# Population responses

```D
DOSE-RESPONSE
RELATIONSHIPS
R
Dr. Alexandra Newton
January 12 2012
1
Goal
To understand dose-response relationships and how these
are affected by antagonists
Albuterol
D
Molecular
R
receptor
Cellular
Organ
[cAMP]
Human
Bronchodilation
D+R
DR
Response
Asthma
Lecture Outline
Dose-Response Relationships
1. Law of mass action and reversible binding
2. Relationship between drug concentration and
receptor occupancy
3. Antagonists (competitive and noncompetitive)
4. Population responses
D
R
Law of Mass Action
rate constant, units M-1 sec-1
k1
D+R
DR
Response
k-1
rate constant, units sec-1
• D and R associate at rate proportional to both [D] and [R]
• DR dissociates at rate proportional to [DR] only
• Reversible
k1
D+R
DR
Response
k-1
Rate of association = k1[D][R] ← proportional to both [D] and [R]
Rate of dissociation = k-1[DR] ← proportional to [DR] only
At steady state, rate of association = rate of dissociation
k1[D][R] = k-1[DR]
k__-1
[D][R]
_____
=
= Kd
[DR]
k1
equilibrium dissociation constant
units = M
Relationship between equilibrium constant and free energy:
DG = -RTlnK
R=1.98 cal/&deg;mol
T=310 &deg;K = 37 &deg;C
Lecture Outline
Dose-Response Relationships
1. Law of mass action and reversible binding
2. Relationship between drug concentration and
receptor occupancy
3. Antagonists (competitive and noncompetitive)
4. Population responses
D
R
Relationship between Drug Concentration and
Response or Receptor Occupancy
D+R
Drug concentration at which drug
effect (response) is half-maximal =
EC50
DR
Response
Drug concentration at which receptor-bound
drug (receptor occupancy) is half-maximal =
Kd
Relationship between Kd and
Receptor Occupancy
Receptor occupancy = fraction of total receptors (RT) occupied by
drug (aka fractional saturation) = [DR]/[RT]
[DR]
[DR]
___
_______
Fractional saturation =
[RT] = [R] + [DR]
k__-1
[D][R]
_____
=
= Kd ← When [D] = Kd, [R] = [DR]
[DR]
and [DR]/[RT] = 0.5
k1
1.0
[DR]
___
[RT]
[DR]
___
[RT]
log Kd
log [D]
Agonists
100
Response
Full agonist: maximal response
Partial agonist: partial response
Inverse agonist: decreases basal response
0
0.1
10
[D], nM
1000
Lecture Outline
Dose-Response Relationships
1. Law of mass action and reversible binding
2. Relationship between drug concentration and
receptor occupancy
3. Antagonists (competitive and noncompetitive)
4. Population responses
D
R
Antagonists
aka inhibitors (I)
Bind to receptor but do not promote response
I+R
IR
Competitive
antagonist I
No response
Noncompetitive
I
antagonist
D
I
I
I
I
D
I
Competitive Antagonist
I
+
Kd
D+R
DR
Ki
IR
Response
Noncompetitive Antagonist
I
+
Kd
D+R
I
+
DR
Ki
D + IR
Kd
Response
Ki
IRD
Kd remains
unchanged
Maximum response
1
_______
is reduced
1 + [I]/Ki
More Definitions
Mixed antagonist: binds to separate site but modulates the ability of agonist to bind
Physiological antagonist: a drug (or endogenous mediator) that antagonizes the effect
of another drug (or endogenous mediator) by producing an opposing physiological
response, typically by a different type of receptor.
Example: epinephrine acting at β1 receptors physiologically opposes the decrease
in heart rate that occurs in response to acetylcholine acting at M2 receptors
Reversible antagonist: reversible binding
Irreversible antagonist: irreversible binding (law of mass action not followed)
Allosteric activator: binds to site independent of agonist binding site and enhances
activity of agonist
Allosteric inhibitor: binds to site independent of agonist binding site and reduces
activity of agonist
Receptor Desensitization
Response decreases with time and/or repetitive stimulation
Potency and Efficacy
Potency refers to the dose that causes a given effect
most potent = lowest EC50
least potent = highest EC50
Efficacy refers to the maximum response (effect)
most efficacious = largest response
least efficacious = smallest response
Lecture Outline
Dose-Response Relationships
1. Law of mass action and reversible binding
2. Relationship between drug concentration and
receptor occupancy
3. Antagonists (competitive and noncompetitive)
4. Population responses
D
R
Quantal Dose-Response Curves
ED50
Median effective dose: produces
specified effect in 50% of patients
LD50
Median lethal dose
Therapeutic index = LD50/ED50
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