. Similarly,
other elements may be required for a useful functional assay.
For example, expression of the glutamate transporter EAAT1
(a glutamate aspirate transporter) is required in some cell
lines to control extracellular glutamate levels (which lead to
receptor desensitization) [8].
While high receptor density may strengthen an agonist
signal, it may also reduce its fidelity. In cases where receptors are pleiotropic with respect to the G-proteins with
which they interact (receptors interact with more than one
G-protein), high receptor numbers may complicate
signaling by recruitment of modulating signaling pathways.
For example, Fig. 6.12 shows a microphysiometry response
to human calcitonin produced in human embryonic kidney
cells transfected with human calcitonin receptor [9]. It can
be seen that the response is sustained. In a transfected cell
line with a much higher receptor density, the response is
not of higher magnitude and is also transient, presumably
because of complications due to the known pleiotropy of
this receptor with other G-proteins. The responses in such
systems are more difficult to quantify, and cumulative
doseeresponse curves are not possible. These factors make
a high receptor density system less desirable for pharmacological testing. This factor must be weighed against the
possible therapeutic relevance of multiple G-protein
coupling to the assay.
FIGURE 6.10 Effects of receptor density on functional assays. (A) Effect of increasing receptor density on potency (pEC50) and maximal response to an
agonist. Left ordinal axis is ratio of observed EC50 and KA as log scale; right ordinal axis as fraction of system maximal response (intrinsic activity). (B)
Observed pEC50 values for isoproterenol for increases in cyclic AMP in rat glioma cells transfected with human b2-adrenoceptors (open circles) and
maximal response to isoproterenol (as a fraction of system maxima, filled circles) as a function of b2-adrenoceptor density on a log scale (fmol/mg
protein). Data redrawn from H. Zhong, S.W. Guerrero, T.A. Esbenshade, K.P. Minneman, Inducible expression of b1-and b2-adrenergic receptors in rat
C6 glioma cells: functional interactions between closely related subtypes, Mol. Pharmacol. 50 (1996) 175e184.
Agonists: the measurement of affinity and efficacy in functional assays Chapter | 6
159
FIGURE 6.11 Effects of coexpressed G-protein (Ga16) on neuropeptide NPY4 receptor responses (NPY-4). (A) Doseeresponse curves for NPY-4.
Ordinates: Xenopus laevis melanophore responses (increases light transmission). Abscissae: logarithms of molar concentrations of neuropeptide Y
peptide agonist PYY. Curves obtained after no cotransfection (labeled 0 mg) and cotransfection with cDNA for Ga16. Numbers next to the curves indicate
mg of cDNA of Ga16 used for cotransfection. (B) Maximal response to neuropeptide Y (filled circles) and constitutive activity (open circles) as a function
of mg cDNA of cotransfected Ga16. PYY, peptide YY.
FIGURE 6.12 Microphysiometry responses to 1 nM human calcitonin. (A) Responses obtained from HEK293 cells stably transfected with low levels of
human calcitonin receptor (68 pM/mg protein). Response is sustained. (B) Response from HEK293 cells stably transfected with high levels of receptor
(30,000 pM/mg protein). Data redrawn from T.P. Kenakin, Differences between natural and recombinant G-protein coupled receptor systems with
varying receptor/G-protein stoichiometry, Trends Pharmacol. Sci. 18 (1997) 456e464.
6.4 Functional experiments:
dissimulation in time
A potential problem when measuring drug activity relates to
the temporal ability of systems to come to equilibrium, or at
least to a steady state. Specifically, if there are temporal
factors that interfere with the ability of the system to return a
cellular response, or if a real-time observation of response is
not possible at the time of exposure to drugs, especially agonists, then the time of exposure to drugs becomes an
important experimental variable. In practice, if responses are
observed in real time, then steady states can be observed and
the experiment designed accordingly. The rate of response
production can be described as a first-order process. Thus, the
effect of a drug ([E]) expressed as a fraction of the maximal
effect of that drug (receptors saturated by the drug, [Em]) is
½E
¼ 1 ekon t ;
½Em (6.3)
where kon is a first-order rate constant for the approach of
the response to the equilibrium value, and t is time. The
process of drug binding to a receptor will have a temporal
component. Fig. 6.13 shows three different rates of
response by an agonist, or by binding of a ligand in general.
The absolute magnitude of the equilibrium binding is the
same, but the time taken to achieve the effect is quite
different. It can be seen from this figure that if response
is measured at t ¼ 1000 seconds, only drug A is at steady
state. If comparisons are made at this time point, the effect
of the other two drugs will be underestimated. As previously noted, if responses are observed in real time, steady
states can be observed and temporal inequality ceases to
be an issue. However, this can be an issue in stop-time experiments, in which real-time observation is not possible
and the product of a drug response interaction is measured
at a given time point. This is discussed further later in the
chapter.
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A Pharmacology Primer
Another potential complication can occur if the
responsiveness of the receptor system changes temporally.
This can happen if the receptor (or host system, or both)
demonstrates desensitization (tachyphylaxis) to drug stimulation (see Chapter 2: How Different Tissues Process Drug
Response). There are numerous systems where constant
stimulation with a drug does not lead to a constant steadystate response, but rather, a “fade” in the response occurs.
This can be due to depletion of a cofactor in the system
producing the cellular response, or a conformational change
in the receptor protein. Such phenomena protect against
overactive stimulation of systems to physiological detriment. Whatever the cause, the resulting response to the
drug is temporally unstable, leading to a dependence of
the magnitude of the response on the time at which the
response was recorded. The process of desensitization can
be a first-order decay according to an exponential function,
the time constant for which is independent of the magnitude
FIGURE 6.13 First-order rate of onset of response for three agonists of
equal potency but differing rates of receptor onset. Ordinates: response at
time t as a fraction of equilibrium response value. Abscissae: time in
seconds. Curve 1: k1 ¼ 3 106 s1/mol, k2 ¼ 0.003 s1. Curve 2:
k1 ¼ 106 s1/mol, k2 ¼ 0.001 s1. Curve 3: k1 ¼ 5 105 s1/mol,
k2 ¼ 0.0005 s1.
of the response. Under these circumstances, the response
tracings would resemble those shown in Fig. 6.14A.
Alternatively, the rate of desensitization may be dependent
on the intensity of the stimulation (i.e., the greater the
response, the more rapid will be the desensitization). Under
these circumstances, the fade in response will resemble the
pattern shown in Fig. 6.14B. These temporal instabilities
can lead to underestimation of the response to the agonist.
If the wrong time point for measurement of response is
chosen, this can lead to a shift to the right of the agonist
doseeresponse curve (Fig. 6.15A) or a diminution of the
true maximal response (see Fig. 6.15B). Temporal studies
must be done to ensure that the response values are not
dependent on the time chosen for measurement.
6.5 Experiments in real time versus
stop-time
The observation of dependent variable values (in functional
experiments, this is cellular response) as they happen (i.e.,
as the agonist or antagonist binds to the receptor and as the
cell responds) is referred to as real time. In contrast, a
response chosen at a single point in time is referred to as
stop-time experimentation. There are certain experimental
formats that must utilize stop-time measurement of responses since the preparation is irreparably altered by the
process of measuring response. For example, measurement
of gene activation through reporter molecules necessitates
lysis of the cell. Therefore, only one measurement of
response can be made. In these instances, the response is a
history of the temporal process of response production from
the initiation of the experiment to the time of measurement
(e.g., the production of the second cellular messenger cyclic
AMP as a function of time). In specially constructed reporter cells, such as those containing an 8-base-pair
FIGURE 6.14 Fade of agonist-induced responses in systems with a uniform rate constant for desensitization [panel (A)] or a rate of desensitization
proportional to the magnitude of the response [panel (B)]. Abscissae: time in seconds. Ordinates: fractions of maximal response; responses ranging from
0.25 to 0.95 maximum. (A) Temporal response multiplied by an exponential decay of rate constant 103 s1. Numbers refer to the concentration of
agonist expressed as a fraction of the EC50. (B) Rate constant for exponential decay equals the magnitude of the fractional response multiplied by a
uniform rate constant 103 s1. For panel (B), the rate of desensitization increases with increasing response.
Agonists: the measurement of affinity and efficacy in functional assays Chapter | 6
161
FIGURE 6.15 Temporal desensitization of agonist response. (A) Patterns of response for a concentration of agonist producing 80% maximal response.
Curve 1: no desensitization. For concentration of agonist [A] ¼ 5 empo50, first-order rate of onset k1 ¼ s/mol, k2 ¼ 103 s1. Curve 2: constant
desensitization rate ¼ kdesen ¼ 103. Curve 3: variable desensitization rate equals rkdesen, where r equals fractional receptor occupancy. (B) Complete
doseeresponse curves to the agonist taken at equilibrium with no desensitization (curve 1), at peak response for constant desensitization rate (curve 2), and
at variable desensitization rate (curve 3). (C) Curves as per panel B but response measured after 10 min equilibration with the agonist.
palindrome sequence called cyclic AMP response element,
receptor activation causes this element to activate a ppromoter region of cyclic-AMP-inducible genes. This, in
turn, causes an increase in transcription of a protein called
luciferase. This protein produces light when brought into
contact with an appropriate substrate, making it detectable
and quantifiable. Therefore, any agonist increasing cyclic
AMP will lead to an increase in luciferase. This is one of a
general type of functional assays (called reporter assays)
where agonism results in the production and accumulation
of a detectable product. The amount of product accumulated after agonism can be measured only once. Therefore,
an appropriate time must be allowed for assumed equilibrium before reading the response. The addition of an
agonist to such an assay causes the production of the second (reporter) messenger, which then goes on to produce
the detectable product. The total amount of product made
from the beginning of the process to the point where the
reaction is terminated is given by the area under the curve
that defines cyclic AMP production. This is shown in
Fig. 6.16. Usually the experimenter is not able to see the
approach to equilibrium (real-time response shown in
Fig. 6.16A) and must choose a time point as the best estimate regarding when equilibrium has been attained.
Fig. 6.16B shows the area under the curve as a function of
time. This area is the stop-time response. This function is
not linear in the early stages during approach to equilibrium
but is linear when a steady state or true equilibrium has
been attained. Therefore, a useful method to determine
whether equilibrium has been achieved in stop-time experiments is to stop the reaction at more than one time point
and ensure that the resulting signal (product formed) is
linear with time. If the relationship between three stop-time
responses obtained at three different time points is linear,
then it can be assumed that the responses are being
measured at equilibrium.
A potential pitfall with stop-time experiments comes
with temporal instability of the responses. When a steadystate sustained response is observed with time, then a linear
portion of the production of reporter can be found (see
Fig. 6.16B). However, if there is desensitization or any
other process that makes the temporal responsiveness of the
system change, the area under the curve will not assume the
linear character seen in sustained equilibrium reactions. For
example, Fig. 6.17 shows a case where the production of
cyclic AMP with time is transient. Under these circumstances, the area under the curve does not assume linearity.
Moreover, if the desensitization is linked to the strength of
signal (i.e., becomes more prominent at higher stimulations) the doseeresponse relationship may be lost. Fig. 6.17
shows a stop-time reaction doseeresponse curve for a
temporally stable system and a temporally unstable system
162
A Pharmacology Primer
magnitude of response is determined by the affinity of A for
the receptor (expressed as the reciprocal of the equilibrium
dissociation constant of the agonistereceptor complex,
denoted KA), and the term s, which describes the intrinsic
efficacy of the agonist. This term quantifies both the power
of the agonist to induce response and the sensitivity of the
system (containing a term quantifying the number of
responding units in the system as the receptor density [Rt]
and the efficiency of the coupling of each receptor to the
stimuluseresponse mechanism of the cell). Doseeresponse
data are fit to the BlackeLeff equation [10]dsee Chapter 3,
DrugeReceptor Theory:
½A sn Em
n n
n
½A s þ ð½A þ KA Þ
n
Response ¼
(6.4)
where n is the slope of the doseeresponse curve. In this
model, the descriptive data of maximal response and the
EC50 (potency described as the concentration of agonist
producing 50% maximal response), which is dependent
upon the specific system generating the curve, can be transformed into predictive data
that
are true for the drug in all
1
systems, namely, affinity KA and efficacy (s, where the
ratio of s values for two drugs is constant and transferrable
across different systems) through two equations. The first
relates the maximal response to efficacy [11]:
Maximal Response ¼
FIGURE 6.16 Different modes of response measurement. (A) Real time
shows the time course of the production of response such as the agoniststimulated formation of a second messenger in the cytosol. (B) The
stop-time mode measures the area under the curve shown in panel (A). The
reaction is stopped at a designated time (indicated by the dotted lines
joining the panels), and the amount of reaction product is measured. It can
be seen that in the early stages of the reaction, before a steady state has
been attained [i.e., a plateau has not yet been reached in panel (A)], the
area under the curve is curvilinear. Once the rate of product formation has
attained a steady state, the stop-time mode takes on a linear character.
where the desensitization is linked to the strength of the
signal. It can be seen that the doseeresponse curve for the
agonist is lost in the stop-time temporally unstable system.
6.6 Quantifying agonism: the
BlackeLeff operational model of
agonism
As discussed in Chapter 3, DrugeReceptor Theory (Section
3.6), the operational model published by Black and Leff
[10] is an excellent theoretical framework to quantify and
think about agonism. For a defined agonist ([A]) in a
functional system which can yield a maximal response
(denoted Em) when the target is fully activated, this model
can be used to predict and quantify response. The
sn Em
.
sn þ 1
(6.5)
And the second relates potency to both affinity (KA) and
efficacy:
EC50 ¼ KA
ð2 þ sn Þ
1=n
1
(6.6)
Eq. (6.4) can be used to compare agonists through an
index that denotes the power of that agonist to produce
activation, namely, a value referred to as a transduction
coefficient and defined as log(s/KA) [12]. This number
takes into account both the maximal response produced by
the agonist and its potency (as an EC50 value). If the slope
of the doseeresponse curve is not significantly different
from unity, then log(s/KA) is the maximal response divided
by the EC50 (i.e., for n ¼ 1, log(s/KA) ¼ log(max/EC50)
[13]dvide infra). Thus ratios of s/KA values (denoted
Dlog(s/KA)) are system-independent estimates of the relative ability of agonists to induce a given response. The use
of log(s/KA) for predicting agonist response and/or receptor
selectivity is specifically discussed in Chapter 9, The
Optimal Design of Pharmacological Experiments (see
Section 9.2.1).
Unlike the analysis for full agonists, certain experimentally derived starting points for the fit are evident for
partial agonists. The first step is to furnish initial parameters
for computer fit to the operational model; the Emax for the
Agonists: the measurement of affinity and efficacy in functional assays Chapter | 6
163
FIGURE 6.17 The effect of desensitization on stop-time mode measurements. Bottom panels show the time course of response production for a system
with no desensitization, and one in which the rate of response production fades with time. The top doseeresponse curves indicate the area under the curve
for the responses shown. It can be seen that whereas an accurate reflection of response production is observed when there is no desensitization, the system
with fading response yields an extremely truncated doseeresponse curve.
system and KA values for each agonist are good starting
points. There are two ways in which the Emax can be
determined in any given functional system. In some cases,
the maximal response to the agonist of interest will equal
the maximal response to agonists for other systems. For
example, a maximal a-adrenoceptor contraction that is
equal in magnitude to that produced by a complete depolarization of the tissue by potassium ion would probably
indicate that both produce the tissue maximal response
(Emax). Also, if a number of agonists for a given receptor
produce the same magnitude of maximal response, then it
would be likely that all saturate the stimuluseresponse
capability of the system and thus produce the system
maximal response. The EC50 value for a partial agonist is a
good estimate of the KA (vide infra). As a starting point for
the KA of even a full agonist, the 100 EC50 can be used
for fitting (see Fig. 6.18). The data then can be fitted to a
general logistic function of variable slope to estimate the
Hill coefficient (Fig. 6.18, top right panel). Finally, with
estimates of KA, Emax, and n, the complete data set can be
fit with varying s values (bottom left panel, Fig. 6.18). It
should be noted that unless a given agonist can be tested in
a system where it produces partial agonism, the KA value
cannot be absolutely determined, since the location parameters of full agonists are controlled by a product of
affinity and efficacy. For example, the relative affinity and
efficacy of the full agonist in Fig. 6.18 is shown as s ¼ 100
and KA ¼ 5 mM, but the curve fits equally well with
s ¼ 1000 and KA ¼ 50 mM. In fact, there are an infinite
number of combinations of s and KA that can fit
164
A Pharmacology Primer
FIGURE 6.18 Fit of the operational model to experimentally determined agonist concentrationeresponse data. The maximal response of the system
either is determined experimentally (if a series of powerful agonists produce the same maximal response, this is a good indicator that the maximal response
is the system maximum) or is assumed from the maximal response of the most powerful agonist. In addition, the KA for the partial agonist is assumed to be
approximated by the EC50, while a first estimate of the KA for the full agonist also may be the EC50 for the full agonist curve. The data are fit to the general
logistic function with variable slope to determine slope n. The initial estimates for Emax, KA1, KA2, and n are used to fit the two curves simultaneously with
varying s values using Eq. (12.1) until a minimum sum of squares for the difference between the predicted and experimental points is obtained.
concentrationeresponse curves to full agonists, and it is the
s/KA ratio that is unique for these types of molecules.
Fig. 6.19 shows the analysis of the full agonist isoproterenol and partial agonist prenalterol. It can be seen that once
the relative efficacy values are determined in one tissue, the
ratio is predictive in other tissues as well. This advantage
can be extrapolated to the situation whereby the relative
efficacy and affinity of agonists can be determined in a test
system and the activity of the agonist then predicted in the
therapeutic systemdsee Chapter 9, The Optimal Design of
Pharmacological Experiments.
Correct estimates of relative affinity and efficacy can
furnish a powerful mechanism for predicting agonist effects
in different tissues. Fig. 6.20A shows the relative response
of guinea pig ileum to the muscarinic agonists oxotremorine and carbachol [14]. It can be seen from this figure
that oxotremorine is two- to threefold more potent than
carbachol. The following question then can be posed: What
will the relative potency of these agonists be in a less
sensitive system? Ostensibly, a 100-fold reduction in the
sensitivity of the system would cause a 100-fold shift to the
right of both concentrationeresponse curves (Fig. 6.20B).
What is, in fact, observed is that the carbachol curve shifts
to the right by a factor of 100 and the maximum is slightly
reduced, while the concentrationeresponse curve to oxotremorine disappears completely! This effect is predicted
by the operational model in this situation. An assessment of
the relative efficacies and affinities of these two agonists
Agonists: the measurement of affinity and efficacy in functional assays Chapter | 6
165
FIGURE 6.19 Concentrationeresponse curves to the b-adrenoceptor agonists isoproterenol (filled circles) and prenalterol (open circles) obtained in
(A) guinea pig left atria and (B) rat left atria. Data fit to the operational model with the following parameters: isoproterenol, KA ¼ 400 nM for both tissues,
s ¼ 100 for rat and 300 for guinea pig left atria; and prenalterol, KA ¼ 13 nM for rat atria and 20 nM for guinea pig atria, s ¼ 0.21 for rat and 0.8 for
guinea pig left atria. Notably, data for the two agonists can be fit with relatively constant ratios of s (0.0021, 0.0027) and KA (30, 20 nM) for both tissues
illustrating the tissue independence of KA and relative s measurements.
FIGURE 6.20 Concentrationeresponse curves to the muscarinic agonists oxotremorine and carbachol in guinea pig ileum (A); oxotremorine is threefold
more potent than carbachol. With no prior knowledge of the relative efficacies of these agonists and with no calculation with the operational model, it
might be supposed that a 100-fold loss in system sensitivity would yield the profile shown in panel (B). Calculation of predicted effects with the
operational model predicts the profile shown in panel (C); the curves shown are actual experimental curves obtained after alkylation of a portion of the
receptor population to produce a 100-fold decrease in sensitivity. Data redrawn from T.P. Kenakin, The Pharmacologic Analysis of Drug Receptor
Interaction, third ed., Lippincott-Raven, New York, 1997, pp. 1e491.
166
A Pharmacology Primer
using the operational model indicates that the affinity of
carbachol is 300 mM, that of oxotremorine is 0.5 mM, and
that carbachol has 200 times the efficacy of oxotremorine.
Thus, the response to the high-affinity, low-efficacy agonist
(oxotremorine) is reduced to a greater extent with diminution of tissue sensitivity than that of the low-affinity,
high-efficacy agonist (carbachol), as predicted by receptor
theory and, in particular, by the operational model. This
effect is discussed in further detail in Section 6.6.1. These
types of predictions illustrate the value of determining the
relative efficacy and affinity of agonists when predicting
effects in a range of systems.
Ideally, while agonist response can be quantified in
terms of the parameters of efficacy (s) and KA for prediction of agonism, it will be seen that there are separate
methods which have been developed to quantify agonism
such as equiactive agonist potency ratios that do not
employ direct fitting of data to the BlackeLeff operational
model (vide infra). In addition to the quantification and
prediction of agonism, there are other important aspects of
agonist response that are relevant to the complete profile of
an agonist drug; these are related to agonist selectivity,
relative dependence of agonist potency on affinity versus
efficacy, secondary effects, and the actual “quality” of the
efficacy these molecules express in biological systems. This
latter factor is quantified under the heading of “biased
signaling.”
6.6.1 Affinity-dependent versus efficacydependent agonist potency
In the early stages of lead optimization, agonism is usually
detectable but at a relatively low level, that is, the lead
probably will be a partial agonist. Partial agonists are the
optimal molecule for pharmacological characterization.
FIGURE 6.21 The effects of chain
length
elongation
on
alkyltrimethylammonium agonists of
muscarinic receptors in guinea pig
ileum. Responses to C7TMA (filled
circles), C8TMA (open circles),
C9TMA (filled triangles), and
C10TMA (open squares). Note the
selective effect on efficacy and lack
of effect on affinity. Drawn from
R.P. Stephenson, A modification of
receptor theory, Br. J. Pharmacol.
11 (1956) 379e393.
This is because partial agonism allows the estimation of the
system-independent properties of drugs, namely, affinity
and efficacy (for partial agonists). Under these circumstances, medicinal chemists have two scales of biological
activity that they can use for lead optimization. The EC50 of
a partial agonist is a reasonable approximation of its affinity
(see Section 6.11.1); therefore, the observed EC50 for weak
agonists in structureeactivity relationships (SARs) studies
can be used to track the effect of changing chemical
structure on ligand affinity. Similarly, the relative maximal
responses of partial agonists can be useful indicators of
relative efficacy (see Section 6.11.3). Thus, partial agonism
provides a unique opportunity for medicinal chemists to
observe the effects of changes in chemical structure on
either affinity or efficacy. Fig. 6.21 shows the effects of
increasing alkyl chain length on a series of alkylammonium
muscarinic agonists [15]. It can be seen from these data that
the increased chain length selectively produces changes in
efficacy while not affecting affinity to any great extent.
It is important to note that it may be very useful to
determine whether an observed agonist potency is more
dependent upon high efficacy or high affinity. In a given
receptor system, two agonists may have identical potency
and thus seem indistinguishable (see Fig. 6.22A). However,
the potency of one agonist may emanate from high efficacy
(denoted “efficacy-dominant”) while the potency of the
other agonist may emanate from high affinity (and
concomitant low efficacy; denoted “affinity-dominant”).
The importance of knowing this is the fact that these agonists will deviate from such identical potency profiles in
systems of different receptor number and/or receptor
coupling efficiency. Specifically, the maximal response to
the efficacy-dominant agonist will be more resistant to
decreases in receptor number than will the lower efficacy
agonist. Therefore, the doseeresponse curve of the high-
Agonists: the measurement of affinity and efficacy in functional assays Chapter | 6
efficacy agonist will shift to the right with decreases in
coupling efficiency, receptor number, or onset of tachyphylaxis (desensitization; see Fig. 6.22, lower left), whereas
the doseeresponse curves to the affinity-dependent agonist
will return a depressed maximal response with no shift to
the right (see Fig. 6.22, lower right). Thus, these agonists
can be equiactive in some tissues but show completely
different profiles of activity in others. In general, efficacydominant agonists are more resistant to tachyphylaxis (or,
at least, an increase in dosage can regain response) and give
a more uniform stimulation to all tissues in vivo. In
contrast, affinity-dominant agonists are more sensitive to
tachyphylaxis (and no increase in dosage can regain
response, and, in fact, the agonist can then function as an
antagonist of other agonists at the receptor) and demonstrate more texture with respect to organ-selective agonism
in vivo. Fig. 6.23 shows the agonist effects of two badrenoceptor agonists; isoproterenol is efficacy-dominant
while prenalterol is affinity-dominant [16]. It can be seen
that the responses to prenalterol are more sensitive to tissue
type, with respect to the maximal response, than are the
responses to isoproterenol. It can also be seen that the
guinea pig extensor digitorum longus muscle produces a
response to isoproterenol but no agonist response to prenalterol. In this tissue, prenalterol functions as a full
competitive antagonist of responses to isoproterenol.
167
It is also important to note the physiological context in
which a synthetic agonist is being placed therapeutically. In
the case of the MC4R receptor, involved in energy homeostasis, there is a natural endogenous antagonist in the
form of AgRP that must be considered in the therapeutic
effects of any synthetic MC4R agonist. Specifically, the
synthetic agonist, in addition to producing activation of the
free receptors in the system to produce primary effect, must
also deal with the endogenous antagonism of the system
produced by AgRP. Therefore, the receptor occupancy of
the synthetic agonist becomes a relevant variable in the
therapeutic system since the receptor occupancy by the
synthetic agonist will affect the intrinsic antagonism due to
the ongoing receptor antagonism by the endogenous AgRP,
i.e., a high intrinsic efficacy would lead to a low receptor
occupancy for response. This, in turn, will lead to little
displacement of endogenous AgRP and less overall
response than that seen with a lower efficacy agonist that
would require a higher receptor and subsequently greater
displacement of AgRP. The displacement of endogenous
AgRP by a new agonist takes place through mass action
according to the Gaddum equation [17]. Thus the receptor
occupancy by endogenous AgRP is given by [AgRP]/KBAgRP/([AgRP]/KB-AgRP þ [Agonist]/KB-agonist þ 1). As can
be seen from this equation, the ability of a new ligand to
reduce the receptor occupancy of AgRP (i.e., reduce AgRP
FIGURE 6.22 Effects of decreasing receptor number on two agonists. The efficacy-dominant agonist has high efficacy (s ¼ 5000) and low affinity
(KA ¼ 1), while the affinity-dominant agonist has low efficacy (s ¼ 50) and high affinity (KA ¼ 0.01). Top curves show that both agonists are equiactive
in a high receptor density system. However, as receptor density decreases in 10-fold increments, the curves for the efficacy-dominant agonist shift to the
right but retain maximal response until a 100-fold shift is attained, while the curves to the affinity-dominant agonist show depressed maxima with any
decrease in receptor number.
168
A Pharmacology Primer
FIGURE 6.23 Dependence of
agonist response on efficiency of
receptor coupling and/or receptor
density. Responses to the highefficacy b-adrenoceptor agonist
isoproterenol [panel (A)] and the
low-efficacy b-adrenoceptor agonist
prenalterol [panel (B)] in thyroxine
pretreated guinea pig right atria (filled circles), rat left atria (open circles), guinea pig left atria (filled
triangles), and guinea pig extensor
digitorum longus muscle (open
squares). Data redrawn from T.P.
Kenakin, D. Beek, Is prenalterol (H
133/80) really a selective beta-1
adrenoceptor agonist? Tissue selectivity resulting from difference in
stimuluseresponse relationships, J.
Pharmacol. Exp. Ther. 213 (1980)
406e413.
FIGURE
6.24 Agonism
and
receptor occupancy. (A) Doseeresponse
curves to two agonists: one with high
efficacy (blue) and one with low efficacy
(red). The designated points produce
equal responses (90% maximum) but
require different receptor occupancies to
do so. (B) Reversal of the receptor occupancy by an antagonist produced by
the two agonists. The low efficacy
agonist produces sufficient receptor occupancy to reverse antagonist occupancy
whereas the high efficacy agonist with
the high receptor reserve does not.
receptor occupancy) is either through concentration
[Agonist] or high affinity KB-Agonist, i.e., [Agonist]/KAagonist ratio. The problem with agonists as displacing ligands is that they may have values of efficacy that lead to
high receptor reserve for response production and this
means their actual percent receptor occupancy is low.
Fig. 6.24 shows DR curves for two agonist of equal affinity
(1 mM) but differing efficacy; agonist blue is a high efficacy
agonist (sA ¼ 200) and agonist red is a low efficacy agonist
(sA ¼ 20). The high efficacy agonist has a high receptor
reserve and thus can produce 90% maximal response by
occupying only 4.7% of the receptors. The low efficacy
agonist requires more receptors (82%) to achieve that same
level of response but both are able to produce 90% maximal
agonist responsedsee Fig. 6.24A. If these agonists were to
compete with AgRP bound to the receptors at an equiactive
agonist response (90%), agonist blue will produce insignificant displacement of AgRP; this is shown as the blue
curve in Fig. 6.24B. The ordinate axis of this figure is the
fractional receptor occupancy for a concentration of AgRP
occupying 50% of the receptors. In contrast, agonist red
displaces a significant fraction of the AgRP. This simulation indicates that a lower efficacy agonist will displace
more AgRP in a physiological system than a high efficacy
agonist and if displacement of AgRP is desirable, then a
lower efficacy agonist would be preferred.
6.6.2 Secondary and tertiary testing of agonists
Table 6.2 indicates two additional levels of testing to fully
characterize agonists. Once it has been determined that a
series of compounds produce concentration-dependent agonism that can be measured reliably with concentratione
response curves, it also is important to determine whether the
test agonist binds to the endogenous orthosteric binding site
of the receptor (used by the natural agonist) or a site separate
Agonists: the measurement of affinity and efficacy in functional assays Chapter | 6
TABLE 6.2 Trilevel testing of agonists.
Activity
Experimental
approach
Rationale
Level 1
Track extent of agonism
l
l
l
Level 2
Determine if agonism is
orthosteric or allosteric
to endogenous agonist
site
l
l
l
l
l
Level 3
Measure temporal characteristics of agonism
l
l
l
l
Quantify
pEC50 and
Max if partial
agonists
Quantify potency
ratios if full
agonists
Quantify agonism
in a systemindependent
manner
Determine
selectivity
Block effects with
target orthosteric
antagonist
Determine effects
of partial agonist
on doseeresponse
curves to full
agonist
Define agonist
properties
Determine
if partial agonist
will block some
endogenous
agonism
Measure
special
properties
GPCRs: test
pK inhibitors/
measure ERK
activity
Proclivity for
desensitization
Characterize
signaling
from that site (see Table 6.2). In the latter case, the agonist
would be allosteric. The usual method of differentiating
these is to determine the sensitivity of the agonism to standard orthosteric antagonists of the target receptor. Lack of
effect of such antagonists suggests an allosteric site (see
Chapter 8: Allosteric Modulation, Fig. 8.45, for an example).
There are fundamental differences in the way orthosteric versus allosteric agonists interact with the natural
system. Thus, while an orthosteric partial agonist initiates
its own response, it will also block the effects of the
endogenous agonist in some cases (see Chapter 7:
Orthosteric Drug Antagonism, Section 7.3.5 and
Fig. 7.13A). In contrast, an allosteric agonist binds to its
own site to allow the natural agonist to cobind to the
169
receptor. The presence of the allosteric agonist may change
the reactivity of the receptor toward the natural agonist,
either decreasing its effect (as would an orthosteric partial
agonist), not changing its effect, or increasing the effects of
the natural agonist [18] (see Fig. 8.15). This is discussed
further in Chapter 8, Allosteric Modulation, under the
heading of allosteric agonism.
Another possibly important aspect of agonism is the
breadth of cellular pathways that an agonist stimulates and/
or the temporal aspect of that stimulation. For example, as
discussed in Chapters 2 and 9, transmembrane receptor
stimulation can result in activation of G-proteins for a rapid
transient response and also a longer lasting, lower level
activation of b-arrestin-mediated kinase activation that
leads to transcription events in the nucleus (see Fig. 6.25).
While early data suggested that b-arrestin mainly causes the
termination of the G-protein effects, subsequent studies
have indicated a rich array of responses emanating from the
b-arrestin intracellular complex [19,20,21,22]. Presently,
there is a large body of evidence to implicate b-arrestin
signaling in a host of diseases including diabetes [23], heart
failure [24], cardiovascular disease [25,26], central nervous
system diseases involving serotonin [27], diseases
involving angiotensin [28,29] and adrenergic signaling
[30,31], and parathyroid hormone (PTH) [32]. There are
data to show that different agonists favor one of these
pathways over the other in some receptor systems; special
agonist assays are required to detect this heterogeneity of
effect, and this is becoming a part of standard characterization of response in agonist discovery programs. This
leads into a major consideration in the quantification of
agonism, namely, the determination and quantification of
biased agonism.
6.7 Biased signaling
Data have emerged in the literature that are incompatible
with a scheme whereby receptors are simple switches (an
active and inactive state), and now it is realized that
different agonists can produce different qualities of agonism as well as varying quantities of agonism (for reviews,
see Refs. [33,34,35,36]). The source of this variance in
agonist quality is the fact that agonists can stabilize
different active states of receptors. These multiple active
states in turn interact differentially with signaling proteins
in the cell as they produce agonism [37]; the stabilization of
different receptor active states through the binding of
different ligands has been observed directly by [19F]nuclear magnetic resonance [38]. When this occurs,
certain cellular pathways will be activated to a greater
extent than others, and the ligands that produce this effect
will produce biased signals. Signaling bias has the potential
to produce therapeutically beneficial effects by emphasizing useful therapeutic signals and minimizing harmful
170
A Pharmacology Primer
FIGURE 6.25 Schematic diagram of seven
transmembrane receptor signaling pathways.
Activation of G-proteins results in a rapid
transient intracellular response. Agonistactivated receptors also may bind b-arrestin
and internalize to form an intracellular complex
for kinases that produce long-term signals
involved in transcription. Separate agonist assays may be required to visualize each of these
activities.
secondary effects. Strategies have been employed to capitalize on biased signaling for therapeutic drugs; one is to
generate data to identify where a given signal is either
especially beneficial or especially harmful to a defined
therapeutic treatment. Genetic knockout animals can be
very helpful in this regard. For example, nicotinic acid
receptor activation (GPR109) in b-arrestin null mice leads
to a lowering of serum fatty acids without the accompanying flushing seen in normal mice [39]; this suggests that
an agonist of GPR109 with b-arrestin activating effects
could be a superior therapy. Similarly, opioid receptor agonists are known to produce analgesia with concomitant
and unwanted respiratory depression. Respiratory depression to opioid agonists is greatly diminished in b-arrestin
knockout mice, suggesting that a ligand that does not cause
receptor association with b-arrestin would produce analgesia with less respiratory depression [40,41,42,43]. Similarly there is a possible indication for PTH in the treatment
of osteoporosis. The fact that PTH does not build bone or
increase the number of osteoclasts in b-arrestin-2 knockout
mice suggests that this signaling pathway is the therapeutically relevant one [44,45] and that a PTH agonist with barrestin biased signaling would be an optimal therapy for
this receptor.
Even if it is not clear whether a bias would provide a
better treatment, i.e., there are no preconceived ideas as to
the desirability of biased signaling, modern screening
practices can be used to identify biased ligands as tools to
evaluate signaling systems. Thus, selective assays for
various signaling pathways are used to identify biased ligands which then are tested in more complex assays (animal models in vivo) to determine whether superior
therapeutic phenotypes can be associated with any defined
bias (see Fig. 6.26).
The term “bias” suggests that receptor activation by a
ligand causes one signaling pathway linked to that receptor
to be activated to a greater extent than another. A useful
representation of such behavior is through a “bias plot,” in
Agonists: the measurement of affinity and efficacy in functional assays Chapter | 6
171
FIGURE
6.26 Screening
for
biased phenotypes. Panel to the left
shows screening data where most
active compounds are represented by
open circles lying furthest to the
right along the Resp1 axis. Conventional discovery schemes would
progress the most active molecules
(filled circles) into more sophisticated models. In light of possible
biased agonism, a larger subset of
the compounds outlined in the red
rectangle are tested in another assay
for a second signaling pathway and
exemplar molecules (red filled circles) from the array progressed into
further tests. These molecules would
be known to be different with
respect to their signaling properties.
FIGURE 6.27 Effects of dibutryl cyclic AMP on myocardial relaxation (lusitropy) and force of contraction (inotropy) responses in rat atria. Panel on
right shows a bias plot where the observed lusitropic effects are expressed as a function of the inotropic effects seen at the same concentration of dibutryl
cyclic AMP. It can be seen that in this tissue, the lusitropic response requires less intracellular messenger to become activated than does the inotropic
response. Data redrawn from T.P. Kenakin, J.R. Ambrose, P.E. Irving, The relative efficiency of b-adrenoceptor coupling to myocardial inotropy and
diastolic relaxation: organ selective treatment for diastolic dysfunction, J. Pharmacol. Exp. Ther. 257 (1991) 1189e1197.
which the response to one process is graphed as a function
of the response produced in another. For example, biased
signal activation can be shown for the cardiac activity by
comparing myocardial inotropy (increased isometric force
of contraction) to lusitropy (increased rate of relaxation) in
response to elevations in intracellular cyclic AMP. As
shown in Fig. 6.27, there is a curved relationship when
myocardial inotropy is graphed as a function of myocardial
lusitropy, i.e., the response is biased toward the production
of greater lusitropy for a given increase in inotropy [46].
Presumably, this is a function of the requirements of the
cell and will be referred to as “system bias”; all agonists
producing elevated cyclic AMP in the myocardial cell will
be subject to this signaling bias. While this conceivably
might be exploited therapeutically, it is of limited application since it is a bias that cannot be manipulated pharmacologically. Bias plots also can be curvilinear due to the
relative sensitivity of the assays used to make the
172
A Pharmacology Primer
FIGURE 6.28 Effects of b-adrenoceptor agonists on G-protein activation of cyclic AMP and b-arrestinereceptor complexation in separate assays for the
effects. Panel on right shows a bias plot where the observed effects on cyclic AMP are expressed as a function of the b-arrestin effects seen at the same
concentration of agonist (EPI, epinephrine; FEN, fenoterol; ISO, isoproterenol). It can be seen that the cyclic AMP assay is generally more sensitive than
the b-arrestin assay causing an observed bias toward the cyclic AMP response in the bias plot. However, this bias is imposed equally on all the agonists
since it is simply due to the differential sensitivity of the two assays. Data drawn from S. Rajagopal, S. Ahn, D.H. Rominger, W. Gowen-MacDonald, C.M.
Lam, S.M. DeWire, Quantifying ligand bias at seven-transmembrane receptors, Mol. Pharmacol. 80 (2011) 367e377.
measurement; this is referred to as “observation bias.” For
example, Fig. 6.28 shows how b-adrenoceptor-mediated
beta-arrestin pharmacologic assays are, in this case, 30fold less sensitive than second messenger assays [47]; a
bias plot of these two responses shows a clearly skewed
relationship. As with system bias, there is no distinction
between agonists with this type of effect, i.e., all agonists
are uniformly affected by observation bias. Observational
bias will vary with types of assays and assay conditions.
However, a third type of bias, termed “ligand bias” can be
operable within system and observational bias which stems
from the stabilization of different receptor active states by
agonists [37]. This type of bias is uniquely related to the
chemical structure of the agonist and thus can be manipulated using medicinal chemistry for possible therapeutic
advantage. When this mechanism is operative, the bias
plots of different ligands, while all subject to system and
observation bias, will show a ligand-dependent heterogeneity (see Fig. 6.29); it is this ligand-specific bias that can
be exploited therapeutically, since it is related to the
chemical structure of the molecule.
Fig. 6.30A shows two ligands interacting with the same
receptor; agonist A stabilizes a conformation that favors
activation of G-proteins, while agonist B stabilizes a
conformation favoring the interaction of the receptor with
b-arrestin. Depending on the physiological outcomes of
each of these signaling pathway activations, agonists A and
B could have very different activity profiles. Fig. 6.30B
shows the relative activation (or lack of activation) of Gprotein and b-arrestin pathways produced by two ligands
for angiotensin receptors. While angiotensin II produces
FIGURE 6.29 Bias plot showing the effects of CCR5 activation by four
chemokines on inositol phosphate production (ordinate values IP1) and the
internalization of CCR5 receptors (abscissae) produced by the same concentration of chemokine receptor in two separate assays. While there is a
bias toward the IP1 response (which could be the result of system and/or
observation bias), it is not homogeneous for all chemokines. This indicates
that something unique to the specific chemokines imposes an added bias to
the signaling, i.e., these molecules stabilize different receptor active states.
Data redrawn from T.P. Kenakin, C. Watson, V. Muniz-Medina, A.
Christopoulos, S. Novick, A simple method for quantifying functional
selectivity and agonist bias, ACS Chem. Neurosci. 3 (2012) 193e203.
activation of both Gq protein and causes the receptor to
associate with b-arrestin (to cause another type of
signalingdsee Chapter 2: How Different Tissues Process
Drug Response, see Fig. 2.24), the biased ligand
TRV120027 does not activate G-proteins but does cause
Agonists: the measurement of affinity and efficacy in functional assays Chapter | 6
173
FIGURE 6.30 Ligand bias due to stabilization of different receptor active conformations. Panel (A) shows a schematic diagram of two receptors
activated by two ligands (A) and (B). Ligand (A) stabilizes a state that preferentially interacts with the G-protein signaling pathway giving an efficacy for
this pathway of sG with an affinity KAG (but also having another efficacy for the b-arrestin pathway sb and KAb) while another agonist (B) has the
opposite bias preferentially activating the b-arrestin pathway. Panel (B) shows an example of such a biased ligand. While angiotensin produces activation
of Gq and b-arrestin signaling, the biased ligand TRV120027 activates only the b-arrestin pathway. Data for panel (B) redrawn from J.D. Violin, S.M.
DeWire, D. Yamashita, D.H. Rominger, L. Nguyen, K. Sciller, Selectively engaging b-arrestins at the angiotensin II type 1 receptor reduces blood
pressure and increases cardiac performance, J. Pharmacol. Exp. Ther. 335 (2010) 572e579.
b-arrestin-based signaling [48]. In this case, the profile of
TRV120027 is an improvement on standard heart failure
treatments such as losartan, as the latter blocks debilitating
vasoconstriction due to elevated angiotensin level while the
former does so and provides beneficial b-arrestin signaling
to the failing myocardial cell [49,50]. In general, biased
signaling can be therapeutically useful in two settings: the
emphasis of a favorable signal or the deletion of an unwanted signal. A key factor in the development of biased
agonists (and antagonists) is the system-independent
quantification of the effect for use in optimization studies.
Biased agonism can be quantified with the BlackeLeff
operational model; the key is to assign an efficacy (s) and
affinity (KA) to the signaling pathway and not total cell
response. The index of agonism that is the theoretically
most sound takes into account the potency of the agonist
(i.e., the location parameter of the agonist concentratione
response curve along the concentration axis; usually the
FIGURE 6.31 Biased signaling as an allosteric system comprised as the
agonist functioning as an allosteric modulator of the receptor protein (the
conduit) as it interacts with guest molecules (signaling proteins). All three
components must be considered when quantifying efficacy.
pEC50) and the maximal response to the agonist. To this
end, a transducer coefficient can be calculated for each
signaling pathway in the form of log(s/KA) [12]. Transducer coefficients describe a molecular allosteric vector
[33] comprised of the agonist (as modulator), receptor (as a
conduit), and signaling protein (as a guestdsee Fig. 6.31).
174
A Pharmacology Primer
In effect, biased agonism is probe-dependent allosterism
directed toward the cellular signaling apparatus; i.e., the
agonist modulator modifies the affinity of the receptor toward the signaling protein and also the molecular outcome
of the result (the efficacy). Biased agonism, through
differing efficacies of the agonists toward signaling pathways, is intuitive but what may not be as intuitively clear is
the need to associate a unique affinity of the agonist for the
receptor as it interacts with each signaling pathway as well.
Thus, the same receptor can have different affinities for
different signaling proteins when the agonist is bound, and
since allosteric energy is reciprocal, this means also that the
receptor will have different affinities for the agonist when
different signaling proteins are bound. For example, there
could be a KA value for a given agonist for a receptor when
it is interacting with a G-protein and another KA for the
same agonist on the same receptor when it interacts with barrestin; this is due to the allosteric nature of receptors
[33,51,52] and is discussed in detail in Section 8.4.3.
This idea is supported by functional and binding experiments; for instance, there is a 50-fold change in the affinity of
[3H]dimethyl-W84 with the allosteric modulator gallamine for
muscarinic M2 receptor changes in the presence of the
cobinding ligand N-methylscopolamine [53]. In functional
studies, the affinity of the N-methyl-D-aspartate (NMDA) receptor antagonist ifenprodil changes by a factor of 10 in the
presence of the cobinding ligand NMDA [54]. Changes in
receptor structure also have been shown with the binding of
signaling proteins to receptors, i.e., binding of Ga16 and/or
Gai2 G-protein subunits to the k-opioid receptor show
changes in conformation in transmembrane domains 6 and 7
and these are concomitant with an 18-fold change in the affinity of the ligand salvanorin [55]. For this reason, it is untenable to utilize a single KA from a single source (i.e.,
binding) in log(s/KA) estimates for different pathways. In
FIGURE 6.32 Concentrationeresponse curves in U373 cells for CCR5
activation with chemokines (CCL3L1,
filled circles), CCL5 (open circles), CCL3
(filled triangles), and CCL4 (open
triangles). Panel (A) for inositol phosphate production and panel (B) CCR5
internalization. Data redrawn from T.P.
Kenakin, C. Watson, V. Muniz-Medina,
A. Christopoulos, S. Novick, A simple
method for quantifying functional selectivity and agonist bias, ACS Chem.
Neurosci. 3 (2012) 193e203.
addition, these data suggest that the binding affinity may have
no relevance to the operational functional affinity in the cell.
Fig. 6.32 shows chemokine-mediated effects for the
CCR5 chemokine receptor for two signaling pathways:
inositol phosphate production and internalization of the
CCR5 receptor [12]. These concentrationeresponse curves
furnished the heterogeneous bias plots shown in Fig. 6.29;
Dlog(s/KA) calculations quantify this heterogeneity in bias
and assign a bias number to each molecule which should be
an independent measure of the ability of the molecule to
induce bias for CCR5 in all cellular systems. An example
of this procedure is given in Table 6.3 and can be thought
of as a stepwise process:
1. Calculate log(s/KA) values for each agonist for each
signaling pathway and then express these for each
pathway as a Dlog(s/KA) value for each agonist when
compared to a selected reference agonist. Which agonist
chosen as the reference does not affect the calculations
but often a natural agonist for the system is chosen as a
contrast to bias of synthetic agonists. The Dlog(s/KA)
values serve as a relative measure of the agonists to activate the selected signaling pathway.
2. When this is done for both pathways (with the same reference agonist used for each pathway), then cross-pathway
comparisons can be made. Thus, DDlog(s/KA) values are
calculated which serve to quantify the relative difference
in selective pathway activation, i.e., bias. It should be
noted that comparison to the reference agonist cancels
both system bias and observation bias and these effects
cease to be a factor in the calculations.
3. The bias of the agonist is then defined as
Bias ¼ 10DD1 Logðs=KA Þ
(6.7)
Agonists: the measurement of affinity and efficacy in functional assays Chapter | 6
TABLE 6.3 Biased signaling for chemokine activation of
CCR5 receptors.
175
transduction ratios (DLog(max/EC50))¼(Dlog(s/KA)). An
additional method of determining Dlog(s/KA) values is
through the methods of Barlow et al. [58]. This method is
discussed more fully in Section 6.8.1 and yields values of
Dlog(s/KA) for two agonists through the slope of the linear
regression (vide infra).
Log transducer coefficients can be used to quantify
agonist-specific signaling bias and also the induction of
bias into endogenous signaling through allosteric modulation (see Chapter 8: Allosteric Modulation). However, there
are factors to consider when predicting possible biased
effects in vivo and these are discussed more fully in
Chapter 9, The Optimal Design of Pharmacological
Experiments.
Agonist
IP1
production
Log(s/KA)
a
Dlog(s/KA)
Log(s/KA)
Dlog(s/KA)a
CCL3
7.75
0
6.58
0
CCL4
8.01
0.26
8.2
1.62
CCL5
8.27
0.52
8.53
1.95
CCL3L1
8.48
0.73
8.82
2.24
DDLog
(s/KA)b
BIASc
CCL3
0
1
CCL4
1.36
23.1
6.7.1 Receptor selectivity
CCL5
1.43
27
CCL3L1
1.51
32.4
Since log(s/KA) is an index of the power that a molecule
has to activate a receptor, transduction ratios (Dlog(s/KA))
can also be used to gauge selective receptor agonism. Thus,
the relative power of two agonists to activate the primary
(therapeutic) receptor [quantified as Dlog(s/KA)therapeutic
values] versus their relative power to activate a secondary
receptor (perhaps denoting a safety hazard or other unwanted activity) is given as Dlog(s/KA)secondary values; the
selectivity index would then be
CCR5R internalization
a
Relative to CCL3.
IP1 versus Internalization.
10DDLog(s/KA).
b
c
It can be seen from Fig. 6.29 that CCL3L1 is uniquely the
most biased toward inducing the greatest amount of CCR5
receptor internalization for a given IP1 response, when
compared to CCL3, CCL4, and CCL5. This may be therapeutically relevant for this chemokine since the gene copy
number for the production of CCL3L1 has been associated
with favorable survival after HIV-1 infection in progression
to AIDS [56]. The data suggest that CCL3L1-mediated
internalization of the CCR5 receptor may yield protection
from further HIV-1 infection by removing CCR5, the target
protein used by the gp120 viral coat protein to infect cells.
The 32.4-fold bias of CCL3L1 for CCR5 internalization
shown in Table 6.3 is consistent with this idea.
It can be seen from Eqs. (6.5) and (6.6) that the parameters of the operational model can translate to observable indices, namely, the potency of an agonist (EC50) and
the maximal response. Under certain circumstances, these
easily observable features of agonism can be utilized to
quantify agonist bias. For example, the logarithm of the
maximal response divided by the EC50 of a
concentrationeresponse curve for an agonist can be used to
quantify agonism [13,57]. Combining Eqs. (6.5) and (6.6)
yields the following expression for max/EC50 in terms of
the BlackeLeff operational model:
sn ð1 þ sn Þ1=n 1 Em
max
(6.8)
¼
EC50
KA ð1 þ sn Þ
In the special circumstance of curves with n ¼ 1, the
max/EC50 then becomes sEm/KA and the values reduce to
DD logðs=KA Þselectivity ¼ logðs=KA Þtherapeutic
D logðs=KA Þsecondary
(6.9)
The interpretation of DDlog(s/KA)selectivity values is
discussed further in Eq. (6.9) and Chapter 9, The Optimal
Design of Pharmacological Experiments.
6.8 Null analyses of agonism
Although the BlackeLeff operational model is the most
sound theoretical framework for agonism, and also offers
the best options for characterizing and quantifying agonism, other null methods have been presented in the literature which can be used to quantify the efficacy and affinity
of agonists. The most straightforward can be applied to
partial agonists, since the location parameter of the partial
agonist concentrationeresponse curve (EC50) is a relatively
close estimate of the affinity (KA), while changes in
maximal response are good indicators of changes in efficacy (see Fig. 6.33).
6.8.1 Partial agonists
As noted in Chapter 2, How Different Tissues Process Drug
Response, the functional EC50 for a full agonist may not,
and most often will not, correspond to the binding affinity
of the agonist. This is due to the fact that the agonist
176
A Pharmacology Primer
FIGURE 6.33 Sensitivity of various descriptive parameters for concentrationeresponse curves to drug receptor parameters. (A) The location parameter
(potency) of curves for full agonists depends on both affinity and efficacy. (B) For partial agonists, the location parameter (EC50, potency) is solely
dependent upon affinity while the maximal response is solely dependent upon efficacy.
possesses efficacy and the coupling of agonist binding to
production of response is nonlinear. In terms of the
BlackeLeff operational model (see Section 6.11.1), the
EC50 is related to the KA by
EC50 ¼
KA
;
ð1 þ sÞ
(6.10)
where s is the term relating efficacy of the agonist and the
efficiency of the receptor system in converting receptor
activation to response (high values of s reflect either high
efficacy, highly efficient receptor coupling, or both). High
values of s are associated with full agonism. It can be
seen from Eq. (6.10) that full agonism produces differences
between the observed EC50 and the affinity (KA).
Eq. (6.10) shows that as s / shows t50 / KA.
Therefore, in general, the EC50 of a weak partial agonist
can be a reasonable approximation of the KA (see Section
6.11.1 for further details). The lower the magnitude of
the maximal response (lower s), the more closely the EC50
will approximate the KA. Fig. 6.34 shows the relationship
between agonistereceptor occupancy for partial agonists
and the response for different levels of maximal
response (different values of s). It can be seen that as the
maximal response / 0, the relationship between
agonistereceptor occupancy and tissue response becomes
linear and EC50 / KA.
A measure of the affinity of a partial agonist can be
obtained using the method devised by Barlow et al. [58].
Using null procedures, the effects of stimuluseresponse
mechanisms are neutralized and receptor-specific effects of
agonists are isolated. This method, based on classical or
operational receptor theory, depends on the concept of
equiactive concentrations of drug. Under these circumstances, receptor stimuli can be equated since it is assumed
that equal responses emanate from equal stimuli in any
given system. An example of this procedure is given in
Section 13.2.1.
Doseeresponse curves to a full agonist [A] and a partial
agonist [P] are obtained in the same receptor preparation.
From these curves, reciprocals of equiactive concentrations
of the full and partial agonist are used in the following
linear equation (derived for the operational model; see
Section 6.11.2):
1
1 sa $KP sa sp
¼ $
þ
;
½A ½P sp $KA sp $KA
(6.11)
where sa and sp are efficacy terms for the full and partial
agonist, respectively, and KA and KP their respective
ligandereceptor equilibrium dissociation constants. Thus,
a regression of 1/[A] upon 1/[P] yields the KB modified
by an efficacy term with the following parameters from
Eq. (6.11):
Slope
sp
KP ¼
1
(6.12)
Intercept
sa
It should be noted that the logarithm of the slope
from the regression described by Eq. (6.11) will also
furnish an estimate of the Dlog(s/KA) values for the agonists for use in calculating biased signaling. It can be seen
from Eq. (6.12) that a more accurate estimate of the affinity
will be obtained
with partial agonists of low efficacy (i.e.,
as sa [sp ; sp sa /0). Double reciprocal plots are known
to produce overemphasis of some values, skew the distribution of data points, and be heterogeneously sensitive to
error. For these reasons, it may be useful to use a metameter
of Eq. (6.11) as a linear plot to measure the KP. Thus, the
KP can be estimated from a plot according to
½P
½P
sA
sa K P
¼
;
(6.13)
1 þ
½A KA
sp
sp K A
Agonists: the measurement of affinity and efficacy in functional assays Chapter | 6
177
FIGURE 6.34 The relationship between the EC50 for partial agonists and the affinity (KA). (A) For higher-efficacy partial agonists (s ¼ 3), the relationship between receptor occupancy and response is hyperbolic (note solid vs. dotted line in right-hand panel, where the dotted line represents a linear
and direct relationship between the occupancy of the receptor by the agonist and the production of response). (B) This deviation lessens with lower
efficacy values for the partial agonist (note panels for agonist with s ¼ 1). (C) With weak partial agonists, the EC50 and KA values nearly coincide (see
panels with s ¼ 0).
178
A Pharmacology Primer
where
KP ¼
Intercept 1 sp = sa .
Slope
(6.14)
Another variant is
1 sp =sa
½A sp KA
¼
½A ½P
sa K p
KP
(6.15)
dependent on efficacy and the efficiency of receptor
stimuluseresponse coupling (receptor occupancy is
maximal and thus affinity is not an issue), the relative
maxima of agonists can be used to estimate the relative
efficacy of agonists. In terms of operational theory, the
maximal response to a given agonist (Max) is given by the
following (see Section 6.11.3):
Max ¼
where:
KP ¼
sp =sa 1
slope
(6.16)
An example of the application of this method to the
measurement of the affinity of the histamine receptor partial
agonist E-2-P (with the full agonist histamine) is shown in
Fig. 6.35 [59]. A full example of the application of this
method for the measurement of the effect of partial agonists
is given in Section 13.2.2.
The other system-independent measure of drug activity
that can be measured for an agonist is efficacy, the power of
the molecule to induce a change in the biological system.
Since the maximal response to an agonist is totally
Emax s
1þs
(6.17)
The relative maximal response to two agonists with s
values denoted s and s0 is given by the following (see
Section 6.11.3):
Max0 s0 ð1 þ sÞ
¼
sð1 þ s0 Þ
Max
(6.18)
It can be seen that the relative maxima are completely
dependent on efficacy, receptor density, and the efficiency
of stimuluseresponse coupling (s ¼ [R]/KE; see Chapter 3:
DrugeReceptor Theory). However, the relationship is not a
direct one. At low values of receptor density the relative
maximal response approximates the relative efficacy of the
two agonists (as s; s0 1, Max’/Max / s0 /s). Eq. (6.18)
FIGURE 6.35 Method of Barlow, Scott, and Stevenson for measurement of affinity of a partial agonist. (A) Guinea pig ileal smooth muscle contraction
to histamine (filled circles) and partial histamine receptor agonist E-2-P (N,N-diethyl-2-(1-pyridyl)ethylamine) (open circles). Dotted lines show equiactive
concentrations of each agonist used for the double reciprocal plot shown in panel (B). (B) Double reciprocal plot of equiactive concentrations of histamine
(ordinates) and E-2-P (abscissae). Linear plot has a slope of 55.47 and an intercept of 1.79 106. This yields a KB (1 sp/sA) ¼ 30.9 mM. (C) Variant of
double reciprocal plot according to Eq. (6.8). (D) Variant of double reciprocal plot according to Eq. (6.10). Data redrawn from T.P. Kenakin, D.A. Cook,
N,N-Diethyl-2-(1-pyridyl)ethylamine, a partial agonist for the histamine receptor in guinea pig ileum, Can. J. Physiol. Pharmacol. 58 (1980) 1307e1310.
Agonists: the measurement of affinity and efficacy in functional assays Chapter | 6
indicates that if both agonists are weak partial agonists in a
given receptor system, then the relative maximal response
will be an approximation of the relative efficacy of the two
agonists. At the least, even in cases where the maxima
approach the system maximum, the rank order of the
maxima of two agonists is an accurate estimate of the rank
order of the efficacy of the agonists.
6.8.2 Full agonists
As discussed previously, the location parameter of a
doseeresponse curve (potency) of a full agonist is a complex amalgam of the affinity and efficacy of the agonist for
the receptor and the ability of the system to process receptor
stimulus and return tissue response. This latter complication can be circumvented by comparing the agonists in the
same functional receptor system (null methods). Under
these circumstances, the receptor density and efficiency of
receptor coupling effects cancel each other, since they are
common for all the agonists. The resulting relative potency
ratios of the full agonists (providing the concentrations are
taken at the same response level for each agonist) are
system-independent measures of the molecular properties
of the agonists, namely, their affinity and efficacy for the
receptor. Such potency ratios for full agonists are sometimes referred to as equimolar potency ratios or EPMRs
(equipotent molar potency ratios) and are a standard
method of comparing full agonists across different systems.
There are three major prerequisites for the use of this
tool in SAR determination. The first is that the agonists
must truly all be full agonists. If one is a partial agonist,
then the system independence of the potency ratio measurement is lost. This is because of the different effects that
variation in receptor density, efficiency of coupling, and
measurement variation have on the location parameters of
doseeresponse curves to partial versus full agonists. For
example, Fig. 6.36 shows the effect of an increase in
179
receptor number on a high-efficacy agonist (s ¼ 500) and
low-efficacy agonist (s ¼ 5). It can be seen from this figure
that the curve for the high-efficacy agonist shifts to the left
directly across the concentration axis, whereas the curve for
the lower efficacy agonist rises upward along the ordinal
axis with little concomitant displacement along the concentration axis, that is, the potency of the full agonist
changes, whereas the potency of the partial agonist does
not. This is because potency is dependent upon efficacy and
affinity to different extents for full and partial agonists.
Therefore, it is inconsistent to track SAR changes for full
and partial agonists with the same tool, in this case, potency
ratios.
Another prerequisite for the use of potency ratios for
agonist SAR is that the ratio be independent of the level of
response at which it is measured. Fig. 6.37 shows dosee
response curves for two full agonists. It can be seen that a
rigorous fit to the data points results in two curves that are
not parallel. Under these circumstances, the potency ratio of
these agonists varies depending on which level of response
the ratio is measured (see Fig. 6.37A). In this situation, the
measure of drug activity is system dependent and not useful
for SAR. However, the nonparallelism of these curves may
be the result of random variation in response measurement
and not a true reflection of the agonist activity. A statistical
test can be done to determine whether these curves are from
a single population of curves with the same slope, that is, if
the data can be described by parallel curves, with the result
that the potency ratio will not be system dependent.
Application of this test to the curves shown in Fig. 6.37A
yields the parallel curves shown in Fig. 6.37B. In this case,
there is no statistical reason why the data cannot be
described by parallel curves (see Appendix: Statistics and
Experimental Design for a detailed description of the
application of this test); therefore, the potency ratio can be
derived from parallel curves with the result that systemindependent data for SAR can be generated.
FIGURE 6.36 Comparative potencies of two agonists in two receptor systems containing the same receptor at different receptor densities. (A) Relative
potency in system with high receptor density (s1 ¼ 500, s2 ¼ 100). The potency ratio ¼ 5. (B) Doseeresponse curves for same two agonists in receptor
system with 1/100 the receptor density. Potency ratio ¼ 1.3.
180
A Pharmacology Primer
FIGURE 6.37 Full agonist potency
ratios. (A) Data fit to individual threeparameter logistic functions. Potency
ratios are not independent of level of
response: At 20%, PR ¼ 2.4; at 50%,
PR ¼ 4.1; and at 80%, PR ¼ 6.9. (B)
Curves refit to logistic with common
maximum asymptote and slope.
PR ¼ 4.1. The fit to common slope
and maximum is not statistically significant from individual fit.
Two full agonists can be compared through EPMR
values fit from curves fit to a generic sigmoidal function to
yield a useful parameter dependent only upon the molecular
properties of the full agonists (see Section 6.11.4):
EPMR ¼
KA ð1 þ s0 Þ
.
K0A ð1 þ sÞ
(6.19)
For full agonists s; s0 [1, allowing the estimate
EC50 ¼ KA/s. Substituting s ¼ [Rt]/KE, the potency ratio of
two full agonists is
EPMR ¼
EC50
KA KE
;
0 ¼
EC50
K0A K0E
(6.20)
where KE is the MichaeliseMenten constant for the activation of the cell by the agonist-bound active receptor complex (a parameter unique to the agonist). It can be seen
from Eq. (6.20) that changes in full agonist potency ratios
reflect changes in either affinity or efficacy, and it cannot
be discerned which of these changes with any given change
in potency ratio.
The third prerequisite for accurate full agonist potency
ratios is that the function connecting initial receptor stimulus given to the cellular response mechanism that yields
observable response be monotonic in nature. Specifically, if
the receptor stimulus is x and the tissue response is y, then
there must be only one value of y for every x; this is shown
in Fig. 2.10. This assumption is defensible for agonists that
stabilize the same receptor active conformation but may not
be valid for biased agonists that do not. Therefore, if two
agonists impart different degrees of stimulus to the receptor
through the differential activation of two signaling pathways, then the composition of the cell may add a layer of
influence into the stimuluseresponse function that is not
constant for each agonist. In other words, if one of the
signaling pathways in a given cell is more important than
another, then the agonist that is biased toward that pathway
will give a greater overall cellular response than a biased
agonist that does not emphasize that same pathway; this is
shown as an alternative version to Figs. 2.10 in 6.38. In
practical terms, this can make full agonist potency ratios
cell type dependent for biased agonists; an example is
shown in Fig. 6.39 for calcitonin biased agonists in two
different cell types [60].
For full agonists, the approximation of the EC50 as
affinity is not useful and other methods must be employed
to estimate affinity. A method to measure the affinity of
high-efficacy agonists has been described by Furchgott
[61]. This method is based on the comparison of the responses to an agonist in a given receptor system under
control conditions and again after a fraction of the receptor
population has been irreversibly inactivated. For some
receptorsdsuch as a-adrenoceptors, muscarinic, serotonin,
and histamine receptorsdthis can be accomplished through
controlled chemical alkylation with site-directed alkylating
agents such as b-haloalkylamines. Thus, equiactive
responses obtained before and after receptor alkylation
are compared in the following double reciprocal relation
(see Section 6.11.5):
1
1 1
1 1q
¼
;
þ $
½A ½A0 q KA q
(6.21)
where [A] and [A0 ] are equiactive agonist concentrations
measured before and after receptor alkylation, respectively;
q is the fraction of receptors remaining after alkylation; and
KA is the equilibrium dissociation constant of the agoniste
receptor complex. Thus, a regression of 1/[A] upon 1/[A0 ]
yields a straight line with given slope and intercept. From
these, the equilibrium dissociation constant of the agoniste
receptor complex can be calculated:
KA ¼
Slope 1
.
Intercept
(6.22)
An example of the use of this approach is given in
Fig. 6.40. The method of Furchgott indicates that the affinity of the muscarinic agonist oxotremorine in guinea pig
ileal smooth muscle is 8.2 mM. The EC50 for half-maximal
contractile response to this agonist is 25 nM (a 330-fold
difference). This underscores the fact that the EC50 for
Agonists: the measurement of affinity and efficacy in functional assays Chapter | 6
181
FIGURE 6.38 Nonmonotonic linkage of receptor stimulus to cellular response. Top panel shows biased agonism where two receptor stimuli combine to
yield a total cellular response. The cell imparts an emphasis to one of the pathways in accordance to its particular physiological requirements. As agonists
produce differential production of the two stimuli, the agonist producing a greater stimulus of the cell-emphasized pathway will yield a greater cellular
response than another agonist that does not. Lower panel shows two agonists activating the receptor where the stimulus from the pathway shown with the
dotted line is more efficiently coupled to cellular response than other pathways. Under these circumstances, the broken line stimulus produces a greater
response thus causing an aberration of the relative order of stimuli at the receptor (compare this figure to Fig. 2.10).
FIGURE 6.39 Cell type dependence on agonist activation of human calcitonin receptors transfected into CHO cells and CV-1 fibroblast-like cells (COS
cells). The relative potency of the agonists is cell type dependent. Agonists are pCal, hCal, and hCGRP. CHO, Chinese hamster; hCal, human calcitonin;
hCGRP, human calcitonin gene-related peptide ovary; pCal, porcine calcitonin. Redrawn from L. Christmanson, P. Westermark, C. Betsholtz, Islet
amyloid polypeptide stimulates cyclic AMP accumulation via the porcine calcitonin receptor, Biochem. Biophys. Res. Commun. 205 (1994) 1226e1235.
full agonists can differ considerably from the KA. A full
example of the use of this method to measure the affinity of
a full agonist is given in Section 13.2.3.
The Furchgott method can be effectively utilized by
fitting the doseeresponse curves themselves to the operational model with fitted values of s (before and after
alkylation) and a constant KA value. Fig. 6.41 shows the
use of nonlinear curve fitting to measure the affinity of the
a-adrenoceptor agonist oxymetazoline in rat anococcygeus
muscle after alkylation of a portion of the receptors with
phenoxybenzamine. These data show how all three curves
can be used for a better estimate of the affinity with
nonlinear curve fitting, a technique not possible with the
double reciprocal plot approach where only two dosee
response curves can be used. The use of three curves increases the power of the analysis since more data are utilized for the fit and all must comply with a single estimate
of KA.
182
A Pharmacology Primer
FIGURE 6.40 Measurement of the affinity of a full agonist by the method of Furchgott. (A) Concentrationeresponse curves to oxotremorine in guinea
pig ileal smooth muscle strips. Ordinates: percent maximal contraction. Abscissae: logarithms of molar concentrations of oxotremorine. Control curve
(filled circles) and after partial alkylation of muscarinic receptors with phenoxybenzamine 10 mM for 12 min (open circles). Lines represent equiactive
concentrations of oxotremorine before and after receptor alkylation. (B) Regression of reciprocals of equiactive concentrations of oxotremorine before
(ordinates) and after (abscissae) receptor alkylation. The regression is linear with a slope of 609 and an intercept of 7.4 107. Resulting KA estimate for
oxotremorine according to Eq. (6.12) is 8.2 mM. Data redrawn from T.P. Kenakin, The Pharmacologic Analysis of Drug Receptor Interaction, third ed.,
Lippincott-Raven, New York, 1997, pp. 1e491.
FIGURE 6.41 Measurement of affinity of a full agonist by the method of
Furchgott [61] utilizing nonlinear curve fitting techniques according to the
operational model. Contractions of rat anococcygeus muscle to a-adrenoceptor agonist oxymetazoline before (circles) and after irreversible receptor
alkylation with phenoxybenzamine (squares: 30 nM for 10 min; triangles:
0.1 mM for 10 min). Curves fit simultaneously to Eq. (6.15) with Emax ¼ 105
and s values for curves of (s1 ¼ 12), (s2 ¼ 2.6), and (s3 ¼ 0.15). The equilibrium dissociation constant for the agonistereceptor complex is 0.3 mM.
Estimation by the double reciprocal plot method is KA ¼ 0.32 mM and by the
Schild method (whereby oxymetazoline is utilized as a competitive antagonist of responses to the higher-efficacy agonist norepinephrine after receptor alkylation is 0.2 mM). Data redrawn from T.P. Kenakin, The
Pharmacologic Analysis of Drug Receptor Interaction, third ed., LippincottRaven, New York, 1997, pp. 1e491.
6.9 Comparing full and partial agonist
activities: Log(max/EC50)
For full agonists, relative potency ratios (ratios of EC50
values where EC50 refers to the concentration of agonist
producing 50% maximal response) provide systemindependent measures of activity. Due to the fact that
changes in system sensitivity produce different magnitudes
of change in the EC50 values of full versus partial agonists,
potency ratios of full and partial agonists are not useful as
system-independent measures of the relative activity of
such agonists. However, a measure of agonist activity that
can fulfill this requirement is the Log(max/EC50) where the
max is the maximal response to the agonist (as a fraction of
the maximal window for measurement of agonist response
in the assay) [57]. Fig. 6.42 shows the relative potency
ratios of two agonists in a tissue with a range of sensitivities
(i.e., receptor densities). It can be seen that, as the lower
efficacy becomes a partial agonist, the potency ratio deviates from the linear relationship seen when both agonists
are full agonists; this means that the resulting potency ratios
are system dependent and cannot be used as predictive
measures of agonism for these two agonists in other systems. In contrast, the Log(max/EC50) values continue to be
linearly related. It can be shown that Log(max/EC50) values
are theoretically a system-independent measure of agonism
by modeling agonists as positive allosteric modulators of
the interaction between receptors and signaling proteins;
under these circumstances, Log(max/EC50) values become
estimates of the logarithm of the ratio of the agonist efficacy and affinitydsee Section 6.11.6 for derivation.
In addition to the fact that Log(max/EC50) retains
linearity in the relationship between the activity of two
agonists over the complete range of tissue sensitivity, there
are other advantages to the scale. Specifically, it reduces the
power of the agonist to induce response to a single number
and this, in turn, can be used in statistical procedures to
assess similarity and difference. Similarly, the relative activity of agonists (as DLog(max/EC50) values) can be
compared to a reference agonist in any system thereby
canceling the system effects of the sensitivity of the system
in which the measurements are made. Thus, a set of
DLog(max/EC50) values in any one system will serve to
Agonists: the measurement of affinity and efficacy in functional assays Chapter | 6
183
FIGURE 6.42 (A) Effects of changes in receptor density on the concentrationeresponse curves for an agonist. At low receptor densities, partial agonism
is observed; at higher receptor densities, full agonism. With increasing receptor density (i.e., tissue sensitivity), the EC50 values for the agonist diminish
but the changes are much less for the agonist when partial agonism is observed than in systems where full agonism is observed. Panel B shows the changes
in the pEC50 values as a function of receptor density. Note the curvature as the agonism becomes partial indicating a system dependence. In contrast, the
Log(max/EC50) values do not deviate from linearity.
characterize the relative agonism for the agonists
(compared to a chosen standard) for all systems. It will be
seen that such a scale can then be compared between systems to assess selectivity and biased signaling. The application of the DLog(max/EC50) scale to biased signaling,
receptor selectivity, cell signaling selectivity, and the effects of receptor mutation are discussed more extensively in
Chapter 8, The Optimal Design of Pharmacological
Experiments.
6.10 Chapter summary and conclusions
l
l
l
l
l
There are practical advantages to measuring biological
responses in functional experiments and numerous formats are available to do this.
Functional responses can be measured near their cytosolic origin (immediately proximal to the activation of
the biological target), further on down in the stimuluse
response mechanism or as an end organ response.
Amplification occurs as the progression is made from
point of origin to end organ response.
Recombinant assays have revolutionized pharmacology
and now functional systems can be constructed with
engineered levels of responsiveness (i.e., through difference in receptor levels or cotransfection of other
proteins).
One possible complication to consider in functional experiments is the dependence of the response on time. If
fade occurs in the response, time becomes an important
factor in determining the magnitude of response.
The complications of time become much more important in stop-time measurements of response, in which
a time is chosen to measure an amount of product
from a biochemical reaction. Observing linearity in
l
l
l
the production of response with respect to time allows
determination that a steady state has been reached.
The best method of quantifying agonism is through
fitting agonist concentrationeresponse curves to the
BlackeLeff operational model.
The use of selective agonist assays has demonstrated
that many agonists produce biased signals in cells; these
biased effects can be quantified through log(s/KA)
values and yield therapeutic superiority over nonbiased
agonists.
Biased agonists can produce cell-dependent agonist potency ratios in whole tissue experiments.
6.11 Derivations
l
l
l
l
l
l
Relationship between the EC50 and affinity of agonists
(Section 6.11.1).
Method of Barlow, Scott, and Stephenson for affinity of
partial agonists (Section 6.11.2).
Maximal response of a partial agonist is dependent on
efficacy (Section 6.11.3).
System Independence of Full Agonist Potency Ratios
(Section 6.11.4).
Measurement of agonist affinity: method of Furchgott
(Section 6.11.5).
Agonism as a Positive Allosteric Modulation of
Receptor-Signaling Protein Interaction to Derive
DLog(max/EC50) Ratios (Section 6.11.6).
6.11.1 Relationship between the EC50 and
affinity of agonists
In terms of the operational model, the EC50 of a partial
agonist can also be shown to approximate the KA. The
184
A Pharmacology Primer
response to an agonist [A] in terms of the operational model
is given as
Response ¼
Emax $½A$s
;
½Að1 þ sÞ þ KA
(6.23)
where Emax is the maximal response of the system, s is a factor
quantifying the ability of both the agonist (in terms of the
agonist efficacy) and the system to generate response (in terms
of the receptor density [Rt] and the efficiency of stimuluse
response coupling KE, s ¼ [Rt]/KE). For a partial agonist, the
maximal response Max < Emax. Therefore, from Eq. (6.23),
Max ¼
Emax $s
.
1þs
(6.24)
For Max < Emax (partial agonist), Eq. (6.24) shows that
s is not considerably greater than unity. Under these circumstances, it can be approximated that (s þ 1) / 1.
Under these circumstances, the equation for EC50 for a
partial agonist reduces to
EC50 ¼
KA
.
ð1 þ sÞ
(6.25)
(6.26)
where Emax is the maximal response capability of the system,
KA refers to the equilibrium dissociation constant of the
agonistereceptor complex, and sA is the term describing
the ability of the agonist to produce response (efficacy, receptor density, and the stimuluseresponse capability of the
system; see Chapter 3: DrugeReceptor Theory). Similarly,
the response produced by a partial agonist [P] is given by
Responsep ¼
E $½P$s
max p .
½P 1 þ sp þ KP
(6.27)
For equiactive responses, Eqs. (6.26) equals (6.27), and
after simplification
1
1 sa $KP sa sp
¼ $
þ
.
½A ½P sp $KA sp $KA
(6.28)
6.11.3 Maximal response of a partial agonist is
dependent on efficacy
In terms of the operational model, response is given by
ResponseA ¼
Emax $½A$sA
;
½Að1 þ sA Þ þ KA
Emax $s
.
1þs
(6.30)
The relative maxima of two agonists is therefore
Max0 s0 ð1 þ sÞ
.
¼
Max0 sð1 þ s0 Þ
(6.31)
It can be seen that as s; s0 [1 then Max’/Max / 1
(i.e., both are full agonists). However, when the efficacy is
low or when the stimuluseresponse coupling is inefficient
(both conditions of low values for s), then s þ 1 / 1 and
Max’/Max ¼ s0 /s (the relative maxima approximate the
relative efficacy of the agonists).
6.11.4 System independence of full agonist
potency ratios
Response ¼
In terms of the operational model, the response to a full [A]
is given by
Emax $½A$sA
;
½Að1 þ sA Þ þ KA
Max ¼
In terms of the operational model, the response to an
agonist [A] in terms of the operational model is given as
6.11.2 Method of Barlow, Scott, and
Stephenson for affinity of partial agonists
ResponseA ¼
where s is a factor quantifying the ability of both the
agonist (in terms of the agonist efficacy) and the system
(in terms of the receptor density [Rt] and the efficiency of
stimuluseresponse coupling KE, s ¼ [Rt]/KE). The
maximal response to the agonist (i.e., as [A] / N) is
(6.29)
Emax ½As
;
½Að1 þ sÞ þ KA
(6.32)
where Emax is the maximal response of the system, and s is
a factor quantifying the ability of both the agonist (in terms
of the agonist efficacy) and the system (in terms of the receptor density [Rt] and the efficiency of stimuluseresponse
coupling KE, s ¼ [Rt]/KE).
From Eq. (6.31), the EC50 for a full agonist is
EC50 ¼
KA
;
1þs
(6.33)
where KA is the equilibrium dissociation constant of the
agonistereceptor complex. For full agonists, s[1; therefore, the EC50 ¼ KA/s. Substituting s ¼ [Rt]/KE, the potency ratio of two full agonists is
Potency Ratio ¼
EC050
K0 K0
¼ A E.
EC50
KA KE
(6.34)
It can be seen that the potency ratio of two full agonists,
as defined by Eq. (6.34), is composed of factors unique to
the agonists and not the system, assuming that the
stimuluseresponse coupling components of KE, being
common for both agonists, cancel.
6.11.5 Measurement of agonist affinity:
method of Furchgott
In terms of classical receptor theory, equiactive responses
to an agonist are compared in the control situation ([A]) and
after irreversible inactivation of a fraction of the receptors
Agonists: the measurement of affinity and efficacy in functional assays Chapter | 6
([A0 ]). Assume that after alkylation, the remaining receptors
equal a fraction q:
½A
½A0 ¼ 0
$q;
½A þ KA ½A þ KA
(6.35)
where KA is the equilibrium dissociation constant of the
agonistereceptor complex. Rearrangement of Eq. (6.35)
leads to
1
1 1
1 1q
¼
.
$ þ $
½A ½A0 q KA q
These receptor species then interact with the cell stimulus
response mechanisms: [RG] with an equilibrium dissociation constant KE to a signaling species [RGE] and [ARG]
producing response with an equilibrium dissociation constant K0 E to a signaling species [ARGE]. The following
species are defined:
(6.36)
The equilibrium dissociation constant of the agoniste
receptor complex (KA) can be obtained by a regression of
1/[A] upon 1/[A0 ]. This leads to a linear regression from which
KA ¼
Slope 1
.
Intercept
(6.37)
An identical equation results from utilizing the operational model. The counterpart to Eq. (6.35) is
½A$s
½A0 $s0
¼ 0
;
½Að1 þ sÞ þ KA ½A ð1 þ s0 Þ þ KA
(6.38)
where s equals the receptor density divided by the magnitude of the transducer function, which depends on the efficiency of receptor coupling and the efficacy of the agonist:
s ¼ [Rt]/KE. The difference between s and s0 is that s0 represents the system with a depleted (through irreversible receptor inactivation) receptor density, that is,
R0t < ½Rt .
1
1 s ðs=s0 Þ 1
¼ 0$ 0þ
.
½A ½A s
KA
(6.39)
Eq. (6.39) can then be used to obtain the KA from a
regression of 1/[A] upon 1/[A0 ].
6.11.6 Agonism as a positive allosteric
modulation of receptoresignaling protein
interaction to derive DLog(max/EC50) ratios
The functional allosteric model (see Chapter 7: Allosteric
Modulation) yields two receptor species that produce
cellular response, namely, [RG] (the spontaneously formed
complex between receptor and G-protein) and [ARG] (the
same complex but also bound to agonist):
+
αKg
AR →
K′a ↓↑
G
+
R
+
A
←
Kg
→
←
ARG
K′E
→
ARGE
↓↑ α K′a
RG
+
A
½RG ¼
½ARG
a½AK0a
(6.40)
½AR ¼
½ARG
a½GKg
(6.41)
½R ¼
½ARG
a½AK0a ½GKg
(6.42)
The receptor conservation equation [Rtot] ¼ [R] þ
[AR] þ [RG] þ [ARG] can be rewritten using Eqs.
(6.40)e(6.42) as
½Rtot ¼ ½G=KG 1 þ a½A = K0A þ ½A==K0A þ 1 (6.43)
where KG and K0 A are equilibrium dissociation constants
(K0 A ¼ 1/K0 a and KG ¼ 1/Kg). Substituting the term in
Eq. (6.43) for [Rtot] and defining the fraction of receptors
RG as rG and ARG as rAG, respectively, yields
rG ¼
½RG
½G=KG
¼
(6.44)
½Rtot ½G=KG 1 þ a½AK0A ½A=K0A þ 1
rAG ¼
½ARG
a½A=K0A ½G=KG
¼
½Rtot ½G=KG 1 þ a½AK0A þ ½A=K0A þ 1
(6.45)
This leads to
G
185
KE
→
RGE
The receptoresignaling protein complex (either
agonist bound or not) interacting with the signaling protein is processed through the BlackeLeff operational
model [9] as a forcing function to generate a response
from the agonist.
½RG=KE þ ½ARG=K0E Em
Response ¼ (6.46)
½RG=KE þ ½ARG=K0E þ 1
The constitutive active state receptor has a natural efficacy sG for the production of response through coupling
to the signaling protein. Rewriting the efficacy of the
active state receptor as sG ¼ [Rtot]/KE and the efficacy of
the agonist-bound active state receptor as sA ¼ [Rtot]/K0 E
further defines the factor b as the ratio of the efficacy of
the nonagonist-bound receptor (sG) and agonist-bound
receptor. The efficacy of the agonist in terms of the
BlackeLeff operational model (sA) therefore yields the
term b as sA/sG and the operational model equation can be
rewritten:
Response ¼
ðrG sG þ rAG bsG ÞEm
rG sG þ rAG bsG þ 1
(6.47)
186
A Pharmacology Primer
Substituting for rG and rAG from Eqs. (6.45) and (6.46)
yields
0
1
absG ½A
B K0A ½G sG ½GC
B
C
@ K G þ K G AE m
Response ¼
½A
s ½G
þ G
þ1
KG
a½G
K0A 1 þ KG ð1þbs
GÞ
(6.48)
Eq. (6.48) defines a sigmoidal curve for the agonist; the
maximal response for this curve is defined as
absG ½G=KG Em
max ¼
1 þ a½G=KG ð1 þ bsG Þ
(6.49)
The maximal response to the agonist must be expressed
as a fraction of the maximal window of response available
in the assay; therefore, no agonist can produce a maximal
response greater than unity (the maximal response window
for the assay). Similarly, the midpoint sensitivity of effect
(denoted EC50) is given as
EC50 ¼
KA ðsG ½G=KG þ 1Þ
1 þ a½G=KG ð1 þ bsG Þ
(6.50)
Combining Eqs. (6.49) and (6.50) yields
max
absG ½G=KG Em
¼
EC50 K0A ðsG ½G=KG þ 1Þ
(6.51)
The ratio max/EC50 (where max refers to the maximal
response to the agonist and the EC50 refers to the concentration of agonist producing 50% of the agonist maximal
response) results in a system-independent parameter
quantifying agonism when utilized as DLog(max/EC50)
values for two agonists (denoted agonist1 and agonist2):
max
a1 b1
a2 b2
¼ Log 0
DLog
Log 0
(6.52)
EC50 12
KA1
KA2
Eq. (6.52) shows that Log(max/EC50) is a combination
of an assay and tissue term and a strictly agonist term
(specifically ab/K0 A):
max
sG ½G=KG Em
ab
Log
¼ Log
(6.53)
þ Log 0
EC50
KA
sG ½G=KG þ 1
The ratio of max/EC50 values, which subtracts and thus
cancels the two Log((sG[G]/KGEm)/(sG[G]/KG þ1)) terms,
is independent of the assay and tissue effects and becomes a
unique identifier for the two agonists: for agonist1 and
agonist2, the DLog(max/EC50) is DLog(ab/K0 A) which is a
system-independent ratio of agonism. Specifically, the
value ab/K0 A is comprised of only drug parameters (a is the
change in the affinity of the receptor for the signaling
protein produced by the binding of the agonist and reciprocally the affinity of the agonist when the signaling protein
interacts with the receptor), K0 A is the equilibrium dissociation of the receptoreagonist complex when the receptor
does not interact with the signaling protein, and b is the
change in the efficacy of the receptor for production of
response produced by the agonist.
The system independence of DLog(max/EC50) values
can also be derived through the BlackeLeff operational
model. Specifically, from the model for agonism [10]:
½A snA Em
n n
n
½A sA þ ð½A þ KA Þ
n
Response ¼
(6.54)
where sA is the efficacy of the agonist, n is the Hill coefficient of the agonist concentrationeresponse curve, and Em
is the maximal response window of the functional assay. It
should be noted that the K0 A value in Eqs. (6.40)e(6.45) in
terms of the BlackeLeff model is the equilibrium dissociation constant of the agonisteresponse complex for agonism with the receptor interacting with the signaling
protein. Therefore, the KA term is the operational equilibrium dissociation constant of the agonistereceptor complex, i.e., agonist binding to the receptor as it interacts
with the signaling protein. If the agonist is viewed as a
modulator of signaling protein interaction, then the operational KA is equal to a/K0 A. This provides expressions for
the maximal response (max) as [10]
max ¼
snA Em
ð1 þ snA Þ
(6.55)
and for the EC50 for half maximal response as [10]
EC50 ¼ KA
ð2 þ snA Þ1=n 1
This leads to an expression for max/EC50 of
1=n
sn 2 þ snA
1 Em
max
¼ A
EC50
KA ð1 þ snA Þ
(6.56)
(6.57)
For n ¼ 1, max/EC50 ¼ s Em/KA; ratios of (max/EC50)
values cancel the tissue Em term and yield a strictly agonistdependent term s/KA. Therefore, ratios of max/EC50 values
(in the form of DLog(max/EC50) values for systems where
the slope of the agonist concentrationeresponse curves is
not significantly different form unity) yield strictly agonist
dependent (and system-independent) values for relative
agonism:
max
sA
DLog
¼ DLog
(6.58)
EC50
KA
Agonists: the measurement of affinity and efficacy in functional assays Chapter | 6
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Chapter 7
Orthosteric drug antagonism
The author produced a series of interactive quizzes to test your understanding of the contents of this chapter. Click on the
link to access it: https://www.elsevier.com/books-and-journals/book-companion/9780323992893.
One of the features of this subject which hither to has been
regarded as mysterious, is that in a homologous series of
drugs some members may not only fail to produce the action typical of the series but may even antagonize the action
of other members.
Alfred Joseph Clark (1885e1941).
7.1 Introduction
Drugs can actively change physiological function, either
directly (agonists) or indirectly through modification of
physiological stimulus. If the modification is inhibitory,
this is referred to as antagonism. This chapter discusses the
blockade of agonist-induced response through interaction
with receptors. Antagonism can be classified operationally,
in terms of the effects of antagonists on agonist dosee
response curves, and mechanistically, in terms of the molecular effects of the antagonist on the receptor protein. The
interference of an agonist-induced response can take
different forms in terms of its effects on agonist dosee
response curves. Specifically, concentration-dependent
antagonism can be saturable (coming to a maximal limit
of the antagonism, irrespective of the antagonist concentration) or apparently unsaturable (concentration-dependent
increases in antagonism with no limit except those imposed
by the drug solubility or the induction of secondary drug
effects). The antagonism can be surmountable (dextral
displacement of the doseeresponse curve with no diminution of maxima) or insurmountable (depression of the
maximal agonist response). Antagonism of receptors can
produce many patterns of concentrationeresponse curves
for agonists, including concentration-dependent surmountable antagonism (Fig. 7.1A), surmountable antagonism that
comes to a maximal limit (Fig. 7.1B), depression of
doseeresponse curves with no dextral displacement
(Fig. 7.1C), and dextral displacement before depression of
maximal response in systems with a receptor reserve for the
agonist (Fig. 7.1D). These patterns should be recognized as
behaviors of antagonists in different systems and are not
A Pharmacology Primer. https://doi.org/10.1016/B978-0-323-99289-3.00001-4
Copyright © 2022 Elsevier Inc. All rights reserved.
necessarily characteristics of the molecular nature of the
antagonism (i.e., more than one molecular mechanism can
produce the same behavior of the concentrationeresponse
curve). Therefore, it is important to discover the molecular
mechanism of the antagonism and not just describe the
antagonistic behavior, as the latter can change with experimental conditions. For example, kinetic factors can cause
some antagonists to produce surmountable antagonism in
some systems and insurmountable antagonism in others.
In general, there are two basic molecular mechanisms by
which receptor antagonism can take place. One is where the
antagonist blocks access of the agonist to the receptor through
steric hindrance (prevents the agonist binding by interfering
with the agonist’s binding site, referred to as orthosteric
antagonism; see Fig. 7.2A). The other is where the antagonist
binds to its own site on the receptor to induce a change in the
reactivity of that receptor to the agonist through a change in its
conformation of the receptor (referred to as allosteric antagonism; see Fig. 7.2B). This chapter deals with orthosteric
antagonism, whereby the agonist and antagonist compete for
the same binding site on the receptor. For orthosteric antagonism, the interaction between the agonist and antagonist is
competitive and the relative affinity and concentrations of the
agonist and antagonist determine which molecule occupies the
common binding site. Whether this results in surmountable or
insurmountable antagonism depends on the kinetics of the
system. In this regard, it is worth considering kinetics as a
prerequisite to a discussion of orthosteric antagonism.
7.2 Kinetics of drugereceptor
interaction
In experimental pharmacology, the sensitivity of the preparation to the agonist is determined in a separate concentrationcurve analysis, the agonist is then removed by washing, and
then the preparation is equilibrated with antagonist (antagonist
added to the preparation for a given period of time). This latter
step is intended to cause the receptors and antagonist to come
to equilibrium with respect to the numbers of receptors bound
by antagonist for any given concentration of antagonist in a
temporally stable manner (i.e., one which will not change with
189
190
A Pharmacology Primer
FIGURE 7.1 Effects of antagonists on agonist doseeresponse curves. (A) Surmountable antagonism with no diminution of maxima and no limiting
antagonism (competitive antagonists). (B) Surmountable dextral displacement to a limiting value produced by an allosteric modulator. (C) Depression of
doseeresponse curves with no dextral displacement produced by noncompetitive antagonists. (D) Dextral displacement with depression of maximum at
higher concentrations produced by noncompetitive antagonists in systems with a receptor reserve for the agonist.
FIGURE 7.2 Schematic diagram of orthosteric effects (two ligands compete for the same binding domain on the receptor) and allosteric effects (whereby
each ligand has its own binding domain and the interaction takes place through a conformational change of the receptor).
Orthosteric drug antagonism Chapter | 7
time). Under these equilibrium conditions, the fraction of receptor bound by the antagonist is determined by the concentration of antagonist in the receptor compartment and the
equilibrium dissociation constant of the antagonistereceptor
complex (denoted KB). Thus, the receptor occupancy by the
antagonist will resemble the onset curve for binding shown in
Fig. 4.3. This will be referred to as the equilibration phase of
the antagonism (see Fig. 7.3). After it is thought that the receptors and antagonist have come to equilibrium according to
concentration and the KB, an agonist concentrationeresponse
curve is then obtained in the presence of the antagonist. The
resulting change in the location parameter (EC50) and/or
maximal asymptote of the agonist concentrationeresponse
curve is then used to determine the extent of antagonism and,
subsequently, to assess the potency of the antagonist. During
this latter phase of the analysis, it is assumed that during the
course of the determination of the agonist response the system
again comes to equilibrium with the three species now present,
namely, the antagonist, receptors, and the agonist. Therefore,
the dissociation of the prebound antagonist from the receptor
must be sufficiently rapid during the period in which the
response to the agonist is obtained for the agonist to bind to the
correct fraction of receptors according to the concentration of
agonist and the equilibrium dissociation constant of the
agonistereceptor complex. If this does not occur, a true
equilibrium condition will not be attained. This can affect how
the antagonism is expressed in the system. This latter time
period will be referred to as the reequilibration period (see
191
Fig. 7.3). In practice, the rate of offset of antagonists generally
can be much lower than the rate of offset of agonists. Under
these conditions, there may be insufficient time for reequilibration to occur, and the agonist may never occupy as many
receptors as mass action dictates, especially at higher agonist
concentrations where higher receptor occupancy is required.
The kinetic equation for the adjustment of receptor
occupancy (rt) by a preequilibrated concentration of an
antagonist [B] with rate of offset k2 upon addition of a fastacting agonist [A] was derived by Paton and Rang [1] as:
rt ¼
½B=KB
½B=KB þ ½A=KA þ 1
½B=KB
½B=KB
½B=KB þ ½A=KA þ 1 ½B=KB þ 1
(7.1)
ek2 ½ð½B=KB þ½A=KA þ1Þ=ð½A=KA þ1Þt .
It is worth considering the effect of varying rates of
offset (k2) and varying time periods allowed for reequilibration of agonist, antagonist, and receptors (time t). From
Eq. (7.1), the equation for agonist occupancy in the presence of an antagonist for the temporal receptor occupancy
for the antagonist can be rewritten as
rA ¼ ð½AKA = ½A = ðKA þ 1ÞÞ 1 w 1 ek2 Ft
(7.2)
þ rB ek2 Ft ;
where
w ¼ ½B=KB =ð½B = KB þ ½A = KA þ 1Þ
(7.3)
rB ¼ ½B=KB =ð½B = KB þ 1Þ
(7.4)
F ¼ ð½B = KB þ ½A = KA þ 1Þ=ð½A = KA þ 1Þ
FIGURE 7.3 Antagonist potency generally is assessed by determining
the sensitivity of the receptor to agonist and then equilibrating with
antagonist. This first period (termed equilibration period) allows the
antagonist and receptor to come to equilibrium in accordance with mass
action (i.e., according to the concentration of the antagonist and KB). Then,
in the presence of the antagonist, agonist is added and response measured.
During the period allowed for collection of response, the agonist, antagonist, and receptors must all come to a new equilibrium according to the
relative concentrations of each and the KA and KB. This period is referred
to as the reequilibration period.
(7.5)
Eq. (7.2) can be evaluated in a number of temporal
situations. Thus, if there is adequate time for reequilibration
of agonist, antagonist, and receptors, true competition between agonist and antagonist for receptors will result.
Under these circumstances, the equation for agonist occupancy in the presence of antagonist can be evaluated by
setting t [k1
in Eq. (7.2) to yield
2
½A=KA
(7.6)
rA ¼
½A=KA þ ½B=KB þ 1
where [A] and [B] are the agonist and antagonist concentrations, respectively, and KA and KB are the respective
192
A Pharmacology Primer
equilibrium dissociation constants of the drugereceptor
complexes. These are the molar concentrations that bind
to 50% of the receptor population and, as such, quantify
the affinity of the antagonist for the receptor. This is the
equation used to quantify the receptor occupancy by the
agonist (which is proportional to the agonist response)
derived by Gaddum [2] (see Section 7.12.1).
The receptor occupancy curve can be converted to
concentrationeresponse curves by processing occupancy
through the operational model for agonism (see Section
3.6). Under these circumstances, Eq. (7.6) becomes
Response ¼
½A=KA sEmax
½A=KA ð1 þ sÞ þ ½B=KB þ 1
(7.7)
It can be seen from Eq. (7.7) that the antagonism will
always be surmountable (i.e., there will be no concentration
of antagonist that causes depression of the maximal
response to the agonist). This is because as [A]/N,
the fractional maximal response/1 (the control
maximal response in the absence of antagonism is given by
s/(1 þ s)).
The other extreme is to assume that there is no effective
reequilibration of agonist, antagonist, and receptors during
the time allotted for response collection. Thus, the fractional receptor occupancy by the antagonist does not
change when agonist is added. Such conditions can occur
when t k1
(i.e., there is a very short period of time
2
available for measurement of agonist response and/or there
is a very slow offset of antagonist from the receptor). Under
these circumstances, Eq. (7.2) becomes
rA ¼
½A=KA
½A=KA ð1 þ ½B=KB Þ þ ½B=KB þ 1
(7.8)
This is formally identical to the equation derived by
Gaddum et al. [3] (see Section 7.12.2) for noncompetitive
antagonism. In this case, it is assumed that the only available receptor population in the presence of a fractional receptor occupancy rB by a noncompetitive antagonist is the
fraction 1rB. Thus, agonistereceptor occupancy is given
by
rA ¼
½A=KA
ð1 rB Þ
½A=KA þ 1
(7.9)
This equation reduces to Eq. (7.8) upon simplification.
In terms of agonist response, Eq. (7.8) becomes
Response ¼
½A=KA sEmax
½A=KA ð1 þ s þ ½B=KB Þ þ ½B=KB þ 1
(7.10)
The maximal response in the presence of antagonist is
given by (1 þ s)/(1 þ sþ[B]/KB). It can be seen that for
low values of s (low-efficacy agonist and/or low receptor
density or poor receptor coupling) the maximal response to
the agonist will be <1. Thus, the two kinetic extremes yield
and insurmountable
surmountable antagonism t [k1
2
1
antagonism t k2 .
The intervening conditions can yield a mixture of
dextral displacement and moderate depression of the
maximal response. This is a condition described by Paton
and Rang [1] as a “hemiequilibrium” state whereby the
agonist, antagonist, and receptors partially but incompletely
come to equilibrium with one another. The agoniste
receptor occupancy under these conditions (when
tk2 ¼ 0.01 to 1) is given by Eq. (7.2). The response is the
operational metameter of that equation; specifically,
Response ¼
½A=KA ð1 ðwð1 ek2 Ft Þ þ rB ek2 Ft ÞÞsEmax
½A=KA ðð1 ðwð1 ek2 Ft Þ þ rB ek2 Ft ÞÞs þ 1Þ þ 1
(7.11)
It is worth considering each of these kinetic conditions
in detail, as these are behaviors that are all observed
experimentally and can be observed for the same antagonist
under different experimental conditions. A summary of
these various kinetic conditions is shown schematically in
Fig. 7.4.
7.3 Surmountable competitive
antagonism
The first condition to be examined is the case where
t [k1
(i.e., there is sufficient time for true reequili2
bration among agonist, antagonist, and receptors to occur).
Under these conditions, parallel dextral displacement of
agonist concentrationeresponse curves results with no
diminution of maxima (Eq. 7.7). This concentratione
response curve pattern is subjected to analyses that utilize
the magnitude of the displacement to yield an estimate of
the affinity of the antagonist. Historically, the first procedure to rigorously define the quantitative relationship
between such displacement and the concentration of
antagonist was Schild analysis.
7.3.1 Schild analysis
When both the agonist and antagonist compete for a
common binding site, the antagonism is termed competitive. Eq. (7.6) used to quantify the receptor occupancy by
the agonist (which is proportional to the agonist response)
was derived by Gaddum [2] (see Section 7.12.1 for derivation). The major pharmacological tool used to quantify
the affinity of competitive antagonists is Schild analysis.
Utilizing this method, a system-independent estimate of the
affinity of a competitive antagonist can be made in a
functional system. The method can also compare the
pattern of antagonism to that predicted by the simple
competitive model, thereby allowing definition of the
mechanism of action of the antagonist. Schild analysis refers to the use of an equation derived by Arunlakshana and
Orthosteric drug antagonism Chapter | 7
193
FIGURE 7.4 The range of antagonist behaviors observed under different kinetic conditions. When there is sufficient time for complete reequilibration (t
[ k1
2 ), surmountable antagonism is observed (panel furthest to the left). As the time for reequilibration diminishes (relative to the rate of offset of the
antagonist from the receptor; tk1
2 ¼ 0.1 to 0.01), the curves shift according to competitive kinetics (as in the case for surmountable antagonism) but
the maxima of the curves are truncated (middle panel). When there is insufficient time for reequilibration, the antagonist essentially irreversibly
occludes the fraction of receptors it binds to during the equilibration period (t k1
2 ) and depression of the maxima occurs with dextral displacement
determined by the extent of receptor reserve for the agonist (panel to the right).
Schild [4] to construct linear plots designed to graphically
estimate the affinity of simple competitive antagonists. The
Schild equation was derived from the Gaddum equation
(Eq. (7.6), see Section 7.12.3):
LogðDR 1Þ ¼ Log½B LogKB
(7.12)
The method is based on the notion that both the concentration of the antagonist in the receptor compartment and
its affinity determine the antagonism of agonist response.
Since the antagonism can be observed and quantified, and the
concentration of the antagonist is known, the affinity of the
antagonist (in the form of KB) can be calculated.
The antagonism is quantified by measuring the ratio of
equiactive concentrations of agonist measured in the presence of and absence of the antagonist. These are referred to
as dose ratios (DRs). Usually, EC50 concentrations of
agonist (concentration producing 50% maximal response)
are used to calculate DRs. An example calculation of a DR
is shown in Fig. 7.5. Thus, for every concentration of
antagonist [B], there will be a corresponding DR value.
These are plotted as a regression of log(DR1) upon log
[B]. If the antagonism is competitive, there will be a linear
relationship between log(DR1) and log[B] according to
FIGURE 7.5 Calculation of equiactive DRs (DR values) from two
doseeresponse curves. DR, dose ratio.
the Schild equation. Under these circumstances, it can be
seen that a value of zero for the ordinate will give an
intercept of the x-axis where log[B] ¼ log KB. Therefore,
the concentration of antagonist that produces a
log(DR1) ¼ 0 value will be equal to the log KB, the
equilibrium dissociation constant of the antagoniste
194
A Pharmacology Primer
receptor complex. This is a system-independent and molecular quantification of the antagonist affinity that should
be accurate for every cellular system containing the receptor. When the concentration of antagonist in the receptor
compartment is equal to the KB value (the concentration
that binds to 50% of the receptors), then the DR will be 2.
Since KB values are obtained from a logarithmic plot, they
are log normally distributed and are therefore conventionally reported as pKB values. These are the negative logarithm of the KB, which are used much like pEC50 values are
used to quantify agonist potency. The negative logarithm of
this particular concentration is also referred to empirically
as the pA2, the concentration of antagonist which produces
a twofold shift of the agonist doseeresponse curve.
Antagonist potency can be quantified by calculating the
pA2 from a single concentration of antagonist producing a
single value for the DR from the equation
pA2 ¼ LogðDR 1Þ Log½B
(7.13)
It should be noted that this is a single measurement.
Therefore, comparison to the model of competitive antagonism cannot be done. The pA2 serves only as an empirical
measure of potency. Only if a series of DR values for a series
of antagonist concentrations yields a linear Schild regression
with a slope of unity can the pA2 value (obtained from the
intercept of the Schild plot) be considered a molecular
measure of the actual affinity of the antagonist for the receptor (pKB). Therefore, a pKB value is always equal to the
pA2. However, the converse (namely, that the pA2 can always be considered an estimate of the pKB) is not necessarily
true. For this to occur, a range of antagonist concentrations
must be tested and shown to comply with the requirements of
Schild analysis (linear plot with slope equal to unity). A
precept of Schild analysis is that the magnitude of the DR
values must not be dependent on the level of response used to
make the measurement. This occurs if the doseeresponse
curves (control plus those obtained in the presence of
antagonist) are parallel and all have a common maximal
asymptote response (as seen in Fig. 7.5).
There are statistical procedures available to determine
whether the data can be fit to a model of doseeresponse
curves that are parallel with respect to slope and all share a
common maximal response (see Appendix: Statistics and
Experimental Design). In general, doseeresponse data can
be fit to a three-parameter logistic equation of the form:
Response ¼
Emax
a
1 þ 10ðLogEC50 Log ½AÞ
(7.14)
where the concentration of the agonist is [A], Emax refers to
the maximal asymptote response, EC50 is the location
parameter of the curve along the concentration axis, and
n is a fitting parameter defining the slope of the curve. A
variant four-parameter logistic curve can be used if the
baseline of the curves does not begin at zero response
(i.e., if there is a measurable response in the absence of
agonist basal):
Response ¼ Basal þ
Emax Basal
a
1 þ 10ðLogEC50 Log ½AÞ
(7.15)
In practice, a sample of data will be subject to random
variation, and curve fitting with nonlinear models most likely
will produce differences in slope and/or maxima for the
various doseeresponse curves. Therefore, the question to be
answered is, does the sample of data come from a population
that consists of parallel doseeresponse curves with common
maxima? Hypothesis testing can be used to determine this (see
Appendix: Statistics and Experimental Design). Specifically,
a value for the statistic F is calculated by fitting the data to a
complex model (where each curve is fit to its own value of n,
EC50, and Emax) and to a more simple model (where a common
Emax and n values are used for all the curves and the only
differences between them are values of EC50) (see Appendix:
Statistics and Experimental Design for further details). If the F
statistic indicates that a significantly better fit is not obtained
with the complex model (separate parameters for each curve),
then this allows fitting of the complete data set to a pattern of
curves with common maxima and slope. This latter condition
fulfills the theoretical requirements of Schild analysis. An
example of this procedure is shown in the Appendix: Statistics
and Experimental Design, Fig. A.14.
If the data set can be fit to a family of curves of common
slope and maximum asymptote, then the EC50s of each
curve can be used to calculate DR values. Specifically, the
EC50 values for each curve obtained in the presence of
antagonist are divided by the EC50 for the control curve
(obtained in the absence of antagonist). This yields a set of
equiactive DRs. If hypothesis testing indicates that individually fit curves must be used, then a set of EC50 values
must be obtained graphically. A common level of response
(i.e., 50%) is chosen and EC50 values are either calculated
from the equation or determined from the graph. With
slopes of the doseeresponse curves near unity, this
approximation is not likely to produce substantial error in
the calculation of DR values and should still be suitable for
Schild analysis. However, this approach is still an
approximation and fitting to curves of common slope and
maxima is preferred. It should be noted that an inability to
fit the curves to a common maximum and slope indicates a
departure from the assumptions required for assigning
simple competitive antagonism.
The measured DRs are then used to calculate
log(DR1) ordinates for the corresponding abscissal logarithm of the antagonist concentration that produced the
shift in the control curve. A linear equation of the form:
y ¼ mx þ b
(7.16)
Orthosteric drug antagonism Chapter | 7
is used to fit the regression of log(DR1) upon log[B].
Usually, a statistical software tool can furnish an estimate
of the error on the slope.
The model of simple competitive antagonism predicts
that the slope of the Schild regression should be unity.
However, experimental data are samples from the complete
population of infinite DR values for infinite concentrations of
the antagonist. Therefore, random sample variation may
produce a slope that is not unity. Under these circumstances,
a statistical estimation of the 95% confidence limits of the
slope (available in most fitting software) is used to determine
whether the sample data could have come from the population describing simple competitive antagonism (i.e., having
unit slope). If the 95% confidence limits of the experimentally fit slope include unity, then it can be concluded that the
antagonism is of the simple competitive type and that random
variation caused the deviation from unit slope. The regression is then refit to an equation where m ¼ 1 and the abscissal
intercept taken to be the logarithm of the KB. An example of
Schild analysis for the inhibition of muscarinic-receptormediated responses of rat tracheae, to the agonist carbachol
by the antagonist pirenzepine, is shown in Fig. 7.6 [5].
If the slope of the regression is not unity or if the
regression is not linear, then the complete data set cannot be
used to estimate the antagonist potency. Under these circumstances, either the antagonism is not competitive or
some other factor is obscuring the competitive antagonism.
An estimate of the potency of the antagonist can still be
obtained by calculating a pA2 according to Eq. (7.13). This
195
should be done using the lowest positive log(DR1) value.
Hypothesis testing can be used to determine the lowest
statistically different value for DR from the family of
curves (see Fig. A.16).
A schematic diagram of some of the logic used in Schild
analysis is shown in Fig. 7.7. It should be pointed out that a
linear Schild regression with a unit slope is the minimal
requirement for Schild analysis but that it does not necessarily prove that a given inhibition is of the simple
competitive type. For example, in guinea pig tracheae,
relaxant b-adrenoceptors and contractile muscarinic receptors coexist. The former causes the tissue to relax, while
the latter counteracts this relaxation and causes the tissue to
contract. Thus, the b-adrenoceptor agonist isoproterenol, by
actively producing relaxation, will physiologically antagonize contractile responses to the muscarinic agonist carbachol. Fig. 7.8 shows a Schild plot constructed from the
concentration-dependent relaxation of guinea pig trachea of
the contractile doseeresponse curves to carbachol [6]. It
can be seen that the plot is linear with a slope of unity,
apparently in agreement with a mechanism of simple
competitive antagonism. However, these opposing responses occur at totally different cell surface receptors and
the interaction is further down the stimuluseresponse
cascade in the cytoplasm. Thus, the apparent agreement
with the competitive model for these data is spurious (i.e.,
the plot cannot be used as evidence of simple competitive
antagonism). An example of the use of this method is given
in Section 13.2.4.
FIGURE 7.6 Schild regression for pirenzepine antagonism of rat tracheal responses to carbachol. (A) Doseeresponse curves to carbachol in the absence
(open circles, n ¼ 20) and presence of pirenzepine 300 nM (filled squares, n ¼ 4), 1 mM (open diamonds, n ¼ 4), 3 mM (filled inverted triangles, n ¼ 6),
and 10 mM (open triangles, n ¼ 6). Data fit to functions of constant maximum and slope. (B) Schild plot for antagonism shown in panel (A). Ordinates:
log(DR1) values. Abscissae: logarithms of molar concentrations of pirenzepine. Dotted line shows best line linear plot. Slope ¼ 1.1 þ 0.2; 95%
confidence limits ¼ 0.9e1.15. Solid line is the best fit line with linear slope. pKB ¼ 6.92. DR, dose ratio. Redrawn from T.P. Kenakin, C. Boselli,
Pharmacologic discrimination between receptor heterogeneity and allosteric interaction: resultant analysis of gallamine and pirenzepine antagonism of
muscarinic responses in rat trachea, J. Pharmacol. Exp. Ther. 250 (1989) 944e952.
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A Pharmacology Primer
FIGURE 7.7 Schematic diagram of some of the logic used in Schild analysis.
FIGURE 7.8 Apparent simple competitive antagonism of carbachol-induced contraction of guinea pig trachea through physiological antagonism of
tracheal contractile mechanisms by b-adrenoceptor relaxation of the muscle. (A) Schematic diagram of the physiological interaction of the muscarinicreceptor-induced contraction and b-adrenoceptor-induced relaxation of tracheal tissue. (B) Schild regression for isoproterenol (b-adrenoceptor agonist)
antagonism of carbachol-induced contraction. The regression is linear with unit slope (slope ¼ 1.02 þ 0.02) apparently but erroneously indicative of
simple competitive antagonism. Redrawn from T.P. Kenakin, The Schild regression in the process of receptor classification, Can. J. Physiol. Pharmacol.
60 (1982) 249e265.
Orthosteric drug antagonism Chapter | 7
7.3.2 Patterns of DoseeResponse curves that
preclude schild analysis
There are patterns of doseeresponse curves that preclude
Schild analysis. The model of simple competitive antagonism predicts parallel shifts of agonist doseeresponse
curves with no diminution of maxima. If this is not
observed, it could be because the antagonism is not of the
competitive type, or because some other factor is obscuring
the competitive nature of the antagonism. The shapes of
doseeresponse curves can prevent measurement of
response-independent DRs. For example, Fig. 7.9A shows
antagonism in which there is a clear departure from parallelism, and in fact a distinct decrease in slope of the curve
for the agonist in the presence of the antagonist is observed.
This is indicative of noncompetitive antagonism. Irrespective of the mechanism, this pattern of curves prevents
estimation of response-independent DR values and thus
Schild analysis would be inappropriate for this system.
Fig. 7.9B shows a pattern of curves with depressed
197
maximal responses but shifts that are near parallel in nature.
This is a pattern indicative of hemiequilibrium conditions
whereby the agonist and antagonist do not have sufficient
time (due to the response collection window) to come to
temporal equilibrium. If this could be determined, then
Schild analysis can estimate antagonist potency from values
of response below where depression of responses occurs
(i.e., EC30). The differentiation of hemiequilibria from
noncompetitive blockade is discussed in Section 7.5.
The pattern shown in Fig. 7.9C is one of parallel shift of
the doseeresponse curves up to a maximal shift. Further
increases in antagonist concentration do not produce further
shifts of the doseeresponse curves beyond a limiting value.
This is suggestive of an allosteric modification of the agonist’s affinity by the antagonist, and other models can be
used to estimate antagonist affinity under these conditions.
This is discussed further in Chapter 8, Allosteric Modulation. Finally, if the agonist has secondary properties that
affect the response characteristics of the system (i.e., toxic
effects at high concentrations), then dextral displacement of
FIGURE 7.9 Patterns of doseeresponse curves produced by antagonists that may preclude Schild analysis. (A) Depression of maximal response with
nonparallelism indicative of noncompetitive blockade. DR values are not response independent. (B) Depressed maxima with apparent parallel
displacement indicative of hemiequilibrium conditions (vide infra). (C) Loss of concentration dependence of antagonism as a maximal shift is attained
with increasing concentrations of antagonist indicative of saturable allosteric blockade. (D) Depressed maximal responses at high concentration of agonist
where the antagonist shifts the agonist response range into this region of depression (indicative of toxic or nonspecific effects of agonist at high concentrations). DR, dose ratio.
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A Pharmacology Primer
the doseeresponse curve into these regions of agonist
concentration may affect the observed antagonism.
Fig. 7.9D shows depression of the maximal response at
high agonist concentrations. This pattern may preclude full
Schild analysis but a pA2 may be estimated.
7.3.3 Best practice for the use of schild
analysis
There are two ways to make Schild analysis more effective.
The first is to obtain log(DR1) values as near to zero as
possible (i.e., use concentrations of the antagonist that
produce a low level of antagonism, such as a twofold to
fivefold shift in the control doseeresponse curve). This will
ensure that the real data are in close proximity to the most
important parameter sought by the analysis, namely, the
abscissal intercept (pKB or pA2 value). If log(DR1)
values are greater than 1.0, then the pKB (or pA2) will need
to be extrapolated from the regression. Under these circumstances, any secondary effects of the antagonist that
influence the slope of the Schild regression will subsequently affect the estimate of antagonist potency. Second,
at least a 30-fold (and preferably 100-fold) concentration
range of antagonist (concentrations that produce an effect
on the control doseeresponse curve) should be utilized.
This will yield a statistically firm estimate of the slope of
the regression. If the concentration range is below this, then
the linear fit of the log(DR1) versus log[B] will produce
large 95% confidence limits for the slope. While unity most
likely will reside within this broad range, the fit will be
much less useful as an indicator of whether or not unity
actually is a correct slope for the antagonist. That unity is
included could simply reflect the fact that the confidence
range is so large.
There are Schild regressions that deviate from ideal
behavior but can still be useful either to quantify antagonist
potency or to indicate the mechanism of antagonism. For
example, Fig. 7.10A shows a linear Schild regression at low
antagonist concentrations that departs from ideal behavior
(increased slope) at higher antagonist concentrations. This is
frequently encountered experimentally as secondary effects
from higher concentrations of either the agonist or the
antagonist come into play, leading to toxicity or other
depressant effects on the system. The linear portion of the
FIGURE 7.10 Some commonly encountered patterns of Schild regressions. (A) Initial linearity with increased slope at higher concentration indicative of
toxic effects of either the agonist or antagonist at higher concentrations. (B) Region of decreased slope with reestablishment of linearity often observed for
saturation of uptake or other adsorption effects. (C) Hyperbolic loss of antagonism indicative of saturable allosteric antagonism.
Orthosteric drug antagonism Chapter | 7
regressions at lower antagonist concentrations can still be
used for estimation of the pKB (if a large enough concentration range of antagonist is used) or for the pA2 (if not).
Fig. 7.10B shows a pattern of antagonism often
observed in isolated tissue studies but not so often in cellbased assays. Saturation of uptake systems for the agonist
or saturation of an adsorption site for the agonist can account for this effect. The linear portion of the regression
can be used to estimate the pKB or the pA2. If there is a loss
of concentration dependence of antagonism, as seen in
Fig. 7.10C, this indicates a possible allosteric mechanism
whereby a saturation of binding to an allosteric site is
operative. This is dealt with further in Chapter 7, Allosteric
Modulation.
One of the strengths of Schild analysis is the capability
of unveiling nonequilibrium conditions in experimental
preparations, such as inadequate time of equilibration or
removal of drugs from the receptor compartment. Fig. 7.11
shows a range of possible experimentally observed but
problematic linear Schild regressions that could be
encountered for competitive antagonists.
7.3.4 Analyses for inverse agonists in
constitutively active receptor systems
In constitutively active receptor systems (where the baseline is elevated due to spontaneous formation of receptor
199
active states; see Chapter 3: DrugeReceptor Theory for full
discussion), unless the antagonist has identical affinities for
the inactive receptor state, the spontaneously formed active
state, and the spontaneously G-protein-coupled state (three
different receptor conformations; see discussion in Chapter
1, What Is Pharmacology? on receptor conformation), it
will alter the relative concentrations of these species; in so
doing it will alter the baseline response. If the antagonist
has higher affinity for the receptor active state, it will be a
partial agonist in an efficiently coupled receptor system.
This is discussed in the next section. If the antagonist has
higher affinity for the inactive receptor, then it will
demonstrate simple competitive antagonism in a quiescent
system and inverse agonism in a constitutively active
system.
The doseeresponse curves reflecting inverse agonism
do not conform to the strict requirements of Schild analysis
(i.e., parallel shift of the doseeresponse curves with no
diminution of maxima). In the case of inverse agonists in a
constitutively active receptor system, the dextral displacement of the agonist concentrationeresponse curve is
accompanied by a depression of the elevated basal response
(due to constitutive activity) (see Fig. 7.12A). This figure
shows the nonparallel nature of the curves as the constitutively elevated baseline is reduced by the inverse agonist
activity. In quiescent receptor systems (nonconstitutively
active), both competitive antagonists and inverse agonists
FIGURE 7.11 Some examples
of
commonly encountered Schild data and
some suggestions as to how antagonism
should be quantified for these systems.
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A Pharmacology Primer
FIGURE 7.12 Schild analysis for constitutively active receptor systems. (A) Competitive antagonism by the inverse agonist in a constitutively active
receptor system with DR values calculated at the EC80. (B) Competitive antagonism by the same inverse agonist in a nonconstitutively active receptor
system. (C) Direct effects of an inverse agonist in systems of differing levels of constitutive activity. Open circles show midpoints of the
concentrationeresponse curves. (D) Schild regression for an inverse agonist in a nonconstitutive assay where the inverse agonist produces no change in
baseline (solid line) and in a constitutively active assay where depression of elevated baseline is observed (dotted line). A small shift to the left of the
Schild regression is observed, leading to a slight overestimation of inverse agonist potency. DR, dose ratio.
produce parallel shifts to the right of the agonist dosee
response curves (see Fig. 7.12B).
The effects of high values of constitutive activity can be
determined for functional systems where function is defined
by the operational model. Thus, it can be assumed in a
simplified system that the receptor exists in an active (R*)
and inactive (R) form and that agonists stabilize (and
therefore enrich the prevalence of) the active form, while
inverse agonists prefer the inactive form. It also is assumed
that response emanates from the active form of the receptor.
Under these circumstances, the fractional response in a
functional system can be derived from the expression
defining the amount of active state receptor coupled to Gprotein. This yields the following expression for response
with a Hill coefficient of unity (see Section 7.12.4):
Response ¼
where s is the efficacy of the full agonist, n is a fitting
parameter for the slope of the agonist concentratione
response curve, KA and KB are the respective equilibrium
dissociation constants of the full agonist and inverse
agonist for the inactive state of the receptor, a and b are the
relative ratios of the affinity of the full and inverse agonist
for the active state of the receptor, and L is the allosteric
constant for the receptor (L ¼ [R*]/[R]).
There are two ways to estimate the potency of an inverse agonist from the system described by Eq. (7.17). The
first is to observe the concentration of inverse agonist that
reduces the level of constitutive activity by 50%, the IC50
of the compound as an active inverse agonist. This is done
by observing the level of constitutive response in the
aL½A=KA s þ bL½B=KB s þ Ls
½A=KA ð1 þ aLð1 þ sÞÞ þ ½B=KB ð1 þ bLð1 þ sÞÞ þ Lðs þ 1Þ þ 1
(7.17)
Orthosteric drug antagonism Chapter | 7
absence of full agonist ([A] ¼ 0) with a variant of Eq.
(7.17):
Constitutive Response ¼
bL½B=KB s þ Ls
½B=KB ð1 þ bLð1 þ sÞÞ þ Lðs þ 1Þ þ 1
(7.18)
Fig. 7.12C shows the effect of increasing levels of
constitutive activity on the midpoint of a curve to an inverse agonist. This shows that with increasing levels of
inverse agonismdeither through increasing intrinsic
constitutive activity (increased L) or increasing levels of
receptor and/or efficiency of receptor coupling (increasing
s)dthe IC50 of the inverse agonist will increasingly be
larger than the true KB. This is important to note, since it
predicts that the value of the pIC50 for an inverse agonist
will be system dependent and can vary from cell type to cell
type (just as does observed potency for positive agonists).
However, in the case of inverse agonists, the effects of
increasing receptor density and/or receptor coupling are
opposite to those observed for positive agonists where increases cause a concomitant increase in observed potency.
This trend in the observed potency of inverse agonism on
system conditions (L and s) can be seen from the midpoint
of the curve defined by Eq. (7.18). This is the IC50 for an
inverse agonist inhibition of constitutive activity:
Observed IC50 ¼
KB ðLðs þ 1Þ þ 1Þ
ðbLð1 þ sÞ þ 1Þ
(7.19)
Eq. (7.19) predicts increasing IC50 with increases in
either L or s. In systems with low-efficacy inverse agonists,
or in systems with low levels of constitutive activity, the
observed location parameter is still a close estimate of the
KB (equilibrium dissociation constant of the ligande
receptor complex, a molecular quantity that transcends test
system type). In general, the observed potency of inverse
agonists defines only the lower limit of affinity.
As observed in Fig. 7.12A, inverse agonists produce
dextral displacement of concentrationeresponse curves to
full agonists and thus produce DRs that may be used in
Schild analysis. It is worth considering the use of DRs from
such curves and the error in the calculated pKB and pA2
produced by the negative efficacy of the inverse agonist and
changes in basal response levels. It can be shown that the
pA2 value for an inverse agonist in a constitutively active
receptor system is given by (see Section 7.12.5)
½Aða 1Þ
pA2 ¼ pKB Log
(7.20)
½Aða 1Þ þ ð1 bÞ
This expression predicts that the modifying term will
always be <1 for an inverse agonist (b < 1). Therefore, the
calculation of the affinity of an inverse agonist from dextral
displacement data (pA2 measurement) will always overestimate the potency of the inverse agonist. However, since
b < 1 and the a value for a full agonist will be » 1, the error
201
most likely will be very small. Fig. 7.12D shows the effect
of utilizing dextral displacements for an inverse agonist in a
constitutively active system. The Schild regression is linear
but is phase-shifted to the right in accordance with the
slight overestimation of inverse agonist potency.
7.3.5 Analyses for partial agonists
Schematically, response is produced by the full agonist
([AR]) complexdwhich interacts with the stimuluse
response system with equilibrium association constant
Kedand the partial agonist (lower efficacy), which interacts with an equilibrium association constant K0 e.
Therefore, there are two efficacies for the agonism: one
for the full agonist (denoted s) and one for the partial
agonist (denoted s0 ). In terms of the operational model for
functional response, this leads to the following expression
for response to a full agonist [A] in the presence of a partial
agonist [B] (see Section 7.12.6):
Response ¼
½A=KA s þ ½B=KB s0
(7.21)
½A=KA ð1 þ sÞ þ ½B=KB ð1 þ s0 Þ þ 1
If the partial agonism is sufficiently low so as to allow a
full agonist to produce further response, then a pattern of
curves of elevated baseline (due to the partial agonism)
shifted to the right of the control curve (due to the antagonist properties of the partial agonist) will be obtained (see
Fig. 7.13A). However, low-efficacy agonists can be complete antagonists in poorly coupled receptor systems and
partial agonists in systems of higher receptor density and/or
coupling efficiency (Fig. 7.13B).
The observed EC50 for partial agonism can be a good
estimate for the affinity (KB). However, in systems of high
receptor density and/or efficient receptor coupling where the
responses approach full agonism, the observed EC50 will
overestimate the true potency of the partial agonist. This can
be seen from the location parameter of the partial agonist in
Eq. (7.22) in the absence of full agonist ([A] ¼ 0):
Observed EC50 ¼
½B=KB
ð1 þ s0 Þ
(7.22)
Fig. 7.13C shows the effect of increasing receptor
density and/or efficiency of receptor coupling on the
magnitude of the EC50 of the partial agonist. Equiactive
DRs still can be estimated from the agonist-dependent region of the doseeresponse curves. For example, Fig. 7.13A
shows DR values obtained as ratios of the EC75. The
resulting Schild regression slightly underestimates the KB
(see Fig. 7.13D). However, the error will be minimal.
Underestimation of the true pKB is also predicted by the
operational model (Section 7.12.7):
s pA2 ¼ pKB Log
(7.23)
ðs s0 Þ
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A Pharmacology Primer
FIGURE 7.13 Schild analysis for a partial agonist. (A) Competitive antagonism by a partial agonist. DR values calculated at EC75 for agonist response.
(B) Schild regressions for antagonism of same receptor in a low receptor-density/coupling-efficiency receptor where no partial agonism is observed. (C)
Doseeresponse curve for directly observed partial agonism. Under some conditions, the EC50 for the partial agonist closely approximates the KB. (D)
Schild regression for a partial agonist in a low receptor/coupling assay where the partial agonist produces no observed response (solid line) and in a high
receptor/coupling assay where agonism is observed (dotted line). A small shift to the right of the Schild regression is observed, leading to a slight underestimation of partial agonist potency. DR, dose ratio.
It can be seen that the modifying term will always be
>1 but will also have a relatively low magnitude (especially for low values of partial agonist efficacy s0 ). Also, in
systems where the partial agonist does not produce a
response (t0 /0), then pA2 ¼ pKB as required by simple
competitive antagonism (as shown in Fig. 7.13B). The use
of DRs for partial agonists where the partial agonist produces a response will always slightly underestimate affinity
by the Schild method (or calculation of the pA2). The
Schild regression for a partial agonist reflects this, in that it
is still linear but slightly shifted to the right of the true
regression for simple competitive antagonism (Fig. 7.13D).
Another method for measuring the affinity of a partial
agonist has been presented by Stephenson [7] and modified
by Kaumann and Marano [8]. The method of Stephenson
compares equiactive concentrations of full agonist in the
absence and the presence of a concentration of partial
agonist to estimate the affinity of the partial agonist. The
following equation is used (see Section 7.12.8):
½A ¼
sp =sa $ð½P=KP Þ$KA
½A0 þ
1 þ ð1 ðsP =sa ÞÞ$ð½P=KP Þ 1 þ ð1 ðsP =sa ÞÞ$ð½P=KP Þ
(7.24)
A regression of [A] upon [A0 ] yields a straight line. The
Kp can be estimated by
½Pslope
sp
$ 1
Kp ¼
(7.25)
1 slope
sa
Orthosteric drug antagonism Chapter | 7
A full example of the use of this method is given in
Section 13.2.5. A more rigorous version of this method has
been presented by Kaumann and Marano [8]. In this method,
the slopes from a range of equiactive agonist concentration
plots are utilized in another regression (see Section 7.12.8):
1
1 ¼ Log½P Log Kp
Log
(7.26)
slope
where m is the slope for a particular regression of equiactive concentrations of an agonist in the absence and presence of a particular concentration of partial agonist [P].
An example of the use of this method for the measurement
of the partial agonist chloropractolol is shown in Fig. 7.14.
The various plots of equiactive concentrations [insets to
panels (A)e(D)] furnish a series of values of m for a series
of concentrations of chloropractolol [9]. These are used in a
regression according to Eq. (7.26) (see Fig. 7.14) to yield
an estimate of the KP for chloropractolol from the intercept
of the regression. Further detail on the use of this method is
given in Section 13.2.5.
203
7.3.6 The method of Lew and Angus: nonlinear
regression analysis
One shortcoming of Schild analysis is an overemphasized
use of the control doseeresponse curve (i.e., the accuracy
of every DR value depends on the accuracy of the control
EC50 value). An alternative method utilizes nonlinear
regression of the Gaddum equation (with visualization of
the data with a Clark plot [10], named for A. J. Clark). This
method, unlike Schild analysis, does not emphasize control
pEC50, thereby giving a more balanced estimate of antagonist affinity. This method, first described by Lew and
Angus [11], is robust and theoretically more sound than
Schild analysis. On the other hand, it is not as visual. Schild
analysis is rapid and intuitive and can be used to detect
nonequilibrium steady states in the system which can
corrupt estimates of pKB. Also, nonlinear regression requires matrix algebra to estimate the error of the pKB.
While error estimates are given with many commercially
available software packages for curve fitting, they are
FIGURE 7.14 Method of Stephenson [7] and Kaumann and Marano [8] used to measure the affinity of the partial b-adrenoceptor agonist chloropractolol
in rat atria. Panels (A)e(D) show responses to isoproterenol in the absence (filled circles) and presence of chloropractolol (open circles). Curves shown in
the presence of 10 nM [panel (A)], 100 nM [panel (B)], 1 mM [panel (C)], and 10 mM [panel (D)] chloropractolol. Note elevated basal responses in
response to the partial agonist chloropractolol. Insets to panels (A)e(D) show plots of equiactive concentrations of isoproterenol in the absence (ordinates)
and presence of chloropractolol according to Eq. (6.24). Slopes from these graphs used for plot shown in panel (E) according to the method of Kaumann
and Marano [8] (see Eq. 7.26). This plot is linear with a slope of 0.95, yielding a KP estimate of 16.5 nM. Data redrawn from T.P. Kenakin, J.W. Black,
The pharmacological classification of practolol and choropractolol, Mol. Pharmacol. 14 (1978) 607e623.
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A Pharmacology Primer
difficult to obtain without these (from first principles). In
contrast, Schild analysis furnishes an estimate of the error
for the pKB from the linear regression using all of the data.
If an estimate of the error is required and the means to
calculate it are not available in the curve fitting software,
manual calculation with Schild analysis is a viable alternative. In general, the method of Lew and Angus still holds
definite advantages for the measurement of competitive
antagonist potency. One approach to rigorously describe
competitive antagonism is to use Schild analysis to visualize the data and the method of Lew and Angus to estimate
the pKB.
To apply this method, the pEC50 values of the control
and shifted doseeresponse curves and the corresponding
concentrations of antagonist [B] values associated with
those pEC50s are used to construct a Clark plot [10] according to the equation
pEC50 ¼ Log ½B þ 10pKB Logc
(7.27)
where pKB and c are fitting constants. Note that the control
pEC50 is used with [B] ¼ 0. The relationship between the
pEC50 and increments of antagonist concentration can be
shown in a Clark plot of pEC50 versus Log([B]þ
10pKB). Constructing such a plot is useful because
although it is not used in any calculation of the pKB, it allows visualization of the data to ensure that the plot is linear
and has a slope of unity.
Although the Clark plot can be used to visualize the
slope relationship between pEC50 and Log([B]þ10pKB),
deviation of the slope from unity is better obtained by
refitting the data to a “power departure” version of Eq.
(7.27):
pEC50 ¼ Log ½Bm þ 10pKB Logc
(7.28)
where m is allowed to vary as part of the nonlinear fit. A
value of F is calculated for comparison of the fits to Eqs.
(7.27) and (7.28), respectively. If the value of F is not significant, then there is no reason to use the power departure
equation and the antagonism can be considered to be simple
competitive. To test for significant deviation from linearity
of the Clark plot (indicating a departure from simple
competitive antagonism at some concentration used in the
experiment), the data are fit to a “quadratic departure”
version of Eq. (7.27):
pEC50 ¼ Log ½B 1 þ n½B10pKB þ 10pKB Logc
(7.29)
where n is allowed to vary with the nonlinear fitting procedure. As with the analysis for slope, a value for F is calculated. If the quadratic departure is not statistically
supported, then the regression can be considered linear.
The method of Lew and Angus uses nonlinear curve
fitting procedures to estimate the pKB. An estimate of the
error calculated with Eq. (7.27) is provided by the estimate
of the fitting error. This is obtained from most commercially fitting programs (or can be calculated with matrix
algebra). An example of this type of analysis is shown in
Fig. 7.15A. The pEC50 values for the doseeresponse
curves and the concentrations of antagonist were fitted to
the equation shown in the panel in Fig. 7.15B to yield the
Clark plot shown in panel B. The resulting pKB value is
8.09 þ 0.145. The data were then refit to the power departure version of the equation, to yield the Clark plot
shown in panel C. The calculated F for comparison of the
simple model (slope ¼ unity) to the more complex model
(slope fit independently) yielded a value for F that is not
greater than that required for 95% confidence of difference.
Therefore, the slope can be considered not significantly
different from unity. Finally, the data were again refit to the
quadratic departure version of the equation, to yield the
Clark plot shown in panel D to test for nonlinearity. The
resulting F indicates that the plot is not significantly
nonlinear.
7.4 Noncompetitive antagonism
From an examination of Eq. (7.1), and noted in Fig. 7.4, if
the rate of offset of the orthosteric antagonist is slow, to the
point that a correct reequilibration cannot occur between
the agonist, antagonist, and receptors during the period of
response collection in the presence of antagonist, then
essentially a pseudoirreversible blockade of receptors will
occur. Thus, when t k1
2 in Eq. (7.1), the agonist will not
access antagonist-bound receptors and a noncompetitive
antagonism will result. This is the opposite extreme of the
case for simple competitive antagonism discussed in Section 7.3.
The term competitive antagonism connotes an obvious
mechanism of action (i.e., two drugs compete for the same
binding site on the receptor to achieve the effect). Similarly,
the term noncompetitive indicates that two drugs bind to the
receptor, and that these interactions are mutually exclusive
(i.e., when one drug occupies the binding site then another
cannot exert its influence on the receptor). However, this
should not necessarily be related to binding loci on the
receptor. Two drugs may interact noncompetitively but still
require occupancy of the same receptor binding site.
Alternatively, the sites may be separate as in allosteric effects (chapter 8).
In an operational sense, noncompetitive antagonism is
defined as the case where the antagonist binds to the receptor and makes it functionally inoperative. This can occur
through preclusion of agonist binding or through some
other biochemical mechanism that obviates agonist effect
on the receptor and thereby blocks response due to agonist.
Under these circumstances, no amount of increase in the
Orthosteric drug antagonism Chapter | 7
205
FIGURE 7.15 Example of application of method of Lew and Angus [10]. (A) Doseeresponse data. (B) Clark plot according to Eq. (7.27) shown. (C)
Data refit to “power departure” version of Eq. (7.27) to detect slopes different from unity (Eq. 7.28). (D) Data refit to “quadratic departure” version of Eq.
(7.27) to detect deviation from linearity (Eq. 7.29).
agonist concentration can reverse the effect of a noncompetitive antagonist. A distinctive feature of noncompetitive
antagonists is the effect they may have on the maximal
agonist response. In situations where 100% of the receptors
need be occupied to achieve the maximal response to the
agonist (i.e., partial agonists), any amount of noncompetitive antagonism will lead to a diminution of the maximal
response. However, in systems where there is a receptor
reserve, there will not be a depression of the maximal
response until such a point where there is sufficient
antagonism to block a fraction of receptor larger than that
required to achieve maximal response. As discussed in
Chapter 2, How Different Tissues Process Drug Response,
the magnitude of the receptor reserve is both system
dependent (dependent on receptor number and the efficiency of stimuluseresponse coupling) and agonist
dependent (intrinsic efficacy). Therefore, noncompetitive
antagonists will have differing capabilities to depress the
maximal response to the same agonist in different systems.
The same will be true for different agonists in the same
system.
The equation describing agonistereceptor occupancy
under conditions of noncompetitive antagonism is given by
Eq. (7.8). The effect of antagonist on the maximal
agonistereceptor occupancy (i.e., as [A]/N) and comparison to the control maximal stimulus from Eq. (7.8) is
Maximal agonist occupancy ¼
1
1 þ ½B=KB
(7.30)
It can be seen that at nonzero values of [B]/KB the
maximal agonistereceptor occupancy will be depressed.
However, as discussed in Chapter 2, How Different Tissues
Process Drug Response, some high-efficacy agonists and/or
some highly coupled receptor systems (high receptor density) yield maximal tissue response by activation of only a
fraction of the receptor population (“spare receptors”).
Thus, a noncompetitive antagonist may preclude binding of
the agonist to all the receptors, but this may or may not
result in a depression of the maximal response to the
agonist. To discuss this further requires conversion of the
agonistereceptor occupancy curve (Eq. 7.8) into tissue
response through the operational model:
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A Pharmacology Primer
Whereby the antagonist precludes agonist activation
and response is produced through interaction of the [AR]
complex with the tissue stimuluseresponse cascade
through the constant KE according to the operational
model. Under these circumstances, the response to an
agonist obtained in the presence of a noncompetitive
antagonist is given by
Response ¼
½A=KA sEmax
½A=KA ð1 þ s þ ½B=KB Þ þ ½B=KB þ 1
(7.31)
Now it can be seen that the maximal response (as a
fraction of the control maximal response) to the agonist (as
[A]/N) is given by
Maximal Response ¼
ð1 þ sÞ
ð1 þ s þ ½B=KB Þ
(7.32)
Here it can be seen that for very efficacious agonists, or
in systems of high receptor density or very efficient receptor coupling (all leading to high values of s), the
maximal response to the agonist may not be depressed in
the presence of the noncompetitive antagonist. Fig. 7.16A
shows the effect of a noncompetitive antagonist on the
receptor response to an agonist in a system with no receptor
reserve (s ¼ 1) is n. It can be seen that the maximal
response to the agonist is depressed at all nonzero values of
[B]/KB. In Fig. 7.16B, the same antagonist is used to block
responses to a highly efficacious agonist in a system with
high receptor reserve (s ¼ 100). From these simulations, it
can be seen that observation of insurmountable antagonism
is not necessarily a prerequisite for a noncompetitive receptor mechanism.
In terms of measuring the potency of insurmountable
antagonists, the data can be fitted to an explicit model. As
shown in Fig. 7.17A, responses to an agonist in the absence
and presence of various concentrations of an insurmountable antagonist are fitted to Eq. (7.31) (Fig. 7.17B) and an
estimate of the KB for the antagonist is obtained. One
shortcoming of this approach is the complexity of the
model itself. It will be seen in the next chapter that allosteric models of receptor antagonism can also yield patterns
of agonist concentrationeresponse curves like those shown
in Fig. 7.17 and that these can be fit equally well to allosteric models. Thus, model fitting can be ambiguous if the
molecular mechanism of the antagonism is not known
beforehand.
Historically, Gaddum et al. [3] devised a method to
measure the affinity of insurmountable antagonists based
on a double reciprocal linear transformation. With this
method, equiactive concentrations of agonist in the absence
([A]) and presence ([A0 ]) of a noncompetitive antagonist
([B]) are compared in a double reciprocal plot describing a
straight line (see Section 7.12.9):
1=½A ¼ 1=ð½A0 ð½B = KB Þ þ 1Þ þ ½B=ðKB KA Þ
(7.33)
According to Eq. (7.33), a regression of values for 1/[A]
upon 1/[A0 ] should give a straight line. The equilibrium
FIGURE 7.16 Effects of a slow offset orthosteric antagonist that essentially does not reequilibrate with agonist and receptors upon addition of agonist to
the system (pseudoirreversible receptor blockade). (A) In this system, a low value of s is operative (i.e., the efficacy of the agonist is low) if there is a low
receptor density and/or poor coupling of receptors. Under these circumstances, little to no dextral displacement is observed for the concentrationeresponse
curves upon antagonism (insurmountable blockade). (B) If the s value is high (high efficacy, high receptor density, highly efficient receptor coupling, high
receptor reserve), then the same antagonist may produce dextral displacement of the concentrationeresponse curves with no depression of maximal
response until relatively large portions of the receptor population are blocked.
Orthosteric drug antagonism Chapter | 7
207
FIGURE 7.17 Fitting of data to models. (A) Concentrationeresponse curves obtained to an agonist in the absence (circles) and presence of an antagonist
at concentrations 3 (triangles) and 30 mM (diamonds). (B) Data fit to model for insurmountable orthosteric antagonism [Eq. 7.31] with Emax ¼ 1,
KA ¼ 1 mM, s ¼ 30, and KB ¼ 1 mM.
dissociation constant of the antagonistereceptor complex is
given by
½B
KB ¼
slope 1
(7.34)
At the time that this method was developed, linear
regression was a major advantage (in lieu of the general
accessibility of nonlinear fitting). However, linearization of
data is known to distort errors and weighting and to
emphasize certain regions of the data set and generally is
not recommended. This is especially true of double reciprocal plots such as that defined by Eq. (7.33). This shortcoming can be somewhat alleviated by a metameter such as
½A0 ½B
½B
¼ ½A0 þ1
þ
½A
KB KA ðKB Þ
(7.35)
where a regression of [A0 ]/[A] upon [A0 ] yields a straight
line, with KB being equal to
KB ¼
½B
intercept 1
(7.36)
Fig. 7.18 shows the procedure for using this method. In
terms of the practical application, an important point to note
is that the maximal response to the agonist must be
depressed by the noncompetitive antagonist for this method
FIGURE 7.18 Measurement of the affinity of a noncompetitive antagonist by the method of Gaddum [Eq. 7.33]. (A) Doseeresponse curves for an
agonist without noncompetitive antagonist present and in the presence of a concentration of antagonist of 1 mM. Dots and connecting lines show
equiactive responses in the absence and presence of the noncompetitive antagonist. (B) Double reciprocal plot of equiactive concentrations of agonist in
the presence (abscissae) and absence (ordinates) of noncompetitive antagonist. Plot is linear with a slope of 32.1. Method of Gaddum [3] indicates that the
equilibrium dissociation constant of the antagonistereceptor complex is [B]/(Slope 1) ¼ 1 mM/(31.2e1) ¼ 33 nM.
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A Pharmacology Primer
to be effective. In fact, the greater the degree of maximal
response inhibition, the more robust is the fit according to
Eq. (7.33). Moreover, data points at the concentrations of
agonist yielding the higher responses (near the depressed
maximal response in the presence of the antagonist) provide more robust fits with this method. An example of the
use of this method is given in Section 13.2.6.
In cases where there is a substantial receptor reserve
such that there is a measurable dextral displacement of the
concentrationeresponse curves, then another reliable
method for determining the affinity of the noncompetitive
antagonist is to measure the pA2 (Log of the molar
concentration that produces a twofold shift to the right of
the agonist concentrationeresponse curve). It can be shown
that for purely noncompetitive antagonists, the pA2 is
related to the pKB with the relation (see Section 7.12.10)
pKB ¼ pA2 Logð1 þ 2½A = KA Þ
(7.37)
Eq. (7.37) predicts that the pA2 is an accurate estimate
of the pKB at low levels of agonistereceptor occupancy
([A]/KA/0). For high values of agonistereceptor occupancy, the observed pA2 will overestimate the true affinity
of the antagonist. However, for low levels of response
(where DRs for insurmountable antagonists likely will be
measured) and for high-efficacy agonists, [A]/KA EC50
for responsedand under these circumstances the pA2 will
be an accurate estimate of the pKB. The use of dextral
displacement to measure the affinity of noncompetitive
antagonists is illustrated in Fig. 7.19. An example of the use
of this technique is given in Section 13.2.7.
FIGURE 7.19 Use of the dextral displacement produced by an insurmountable antagonist to estimate dose ratios and subsequent pA2 values.
Response according to model for orthosteric noncompetitive blockade [Eq.
7.31 with Emax ¼ 1, s ¼ 3, KA ¼ 0.3 mM, KB ¼ 1 mM] for 1 and 3 mM
antagonist. Dose ratios measured at response ¼ 0.24 for 1 mM antagonist
and response ¼ 0.15 for 3 mM antagonist. Resulting pA2 values are close
estimates of the true pKB (6.0) as modified by the [A]/KA term [see Eq.
7.37].
7.5 Agonisteantagonist hemiequilibria
All models of antagonism assume that sufficient time is
allowed for equilibrium to be established among the receptors, the agonist, and the antagonist. For experiments
carried out in real time, the approach to steady-state
response for an agonist in the presence of a preequilibrated concentration of antagonist can be observed and the
conditions of the experiment can be adjusted accordingly to
make measurements at equilibrium. As discussed for
binding experiments, the time required to achieve equilibrium with an agonist in the presence of an antagonist may
be much longer than the time required for only the agonist
if the rate of offset of the antagonist is much slower than
that of the agonist. Unlike binding experiments, where the
tracer ligand and displacing ligand are added together to
start the reaction, functional experiments are usually done
in a mode whereby the agonist doseeresponse curve is
obtained in the presence of the antagonist in a preparation
where the antagonist has been preequilibrated with the
tissue. This preequilibration period is designed to be sufficient to ensure that equilibrium has been attained between
the receptors and the antagonist. Under these conditions,
as the agonist is added the receptors must reequilibrate with
the added agonist and the antagonist already bound to the
receptor population. Given sufficient time, this occurs according to the Gaddum equation, but the time may be
longer than if the agonist were equilibrating with an empty
receptor population. This is because the agonist can bind
only when the antagonist dissociates from the receptor. If
this is a slow process, then it may take a great deal of time,
relative to an empty receptor population, for enough
antagonist to dissociate for attainment of equilibrium receptor occupancy by the agonist.
As discussed in Section 7.2, the kinetic equation for the
adjustment of receptor occupancy (rt) by a preequilibrated
concentration of a slow-acting antagonist [B] with rate of
offset k2 upon addition of a fast-acting agonist [A] is given
by Eq. (7.1) [1]. As considered in Section 7.3, if there is
sufficient time for reequilibration among agonist, antagonist, and receptors, then simple competitive surmountable
antagonism results. Similarly, as further described in Section 7.4, if there is no reequilibration (due to insufficient
time and/or a very slow offset of the antagonist), then
noncompetitive insurmountable antagonism results. Between these two kinetic extremes are conditions where the
agonist, antagonist, and receptors can partially reequilibrate. These conditions were described by Paton and Rang
[1] as hemiequilibria. The shortfall with respect to reequilibration occurs at the high end of the agonistereceptor
occupancy scale. Fig. 7.20A shows the time course for the
production of a response by a high concentration of agonist
in a hemiequilibrium system with a slow offset antagonist.
It can be seen from this figure that with the parameters
Orthosteric drug antagonism Chapter | 7
209
FIGURE 7.20 Increasing times for measurement of response for a slow-acting orthosteric antagonist (k2 ¼ 1/ms) for [B]/KB ¼ 3. (A) shows the kinetics
of response production by a concentration of the agonist producing maximal response ([A]/KA ¼ 100). It can be seen that a rapid initial increase in
response (due to occupation of unoccupied receptors) is followed by a slower phase where the agonist and antagonist reequilibrate with the receptor
population. If only 2 min are allowed for measurement of response, a severely depressed concentrationeresponse curve results. (B) With increasing
equilibration times, the maxima increase until at 40 min simple competition with no depression of the maximal response is observed.
chosen (k2 ¼ 103/s, [B]/KB ¼ 3, [A]/KA ¼ 100), a true
maximal response is not attained until data are collected
over a period of 55 min. Therefore, if the period for
response collection is <55 min, a truncated response will
be measured. This will not be nearly as prevalent at lower
agonistereceptor occupancies. The result of such highlevel response truncation is a shifted concentratione
response curve with depressed maximal responses (as
shown in Fig. 7.20B). It can be seen that if sufficient time is
allowed, the insurmountable antagonism becomes
surmountable.
A characteristic of hemiequilibria is the observation of a
depressed plateau of maximal responses. Thus, while a
truly insurmountable antagonist will eventually depress the
concentrationeresponse curves to basal levels, hemiequilibrium conditions can produce partial but not complete
inhibition of the agonist maximal response. This is shown
in Fig. 7.21.
Practical problems with hemiequilibria can be avoided
by allowing sufficient time for equilibrium to occur.
However, there are some situations where this may not be
possible. One is where the functional system desensitizes
during the span of time required for equilibrium to be
attained. Another is where the actual type of response being
measured is transitory; one example is the measurement of
calcium transients where a spike of effect is the only
response observed in the experimental system.
Hemiequilibria can be exacerbated in slow diffusion
systems. In systems composed of cells in culture, there is
little formal architecture (such as might be encountered in a
whole tissue) that would hinder free diffusion. Such
obstruction could intensify the effects of a removal process
such as adsorption of drug to the side of the culture well.
However, there is a possible effect of the thin unstirred
water layer coating the surface of the cell monolayer. Free
diffusion is known to be slower in unstirred, versus stirred,
bodies of water. In isolated tissues where organ baths are
oxygenated vigorously, the effects of unstirred layers can
be minimized. However, in 96- and 384-well formats for
FIGURE 7.21 Hemiequilibrium among antagonist, agonist, and receptors. Hemiequilibrium condition according to Eq. (7.11) resulting in a
depressed maximal response to the agonist that reaches a plateau
(k2 ¼ 5 105/s, s ¼ 10, t ¼ 90 min). Antagonist concentrations of
0 ¼ control curve farthest to the left; [B]/KB ¼ 1, 3, 10, 30, and 100, with
dotted lines showing what would be expected from purely noncompetitive
behavior of the same antagonist (no reequilibration). Pure surmountable
blockade would be observed for response times of 200 s.
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A Pharmacology Primer
cells in culture, such stirring is not possible. In these cases,
unstirred layers, for some ligands where there is an avid
adsorption mechanism capable of removing the ligand from
the receptor compartment, may be a factor causing an
exaggeration of the apparent loss of drug potency due to
adsorption. Reduced diffusion due to unstirred layers also
may play a role in the observed magnitude of agonist
response in systems where hemiequilibria could be a factor.
In these cases, there could be a practical problem in classifying competitive receptor antagonism erroneously as
noncompetitive antagonism (where maximal responses also
are depressed).
7.6 Resultant analysis
Schild analysis, like all pharmacological tools, is necessarily predicated on the idea that the drugs involved have
one and only one pharmacological activity. This often may
not be the case and selectivity is only a function of concentration. If the concentrations used in the assay are below
those that have secondary effects, then the tool will furnish
the parameter of interest with no obfuscation. However, if
secondary effects are operative in the concentration range
required to measure antagonism, then the resulting parameter may be tainted by this secondary activity. One
approach to nullify these effects for simple competitive
antagonists is through the use of resultant analysis.
Derived by Black and colleagues [12], this procedure
essentially allows calculation of the potency of a test
antagonist through measurement of the added effects this
test antagonist has on another antagonist (referred to as the
reference antagonist). The idea is that the initial response is
obtained in the presence of the test antagonist and then
again in the presence of both antagonists. The secondary
effects of the test antagonist will be operative in both the
initial and subsequent doseeresponse curves. Therefore,
under null conditions these effects will cancel. This allows
the antagonist portion of the test antagonist activity to be
observed as an added component to the antagonism of a
known concentration of a known reference antagonist. The
principle of additive DRs [1] then can be used to isolate the
receptor antagonism due to the test antagonist.
In practice, a series of Schild regressions is obtained for
the reference antagonist in the absence and presence of a
range of concentrations of the test antagonist. The dextral
displacements, along the antagonist concentration axis of
these regressions, are utilized as ordinates for a resultant
plot in the form of ratios of Log(DR1) values for the
different Schild plots. These are designated k. The k values
are related to the concentrations of the test antagonist by the
equation (see Section 7.12.11):
Logðk 1Þ ¼ Log
½Btest LogKBtest
(7.38)
An example of the procedure is shown in Fig. 7.22.
Specifically, a series of Schild analyses were done for the
reference antagonist scopolamine in the presence of
different concentrations of the test antagonist atropine. The
resultant plot according to Eq. (7.38) yields an estimate of
the KB for atropine as the intercept (Log(k1) ¼ 0). If
atropine had secondary effects on the system, this procedure would cancel them and allow measurement of the receptor antagonism. An example of this procedure is given
in Section 13.2.8.
7.7 Antagonism in vivo
In vivo systems usually have endogenous levels of agonism
due to physiologically relevant levels of hormones and/or
neurotransmitters. Under these conditions, antagonist
response will be seen as a depression of ambient response
as the antagonist is absorbed and enters the receptor
compartment followed by a waning effect as the antagonist
is cleared out of the receptor compartment. The previous
discussions of orthosteric antagonism describe two distinct
patterns of antagonism of agonist effect: competitive
characterized as parallel displacement to the right of DR
curves with no depression in maximal response and
noncompetitive characterized by dextral displacement
concomitant with depression of maximal response. While
these are distinct patterns in vitro they more or less yield the
same profile in vivo (see Fig. 7.23A). It is interesting to
note that both competitive and noncompetitive antagonists
produce nearly identical patterns in vivo suggesting that the
in vitro profile of antagonists may have little therapeutic
relevance e see Fig. 7.23B and C. However, while this is
true from a mechanistic viewpoint, it should be noted that
orthosteric noncompetitive antagonism is often related to a
slow offset rate from the receptor and if this is the case,
then the in vivo effects of a noncompetitive antagonist will
be considerably different from a fast offset competitive
antagonist. Kinetically, a slow offset noncompetitive
antagonist will demonstrate better target coverage in vivo.
Therapeutically, antagonists are used in vivo to block
inappropriate signaling but differences in antagonist effects
can occur when antagonists interact with in vivo physiological systems in real time. These differences arise from
the interaction of:
1. Agonists with efficacy (either positive as in partial agonism or negative as inverse agonism) interact with complex multi-organ physiological systems where a range
of tissue sensitivities and setpoints of basal activity.
2. Antagonists only produce blockade when bound to the
target and in vivo concentration is never constant; therefore the persistence of binding determines target coverage.
It is worth considering these effects separately.
FIGURE 7.22 Pharmacological, resultant analysis of atropine. Panels (A)e(D): doseeresponse curves to carbachol in the absence (filled circles) and presence
of various concentrations of the reference antagonist scopolamine. (A) Scopolamine ¼ 1 (open diamonds), 3 (filled triangles), 10 (open inverted triangles), and
30 nM (filled squares). (B) As for A, except experiment carried out in the presence of 3 nM atropine. Concentration of scopolamine ¼ 3, 10, 30, and 100 nM.
Dotted line shows control curve to carbachol in the absence of atropine. (C) As for B, except atropine ¼ 10 nM and scopolamine 10, 30, 100, and 300 nM. (D) As
for C, except atropine ¼ 30 nM. (E) Schild regression for scopolamine in the absence (filled circles) and presence of atropine 3 (open circles), 10 (filled triangles),
and 30 nM (open inverted triangles). (F) Resultant plot for atropine according to Eq. (7.38). Log(f1) values (see text, vs. log[atropine]). Data redrawn from T.P.
Kenakin, C. Boselli, Pharmacologic discrimination between receptor heterogeneity and allosteric interaction: resultant analysis of gallamine and pirenzepine
antagonism of muscarinic responses in rat trachea, J. Pharmacol. Exp. Ther. 250 (1989) 944e952.
FIGURE 7.23 In vivo translation of antagonism. Panel A shows DR curves to the
endogenous agonist in vitro and the effects of a
competitive and noncompetitive antagonist.
Within the physiological range of response to
the endogenous agonist, the effects of both
types of antagonist are identical with differences appearing only at the higher doses of
agonist. Panel to the right shows the effect on
endogenous response by antagonism. The
in vivo effect of a range of doses of a
competitive (panel B) and noncompetitive
(panel C) antagonist.
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A Pharmacology Primer
7.7.1 Antagonists with efficacy in vivo
Antagonists with positive efficacy can produce positive
partial agonism the magnitude of which will depend on the
sensitivity of the tissue (see Fig. 6.23). However, in vivo,
such an antagonist must also deal with any ambient positive
agonism of the organism. For example, animals under
various types of anesthesia will have varying levels of heart
rate depending on the endogenous level of catecholamines
present. Thus, the anesthetic urethane produces a high
resting heart rate while chloralose pentobarbital produces a
lower resting heart rate (lower level of ambient catecholamines). b-Blockers with varying levels of positive efficacy
produce a range of effects under these conditions as shown
in Fig. 7.24. Specifically, three b-blockers with varying
levels of positive efficacy (pirbuterol > prenalterol > pindolol) produce either a positive in vivo response
(agonism) to a depression of basal response. This range is
produced by the interplay of the magnitude of the positive
efficacy of the b-blocker, the sensitivity of the tissue, and
the ambient setpoint of the physiological system.
Efficacy is the result of the stabilization of a receptor
conformation and this can be made manifest in physiological systems in many forms. For example, there are
antagonists that actively internalize receptors to reduce the
cell surface receptor density. The natural MC4R antagonist
AgRP has been shown to actively internalize MC4R e see
Fig. 7.25Adand this would be predicted to produce an
inverse-agonist-like effect in vivo as any constitutively
active receptor activity would be negated by receptor
internalizationdsee Fig. 7.25B.
Antagonist efficacy can be hidden by concurrent effects
masking each other and this can be differentiated through
real-time kinetics. Specifically, if a record of drug interaction can be collected in real time, then the dimension of
time can unveil multiple processes that otherwise would not
be evident in stop time experimental mode. For example,
ambenonium is an antimuscarinic receptor blocker that
antagonizes responses to acetylcholine. However, it also is
an inhibitor of acetylcholinesterase, which metabolizes
acetylcholine as it diffuses toward the receptor and this can
increase responses to acetylcholine by allowing more of the
agonist to reach the receptor. Therefore, a cancellation of
effects can occur: increased response due to the blockade of
acetylcholine destruction and decreased response due to
receptor blockade. If a tissue is equilibrated with ambenonium at certain concentrations, these effects cancel and it
appears that ambenonium does nothing to acetylcholine
responses. However, if the addition of ambenonium is
observed in real time, the fact that the two processes of
enzyme inhibition and receptor blockade have different
rates of onset enables observation of the two events; this is
illustrated in Fig. 7.26 [13]. The dimension of time reveals
and dissociates the two processes.
FIGURE 7.24 Heart rate in anesthetized cats to b-blocker/partial agonists. Chloralose pentobarbital anesthesia produced low heart rates (A: 105 bpm, B:
120 bpm, C: 132 bpm) and urethane anesthesia produced high heart rates (A: 186 bpm, B: 224 bpm, C: 169 bpm). The combination of resting catecholamine levels and the intrinsic efficacy of the b-blockers resulted in a range of effects from increased to decreased heart rates. From TP Kenakin, (1986)
Tissue and receptor selectivity: similarities and differences. Advances in Drug Research Vol. 15, ed. by B. Testa, pp. 71e109, Academic Press, Inc.,
London.
Orthosteric drug antagonism Chapter | 7
213
FIGURE 7.25 Receptor internalization by an inverse agonist. (A) The active internalization of MC4R by the agonist a-MSH and the antagonist AgRP.
(B) Effects of a standard antagonist and inverse agonist o n observed effect of a system with and without constitutive activity. Redrawn from A. Breit, K
Wolff, H Kalwa, H Jarry, T Büch, T Gudermann (2006) The natural inverse agonist Agouti-related protein induces arrestin-mediated endocytosis of
melanocortin-3 and -4 receptors. J. Biol. Chem. 281, 3,7447e37,456.
FIGURE 7.26 Dual opposite effects of an antagonist revealed
through real-time kinetics. Acetylcholine is normally metabolized by
acetylcholinesterase in tracheal tissue thus reducing the response to
this agonist when added exogenously. The blockade of acetylcholinesterase by neostigmine increases
the concentration of the agonist at
the receptor and thus increases the
response [panel (A)]. The antagonist
ambenonium blocks receptors (to
reduce response) and acetylcholinesterase (to increase response);
1 mM ambenonium has little effect
of response when observed at equilibrium [panel (B)]. However, the
two processes are revealed when the
response is viewed in real time as a
biphasic increase and decreased
response. This is shown with a
higher concentration of ambenonium [panel (C)d10 mM]. Data
redrawn from T.P Kenakin, D.
Beek, Self-cancellation of drug
properties as a mode of organ
selectivity: the antimuscarinic effects of ambenonium, J. Pharmacol.
Exp. Therap. 232 (1985) 732e740.
214
A Pharmacology Primer
7.7.2 Kinetics of target coverage
Antagonists block response in vivo only when they are
associated with the target; therefore diffusion in, to, and
from the receptor compartment is important. Persistent association of drugs with the target can be an advantage for
drugs with restricted pharmacokinetics. Real-time in vivo
concentration of the drug is given by
Ct ¼
ka F Dose Kt
e eka t
Vðka KÞ
(7.39)
where ka is the rate of absorption, K the rate of elimination,
V the volume of distribution, and F the bioavailability (for
an oral drug). It can be seen from Eq. (7.39) that a high rate
of clearance can lead to low in vivo concentrations of drug
in the receptor compartment. In addition to dissociation rate
from the target, the restricted diffusion in receptor compartments in vivo also can lead to differences in target
coverage. Fig. 7.27A shows the plasma concentration of
the antipsychotic drug risperidone and the dopamine D2 receptor occupancy in the brain as measured by positron
emission tomography as a function of time [14]. The
dissimulation between central compartment drug concentration and brain receptor occupancy can be seen, i.e., the
plasma concentration falls at an approximately sixfold
greater rate than does receptor occupancy. Yet another
outcome of restricted diffusion is the propensity of drugs
to rebind to targets after they have dissociated when the
exit route for diffusion away from the target is restricted
[15]. Fig. 7.27B shows how receptor rebinding can greatly
reduce the removal of antagonism in vivo.
While diffusion is important in vivo, the kinetics of the
actual rate of drug dissociation from the target can be a
more important determinant of the quality of therapeutic
drug action in vivo since the pharmacokinetics loads the
receptor compartment and then the association (k1) and
dissociation (k2) rates of the molecule to and from the receptor determine reversal of drug effect. It is relevant to
note that the determination of antagonist potency is carried
out in a closed system (equilibrium mass action kinetics,
where the drugs and targets are equilibrated and concentrations are kept constant). However, these antagonists are
then used in open systems where the concentration is variable and dependent on time (see Fig. 7.28).
The open nature of in vivo systems (drug concentration
is never constant) makes time an important variable in
therapeutic drug activity. Thus, an antagonist is therapeutically useful only when bound to the receptor and this, in
turn, will be dependent upon its dissociation rate from the
protein surface. Under these circumstances, two antagonists
could have identical affinities but still be different in terms
of their rate of dissociation from the target and thus give
very different target coverage valuesdsee Fig. 7.29. This
illustrates how potency is only part of the required profile;
for adequate target coverage (where the target is blocked by
the antagonist for a therapeutically useful length of time),
FIGURE 7.27 In vivo target coverage. (A) Time dependence of the receptor occupancy for the antipsychotic drug risperidone in the human brain
through Positron Emission Tomography (PET) imaging (open circles, solid line) compared to the plasma levels of the drug in the central compartment
(filled circles, dotted line). (B) Receptor rebinding of an antagonist in a restricted diffusion compartment. With no restricted diffusion, the off-rate is rapid
(open diamonds). With restricted diffusion, receptor rebinding occurs slowing the off-rate (filled circles). A higher receptor density exacerbates this effect
(open circles). (A). Redrawn from A Takano, T Suhara, Y Ikoma, F Yasuno, J Maeda, T Ichimiya et al. (2004) Estimation of the time-course of dopamine
D2 receptor occupancy in living human brain from plasma pharmacokinetics of antipsychotics. Int J Neuropsychopharmacol 7: 19e26. (B). Redrawn
from G Vauquelin, SJ Charlton (2010) Long-lasting target binding and rebinding as mechanisms to prolong in vivo drug action. Br. J Pharmacol. 161:
488e508.
Orthosteric drug antagonism Chapter | 7
FIGURE 7.28 Concentration of an antagonist when tested in an in vitro
test system (red curve) versus how it is used therapeutically (in vivo open
system; blue curve). While the concentration is constant in the in vitro
system, it is not so in an in vivo system. In the latter, the rate of receptor
offset (k2) becomes important in determining how well the antagonist
blocks the target. The rate of receptor onset is k1.
215
the binding of the antagonist must be persistent (i.e., of
slow offset) to maximize target coverage in the face of
variable pharmacokinetics. For example, two hypothetical
antagonists A and B are equiactive (KB ¼ 10 nM) but one
has a rate of offset of 0.007/s M and rate of onset of
7 105/s (KB ¼ 0.002/s M/7 105/s ¼ 109 M) and the
other has a rate of offset of 0.002/s M and rate of onset of
2 105/s (KB ¼ 0.002/s M/2 105/s ¼ 109 M);
see
Fig. 7.29. At equilibrium, a concentration of 3 nM gives the
same target coverage in a closed system (receptor occupancy of 75%). However, when the system is open and the
concentration in the media surrounding the target goes to
zero, then the target coverage is given by the amount of
antagonist bound to the receptor, and this, in turn, is given
by the first-order rate of offset of the antagonist from the
receptor, which is given by
rt ¼ re ekt ;
(7.40)
FIGURE 7.29 Integrated offset curves for antagonists as a measure of target coverage. The antagonist in red has a rate of offset 3.5 times greater than the
antagonist in blue. Red and blue lines represent receptor occupancy, with time, for six concentrations of antagonist corresponding to [B]/KB values of 0.01,
0.03, 1, 3, 10, and 30 (KB ¼ 100 nM). Integrated values of antagonist occupancy from time t ¼ 0 to 5t1/2 show a much higher degree of receptor
occupancy for the blue antagonist (top right panel).
216
A Pharmacology Primer
where rt and re are the fractional receptor occupancies at
time t and equilibrium (time zero), respectively, and k is
the rate of offset. A measure of target coverage can be
gained from the area under the curve of the offset curves
(as with pharmacokinetics; see Chapter 11), and this can
be estimated from the integral of Eq. (7.40) over a given
time period. One estimate for this is the time from zero
(antagonist in the bathing medium at the maximal concentration) and five times the half time for offset:
Z t¼5$t1=2
re 1 eðk$5$0:695Þ=k
re ekt
kt
¼
re e ¼
k
k
t¼0
0:97re
(7.41)
¼
k
where t1/2 ¼ 0.693/k. Fig. 7.29 shows the target coverage
for these two antagonists as calculated by Eq. (7.41) for a
range of concentrations. It can be seen that, for any given
concentration, the coverage by the slower offset antagonist
is considerably higher than for the faster offset
antagonist and that this effect increases with increasing
antagonist concentration. In light of this effect, it would
be useful to measure the rate of offset of candidate antagonists in the final stages of a discovery program to detect differences that may be relevant therapeutically.
where [A] is the concentration of agonist; KA and KB are
the equilibrium dissociation constants of the agonist and
antagonistereceptor complexes, respectively; n is a fitting
coefficient; and s is the efficacy term for the operational
model. The experimental preparation is then washed free
of antagonist for a period of time. During this process,
the preparation is challenged with a concentration of
agonist which produces approximately a 40%e80%
maximal response. In the example shown in Fig. 7.30A,
the assay is challenged repeatedly with 100 nM agonist
periodically over a period of 180 min (while washing
with antagonist-free media). The responses to the single
agonist challenges are then used to fit complete
concentrationeresponse curves, according to the original
model used to fit the data, with the original parameters
for the curve but with different values of [B]/KB (see
Fig. 7.30B). The values of [B]/KB that are used to fit the
agonist data then are used to calculate a receptor occupancy
value according to mass action (see table in Fig. 7.30C):
rt ¼
rt ¼ ekt
To fully define antagonist profiles in vivo it is important to
quantify the dissociation rate of an antagonist from the
receptor. This can be done in an in vitro functional assay by
obtaining an equilibrium submaximal level of receptor
blockade, fitting the obtained curve with the appropriate
model, and then measuring the response to the agonist over
a period of antagonist-free wash. The single values of
response during the offset period are fitted to the antagonist
model used to fit the equilibrium data and the virtual
antagonist concentration is calculated. These virtual
antagonist concentrations are then converted to receptor
occupancies, and the resulting relationship of receptor occupancy with time is fitted to a first-order rate of decay to
yield the rate of offset of the antagonist from the receptor.
Thus, a concentrationeresponse curve for the agonist is
obtained in the absence and presence of a defined concentration of antagonist. The ideal concentration for use in
this procedure is one that does not completely obliterate the
response but rather produces a receptor system that still
yields a concentrationeresponse curve to the agonist. The
control and antagonist-treated curves are fit to an appropriate model of antagonism (see Chapter 9: The Optimal
Design of Pharmacological Experiments); as an example,
Fig. 7.30 shows insurmountable antagonism fit to the
model for orthosteric noncompetitive antagonism:
½A sn
½A sn þ ð½Að1 þ ½B=KB Þ þ KA ½B=KB þ KA Þn
(7.42)
n
n
(7.43)
The values of rt (ordinate as ln(rt) values) are plotted as
a function of time (abscissae) according to a first-order
model of offset:
7.7.3 Kinetics of dissociation
Response ¼
½B=KB
1 þ ½B=KB
(7.44)
As a natural logarithmic metameter,
Lnðrt Þ ¼ kt
(7.45)
The slope of the resulting linear regression (see
Fig. 7.30D) is an estimate of the negative value of the rate
constant for receptor offset. For the example shown in
Fig. 7.30 (insurmountable blockade), k ¼ 0.003/min. This
procedure can be used for any pattern of blockade. For
example, surmountable (apparently competitive) blockade
can be fit to the model:
½A sn
n
þ ð½A þ KA ð1 þ ½B=KB ÞÞ
n
Response ¼
n
½A sn
(7.46)
The same process then can be applied (see Fig. 7.31).
The therapeutic setting for drug use is in vivo and as such,
the variable of concentration is always changing with drug
absorption and subsequent clearance. This makes the rate at
which a molecule dissociates from the target important in
terms of target coverage, i.e., little effect with a potent
antagonist will be seen in vivo if it rapidly dissociates from
the receptor and is cleared from the body. Thus, the rate of
offset of a molecule is a property separate from potency that
is relevant to the therapeutic value of an antagonist. A
measure of antagonist potency and target coverage (rate of
dissociation from the receptor) can be obtained under
certain circumstances using a coaddition format (agonist
and antagonist added simultaneously to the assay) if responses are sustained and if they can be observed in real
Orthosteric drug antagonism Chapter | 7
217
FIGURE 7.30 Measurement of offset rate for a noncompetitive antagonist. (A) Doseeresponse curves shown for control (no antagonist) and in the
presence of a submaximal concentration of noncompetitive antagonist. The response to an EC80 concentration of agonist (blue circle) is measured at
various wash times. (B) Doseeresponse curves fit to a model of noncompetitive blockade consistent with the potency of the antagonist (pKB) and the
position and shape of the control and blocked doseeresponse curves. (C) The fit doseeresponse curves yield virtual values of [B]/KB as the antagonist is
washed off the receptor. These [B]/KB values are converted to receptor occupancies through the mass action equation. (D) A plot of ln r receptor occupancy versus time is used to calculate a rate of offset (slope of the straight line).
time [16,17]; this protocol was discussed previously in
terms of binding in Chapter 4, Pharmacological Assay
Formats: Binding, in the discussion on antagonist equilibration times (Section 4.4.2). The responses to a range of
concentrations of a fast-acting agonist are observed in real
time with a slower acting antagonist added simultaneously;
under these circumstances, the receptor occupancy for the
full agonist (rA), having a rate of onset and offset of k1 and
k2, respectively, added simultaneously with an antagonist
having on and off rates of k3 and k4, respectively, is
calculated by Eq. (4.27) [18]. The receptor occupancy rA is
then converted to the term [A]/KA through the mass action
relationship [A]/KA ¼ rA/(1rA). The response to the
agonist in the presence of the antagonist is then calculated
with the equation for competitive antagonism (Eq. 7.7).
Fig. 7.32A shows the responses to a range of agonist
concentrations measured in real time when the agonist is
added simultaneously with a slower onset antagonist at a
concentration of 30 KB. It can be seen that a two phase
response is observed as the faster onset agonist produces an
initial rapid agonism that is subsequently blocked by the
slower onset antagonist. The relative rates of increase and
decrease of agonism are dependent upon the rate constants
k1, k2, k3, and k4; therefore, the complete set of data can be
fit with Eq. (4.27) at the various concentrations of agonist
to obtain unique values for these four rate constants. In the
simulation shown in Fig. 7.32B, the data fits to a system
where the rate constants for the agonist are k1 ¼ 106 M/s
and k2 ¼ 0.1/s, and the rate constants for the antagonist are
k3 ¼ 106 M/s and k4 ¼ 0.003/s. This provides two separate
218
A Pharmacology Primer
FIGURE 7.31 Measurement of offset rate for a competitive (surmountable) antagonist. (A) Doseeresponse curves shown for control (no antagonist) and
in the presence of a submaximal concentration of noncompetitive antagonist. The response to an EC80 concentration of agonist (blue circle) is measured at
various wash times. (B) Doseeresponse curves fit the model for simple competitive orthosteric antagonism or allosteric surmountable antagonism model;
virtual values of [B]/KB used to fit the appropriate location of the shifted curves with time. (C) The fit doseeresponse curves yield virtual values of [B]/KB
as the antagonist is washed off the receptor. These [B]/KB values are converted to receptor occupancies through the mass action equation. (D) A plot of ln
r receptor occupancy versus time is used to calculate a rate of offset (slope of the straight line).
FIGURE 7.32 Simultaneous determination of antagonist potency and rate of offset through real-time analysis of agonist/antagonist coaddition. (A)
Responses to a fast-acting agonist added with a 30KB concentration of slower onset antagonist to reveal a complex pattern of increased followed by
decreased response. (B) Fitting Eq. (4.27) to determine rA followed by transformation to response through [A]/KA ¼ rA/(1rA) and the BlackeLeff
operational model [Eq. 7.7] fits the patterns with the kinetic constants shown on the graph. Procedure for rA published in Refs. [14,15].
Orthosteric drug antagonism Chapter | 7
and valuable pieces of information about the antagonist: the
potency (through KB ¼ k4/k3 ¼ 3 nM) and rate of offset
(k4) which can be used to gauge receptor target coverage
in vivo.
7.7.4 Estimating antagonist dissociation with
hemiequilibria
Hemiequilibria can be used in certain cases to estimate the
rate of dissociation of antagonists. As shown in Fig. 7.20, if
there is an insufficient time available to measure response
to an agonist in the presence of an antagonist, then the
maximal response to the agonist is depressed. In fact, it can
be shown that the degree of depression of the maximal
response is inversely proportional to the dissociation rate of
the antagonist and the magnitude of the window in time
available to observe response. This latter factor can be a
feature of a given functional assay (i.e., calcium transient
response using Fluorescence Imaging Plate Reader format);
therefore, the measurement in such a system can lead to a
useful estimation of antagonist dissociation rate. This latter
factor is a very important property of an antagonist that will
be used in vivo since it will determine target coverage (vide
infra).
Fig. 7.33A shows the effect of increasing concentrations
of a slowly dissociating antagonist in a hemiequilibrium
system; it can be seen from this figure that as dextral displacements of the concentrationeresponse curves occur, so
too does the maximal response to the antagonist to a
limiting value (as shown in Fig. 7.21). This limiting
depression of the maximal response is dependent on the
time available to measure response and the dissociation rate
of the antagonist (k2). Setting [A]/KA/N in Eq. (7.11)
219
yields an expression for the maximal response to the
agonist (with efficacy s) in the presence of an antagonist
with dissociation rate k2 in a system where the time window for observation for response is t:
Agonist Maximal Response ¼
ð1 ek2 t Þðs þ 1Þ
(7.47)
ð1 ek2 t Þs þ 1
The maximal response can be expressed as a function of
antagonism observed (quantified as the DR1) to yield a
curve that is characteristic of a given antagonist with a
given dissociation ratedthis is shown in Fig. 7.33B.
Fig. 7.34 shows curves for a set of antagonists with a range
of dissociation rates in a given system with the same
agonist (s and t constant).
Useful dissimulations between in vivo antagonist concentrations and blockade of response can be obtained if the
rate of receptor dissociation of the antagonist is less than
the rate of drug clearance. Thus, a slowly dissociating
antagonist may be more valuable as a therapy than an
equipotent rapidly dissociating antagonist. As shown in
Fig. 7.35, a persistent binding can turn a drug with transient
pharmacokinetics into one with once-a-day dosing. For this
reason, it is extremely important to measure dissociation
rates of drugs, as these can be useful predictors of effects
in vivo.
7.8 Blockade of indirectly acting
agonists
A unique pattern of antagonism can be observed if a
competitive antagonist blocks the effects of an endogenously released natural agonist; the ligand doing this is
referred to as an “indirect” agonist [19]. For example,
FIGURE 7.33 (A) Response to an agonist of KA ¼ 1 mM, s ¼ 10 in a system of t ¼ 300 s for an antagonist of KB ¼ 10 nM and k2 ¼ 104/s. (B)
Maximal response to the agonist as a function of the degree of antagonism expressed as a value of dose ratio 1.
220
A Pharmacology Primer
where q is the size of the pool of released agonist, KE is the equilibrium dissociation constant of the released agonistereceptor
complex, KA is the equilibrium constant for the complex of
the indirect agonist and site of release, [B] is the concentration
of antagonist, and KB is the equilibrium dissociation constant of
the antagonistereceptor complex. Of note is the fact that the
maximal response to the indirect agonist in the presence of
the antagonist (as [A]/KA/N) is given as
Maximal ResponseA ¼
FIGURE 7.34 Relationship between magnitude of antagonism [abscissal
axis as log(DR1) value] and maximal response in a kinetically
compromised system (as shown in Fig. 7.33). Response to an agonist of
KA ¼ 1 mM, s ¼ 10 in a system of t ¼ 300 s for an antagonist of
KB ¼ 10 nM and various values of dissociation rates (from k2 ¼ 3 103/
s to k2 ¼ 104/s). DR, dose ratio.
q=KE
q=KE þ ½B=KB
(7.49)
It can be seen from Eq. (7.49) that the size of releasable
pool determines whether surmountable or insurmountable
antagonism will be seen, even with fast-acting competitive
antagonists. Fig. 7.36B shows the effects of a competitive
antagonist on an indirect agonist, and Fig. 7.36C shows
actual data from such a system. In this case, the b-adrenoceptor antagonist propranolol blocks the effects of
endogenously released norepinephrine by the indirect
agonist tyramine [19].
7.9 Irreversible antagonism
FIGURE 7.35 An antagonist with a very slow dissociation rate from the
receptor could produce complete target coverage (black line) with once-aday dosage even if the clearance for this antagonist does not support oncea-day dosage for drug levels in the central compartment (red line).
tyramine is taken up by sympathetic nerve endings and this
results in the release of neuronal norepinephrine, which can
then act on postsynaptic b-adrenoceptors (see Fig. 7.36A).
The equation predicting the fractional agonist effect to the
indirectly acting agonist ([A]) in these cases is given as (see
Section 7.12.12 for derivation)
Fractional EffectAB ¼
½A=KA ½qKE
½A=KA ð½q=KE þ ½B=KB þ 1Þ þ ½B=KB þ 1
(7.48)
Equilibrium between antagonists and receptors is achieved
when the number of bound molecules dissociating from
receptors equals the number of molecules binding to the
receptors per unit time. If there is appreciable antagonist
dissociation, a submaximal level of antagonism can be
attained, i.e., the blockade will not progress to completion
at all concentrations. In cases where the rate of dissociation
is extremely low (compared to the window of time available to observe effect), the rate of reversal of antagonism in
the presence of drug-free medium will be correspondingly
slow, a condition often referred to as “pseudoirreversible”
inhibition. However, there are cases whereby a chemical
reaction between the antagonist and receptor can take place,
to lead to a truly irreversible species. When this occurs, all
concentrations of antagonists, when equilibrated with the
receptor for a sufficient length of time, will completely
block available receptors, i.e., it is a chemical reaction that
goes to completion (or until the reactive chemical species
reacts with other components of the system such as H2O to
dissipate). An example of this is shown in Fig. 7.37A where
the b-haloalkylamine, phenoxybenzamine (POB), forms a
reactive aziridinium ion species which goes on to alkylate
histamine, muscarinic, and a-adrenergic receptors. Thus,
equilibration of a receptor preparation with a b-haloalkylamine will cause increased receptor antagonism with
increasing time of equilibration, until complete blockade is
observed (see Fig. 7.37B): this is in contrast to a pseudoirreversible antagonist which, at some point, will reach a
submaximal level of antagonism (see Fig. 7.37C). In the
case of truly irreversible blockade, washing the receptor
Orthosteric drug antagonism Chapter | 7
221
FIGURE 7.36 (A) Indirect antagonism by a competitive antagonist of responses to an indirect agonist causing the release of an endogenous agonist. A
model system is shown whereby tyramine causes the release of neuronal norepinephrine acting on postsynaptic b-adrenoceptors. These postsynaptic
receptors are blocked by the b-blocker propranolol. (B) The effects of an antagonist on responses to an indirectly acting agonist according to Eq. (7.47);
for this simulation qKE ¼ 10. (C) Positive chronotropic responses in rat atria to tyramine blocked by propranolol. Curve shown for control (filled circles)
and in the presence of propranolol 10 (open circles), 50 (filled triangles), and 200 nM (open triangles). Data for panel (C) redrawn from J.W. Black, D.H.
Jenkinson, T.P. Kenakin, Antagonism of an indirectly acting agonist: block by propranolol and sotalol of the action of tyramine on rat heart, Eur. J.
Pharmacol. 65 (1980) 1e10.
with drug-free medium will not reverse the antagonism.
Since a wide range of antagonist concentrations will produce complete blockade, it is not possible to determine an
equilibrium dissociation constant for antagonism, i.e., to
quantify the potency of an irreversible antagonist, through
regular means. In these cases, a procedure modified from
one used to quantify irreversible enzyme inactivation can
be used. Fig. 7.38 shows the effect of POB alkylation of
histamine receptors on the histamine response in guinea pig
ileum; in this case, 3-minute exposures to increasing concentrations of POB causes irreversible dextral displacement
of the concentrationeresponse curve until the receptor
reserve for the agonist is removed. This is followed by
depression of the maximal response as greater receptor
removal is produced. The inhibition of histamine function
progresses at various rates as a function of POB concentration. The effect of alkylation on histamine receptor can
be calculated by fitting the BlackeLeff operational model
to the data with various values for s; as concentratione
response curves shift to the right, decreasing values of s are
used to simulate the reduction in receptor number (since
s ¼ [Rt]/KEdsee Section 3.7: DrugeReceptor Theory).
Fig. 7.38C shows the increasing antagonism with POB
concentration expressed as a rate of receptor alkylation
plotted as a function of POB concentration. The resulting
plot can be fit with a MichaeliseMenten function according
to the equation:
Rate of Receptor Inactivation ¼
½POBy
½POB þ Kinact
(7.50)
222
A Pharmacology Primer
FIGURE 7.37 Irreversible receptor antagonism. (A) Chemical alkylation of histamine receptors by POB. This molecule forms a chemically reactive
aziridinium ion in H2O which then can alkylate various groups on protein; the structure of POB causes it to bind to the active histamine binding site,
therefore this site is occluded when the POB alkylates the protein. (B) The effect of a single concentration of alkylating agent is equilibrated with the
receptor preparation for increasing lengths of time. (C) For a pseudoirreversible antagonist that has an appreciable rate of dissociation, there will be a point
where an equilibrium will be reached that causes submaximal receptor antagonism. POB, phenoxybenzamine.
where y is the maximal rate of inactivation and Kinact is the
concentration of POB producing half maximal receptor
inactivation. While this strategy is used to characterize
time-dependent (irreversible) enzyme inhibition in pharmacokinetic studies, it is not easily applicable to irreversible
antagonism of receptors. More often a given concentration
and time of exposure is used to irreversibly inactivate a
fraction of receptors. For example, Fig. 9.5 shows responses of rat anococcygeus muscle to norepinephrine
and oxymetazoline before and after irreversible alkylation
of various portions of the a-adrenoceptor population; these
effects were achieved by defined exposures of the preparation to specific concentrations of POB (i.e., 30 nM for
10 min and 0.1 mM for 10 min).
7.10 Chemical antagonism
Antagonism of agonist responses can be produced by a
chemical depletion of the agonist by a scavenging species,
i.e., an antibody inactivating a peptide agonist. Agonist
response can be modeled with the BlackeLeff operational
model (see Chapter 3: DrugeReceptor Theory, Section 6):
Afree sEm
Response ¼ (7.51)
Afree ðs þ 1Þ þ KA
where [Afree] is the free unbound concentration of agonist,
KA is the equilibrium dissociation constant of the agoniste
receptor complex, and s the efficacy of the agonist. It is
useful to consider two kinetic extremes. In the first, reversible kinetics is assumed in which the antibody, ligand, and
receptor interact according to reversible mass action kinetics. A second condition assuming the binding of the
chemical antagonist is essentially irreversible and thus precludes all interaction of the agonist with the receptor. It will
be seen that extremely different antagonist kinetics are predicted by these two boundary conditions.
In the case of reversible kinetics, it is assumed that the
antibody binds reversibly to agonist and that the complex
Orthosteric drug antagonism Chapter | 7
223
FIGURE 7.38 Quantification of histamine receptor alkylation. (A) Concentrationeresponse curves to histamine in guinea pig ileum in the absence
(filled circles) and after 3 min exposure to POB at the concentrations shown in the key on the figure. (B) Depression of free histamine receptors at various
concentrations of POB for 3 min as a rate (over the 3-min period). (C) The rates of histamine receptor alkylation obtained in panel (B) plotted as a function
of POB concentration. This yields a plot with maximum of y ¼ 0.33/s and Kinact ¼ 0.15 mM. POB, phenoxybenzamine.
can no longer interact with the receptor (Fig. 7.39A); the
response is produced by free agonist [Afree], where [Afree] is
given by (see derivations in Section 7.12.13)
Afree ¼ ½AT 1=2ð½AT þ KB þ w
ðð½AT Þ þ KB þ wÞ2 4½AT wÞÞ0:5
(7.52)
[AT] is total agonist, KB is the equilibrium dissociation constant of the agonisteAb complex, and w is the concentration of Ab. This model predicts dextral displacements of
the concentrationeresponse curves to the agonist with
increasing antibody concentration; these can be quantified
and expressed as a pseudo-Schild regression (see
Fig. 7.39B). A discerning feature of this model is that there
will be differences in the potency of the antibody as an
antagonist with differences in the cell surface receptor density of the cell producing functional response and these are
related to the magnitude of the receptor reserve to the
agonist in the system. The antibody will show the highest
potency in systems of high sensitivity to the agonist (largest
receptor reserve for the agonist). Under these circumstances, parallel dextral displacements of the agonist
concentrationeresponse curves will be seen (see
Fig. 7.39C). In systems of lower sensitivity to the agonist,
there will be an increase in the slopes of the concentratione
response curves (see Fig. 7.39D) and a reduction in the potency of the antibody as an antagonist (Fig. 7.39).
Another condition was chosen whereby the antibody
binds the agonist and precludes all interaction with the
receptor, i.e., there is no competition between agonist,
the antibody, and the receptor. Under these circumstances,
the binding of the antibody to the receptor is given by
½AAb ¼
ð½AT Þw
ð½AT ÞKB
(7.53)
which yields another equation for [Afree]:
Afree ¼
½AT 2 þ ½AT KB Aw
½AT þ KB
(7.54)
224
A Pharmacology Primer
FIGURE 7.39 Reversible chemical antagonism. (A) A chemical antagonist (in this case an antibody, Ab) binds to the agonist to prevent its interaction
with the receptor. (B) Apparent Schild regressions to the antibody as it blocks agonist response. Two extremes are shown: I (filled circles) is the Schild
regression in a system of high agonistereceptor reserve (s for agonist ¼ 1000). Other systems shown are s ¼ 10 (1% of the receptors shown in I, open
circles), s ¼ 1 (0.1% receptors, filled triangles), and system II (s ¼ 0.1, 0.01% receptors, open triangles). (C) Effect of the antibody on
concentrationeresponse curves to the agonist in a high sensitivity system (s ¼ 1000). (D) Effect of the antibody on concentrationeresponse curves to the
agonist in a low sensitivity system (s ¼ 0.1). It should be noted that changes in the sensitivity to the agonist need not be solely due to differences in
receptor density but rather can also be due to differences in the efficiency of receptor coupling.
Substitution of [Afree] into Eq. (7.52) yields responses to
the agonist in this type of system. As shown in Fig. 7.40A, the
apparent Schild regressions for this type of system differ less
in terms of their location parameter along the antibody concentration axis (i.e., antibody potency) but do differ in terms of
increasing slope. Fig. 7.40B shows the effect of the antibody
on the agonist concentrationeresponse curves in a system of
high sensitivity to the agonist (high agonistereceptor reserve,
s ¼ 1000); it can be seen that the dextral displacement of the
curves is accompanied by an increased slope. Fig. 7.40C
shows the effect of the antibody on a lower sensitivity system
(s ¼ 1). In this case, less dextral displacement is seen.
A variant on the theme of chemical antagonism is where
a chemical scavenger may abstract the concentration of
competitive antagonist in a system (see Fig. 7.41A). As in
the previous section, the effects of the chemical antagonism
(antibody binding) will be seen through changes in the
effects of the receptor antagonist where two kinetic conditions are modeled. In the first, reversible kinetics is
assumed between the antibody, antagonist, and receptor; it
is assumed that these species interact according to reversible mass action kinetics.
Receptor antagonism is assumed to be due to interaction
of the receptor with free antagonist [Bfree] which is given by
(see derivations in Section 7.12.14)
1
Bfree ¼ ½BT ½BAb ¼ ð½BT þ KBAb þ w
2
2
0:5 ð½BT þ KBAb þ wÞ 4½BT wÞ
(7.55)
where [BT] and [BAb] refer to the total antagonist concentration and antagonist bound to the antibody, respectively,
Orthosteric drug antagonism Chapter | 7
225
FIGURE 7.40 Irreversible chemical antagonism. (A) Apparent Schild regressions to the antibody as it blocks agonist response. Two extremes are
shown: I (filled circles) is the Schild regression in a system of high agonistereceptor reserve (s for agonist ¼ 1000). Other systems shown are s ¼ 100
(10% of the receptors shown in I, open circles), s ¼ 10 (1% receptors, filled triangles), and system II (s ¼ 1, 0.1% receptors, open triangles). (B) Effect of
the antibody on concentrationeresponse curves to the agonist in a high sensitivity system (s ¼ 1000). (C) Effect of the antibody on concentratione
response curves to the agonist in a low sensitivity system (s ¼ 1). It should be noted that changes in the sensitivity to the agonist need not be solely due to
differences in receptor density but rather can also be due to differences in the efficiency of receptor coupling.
w refers to the concentration of antibody, and KBAb the
dissociation constant for the antagonisteantibody complex.
Response to the agonist [A] is then calculated from
Response ¼ ð½A=KA ÞsA Em
½A=KA ð1 þ sA Þ þ Bfree =KB þ 1
(7.56)
where KA and KB refer to the equilibrium dissociation constants of the agonistereceptor and antagonistereceptor complexes, respectively, and Em the maximal response of the
system. Fig. 7.41B shows the antagonism to the antagonist
in the form of a Schild regression. It can be seen that the presence of the antibody reduces the potency of the antagonist and
that the slope is minimally affected; the regressions are shifted
to the right with increasing concentrations of antibody.
Another possibility is that the antibody binds the
antagonist irreversibly and thus precludes all interaction
with the receptor, i.e., there is no competition between the
antagonist, antibody, and the receptor. Under these circumstances, the concentration of free antagonist is given by
ð½BT þ ½BT ÞKBAb ½BT w
½BT þ KBAb
2
Bfree ¼
(7.57)
The response is then calculated by substituting for
[Bfree] into Eq. (7.56). The antagonism is similar to that
seen in the previous simulation (see Fig. 7.41B), except the
relationship between antagonist potency and antibody
concentration differs considerably. This is reflected in the
curvilinear effects on the Schild regressions to the antagonist (see Fig. 7.41C).
226
A Pharmacology Primer
FIGURE 7.41 Chemical abstraction of an antagonist by another species (i.e., antibody). (A) Response to an agonist A is blocked by a competitive
antagonist B but this antagonist also may be bound to a species (i.e., in this case, antibody) that renders it unable to interact with the receptor a block
agonist response. (B) Reversible binding of the antagonist to the antibody. Binding of the antagonist to the antibody causes the Schild regression to the
antagonist to be shifted to the right along the antagonist concentration axis. Schild regressions for the antagonist in the absence (filled circles) and presence
of a range of concentrations of antibody: 1 (open circles), 10 (filled triangles), 100 (open triangles), and 1 mM (open diamonds). It is assumed that the
equilibrium dissociation of the antagonist for the receptor (KB) is 10 nM and for the antibody complex (KB-Ab) is 1 mM. (C) Irreversible binding of the
antagonist to the antibody. Schild regressions for the antagonist in the absence (filled circles) and presence of various concentrations of antibody: 0.3 (open
circles), 1 (filled triangles), 2 (open triangles), and 5 mM (open diamonds). It is assumed that the equilibrium dissociation of the antagonist for the receptor
(KB) is 10 nM and for the antibody (KB-Ab) is 1 mM.
7.11 Chapter summary and conclusions
l
l
l
Molecules that retard the ability of agonists to initiate
biological signals are called antagonists.
Two general molecular modes of antagonism are
orthosteric (where the agonist and antagonist compete
for the same binding site on the protein) and allosteric
(where there are separate binding sites on the receptor
for both the agonist and the antagonist and the effects
of the antagonist are transmitted through the protein).
These different molecular mechanisms for antagonism
can produce varying effects on agonist doseeresponse
curves ranging from shifts to the right with no
l
l
l
diminution of the maxima (surmountable antagonism)
to depression of the maximal response (insurmountable
antagonism) with or without a shift of the curve.
The kinetics of offset of the antagonist from the receptor
can dictate whether surmountable or insurmountable
antagonism is observed.
The most common method used to measure the affinity
of surmountable competitive antagonists is Schild analysis. This method is visual and also useful to detect
nonequilibrium steady states in receptor preparations.
The method of Lew and Angus allows the advantage of
nonlinear fitting techniques to yield competitive antagonist pKB values.
Orthosteric drug antagonism Chapter | 7
l
l
l
l
l
l
The same principles (Schild analysis) can be applied to
competitive antagonists that demonstrate either positive
(partial agonists) or negative (inverse agonists) effect.
In systems where there is insufficient time for the
agonist, antagonist, and receptor to equilibrate according to mass action, slow offset antagonists can produce
essentially irreversible occlusion of a portion of the receptor population. This can result in insurmountable
antagonism.
The degree of depression of the maximal response to
agonists with slow offset pseudoirreversible antagonists
is inversely proportional to the efficacy of agonist and
receptor density (i.e., agonists in systems with high receptor reserve are resistant to depression of maximal
response by antagonists).
In some systems with truncated response observation
times and utilizing slow-acting antagonists, a depression
of the maximal response can be observed that is due to
the kinetics of offset of the molecules and not a molecular mechanism of antagonism (hemiequilibrium
conditions).
A method called resultant analysis can be used to measure the receptor blockade produced by an antagonist
with secondary properties.
Antagonism in vivo is greatly affected by the rate of
offset of the antagonist as concentration is never constant. A slow offset predicts good target coverage
in vivo.
l
Chemical antagonism: abstraction of antagonist concentration (Section 7.12.14).
7.12.1 Derivation of the Gaddum equation for
competitive antagonism
Analogous to competitive displacement binding, agonist
[A] and antagonist [B] compete for receptor (R) occupancy:
where Ka and Kb are the respective ligandereceptor
association constants. The following equilibrium constants
are defined:
½R ¼
l
l
l
l
l
l
l
l
l
l
l
l
Derivation of the Gaddum equation for competitive
antagonism (Section 7.12.1).
Derivation of the Gaddum equation for noncompetitive
antagonism (Section 7.12.2).
Derivation of the Schild equation (Section 7.12.3).
Functional effects of an inverse agonist with the operational model (Section 7.12.4).
pA2 measurement for inverse agonists (Section 7.12.5).
Functional effects of a partial agonist with the operational model (Section 7.12.6).
pA2 measurements for partial agonists (Section 7.12.7).
Method of Stephenson for partial agonist affinity measurement (Section 7.12.8).
Derivation of the method of Gaddum for noncompetitive antagonism (Section 7.12.9).
Relationship of pA2 and pKB for insurmountable
orthosteric antagonism (Section 7.12.10).
Resultant analysis (Section 7.12.11).
Blockade of indirectly acting agonists (Section
7.12.12).
Chemical antagonism: abstraction of agonist concentration (Section 7.12.13).
½AR
½AKa
½BR ¼ Kb ½B½R ¼
Kb ½B½AR
½AKa
(7.58)
(7.59)
Total Receptor Concentration ½Rtot ¼ ½R þ ½AR þ ½BR
(7.60)
These lead to the expression for the response-producing
species [AR]/[Rtot] (denoted as r):
r¼
½AKa
½AKa þ ½BKb þ 1
(7.61)
Converting to equilibrium dissociation constants
(KA ¼ 1/Ka) leads to the Gaddum equation [4]:
r¼
7.12 Derivations
l
227
½A=KA
½A=KA þ ½B=KB þ 1
(7.62)
7.12.2 Derivation of the Gaddum equation for
noncompetitive antagonism
The receptor occupancy by the agonist is given by mass
action:
rA ¼
½A=KA
½A=KA þ 1
(7.63)
It is also assumed that the antagonist produces an
essentially irreversible blockade of receptors, such that the
agonist can activate only the fraction of receptors not bound
by the antagonist. If the fractional receptor occupancy by
the antagonist is given by rB, then the agonistereceptor
occupancy in the presence of the antagonist is given by
rA ¼
½A=KA
ð1 rB Þ
½A=KA þ 1
(7.64)
Defining rB as [B]/([B]þKB), substituting this into Eq.
(7.62), and rearranging yields
rA ¼
½A=KA
½A=KA ð1 þ ½B=KB Þ þ ½B=KB þ 1
(7.65)
228
A Pharmacology Primer
7.12.3 Derivation of the schild equation
In the presence of a competitive antagonist, the responseproducing species ([AR]/[Rtot] ¼ r0 ) is given by the Gaddum equation as
r0 ¼
½BR ½B½R (7.76)
½R ½R
(7.77)
aL ¼
½AR ½AR
(7.78)
bL ¼
½BR ½BR
(7.79)
bKb ¼
L¼
0
½A =KA
½A =KA þ ½B=KB þ 1
0
(7.66)
In the absence of antagonist ([B] ¼ 0),
½A=KA
r¼
½A=KA þ 1
(7.67)
Let KA ¼ 1=Ka ;
For equal responses (r0 ¼ r),
½A0 =KA
½A=KA
¼
0
½A =KA þ ½B=KB þ 1 ½A=KA þ 1
(7.68)
Defining [A0 ]/[A] as DR (the ratio of equiactive doses)
and rearranging yields
DR 1 ¼
½B
KB
rRESP ¼
Response ¼
The logarithmic metameter of this is the Schild
equation:
LogðDR 1Þ ¼ Log
½B LogKB
(7.70)
In terms of the operational model, the equation corresponding to Eq. (7.60) is
r¼
½As
½A=KA ð1 þ sÞ þ 1
(7.71)
where s is the receptor concentration divided by the
coupling constant for tissueeagonist response production
(see Chapter 3: DrugeReceptor Theory) (s ¼ [Rt]/KE).
The counterpart to Eq. (7.69) is
r0 ¼
½A0 s
½A =KA ð1 þ sÞ þ ½B=KB þ 1
0
(7.72)
Rearrangement of these equations leads to the Schild
equation (Eq. 7.68) as well.
7.12.4 Functional effects of an inverse agonist
with the operational model
Equilibrium equations:
½AR
Ka ¼
½A½R
(7.73)
Kb ¼
½BR
½B½R
(7.74)
aKa ¼
½AR ½A½R (7.75)
KE ¼ 1=Ke .
(7.80)
½AR þ ½BR þ ½R ;
½AR þ ½BR þ ½R þ ½AR þ ½BR þ ½R
(7.81)
Response ¼
(7.69)
KB ¼ 1=Kb ;
rRESP ½Rt rRESP s
; and (7.82)
¼
rRESP ½Rt þ KE
rRESP s þ 1
aL½A=KA s þ bL½B=KB s þ Ls
½A=KA ð1 þ aLð1 þ sÞÞ þ ½B=KB ð1 þ bLð1 þ sÞÞ þ Lðs þ 1Þ þ 1
(7.83)
7.12.5 pA2 measurement for inverse agonists
The pA2 calculation is derived by equating the response
produced by the full agonist in the absence of the inverse
agonist [with [B] ¼ 0] to the response in the presence of a
concentration of the inverse agonist that produces a DR of
2 (by definition the pA2). For calculation of KB from
10pA2,
2aL½A=KA s þ bL 10pA2 =KB s þ Ls
pA
2½A=KA ð1 þ aLð1 þ sÞÞ þ 10 2 =KB ð1 þ bLð1 þ sÞÞ
þLðs þ 1Þ þ 1
¼
aL½A=KA s þ Ls
½A=KA ð1 þ aLð1 þ sÞÞ þ Lðs þ 1Þ þ 1
(7.84)
which leads to
10pA2 ¼ KB ½A=KA sða 1Þ
½A=KA ða 1Þ þ ð1 bÞ
(7.85)
It can be seen from Eq. (7.85) that for a neutral antagonist (b ¼ 1), the correction term reduces to unity. Therefore, as expected, 10pA2 ¼ KB . The negative logarithmic
metameter of yields the expression for the pA2:
½Aða 1Þ
pA2 ¼ pKB log
(7.86)
½Aða 1Þ þ ð1 bÞ
Orthosteric drug antagonism Chapter | 7
7.12.6 Functional effects of a partial agonist
with the operational model
which further results in
pA2 ¼ pKB Log
Equilibrium equations:
½AR
½A½R
(7.87)
½ARE
½AR½E
(7.88)
½BR
½B½R
(7.89)
Ka ¼
Ke ¼
Kb ¼
½BRE
K0e ¼
½BR½E
Let KA ¼ 1/Ka, KB ¼ 1/Kb, KE ¼ 1/Ke, and K0E ¼
1=K0 .
Thus,
rA ¼
½A=KA
½A=KA þ ½B=KB þ 1
(7.91)
rB ¼
½B=KB
½A=KA þ ½B=KB þ 1
(7.92)
½ARE þ ½BRE
½AR=KE þ ½BR=K0E
Response ¼
¼
½ARE þ ½BRE þ 1 ½AR=KE þ ½BR=K0E þ 1
rA ½Rt =KE þ rB ½Rt =K0E
¼
rA ½Rt =KE þ rB ½Rt =K0E þ 1
(7.93)
Let s ¼ ½Rt =KE and s0 ¼ ½Rt =K0E :
Response ¼
½A=KA s þ ½B=KB s
(7.94)
½A=KA ð1 þ sÞ þ ½B=KB ð1 þ s0 Þ þ 1
7.12.7 pA2 measurements for partial agonists
As with Section 7.12.5 (inverse agonists), the pA2 is
derived by equating the response produced by the full
agonist in the absence of the partial agonist with [B] ¼ 0 to
the response in the presence of a concentration of the partial
agonist that produces a DR of 2 (by definition, the pA2).
For calculation of KB from 10pA2 ,
s ðs s0 Þ
(7.97)
7.12.8 Method of Stephenson for partial
agonist affinity measurement
In terms of the operational model, the response produced
by an agonist [A0 ] obtained in the presence of a concentration of partial agonist [P] is given by [20]
Responseap ¼
(7.90)
229
Emax ½A0 sa
½A ð1 þ sÞ þ KA ð1 þ ½P=KP Þ
0
E ½PsP
max
þ ½P 1 þ sp þ KP ð1 þ ½A0 =KA Þ
(7.98)
where Emax is the maximal response of the system, KA and
Kp are the equilibrium dissociation constants of the full and
partial agonistereceptor complexes, and sa and sp reflect
the efficacies of the full and partial agonist. In the absence
of the partial agonist, the response to the full agonist [A] is
given by
Responseap ¼
Emax ½Asa
½Að1 þ sa Þ þ KA
(7.99)
Comparing equiactive responses to the full agonist in
the absence ([A]) and presence ([A0 ]) of the partial agonist
(Responseap ¼ Responsea) and rearranging yields
½A0 1 þ 1 sp =sa $ ½P=Kp
sp =sa $ ½P=Kp $KA
þ
1 þ 1 sp =sa $ ½P=Kp
½A ¼
(7.100)
This is an equation for a straight line with slope:
1
sp
½P
(7.101)
Slope ¼ 1 þ 1 $
Kp
sa
Rearranging,
Kp ¼
½Pslope
sp
$ 1
1 slope
sa
(7.102)
From Eq. (7.101), it can be shown that, for a range of
2½A=KA s þ ½B=KB s
½A=KA s
¼
2½A=KA ð1 þ sÞ þ ½B=KB ð1 þ s0 Þ þ 1 ½A=KA ð1 þ sÞ þ 1 concentrations of [P] yielding a range of slopes according
(7.95) to regressions of equiactive agonist concentrations, KP can
be estimated from the following regression [9]:
which reduces to
1
0
1 ¼ Log ½P LogKp
(7.103)
Log
KB ½A=KA ðs=s Þ
slope
10pA2 ¼
(7.96)
0
½A=KA ðs=s 1Þ
230
A Pharmacology Primer
7.12.9 Derivation of the Method of Gaddum
for noncompetitive antagonism
In this model, it is assumed that the noncompetitive
antagonist reduces the fraction of available receptor population. Therefore, equating stimuli in the absence and
presence of noncompetitive antagonist:
½As
½A0 s0
¼ 0
½Að1 þ sÞ þ KA ½A ð1 þ s0 Þ þ KA
(7.104)
The receptor population is reduced
by a fraction r upon
0
antagonist binding. Therefore, Rt ¼ ð1 rÞ½Rt , resulting in s0 ¼ s(1r). Rearrangement of the equation:
½A0 sð1 rÞEmax
Response ¼ 0
½A ð1 þ sð1 rÞÞ þ KA
Response ¼
½A0 =KA sEmax
½A=KA ð1 þ s þ ½B=KB Þ þ ½B=KB þ 1
(7.106)
For equiactive responses,
½A0 =KA sEmax
½A=KA sEmax
¼
½A =KA ð1 þ s þ ½B=KB Þ þ ½B=KB þ 1 ½A0 =KA ð1 þ sÞs þ 1
(7.107)
0
1=½A ¼ 1=½A ðð½B = KB Þ þ 1Þ þ ½B=ðKB KA Þ
2½A=KA sEmax
½A=KA sEmax
¼
pA
2½A=KA ð1 þ sÞ þ 10 2 =KB þ 1 ½A=KA ð1 þ sÞ þ 1
(7.112)
Simplifying this yields
10pA2 ¼ KB ;
KB ¼
½B
slope 1
(7.113)
as predicted by the Schild equation (i.e., pA2 ¼ pKB) of
unit slope.
An analogous procedure can equate the empirical pA2
to pKB for noncompetitive antagonists. Utilizing the
equation for agonist response in the presence of a
noncompetitive antagonist (Eq. 7.10), equiactive concentrations with a DR of 2 in the presence and absence of
antagonist are given by
2½A=KA sEmax
2½A=KA 1 þ s þ 10pA2 =KB þ 10pA2 =KB þ 1
¼
(7.108)
Therefore, a double reciprocal plot of equiactive agonist
concentrations in the presence (1/[A0 ] as abscissae) and
absence (1/[A] as ordinates) of the antagonist should yield a
straight line. The equilibrium dissociation constant of the
antagonist is calculated from
(7.111)
The relationship between equiactive agonist concentrations in the absence and presence of antagonist to yield a
DR of 2 ½B ¼ 10pA2 is then calculated by equating
Rearrangement of the equation yields
0
½A=KA sEmax
.
½A=KA ð1 þ sÞ þ ½B=KB þ 1
(7.105)
Substitution for r in terms of the receptor occupancy by
the antagonist (r ¼ [B]/KB/([B]/KBþ1)) results in
Response ¼
presence of the antagonist (denoted rAB) ([A]/KA/([A]/
KAþ[B]/KAþ1)). This yields
½A=KA sEmax
½A=KA ð1 þ sÞ þ 1
(7.114)
Simplification of this relationship yields an equation
relating pA2 and KB:
10pA2 ¼
KB
1 þ 2½A=KA
pKB ¼ pA2 Logð1 þ 2½A = KA Þ
(7.115)
(7.116)
(7.109)
7.12.11 Resultant analysis
7.12.10 Relationship of pA2 and pKB for
insurmountable orthosteric antagonism
The receptor occupancy for an agonist [A] in the presence
of a test antagonist [Btest] is given as
It is useful to describe agonist response in the presence of
any antagonist as
Response ¼
rA ð1 rB ÞsEmax
rA ð1 rB Þs þ 1
(7.110)
where rA and rB are the agonist and antagonist fractional
receptor occupancies, respectively. For simple competitive
antagonism, rB is given by [B]/KB/([B]/KBþ[A]/KAþ1) to
yield the well-known Gaddum equation for simple competitive antagonism for agonistereceptor occupancy in the
r¼
½A
½A þ KA 1 þ ½Btest =KBtest
(7.117)
Similarly, receptor occupancy equal to the previous
occupancy (agonist concentration [A0 ]) in the presence of
the test antagonist and a reference antagonist [B0 ] is given
as
r0 ¼
½A0 ½A þ KA ð1 þ ½B =KB þ ½Btest =KBtest Þ
0
(7.118)
Orthosteric drug antagonism Chapter | 7
If equal responses to the agonist under these two conditions (leading to equal receptor occupancies for the same
agonist, r ¼ r0 ) are compared, then equating Eqs. (7.118)
and (7.119) and rearranging yields
½A
½B0 ½Btest ¼ r0 ¼ 1 þ
$ 1þ
½A
KB
KB test
(7.119)
where r0 is the DR for the agonist. A DR r for antagonism
by the reference antagonist is defined in the absence of the
test antagonist ([Btest] ¼ 0):
r¼
1½B
KB
(7.121)
A term k is derived, which is [B]/[B0 ]; specifically, the
ratio of reference antagonist concentrations gives equal
log(DR1) values (the shift, along the antagonist axis, of
the Schild regressions) in the presence of various concentrations of test antagonist. This yields the resultant plot:
Logðk 1Þ ¼ Logð½Btest Þ LogKBtest
For reversible kinetics of an antibody binding to the
agonist, it is assumed that only free agonist ([Afree]) binds
to the receptor to produce the response:
½AAb ¼
½A=KA q
¼ ½j
½A=KA þ 1
(7.123)
where q is the size of releasable pool and KA is the dissociation constant of the indirect agonist ([A]) and site of
release. The fractional receptor occupancy by the released
endogenous agonist in the presence of a competitive antagonist ([B]) is given as
Fractional EffectAB ¼
½jKE
½j=KE þ ½B=KB þ 1
(7.124)
where KB is the equilibrium dissociation constant of the
antagonistereceptor complex. Substituting for [j] from
Eq. (7.123) yields
(7.126)
ð½AT ½AAb Þz
ð½AT ½AAb þ KB Þ
(7.127)
where z is the concentration of antibody. This leads to
½AAb 2 ½AAb ðz þ ½AT þ KB Þ þ ½ATz ¼ 0
(7.128)
One solution for which is
1
½AAb ¼
2
0:5 ½AT þ KB þ z ð½AT þ KB þ zÞ2 4½AT z
(7.129)
7.12.12 Blockade of indirectly acting agonists
½Endogenous Agonist ¼
Afree ¼ ½AT ½AAb where [AT] and [AAb] refer to the total concentration of
agonist and concentration bound to the antibody,
respectively.
Considering the amount of agonist bound to the antibody as
(7.122)
It is assumed that a mass action process leads to the release
of an endogenous agonist j by
½A=KA ½q=KE
½A=KA ð½qKE þ ½B=KB þ 1Þ þ ½B=KB þ 1
(7.125)
7.12.13 Chemical antagonism: abstraction of
agonist concentration
(7.120)
Schild plots for the test antagonist alone and the test
antagonist plus a range of concentrations of reference
antagonist are obtained. Equieffective DRs are compared.
Therefore, the ratio of the DR produced by both the test and
reference antagonist (r0 ) is equated to the DR for the
reference antagonist alone (r). Simplifying yields
1 þ ½B=KB ¼ 1 þ ½B0 =KB ð1 þ ½Btest = KBtest Þ
Fractional EffectAB ¼
231
Which leads to
1
Afree ¼ ½AT ½AAb ¼ ð½AT þ KB þ z
2
0:5 2
ð½AT þ KB þ zÞ 4½AT z
(7.130)
Agonist response then is calculated with the Blacke
Leff operational model using [Afree]:
Response ¼ Afree sEm
Afree ðs þ 1Þ þ KA
(7.131)
7.12.14 Chemical antagonism: abstraction of
antagonist concentration
Bfree ¼ ½BT ½BAb (7.132)
232
A Pharmacology Primer
where [BT] and [BAb] refer to the total antagonist concentration and antagonist bound to the antibody, respectively.
The binding of the antagonist to the receptor is given by
½BAb ¼
ð½BT ½BAb Þw
ð½BT ½BAb þ KBAb Þ
(7.133)
where w refers to the concentration of antibody, and KBAb
is the dissociation constant for the antagonisteantibody
complex.
This yields
½BAb ½BAb ðw þ ½BT þ KBAb Þ þ ½BT w ¼ 0 (7.134)
2
One solution for which is
½BAb ¼
0:5 1
½BT þ KBAb þ w ð½BT þ KBAb þ wÞ2 4½BT w
2
(7.135)
Which leads to
1
Bfree ¼ ½BT ½BAb ¼ ð½BT þ KBAb þ w
2
0:5 ð½BT þ KBAb þ wÞ2 4½BT w
(7.136)
References
[1] W.D.M. Paton, H.P. Rang, The uptake of atropine and related drugs
by intestinal smooth muscle of the Guinea pig in relation to acetylcholine receptors, Proc. R. Soc. Lond. [Biol.] 163 (1965) 1e44.
[2] J.H. Gaddum, The quantitative effects of antagonistic drugs,
J. Physiol. Lond. 89 (1937) 7Pe.
[3] J.H. Gaddum, K.A. Hameed, D.E. Hathway, F.F. Stephens, Quantitative studies of antagonists for 5-hydroxytryptamine, Q. J. Exp.
Physiol. 40 (1955) 49e74.
[4] O. Arunlakshana, H.O. Schild, Some quantitative uses of drug antagonists, Br. J. Pharmacol. 14 (1959) 48e58.
[5] T.P. Kenakin, C. Boselli, Pharmacologic discrimination between
receptor heterogeneity and allosteric interaction: resultant analysis of
gallamine and pirenzepine antagonism of muscarinic responses in rat
trachea, J. Pharmacol. Exp. Therapeut. 250 (1989) 944e952.
[6] T.P. Kenakin, The Schild regression in the process of receptor
classification, Can. J. Physiol. Pharmacol. 60 (1982) 249e265.
[7] R.P. Stephenson, A modification of receptor theory, Br. J. Pharmacol. 11 (1956) 379e393.
[8] A.J. Kaumann, M. Marano, On equilibrium dissociation constants
for complexes of drug receptor subtypes: selective and nonselective
interactions of partial agonists with two b-adrenoceptor subtypes
mediating positive chronotropic effects of ()isoprenaline in kitten
atria, Naunyn Schmiedebeberg’s Arch. Pharmacol. 219 (1982)
216e221.
[9] T.P. Kenakin, J.W. Black, The pharmacological classification of
practolol and choropractolol, Mol. Pharmacol. 14 (1978) 607e623.
[10] M. Stone, J.A. Angus, Developments of computer-based estimation
of pA2 values and associated analysis, J. Pharmacol. Exp. Therapeut.
207 (1978) 705e718.
[11] M.J. Lew, J.A. Angus, Analysis of competitive agonist-antagonist
interactions by nonlinear regression, Trends Pharmacol. Sci. 16
(1996) 328e337.
[12] J.W. Black, V.P. Gerskowich, P. Leff, Analysis of competitive
antagonism when this property occurs as part of a pharmacological
resultant, Br. J. Pharmacol. 89 (1986) 547e555.
[13] T.P. Kenakin, D. Beek, Self-cancellation of drug properties as a
mode of organ selectivity: the antimuscarinic effects of ambenonium,
J. Pharmacol. Exp. Therapeut. 232 (1985) 732e740.
[14] A. Takano, T. Suhara, Y. Ikoma, F. Yasuno, J. Maeda, T. Ichimiya,
et al., Estimation of the time-course of dopamine D2 receptor occupancy in living human brain from plasma pharmacokinetics of
antipsychotics, Int. J. Neuropsychopharmacol. 7 (2004) 19e26.
[15] G. Vauquelin, S.J. Charlton, Long-lasting target binding and
rebinding as mechanisms to prolong in vivo drug action, Br. J.
Pharmacol. 161 (2010) 488e508.
[16] D.A. Sykes, H. Moore, L. Stott1, N. Holliday, J.A. Javitch,
J.R. Lane, et al., Extrapyramidal side effects of antipsychotics are
linked to their association kinetics at dopamine D2 receptors, Nat.
Commun. 8 (2017) 763.
[17] D.A. Sykes, M.R. Dowling, J. Leighton-Davies, T.C. Kent,
L. Fawcett, E. Renard, et al., The Influence of receptor kinetics on
the onset and duration of action and the therapeutic index of
NVA237 and tiotropium, J. Pharmacol. Exp. Therapeut. 343 (2012)
520e528.
[18] H.J. Motulsky, L.C. Mahan, The kinetics of competitive radioligand
binding predicted by the law of mass action, Mol. Pharmacol. 25
(1984) 1e9.
[19] J.W. Black, D.H. Jenkinson, T.P. Kenakin, Antagonism of an indirectly acting agonist: block by propranolol and sotalol of the action
of tyramine on rat heart, Eur. J. Pharmacol. 65 (1980) 1e10.
[20] P. Leff, I.G. Dougall, D. Harper, Estimation of partial agonist affinity
by interaction with a full agonist: a direct operational model-fit
approach, Br. J. Pharmacol. 110 (1993) 239e244.
Chapter 8
Allosteric modulation
When one tugs at a single thing in nature, he finds it
attached to the rest of the world.
John Muir.
Whatever affects one directly, affects all indirectly . This
is the interrelated structure of reality.
Martin Luther King Jr.
8.1 Introduction
A major molecular mechanism of receptor interaction involves the binding of a molecule to its own site on the
receptor, which is separate from the binding site of the
endogenous agonist. When this occurs, the interaction between the agonist and the molecule takes place via the receptor protein. This is referred to as an allosteric
interaction (for a schematic diagram, see Fig. 6.2) and the
molecules with this mode of action are referred to as allosteric modulators. Thus, an allosteric modulator produces a
conformational change in the shape of the receptor, which
in turn changes the affinity or efficacy of the receptor for
the agonist and/or changes the receptor function.
Allosteric modulators produce saturable effects (i.e., a
maximum effect is produced, after which further increases in
modulator concentration have no further effect). This is
because the allosteric effect is linked to occupancy of the
allosteric site, and this saturates with complete occupancy of
that site. Operational effects on doseeresponse curves do not
always unambiguously indicate a molecular mechanism, in
that experiments can reveal combinations of compatible
operational and mechanistic classifications (i.e., an allosteric
molecular mechanism can produce either surmountable or
insurmountable effects on doseeresponse curves depending
on the system). Also, since allosteric effects produce a
change in shape of the receptor, it cannot be assumed a priori
that a uniform modulatory effect on agonism will result.
In fact, it will be seen that some allosteric ligands
produce antagonism of the binding of some ligands and an
increase in the affinity of the receptor for other ligands
(note the stimulation of the binding of [3H]-atropine by
alcuronium in Fig. 4.14). In addition, the effect of an
allosteric ligand on a receptor probe (this can be an agonist
or radioligand) is dependent on the nature of the probe (i.e.,
A Pharmacology Primer. https://doi.org/10.1016/B978-0-323-99289-3.00002-6
Copyright © 2022 Elsevier Inc. All rights reserved.
a conformational change that increases the affinity of the
receptor for one agonist may decrease it for another). For
example, while the allosteric ligand alcuronium produces a
10-fold change in the affinity of the muscarinic m2 receptor
for acetylcholine (ACh), it produces only a 1.7-fold change
in the affinity for arecoline [1]. These effects make
consistent nomenclature for allosteric ligands difficult, and
for this reason modulation in this sense means modification,
either in a positive or negative direction.
8.2 The nature of receptor allosterism
The word allosteric comes from the Greek allos, meaning
different, and steric, which refers to arrangement of atoms
in space. As a word, allostery literally means a change in
shape. Specifically, in the case of allosterism of proteins,
the change in shape is detected by its interaction with a
probe. Therefore, there can be no steric interference at this
probe site. In fact, allosteric effects are defined by the
interaction of an allosteric modulator at a so-called allosteric binding site on the protein to affect the conformation
at the probe site of the protein. Since the probe and
modulator molecules do not interact directly, their influence
on each other must take place through a change in shape of
the protein. Historically, allosteric effects have been studied
and described for enzymes. Early discussions of allosteric
enzyme effects centered on the geography of substrate and
modulator binding. Koshland [2], a pioneer of allosteric
enzyme research, classified the binding geography of enzymes in terms of “contact amino acids” and intimate parts
of the active site for substrate binding, and “contributing
amino acids,” those important for preservation of the tertiary structure of the active site but which did not play a
role in substrate binding. Finally, he defined “noncontributing amino acids” as those not essential for enzyme
catalysis but perhaps serving a structural role in the
enzyme. Within Koshland’s hypothesis, binding to these
latter two categories of amino acids constituted a mechanism of allosterism rather than pure endogenous ligand
competition. Within this context, pharmacological antagonists can bind to sites distinct from those utilized by the
endogenous agonist (i.e., hormone, neurotransmitter) to
alter binding and subsequent tissue response (Fig. 8.1).
Some of these differences in binding loci can be discerned
233
234
A Pharmacology Primer
FIGURE 8.1 Enzyme ortho- and allosterism as presented by Koshland
[2]. Steric hindrance whereby the competing molecules physically interfered with each other as they bound to the substrate site was differentiated
from a direct interaction where only portions of the competing molecules
interfered with each other. If no direct physical interaction between the
molecules occurred, then the effects were solely due to effects transmitted
through the protein structure (allosteric).
through point mutation of receptors. For example, differences in amino acids required for competitive antagonist
binding and allosteric effector binding can be seen in
mutant muscarinic m1 receptors where substitution of an
aspartate residue at position 71, but not at positions 99 and
122, affects the affinity of the allosteric modulator gallamine but not the affinity of the competitive antagonist
radiolabeled [3H]-N-methylscopolamine [3].
Allosteric sites can be remote from the enzyme’s active
site. For example, the binding site for nevirapine, an allosteric modulator of HIV reverse transcriptase, is 10 Å away
from the enzyme’s active site [4]. Similarly, allosteric inhibition of b-lactamase occurs 16 Å away from the active
site [5]. The binding site for CP320626 for glycogen
phosphorylase b is 33 Å from the catalytic site and 15 Å
from the site for cyclic adenosine monophosphate (AMP)
[6]. A visual demonstration of the relative geography of
allosteric binding and receptor active sites can be seen in
Fig. 8.2. Here, the integrin lymphocyte functione
associated antigen-1 (LFA-1), which binds to molecules on
other cell membranes to mediate cell adhesion, has a receptor probe active site binding the intercellular adhesion
molecule-1, and an allosteric binding site for the drug
lovastatin in a deep hydrophobic cleft next to the a7 helix
(see Fig. 8.2) [7].
While visualization of the relative binding sites for receptor probes and allosteric modulators is conceptually
helpful, preoccupation with the geography of ligand binding is needlessly confining since the actual binding sites
involved are secondary to the mechanism of allosterism. As
FIGURE 8.2 Model of LFA-1 showing the binding domain of ICAM-1
(the endogenous ligand for this protein) and the binding site for lovastatin,
an allosteric modulator for this protein. ICAM-1, intercellular adhesion
molecule-1. Redrawn from M.R. Arkin, J.A. Wells, Small-molecule inhibitors of proteineprotein interactions: progressing towards the dream,
Nat. Rev. Drug Discov. 3 (2004) 301e317.
shown by the preceding examples, the modulator and probe
binding sites need not be near each other for allosteric effects to occur (i.e., the binding of the modulator does not
necessarily need to produce a deformation near the receptor
probe site). In fact, there are data to suggest that the relative
geometry of binding is immaterial, except for the fact that
the receptor probe and modulator must bind to exclusively
different sites.
Just as the location of allosteric sites is secondary to the
consequences of allosteric effect, there is evidence to suggest that the structural requirements of allosteric sites may
be somewhat more permissive with respect to the chemical
structures bound to them (i.e., the structureeactivity relationships for allosteric sites may be more relaxed due to
the fact that allosteric proteins are more flexible than other
proteins). For example, as shown in Fig. 8.3A, structurally
diverse molecules such as efavirenz, nevirapine, UC-781,
and Cl-TIBO all bind to HIV reverse transcriptase [8].
Similarly, the HIV entry inhibitors Sch-C, Sch-D,
UK427,857, aplaviroc, and TAK779 all demonstrate prohibitive binding (consistent with binding at the same site)
for the chemokine C receptor type 5 (CCR5) receptor (see
Fig. 8.3B [9]).
It is useful to think of allosteric binding, not in terms of
deformation of the receptor active site, but rather as a lever
to lock the receptor into a given conformation. As discussed in Chapter 1 What Is Pharmacology?, receptors and
other biologically relevant proteins are a dynamic system of
interchanging conformations referred to as an ensemble.
These various conformations are sampled according to the
Allosteric modulation Chapter | 8
235
FIGURE 8.3 Diversity of structures that interact with the (A) HIV reverse transcriptase inhibitor binding site [8] and (B) the CCR5-receptor-mediating
HIV-1 fusion [9]. CCR5, chemokine C receptor type 5.
thermal energy of the system; in essence, the protein roams
on a conceptual “energy landscape.” While there are
preferred low-energy conformations, the protein has the
capacity to form a large number of conformations. An
allosteric modulator may have a high affinity for some of
these and thus bind to them preferentially when they are
formed. Thus, by selectively binding to these conformations, the allosteric modulators stabilize them at the
expense of other conformations. This creates a bias and a
shift in the number of conformations toward the ligandbound conformation (see Section 1.11 of Chapter 1, What
Is Pharmacology?, for further details).
The fact that the allosterically preferred conformation
may be relatively rare in the library of conformations
available to the receptor may have kinetic implications.
Specifically, if the binding site for the modulator
appears only when the preferred conformation is formed
spontaneously, then complete conversion to allosterically
modified receptors may require a relatively long period of
equilibration. For example, the allosteric p38 mitogenactivated protein (MAP) kinase inhibitor BIRB 796
binds to a conformation of MAP kinase requiring movement of a Phe residue by 10 Å (so-called out conformation). The association rate for this modulator is
8.5 105 M1/s, 50 times slower than that required
for other inhibitors (4.3 107 M1/s). The result is that
while other inhibitors reach equilibrium within 30 min,
BIRB 376 requires two full hours of equilibration
time [10].
8.3 Unique effects of allosteric
modulators
Orthosteric molecules (i.e., antagonists, partial agonists,
inverse agonists) that preclude access of other molecules
such as agonists to the receptor can be thought of as producing a preemptive type of system, i.e., there is a common
maximal result for all such antagonists in the form of an
inactivated (or in the case of partial agonists, a partially
activated) receptor to all agonists. In contrast, allosteric
molecules are permissivedallowing the interaction of the
receptor protein with other molecules. The fact that allosteric effects are saturable (i.e., the effect ceases when the
allosteric site is fully occupied) and that allosterism is
permissive causes allosteric modulators to have a unique
range of activities. These are
1. Allosteric modulators have the potential to alter the
interaction of very large proteins: The fact that global
conformations of the receptor are stabilized by allosteric
modulators has implications for their effects. Specifically, this opens the possibility of changes in multiple
regions of the receptor instead of a single point change
in conformation, and with this comes the possibility of
changing multiple points of contact between the receptor and other proteins (see Fig. 8.4). An example of the
global nature of the conformational changes caused by
allosteric interaction is evident from the interaction of
CP320626 with glycogen phosphorylase b. In this
case, the binding of this allosteric modulator causes
236
A Pharmacology Primer
the release of 9 of 30 water molecules from a cavity
capped by a-helices of the enzyme subunits [6]. Such
global conformational effects mean that small allosteric
molecules can influence the interactions of large proteins. For example, HIV-1 entry is mediated by
the interaction of the chemokine receptor CCR5
and the HIV viral coat protein gp120, both large
(70e100 kDa) proteins. Analysis by point mutation indicates that all four extracellular loops of the receptor
and multiple regions of gp120 associate for HIV fusion
[10e13], yet small allosteric molecules such as
aplaviroc and Sch-D (0.6% of their size) are able to
FIGURE 8.4 Schematic diagram of a G-protein-coupled receptor
(GPCR) in a native conformation (black) and allosterically altered
conformation (red). When these are superimposed upon each other, it can
be seen that more than one region of the receptor is altered upon allosteric
modulation (see circled areas).
FIGURE 8.5 Cartoons showing the relative size of the CCR5 receptor, gp120 HIV
viral coat protein, the natural ligand for the
CCR5 receptor (the chemokine MIP-1a),
and GW873140 (aplaviroc) [9], an allosteric modulator that blocks the interaction
of CCR5 with both MIP-1a and gp120.
CCR5, chemokine C receptor type 5.
block this interaction at nanomolar concentrations (see
Fig. 8.5). In general, the stabilization of receptor conformations by allosteric ligands makes possible the
alteration of large proteineprotein interactions, making
this a potentially very powerful molecular mechanism
of action.
2. Allosteric modulators have the potential to modulate
but not completely activate and/or inhibit receptor
function: One of the key properties of allosteric modulators is their saturability of effect. With this comes the
capability to modulate but not necessarily completely
block agonist-induced signals. This stems from the fact
that while the allosterically modified receptor may have
a diminished affinity and/or efficacy for the agonist, the
agonist may still produce receptor activation in the presence of the modulator. This submaximal effect on
ligandereceptor interaction is shown in Fig. 4.11, where
it is seen that the apparent displacement of bound 125IMIP-1a from the chemokine C receptor type 1 by the
allosteric ligand UCB35625 is incomplete (i.e., the
125
I-MIP-1a still binds to the receptor but with a lower
affinity). An orthosteric antagonist binding to the same
binding site as MIP-1a necessarily must completely
reverse the binding of MIP-1a. In general, this leads to
the possibility that allosteric modulators can modify
(i.e., reduce or increase by a small amount) endogenous
agonist signals without completely blocking them.
The saturability of the binding to the allosteric site also
offers the potential to dissociate duration of effect from
magnitude of effect. Since allosteric effects reach an
asymptotic value upon saturation of the allosteric site,
there is the potential to increase the duration of
Allosteric modulation Chapter | 8
allosteric effect by loading the receptor compartment
with large concentrations of modulator. These large
concentrations will have no further effect other than to
prolong the saturated allosteric response. For example,
consider a system where the therapeutic goal is to produce a 10-fold shift to the right of the agonist dosee
response curve. A concentration of an orthosteric simple competitive antagonist of [B]/KB ¼ 10 will achieve
this, and the duration of this effect will be determined
by the kinetics of washout of the antagonist from the receptor compartment and the concentration of antagonist.
A longer duration of action of such a drug could be
achieved by increasing the concentration, but this
necessarily would increase the maximal effect as well
(i.e., [B]/KB ¼ 100 would produce a 100-fold shift of
the curve). In contrast, if an allosteric modulator with
a ¼ 0.1 were to be employed, an increased concentration would increase the duration of effect but the antagonism would never be greater than 10-fold (as defined
by the cooperativity factor a). Thus, the saturability of
the allosteric ligand can be used to limit effect but increase the duration.
3. Allosteric modulators have the potential to preserve
physiological patterns: The fact that allosteric modulators alter the signaling properties and/or sensitivity of
the receptor to physiological signaling means that their
effect is linked to the receptor signal. This being the
case, allosteric modulators will augment or modulate
function in a reflection of the existing pattern. This
may be especially beneficial for complex signaling patterns such as those found in the brain. For this reason,
the augmentation of the cholinergic system in Alzheimer’s disease with cholinesterase inhibitors (these
block the degradation of ACh in the synapse and thus
potentiate response in accordance with neural firing)
has been one approach to treatment of this disease
237
[14]. However, there are practical problems with this
idea associated with nonspecific increase in both nicotinic and muscarinic receptor when only selective nicotinic function is required. This has opened the field for
other strategies, such as selective allosteric potentiation
of ACh receptor function [15,16]. In general, as a theoretical approach, allosteric control of function allows
preservation of patterns of innervation, blood flow,
cellular receptor density, and efficiencies of receptor
coupling for complex systems of physiological control
in the brain and other organs.
4. Allosteric modulators may yield therapies with
reduced side effects: In cases where augmentation of
physiological effect is required (i.e., Alzheimer’s disease), allosteric potentiation of effect would be expected
to yield a lower side-effect profile. This is because modulators with this action would produce no direct effect
but rather produce actions only when the system is
active through presence of the endogenous agonist.
5. Allosteric antagonists can produce texture in antagonism: Just as a given allosteric modulator can produce
different effects on different receptor probes, different
modulators can produce different effects on the same
modulator. For example, Table 8.1 shows the effects
of different allosteric modulators on common agonists
of muscarinic receptors. It can be seen from these
data that different allosteric modulators have the ability
to antagonize and potentiate muscarinic agonists,
clearly indicative of the production of different allosteric conformational states. Similarly, the allosterically
modified CCR5 receptor demonstrates heterogeneity
with respect to sensitivity of antibody binding. In this
case, antibodies such as 45531, binding to a specific
region of the receptor, reveal different conformations
stabilized by aplaviroc and Sch-C, two allosteric modulators of the receptor. This is shown by the different
TABLE 8.1 The effects of different allosteric modulators on common agonists of muscarinic receptors.
Receptor
Receptor probe
Modulator
Effecta
Differenceb
m3
Bethanechol
Strychnine
49 potentiation
73
Brucine
0.67 inhibition
m2
m2
a
c
P-TZTP
Acetylcholine
Alcuronium
4.7 potentiation
Brucine
0.13 inhibition
Vincamine
18 potentiation
Eburnamonine
0.32 inhibition
36
31
a Value for changes in potency.
Ratio of a values for the two modulators.
3-(3-pentylthio-1,2,5-thiadiazol-4-yl)-1,2,5,6-tetrahydro-1-methylpyridine.
From J. Jakubic, I. Bacakova, E.E. El-Fakahany, S. Tucek, Positive cooperativity of acetylcholine and other agonists with allosteric ligands on muscarinic
acetylcholine receptors, Mol. Pharmacol. 52 (1997) 172e179.
b
c
238
A Pharmacology Primer
FIGURE 8.6 Binding of the CCR5 antibody 45531 to native receptor
(peak labeled solvent) and in the presence of 1 mM Sch-C (blue line) and
1 mM aplaviroc (magenta peak). CCR5, chemokine C receptor type 5.
Different locations of the distributions show different binding sensitivities
to the antibody indicative of different receptor conformations. Data
courtesy of S. Sparks and J. Demarest, Dept of Clinical Virology,
GlaxoSmithKline.
affinity profiles of the antibody in the presence of each
modulator (see Fig. 8.6). This also has implications for
the therapeutic use of such modulators. In the case of
Sch-D and aplaviroc in Fig. 8.6, the allosterically
blocked receptors are similar in that they do not support
HIV entry but quite dissimilar with respect to binding of
the 45531 antibody. This latter fact indicates that the
allosteric conformations produced by each modulator
are not the same, and this could have physiological consequences. Specifically, it is known that HIV spontaneously mutates [17,18] and that the mutation in the viral
coat protein can lead to resistance to CCR5-entry inhibitors. For example, passage of the virus in the continued
presence of the CCR5 antagonist AD101 leads to an
escape mutant able to gain cell entry through use of
the allosterically modified receptor [19,20]. It would
be postulated that production of a different conformation with another allosteric modulator would overcome
viral resistance, since the modified virus would not be
able to recognize the newly formed conformation of
CCR5. Thus, the texture inherent in allosteric modification of receptors (different tertiary conformations of
protein) offers a unique opportunity to defeat the accommodation of pathological processes to chronic
drug treatment (in this case viral resistance).
6. Allosteric modulators can have separate effects on
agonist affinity and efficacy: Allosteric modulators
produce a new protein conformation; therefore, the
resulting effect on endogenous ligands need not be uniform, i.e., the changes need not be in the same direction
(antagonism or potentiation). This opens the possibility
that an allosteric modulator could change agonist efficacy in one direction and affinity in another. For
example, the CCR5 allosteric modulator aplaviroc
completely blocks CCL5-mediated agonism but only
minimally affects the binding of the chemokine CCL5
to the receptor [9,21]. Thus, while the steps leading to
G-protein activation and subsequent cellular response
are completely blocked, the high affinity binding of
CCL5 is not greatly affected, i.e., aplaviroc has little effect on CCL5 affinity but a strong negative effect on
CCL5 efficacy. A similar effect is seen with CPCCOEt
(7-hydroxyiminocyclopropan[b]chromen-1a-carboxylic
acid ethyl ester) which does not interfere with glutamate
binding in CHO cells naturally expressing human
GluR1b receptors but completely blocks their responses
to glutamate [22].
A useful combination of such effects is where an allosteric antagonist modulator decreases agonist efficacy
but increases agonist affinity. The mechanism of this
effect relates to the reciprocal nature of allosteric energy. Since the modulator increases the affinity of the
agonist, the agonist will also increase the affinity of
the modulator; this has been shown experimentally
[23]. The profile of such a molecule would demonstrate
increased antagonist potency with increased concentrations of agonist, i.e., the presence of higher agonist concentrations promotes higher affinity antagonist binding,
and leads to more antagonism. This is observed with antagonists such as ifenprodil (for N-Methyl-D-aspartate
(NMDA) receptors [24]) and Org27569 (for cannabinoid receptors [25]).
7. Allosteric modulators may have an extraordinary
selectivity for receptor types: Another discerning
feature of allosterism is the potential for increased
selectivity. Physiological binding sites for endogenous
ligands (hormones, neurotransmitters) may be conserved between receptor subtypes, predicting that it
would be difficult to attain selectivity through interaction at these sites. For example, it could be postulated
that it would be difficult for orthosteric antagonists
that bind to the ACh recognition site of muscarinic receptors to be selective for muscarinic subtypes (i.e.,
teleologically these have all evolved to recognize
ACh). However, the same is not true for the surrounding scaffold protein of the ACh receptor, and it is in
these regions that the potential for selective stabilization
of receptor conformations may be achieved [26e30].
8. Allosteric modulators exercise “probe dependence”:
Another particularly unique aspect of allosteric mechanisms is that they can be very probe specific (i.e., a
conformational change that is catastrophic for one receptor probe may be inconsequential to another). This
is illustrated in Fig. 8.7, where it can be seen that the
allosteric modulator eburnamonine produces a 25-fold
Allosteric modulation Chapter | 8
FIGURE 8.7 Effect of the allosteric modulator eburnamonine on the
affinity of muscarinic agonists on m2 receptors. It can be seen that while
no change in potency is observed for APE, pilocarpine is antagonized and
arecoline is potentiated, illustrating the probe dependence of allosterism.
APE, arecaidine propargyl ester. From J. Jakubic, I. Bacakova, E.E. ElFakahany, S. Tucek, Positive cooperativity of acetylcholine and other
agonists with allosteric ligands on muscarinic acetylcholine receptors,
Mol. Pharmacol. 52 (1997) 172e179.
antagonism of the muscarinic agonist pilocarpine, no effect on the agonist arecaidine propargyl ester, and a 15fold potentiation of the agonist arecoline [1].
Allosteric probe dependence can have negative effects.
For example, allosteric modification of an endogenous
signaling system requires the effect to be operative on
the physiologically relevant agonist. There are practical
circumstances where screening for new drug entities in
this mode may not be possible. For example, the
screening of molecules for HIV entry theoretically
should be done with live AIDS virus, but this is not
possible for safety and containment reasons. In this
case, a surrogate receptor probe, such as a radioactive
chemokine, must be used and this can lead to dissimilation in activity (i.e., molecules may modify the effects
of the chemokine but not HIV). This is discussed specifically in relation to screening in Chapter 11, The Drug
Discovery Process.
Another case is the potentiation of cholinergic signaling
for the treatment of patients with Alzheimer’s disease. It
has been proposed that a reduction in cholinergic function results in cognitive and memory impairment in this
disease [15,16]. As discussed previously, an allosteric
potentiation of cholinergic function could be beneficial
therapeutically, but it would have to be operative for the
natural neurotransmitterdin this case, ACh. This
agonist is unstable and difficult to use as a screening
tool and surrogate cholinergic agonists have been used
in drug discovery. However, effects on such surrogates
may have no therapeutic relevance if they do not translate to concomitant effects on the natural agonist. For
example, the cholinergic test agonist arecoline is potentiated 15-fold by the allosteric modulator eburnamonine
but no potentiation, in fact a threefold antagonism, is
239
observed with the natural agonist ACh [1]. Similarly,
the allosteric potentiating ligand LY2033298 causes
agonist-dependent differential potentiation of ACh and
oxotremorine [31]. Current data suggest that if the natural agonist (e.g., ACh) cannot be used in the screening
process, then the modulator must be tested early in the
development process to ensure beneficial effects with
the natural system. This also is relevant to targets
with multiple natural agonists such as glucagon-like
peptide 1 (GLP-1). Specifically, it has been shown
that the allosteric potentiation of GLP-1 effect by
NOVO2 produces a 25-fold potentiation of the minor
natural agonist for this receptor oxyntomodulin but
only a fivefold potentiation of the main natural agonist
GLP-1(7e36)NH2 [32].
Allosteric probe dependence can be an issue with antagonists as well in cases where a given modulator has differential blocking effects on different interactants with
the receptor. For instance, the chemokine receptor
CCR5 binds HIV-1 to mediate infection and CCR5 allosteric antagonists block this effect. However, it has been
shown that allosteric modulators have differing relative
potency as blockers of HIV entry and CCL3L1-induced
CCR5 internalization [33]. This could lead to preservation of natural CCR5 receptor internalization through
chemokine binding, an effect identified as being potentially favorable in progression to AIDS after HIV-1
infection [34]. This suggests that a superior allosteric
modulator would block the utilization of CCR5 by
HIV-1 but otherwise allow normal chemokine function
for this receptor [33]. Such effects underscore the
importance of probe dependence in the action of allosteric modulators.
9. Allosteric modulators can be used for target salvage:
Texture in antagonism can lead to a unique approach to
the therapeutic evaluation of biological targets. For
example, if a receptor is required for normal physiological function, then eliminating this target pharmacologically is prohibited. This can lead to the elimination of a
therapeutic opportunity if that same target is involved in
a pathological function. Such a case occurs for the chemokine X-type receptor CXCR4, since loss of normal
CXCR4 receptor function may be deleterious to normal
health. It specifically has been shown that deletion of
the genes known to mediate expression of the CXCR4
receptor or the natural agonist for CXCR4 (stromal
cellederived factor 1-a, SDF-1a) is lethal and leads
to developmental defects in the cerebellum, heart, and
gastrointestinal tract as well as hematopoiesis [35e37]
(i.e., this receptor is involved in normal physiological
function and interference with its normal function will
lead to serious effects). However, this receptor also mediates entry of the X4 strain of HIV virus, leading to
AIDS. Therefore, an allosteric modulator that could
240
A Pharmacology Primer
TABLE 8.2 Comparison of properties of orthosteric and allosteric ligands.
Orthosteric antagonists
Allosteric modulators
Orthosteric antagonists block all agonists with equal potency
Allosteric antagonists may block some agonists but not others
(at least as well)
There is a mandatory link between the duration of effect and the
intensity of effect
Duration and intensity of effect may be dissociated (i.e., duration can be prolonged through receptor compartment loading
with no target overdose)
High concentrations of antagonist block signals to basal levels
Receptor signaling can be modulated to a reduced (but not to
basal) level
Less propensity for receptor subtype effects
Greater potential for selectivity
No texture in effect (i.e., patterns of signaling may not be
preserved)
Effect is linked to receptor signal. Thus, complex physiological
patterns may be preserved
All antagonist-bound receptors are equal
Texture in antagonism where allosterically modified receptors
may have different conformations from each other may lead
to differences in resistance profiles with chronic treatment
discern between the binding of HIV and the natural
agonist for CXCR4 (SDF-1a) could be a very beneficial
drug. The probe-dependent aspect of allosteric mechanisms could still allow CXCR4 to be considered as a
therapeutic target in spite of its crucial role in normal
physiology. Suggestions of ligand-mediated divergence
of physiological activity and mediation of HIV entry
have been reported for CXCR4 in peptide agonists
such as peptide RSVMLSYRCPCRFFESH (RSVM)
and peptide ASLWLSYRCPCRFFESH (ASLW). These
peptides are not blocked by the CXCR4 antagonist
AMD3100, an otherwise potent antagonist of HIV entry, suggesting a dissociation of signaling and HIV
binding effects [38]. Similar dissociation between HIV
and chemokine activity also is observed with other peptide fragments of SDF-1a [39]. These data open the
possibility that allosteric molecules can be found that
block HIV entry but do not interfere with CXCR4mediated chemokine function.
From the point of view of agonist activation, allosteric
modulation can be thought of in terms of two separate effects. These effects may not be mutually exclusive and both
can be relevant. The first, and most easily depicted, is a
change in affinity of the receptor toward the agonist. The
most simple system consists of a receptor [R] binding to a
probe [A] (a probe being a molecule that can assess receptor
behavior; probes can be agonists or radioligands) and an
allosteric modulator [B] [40,41]:
The unique properties of allosteric modulators are
summarized in Table 8.2.
The equation for receptor occupancy for an agonist [A] in
the presence of an allosteric ligand [B] is given by (see
Section 8.7.1)
8.4 Functional study of allosteric
modulators
In essence, an allosteric ligand produces a different receptor if the tertiary conformation of the receptor is
changed through binding. These different tertiary conformations can have a wide range of effects on agonist
function. A different receptor conformation can change its
behavior toward G-proteins (and hence the cell and
stimuluseresponse mechanisms) or the agonist, or both.
Under these circumstances, there is a range of activities
that allosteric ligands can have on agonist doseeresponse
curves.
½AR
½A=KA ð1 þ a½B=KB Þ
;
¼
½A=KA ð1 þ a½B=KB Þ þ ½B=KB þ 1
Rtot
(8.1)
where KA and KB are the equilibrium dissociation constants
of the agonist and antagonist receptor complexes, respectively, and a is the cooperativity factor. Thus, a value for
a of 0.1 means that the allosteric antagonist causes a 10fold reduction in the affinity of the receptor for the agonist.
This can be seen from the relationship describing the affinity of the probe [A] for the receptor, in the presence of varying concentrations of antagonist:
Kobs ¼
KA ð½B=KB þ 1Þ
.
ð1 þ a½B=KB Þ
(8.2)
Allosteric modulation Chapter | 8
It can be seen that a feature of allosteric antagonists is
that their effect is saturable (i.e., a theoretically infinite
concentration of [B] will cause Kobs to reach a maximal
asymptote value of KA/a). This is in contrast to simple
competitive antagonists where the degree of antagonism is
theoretically infinite for an infinite concentration of antagonist. Therefore, the maximal change in affinity that can be
produced by the allosteric modulator is Kobs/KA¼KA/
aKA ¼ a1. Thus, a modulator with a ¼ 0.1 will reduce
the affinity of the receptor for the agonist by a maximal
value of 10.
As well as changing the affinity of the receptor for an
agonist, an allosteric effect could just as well change the
reactivity of the receptor to the agonist. This could be reflected in a complete range of receptor effects (response
production, internalization, desensitization, and so on).
This is depicted schematically in Fig. 8.8, where the
agonist-bound receptor goes on to interact with the cell in
accordance with the operational model for receptor function
[42]. Experimental data are fit to a mathematical model of
allosteric function, the most simple version being an
amalgam of the allosteric binding model [40,41] with the
BlackeLeff operational model for receptor function [43].
This leads to the following equation (see Section 8.9.2)
[25,43,44]:
Response ¼
sA ½A=KA ð1 þ ab½B=KB Þ þ sB ½B=KB
½A=KA ð1 þ a½B=KB Þ þ sA ð1 þ ab½B=KB ÞÞ
þ½B=KB ð1 þ sB Þ þ 1
(8.3)
where KA and KB are the equilibrium dissociation constants
for the agonistereceptor and modulatorereceptor complexes, respectively; sA and sB, the efficacies of the agonist
FIGURE 8.8 Parsimonious model for functional receptor allosterism
[43]. A tracer ligand [A] (agonist) binds to the receptor and the resulting
complex (ARE) can produce response. Similarly, the allosteric modulator
B can simultaneously bind to the receptor and produce response through
the complex BRE and can modify the agonist response through the species
ABRE. Binding to the receptor is described by the allosteric binding model
[40,41] and response is described by the BlackeLeff operational
model [42].
241
and modulator, respectively; a, the allosteric effect on affinity (on both the agonist and reciprocally on the modulator),
and b, the modification of the efficacy of the agonist produced by the modulator. Therefore, the minimal parameters
to fully characterize a modulator are KB, sB, a, and bdsee
Fig. 8.9. It will be seen that affinity of modulators is conditional and depends on the nature and concentration of the
cobinding ligand and also the magnitude of a and b.
The model described by Eq. (8.3) predicts virtually any
effect a modulator can have on the concentrationeresponse
curve to the agonist. If the modulator has no direct action
on the receptor (sB ¼ 0), then eight possible effects on
agonism can occur, resulting from combinations of an increase, no effect, or a decrease of affinity (a) and the same
possibilities with efficacy (b). These effects are shown in
Fig. 8.10. If the modulator has direct agonist activity (sB s
0), then there are nine further possible combinations (see
Fig. 8.11). As can be seen from Figs. 8.10 and 8.11, there
are basically 17 possible patterns that can be produced by
allosteric modulators [45].
As a preface to a discussion of various allosteric phenotypes, it is worth considering the general effects of
allosteric modification of affinity (a) and efficacy (b). Eq.
(8.3) predicts that even when the modulator reduces the
affinity of the receptor for the agonist (a < 1), the effects
will be surmountable with respect to the agonist (i.e., the
agonist will produce the control maximal response). This
can be seen from Eq. (8.3) when [A]/N and where
the maximal response therefore approaches unity. If the
signaling properties of the receptor are not altered by the
allosteric modulator, then the concentrationeresponse
curve to the agonist will be shifted either to the right (if
a < 1; see Fig. 8.12A) or to the left (a > 1; see Fig. 8.12B).
The distinctive feature of such an allosteric effect is that
FIGURE 8.9 Minimal parameters needed to characterize and quantify
receptor allosterism. Direct effects of the modulator are quantified by an
efficacy term sB through the BlackeLeff operational model while the
modification of the endogenous agonist effects are described by a,
the effect of the modulator on agonist affinity, and b, the effect of the
modulator on agonist efficacy.
242
A Pharmacology Primer
FIGURE 8.10 Effects of allosteric modulators with
various properties on agonist response as predicted by Eq.
(8.3) (sA ¼ 3, KA ¼ 10 mM, KB ¼ 10 nM, sB ¼ 0). Panels
from top row left to right (a ¼ 30, b ¼ 5), (a ¼ 1, b ¼ 5),
and (a ¼ 0.01, b ¼ 5); middle row left to right (a ¼ 30,
b ¼ 1), middle panel no curves since a ¼ b ¼ 1, then
(a ¼ 0.01, b ¼ 1); bottom row left to right (a ¼ 30,
b ¼ 0.3), (a ¼ 1, b ¼ 0.3), and (a ¼ 0.01, b ¼ 0.3).
FIGURE 8.11 Effects of allosteric modulators with
direct agonist efficacy and various properties on agonist
response as predicted by Eq. (8.3) (sA ¼ 3,
KA ¼ 10 mM, KB ¼ 10 nM, sB ¼ 0.25). Panels from
top row left to right (a ¼ 30, b ¼ 5), (a ¼ 1, b ¼ 5),
and (a ¼ 0.01, b ¼ 5); middle row left to right (a ¼ 30,
b ¼ 1), middle panel no curves since a ¼ b ¼ 1, then
(a ¼ 0.01, b ¼ 1); bottom row left to right (a ¼ 30,
b ¼ 0.3), (a ¼ 1, b ¼ 0.3), and (a ¼ 0.01, b ¼ 0.3).
while the displacements are parallel with no diminution of
maxima, there is a limiting value (equal to a1) to the
maximal displacement. Fig. 8.13A shows an experimentally observed allosteric displacement of ACh effects in
cardiac muscle by the allosteric modulator gallamine and
the saturable maximal effect (Fig. 8.13B) [46]. An example
of applying this type of analysis to NAM data is given in
Section 13.2.9.
8.4.1 Phenotypic allosteric modulation profiles
In practical terms, there are five phenotype allosteric profiles usually seen in discovery. These phenotypes emerge
because of various combinations of cooperativity with
respect to affinity (a) and efficacy (b) as well as direct
agonism (sB):
1. Negative allosteric modulators (NAMs): a < 1 and/or
b < 1. These ligands reduce the affinity and/or the efficacy of agonists (panel A in Fig. 8.14).
a. NAM-agonists: These are NAMs that also possess
intrinsic efficacy (sB) and thus produce response in
their own right (panel C in Fig. 8.14).
2. Positive allosteric modulators (PAMs): a > 1 and/or
b > 1: These ligands increase the affinity and/or the efficacy of agonists (panel B in Fig. 8.14).
a. PAM-agonists: These are PAMs that have intrinsic
efficacy (sB) and thus directly produce agonist
response (panel D in Fig. 8.14).
b. PAM-antagonists: These have a > 1 but b < 1 and
produce antagonism while increasing the affinity
of the agonist (i.e., ifenprodil [24])dpanel E in
Fig. 8.14.
Allosteric modulation Chapter | 8
243
FIGURE 8.12 Functional responses in the
presence of allosteric modulators as simulated
with Eq. (8.3) (s ¼ 30). (A) Allosteric antagonism. Agonist KA ¼ 0.3 mM, a ¼ 0.05,
and KB ¼ 1 mM. Curve farthest to the left is
control in absence of modulator. From left to
right, concentrations of modulator equal 3,
10, 30, and 100 mM. Arrow indicates effect of
modulator. Note the limited shift to the
right. (B) Allosteric potentiation. Agonist
KA ¼ 30 mM, a ¼ 10 mM, KB ¼ 3 mM.
Curve farthest to the right is control in
absence of modulator. From right to left,
concentrations of modulator equal 3, 10, 30,
and 100 mM. Arrow indicates effect of
modulator. Note the limited shift to the left.
FIGURE 8.13 Operational model fit of the
allosteric effects of gallamine on electrically
evoked contractions of guinea pig left
atrium. (A) Doseeresponse curves obtained
in the absence (filled circles) and presence
of gallamine 10 (open circles), 30 (filled
triangles), 100 (open triangles), 300 (filled
squares), and 500 mM (open squares). Data
fit to operational model (Eq. 8.4) with
KA ¼ 30 nM, Emax ¼ 200, s ¼ 1. Data fit
for gallamine KB ¼ 1 mM and a ¼ 0.0075.
(B) Ratio of observed EC50 values (EC0 50
for curve in presence of gallamine/EC50
control curve) as a function of concentrations of gallamine. Data fit to rectangular
hyperbola of max ¼ 134 (1/maximum ¼ a ¼ 0.0075). Data redrawn from A. Christopoulos, Overview of receptor allosterism, in S.J. Enna, M. Williams,
J.W. Ferkany, R.D. Porsolt, T.P. Kenakin, J.P. Sullivan (Eds.), Current Protocols in Pharmacology, vol. 1, John Wiley and Sons, New York, NY,
pp. 1.21.21e1.21.45.
As a preface for discussion of these allosteric phenotypes, it is useful to consider a property common to many
of them, namely, allosteric agonism.
8.4.2 Allosteric agonism
There is no a priori reason that allosteric agonism should
differ from conventional agonism (i.e., the modulator stabilizes an active state of the receptor to induce response);
this is underscored by setting [A]/0 in Eq. (8.3) and
seeing that it reduces to the standard BlackeLeff equation
for agonism for the modulator:
Response ¼
sB ½B=KB
½B=KB ð1 þ sB Þ þ 1
(8.4)
Under these circumstances, the efficacy of an allosteric
agonist (sB) can be quantified with the BlackeLeff model,
as for any agonist. However, what is different from
orthosteric agonism is the fact that the effect of the allosteric agonist on the endogenous agonist signaling can be
complex and very different from the standard antagonism
seen with orthosteric partial agonists. These effects depend
on the magnitude of a and bdsee Fig. 8.15.
The other relevant aspect of allosteric agonism is the
possibility that the allosteric agonist may produce biased
agonism (see Chapter 5: Agonists: The Measurement of
Affinity and Efficacy in Functional Assays, Section 5.7, for
further details). It is known that allosteric agonism can be
associated with biased agonism [47] (see Fig. 8.16);
therefore, this must be considered in the overall profile of
the allosteric modulator.
8.4.3 Affinity of allosteric modulators
A basic tenet of allosteric analysis is that the full activity of
an allosteric modulator cannot be assessed in isolation; by
definition, the properties of an allosteric modulator are
linked to the molecule cobinding to the receptor. Because
of this cooperative nature of allosteric modulators (i.e., their
activity is conditional upon the cobinding ligand), it is
244
A Pharmacology Primer
FIGURE 8.14 Phenotypic allosteric modulators. (A) NAMs reduce the sensitivity of the receptor to the agonist. (B) PAMs increase agonist sensitivity to
agonism. (C) NAM-agonists decrease receptor sensitivity to endogenous agonism but also directly activate the receptor to produce response. (D) PAMagonists increase receptor sensitivity to endogenous agonism and also have direct agonist action. (E) PAM-antagonists increase the binding of the agonist
to the receptor but preclude this binding from producing agonist response. NAM, negative allosteric modulator; PAM, positive allosteric modulator.
FIGURE 8.15 Effect of allosteric partial agonists on
endogenous agonist response. For molecules with
a > 1, sensitization concomitant with direct agonism is
observed (far left panel). Direct allosteric agonism with
no interference with endogenous agonism also can
occur (a ¼ 1, middle panel) as well as direct agonism
and decreased sensitivity to endogenous agonism
(a < 1)dfar right panel.
worth examining what is meant by the observed “affinity”
of an allosteric modulator. In terms of binding, radioligand
binding (as denoted by r*, the fraction of receptors bound
to a radioligand) is given by Eq. (4.10). This leads to an
equation for the ratio of the observed IC50 of a modulator
inhibiting radioligand binding to the KB for modulator of
IC50 ¼ KB
ð1 þ ð½A =Kd ÞÞ
ð1 þ að½A =Kd ÞÞ
(8.5)
where Kd and KB are the equilibrium dissociation constants
of the radioligandereceptor complex and modulatore
receptor complexes, respectively, and a is the effect of
the modulator on the affinity of the radioligand. It can be
seen from Eq. (8.5) that the observed affinity of an allosteric modulator (IC50) depends not only on the magnitude
of the KB but also on the nature (a) and concentration [A*]
of the cobinding ligand, in this case the radioligand.
Unlike orthosteric ligands, allosteric modulators have
the potential to increase radioligand binding (a > 1 for
PAMs) as well as decrease it (a < 1 for NAMs)dsee
Fig. 4.13. Fig. 8.17 shows the effect of various types of
allosteric modulators on radioligand binding (it is assumed
Allosteric modulation Chapter | 8
IC50 ð½A=KA Þð1 þ sA Þ þ 1
.
¼
ða½A=KA Þð1 þ bsA Þ
KB
FIGURE 8.16 Bias plot (see Section 5.7 of Chapter 5: Agonists: The
Measurement of Affinity and Efficacy in Functional Assays) for muscarinic agonism on m2 receptors. Ordinate values characterize G-protein
activation through [35S] GTPgS binding expressed as a function of
ERK1/2 activation for the same concentration of agonist. Allosteric agonists (open symbols) show a bias toward G-protein response while
muscarinic orthosteric agonists (filled symbols) have an opposite bias toward ERK1/2 signaling. Data redrawn from K.J. Gregory, N.E. Hall, A.B.
Tobin, P.M. Sexton, A. Christopoulos, Identification of orthosteric and
allosteric site mutations in M2 muscarinic acetylcholine receptors that
contribute to ligand-selective signaling bias, J. Biol. Chem. 285 (2010)
7459e7474.
FIGURE 8.17 Radioligand binding produced by a reference concentration of radioligand [A*] ¼ Kd. For a < 1, the affinity of the receptor is
reduced causing a concomitant reduction in the radioligand binding. No
effect on binding is produced with a ¼ 1 while an enhancement of binding
is seen for a > 1. Open circles show the half maximal concentrations for
the various curves. It can be seen that there is little effect on IC50 values
(concentration producing 50% inhibition of binding) for a values <1 while
dramatic effects are seen on EC50 values (concentrations for half maximal
radioligand binding) when a > 1.
that [A*]/Kd ¼ 1) where it can be seen that the IC50 (open
circles on curves) of NAM antagonists is relatively stable
while for PAMs the observed potency varies greatly with a.
An expression corresponding to the one for radioligand
binding (Eq. 8.5) for the effect of a modulator on agonist
function is
245
(8.6)
where the terms are as for Eq. (8.3). As with Eq. (8.5), the
observed functional affinity of the modulator is subject to
the magnitude of KB as well as the concentration of [A]
and the nature of the cobinding ligand as it modifies the agonist’s affinity (a) and efficacy (b).
At this point, it is important to differentiate NAMs from
PAMs in terms of affinity estimates. As seen in the binding
curves in Fig. 8.17, the EC50 estimates for NAMs are
uniform, i.e., they do not change with values of a. What
this means is the initial affinity of an NAM (i.e., the pKB)
does not change with a and b values and basically NAM
activity can be measured like that of any other antagonist.
However, this does not mean that the antagonist activity of
NAMs is identical to that of any orthosteric antagonist.
Specifically, the values of a and b determine the maximal
extent of antagonism. For example, for an NAM with
a ¼ 0.1, the maximal dextral displacement of an agonist
concentrationeresponse curve will be 10 irrespective of
how high a concentration is in the receptor compartment.
This is in contrast to an orthosteric antagonist which can
produce virtually limitless antagonism depending on the
concentration present. It also is important to consider the
interaction between antagonists and agonists when they are
together in the receptor compartment. For competitive antagonists, the presence of the agonist produces a diminution
in the observed effect of the antagonist (in terms of the
IC50, the concentration of antagonist producing 50%
diminution of agonist effect) since the two ligands have to
compete for the same binding site. This is made manifested
in the so-called ChengePrusoff linear relationship between
the IC50 of the antagonist and the concentration of agonist
presentdsee Fig. 4.8. Ostensibly, it might be supposed that
the presence of an agonist should have no effect on the IC50
of an NAM since they bind at separate sites on the receptor
protein. However, this is not the case since the binding of
both the agonist and NAM is related by the value of a, i.e.,
the NAM binds differently when an agonist is present. This
is shown graphically in Fig. 8.18 where it can be seen that
for NAMs, depending on values of a and b, NAMs
demonstrate a curvilinear type of “ChengePrusoff” relationship between the agonist concentration and antagonist
activity. This is due to the necessarily linked allosteric
energy between the orthosteric agonist binding site and
the allosteric site. Specifically, just as the NAM reduces the
affinity of the agonist for the receptor, so too does the
agonist reduces the affinity of the receptor for the NAM.
In contrast, the potency of PAMs is completely
dependent on the presence of the cobinding ligand (see
Fig. 8.17); this is due to the nature of the energy linkage
between the orthosteric agonist binding site and the PAM
246
A Pharmacology Primer
FIGURE 8.18 Relationship between the concentration of agonist in the receptor compartment and the observed antagonism for an orthosteric antagonist
(solid straight line) and two NAMs with values a ¼ 103 and a ¼ 103/b ¼ 104 (broken lines). It can be seen that as the concentration of agonist
increases, the observed antagonism of both types of antagonist decreases. NAM, negative allosteric modulator.
and the a term in Eq. (8.6). If a 1, as for NAMs, Eq.
(8.6) reduces to a form of the ChengePrusoff equation (see
Eq. 4.11 for binding) but has a little effect on the initial
affinity of the NAM. In contrast, when a[0 (as for a
PAM), then even the initial affinity of the PAM is greatly
affected by the presence of the agonist.
Fig. 8.18 shows the effect of either radioligand (for
binding) or agonist concentration (for function) on the
observed potency of a modulator. For this figure, standard
conditions for assessing antagonist activity were used.
Specifically, the level of agonist used for the IC50 experiment was one that gives 80% of the maximal response
(R ¼ 0.8), while the level of radioligand binding chosen
was [A*]/Kd ¼ 1 to yield 50% binding. It can be seen that
the effects of ligand cobinding (either agonist for function
or radioligand concentration for binding) is limited for
allosteric antagonists but can be very substantial for PAMs.
8.4.4 Negative allosteric modulators
NAMs are antagonists with specific properties. Although
their observed potency is conditional with respect to
FIGURE 8.19 Effect of varying diminutions of affinity
(panel A) or efficacy (panel B) for NAMs blocking agonist
response. Changes in affinity (a values) can only change the
location parameter of the agonist concentrationeresponse
curve, whereas changes in efficacy (b) can change both the
location parameter and the maximal response to the agonist.
NAM, negative allosteric modulator.
cobinding ligand, Eqs. (8.5) and (8.6) and Fig. 8.18 (for
a < 1) indicate that these effects are relatively limited (at
least when compared to PAMs). Antagonism can occur for
a values <1 and/or b values <1dsee Fig. 8.19. In cases
where the maximal response is not changed (b ¼ 1) and the
antagonist produces parallel shifts to the right of the
doseeresponse curve (due to a < 1) with no diminution of
the maximal response, the first approach used to quantify
potency might be a Schild analysis (see Chapter 7:
Orthosteric Drug Antagonism, Section 7.3.1). In cases
where the value of a is low (i.e., a ¼ 0.01), a 10-fold
concentration range of the antagonist would cause shifts
commensurate with those produced by a simple competitive antagonist. However, the testing of a wide range of
concentrations of an allosteric antagonist would show the
saturation of the allosteric binding site as revealed by an
approach to a maximal value for the antagonism. The
Schild equation for an allosteric antagonist is given by (see
Section 8.9.3)
½Bð1 aÞ
LogðDR 1Þ ¼ Log
.
(8.7)
a½B þ KB
Allosteric modulation Chapter | 8
247
binding to its own site on the receptor separate from that of
the agonist. This ambiguity underscores the failure of
observing patterns of concentrationeresponse curves to
determine molecular mechanism of action and how different
experimental approaches to discerning allosteric versus
orthosteric mechanisms are requireddsee Section 8.7.
Eq. (8.3) defines the allosteric noncompetitive antagonism of receptor function and predicts insurmountable effects on agonist maximal response (i.e., as [A] / N); the
expression for the maximal response is:
Maximal Response ¼
FIGURE 8.20 Schild regressions for allosteric antagonists of differing
values of a. Dotted line shows the expected Schild regression for a simple
competitive antagonist. With allosteric antagonists of lower values for a,
the regression reaches a plateau at higher antagonist concentrations (i.e.,
curvature occurs at higher antagonist concentrations).
Expected Schild regressions for allosteric antagonists
with a range of a values are shown in Fig. 8.20. It can be
seen that the magnitude of a is inversely proportional to the
ability of the allosteric antagonist to appear as a simple
competitive antagonist (i.e., the lower the value of a, the
more the antagonist will appear to be competitive). Examples of this type of analysis are given in Sections 13.2.9
and 13.2.13 of Chapter 13, Selected Pharmacological
Methods.
The foregoing discussion has been restricted to allosteric ligands that reduce the affinity of the receptor for the
agonist (i.e., allosteric antagonists or modulators). Since
allosteric change is the result of a conformational change in
the receptor, there is no a priori reason for allosterism to
produce only a reduced agonist affinity, and increases in the
affinity of the receptor for agonists (note the stimulation of
the binding of [3H]-atropine by alcuronium in Fig. 4.13)
have been documented. However, separate from ligand
binding, another possible allosteric effect is to render the
receptor insensitive to agonist stimulation (i.e., remove the
capacity for agonist response). This may or may not be
accompanied by a change in the affinity of the receptor for
the agonist and is simulated in Eq. (8.3) by setting b < 1.
In the special case where the modulator does not affect
the affinity of the receptor or the agonist (a ¼ 1) and where
b ¼ 0 (the modulator prevents receptor activation by the
agonist), Eq. (8.3) becomes identical to the one describing
orthosteric noncompetitive antagonism derived by Gaddum
et al. [48] (see Eq. 6.10). However, while the equation is
identical and the pattern of concentrationeresponse curves
is the same as that for an orthosteric antagonist, it should be
noted that the molecular mechanism is completely different,
whereas the system described by Gaddum et al. consists of
a slow offset antagonist occluding the agonist binding site,
the system described by Eq. (8.3) consists of the modulator
ð1 þ sÞ
.
ð1 þ s þ a½B=KB Þ
(8.8)
It can be seen that, just as in the case of orthosteric
noncompetitive antagonism for high-efficacy agonists or in
systems of high receptor density and/or very efficient receptor coupling (high s values, basically systems where
there is a receptor reserve for the agonist), the maximal
response may not be depressed until relatively high concentrations of antagonist are present. Under these circumstances, there may be dextral displacement with no
diminution of maximal response until fairly considerable
receptor antagonism is achieved (e.g., see Fig. 7.16B). The
difference between the orthosteric system described in
Chapter 6, Orthosteric Drug Antagonism, and the allosteric
system described here is that there can be an independent
effect on receptor affinity. No such effect is possible in an
orthosteric system. Fig. 8.21 shows concomitant effects on
receptor affinity for the agonist in allosteric noncompetitive
systems. Fig. 8.21A shows the effects of an allosteric
modulator that prevents agonist-receptor activation and also
decreases the affinity of the receptor for the agonist by a
factor of 20 (a ¼ 0.05). It can be seen from this figure that
the EC50 agonist concentrations shift to the right as the
maximal response to the agonist is depressed. An example
of a method to measure the affinity of a noncompetitive
antagonist with possible allosteric mechanism is given in
Section 13.2.10.
In contrast, Fig. 8.21B shows the effects of a modulator
that not only prevents agonist activation of the receptor but
also increases the affinity of the receptor for the agonist
(a ¼ 50). Here, it can be seen that as the maximal response
to the agonist is depressed by the modulator, the sensitivity
of the receptor to the agonist actually increases. It should be
noted that a shift of EC50 values to the left should not
automatically be expected when an allosteric modulator
increases the affinity of the receptor for the agonist. This is
because if there is a large receptor reserve in the system, the
EC50 will naturally shift to the right with noncompetitive
blockade. Therefore, what is observed is an average of the
effect shifting the curves to the right and the increased affinity shifting curves to the left. The example shown in
Fig. 8.21B was deliberately modeled in a system with little
248
A Pharmacology Primer
FIGURE 8.21 Effect of insurmountable
allosteric antagonists that block receptor
signaling to the agonist and also affect affinity of the receptor for the agonist. (A) Responses according to Eq. (8.3) with s ¼ 3,
KA ¼ 0.1 mM,
a ¼ 0.03 mM,
and
KB ¼ 1 mM. Curves from left to right: control
(no modulator present) and curves in the
presence of modulator concentrations 3, 10,
30, and 100 mM. Open circles show the EC50
of each concentrationeresponse curve (and
also the shift to the right of the location
parameter of each curve with increasing
modulator concentration). (B) Responses
with s ¼ 3 mM, KA ¼ 0.1 mM, a ¼ 50 mM, KB ¼ 1 mM. Curves from left to right: control (no modulator present) and curves in the presence of modulator
concentrations 20 nM, 50 nM, 0.2 mM, and 0.5 mM. Open circles show the EC50 of each concentrationeresponse curve. In this case, the modulator blocks
signaling but increases the affinity of the receptor to the agonist. Note also that lower concentrations of antagonist block responses (as compared to panel (A)).
FIGURE 8.22 Insurmountable allosteric
blockade of CCR5-mediated calcium transient responses produced by the chemokine
agonist RANTES by (A) Sch-C: control
(filled circles) and presence of Sch-C 10
(open circles) and 30 nM (filled triangles);
n ¼ 4. Data fit with Eq. (8.3), s ¼ 16, KA
RANTES ¼ 120 nM,
a ¼ 0.14,
and
KB ¼ 12.6 nM. (B) Blockade of RANTES
response with UK427,857 3 nM (open circles); n ¼ 4. Data fit with Eq. (8.6), s ¼ 16,
KA RANTES ¼ 140 nM, a ¼ 0.2, and
KB ¼ 2 nM. CCR5, chemokine C receptor
type 5. Redrawn from C. Watson, S. Jenkinson, W. Kazmierski, T.P. Kenakin, The
CCR5 receptor-based mechanism of action
of 873140, a potent allosteric noncompetitive HIV entry-inhibitor, Mol.
Pharmacol. 67 (2005) 1268e1282.
to no receptor reserve to illustrate the effect of allosterism
on the EC50 values. Fig. 8.22A shows the effect of the
allosteric modulator Sch-C on the responses of the CCR5
chemokine receptor to the chemokine RANTES, and
Fig. 8.22B shows the effect of the allosteric modulator
UK427,857. An example of the method to measure allosteric affinity with such a pattern of DR curves is given in
Section 13.2.14.
Since allosteric change is the result of a conformational
change in the receptor, there is no reason for allosterism to
produce only a reduced agonist affinity, and in fact such
changes can lead to increases in the affinity of the receptor
for the agonist (note the stimulation of the binding of [3H]atropine by alcuronium in Fig. 4.14). Various combinations
of a and b control both the location of the agonist
concentrationeresponse curve and the maximal response.
A special case of NAM action is where b < 1 and a > 1.
These ligands are PAM-antagonists since they sensitize the
receptor to agonism but preclude agonist function as well;
this leads to the profile shown in Fig. 8.23. These opposing
actions on affinity and efficacy underscore the allosteric
properties that determine the ultimate phenotype of the
modulator (i.e., NAM or PAM). Specifically, this is
determined by the ab product. Therefore, if the ab product
is <1, the overall profile is that of an NAM; if ab > 1, a
PAM. It follows that PAM-antagonists will functionally be
special types of NAMs if ab < 1. Worthy of note for PAMantagonists is the fact that their observed potency is
considerably greater than their binding KB (due to the
positive effect of high a valuesdsee Eq. 8.6). As noted
previously, this causes the EC50 of the agonist to actually
decrease instead of increase during the process of receptor
antagonism. In practical terms, this can lead to a favorable
profile, in that the potency of these antagonists increases as
the concentration of agonist increases; two examples of
these types of ligands are ifenprodil [24] and Org27569
[25]. Another profile possible is a reverse pattern of
sensitivity change to agonism, namely, a reduction of
Allosteric modulation Chapter | 8
FIGURE 8.23 Increased potency of a PAM-antagonist due to the presence of the agonist. The reciprocal effect of the agonist on the affinity of
the PAM causes antagonism to occur at concentrations of PAM much
lower than the binding KB. Open circles show the position of the EC50
values of the agonist. PAM, positive allosteric modulator.
produce IC50 curves that do not reach zero effect (see
Fig. 8.25 for agonist effect ¼ 0.8 and 0.95). These types
of curves are viewed as “displacement” curves for
orthosteric binding (i.e., the antagonist displaces the
agonist to induce antagonism), but this is not the case for
allosteric modulators. Rather, these ligands reset the affinity of the receptor for the agonist; therefore, the curve
does not reflect displacement but a newly adjusted binding
affinity.
In general, complete NAM activity can be quantified by
fitting agonist concentrationeresponse curves in the
absence and presence of a range of concentrations of
modulator to Eq. (8.3). It should be noted that only b effects will depress the maximal response; this is shown by a
metameter of Eq. (8.3) when [A] / N:
Maximal response ¼ sA ð1 þ ab½B=KB Þ=ð1 þ a½B=KB
þsA ð1 þ ab½B=KB ÞÞ
affinity (a < 1) but an increase in efficacy (b > 1): this
pattern is shown in Fig. 8.24A. Fig. 8.24B illustrates an
important feature of allosterism, namely, that allosteric effects are saturable. Thus, noncompetitive blockade is produced at a range of concentrations of NAM up to the point
where the allosteric binding sites are saturated; then
antagonism reaches a limiting value.
NAM activity can be rapidly quantified by testing a
range of modulator concentrations in a functional preparation preequilibrated with agonist (usually to an 80%
response level). This leads to the standard IC50 type of
profile yielding an inverted sigmoid concentratione
response curve to the modulatordsee Fig. 8.25. This
figure illustrates how the IC50 of an NAM can change with
the level of agonist stimulation, and also how the maximal
asymptote can be affected by the level of agonism (in
keeping with the saturability of allosteric effect). Thus, at
high levels of agonism with NAMs of limited a/b values
(i.e., 1<a < 20), the limited alteration of agonist affinity
can be overcome by high agonist concentrations to
249
(8.9)
where it can be shown that if there is no effect on efficacy
(b ¼ 1), then the maximal response according to Eq. (8.9)
in the presence of all concentrations of modulator will be
sA/(1 þ sA) which is the maximal response with no modulator present. Changes in a only affect the sensitivity along
the agonist concentration axis. In general, in order to differentiate a and b effects for an NAM, it is necessary to have
effects in a system where there is little to no receptor
reserve for the agonist. In such a system, b < 1 will result
in a depression of maximum where a < 1 will not. The
important data needed to characterize NAM activity are
KB, a, and b.
As with orthosteric partial agonists, allosteric ligands
can produce a direct agonist effect (quantified by sB) as
well as affecting the affinity (a) and/or efficacy (b) of other
agonists. If a < 1 and/or b < 1, a decreased sensitivity to
other agonists occurs and these will be NAM-agonists. In
general, as with all allosteric ligands, these ligands can be
characterized with KB, a, and b and additionally will have a
value for efficacy for direct agonism (sB). The effect on
FIGURE 8.24 Effect of an allosteric
modulator that changes both the affinity and
efficacy of the agonist for the receptor. (A)
Modulator increases the efficacy but decreases the affinity of the agonist for the
receptor. Responses modeled with Eq. (8.3)
with a ¼ 0.01, b ¼ 5, and s ¼ 1. Curves
shown for [B]/KB ¼ 0, 1, 3, 10, 30, and 100.
(B) Modulator decreases both the efficacy
and affinity of the agonist. However, the
decrease in efficacy is modest and a new
plateau of agonist is observed (response not
blocked to basal levels). Responses modeled
with Eq. (8.3) with a ¼ 0.3, x ¼ 0.5, and
s ¼ 1. Curves shown for [B]/KB ¼ 0, 1, 3,
10, 30, and 100.
250
A Pharmacology Primer
FIGURE 8.25 Effect of an NAM that reduces the affinity of the agonist
by a factor of 100 on various levels of preequilibrated response. Open
circles show the location parameter (IC50) of the inhibition curves. It can
be seen that with increasing levels of agonist (higher response) the curves
shift to the right and also fail to reach complete inhibition. NAM, negative
allosteric modulator.
endogenous agonist sensitivity can be variable depending
on the magnitude(s) of a and bdsee Fig. 8.15 (Fig. 8.26).
8.4.5 Positive allosteric modulators
Positive allosteric modulation of failing physiological systems can be a theoretically favorable therapy in cases where
a and/or b > 1 leads to sensitization to endogenous
signaling. At this point, it is important to distinguish between system maximal response and target maximal
response. Agonists can produce identical maximal responses in one of two ways: they could have identical efficacy values or they both may exceed the capability of
some step in the cellular stimuluseresponse cascade to
produce saturation of that step. When this occurs for highefficacy agonists, they will have the same observed
maximal response. Under these circumstances, increases in
efficacy (as would be produced by b > 1) will not be
FIGURE 8.26 Schematic diagram
showing the energetically compulsory relationship between agonist
and PAM binding and the possible
resulting effects on agonist concentrationeresponse curves. PAM, positive allosteric modulator.
registered as an increased observed maximal response but
rather as a shift to the left of the concentrationeresponse
curve with no change in maximumdsee Fig. 8.27. An
example of the application of this type of analysis is given
in Section 13.2.15.
An optimal assay system has the target maximal
response to be less than the system maximal response so
that positive b values would be differentiated from positive
a values. If such a system is not available, it may be
possible to create it by reducing the receptor density in the
functional assay to a point where the full agonist then
produces only partial agonism [49]. For example,
Fig. 8.28A shows the PAM effects of amiodarone on ACh
responses on muscarinic M3 receptors; a threefold sensitization of response is observed. Since it cannot be determined whether efficacy is altered by amiodarone (this
causes an increased maximal response of partial agonism),
all that can be determined from this graph is that the ab
product is approximately 3. However, a 98% reduction of
ACh receptors by alkylation with phenoxybenzamine
treatment (Fig. 8.28B) now makes ACh a partial agonist in
this preparation. Repeat treatment with amiodarone in this
assay (Fig. 8.28C) reveals that amiodarone does indeed
have an effect on efficacy (b ¼ 1.8); the ab product is the
same as that found in panel A [49].
Because the activity of allosteric modulators depends
upon cobinding ligands, many modulator assays are conducted in the presence of a low concentration of cobinding
ligand, i.e., agonist. In view of the known probe dependence of allosterism (i.e., a modulator can produce quite
different effects with different cobinding ligands), it is
essential that therapeutic modulators be tested with the
endogenous, naturally occurring agonist. The main assays
for PAM discovery and characterization involve the
assessment of agonist sensitivity; to do this, a probe concentration of agonist must be chosen to give the optimal
sensitivity to PAM activity. As shown in Fig. 8.29, a
concentration of agonist producing approximately 30%
maximum offers the largest window to see PAM effects.
Allosteric modulation Chapter | 8
251
FIGURE 8.27 Effects of PAMs on agonist
concentrationeresponse curves. (A) Increases in the affinity of the agonist
(a ¼ 20) can only affect the location of the
concentrationeresponse curves along the
concentration axis. Shifts are concentration
dependent until the allosteric site is
completely occupied where a maximal
asymptote for the potentiation is seen. (B)
Effect of a PAM that increases the efficacy
of the agonist (b ¼ 20). If the agonist is a
partial agonist, then the maximal response
will increase until either the agonist saturates a step in the system stimuluseresponse
cascade (and the system maximum is
attained) or the maximal effect of the PAM
on the receptor is obtained. In the example
shown, the latter mechanism is not the case since a further shift to the left of the concentrationeresponse curves is seen after the maximal response has
reached a limiting value. PAM, positive allosteric modulator.
FIGURE 8.28 Elucidation of separate a and b values for a full agonist. (A) Effect of 30 mM amiodarone on responses to acetylcholine for [3H]IP
metabolism mediated by muscarinic M3 receptors; responses in absence (filled circles) and presence (open circles) of amiodarone. (B) Effect of receptor
alkylation (POB 1 mM) on M3 responses to acetylcholine. Diminution of response corresponds to a 98% reduction in receptor number. Responses before
(filled circles) and after (open circles) treatment with POB. (C) Effect of 30 mM amiodarone on acetylcholine responses after POB treatment. Responses in
the absence (filled circles) and presence (open circles) of amiodarone. Note how the partial agonist character of acetylcholine now allows determination of
a unique b value and how the ab product still corresponds to the value in panel (A). POB, phenoxybenzamine. Redrawn from E. Stahl, G. Elmslie, J. Ellis,
Allosteric modulation of the M3 muscarinic receptor by amiodarone and N-ethylamiodarone: application of the four-ligand allosteric two-state model,
Mol. Pharmacol. 80 (2011) 378e388.
FIGURE 8.29 Optimal levels of agonist
response to view PAM effects. It can be
seen that for a PAM that produces a 20-fold
sensitization to the agonist (panel A), the
largest window to observe potentiation is
seen at preexisting agonist levels producing
30% (panel B); this window is not dependent upon the maximal effect of the PAM
but is true for all PAM effects. PAM, positive allosteric modulator.
252
A Pharmacology Primer
FIGURE 8.30 Potentiation of a preexisting agonist response level of
30% by various concentrations of a PAM that produces a maximal
sensitization of the agonist concentrationeresponse curve to the agonist of
20-fold. The curve to the right inset is the concentrationeresponse curve to
the PAM as it produces sensitization to the agonist. This curve is a rapidly
determined representation of the PAM effect with a location parameter
(termed the R50) reflecting KB, a, and b (see Eq. 8.12) and the maximal
response reflecting aspects of a and b. PAM, positive allosteric modulator.
At this point, it is worth considering an extremely useful
PAM assay, namely, the EC30-sensitization assay (also
referred to as the R50 assay, vide infra). Here, the PAM
effects are assessed by testing a range of modulator concentrations in a system with a preexisting EC30 response of
the agonist; increases in this activity reflect either direct
modulator agonism, or PAM activity, or bothdsee
Fig. 8.30. The EC30-PAM curve is very instructional as it
can quantify the potency and maximal effect of a PAM. An
equation for this curve can be derived to illustrate this.
First, the [A]/KA value for the level of basal agonism is
derived where R ¼ fraction of basal endogenous agonism.
The [A]/KA value is
f¼
R
sA ð1 RÞ R
(8.10)
Substituting [A]/KA for f, reformatting Eq. (8.3), and
solving for response in terms of [B] yield
Response ¼
½B=KB ðsB þ fsA abÞ
½B=KB ð1 þ sB þ fað1 þ sA bÞÞ þ fð1 þ sA Þ þ 1
(8.11)
Eq. 8.11can be used to calculate the response to the
agonist in the presence of a range of concentrations of
PAMs (where sB ¼ 0) or PAM-agonists (where sB s 0)
concentrations; a sigmoidal curve is predicteddsee
Fig. 8.31 for a PAM (sB ¼ 0). It can be seen from the
curves shown in Fig. 8.31 that the sensitivity and maximal
response to PAM activity increases with the magnitude of a
making the PAM-EC30 curve a useful index of PAM
activity.
The midpoint of the EC30-PAM curve (referred to as a
log value of pR50) is given by
pR50 ¼
KB ðfð1 þ sA Þ þ 1Þ
1 þ sB þ fað1 þ sA bÞ
(8.12)
FIGURE 8.31 PAM concentrationeresponse curves for potentiation of
agonist EC30 effects for PAMs of varying maximal effects on agonist affinity. Shown are curves (from minimum effect to maximum) of a ¼ 2, 3,
5, 10, and 20. The location parameter of the curves (AC50) reflects the
ability of the PAM to potentiate agonist response. PAM, positive allosteric
modulator.
It can be seen from Eq. 8.12 that the potency of a PAM
producing sensitization to the agonist in an EC30-PAM is
dependent upon a, b, and KB and thus gives a good first
estimate of PAM activity with a minimal array of concentrations. In addition, if it is known that the maximal effect
of the endogenous agonist is less than the system maximum
(i.e., a given target elevates cyclic AMP, and the maximal
stimulation of the target by a full agonist is below what the
assay yields for forskolin), then the effects of the PAM can
be tested on an EC100 concentration of agonist to determine
the possible effects of b elevation.
It is useful to discuss the pattern of effects seen with
PAMs possessing direct agonist activity (sB > 0; PAMagonists). In these cases, the potentiation of a full agonist
response can be quantified with an R50 curve (i.e.,
Fig. 8.30) and the direct agonism through fitting direct
response to the BlackeLeff operational model. The model
predicts that the potentiation curve will always lie to the left
of the direct agonism curve; this behavior is shown for the
muscarinic PAM-agonist 1-(4-methoxybenzyl)-4-oxo-1,4dihydroquinoline-3-carboxylic acid, Benzyl quinolone
carboxylic acid (BQCA) producing PAM-agonist effects
for IP-1 production through muscarinic receptors to ACh in
Fig. 8.32.
The equilibrium dissociation constant of the ligande
receptor complex (Kd) can be a very predictive parameter,
since it links the in vivo concentrations with what might be
expected pharmacodynamically at the receptor (when the
concentration is equal to Kd, then 50% of the receptors are
occupied by the ligand). The two types of drug where the
Kd cannot automatically be applied to the relationship between concentration and effect are
Allosteric modulation Chapter | 8
253
FIGURE 8.32 Effects of a PAM-agonist
BQCA on ACh-mediated responses of
muscarinic M1 receptors in CHO cells. (A)
Doseeresponse curves for ACh in absence
(filled circles) or presence of increasing concentrations of BQCA: 100 nM (open circles),
1 mM (filled triangles), 10 mM (open triangles), and 100 mM (filled diamonds). (B)
Sensitization (R50) curve shown in red and
direct agonist curve shown in blue (dotted
line). The sensitization curve lies to the left of
the direct agonist curve as predicted by the
functional allosteric model. PAM, positive
allosteric modulator; Ach, acetylcholine. S.
Bdioui S, J. Verdi J, N. Pierre N et al. Equilibrium Assays Are Required to Accurately
Characterize the Activity Profiles of Drugs
Modulating Gq-Protein-Coupled Receptors.
Mol Pharmacol. 94, 2018, 992e1006.
1. High efficacy full agonists since the efficacy of the
agonist can produce large sinistral displacement of
concentrationeresponse curves for function versus receptor occupancy.
2. PAMs where the affinity is conditional upon the cobinding ligand (usually the endogenous agonistdsee
Section 8.4.3).
The value of predictive parameters determined from
pharmacodynamic models is illustrated by the varied effects of a PAM-agonist shown in Fig. 8.33. It can be seen
that a concentration of PAM-agonist equal to the Kd value
can produce quite different observable profiles in tissues of
varying sensitivity to the endogenous agonist (as shown by
the changes in the receptor levels [Rt]). In tissues of low
sensitivity, little sensitization but an increased maximal
response is observed. In more sensitive tissues, increased
maximal response with increased sensitivity evolving to a
direct agonist effect is seen. In very sensitive tissues, no
further increase in maximal response is seen but powerful
agonism and sensitization are observed. The point of the
simulation is that these varied behaviors can all be predicted by a single set of molecular parameters, in this case a
low level of direct efficacy (3.3% of the endogenous
agonist) and an effect on affinity of a ¼ 5 and on efficacy
of b ¼ 5. This underscores the value of determining these
predictive parameters in test systems.
FIGURE 8.33 The effects of a PAM-agonist (a ¼ 5, b ¼ 5, KB ¼ 1 mM) in a low receptor density preparation (sA ¼ 1.0), and in functional assays with
increasing numbers of receptors (sA ¼ 10, sA ¼ 300). It can be seen that the pattern of effect changes from increased maxima and sinistral displacement
(sA ¼ 1.0), to only sinistral displacement (sA ¼ 10) to direct agonism and sinistral displacement (sA ¼ 300). All of these different patterns are accommodated by the single set of allosteric parameters. Curves in the absence (filled circles) and presence of the PAM-agonist 0.03 (open circles), 0.3 (filled
triangles), and 3 mM (open triangles). PAM, positive allosteric modulator.
254
A Pharmacology Primer
FIGURE 8.34 General scheme
for quantifying allosteric effects
to identify the five major allosteric phenotype molecules (see
Section 8.4.1). The major steps
include determination of a direct
agonist effect, identification of
effect on agonist response
(sensitization or antagonism), and
quantification of the maximal
parameters (a, b) and their relationship to the potency of the
modulator (KB). If the appropriate
system is available, determination
of the separate effects of the
modulator on affinity and efficacy
of the agonist can be done.
In general, a logical scheme for the assessment of
allosteric function can be derived which identifies the
important properties of potential allosteric modulators,
namely, a, b, KB, and sB. Assuming that the initial screen
for new molecules utilizes a functional system with a low
level of endogenous agonism present (i.e., a one-shot EC30
assay), Fig. 8.34 shows one example of a potentially useful
approach to the quantification of all allosteric modulator
activity.
8.4.6 Quantifying PAM activity in vivo
As noted previously, the potency of PAM is dependent
upon the concentration of the cobinding ligand making
estimations of PAM target coverage in vivo problematic
from simple affinity measurements such as KB. What is
required is the observed potency in the presence of the
physiological concentration of natural agonist in vivo and
this may not be obtainable. However, the R50 curve seen
in vivo can still be a way to compare PAMs in vivo if it is
assumed that each PAM binds in a compartment with a
constant concentration of natural agonist. This can be done
from the midpoint and maximal asymptote of the R50 curve
since this yields an useful parameter of PAM activity.
Specifically, it can be seen that the parameter max/R50
(where R50 is EC50 of the R50 curve) of this curve (see
Fig. 8.32B) furnishes a parameter of agonist potentiation
that, when used as a ratio, provides a system-independent
measure of the power of the PAMs involved to potentiate
agonist responsedsee Section 8.9.4 for derivation. Specifically, differences between Log(max/R50) values of R50
curves yield differences between the molecular systemindependent parameters describing PAM activity, namely,
a, b, and KB:
max
ab
DLog
¼ DLog
(8.13)
R50
KB
This parameter can be used to measure the relative effects of PAMs in vivo which can be useful because the
effective activity of PAMs is expressed only in the presence
of the natural agonist and the impact of this is relatively
unknown in vivo. Thus, pharmacological null experiments
comparing R50 curves in vivo can be used to compare
PAMs in a system independent manner by simply
comparing the effects of the PAMs on natural ambient
agonist activity in the in vivo systemdsee Fig. 8.35.
The accurate translation of concentrations from in vitro
to in vivo experiments must be assumed when comparing
in vitro to in vivo data. While the concentration of
endogenous agonist ceases to be an issue in the in vivo
comparison of PAM effects with Eq. 8.13, the actual
in vivo concentrations of PAM are still a critical factor.
This analysis can be used also to determine Absorption,
Distribution, Metabolism, Excretion (ADME) receptor
compartment concentrations of PAMs in vivo since the
DLog(max/R50) value depends on the same in vivo ADME
Allosteric modulation Chapter | 8
255
FIGURE 8.35 Comparison of R50
curves for two PAMs yielding a
DLog(max/R50) value of 0.8. This
number depends only on a, b, and
KB and therefore can be used as a
system-independent measure of
PAM activity. PAM, positive allosteric modulator.
FIGURE 8.36 Simulation of in vivo PAM data showing how the theoretically predicted DLog(max/R50) value (which predicts the curve labeled
PAM1) does not comply with the observed curve for PAM1. This suggests
a difference in receptor compartment concentrations perhaps through
ADME properties in vivo. Irregardless of the mechanism, these are useful
practical data to show the relative ineffectiveness of PAM1 in vivo. PAM,
positive allosteric modulator.
characteristics for the PAMs (an unlikely scenario).
Fig. 8.36 shows two Log(max/R50) curves for two theoretical PAMs; the data for PAM1 are shown with open
circles and for PAM2 with filled circles. The predicted
dotted line curve from in vitro analysis of these two PAMs
indicates that in vivo, PAM1 is considerably less potent
than expected. This suggests a difference in ADME properties resulting in a lower target coverage value.
8.4.7 NAM/PAM induced agonist bias
Since allosteric molecules are permissive (i.e., there is the
potential that the endogenous signal may still be physiologically present) there is always the possibility that the
modulator will affect the nature of the endogenous signal. In
cases where the endogenous signal involves the activation
of pleiotropic cellular signaling cascades, there is the possibility, just as with the production of biased agonism (see
Section 5.7) with direct allosteric agonists, that a modulator
will create bias in the endogenous agonist signal. This has
been shown for PAMs (NOVO potentiation of GLP-1 [32],
cinacalcet potentiation of calcium effects [50,51]) and
NAMs (LP1805 blockade of neurokinin A [52]; and
AMD3100 blockade of SDF-1a analogs [38], Indole1
blockade of PGD2 [53], mGlu5 receptor blockade by
M-5MPEP [54]).
For this reason, PAM and NAM effects must be verified
for the therapeutically relevant signaling pathway. This can
be quantified with simple assays basically measuring the
bias in the natural agonist to different signaling pathways
induced by the allosteric ligand. Essentially the allosteric
effect for each signaling pathway is quantified (determine
ab values for each pathway) and then the ratio taken for the
induced bias [55]dsee derivation Section 8.9.5. For
example, ogerin, the allosteric modulator for the hydrogen
sensing receptor GPR68, is a PAM for Gseproteinmediated signaling and an NAM for Gq-protein-mediated
signaling [56]; this leads to a 22-fold induced bias by
ogerin toward Gs proteindsee Fig. 8.37.
8.4.8 Optimal assays for allosteric function
There are some general predictions that can be made from
the models and equations utilized to describe allosteric
function. One is that the sA for the probe agonist is not
necessarily relevant, i.e., the maximal effect of PAMs and
NAMs will not be affected by the magnitude of the receptor
reserve of the probe agonist. However, using systems
where the probe agonist is a partial agonist (or at least
where the Em of the system is greater than the maximal
response of the receptor targetdsee Fig. 8.27) offers a
unique capability to differentiate b from a effects. This can
256
A Pharmacology Primer
FIGURE 8.37 Allosterically induced
bias. The effects of the allosteric GPR68
ligand ogerin on Gs and Gq responses to
hydrogen ion. Responses to hydrogen ion
in the absence (filled circles) and presence
(open circles) of ogerin (10 mM). For Gs,
ogerin is a PAM with an ab value of 12.
For Gq, ogerin is an NAM with an ab
value of 0.54. Ogerin thus produces a
22-fold induced bias toward Gs over Gq
signaling. PAM, positive allosteric modulator; NAM, negative allosteric modulator.
Data redrawn from X.-P. Huang, J. Karpiak, W.K. Kroeze, H. Zhu, X. Chen, S.S.
Moy et al., Allosteric ligands for the pharmacologically dark receptors GPR68 and
GPR65, Nature 527 (2015) 477e483.
FIGURE 8.38 General effects of different types of allosteric PAM effects on agonist response. PAM effects based on increased a (affinity) will
only make preexisting agonism occur at lower levels of stimulation but
will not increase maximal response; this will only be seen with changes in
b. PAM, positive allosteric modulator.
be useful, since the dependence of an allosteric activity on
a as opposed to b can be therapeutically relevant. For the
potentiation of failing physiological responses, it should be
noted that potentiation of agonism through increased affinity (a > 1) will only increase the sensitivity of the system to the existing level of endogenous agonism; if this is
too low to be of physiological significance to begin with,
then the modulator will not improve the situation. However, if efficacy is increased (b > 1), there is the potential to
create a signal where there was none and thus correct
pathologically low levels of endogenous signaling (see
Fig. 8.38). A method to change systems sensitivity to
obtain values of b is shown in Fig. 8.28 [49].
8.5 Functional allosteric model with
constitutive activity
The functional allosteric model resulting from the amalgam
of the StocktoneEhlert allosteric binding model [40,41]
and the BlackeLeff operational model [42] cannot
accommodate spontaneous constitutive receptor activity.
However, the extended ternary complex model [57] does
have this option with the coexisting active and inactive
receptor species. The incorporation of the extended ternary
complex model into the functional allosteric model
(Fig. 8.39A) provides a model that allows the receptor to
form a spontaneous active species ([Ra]), and bind to an
agonist and allosteric modulator simultaneouslydsee
Fig. 8.39B. Since the spontaneously formed receptor active
state can signal with no agonist present, the root efficacy for
the system is assigned to the active state receptor (denoted
sR) thus any modification of efficacy is produced by factors
of sR.
The parameters for the model shown in Fig. 8.39B are:
sR ¼ efficacy of spontaneously formed receptor activestate
a ¼ power of agonist [A] to promote the active state
(efficacy of A)/differential affinity of the agonist for
the active versus inactive receptor state
b ¼ effect of receptor state on the affinity of the
modulator
g ¼ power of agonist to promote agonist active state by
changing affinity of agonist for the receptor (conventional a in the functional allosteric model)
n ¼ conditional efficacy of the modulator with the
agonist bound to the inactive receptor state/augmentation of response from spontaneous active receptor state
and binding of modulator
L ¼ ability of the receptor to spontaneously produce the
active state (constitutive activity)
d ¼ tripartite effect of agonist and modulator on formation of the active state
f ¼ augmentation for production of agonism through
agonist binding (fsR ¼ sA, conventional agonist
efficacy)
s ¼ modification of agonist-mediated response through
species bound by modulator B (conventional b ¼ sfsR),
change in the spontaneously active state produced by
modulator
Allosteric modulation Chapter | 8
257
FIGURE 8.39 Schematic diagram of construction of
the functional allosteric model with constitutive receptor activity. (A) Three models make up the final product: the StocktoneEhlert allosteric binding model
(yellow surface), BlackeLeff operational model (pink
surface), and extended ternary complex model (blue
surface). (B) Explicit species of the model shown
interconnected with allosteric functions.
m ¼ augmentation of agonist response once agonist is
bound (component of conventional b in functional allosteric model)/effect of tripartite agonist, modulator, receptor complex on agonist efficacy
ε ¼ efficacy of the modulator for the inactive state
(sB ¼ εsR)
There are four types of parameter dictating model
behavior:
Response ¼
are bound to the receptor. As shown previously, system
parameters sR and L as well as agonist-specific parameters a and f change agonist response in this setting.
However, the new interactions seen when both ligands
are bound are shown by changes in g, s, m, and d.
The explicit equation describing response to an agonist
A in the presence of an allosteric modulator B in a system
with constitutively active receptors is given by:
½A=KA sA ðaLf þ g½B=KB ðεn þ aLbdamfÞÞ þ sR ½B=KB ðε þ bsLÞ þ LsR
½A=KA ð1 þ aL þ g½B=KB ð1 þ aLbdÞ þ sR ðg½B=KB ðεn þ aLbdamfÞ þ aLfÞÞ þ ½B=KB ð1 þ bL þ sR ðε þ bsLÞÞ þ Lð1 þ sR Þ þ 1
[8.13a]
(1) System parameters: The two parameters that control
the system sensitivity are L (the proclivity of the
receptor to spontaneously form the active state) and
sR, the intrinsic efficacy of the active state receptor to
produce response. Basal activity is modified by L and
basal activity and agonist response by changes in sR.
(2) Agonist parameters: The parameters that control
agonist response are: a and f (with agonist response
also modified by system parameters sR and L).
(3) Modulator parameters: In addition to the system parameters sR and L (not shown), direct modulator activity is modified by changes in b, s, and ε.
(4) Conditional “tripartite” parameters: These cause a
change when both agonist and modulator interact with
the receptor. Some parameters have no effect on individual responses to only agonist or only modulator
but do have an effect when both agonist and modulator
This model (derived in Section 8.9.6) thus allows for
elevated basal activity and inverse agonism in an allosteric
system (see Fig. 8.40). The pattern shown in Fig. 8.40
shows elevated basal activity due to constitutive receptor
activity (L ¼ 1), dextral displacement, and depressed
maximal agonist response by an NAM with concomitant
inverse agonism.
8.6 Internal checks for adherence to
the allosteric model
An important criterion for concluding mechanism from
verisimilitude to models is adherence to intrinsic internal
checks within the model that predict complex behaviors.
Fig. 8.41 shows the observed behavior of a PAM agonist in
systems of varying sensitivity. In very sensitive systems,
direct agonism is observed (Fig. 8.41B); in very insensitive
258
A Pharmacology Primer
FIGURE 8.40 Simulated effects of an NAM producing inverse agonism, dextral displacement of DR curves, and
depression of maximal response. Parameters for model: b < 1
(modulator has preferred affinity for Ri); d < 1 (modulator inhibits active state formation when agonist bound); s < 1
(modulator also negatively affects production of response
through agonist-bound active state receptor).
FIGURE 8.41 Effect of tissue sensitivity on a PAM-agonist. (A) Medium sensitivity shows sinistral displacement of the DR curve. (B) In a highly
sensitive tissue, the direct agonism is revealed. (C) In a tissue of low sensitivity where the agonist is no longer a full agonist but rather a partial agonist, the
effect on efficacy is revealed. Redrawn from S. Bdioui, J. Verdi, N. Pierre, E. Trinquet, T. Roux, T. Kenakin, The pharmacologic characterization of
allosteric molecules: Gq protein activation J. Recept. Signal Transd. 39 (2019) 106e113.
systems, effects on efficacy are revealed (Fig. 8.41C). This
type of behavior can be tested experimentally in tissues
where receptor number can be manipulated. One mechanism to do this is through controlled alkylation of receptors. As seen in Fig. 8.42, the dose response data for
BQCA potentiation of acetylcholine responses can be fit
with the functional allosteric model over a wide range of
system sensitivities. Specifically, in control cells, BQCA
produces sinistral displacement of curves and direct agonism (Fig. 8.42A). When receptors are alkylated with
Allosteric modulation Chapter | 8
259
FIGURE 8.42 Effects of the PAM agonist BQCA on
acetylcholine IP1 responses in CHO cell transfected
with muscarinic M1 receptors with alkylation by phenoxybenzamine (POB) to reduce the receptor number.
(A) BQCA produces direct agonist response and
sensitization of receptors to acetylcholine. Sensitization
observed in less sensitive tissues but no direct agonism
(panels B, C). When receptor density is low enough to
render acetylcholine a partial agonist BQCA reveals a
beta effect and increases maximal response. Redrawn
from S. Bdioui, J, Verdi, N. Pierre, E. Trinquet, T.
Roux, T. Kenakin, The pharmacologic characterization
of allosteric molecules: Gq protein activation, J.
Recept. Signal Transd. 39, 106e113.
phenoxybenzamine to reduce cell sensitivity, the BQCA
pattern changes to no agonism with only sinistral
displacement (Fig. 8.42B and C). Further decrease in
system sensitivity through phenoxybenzamine alkylation
causes acetylcholine to function as a partial agonist and
reveals the effects of BQCA on efficacy (Fig. 8.42D). So in
the case of BQCA, the internal check of having all data fit
to the model under varying circumstances is upheld thus
giving confidence that the model adequately describes
BQCA.
The BQCA data shown in Fig. 8.42 were generated in
an equilibrium assay, namely production of inositol phosphate due to Gq-protein activation by the muscarinic receptor [58]. This same pathway can also be monitored
through calcium in a calcium transient response assay
although this assay is a hemiequilibrium assay capturing
only the first few seconds of response. The functional
allosteric model Eq. (8.3) defines a rigorous relationship
between the concentration of allosteric modulator ([B]) and
the resulting maxima and location parameters (EC50 values)
of the concentration response curves. Complete agreement
to the predictions of the allosteric model is a required
prerequisite to the acceptance of an allosteric mechanism. A
corollary to this requirement is that the assay truly reflects
the effects of the ligands involved. Fig. 8.43 shows the
effect of the muscarinic receptor PAM-Agonist BQCA on
responses to ACh. A coaddition protocol where the BQCA
and ACh are added simultaneously was employed to yield
what appears to be a correct profile for PAM-Agonism (i.e.,
direct agonist effect and potentiation of ACh responsesd
see Fig. 8.15A). However, these data were obtained from a
calcium transient assay known to be in hemiequilibrium
and thus not to yield correct response patterns with respect
to real time (i.e., see Sections 7.2 and 7.5). Attempts to fit
the pattern of concentrationeresponse curves shown in
Fig. 8.43A to the functional allosteric model fail indicating
that, even though an observed pattern of curve seems to fit
the PAM-Agonist pattern, the data do not support an allosteric mechanism for BQCA [59]. When values of a, b, sB,
and KB were chosen to fit the response to one concentration
of BQCA, the prediction for the other concentration failed
to fit the prediction (Fig. 8.43B and C). In contrast, when an
equilibrium assay is used to measure the effects (i.e.,
inositol phosphate metabolism), the complete set of curves
fits to a uniform set of allosteric parameters (a ¼ 12, b ¼ 2,
sB ¼ 0.24sA, KB ¼ 5 mMdsee Fig. 8.42).
Another internal check for verisimilitude of data to
models is that the laws governing the model are adhered to.
For true allosteric effects to be the mechanism, then the
allosteric energy between the two binding sites must be
equal and the allosteric effect of one ligand on the other
described by reciprocally the same as the energy of the other
ligand on the original one. This is illustrated by the data
shown in Fig. 8.44. Specifically, AZ1729 (4-Fluoro-N-[3-[2[(aminoiminomethyl)amino]-4-methyl-5-thiazolyl]phenyl]
benzamide) and cmpd 58 ((S)-2-(4-chlorophenyl)-3,3dimethyl-N-(5-phe-nylthiazol-2-yl)butanamide) are allosteric modulators of the free fatty acid receptor 2 (FFAR2)
260
A Pharmacology Primer
FIGURE 8.43 Effects of a PAM-agonist BQCA on AChmediated responses of CHO cells transfected with M1 receptors employing the coaddition format (BQCA and ACh
added together). (A) Calcium assay; doseeresponses of
ACh in absence (filled circles) or presence of BQCA: 1 (red
open circles) and 10 mM (blue filled triangles). (B) Theoretically predicted effects of an agonist in presence of
increasing concentrations of PAM agonist with positive a
and b activity according to Eq. (8.3). Data for control curve
and curve in the presence of 10 mM BQCA are fit with parameters a ¼ 110, b ¼ 1.8, sB ¼ 0, KB ¼ 5 mM; calculated
curves with those parameters shown in dotted lines. These
parameters fit the curve for 10 mM BQCA but not 1 mM
BQCA. (C) Data for control curve and curve in the presence
of 1 mM BQCA are fit with parameters a ¼ 25, b ¼ 12,
sB ¼ 0.15 sA, KB ¼ 5 mM; calculated curves with those
parameters shown in dotted lines. Calculated curves fit for
1 mM BQCA but not for 10 mM BQCA. PAM, positive
allosteric modulator. S. Bdioui S, J. Verdi J, N. Pierre N,
et al., Equilibrium assays are required to accurately characterize the activity profiles of drugs modulating Gq-protein-coupled receptors. Mol. Pharmacol. 94
(2018) 992e1006.
FIGURE 8.44 Allosteric coreciprocal effects of AZ1729 and Cmp58 in neutrophils exposed to different concentrations of AZ1729 in presence of
Cmp58 in concentrations of from 10 to 1000 nM (panel A) or neutrophils exposed to concentrations of Cmp58 in presence of AZ1729 in concentrations
up to 1000 nM (panel B). Allosteric parameters for both sets of DR curves are consistent with the allosteric model. Redrawn from S. Lind, A. Holdfeldt, J.
Mårtensson, M. Sundqvist, TP. Kenakin, L. Björkman, H. Forsman, C. Dahlgren Interdependent allosteric free fatty acid receptor 2 modulators synergistically induce functional selective activation and desensitization in neutrophils Biochim Biophys Acta Mol. Cell Res. 1867 (6) (2020)118689.
that do not produce direct activation of the receptor.
However, they do reciprocally convert the other into a
powerful agonist when added together [60]. This system
gives a propitious opportunity to test the reciprocal allosteric energy internal check as the allosteric constants
describing the effects on AZ1729 by cmpd 58 and, separately, the allosteric constants governing the effects of
cmpd 58 on AZ1729. If true allostery determines this
interaction, then the a and b values for AZ1729 acting on
cmpd 58 should be the same as the a and b values for
cmpd 58 acting on AZ1729. As shown in Fig. 8.44, this
was shown to be the case thus confirming a true allosteric
interaction between these ligands.
8.7 Methods for detecting allosterism
Under certain conditions, allosteric modulators can behave
identically to orthosteric ligands. For example, a modulator
antagonist with a < 0.03 for a number of agonists produces apparent nonspecific simple competitive antagonism
within a limited concentration range. However, it can be
seen from Section 8.3 that allosteric modulators possess a
number of unique properties, making them different from
orthosteric ligands (see also Table 8.2). For this reason, it
is important to differentiate allosteric from orthosteric ligands. The major approaches to doing so involve the
properties of saturability of effect and probe dependence
Allosteric modulation Chapter | 8
for antagonists and loss of sensitivity to classical antagonists for agonists.
Beginning with agonists, the usual method of determining the identity of the biological target for an agonist is
to block the effect with antagonists for that same target
(receptor). However, if an agonist produces its effect
through binding to a site separate from the one bound by
the antagonist, the responses may not be sensitive to
antagonism. For example, the classical muscarinic receptor
agonist carbachol produces inhibition of cyclic AMP responses due to activation of muscarinic m2 receptors. The
effect is blocked by the classical muscarinic receptor
antagonist 3-Quinuclidinyl_benzilate (QNB) (Fig. 8.45A).
However, the muscarinic m2 allosteric agonist alcuronium
also activates the receptor but the effects are totally
impervious to QNB (Fig. 8.45B) [61]. In this circumstance,
the criterion of blockade by a classical receptor antagonist
is not met.
Modulators can be classified as potentiators of effect or
antagonists. If potentiation is observed, it is clearly an
allosteric effect, as orthosteric obfuscation of the agonist
binding site cannot lead to potentiation of agonism.
261
Antagonism can be unclear; therefore, the concepts of
saturability of effect and probe dependence may need to be
actively pursued to tease out allosteric mechanisms. If a
clear plateau of effect is observed, then allosterism is
implicated (see Fig. 8.25B). If an allosteric antagonism
does not interfere with receptor function, then surmountable antagonism will be observed [Eq. 8.3 when b ¼ 1]. A
limited Schild analysis may not detect the characteristic
curvilinearity of allosteric blockade (Fig. 8.20). Therefore,
detection of possible allosterism requires extension of
normal concentration ranges for testing of blockade (see
Fig. 8.46).
Differentiation of orthosterism and allosterism also
can be made by using different receptor probes. For
orthosteric antagonists, the choice of agonist is immaterial
(i.e., the same pKB will result). However, this is not true
of an allosteric effect where a and b values may be unique
for every receptor probe. This is a logical consequence of
the allosteric model in which it can be seen that mathematical terms exist containing the concentration of the
antagonist, the a and b values for allosterism, and the
concentration of agonist [[A]/KA sab[B]/KB term in both
FIGURE 8.45 Ligand-target validation.
Lack of sensitivity of putative agonist effect
to classical receptor antagonists. (A) Inhibition of cyclic AMP due to activation of
muscarinic m2 receptors by the classical
muscarinic agonist carbachol in the absence
(filled circles) and presence (open circles) of
the classical muscarinic antagonist QNB
present in a concentration that shifts the
agonist curve to the location shown by the
dotted line. This concentration of QNB
completely blocks the response. (B) Inhibition of cyclic AMP through activation of muscarinic m2 receptors by the allosteric agonist alcuronium in the
absence (filled circles) and presence (open circles) of the same concentration of QNB. In this case, the response is insensitive to this concentration of the
antagonist. Data redrawn from J. Jakubic, L. Bacakova, V. Lisá, E.E. El-Fakahany, S. Tucek, Activation of muscarinic acetylcholine receptors via their
allosteric binding sites, Proc. Natl. Acad. Sci. U.S.A. 93 (1996) 8705e8709.
FIGURE 8.46 Schild regression for allosteric modulator of
KB ¼ 200 nM that has a ¼ 0.03 for the agonist. It can be seen
that the regression is linear with unit slope at dose ratios <10.
However, extension of concentrations greater than 300 nM reveals saturation of the antagonism and a curvilinear portion of the
Schild regression (indicative of allosteric antagonism).
262
A Pharmacology Primer
FIGURE 8.47 Effects of aplaviroc, an
allosteric modulator of the CCR5 receptor,
on the binding of the chemokine 125I-MIP1a [panel (A)] and 125I-RANTES [panel
(B)]. It can be seen that aplaviroc blocks the
binding of MIP-1a but has very little effect
on the binding of RANTES. Such probe
dependence is indicative of allosteric effect.
CCR5, chemokine C receptor type 5. Data
from C. Watson, S. Jenkinson, W. Kazmierski, T.P. Kenakin, The CCR5 receptorbased mechanism of action of 873140,
a potent allosteric non-competitive HIV
entry-inhibitor, Mol. Pharmacol. 67 (2005)
1268e1282.
the numerator and denominator of Eq. (8.3)]. This allows
the magnitude of both a and b to moderate the degree of
antagonism. Since these constants are unique for every
receptor probe, then the antagonism may also depend on
the nature of the receptor probe (agonist). Fig. 8.47 shows
probe dependence on the CCR5 receptor with the allosteric modulator aplaviroc. It can be seen that the affinity
of 125I-MIP-1a is decreased considerably (a < 0.03)
while the affinity for 125I-RANTES is unchanged (a
estimated to be 0.8 [9]).
l
l
l
8.8 Chapter summary and conclusions
l
l
l
l
l
l
Allosteric modulators affect the interaction of the receptor and probe molecules (i.e., agonists or radioligands)
by binding to separate sites on the receptor. These effects are transmitted through changes in the receptor
protein.
Allosteric modulators possess properties different from
orthosteric ligands. Specifically, allosteric effects are
saturable and probe dependent (i.e., the modulator
may produce different effects for different probes).
Saturation occurs because allosteric effects reach an
asymptote when the allosteric site is fully occupied.
For this reason full shift assays are required to determine the maximal values of a and/or b.
Allosteric effects can result in changes in affinity and/or
efficacy of agonists.
Sole effects on affinity (with no change in receptor
function) result in surmountable antagonism. The
dextral displacement reaches a maximal value leading
to a curvilinear Schild regression.
Allosteric modulators that block receptor function can
produce insurmountable antagonism. In addition, modulators that block function also can alter (increase or
decrease) affinity.
Allosteric modulators can also potentiate agonist
response (PAMs); this can result in a shift in the agonist
l
concentrationeresponse curve through increased affinity or increased agonist efficacy.
Direct allosteric agonism can be quantified with the
BlackeLeff operational model and possible signaling
bias should be explored.
The observed potency of antagonists is modified by
cobinding ligand activity to only a modest extent and
thus observed KB values in functional or even binding
assays are reasonable estimates of antagonist potency;
this is not the case with PAMs.
PAM effects through alteration of affinity (a) and efficacy (b) differ physiologically and this may be relevant
to target therapeutic value.
Both PAMs and NAMs may alter the quality of the
endogenous signal by inducing bias; therefore, therapeutic relevance of the effect should be verified.
8.9 Derivations
l
l
l
l
l
l
Allosteric model of receptor activity (Section 8.9.1).
Effects of allosteric ligands on response: changing efficacy (Section 8.9.2).
Schild analysis for allosteric antagonists (Section 8.9.3).
Application of Log(max/R50) values from R50 curves to
quantify the effects of PAMs (Section 7.7.4).
Quantifying allosterically mediated induced bias in agonism (Section 8.9.5).
Functional allosteric model with constitutive receptor
activity (Section 8.9.6).
8.9.1 Allosteric model of receptor activity
Consider two ligands ([A] and [B]), each with its own
binding site on the receptor with equilibrium association
constants for receptor complexes of Ka and Kb, respectively. The binding of either ligand to the receptor modifies
the affinity of the receptor for the other ligand by a factor a.
There can be three ligand-bound receptor species, namely,
[AR], [BR], and [ARB].
Allosteric modulation Chapter | 8
The resulting equilibrium equations are
The receptor conservation equation for total receptor
[Rt] is
Ka ¼
½AR
;
½A½R
(8.14)
Kb ¼
½BR
;
½B½R
(8.15)
aK ¼
½ARB
;
½BR½A
aKb ¼
and
½ARB
.
½AR½B
(8.16)
(8.17)
Solving for the agonist-bound receptor species [AR]
and [ARB] as a function of the total receptor species
([Rtot] ¼ [R]þ[AR]þ[BR]þ[ARB]) yields
½AR þ ½ARB
ð1=a½BKb Þ þ 1
.
¼
Rtot
ð1=a½BKb Þ þ ð1=aKa Þ þ ð1=a½AKa Kb Þ þ 1
(8.18)
Simplifying and changing association to dissociation
constants (i.e., KA ¼ 1/Ka) yields
r¼
½A=KA ð1 þ a½B=KB Þ
.
½A=KA ð1 þ a½B=KB Þ þ ½B=KB þ 1
(8.19)
8.9.2 Effects of allosteric ligands on response:
changing efficacy
The receptor can bind both the probe (agonist, radioligand,
[A]) and allosteric modulator ([B]). The agonist-bound receptor signal through the normal operational model ([AR]
complex interacting with cellular stimuluseresponse machinery with association constant Ke) and in a possibly
different manner when the allosteric modulator is bound
Response ¼
½ABR
;
a½BKb
½ABR
½BR ¼
;
a½AKa
½R ¼
½Rt ¼ ½R þ ½AR þ ½BR þ ½ABR
and
½ABR
:
a½BKb ½BKb
(8.20)
rA=B=AB ¼
½A=KA þ ½B=KB þ a½A=KA ½B=KB
(8.24)
½A=KA ð1 þ a½B=KB Þ þ ½B=KB þ 1
where KA ¼ 1/Ka and KB ¼ 1/Kb.
According to the operational model, response is given
by the fractional receptor species interacting with a common pool of cellular effector (maximal effector ¼ Em):
½AR=KE þ ½BRK00E þ ½ABR=K0E Em
Response ¼
½AR=KE þ ½BRK00E þ ½ABR=K0E þ 1
(8.25)
where KE, K0E , and K00E are the operational equilibrium
dissociation constants of the receptor speciesecellular
effector complexes.
The actual amount of receptor species (e.g., [AR]) is
given by the fraction of receptor species multiplied by the
total number of receptors (rA ¼ [AR]/[Rt]) and defines the
fractional response (rRes) as
rA ½Rt =KE þ rB ½Rt =KE00 = þ rAB ½Rt =KE0
(8.26)
rA ½Rt =KE þ rB ½Rt =KE00 þ rAB ½Rt =KE0 þ 1
Defining sA as [Rt]/KE, sB as ½Rt K00E , and sAB as
½Rt K00E allows expression of Eqs. (8.25) and (8.26) as
rRes ¼
rRes ¼
rA sA þ rB sB þ rAB sAB
rA sA þ rB sB þ rAB sAB þ 1
(8.22)
(8.27)
Further defining sAB/sA as b yields
(8.28)
8.9.3 Schild analysis for allosteric antagonists
From Eq. (8.3), the observed EC50 for the agonist, in the
presence of a concentration of allosteric antagonist [B], is
given by
EC050 ¼
(8.21)
(8.23)
The potential response producing species are [AR],
[BR], and [ABR]; therefore, the fraction of receptors that
may produce response is given by
sA ½A=KA ð1 þ ab½B=KB Þ þ sB ½B=KB
½A=KA ð1 þ a½B=KB þ sA ð1 þ ab½B=KB ÞÞ þ ½B=KB ð1 þ sB Þ þ 1
(complex [ABR] interacting with cell with association
constant K0E ).
The equilibrium species are
½AR ¼
263
EC50 ð½B=KB þ 1Þ
;
ð1 þ a½B=KB Þ
(8.29)
where EC50 refers to the EC50 of the control
concentrationeresponse curve in the absence of modulator.
The ratio of the EC50 values (concentrations of agonist producing 50% response in the presence and absence of the
allosteric antagonist) is given by
264
A Pharmacology Primer
EC050
ð½B=KB þ 1Þ
.
¼ DR ¼
ð1 þ a½B=KB Þ
EC50
(8.30)
This leads to the logarithmic metameter form of the
Schild equation:
½Bð1 aÞ
LogðDR 1Þ ¼ Log
.
(8.31)
a½B þ KB
8.9.4 Application of Log(Max/R50) values from
R50 curves to quantify the effects of PAMs
PAM specific
System specific
max
ab
sA ½A=KA
¼
R50
KB ð½A=KA ð1 þ bsA ÞÞ þ 1
(8.37)
Therefore, ratios of max/R50 values can provide systemindependent estimates of the relative activity of PAMs in
potentiating agonist response:
max
ab
ab
DLog
¼ Log
e Log
(8.38)
R50 AB
KB A
KB B
The model for allosteric effects in functional systems defines agonist response as [25,43,44]
Response ¼
sA ½A=KA ð1 þ ab½B=KB Þ
½A=KA ð1 þ a½B=KB þ sA ð1 þ ab½B=KB ÞÞ þ ½B=KB þ 1
where a is the effect of the modulator ([B]) on the affinity
of the agonist for the receptor and b is the effect of the
modulator on the efficacy of the agonist. This equation
can be rewritten in terms of the modulator as the active
species to
Response ¼
max ¼
absA ½A=KA
ð1 þ a½A=KA ð1 þ bsA ÞÞ
(8.34)
and the half maximal effect of the R50 curve (defined as the
R50)
R50 ¼
8.9.5 Quantifying allosterically mediated
induced bias in agonism
In terms of the BlackeLeff operational mode [42], the
transduction coefficient [62] for agonism is given as
absA ½B=KB ð½A=KA Þ þ sA ð½A=KA Þ
½B=KB ð1 þ a½A=KA ð1 þ bsA ÞÞ þ ½A=KA ð1 þ sA Þ þ 1
The R50 curve for a potentiating modulator (PAM)
increasing the effect of an ambient agonist response due to
a presence of agonist acting on the receptor (in the form of
[A]/KA) requires a value for max; this is given as
KB ð½A=KA ð1 þ sA Þ þ 1Þ
ð1 þ a½A=KA ð1 þ bsA ÞÞ
(8.35)
This leads to the ratio of max/R50 as
max
absA ½A=KA
¼
R50
KB ð½A=KA ð1 þ bsA ÞÞ þ 1
(8.36)
which is a mixture of tissue-specific and agonist-specific
factors:
(8.32)
(8.33)
Log(s/KA). In the presence of a saturating concentration of
a PAM [B], the response to the agonist is given as
Response01 ¼
½Ab1 sA1
½Að1 þ b1 sA1 Þ þ KA1 =a1
(8.39)
where the efficacy of the agonist [A] is bsA1 and the affinity
of agonist [A] for the receptor is aKA1. Therefore, the transduction coefficient of the agonist in the presence of the allosteric modulator is Log(a1b1sA/KA1). Therefore, the
logarithm of the ratio of transducer coefficient values in
the absence and presence of the modulator is given as
modulator
sA1
DLog
¼ Logða1 b1 Þ
(8.40)
KA1
This is repeated for another signaling pathway (designated pathway 2) to yield
modulator
sA2
DLog
¼ Logða2 b2 Þ
(8.41)
KA2
Allosteric modulation Chapter | 8
The logarithm of the induced bias is given as the difference of the Log(ab) values as
Log½Induced Bias ¼ Logða1 b1 Þ Logða2 b2 Þ ¼ DLogðabÞ
(8.42)
Leading to the induced bias as
Induced Bias ¼ 10DLogðabÞ
(8.43)
8.9.6 Functional allosteric model with
constitutive receptor activity
The receptor species, defined in terms of the most complex
species [ARaB], are given by
½ARiB ¼ ½ARaB=dabL
(8.44)
½RaB ¼ ½ARaB=dag½AKa
(8.45)
½Ra ¼ ½ARaB=bdag½AKa ½BKb
(8.46)
½Ri ¼ ½ARaB=Lbdag½AKa ½BKb
(8.47)
½RiB ¼ ½ARaB=gdabL½AKa
(8.48)
defined as some fraction or multiple of the intrinsic efficacy
of the active state receptor defined as sR ¼ [Rt]/KE where
KE ¼ 1/Ke. For example, the response emanating from the
[Ra] species is given by rRAsR where rRA is the fraction of
receptors in the Ra state.
The explicit expressions for calculation of the various
receptor species are obtained by multiplying the expressions by abgdL[A]Ka[B]Kb and converting Ka ¼ KA and
K b ¼ K B:
½Ri ¼ 1
(8.52)
½Ri ¼ L
(8.53)
½ARi ¼ ½AKA
(8.54)
½ARa ¼ aL½A=KA
(8.55)
½RiB ¼ ½BKB
(8.56)
½RaB ¼ bL½B=KB
(8.57)
½ARiB ¼ g½A=KA ½B=KB
(8.58)
½ARaB ¼ abdgL½A=KA ½B=KB
(8.59)
The receptor conservation equation then becomes:
½Rt ¼ ½A=KA ð1 þ aL þ g½B = KBð1 þ abdLÞÞ þ ½B=KBð1 þ bLÞ þ L þ 1
½ARa ¼ ½ARaB=bdg½BKb
(8.49)
½ARi ¼ ½ARaB=dgabL½BKb
(8.50)
The receptor species, defined in terms of the most
complex species [ARaB], are given by the receptor conservation equation which is:
½Rt ¼ ½ARaB þ ½ARiB þ ½RaB þ ½RiB þ ½ARa
þ ½ARi þ ½Ra þ ½Ri
(8.51)
Coding for the operational model requires expression of
each receptor species as a fraction of [Rt] and then multiplying by an efficacy factor. For this model, efficacy is
Response ¼
265
(8.60)
Considering activation through the BlackeLeff model
(production of E species), the response producing receptor
species are given by
½RiBE ¼ εsR ½B=KB
(8.61)
½ARiBE ¼ gεn½A=KA ½B=KB
(8.62)
½RaE ¼ LsR
(8.63)
½RABE ¼ LbssR ½B=KB
(8.64)
½ARE ¼ afLsR ½A=KA
(8.65)
½ARaBE ¼ abdgsmfL½A=KA ½B=KB
(8.66)
½A=KA sR ðaLf þ g½B=KB ðεn þ aLbdsmfÞÞ þ sR ½B=KB ðε þ bsLÞ þ LsR
½A=KA ð1 þ aL þ g½B=KB ð1 þ aLbdÞ þ sR ðg½B=KB ðεn þ aLbdsmfÞ þ aLfÞÞ þ ½B=KB ð1 þ bL þ sR ðε þ bsLÞÞ þ Lð1 þ sR Þ þ 1
(8.67)
266
A Pharmacology Primer
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Chapter 9
The optimal design of pharmacological
experiments
We become what we behold. We shape our tools and then
our tools shape us.
Marshall McLuhan (1911e1980).
No amount of experimentation can ever prove me right; a
single experiment can prove me wrong.
Albert Einstein (1879e1955).
. The prismatic qualities of the assay distort our view in
obscure ways and degrees .
James W. Black (1924e2010), Nobel Lectures: Physiology and
Medicine.
9.1 Introduction
Pharmacology is unique in that it encompasses the methodology to convert descriptive data on drug effect (observed
potency and activity in a given system) to predictive data
(parameters that can be used to predict drug activity in all
systems). This is done through a combination of the application of null experiments and the comparison of data to
mathematical models. There are pharmacological tools and
techniques designed to determine system-independent measures of the potency and efficacy of drugs; however, in order
to apply them effectively, the molecular mechanism of the
drug must be known beforehand. In new drug discovery, this
is seldom the case, and in fact the observed profile of the
molecules must be used to discern their molecular mechanism. In this setting, it is not always possible to apply the
correct technique or model for quantification of drug activity,
and the tool chosen for analysis is based on initial observation
of drug activity, that is, the process is data driven. In practical
terms, a wide range of potential drug behaviors can be
described by a limited number of molecular models, and it is
useful to describe these and their application in the drug
discovery process. In general, drugs can be divided into two
initial types: those that do and those that do not initiate a
directly observable pharmacological response in the tissue.
A Pharmacology Primer. https://doi.org/10.1016/B978-0-323-99289-3.00014-2
Copyright © 2022 Elsevier Inc. All rights reserved.
9.2 The optimal design of
pharmacological experiments
As discussed in Chapter 1, What Is Pharmacology?, pharmacology is a unique discipline, in that it can interpret the
behavior of molecules in different physiological systems in
terms of the molecular properties of those molecules. This
process can be divided into four parts:
1. Defining the experiment: The main objective of pharmacological experiments is to quantify the molecular
properties of drugs in a system-independent manner to
in turn derive parameters that can be used to predict
drug activity in all systems. The four minimal properties
that allow characterization of all pharmacodynamic activities are [1]:
a. Drug efficacy (or efficacies): The property of the
molecule that causes the pharmacological target to
change its behavior toward the cell.
b. Drug affinity: The concentrations at which the molecule binds to and stays associated with the target.
c. Whether the molecule interacts with the target in an
orthosteric (same binding site as the endogenous
activator of the target) or allosteric (separate site)
manner.
d. Dissociation kinetics of the molecule to determine
target coverage in open systems (i.e., in vivo).
2. Conducting the experiment: The application of null
methods to isolate characteristic drug properties, as
well as the comparison of data to pharmacological
models to determine mechanism of action and systemindependent parameters of drug activity.
3. Interpretation of experimental data: How do we
gauge progress in terms of improvement of drug activity
in the drug discovery and development process?
4. Predicting drug activity in all (including the therapeutic) systems: How do we apply the parameters
quantifying drug activity to in vivo therapeutic systems
to predict useful activity?
269
270
A Pharmacology Primer
The first of these points to be discussed is the aim of the
pharmacological experiment, namely, the determination of
parameters that can characterize drug activity in molecular
terms.
9.2.1 Drug efficacy
The first observable effect of a drug in a biological preparation is the initiation of some pharmacological effect
(referred to as response). If this is seen, then it must be
determined that it is specific for the biological target of
interest (i.e., not a general nonspecific stimulation of the
cell) and that a concentrationeresponse relationship can be
determined. Once activity for a given molecule has been
confirmed by retest at a single concentration, a dosee
response curve for the effect must be determined; the biological effect must be related to the concentration in a
predictive manner.
A frequently asked question at this point is, does the
array of responses for given concentrations represent a true
doseeresponse relationship, or just random noise around a
given mean value? It is useful to demonstrate approaches to
this question with an example. Assume that a compound is
tested in doseeresponse mode, and 11 “responses” are
obtained for 11 concentrations of compound giving a
maximal ordinal response of 7.45%. On the one hand, it
might not be expected that noise could present a sigmoid
pattern indicative of a concentrationeresponse curve
(although such patterns might be associated with location
on plates or counters). However, a maximal ordinate
response of 7.45% also is extremely low. A useful rule of
thumb is to set the criterion of >3s (where s is the standard error of the mean) of basal noise responses as the
definition of a real effect. In this case, the signal from 1325
wells (for the experiment run that same day; historical data
should not be used) obtained in the presence of the lowest
concentration of compound (10 mM, assumed to be equivalent to basal response) yielded a mean percent response of
0.151% with a standard deviation of 1.86%. Under these
circumstances, 3s ¼ 5.58%. With this criterion, the
response to the agonist would qualify as a signal above
noise levels.
A pharmacological method for determining whether a
very low level of response constitutes a real doseeresponse
curve is to use a maximal concentration of the “very weak
partial agonist” to block responses to a standard full
agonist. The basis for this method is the premise that the
EC50 of a weak partial agonist closely approximates its
affinity for the receptor. For example, assume that a fit to
the data points shows a partial agonist to have a maximal
response value of 8% and EC50 of 3 mM. Under these circumstances, the doseeresponse curve to the standard
agonist would be shifted 10-fold to the right by 30 mM of
the weak partial agonist. This could indicate that the 8%
represents a true response to the compound. Also, it could
furnish a lead antagonist series for the screening program.
However, this method requires considerable follow-up
work for each compound.
Another method of detecting a doseeresponse relationship is to fit the data to various models for dosee
response curves. This method statistically determines
whether or not a doseeresponse model (such as a logistic
function) fits the data points more accurately than simply
the mean of the values; this method is described fully in
Appendix: Statistics and Experimental Design. The
simplest approach would be to assume no doseeresponse
relationship and to calculate the mean of the ordinate data
as the response for each concentration of ligand (horizontal
straight line parallel to the abscissal axis). A more complex
model would be to fit the data to a sigmoidal dosee
response function. A sum of squares can be calculated for
the simple model (response mean of all response) and
then for a fit of the data set refit to the four parameter logistic shown previously. A value for the F statistic can then
be calculated, which determines whether there is a statistical basis for assuming there is a doseeresponse relationship. An example of this procedure is given in Appendix:
Statistics and Experimental Design (see Fig. A.13). The
remainder of this discussion assumes that it has been
determined that the drug in question produces a selective
pharmacological response in a biological preparation that
can be defined by a concentrationeresponse curve, that is,
it is an agonist. Once a target-related agonism has been
determined, then this activity must be quantified and a
structureeactivity relationship (SAR) for that activity
determined.
A first step in this process is to compare the maximal
response to the test agonist with the maximal response
capability of the biological preparation. If there is no statistical difference between the maximal response of the
agonist and to the maximal response of the tissue, then the
drug is a full agonist. If the magnitude of the maximal
response to the agonist is lower than that of the tissue, then
the drug is a partial agonist. There is separate information
that can be gained from either of these two categories of
agonist, as discussed in Chapter 6, Agonists: The Measurement of Affinity and Efficacy in Functional Assays.
It is useful to redefine what is meant by “efficacy.” In
light of the fact that receptors themselves can spontaneously form active states that impart a cellular response (see
Chapter 3, DrugeReceptor Theory, Section 3.10), it is
insufficient to label efficacy as the excitation of receptors to
produce a response. Rather, efficacy is better defined as the
property of a molecule that causes the target (receptor) to
change its behavior toward the cell when the molecule is
bound; this includes negative efficacy as would be observed
in an inverse agonist that reverses constitutive receptor
activity. Historically, definitions of efficacy were hampered
The optimal design of pharmacological experiments Chapter | 9
by the paucity of assay systems available to gauge the
direct effect of drugs. Until as recently as 20 years ago,
overt cellular response was used to assess drug effect. For
example, the disappearance of response after chronic agonism was assumed to relate to the desensitization linking
this process with agonism, i.e., intense activation of receptors was the impetus for internalization. However, the
subsequent availability of imaging techniques measuring
receptor internalization indicates that some antagonists that
are devoid of direct stimulating properties can cause active
internalization of receptors [2,3]. The mechanism responsible is postulated to be the stabilization of receptor conformations by these antagonists that are prone to
phosphorylation and subsequent internalization.
The advent of an increasing number of assays to gauge
receptor behavior has uncovered a range of different “efficacies” for drugs and has also blurred the lines of taxonomy of drug classification [4]. In other words, the simple
classes of agonist, antagonist, etc., do not fully describe
drugs as they can have many efficacies that qualify for
many different classifications. Fig. 9.1 shows a schematic
diagram of some of the known behaviors of receptors and
also the phenotypic activities these behaviors can mediate.
The fact that many biological targets (i.e., receptors) control
pleiotropic cellular signals raises the specter of multiple
efficacies for a single molecule; these usually are related to
the unique ensemble of receptor conformations stabilized
by the molecule. Given the term “pluridimensional
271
efficacy” [5], this property of drugs makes simple classification of efficacy difficult, i.e., a given molecule may be an
agonist, antagonist, inverse agonist, and/or bias agonist for
a collection of pathways. For example, the cannabinoid
ligand desacetyllevonantradol is a positive agonist for CB1mediated Gi1 and Gi2 activation but is an inverse agonist
for Gi3-mediated effects [6].
The inability of simple labels to characterize drug activity is underscored by the many subclassifications of the
general class of drugs known as b-blockers (antagonists of
b-adrenoceptorsdsee Fig. 2.26). In fact, one area where
the secondary effects of drugs play a prominent part is in
cardiovascular drug studies for congestive heart failure [7].
There are theoretical reasons for supposing that b-blocking
drugs may be of benefit in this area. Accordingly, a large
number of these were tested in clinical trials and, interestingly, of 16 b-blockers tested, only three showed favorable
outcome, with carvedilol emerging prominently [7] (see
Fig. 9.2). Interestingly, the unique combination of carvedilol activities (b- and a-blockade, antioxidant, antiendothelin, and antiproliferative effects) may be the
discerning factor for utility in congestive heart failure. In
accordance with the notion that disease is a complex system
failure where numerous factors contribute to morbidity, the
various properties of adrenoceptor-active ligands that may
contribute negatively to treatment of congestive heart failure are listed in Table 9.1. In general, this underscores the
fact that the therapeutic value of a drug may be due to a
FIGURE 9.1 Various drug activities shown in red bordered rectangles caused by interference with various receptor activation and regulation mechanisms in the cell.
272
A Pharmacology Primer
FIGURE 9.2 Of the 16 b-blockers that have been studied in clinical trials for treatment of congestive heart failure, three have been shown to have
measurably favorable effects, with carvedilol emerging as the most efficacious. Carvedilol has a number of activities in addition to b-adrenoceptor affinity
that may make it efficacious in the treatment of congestive heart failure. Data from M. Metra, L. Dei Cas, A. di Lenarda, P. Poole-Wilson, Beta-blockers in
heart failure: are pharmacological differences clinically important?, Heart Fail. Rev. 9 (2004) 123e130.
TABLE 9.1 Potentially deleterious effects of adrenergic receptor activity in heart failure and cardiovascular
remodeling.
Effect
b1-adrenoceptor mediated
b2-adrenoceptor mediated
a1-adrenoceptor mediated
Positive inotropic
þþþ
þþ
þ
Positive chronotropic
þþþ
þþ
0
Myocyte hypertrophy
þþþ
þ
þþ
Fibroblast hyperplasia
þþþ
þ
NA
Myocyte toxicity
þþþ
þ
þ
Myocyte apoptosis
þþ
Tachyarrhythmias
þþ
þþ
þ
Vasoconstriction
0
þþ
Sodium retention
0
0
þþ
Renin secretion
þ
0
0
þ, positive effect; , negative effect; 0, null effect; NA, not assessed.
From M. Metra, L. Dei Cas, A. di Lenarda, P. Poole-Wilson, Beta-blockers in heart failure: are pharmacological differences clinically important?, Heart Fail.
Rev. 9 (2004) 123e130.
The optimal design of pharmacological experiments Chapter | 9
constellation of efficacies; therefore, these all should be
explored. The increasing number of functional assays
available through an increasing number of technological
advances makes such efforts increasingly practical.
As discussed in Chapter 5, Agonists: The Measurement
of Affinity and Efficacy in Functional Assays, the
BlackeLeff operational model is used to quantify agonism
and assigned efficacy (in the form of a parameter s) and
affinity (the term KA) to agonists that can be used to predict
agonism in other systems (vide infra) with the following
equation [8]:
½A sn Em
n n
n
½A s þ ð½A þ KA Þ
n
Response ¼
(9.1)
where n is the slope coefficient for the concentratione
response curves and Em is the maximal response capability
of the system. It is essential to have independent knowledge
of Em; the n can be obtained from fitting the Hill equation
to the data. The KA is a very important parameter since it
controls the value of s given by the model; it is the equilibrium dissociation constant of the agonistereceptor complex
which is roughly equal to the reciprocal of the agonist affinity. However, in terms of functional agonism and the use of
this model, the KA is specifically the concentration around
where concentrationeresponse curves collapse upon diminution of receptor density and/or reduction of signaling
capability of the system (see Fig. 9.3).
FIGURE 9.3 The BlackeLeff operational model utilizes the equilibrium
dissociation constant of the agonistereceptor complex. The model predicts
that diminution of response capability (either through diminution of the
receptor number or some other decrease in the translation of receptor-based
stimulus into tissue response) will cause the concentrationeresponse
curves for the agonist to shift to the right until the concentrations of the
agonist approach the KA value. With further decrease in response capability the concentrationeresponse curves will show depressed maxima
with the EC50 values approximating the KA value. The appropriate value
for agonist affinity for any models utilizing the BlackeLeff operational
model for signaling must adhere to the requirement predicted for the KA in
the model shown above.
273
The KA value (also referred to as the operational affinity) may or may not be the binding affinity measured in
binding experiments, so this should not be assumed.
Ideally, this model should be fit to partial agonists where
the KA value closely approximates the EC50; under these
circumstances, there is no ambiguity about the KA value.
For full agonists, an infinite combination of s and KA
values will fit a curve which is why s/KA ratios are used to
quantify bias and receptor selectivitydsee Chapter 6, Agonists: The Measurement of Affinity and Efficacy in
Functional Assays, Section 6.6. Under these circumstances,
a value approximately 100 the EC50 is routinely chosen
as a starting value for the computer fit to Eq. (9.1).
Efficacy has the dual properties of quantity and quality.
Considering the quantity of efficacy first, this reflects the
strength which a given molecule has to activate in a given
signaling pathway, and it is quantified as the magnitude of
s. In this regard, the receptor density of the tissue
(e.g., cells) in a given functional assay can be extremely
useful as a variable controlled by the experimenter. As
shown in Fig. 9.4, low receptor density preparations will
allow facile quantification of agonist affinity (KA) and in
some cases also of s through fitting to the operational
model. Higher receptor density preparations can be used to
detect efficacy and/or inverse agonism (see Fig. 9.4). With
regard to the magnitude of efficacy, it also is useful to
determine whether the potency of the agonist is primarily
due to high affinity or high efficacy, since these differences
translate to how robust the agonism will be in tissues of
varying sensitivity (see Chapter 6, Agonists: The Measurement of Affinity and Efficacy in Functional Assays,
Section 6.6.1). Fig. 9.5 shows doseeresponse curves to two
agonists for a-adrenoceptors in the rat anococcygeus
muscle; oxymetazoline is an affinity-dominant agonist
while norepinephrine is an efficacy-dominant agonist [9]. It
can be seen that while oxymetazoline is more potent than
norepinephrine in the native tissue, reduction in the sensitivity of the tissue through chemical alkylation of the receptors (reduction in receptor number) produces a
disproportionate decrease in the response to the lower efficacy agonist (oxymetazoline). This would translate to a
greater variability in the agonism to oxymetazoline (vs.
norepinephrine) in various organ systems.
As well as the quantity of efficacy, agonists can also
differ in the quality of efficacy they impart to cells if the
receptor they activate interacts pleiotropically with multiple
signaling systems. This mechanism is extensively described
in the section on biased signaling (Section 5.7) and highlights the fact that it should not be assumed that new synthetic agonists will produce an identical signaling pattern to
that of the natural endogenous agonist. The first requirement to quantify bias is to have the selective assays to
characterize the various separate signaling pathways of
interest, e.g., GTPgS for G-protein activation and
274
A Pharmacology Primer
FIGURE 9.4 Effect of varying receptor density on detection capability of functional assays to characterize various types of pharmacologic ligand.
FIGURE 9.5 Rat anococcygeus muscle responses to oxymetazoline (open circles) and norepinephrine (filled circles). Three separate tissue treatments
are shown. (A) Control tissue. (B) Tissue treated with 30 nM a-adrenoceptor alkylating agent phenoxybenzamine for 10 min and then washed for 1 h with
solution containing sodium thiosulfate to remove aziridinium ion and then 1 h with drug-free medium. (C) Tissue treated with a further 0.1 mM phenoxybenzamine for 10 min and then washed for 1 h with solution containing sodium thiosulfate to remove aziridinium ion and then 1 h with drug-free
medium. Redrawn from T.P. Kenakin, The relative contribution of affinity and efficacy to agonist activity: organ selectivity of noradrenaline and oxymetazoline, Br. J. Pharmacol. 81 (1984) 131e141.
The optimal design of pharmacological experiments Chapter | 9
Bioluminescence Resonance Energy Transfer (BRET) for
b-arrestin association. Then s and KA values are calculated
for each agonist for each pathway [10]; it cannot be
assumed that a given agonist will have the same KA value
for activation of the two pathways [11]. The “power” of
each agonist to activate each pathway is calculated as the
ratio log(s/KA). It is of paramount importance that all log(s/
KA) estimates be expressed as a ratio to a reference agonist
in each pathway and that the reference must be the same for
each pathway. Thus the transferrable value of relative
agonism for each pathway is Dlog(s/KA) and the transferrable value for bias between pathways is DDlog(s/KA);
BIAS ¼ 10DDlog(s/KA). This procedure cancels system
and measurement bias always present due to the sensitivity
of the assays and the intrinsic efficiency of each pathway in
the cells. An example of this procedure is shown in
Fig. 9.6, where it is seen that although the agonist depicted
in blue is 5.5-fold less active as an activator of pathway 1, it
is 15-fold more biased for activation of pathway 1 over
pathway 2. This underscores the independence of efficacy
and bias, i.e., efficacy determines if agonism appears and
bias determines at what relative concentration it appears
when it does (between pathways).
Large-scale fitting of the BlackeLeff model to
numerous concentrationeresponse curves can be problematic for logistical reasons and there are circumstances
where ratios of maximal response to EC50 values (Log(max/EC50)) can be very useful [12]. There are certain circumstances in which bias and receptor selectivity
procedures may utilize DLog(max/EC50) in the same
manner as Dlog(s/KA)dsee Section 6.9. Thus Log(max/
275
EC50) values can be related to the BlackeLeff operational
model with the relationship [13]dsee Chapter 6, Agonists:
The Measurement of Affinity and Efficacy in Functional
Assays:
Em sn ð2 þ sn Þ1=n 1
Max
(9.2)
¼
EC50
KA ð1 þ sn Þ
Thus, when the Hill coefficients of concentratione
response curves are not significantly different from unity, it
can be seen that DLog(max/EC50) ¼ Dlog(s/KA). When
ns1, then there will be a variable error between DLog(max/EC50) and Dlog(s/KA) values [12]. However, the
magnitude of this error is relatively small and the use of
DLog(max/EC50) values for early calculations on large data
sets to identify compounds of interest may be an acceptable
strategy.
In general, it is important to assess agonist selectivity
for candidate molecules both from the point of view of
intracellular selectivity (signaling bias) and extracellular
selectivity (receptor selectivity). At this point, it is useful to
discuss the various applications of DLog(s/KA) and/or
DLog(max/EC50) values as measures of agonism. As seen
in Fig. 9.6, DLog(s/KA) is useful to quantify signaling bias
but a further refinement of this technique can be obtained
with replicate data and statistical analysis. Replicate estimates of either Log(s/KA) or Log(max/EC50) values can be
used to calculate a pooled variance from the complete data
set and this, in turn, can provide a useful standard to assess
significance of differences. Fig. 9.7 shows the general
scheme whereby replicate measurements furnish mean
values of Log(s/KA) and the pooled variance yields 95%
FIGURE 9.6 The quantification of signaling bias using DDlog(s/KA) values. Concentrationeresponse curves for two agonists are obtained for each
signaling pathway and the activity of each agonist in each pathway by fitting data with the BlackeLeff operational model; a value for log(s/KA) is
determined for each curve in each pathway. A reference agonist is chosen and all other agonists compared to that reference through calculation of Dlog(s/
KA) values for each pathway. Providing the same reference agonist is utilized for both pathways, DDlog(s/KA) values then provide an estimate of the
relative activity of each pathway for activation of the various pathways, i.e., log(BIAS) ¼ DDlog(s/KA).
276
A Pharmacology Primer
FIGURE 9.7 Schematic diagram
of the statistical analysis of bias.
Estimates of agonism are obtained in
individual Log(max/EC50) values to
yield a mean and standard error for
each agonist in each signaling
pathway; 95% confidence limits can
be calculated on these using the
pooled variance (see text). A within
group comparison of the agonists
(within a given signaling pathway) is
then made through DLog(max/EC50)
values with concomitant estimates of
95% confidence limits. Finally, a
between group measurement is made
with DDLog(max/EC50) values with
appropriate 95% confidence limits.
confidence limits on the estimate. This is continued within a
group of agonists to yield DLog(s/KA) values of tests
agonism versus that produced by a chosen test agonist.
Again, the pooled variance, through a slight modification of
the formula (see Fig. 9.7), provides the 95% confidence
limits (c.l.) for the estimate of differences. Finally, once
DLog(s/KA) values are normalized for each signaling
pathway, DDLog(s/KA) values quantify the relative bias an
agonist has for any of the pathways. The pooled variance
again is used to furnish 95% c.l. on the estimate of bias to
assess significance (Fig. 9.7). An example of this is shown
in Table 9.2 for dopamine agonists for the dopamine D2L
receptor mediating cyclic adenosine monophosphate
(AMP) and extracellular signaleregulated kinase (ERK)
responses [14]; the data are shown graphically in Fig. 9.8.
The application of 95% c.l. on experimental estimates is
extremely useful; for example, it can be seen from Table 9.2 and Fig. 9.8 that while there is threefold bias toward
ERK for FAUC335, this value does not achieve statistical
significance as shown by the inclusion on the value
0 within the 95% c.l. of the estimate in DDLog(s/KA).
With the advent of biased signaling has come the realization that different agonists will produce a different
mixture of signaling activations in cells; the cell then
combines these to produce a phenotypic response. Thus,
agonist efficacy has quality as well as quantity and it may
be that the therapeutically important aspect of agonism is
the quality of response as well as the strength of response.
The fact that ligands in general may have many efficacies
leads to the notion that it is the collection of these that
contribute most to therapeutic value (i.e., see Fig. 9.2).
Radar plots depicting the component cellular signaling
pathways activated by agonists have been used to characterize agonists in so-called webs of efficacy [15,16].
Fig. 9.9 shows such radar plots for opioid receptors and five
signaling pathways; the phenotypic mix of signaling by
each agonist is readily apparent through the geometric
shape of the radar plot. Another approach is to treat the
various values of DLog(s/KA) or DLog(max/EC50) values
for signaling pathways and cluster them with programs
designed to cluster genes [17,18]. Fig. 9.10 shows this type
of clustering analysis for 15 opioid receptor agonists producing responses in six functional assays [17]. The pattern
of signaling produces the groups of agonists shown indicating that the features of biased activation of the receptor
within these groups are uniquely similar; this textured
classification of ligands may be useful to link in vitro to
in vivo phenotypes in therapy. Fig. 9.11 shows a more
TABLE 9.2 Statistical analysis of dopamine receptor signaling bias: cyclic AMP versus b-Arrestin.
cAMP
1
2
3
Log(s/
KA)
Mean
(xijLxmean)2
sij2
Quinpirole
8.600
8.700
0.0100
0.0708
Reference
8.300
7-OHDPAT
Dopamine
8.900
8.923
9.000
8.477
8.680
8.730
9.000
FAUC335
8.790
8.953
8.450
8.507
8.720
8.699
8.450
8.922
8.475
7.100
7.100
6.600
FAUC321
7.700
FAUC346
6.000
7.358
7.700
0.220
dferror [
30.000
Mean
Log(max/
KA)
0.0867
0.0400
8.40
8.200
Quinpirole
8.700
Reference
0.0400
0.0400
8.62
8.600
0.0900
8.18
8.100
0.1828
9.17
9.600
0.0025
0.0263
0.03
0.74
5.527
0.77
0.0890
0.0541
0.0036
0.0004
0.226
0.35
1.19
15.465
1.09
0.0005
9.40
9.150
0.29
0.30
1.975
0.46
0.0298
8.95
9.000
0.00
0.21
1.636
0.21
0.0189
8.61
8.750
0.2106
0.0000
0.2500
0.31
0.66
4.576
0.53
0.3452
8.84
9.200
0.23
0.585
0.13
0.0977
8.39
8.300
1.60
0.48
3.043
1.12
0.0803
7.28
7.000
0.0469
0.2500
0.0000
0.0900
1.26
0.97
9.247
0.78
1.94
0.00
1.002
1.46
1.00
0.83
6.813
0.17
0.0044
7.958
6.183
0.0336
0.1308
0.66
1.32
20.700
0.17
1.34
0.35
2.242
0.51
2.52
0.03
0.926
2.55
0.1736
6.441
0.0544
7.54
0.45
2.814
2.21
2.86
0.52
0.305
2.89
Dopamine
3
FAUC335
4
FAUC321
5
FAUC346
6
7.350
7.03
0.2433
0.3211
8.23
0.1111
8.800
8.000
8.49
7.900
7.98
0.1675
0.2025
5.85
0.1225
2.18
2
7.500
0.0544
0.0900
7-OH-DPAT
8.200
0.34
0.0658
1
8.940
0.1702
0.0619
5.925
SPO
OLED [
0.00
(xijLxmean)2
0.0900
6.600
5.950
1
sij2
0.0900
7.442
6
Dlog(s/
KA)
0.2500
8.000
7.400
0.00
BIAS
0.1600
6.842
5
0.00
DDlog(s/
KA)
0.0054
9.000
7.600
Dlog(s/
KA)
0.0729
8.625
4
pERK
0.0100
5.400
6.200
6.11
5.950
5.59
T [ 2.0300
bold ¼ mean values; italics ¼ 95% confidence limits.
From N. Tschammer, S. Bollinger, T. Kenakin, P. Gmeiner, Histidine 6.55 is a major determinant of ligand-biased signaling in dopamine D2L receptor. Mol. Pharmacol. 79 (2011) (3) 575e585.
278
A Pharmacology Primer
FIGURE 9.8 Graphical representation of bias data calculated in Table 9.2. Values of DDLog(s/KA) shown for five test agonists (with quinpirole as the reference agonist); bars represent 95% confidence limits. Any
95% c.l. that crosses the ordinate value of DDLog(s/KA) ¼ 0 indicates that
the bias is not significant at the P < .05 level.
sophisticated application of clustering using label-free dynamic mass redistribution readouts of cellular responses to
opioid agonists [19]. It can be seen that with the increased
types of signals and the finer the measurement of subtle
FIGURE
9.9 DLog(max/EC50)
values (with DAMGO as the reference agonist) for six opioid receptor
agonists in five signaling pathways.
Values >0 indicate bias toward that
pathway while values <0 indicate
the reverse. Data taken from T.
Kenakin, New lives for seven transmembrane receptors as drug targets,
Trends Pharmacol. Sci. 36 (2015)
705e706.
differences in response comes a more textured delineation
of signaling differences.
As seen in Fig. 9.11, the fact that efficacy quality emanates from biased signals from the activated receptor leads
to the imposition of cell type on these heterogeneous signals, i.e., phenotypic responses can be unique to the receptor host cell. Simple techniques used to quantify biased
signaling such as biased plots (see Fig. 6.29) also can be
used to detect these cell phenotypes. Fig. 9.12 shows bias
plots for muscarinic agonists for muscarinic M3 receptors
transfected into two different cell types (HCT-15 cells and
PC-3 cells) where it can be seen that carbachol is uniquely
biased toward PC-3 cells [20].
In vitro estimates of biased signaling indicate possible
differences that can carry over to in vivo systems but the
translation may be variable depending on whether the bias
is rooted in efficacy or affinity. Bias, being a function of sA/
KA, can be achieved by selective efficacy or affinity (or
both) but, just as is seen with efficacy-dominant agonists,
bias due to selective efficacy is more robust in terms of
transferring to systems of varying sensitivity. As noted
previously, affinity-based potency is more subject to decreases in tissue sensitivity and the same is true for bias.
Fig. 9.13 shows two agonists with a bias factor for two
signaling pathways (solid and dotted lines) of 10. The
agonist in Fig. 9.13A is due to selective efficacy (Pathway1
The optimal design of pharmacological experiments Chapter | 9
279
FIGURE 9.10 Clustering of 15 opioid agonists on the
basis of signaling (Log(max/EC50) values) in six
functional assays. Redrawn from T. Kenakin, T. New
Lives for Seven Transmembrane Receptors as Drug
Targets Trends Pharmacol Sci, 36 (2015) 705e706;
data from H. Deng, H. Sun, Y. Fang, Label-free cell
phenotypic assessment of the biased agonism and efficacy of agonists at the endogenous muscarinic M3
receptors, J. Pharmacol. Toxicol. Methods 68 (2013)
323e333.
sA ¼ 10, KA ¼ 100 mM; Pathway2 sA ¼ 1, KA ¼ 100 mM)
whereas the agonist in Fig. 9.13B has a bias of 10 through
selective affinity (Pathway1 sA ¼ 1, KA ¼ 1 mM; Pathway2
sA ¼ 10, KA ¼ 100 mM). It can be seen from this figure
that as the tissue sensitivity is reduced, the relative responses of the agonists for the two pathways change until
in tissues of low sensitivity, the bias is actually reversed.
A single number for agonism [either DLog(s/KA) or
DLog(max/EC50)] facilitates comparisons of full and partial
agonists in the setting of receptor mutation. One particular
problem in assessing the effects of mutation on receptor
signaling is the fact that the mutated receptor may be
expressed and handled differently in the host cell from the
wild-type receptor and this, in turn, alters total signaling
characteristics of agonists. However, comparison to a
common standard agonist as is done for the assessment of
bias (see Fig. 9.6) cancels effects of cell disposition on
different receptor proteins and allows for the systemindependent assessment of the mutation. The main difference in this procedure is that unlike the assessment of
signaling bias for new agonists where the reference agonist
is the natural endogenous agonist, the question for mutation
is usually “what does receptor mutation do to natural
signaling?” Therefore, the reference agonist becomes a
synthetic agonist and the comparison made for the natural
agonist. Table 9.3 shows the effects of the dopamine
D2LH3836.55A mutation on the signaling of dopamine (with
the reference agonist as quinpirole) [14]. It can be seen
from Table 9.3A, the mutation has little effect on cyclic
AMP signaling but a profound loss of effect for ERK
280
A Pharmacology Primer
FIGURE 9.11 Label-free assay data for clustering agonist activity. (A) Schematic representation of DMR showing typical data outputs for different
signaling pathways. (B) DMR data for 29 opioid ligands in 13 assay conditions at 3 timepoints. DMR, dynamic mass redistribution. (A) Redrawn from
panel (A) T. Kenakin, A holistic view of GPCR signaling Nature Biotech. 28 (2010) 928e929; (B) Redrawn from Morse, E Tran, H Sun, R Levenson, Y
Fang, Ligand-directed functional selectivity at the mu opioid receptor revealed by label-free integrative pharmacology on-target. PLos One 6 (2011)
e25643, 1e13.
FIGURE 9.12 Bias plots for seven
muscarinic M3 receptor agonists in
two cell lines. It can be seen that the
bias between acetylcholine (Ach)
and carbachol (Carb.) differs markedly in that Ach is biased toward
signaling in HT-15 cells and carbachol biased toward signaling in PC-3
cells. Data taken from H. Deng, H.
Sun, Y. Fang, Label-free cell
phenotypic assessment of the biased
agonism and efficacy of agonists at
the endogenous muscarinic M3 receptors. J. Pharmacol. Toxicol.
Meth. 68 (2013) 323e333.
(101.12 ¼ 0.076). This indicates that receptor mutation
creates a 1.1/0.076 ¼ 14.5-fold bias in natural dopamine
signaling toward ERK.
The effects of mutation can be assessed with the
DLog(s/KA) or DLog(max/EC50) scales even for a single
agonist with a slightly different procedure. Table 9.4 shows
the effects of thrombin signaling on the protease-activated
receptor 1 (PAR-1) receptor. In this case, a signaling
pathway is chosen for reference and then the effects of the
agonist (thrombin) are assessed for the other signaling
pathways for wild-type and mutated receptor. It can be seen
from Table 9.4 that mutation causes little effect on RhoA
signaling but a statistically significant effect (5.27, 95% c.l.
1.98e13.98) on phosphoinositol (PI) hydrolysis; specifically, thrombin-induced PI hydrolysis is selectively
enhanced (compared to Gi or RhoA signaling) by receptor
mutation [21].
Another measure of agonist value is its selectivity for
the therapeutic target (over other receptors). Here transducer ratios [Dlog(s/KA) or DLog(max/EC50) values] can
be useful and offer an advantage of providing an insight
that may add value to simple agonist potency ratio measurements since DLog(s/KA) and/or DLog(max/EC50)
values allow comparison of partial to full agonism
FIGURE 9.13 The use of Dlog(s/KA) values to provide predictive measures of receptor selectivity. For the agonist shown in panels (A) and (B) and
another agonist shown in panels (C) and (D), the relative capability to activate two receptor types (therapeutic receptor in solid lines, secondary receptor in
dotted lines) are shown. The agonist in the top panels (A and B) is selective for the therapeutic receptor because of a low efficacy for the secondary
receptor. However, this agonist does have a higher affinity for the secondary receptor and this causes the Dlog(s/KA) value to be negative. As can be seen
in panel (B), in tissues of higher sensitivity, the secondary receptor activity actually becomes dominant over the therapeutic receptor activity. This
possibility is predicted by the Dlog(s/KA) values. In contrast, the positive Dlog(s/KA) value for the agonist shown in panels (C) and (D) suggests that this
agonist is truly more selective for the therapeutic receptor in all systems, i.e., tissues of low sensitivity [panel (C)] and high sensitivity [panel (D)].
TABLE 9.3 Quantification of the effects of dopamine receptor mutation on dopamine signaling.
(A) effective of mutation on cyclic AMP signaling: Mutation has insignificant effect of dopamine cAMP signaling
WT cAMP
Agonist
Log(s/KA)
Quinpirole
8.68
Dopamine
8.7
Dlog(s/KA)
0.02
Between
Receptor
D2LH3936.55A cAMP
DDLog(s/KA)
BIAS
Dlog(s/KA)
0.04
1.1
0.06
Log(s/KA)
Agonist
6.69
Quinpirole
6.75
Dopamine
(B) Effect of mutation of pERK signaling: Mutation causes a significant (13.2-fold) decrease in ERK signaling
WT ERK
Between
Quinpirole
8.41
Dopamine
8.62
0.21
1.12
Receptor
0.076
D2LH3936.55A ERK
0.91
7.36
Quinpirole
6.45
Dopamine
Data from N. Tschammer, S. Bollinger, T. Kenakin, P. Gmeiner, Histidine 6.55 is a major determinant of ligand-biased signaling in dopamine D2L receptor.
Mol. Pharmacol. 79 (2011) (3) 575e585.
TABLE 9.4 Effects of mutation on thrombin signaling on PAR-1 receptors.
Wild-type PAR-1
Between receptors
Dlog(s/
KA)
DDLog(s/
KA)
BIAS D 95%
c.l.
Pathway
Log(s/KA)
Gi (ref)
8.35 0.23
RhoA
9.54 þ 0.23
1.19 0.3
0.24 0.42
0.58, 0.22e1.54
PI
hydrolysis
8.53 0.2
0.18 0.3
0.72 0.42
5.27, 1.98e3.98
NA ECL2 mutation
Dlog(s/
KA)
Log(s/KA)
Pathway
8.14 0.23
Gi (ref)
0.95 0.3
9.09 0.23
RhoA
0.9 0.3
9.04 0.2
PI
hydrolysis
Data from A.G. Soto, T.H. Smith, B. Chen, S. Bhattacharya, I.C. Cordova, T. Kenakin et al., N-linked glycosylation of protease-activated receptor-1 at extracellular loop 2 regulates G-protein signaling bias, Proc. Nat. Acad. Sci. U.S.A. 112 (2015) E3600eE3608.
282
A Pharmacology Primer
(something not possible with potency ratios Section 6.9).
Specifically, a given agonist could have a favorable
potency ratio over a secondary receptor in a sensitive
tissue that may not transfer to less sensitive tissues if the
therapeutic agonist selectivity depends primarily on affinity
(vs. efficacy). However, since DDlog(s/KA) values
take maximal response (as well as potency) into account,
these may be more accurate for prediction of selectivity in
a range of tissues. The procedure used for quantifying
bias can also be used to quantify receptor selectivity; in
this case, concentrationeresponse curves for an
agonist acting on two receptors are used instead of two
pathways. As shown in Section 5.7.1, a selectivity index is
obtained:
s
s
DDlog
¼ Dlog
KA selectivity
KA therapeutic
Dlog
s
KA
(9.3)
secondary
where Dlog(s/KA)therapeutic represents the selectivity of the
test agonist (over a reference agonist) for the therapeutic
receptor and Dlog(s/KA)secondary represents the relative activity of the test agonist (over a reference agonist) for a secondary receptor. A positive value of DDlog(s/KA)selectivity
indicates a positive selectivity for the therapeutic receptor
even when appearances suggest otherwise; this is shown
in Fig. 9.14. Fig. 9.14A suggests that the agonist with
the solid line curve is more selective than the one with the
dotted line curve, yet the DDlog(s/KA) value is negative
[DDlog(s/KA) ¼ 0.48; fractional (s/KA)selectivity values].
However, it can be seen that in a tissue of increased sensitivity, the dotted line agonist is now more potent on the secondary receptor [in keeping with the DDlog(s/KA)
ratiodFig. 9.14B]. In contrast, Fig. 9.14C shows two
agonists where the DDlog(s/KA) ratio is positive [DDlog(s/
KA) ¼ 1.22]; in tissues of higher sensitivity this selectivity
stays constantdFig. 9.14D. This is because log(s/KA)
indices take into consideration whether agonists are affinity
dominant or efficacy dominant in producing their response.
An example of the use of DDLog(max/EC50) values to
assess receptor selectivity is shown in Fig. 9.15 for a range
of agonists for 5-HT2A,B,C receptors [22]. From these
curves, DDLog(max/EC50) values can be calculated for the
agonists in assessing agonism at 5-HT2A receptors versus
activity at 5-HT2B and 5-HT2C receptors (see Table 9.5).
An example of the application of this method is given in
Section 13.2.12. A useful representation of multiple receptor selectivity can be gained from expressing the data
shown in Table 9.5 in a radar plotdsee Fig. 9.16. In panel
FIGURE 9.14 Two sets of biased agonists both with a bias toward one of the signaling pathways of 10. The bias in row A is due to a 10-fold difference
in efficacy whereas the bias in row B is due to a 10-fold difference in affinity. It can be seen that the bias between agonists is preserved when efficacy is the
main variable whereas unpredictable differences occur at low tissue sensitivities when affinity is the important variable.
The optimal design of pharmacological experiments Chapter | 9
283
FIGURE 9.15 Calcium assay functional activity for 8 5-HT agonists on 3 5-HT subtype receptors. Data redrawn from A.A. Jensen, J.D. McCorvy, S.
Leth-Petersen, C. Bundgaard, G. Liebscher, T.P. Kenakin et al., Detailed characterization of the in vitro pharmacological and pharmacokinetic
properties of N-(2-hydroxybenzyl)-2,5-dimethoxy-4-cyanophenylethylamine (25CN-NBOH), a highly selective and brain-penetrant 5-HT2A receptor
agonist, J. Pharmacol. Exp. Ther. 361 (2017) 441e453.
A, the power of the various agonists for all three 5-HT
receptor types, expressed as a ratio (DLog(max/EC50)) to
the standard which in this case is 5-HT itself, is shown. It
can readily be seen that DOI, Cimbi-36, and 25I-NBOMe
are relatively equiactive on all three receptor types while
the other agonists show a measure of selectivity for 5HT2A. Another way to express this is to calculate the
actual selectivity for each receptor subtype versus 5HT2Adthrough
DDLog(max/EC50)
valuesdsee
Fig. 9.16B.
In general, efficacy can be characterized in terms of the
following headings:
1. What types of efficacy does the molecule possess?
2. For pleiotropic signaling, does the molecule produce a
biased signal?
3. Is the agonism affinity driven or efficacy driven?
4. How selective is the agonism?
A schematic diagram illustrating the process of efficacy
classification is given in Fig. 9.17.
9.2.2 Affinity
The next system-independent descriptor of a drug molecule
is its affinity for the target. As pointed out in Section 5.8,
while the EC50 (concentration producing half maximal
agonism) for a weak partial agonist is a close measure of the
KA (equilibrium dissociation constant of the agoniste
receptor complex and also the reciprocal of the affinity), the
EC50 cannot be used as a measure of affinity for a full agonist.
In general, affinity measurements are much more
important descriptors of antagonists, defined as ligands that
interfere with the production of pharmacological response by
an agonist. Every compound made by medicinal chemists for
an antagonist program must be tested for potency at the primary target, and the most expeditious means of doing this is
through a pIC50 curve. This is where a stimulus is given to the
system (i.e., an 80% maximal concentration of agonist activating the receptor) and then a range of concentrations of
antagonist added to determine inhibition of that response.
There are a number of reasons for this approach:
1. It is less labor intensive than analyzing full agonist
concentrationeresponse curves (see Fig. 9.18).
2. It can cover a wide range of antagonist concentrations
(to find where antagonism begins). This is imperative
in a “data-driven” system, where the activities of test
molecules are unknown.
3. Unless a high concentration of agonist is used for simple competitive blockade, the pIC50 will be, at most, a
two to six times underestimation of the true pKB but
not more than that. However, pIC50 values can still be
used to track potency since a correction factor usually
will be common to all molecules.
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A Pharmacology Primer
TABLE 9.5 5-HT2A receptor selectivity of agonists over 5-HT2B and 5-HT2C receptors calculated with DDLog(max/EC50) values.
5-HT2A
Log(max/
EC50)
5-HT2A
Dlog(max/
EC50)
5-HT2B
Log(max/
EC50)
5-HT2B
DLog(max/
EC50)
5-HT2C
Log(max/
EC50)
5-HT2C
Dlog(max/
EC50)
5-HT2A versus 5HT2B DDLog(max/EC50)
Selectivity 5HT2A over 5HT2B
5-HT2A versus 5HT2C DDLog(max/EC50)
Selectivity 5HT2A over 5HT2C
5-HT
9.21
0.00
9.14
0.00
9.52
0.00
0.00
1.00
0.00
1.00
25CNNBOH
8.81
0.40
7.01
2.13
7.63
1.89
1.73
53.70
1.48
30.44
DOI
8.01
1.20
8.67
0.47
8.46
1.06
0.73
0.19
0.14
0.72
251MBOMe
9.29
0.08
7.95
1.19
8.94
0.58
1.27
18.51
0.66
4.57
Cimbi36
8.74
0.47
8.03
1.11
9.00
0.52
0.64
4.33
0.05
1.12
25CNNBOMe
8.86
0.35
7.82
1.32
8.03
1.49
0.97
9.37
1.14
13.77
25CNNBF
7.68
1.53
5.41
3.73
6.26
3.26
2.21
160.80
1.73
53.93
25CNNBMD
8.17
1.04
6.15
2.99
6.17
3.35
1.95
89.53
2.31
204.58
Data from A.A. Jensen, J.D. McCorvy, S. Leth-Petersen, C. Bundgaard, G. Liebscher, T.P. Kenakin et al., Detailed characterization of the in vitro pharmacological and pharmacokinetic properties of N-(2hydroxybenzyl)-2,5-dimethoxy-4-cyanophenylethylamine (25CN-NBOH), a highly selective and brain-penetrant 5-HT2A receptor agonist, J. Pharmacol. Exp. Ther. 361 (2017) 441e453.
The optimal design of pharmacological experiments Chapter | 9
285
FIGURE 9.16 5-HT receptor selectivity for seven agonists (relative to 5-HT) in 3 5-HT receptor subtypes. (A) DLog(max/EC50 values). DLog(max/
EC50) values <0 indicate selectivity away from receptor (black ¼ 5-HT2A, blue ¼ 5-HT2B, red ¼ 5-HT2C) when compared to 5-HT. (B) Selectivity for 5HT2A versus 5-HT2B (blue line) and 5-HT2A versus 5-HT2C (red line) through DDLog(max/EC50 values). Values of DDLog(max/EC50) > 0 indicate
selectivity of the test agonist greater than 5-HT and values of DDLog(max/EC50) < 0 indicate 5-HT has a greater selectivity than the test agonist. For both
data from A.A. Jensen, J.D. McCorvy, S. Leth-Petersen, C. Bundgaard, G. Liebscher, T.P. Kenakin, H.Bräuner-Osborne, J. Kehler, J. Langgaard
Kristensen Detailed Characterization of the In Vitro Pharmacological and Pharmacokinetic Properties of N-(2-Hydroxybenzyl)-2,5-Dimethoxy-4Cyanophenylethylamine (25CN-NBOH), a Highly Selective and Brain-Penetrant 5-HT2A Receptor Agonist J. of Pharmacol. and Exp. Ther. 361
(2017) 441e453.
FIGURE 9.17 Schematic diagram for logistical
scheme for the evaluation of agonism. A decrease in
basal effect after addition of the agonist suggests
that the system is constitutively active and that the
ligand is an inverse agonist. Positive agonism is
analyzed with the BlackeLeff operational model to
determine efficacy (s) and affinity (KA). This can be
done in assays for different signaling systems to
determine possible bias which is then quantified
with DDlog(s/KA) values. Partial agonists also can
be evaluated for activity in blocking responses to
full agonists (see Section 6.3.5 in Chapter 6,
Orthosteric Drug Antagonism).
4. Effects on maximal antagonism in a pIC50 mode can
detect partial agonists, allosteric modulation, and inverse agonism.
The determination of antagonist potency through
determination of a pIC50 is a facile method but it does not
automatically yield a system-dependent measure of potency, that is, the true aim of an antagonist program is to
determine the molecular system-independent measure of
affinity, namely, the pKB (log of the molar equilibrium
dissociation constant of the antagonistereceptor complex).
This latter value can be applied to all systems where the
286
A Pharmacology Primer
FIGURE 9.18 Panel on the left shows the effects of a simple competitive antagonist on full concentrationeresponse curves to an agonist. An alternative
method to gauge the effects of the antagonist is to add increasing concentrations of antagonist onto a preparation prestimulated with a concentration of
agonist that produces 80% maximal response (red circles). The antagonist reduces the effect of the EC80 concentration to define the sigmoidal curve shown
on the right-hand panel. This curve concisely reports the potency of the antagonist (through the pIC50) with a fraction of the number of data points.
antagonist is to be tested. Therefore, it is worth considering
the relationship between the readily obtainable pIC50 and
the desired pKB.
For competitive antagonists, the observed pIC50 depends upon the magnitude of the strength of stimulus given
to the system. Therefore, the potency of the antagonist (as
measured by the pIC50) for inhibiting a 50% maximal
agonism will be lower than that for driving the system at
80% maximal stimulus (see Fig. 9.18A). The relationship
between the pIC50 and pKB under these circumstances (for
pure competitive antagonism) is
pKB ¼ pIC50 þ Logð½A = KA Þ þ 1;
(9.4)
where the strength of stimulus to the system is given by
[A]/KA ([A] is the concentration of agonist and KA is the
equilibrium dissociation constant of the agonistereceptor
complex). This relation (often referred to as the Chenge
Prusoff correction [23]) is valid only for systems where
the Hill coefficient for the concentrationeresponse curves
is unity and where the KA is known. Most often in functional antagonist programs, the effects are against a
concentrationeresponse curve for functional activity,
which is defined by a curve of observed slope and location
(EC50) but where the KA is not known and n s 1. Under
these circumstances, it can be shown that the relationship
between the IC50 and the KB in functional experiments is
given by (as defined by Leff and Dougall [24] and derived
in Section 9.7.1):
KB ¼
IC50
n 1=n
ð2 þ ð½A=EC50 Þ Þ
1
;
(9.5)
where the concentration of agonist is [A], the concentration
of agonist producing 50% maximal response is EC50, and n
is the Hill coefficient of the agonist doseeresponse curve.
From Eq. (9.5), it can be seen that the KB, which is a
system-independent estimate of antagonist potency, can
be made from an estimate of the IC50 that is corrected for
the level of agonism. However, this is required only for a
competitive antagonist and not for noncompetitive antagonists. In the latter case, the pIC50 corresponds directly to the
pKB (see Fig. 9.19). The reason for the difference between
the pIC50 correspondence (or lack of it) in competitive
versus noncompetitive systems is the dextral displacement
of the agonist concentrationeresponse curve produced by
the antagonism. Thus, in competitive systems, the dextral
displacement causes the disparity between pIC50 and pKB
values (Fig. 9.19A). In purely noncompetitive systems,
there is no dextral displacement and the pIC50 corresponds
to the pKB (Fig. 9.19B). Between these two extremes are
systems where a small dextral displacement is produced,
even under conditions of noncompetitive blockade, due to
a receptor reserve in the system or perhaps a hemiequilibrium state. Under these circumstances, there will be a
low-level difference between the pIC50 and pKB, less
than that for pure competitive antagonist systems but
The optimal design of pharmacological experiments Chapter | 9
287
FIGURE 9.19 pIC50 curves measured under different levels of agonist stimulation. (A) Simple competitive antagonist. In this case, the magnitude of the
agonist response produces an inverse effect on the observed potency of the antagonist. The color-coded pIC50 curves reflect full-scale inhibition (control is
normalized to be 100%); it can be seen that the antagonist appears more potent in blocking the lower agonist stimulation (red curve) than the higher level
of agonist stimulation (magenta). (B) The same is not true for insurmountable noncompetitive antagonism. With these types of antagonist, the level of
stimulation does not affect the observed potency of the antagonist when measured in a pIC50 mode.
enough to prevent an absolute correspondence. An example
of the use of the pIC50 to quantify antagonism is given in
Section 13.2.11.
There are two reasons why use of pIC50 values early in
antagonist discovery programs is adequate. The first is that
the absolute error, if the EC80 concentration for agonism is
used for measurement of the IC50, is small (at most a
fivefold error). Second, any correction will be uniform for a
series of molecules with the same mechanism of action;
therefore, the relative changes in the pIC50 should reflect
corresponding relative changes in the pKB.
There are two characteristic properties of pIC50 curves
of interest that can yield valuable information about
antagonist activity. The first is the potency (pIC50)
discussed previously. The second is the maximal degree of
antagonism. If the antagonist reduces the EC80 effect of the
agonist to the baseline (0% response), then this is consistent
with “silent” antagonism, whereby the antagonist has no
efficacy, and also with a normal orthosteric mechanism of
antagonism. However, if the maximal degree of antagonism
does not attain baseline values, then further valuable information about the mechanism of action of the antagonism
can be deduced.
There are two possible reasons for the pIC50 curve to
fall short of the baseline (produce <100% inhibition). One
is that the antagonist demonstrates partial agonism in the
system, that is, the elevated baseline is due to a direct
agonism produced by the antagonist (see Fig. 9.20Adsee
288
A Pharmacology Primer
FIGURE 9.20 Inhibition curves in pIC50 mode that do not show complete inhibition. (A) A partial agonist will depress the agonist response only to the
point equal to the maximal direct agonist effect of the partial agonist. (B) An allosteric modulator that produces a submaximal decrease in affinity or
efficacy of the agonist can also produce an inhibition curve that does not extend to basal (zero response) levels.
also Chapter 7, Orthosteric Drug Antagonism, Section
7.3.5). This can be confirmed in separate experiments
where the direct effects of the “antagonist” are observed.
Another possibility is a limited saturable blockade of
agonist effect, which does not allow complete obliteration
of the induced agonist effect (see Fig. 9.20B). This is discussed more fully in Chapter 4, Pharmacological Assay
Formats: Binding (see Figs. 4.9 and 4.10).
The other possibility is that the pIC50 curve may extend
below the baseline; see Fig. 9.21. The most common reason
for this is that what is perceived to be the baseline (“zero”
response) is really a spontaneously elevated baseline due to
constitutive receptor activity (see Section 3.10). If the
antagonist has negative efficacy (inverse agonist activity),
then this elevation will be reversed and the pIC50 curve will
extend beyond the baseline (see Fig. 9.21).
Before discussing the determination of antagonist
mechanism by observation of antagonist effects on full
agonist concentrationeresponse curves, it is worth
considering the pA2 (log molar concentration of the
antagonist that causes a twofold shift to the right of the
agonist concentrationeresponse curve) as a mechanismindependent measure of antagonist potency. This estimate
of the pKB is an even better estimate than the pIC50 since
The optimal design of pharmacological experiments Chapter | 9
289
FIGURE 9.21 An inverse agonist could produce antagonism below basal levels if the basal response is due to an elevated constitutive activity.
the differences between pKB and pA2 values are very small.
The basis for the use of the pA2 stems from the fact that an
antagonist will produce little to no effect on an agonist
response until it occupies approximately 50% of the receptor population. In a purely competitive system, when
antagonist occupancy reaches 50%, then the dose ratio
(DR) for an agonist is 2 (by definition, the log of the
molar concentration of antagonist is the pA2). Therefore,
determination of the concentration that produces a twofold
shift to the right of any agonist concentrationeresponse
curve by any antagonist is a useful way to estimate
antagonist potency. The major problem with this approach
is the lack of parallelism in agonist concentrationeresponse
curves. However, judicious measurement of DRs (e.g., at
levels of response lower than 50%) can overcome this
obstacle [25]. Fig. 9.22 shows how pA2 measurements can
be made in almost any condition of receptor antagonism.
The relationships between the pA2 and the pKB are derived
in Section 9.7.2 for orthosteric insurmountable effects and
Section 9.7.3 for allosteric insurmountable effects.
Data-driven analysis of antagonism relies upon the
observed pattern of agonist concentrationeresponse curves
produced in the presence of varying concentrations of the
antagonist. As a prerequisite to the discussion of the various
molecular mechanisms of antagonism and how they are
analyzed, the effect of antagonists on the parameters of
agonist concentrationeresponse curves should be determined. This can be done statistically. In general, while
antagonists can produce numerous permutations of effects
on agonist concentrationeresponse curves, there are some
pharmacologically key effects that denote distinct receptor
activities. Thus, an antagonist may
1. Alter the baseline of concentrationeresponse curves.
2. Depress the maximal response to the agonist.
3. Change the location parameter of the concentratione
response curves.
A data-driven process classifies curve patterns and associates them with molecular mechanism; a schematic diagram of this process for antagonists is shown in Fig. 9.23.
Assuming that the effects on baseline and maxima are clear
(either obvious or discernible with an F-test), then certain
models of interaction between receptors, agonists, and antagonists can be identified. It can be seen from Fig. 9.23
that a first step would be to observe possible changes in the
baseline in the presence of the antagonist. If the baseline is
increased, this suggests that the antagonist is demonstrating
partial agonist activity in the preparation. Under these circumstances, the data can be described by the model for
partial agonism (see Chapter 7, Orthosteric Drug Antagonism, Section 7.3.5). Alternatively, if the baseline is
decreased, this could be a constitutively active receptor
system, and the antagonist could be demonstrating inverse
agonism (see Chapter 7, Orthosteric Drug Antagonism,
Section 7.3.4).
The next consideration is to determine whether the
antagonism is surmountable or insurmountable. In the case
of surmountable antagonism, a Schild analysis is carried
out (DRs can be used from curves generically fit to four
parameter logistic equations; see Chapter 7, Orthosteric
Drug Antagonism, Section 7.3). The behavior of the relationship between log(DR1) values and the logarithm of
the molar concentrations of antagonist can be used to
determine whether the antagonism best fits an orthosteric or
allosteric mechanism. If the Schild regression is linear with
unit slope, then a GaddumeSchild model of orthosteric
competitive antagonism is used to fit the data (see Chapter
7, Orthosteric Drug Antagonism, Section 7.3.1). If there is
curvature in the Schild regression resulting from attainment
of a saturably maximal DR, this would suggest that a surmountable allosteric mechanism of action is operative (see
Fig. 8.20). In this case, it is assumed that the allosteric
modulator alters (reduces) the affinity of the agonist for the
290
A Pharmacology Primer
FIGURE 9.22 Patterns of insurmountable antagonism through three different molecular mechanisms. In each case, the concentration of antagonist that
produces between a 1.8- and 4-fold shift to the right of the agonist concentrationeresponse curve can be used to calculate the pA2, which, in turn,
furnishes a reasonably accurate estimate of the pKB. If depression of the maximal response is observed, then approximately parallel regions of the
concentrationeresponse curves should be used to calculate the dose ratios. Redrawn from T.P. Kenakin, S. Jenkinson, C. Watson, Determining the potency
and molecular mechanism of action of insurmountable antagonists, J. Pharmacol. Exp. Ther. 319 (2006) 710e723.
receptor but does not interfere with the agonist’s ability to
induce a response. The model for this type of interaction is
discussed further in Chapter 8, Allosteric Modulation,
Section 8.4.
If the antagonism is insurmountable, then there are a
number of molecular mechanisms possible. The next
question to ask is if the maximal response to the agonist can
be completely depressed to basal levels. Alternatively, this
could be due to a hemiequilibrium condition (see Section
7.5), which produces a partial shortfall to true competitive
equilibrium leading to incomplete depression of the
maximal response but also antagonisteconcentrationrelated dextral displacement of the concentratione
response curve to the agonist (see Fig. 8.24A). Another
way in which a partial depression of the maximal response
could occur is through an allosteric mechanism whereby
the antagonist modulator produces an alteration in the efficacy of the agonist. This can result in a different steady
state, whereby the curve is partially depressed but no
further dextral displacement is observed (see Fig. 8.24B).
The complete model for such an allosteric mechanism (with
partial sparing of agonist function) is discussed in Section
8.4. While the models used to describe allosteric alteration
of both affinity and efficacy of receptors are complex and
require a number of parameters, the identification of such
effects (namely, incomplete antagonism of agonist
response) is experimentally quite clear and straightforward.
Less straightforward is the differentiation of orthosteric
versus allosteric antagonism, when the antagonist produces
an insurmountable and complete blockade of the agonist
The optimal design of pharmacological experiments Chapter | 9
291
FIGURE 9.23 Schematic diagram of steps involved in analyzing pharmacological antagonism. Key questions to be answered are in purple, beginning
with assessments of changes in baseline, followed by assessment of whether or not the antagonism is surmountable, and followed by assessment of
possible probe dependence and/or saturability.
response. Specifically, there are two completely different
mechanisms of action for receptor blockade that can present
nearly identical patterns of concentrationeresponse curves.
Orthosteric insurmountable antagonism occurs when the
antagonist binds to the agonist binding site and the rate of
offset of the antagonist is insufficient for complete reequilibration of agonist, antagonist, and receptors (see Section
7.4 for further details). Allosteric antagonism can produce
insurmountable antagonism as well. As discussed in
Chapter 8, Allosteric Modulation, what is required to
delineate orthosteric versus allosteric mechanism is the
conscious testing of predictions of each mechanism through
experiment. Thus, the blockade of a range of agonists
through a large range of antagonist concentrations should
be carried out to detect possible saturation of effect and
probe dependence (see Section 8.7 for further discussion).
As with agonism, there are a number of general statements that can be made about the study of antagonism in
drug-discovery programs. These are
1. The pA2 is a good estimate of the pKB for any mechanism of antagonism.
2. Allosteric antagonism can masquerade as orthosteric
antagonism under a variety of circumstances.
3. If a compound is an antagonist, it does not mean it also
does not have efficacy (partial agonists, inverse
agonists).
4. Goodness of fit is not a reliable approach to determination of mechanism of action e vide infra.
Empirical measures of antagonist potency can be used
in discovery programs to guide medicinal chemistry to
optimize activity, but the ultimate aim of pharmacodynamic
studies is the measurement of the KB, the equilibrium
dissociation constant of the antagonistereceptor complex,
since this is a system-independent estimate of the activity of
the antagonist. Toward this end, the mechanism of action of
the molecule is required to fully understand what behaviors
will be seen therapeutically. The first requirement for this
process is to obtain a set of concentrationeresponse curves
for agonism in the absence and presence of a range of
concentrations of the molecule (either antagonist or
modulator). Inspection of these patterns often suggests the
first clue as to which model should be applied for analysis;
although this can be misleading, as suggested by F. Klein
(Reed and Simon: Methods of modern mathematical
physics), “. Everyone knows what a curve is, until he has
studied enough mathematics to become confused through
292
A Pharmacology Primer
the countless number of possible exceptions.” This initial
comparison is then subjected to a rigorous quantitative
analysis; the comparison of data to mathematical models
will be discussed further in this chapterdsee Section 9.3.
9.2.3 Orthosteric versus allosteric mechanisms
As discussed previously, there are a number of important
differences between molecules that interact with the biological target in an orthosteric manner (binding to the same
site as the endogenous agonist or substrate) or allosterically
(binding to a site removed from that site). The main differences center around the behavior of the target toward the
endogenous signaling system. For orthosteric drugs, the
result is preemptive, in that the endogenous agonist or
substrate is not allowed to bind to the target and impart any
effect; this leads to a defined set of behaviors of the target
toward the endogenous system based on steric hindrance
(see Fig. 9.24). In contrast, there is a great deal more
variability of the endogenous system behavior when an
allosteric molecule is present. These effects can be
permissive, in that the endogenous signaling system may
still function to a certain extent, i.e., the response may be
blocked, partially blocked, potentiated, or otherwise
altered. That is, the quality of the signal may change.
For example, the allosteric modulator LP1805 [N,N-(2methylnaphthyl-benzyl)-2-aminoacetonitrile] binds to
NK-1 receptors and modifies the quality of the signal
produced by the endogenous agonist neurokinin A. Specifically, while neurokinin A activates both Gs and Gq
FIGURE 9.24 Panel on left shows
orthosteric (steric hindrance) antagonism of signaling; this preempts any
other activation of the target. Panel on
the right shows an allosteric system
where the ligand allows the signaling
molecules to bind to possibly produce
response (a permissive system).
proteins, in the presence of LP1805 the Gs protein response
to neurokinin A is potentiated while the Gq response is
blocked [26]dsee Fig. 9.25.
Allosteric effects can be confirmed in separate experiments (see Chapter 8, Allosteric Modulation, Section 8.7).
In general, allosterism, while it can appear as an orthosteric
antagonism under a variety of conditions, may be uncovered through observing the extremes of the antagonist
behavior. There are three characteristic features of allosteric
modulators. They are
1. Probe dependence: An allosteric effect observed with
one receptor probe (i.e., agonist, radioligand) could be
completely different for another probe; see Figs. 4.14
and 8.47.
2. Saturability of effect: That is, when the allosteric site is
fully saturated, the effect stops; see Fig. 4.10.
3. There can be separate effects on probe affinity and
efficacy.
This latter feature can be extremely important since
selective effects on efficacy can be detected only in functional, not binding, assays. Fig. 9.26 shows the selective
inhibition of aplaviroc on the C-C chemokine receptor type
5 (CCR5)-mediated responses to the chemokine RANTES.
It can be seen that the binding of RANTES is minimally
affected, while the calcium transient response to the chemokine is completely blocked [27]. This can be quantified
with a functional allosteric model (Eq. 8.3), where there is
minimal effect on affinity (a ¼ 0.7) but complete inhibition
of formation of the receptor state (b ¼ 0); see Fig. 9.26.
The optimal design of pharmacological experiments Chapter | 9
293
Given that orthosteric and allosteric mechanisms produce
very different profiles of activity, it is very important to
design experiments to identify these mechanisms.
9.3 Null experiments and fitting data to
models
FIGURE 9.25 Bias imposed by an allosteric ligand on a natural
signaling system. While the endogenous agonist (neurokinin A) causes the
receptor to couple to and activate Gq and Gs protein, after binding of the
allosteric ligand LP1805, neurokinin A only permits Gq signaling to occur.
Data from E.L. Maillet, N. Pellegrini, C. Valant, B. Bucher, M. Hibert, J.J. Bourguignon, A novel, conformation-specific allosteric inhibitor of the
tachykinin NK2 receptor (NK2R) with functionally selective properties,
FASEB J. 21 (2007) 2124e2134.
This separation of effect on affinity and efficacy of agonists
can lead to some interesting and useful effects. For
example, Fig. 9.27 shows the effect of the modulator
ifenprodil on responses to N-methyl-D-aspartate (NMDA)
[28]. It can be seen that this potency of ifenprodil actually
increases with increasing concentrations of NMDA, that is,
the agonist increases the affinity of the antagonist. This can
be observed in modulators that block function (b ¼ 0) but
increase the affinity to the agonist (a > 1). Since allosteric
effects are reciprocal, the agonist will also increase the
affinity of the receptor to the modulator. It can be seen that
such effects may be therapeutically useful, since the activity
of the antagonist increases with the activity of the system.
Experimental pharmacology is based on the null technique
since the biochemical reactions that transform receptor
activation to cellular response are largely unknown. Null
methods obviate the requirement for understanding these
mechanisms, i.e., it is assumed that equal receptor effects of
drugs in any given system are translated in an identical
fashion by the cell. Under these circumstances, equiactive
ratios of drug concentration are independent of the cellular
stimuluseresponse process. As discussed in Chapter 6,
Agonists: The Measurement of Affinity and Efficacy in
Functional Assays, Section 6.8.2, a basic requirement of
this method is that the function linking the initial membrane
drug event that triggers response and the end organ
response is monotonic in nature. Failure to comply with
this requirement renders null methods such as the comparison of agonist DRs invalid (see Section 6.7).
As a preface to a specific discussion of the use of datadriven analyses, it is useful to consider the application of
surrogate parameters. Ideally, pharmacological data should
directly be fit to specific models and parameters derived
from that direct fit. However, there are cases where the
specific models predict surrogate parameters that can be
derived without fitting data to a specific model. This can be
an advantage. For example, equiactive DRs from parallel
concentrationeresponse curves shifted to the right by the
antagonist can be used in Schild analysis; therefore, DR
values can be used as surrogates for the analysis of
FIGURE 9.26 Inhibition curves for the allosteric modulator for CCR5 receptors, aplaviroc in blocking the binding of the chemokine RANTES (blue
curve) and the CCR5-mediated calcium transient response to RANTES (red curve). It can be seen that aplaviroc produces a differentially greater inhibition
of efficacy (agonist response) than affinity (binding species). Equations next to the curve illustrate that different receptor species mediate the response
production in each assay. Data redrawn from T.P. Kenakin, Collateral efficacy in drug discovery: taking advantage of the good (allosteric) nature of 7TM
receptors. Trends Pharmacol. Sci. 28 (2007) 407e415.
294
A Pharmacology Primer
FIGURE 9.27 Noncompetitive allosteric antagonism of NMDA responses by ifenprodil. (A) Concentrationeresponse curves to NMDA in rat cortical
neurons in the absence (filled circles) and presence of ifenprodil (0.1 mM, filled diamonds; and 1 mM, filled triangles). (B) pIC50 curves for ifenprodilblocking 10 and 100 mM NMDA. Note the increase in ifenprodil potency with increasing activation by NMDA. Data redrawn from J.N.C. Kew, G.
Trube, J.A. Kemp, A novel mechanism of activity-dependent NMDA receptor antagonism describes the effect of ifenprodil in rat cultured cortical neurons.
J Physiol. 497 (1996) 761e772. See Fig. 7.21B in Chapter 7, Allosteric Modulation for further details.
antagonism without the need to fit to the explicit model.
Under these circumstances, the data can be fit to a generic
sigmoidal curve of the form:
Response ¼ Basal þ
Max Basal
a
1 þ 10ðLogEC50 Log½AÞ
(9.6)
and the shift in EC50 values used to calculate DR estimates
for Schild analysis (see Section 7.3.1). There are certain instances in data-driven pharmacological analyses where it is
useful to use such surrogate parameters.
Ultimately, drug activity must be characterized in terms
of system-independent molecular parameters, and these are
integral parts of mathematical models used to describe
pharmacodynamics events. The usual process for determining this is to assess the veracity of various
FIGURE 9.28 Three mechanisms of orthosteric interaction of an antagonist and agonist for a competition
between the antagonist (B) and agonist (A) for a common
binding site. Top panel: the antagonist has no observable
direct effect. Middle panel: the same type of antagonist
but, in this case, the antagonist has sufficient positive
efficacy to produce an elevated baseline. Bottom panel:
an antagonist that has selective affinity for the inactive
state of the receptor and where the system is such that
sufficient spontaneously formed receptor active state is
present to produce an elevated baseline in the absence of
agonist. In this case, the ligand produces a decrease in the
basal response.
pharmacodynamic models of two molecule single target
systems as descriptors of concentrationeresponse curve
datadi.e., how well does a given model fit? There are
surprisingly few models required to fit a bewildering range
of possible pharmacodynamic behaviors. For orthosteric
surmountable effects, Fig. 9.28 shows three of these, classified by their description of antagonist effects on basal
tissue response; Fig. 9.29 shows the model for orthosteric
insurmountable effects. A wide range of allosteric effects
(see Figs. 7.10 and 7.11) can be described by a single
equation (with a variant where sB ¼ or s 0)dsee
Fig. 9.30. It should also be noted that “goodness of fit”’ is
not proof of veracity of the model since a number of models
often can describe the same pharmacodynamic behavior.
For example, Fig. 9.31 shows a pattern of dextral
The optimal design of pharmacological experiments Chapter | 9
FIGURE 9.29 An orthosteric antagonist that produces insurmountable
effects on the agonist concentrationeresponse curves through persistent
occupancy of the receptor.
295
displacement of concentrationeresponse curves with
concomitant depression of maximal response that is
consistent with three molecular modes of action. How well
a given equation fits a set of data is assessed through the
magnitude of the squares of the differences between
the actual data and the value for the data predicted by the
equation (for an explanation of sum of squares, see Appendix: Statistics and Experimental Design). This often can
be capricious as, again, a number of equations may yield
FIGURE 9.30 Models for allosteric modulation of
agonist (A) response by an allosteric modulator (B) that
produces no direct agonism (top panel) or produces a
direct agonist response (efficacy of modulator ¼ sB;
bottom panel). Descriptions of parameters of the main
equation (Eq. 8.3) described in Section 8.4 of Chapter 8,
Allosteric Modulation.
FIGURE 9.31 Three mechanisms producing dextral displacement and depression of maximal responses of agonist concentrationeresponse curves. A
slowly dissociating orthosteric antagonist (Chapter 6, Orthosteric Drug Antagonism, Section 6.4), an allosteric antagonist that decreases agonist efficacy
(Chapter 7, Allosteric Modulation, Section 7.4.4), or the competitive antagonism of an endogenous agonist released by the agonist (Section 6.8) all could
produce the pattern of concentrationeresponse curves seen in the left panel.
296
A Pharmacology Primer
FIGURE 9.32 Simulation data set fit to an allosteric model panel (A) and to an orthosteric model panel (B). The data points circled with the dotted line
were altered very slightly to cause the sum of squares for computer fit of the points to the model to favor either the allosteric or orthosteric model. It can be
seen that very small differences can support either model even though they describe completely different molecular mechanisms of action.
very similar values for the sum of squares. Fig. 9.32 shows
a hypothetical data set fit to the allosteric model in
Fig. 9.32A and the orthosteric model in Fig. 9.32B. The
circled data points were changed very slightly to cause an
F-test to prefer either model for each respective model,
illustrating the fallacy of relying on computer fitting of data
and statistical tests to determine a molecular mechanism.
9.4 Interpretation of experimental data
The lead optimization phase of discovery and development
is the iterative process of testing molecules, assessing their
activity, and synthesizing new molecules based on that data
(determining an SAR). If there is a single index of activity,
then the attainment of an improved potency (as determined
by statistics) is a useful approach. One way to do this is to
test the molecules repeatedly, determine a mean value with
a measure of variation (standard deviation), and use those
measurements to determine a confidence limit for that estimate. One proposed confidence limit that rapidly leads to
comparison of multiple estimates is the 84% confidence
limit of a mean [29]. For example, if four measurements
yield a mean estimate pIC50 of 7.1 with a standard deviation (sx) of 0.13, then the 84% confidence limits can be
calculated as
Confidence limit ¼ sx $t0:16 $ðnÞ1=2 ;
(9.7)
where the t0.16 is the value for 84% confidence limits and
the standard deviation based on a sample (sx) is
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
nSx2 ðSxÞ2
sx ¼
(9.8)
nðn 1Þ
In this example, t ¼ 1.72; therefore, the 84% confidence
limits for this estimate are 7.1 (1.72 0.13) ¼
7.1 0.22 ¼ 6.9e7.32. This means that 84% of the time,
the true value of the pIC50 will lie between those values
based on this estimate. The significance of the 84% confidence limits lies in the statistical evidence that it may be
concluded that two samples from different populations (i.e.,
two pIC50s) are different if their 84% confidence limits do
not overlap [29]. This provides a simple method of sorting
through a series of compounds to determine which changes
in chemical structure produce statistically significant improvements in activity. For example, Table 9.6 shows a
series of pIC50 values for a range of related compounds;
these data are shown graphically in Fig. 9.33. It can be seen
from these data that significant improvements in potency,
from the base compound 1, are achieved with compounds
6, 8, 9, and 10.
TABLE 9.6 Primary activity data for a series of
compounds.
Number
Compound
pIC50
STD
84% Conf.
Limit
1
ACS55542
7.1
0.13
6.81e7.38
2
ACS55549
7.25
0.13
6.67e7.23
3
ACS55546
6.9
0.15
6.57e7.3
4
ACS55601
7.36
0.17
7e7.73
5
ACS55671
7.2
0.16
6.85e7.55
6
ACS55689
7.75
0.16
7.4e8.5
7
ACS55704
7.5
0.07
7.35e7.65
8
ACS55752
7.8
0.14
7.49e8.1
9
ACS55799
7.65
0.1
7.43e7.87
10
ACS55814
7.86
0.12
7.6e8.1
The optimal design of pharmacological experiments Chapter | 9
FIGURE 9.33 Graphical display of data shown in Table 9.6. The first
compound in the series had a pIC50 of 7.1 (shown in red); bars represent
84% confidence limits. Compounds 2e5 had estimates of 84% confidence
limits that cross the 84% limits of the original compound; therefore, no
improvement in activity was produced by these changes in structure.
However, compounds 6, 8, 9, and 10 (in blue) had means and 84% confidence limits that were different from that of the original compound;
therefore, these represent improvements in activity.
The conventional level of significance chosen for true
difference is 95% confidence (see Chapter 12 Appendix
Statistics and Experimental Design), but there are practical
reasons for using a less stringent level for SAR analysis.
Usually, a single change in chemical structure is made to
assess a change in activity; this allows for a systematic
analysis of the relationship between chemical structure and
pharmacological activity. However, it may be that a single
change in structure may not produce a large improvement
in activity, that is, it may take more than one change to
produce a large improvement. Therefore, small improvements in activity can be utilized by choosing a less stringent
criteria for compound progressiondsee Fig. 9.34. An
analogy from baseball would be to ask whether all efforts
should be aimed at making a home run (>95% confidence)
as opposed to a less ambitious goal of two base hits (two
rounds of >84% confidence).
It is imperative to have a simple unambiguous scale of
activity to guide SAR, but there can be more than one such
guide required (multivariate SAR). For example, if two
related targets or activities are involved and selectivity
between the two is required, then the scale of absolute
activity and the ratio between two activities (selectivity) are
relevant [30]. Table 9.7 shows the activity of 10 compounds with activities on two receptors; the aim of the
program is to optimize the activity on receptor A and
minimize the concomitant activity on receptor B (optimize
the potency ratio of A to B). The standard deviation for the
ratio of activities on A and B is given by
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ðnA 1Þs2xA þ ðnB 1Þs2xB
sA=B ¼
.
(9.9)
nA þ nB 2
297
FIGURE 9.34 Compound activity depicted as a Boltzmann distribution
of values (with the peak representing the mean value and the width of the
curve representing variation). The object is to change the mean activity to
the right of the previous value (increasing activity). The compound
denoted by the blue curve has a mean value that exceeds the 84% confidence band of the previous value but this is less than a value>the 95%
confidence band. However, the next compound that exceeds the 84%
confidence limits of the blue compound exceeds the 95% confidence limits
of the original starting compound. Thus, a better compound is produced in
two steps.
The corresponding confidence limit on the selectivity
ratio is given as
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1
1
(9.10)
þ .
Confidence limit ¼ t$sA=B
nA nB
With the assessment of the error on the ratio comes the possibility to statistically assess differences in selectivity between compounds. For example, for given compounds 1
and 2, the standard deviation of the selectivity is given as
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
df 1 sðA=BÞt2 þ df 2 sðA=BÞ22
sdiff ¼
(9.11)
df 1 þ df 2
where df1 ¼ N12 where N1 is the sum of the values used to
calculate selectivity 1 and df2 is N21 where N2 is the sum
of the values used to calculate selectivity 2. This, in turn,
allows the calculation of the confidence limits for the selectivity of compounds as
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1
1
Confidence limit ¼ t$sdiff
þ .
(9.12)
N1 N2
Just as the effects of changes in chemical structure on
the primary activity could be rapidly tracked through
overlap of 84% confidence limits of the primary pIC50s, the
effects of structural changes on selectivity can be tracked
through overlap of 84% confidence limits on selectivity.
The data shown in Table 9.7 and Fig. 9.35 illustrate a
298
A Pharmacology Primer
TABLE 9.7 Primary activity data D selectivity data for a series of compounds.
Compound
pIC50 recept. A
STDA
nA
pIC50 recept. B
STDB
nB
STDA/B
84% c.l. of selectivity
1
ACS66002
6.95
0.31
10
6.32
0.36
19
DpIC50ALB
0.625
0.434
0.38e0.87
2
ACS68013
7.49
0.201
4
5.86
0.25
14
1.63
0.279
1.4e1.86
3
ACS62071
8.18
0.269
14
8.63
0.36
18
0.451
0.443
0.68 to 0.22
4
ACS64003
8.67
0.168
9
6.12
0.32
21
2.553
0.346
2.35e2.75
5
ACS60052
9.12
0.26
17
9.04
0.29
14
0.084
0.426
0.14 to 0.30
6
ACS58895
9.38
0.2
10
8.32
0.33
9
1.064
0.419
0.78e1.35
7
ACS61004
8
0.14
8
7.9
0.32
7
0.1
0.388
0.2 to 0.4
8
ACS64021
7.8
0.16
6
8.3
0.21
5
0.500
0.319
0.8 to 0.2
9
ACS67091
8.4
0.11
7
7.9
0.34
7
0.5
0.391
0.19e0.8
10
ACS68223
8.9
0.13
8
7.85
0.25
6
1.05
0.328
0.78e1.3
DpIC50A-B, logarithm of the ratio of potencies for receptor A versus receptor B; STDA/B, standard deviation of the selectivity of activity of receptor A versus receptor B according to Eq. (9.11); 84% c.l. of selectivity, the
84% confidence limits of the selectivity according to Eq. (9.12).
The optimal design of pharmacological experiments Chapter | 9
299
A slightly more rigorous or novel approach may be
required for the delivery of a drug that will be novel in the class
or a completely new therapeutic entity. When the program is
focused on such a chemical target, the preceding questions are
still relevant, as well as a few additional questions:
l
l
Is the molecule different from previous molecules and
all other available therapy?
Does this molecule incorporate the newest knowledge
of disease and pharmacology?
Another feature of this latter type of program is the need
for more critical path assays to define and differentiate
unique activity.
9.5 Predicting therapeutic activity in all
systems
FIGURE 9.35 Multivariate structureeactivity relationships. (A) Compound data summarized in Table 9.3 expressed as the pIC50 for the therapeutically relevant activity (activity A) as abscissae and the logarithm of
the selectivity of the same compound for activity A versus B (high number
is favorable) as ordinates. Bars represent standard deviations. Compound 1
(red) represents the original molecule in the active series. Note also how
the most selective compound (compound 4) is not the most potent compound (compound 6). (B) Graph representing the logarithms of the
selectivity of the compounds shown in panel (A) with bars showing 84%
confidence limits. Compounds with 84% confidence limits outside of the
limits of the original compound (compound 1 in red) represent compounds
either less selective (compounds 3, 5, 8), of equal selectivity (compounds
6, 7, 9, 10), or greater selectivity (compounds 2, 4).
complication of multivariate SAR. Specifically, there might
be separate SAR for primary activity and selectivity,
making integration of both activities into one molecule
difficult. As seen in Fig. 9.35A, the most potent compound
is not the most selective.
The type of critical path, and whether primarily single
variate or multivariate SAR is operative, sometimes depends on the type of drug the program is aimed at delivering. A therapeutically useful drug may simply be an
improvement over existing therapy in the class. The primary questions to be answered are the following:
l
l
l
l
Is the molecule active at primary target? (Potency and
efficacy).
Is the molecule promiscuous? (Selectivity).
Is the molecule toxic? (Safety pharmacology).
Is the molecule absorbed, distributed, and does it have
sufficient t1/2? (Adequate drug-like qualities and
pharmacokinetics).
The final step in the drug-discovery lead optimization process
is the application of drug activity parameters to predict therapeutic utility in all systems. As pointed out in Chapter 2, How
Different Tissues Process Drug Response (see Fig. 2.1), a
unique feature of pharmacology as a scientific discipline is that
it provides the capability to use pharmacodynamic models to
predict drug profiles in a host of tissues from parameters
measured in just one system. The quantification of the four
basic properties of drugs was discussed in Section 9.2, and
these are based on the system-independent parameters of drug
activity that can be used in the prediction of observed activity
in the ways outlined in the following sections.
9.5.1 Predicting agonism
The magnitude of s for any agonist in any system is unique
to that agonist in that system; it is not transferable across
different tissues. This is because it is subject to receptor
density and the efficiency of receptor coupling in the tissue
as well as the intrinsic efficacy of the agonist. However,
ratios of s values are transferable; therefore, for any two
agonists, i.e., agonist1 and agonist2 in a system, the desired
parameter is the ratio s1/s2; this is transferable and it is this
ratio that allows prediction of relative agonism for these
two agonists in any system.
Concentrationeresponse curves for two agonists
(agonist1 and agonist2) are shown in Fig. 9.36: the s1/s2
ratio of the agonists is 600. The relative agonist activity of
agonist1 and agonist2 can now be calculated in any other
tissue if a concentrationeresponse curve for one of the
agonists is observed in that tissue. For example, assume the
s1/s2 ratio of 600 is obtained in a test system and the EC50
of agonist1 is 330 nM. Then if agonist1 is found to have an
EC50 of 16.3 mM in a therapeutic system (a 49.4-fold
diminution of potency), the s value for agonist1 in that
system can be determined (Step 2, Fig. 9.36). This is done
through application of one of two equations published by
300
A Pharmacology Primer
FIGURE 9.36 Prediction of agonism using the BlackeLeff operational model. Top left panel: The responses to a test agonist (red) and reference agonist
(blue) are quantified with the BlackeLeff operational model to yield a ratio of efficacy values for the two agonists in this test system. Top right panel: The
change in potency for the reference agonist in the therapeutic system is used to quantify the change in efficacy of the reference agonist through Eq. (9.15).
Bottom right panel: The same ratio change in efficacy (between the test and therapeutic system) is applied to the ratio of the test agonist to predict the
responses of the test agonist in the therapeutic system.
Black et al. [13]. These equations link the maximal
response and potency (EC50) to s and KA values through
Maximal Response ¼
sn Em
sn þ 1
(9.13)
and
EC50 ¼ KA
ð2 þ sn Þ1=n 1
(9.14)
It is assumed that the affinity of the agonist has not changed
between the test and therapeutic system (same KA value used to
fit the data). This may not be a valid assumption when this model
is used to fit activation of different signaling pathways for the
same agonistdvide infra. The efficacy of agonist1 in the therapeutic system is calculated with a ratio derived from Eq. (9.14)
1=n
2 þ snðTestÞ
1
EC50ðTherapeuticÞ
DPotency ¼
¼ 1=n
EC50ðTestÞ
1
2 þ snðTherapeuticÞ
(9.15)
Thus
a
49.4-fold
diminution
of
potency
(EC50(Test) ¼ 330 nM, EC50(Therapeutic) ¼ 16.3 mM) and
application of Eq. (9.15) yields a s value for agonist1 in the
therapeutic system of 60. This ratio diminution of efficacy
(s1Therapeutic/s1Test ¼ 60/3000 ¼ 0.02) will be imposed on
all agonists in the two systems, and therefore it also applies
to agonist2. This means that the operational s value for
agonist2 in the therapeutic system will be s2Testsratio ¼ 50.02 ¼ 0.1. Application of the model thus predicts a low level of agonism for agonist2 in the therapeutic
systemdsee Step 3 in Fig. 9.37).
A valuable application of the above technique is in the
prediction of possible observable partial agonist activity for
antagonists that possess low levels of efficacy. No response
(i.e., “silent” antagonism) may be observed if the test system has a low receptor level and/or low efficiency of receptor coupling. However, in vivo, if a low efficacy
antagonist interacts with a very sensitive tissue, it may
produce an agonist response, and there are cases where this
may be harmful. Therefore, the determination of any
The optimal design of pharmacological experiments Chapter | 9
301
FIGURE 9.37 The interplay of
relative efficacy (ordinate scale) and
bias (abscissal scale). It can be seen
that the antagonism of responses
produced by low efficacy ligands can
still be influenced by bias.
possibility of agonism with antagonists should be made in
very sensitive test systems (i.e., see Fig. 9.4).
As noted previously, efficacy predictions using the
BlackeLeff operational model are valid when the agonists
produce their response through the same signaling
pathway but may vary in cases of biased agonism in
systems where the cell controls the relative importance of
the various signaling pathways involved (see Section 6.7).
For this reason, the determination of s and KA values
should be strictly linked with the specific signaling
pathway in the form of transducer ratios Dlog(s/KA). It
should also be noted that while bias estimates [in the form
of DDlog(s/KA) values] determine at what relative concentration a given selective agonism will occur, they will
not in themselves predict whether agonism will occur at
all; this is still determined by the actual value of s (as
discussed above). This is highlighted by the array of
biased ligands shown in Fig. 9.37. In this case, two
signaling systems (e.g., G-protein activation and b-arrestin
signaling) controlled by the same receptor are monitored
for biased agonism; the ordinate axis refers to the relative
efficacy of the agonists for the two signaling pathways and
the abscissal axis shows the actual bias of the agonists.
Since both efficacy and affinity may vary with the
signaling pathway being measured, different patterns of
biased effects may be observed. Thus, a biased ligand
could produce selective antagonism of an unwanted
pathway or selective agonism of a preferred pathwaydsee
Fig. 9.37. This underscores the importance of linking efficacy measurements with bias measurements in the
complete assessment of biased ligands.
9.5.2 Predicting binding
The equilibrium dissociation constant of the ligande
receptor complex (Kd) can be a very predictive parameter,
since it links the in vivo concentrations with what might be
expected pharmacodynamically at the receptor (when the
concentration is equal to Kd then 50% of the receptors are
occupied by the ligand). The two types of drug where the
Kd cannot automatically be applied to the relationship between concentration and effect are
1. High efficacy full agonists since the efficacy of the
agonist can produce large sinistral displacement of
concentrationeresponse curves for function versus receptor occupancy.
302
A Pharmacology Primer
2. Positive allosteric modulators (PAMs) where the affinity is conditional upon the cobinding ligand (usually
the endogenous agonistdsee Section 8.4.3 in Chapter
8, Allosteric Modulation).
The value of predictive parameters determined from
pharmacodynamic models is illustrated by the varied effects of a PAM-agonist shown in Fig. 7.33. It can be seen
that a concentration of PAM-agonist equal to the Kd value
can produce quite different observable profiles in tissues of
varying sensitivity to the endogenous agonist (as shown by
the changes in the receptor levels [Rt]). In tissues of low
sensitivity, little sensitization but an increased maximal
response is observed