Introduction / pH / Activity / pH measurement / pKa / LogP / Partition Solvents / Use of LogP / Methods / Refs
A guide to Log P and pKa
measurements and their use
By Mark Earll BSc(Hons) CChem MRSC (C) Copyright 1999-2006, All rights
reserved.
Return to Mark's Analytical Chemistry Index Page
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Disclaimer: This article is for guidance and educational purposes only. The
author can accept no responsibility for loss or damage however caused. The
author recommends that manufacturers advice be consulted exclusively
when using any laboratory products.
PREFACE TO 2006 REVISION: This page was written in 1999 and can be
seen as summarising my practical knowledge of the field at that time. Things
have moved on particularly in the area of high throughput measurements. For
the latest in high throughput pKa and LogP measurements I suggest you
contact Sirius Analytical Instruments and for high throughput permeability
contact Pion Inc. I will continue to add things to this site on the use of
physical chemistry measurements in QSAR modelling. Please see section 1.7.
to 1.9.
Table of Contents:
•
•
Introduction
Contents
•
LogP/pKa measurement
techniques
•
•
Understanding pKa and
Log P measurements.
o The pH scale
o Activity
o Practical pH
measurement
o pKa or
Dissociation
Constant
o Log P and
Partition
Coefficients
o Choice of
partition solvent
o How are LogP
results related to
activity?
o How are LogP
results related to
solubility?
o What do LogP
values mean in
practice?
Measurement strategy
Aqueous Titration
using Sirius
instruments
o Yesuda-Shedlovsky
experiment
o Ion Pair Log P's
o pKa by Manual
Titration
o pKa by U.V.
Spectroscopy
o pKa by Solubility
Method
o Filter Probe
Measurements
o Log D and Log P
by Filter Probe
Method
o Log P by Shake
Flask
o Log P by HPLC
References
Appendix 1 - Calculating
Log D and % ionised
Appendix 2 - Worked
example calculations
o
•
•
•
The following Javascript
calculators will help you
calculate % ionised and
Log D from pKa and Log
P values:
Percent Ionised
Log D
Table of pKa values:
(Coming soon)
Introduction / pH / Activity / pH measurement / pKa / LogP / Partition Solvents / Use of LogP /
Methods / Refs / Top
Introduction
The pKa or 'Dissociation Constant' is a measure of the strength of an acid or a base.
The pKa allows you to determine the charge on a molecule at any given pH.
The Partition Coefficient is a measure of how well a substance partitions between a lipid
(oil) and water.
pKa and Log P measurements are useful parameters for use in understanding the
behaviour of drug molecules. Different ionic species of a molecule differ in physical
chemical and biological properties and so it is important to be able to predict which ionic
form of the molecule is present at the site of action. The Partition Coefficient is also a
very useful parameter which may be used in combination with the pKa to predict the
distribution of a drug compound in a biological system. Factors such as absorption,
excretion and penetration of the CNS may be related to the Log P value of a drug and in
certain cases predictions made.
The measurement of pKa and Log P values are not straightforward. Experiments must be
very carefully performed under standard conditions to ensure the results are valid and
require interpretation of data which takes time and experience. In addition no one method
is available for all compounds due to problems of insolubility, lack of removable protons
and extreme values.
This guide gives the theoretical basis of the pKa and LogP parameters as well as
describing the techniques that can be used to measure them indicating which methods are
appropriate for problem samples. I have also briefly indicated the use of these
measurements in rational drug design.
For more information please see the References section.
Introduction / pH / Activity / pH measurement / pKa / LogP / Partition Solvents / Use of LogP /
Methods / Refs / Top
1.0 Understanding pKa and Log P measurements.
1.1 The pH scale
Arrhenius 1887 was the first person to give a definition of an acid and a base, namely that
an Acid gives rise to excess of H+ in aq solution whereas a Base gives rise to excess of
OH- in solution. This was refined by Bronsted-Lowry in 1923 such that a proton donor
was defined as an acid and a proton acceptor as a base They also introduced the familiar
concept of the conjugate Acid - Base pair. The final refinement to Acid Base theory was
completed by Lewis in 1923 who extended the concept to an Acids being an e -pair
acceptor and a base a e -pair donor.
The pH concept was introduced in 1909 by the Danish chemist S.P.L.Sorenson
pH is defined by the negative logarithm of the hydrogen ion activity:
where aH = activity of the hydrogen ion
The pH scale derives from the characteristics of the auto-dissociation of Water. Pure
water has a low conductivity and is only slightly ionised however does Water dissociate
slightly into Hydronium ions and hydroxide ions:
or
The concentration of H+ and OH- ions, which are equal, are 1x 10-7 ions per litre The
equilibrium constant (or ion product ) for the dissociation of water, Kw, is
by taking logs of both side we get:
Using the standard abbreviation p for {-log10} we get:
This equation sets the pH scale to 0-14, which gives a convenient way to express 14
orders of magnitude of [H+]. Any solution with pH>7 contains excess hydroxyl ions and
is alkaline; those with pH<7 are acidic, containing excess hydrogen ions
pH scale
Introduction / pH / Activity / pH measurement / pKa / LogP / Partition Solvents / Use of LogP /
Methods / Refs / Top
1.2 Activity
A complication arises in electrochemistry due to the non-ideal nature of ions in solution.
The activity of an ion at infinite dilution is equal to its concentration but as the
concentration increases ionic attraction and incomplete hydration results in a drop in
effective concentration. This means the law of Mass Action is only valid when activities
are used in place of concentrations
Activity is defined as the "apparent concentration" of an ionic species, due to the
attraction which ions can exert on one another and the incomplete hydration of ions in
solutions that are too concentrated. The lower the concentration the less the interaction
becomes. At infinite dilution activity coefficients approach unity
The activity of a species X is equal to the product of its concentration and its activity
coefficient,
The pH from an electrode relates to {H+} not [H+] though below Ionic strength of 0.01
these terms are very close between pH 2 and pH 10
Introduction / pH / Activity / pH measurement / pKa / LogP / Partition Solvents / Use of LogP /
Methods / Refs / Top
1.3 Practical pH measurement
A pH electrode consists of a pH sensor which varies in proportion to the {H+} of the
solution and a reference electrode which provides a stable constant voltage. The output is
in mV which needs to be converted to pH units.
Where Ec = reference potential
Nf = Nernstian slope factor = Nf=2.3RT/nF = 59.1 at 25 C
Where R=Gas constant
T=abs Temp in Kelvin
F=faraday constant
n=Valance factor
As can be seen from the equation the slope factor is temperature dependent
the pH is derived from:
At pH 7 where {H+}={OH-} the voltage from the electrode is zero, this is called the
Isopotential Point. In theory this point is temperature independent. IUPAC-NBS
operational pH scale is defined as the pH relative to a standard buffer measured using
hydrogen electrode. In practice a pH electrode is calibrated with a standard pH 7.00
buffer to determine the isoelectric point and a standard buffer at either pH 4 or 9 to
determine the slope. Conventional pH meters will read accurately over a range 2.5 - 11.
Beyond this their accuracy is dubious.
In recent years Sirius Analytical Instruments have produced a series of dedicated
pKa/LogP instruments. In the PCA 101 pKa instrument the calibration is carried out in a
more sophisticated way adding empirical correction factors at the extreme ends of the pH
spectrum where the electrode behaviour is non-ideal. In this way measurements at pH 1
or 13 are possible. This is based on the work of Alex Avdeef (1)
Introduction / pH / Activity / pH measurement / pKa / LogP / Partition Solvents / Use of LogP /
Methods / Refs / Top
1.4 pKa or dissociation constant
Bronsted was the first to show the advantage of expressing the ionisation of both acids
and bases the same scale. He made an important distinction between Strong and weak
bases:
Strong acids and bases - defined as completely ionised in pH range 0-14
Weak acids and bases - defined as incompletely ionised in pH range 0-14
The pKa or ionisation constant is defined as the negative logarithm of the equilibrium
coefficient of the neutral and charged forms of a compound. This allows the proportion of
neutral and charged species at any pH to be calculated, as well as the basic or acidic
properties of the compound to be defined.
"Thermodynamic Ionisation Constants" require the use of activities, being an "Infinite
Dilution" definition. The measurement of activities is highly impractical, so in practice a
high ionic strength swamping background electrolyte is used to give a "Constant Ionic
Medium" pH definition. This is closely related to the thermodynamic definition. Such
pKa values are independent of concentration and are of the type usually quoted in the
literature.
Thermodynamic Ionisation constants
for acids:
where{ } = activity in Mole litre-1
pKa = -log10(Ka)
for bases
pKa = -log10(Ka)
At a given temp these are Thermodynamic Ionisation constants, which are independent
of concentration. KTa. Since log 1 = 0 the pKa corresponds to the pH at which the
concentration of ionised and neutral forms are equal.
Ionisation constants that measured by Spectroscopy are "Concentration Ionisation
Constants" These constants are measured ignoring activity effects and are dependent on
concentration. It is therefore important that the concentration of the compound measured
is quoted. Comparison of different compounds is only valid if their concentrations are
identical.
Concentration Ionisation constants
where [] = conc
These result from spectroscopic measurements where concentrations are used due to the
beer lambert law.
The "Thermodynamic" Ionisation Coefficient is related to the "Concentration" Ionisation
Coefficient by:
where f=activity coefficient
pKa values are temperature dependent in a non-linear and unpredictable way. Samples
measured by potentiometry are held at a constant temperature using a water jacket and
thermostated water bath. Spectroscopic values are measured at ambient temperature. No
pKa value should ever be quoted without the temperature. There is the additional
question of whether pKa values should be measured at biological temperature as well as
the standard 25 degrees. The former would have more meaning to biologists and the latter
to chemists. Standard practice is to measure pKa’s at 25’C
A useful formula for calculating the % ionisation of a compound at a particular pH from
its pKa is
(Where charge = 1 for bases and -1 for acids)
% ionised plots of an Acid and a Base with a pKa of 8.0:
Acid
with
pKa
=
8.0
Base
with
pKa
=
8.0
Introduction / pH / Activity / pH measurement / pKa / LogP / Partition Solvents / Use of LogP /
Methods / Refs / Top
1.5 Log P and Partition Coefficients
The Partition Coefficient itself is a constant. It is defined as the ratio of concentration of
compound in aqueous phase to the concentration in an immiscible solvent, as the neutral
molecule. In practical terms the neutral molecule exists for bases > 2 pKa units above the
pKa and for acids > 2 pKa units below. In practice the Log P will vary according to the
conditions under which it is measured and the choice of partitioning solvent.
Partition Coefficient
Partition Coefficient, P = [Organic] / [Aqueous] Where [] = concentration
Log P= log10 (Partition Coefficient)
NOTE:
Log P = 1 means 10:1 Organic:Aqueous
Log P = 0 means 1:1 Organic:Aqueous
Log P = -1 means 1:10 Organic:Aqueous
Log D is the log distribution coefficient at a particular pH. This is not constant and will
vary according to the protogenic nature of the molecule. Log D at pH 7.4 is often quoted
to give an indication of the lipophilicity of a drug at the pH of blood plasma.
Distribution Coefficient
Distribution Coefficient, D = [Unionised] (o) / [Unionised] (aq) + [Ionised] (aq)
Log D = log10 (Distribution Coefficient )
LogD is related to LogP and the pKa by the following equations:
for acids
for bases
The graphs below show the distribution plots of an acid a base and a zwitterion
Acid pKa = 8
Base pKa =8
Zwitterion pKa (base) = 5.6 & (acid) = 7.0
Ion Pair Partitioning
In practice not only neutral molecules but also ion pairs may partition. The charged
species may pair with a reagent ion or even, in certain cases, itself. This leads to great
complication of the experimental determination. Both the Log P and the LogD values
may be affected if one or more of the charged species partitions. Ion pairing effects may
be fully determined with the Sirius PCA101 or GL-pKa instrument, but at least two to
three titrations need to be carried out. Ion pairing effects will cause errors in any
spectroscopic measurements.
Both the ionic strength and the type of counter ion used in solution have a pronounced
effect on the ion pairing phenomenon. The high ionic strength used in the potentiometric
determinations in the Sirius PCA101 instrument tends to encourage ion pairing effects.
The spectroscopic measurements of Log P are measured at a much lower ionic strength,
hence comparisons will be invalid.
The question arises how valid is the use of a background electrolyte? Typically 0.1M of a
background electrolyte is used. This is very close to the biological level of 0.16M. The
type of electrolyte is also called into question. 0.15 M KCl is generally used due to its
similarity with NaCl. NaCl cannot be used because of the "sodium effect" on the
electrode at high pH. Measurements in KCl have been found to match those in NaCl
almost exactly. Initially the Sirius Instruments used KNO3, as used in the development of
Metal Ligand binding titrations, from which the titrimetric method was developed. KNO3
is obviously alien to most biological systems.
Introduction / pH / Activity / pH measurement / pKa / LogP / Partition Solvents / Use of LogP /
Methods / Refs / Top
1.6 Choice of Partition solvent
The choice of partition solvent has been subject to debate in recent years. The most
commonly used solvent has been octan-1-ol after the work of Leo and Hansch at Pomona
college California. Octanol was chosen as a simple model of a phospholipid membrane;
however it has shown serious shortcomings in predicting Blood-brain barrier or skin
penetration. More recently a group at ICI in 1989, (Leahy, Taylor and Wait) have
proposed the use of four critical solvents for modelling biological membranes. These are
octanol, chloroform, cyclohexane and propylene glycol dipelargonate (PGDP). Log P
values measured in these different solvents show differences principally due to hydrogen
bonding effects. Octanol can donate and accept hydrogen bonds whereas cyclohexane is
inert. Chloroform can donate hydrogen bonds whereas PGDP can only accept them.
Octanol
amphiprotic
(Hbonding)
Chloroform
proton
donor (Hbonding)
PGDP
proton
acceptor
(Hbonding)
Alkane
inert
Phospholipid
Phospholipid
Model: (ref 8)
Which solvent to use is debatable; however delta log P values have been found to be
useful in several QSAR studies.
log P(octanol-water) - logP(PGDP-water)
predicts cardioselectivity in oxypropanolamines
(ref 5)
log P(octanol-water) - logP(alkane-water)
has been suggested reflects hydrogen bonding
capacity, which has implications for skin
penetration. Compounds with high log P values
and low H bonding capacity can readily get past
ester/phosphate groups in skin membranes. (ref
6)
log P(octanol-water) -logP (cyclohexane-water)
correlates inversely with Log(Cbrain/Cblood)
for a series of H2-receptor histamine
antagonists (ref 7)
Liposomes.
Recently partitioning experiments have been carried out with Liposomes. Liposomes are
self assembling model membranes composed of phopholipid groups such as
phosphatadylcholine. The lipid molecule is dissolved in chloroform and deposited by
evaporation onto a large surface such as a large round bottomed flask. The liposome is
then hydrated by adding water and agitated. The lipids then self assemble to form lipid
bilayers which form spheres, often concentric (multilammellar). For partitioning
experiments it has been found that Unilamellar (single layer) liposomes are required.
These can be formed by a a combination of freeze-thawing and extrusion through a fine
filter or french press under pressure.
Neutral LogP values from liposomes tend to be very similar to those measured in octanol
but the ion-pair LogP values differ. The "Surface Ion Pair" log P is found to be much
higher in bases, zwitterions and amphophiles. The values for acids tend to be similar to
the octanol values. This reflects the increased potential for partitioning of molecules with
basic groups into membranes.
QSAR studies have found improved correlations with liposome derived "Surface Ion
Pair" LogP values.
It should be realised that for some compounds it is not possible to make measurements
due to insolubility, impurity or instability reasons. It is practically impossible to make
measurements on highly insoluble compounds, although pKa values may sometimes be
measurable by aqueous-methanol titrations. In practical terms results become
meaningless for compounds with extreme insolubility.
Introduction / pH / Activity / pH measurement / pKa / LogP / Partition Solvents / Use of LogP /
Methods / Refs / Top
1.7 How are Log P results related to biological activity?
Relationships between Log P and activity are often found in series where structural
modifications have not significantly affected the pKa values. Hansch in 1964 showed that
these relationships were often parabolic hence the relationship often leads to an optimum
value for the log P for a desired activity or selective distribution. Relationships of the
type:
Activity= m log P + k’ (linear)
Activity= m log P - c(log P)2 - k(parabolic)
Activity= m log P - c(blog P +1) - k (rectilinear) (where m, k and c are constants)
are generated using regression analysis to correlate observed biological data with
measured partition coefficients.
The best way of relating LogP, pKa and other physico-chemical data to biological
activity is using Multivariate techniques such as Principal Components Analysis and
Partial Least Squares Regression. To understand these techniques and for software to
do this please visit Umetrics at www.umetrics.co.uk
It must be remembered that measured log P values only correlate with activity in certain
instances. The use of organic solvents to model complex biolipids is very simplistic
and cannot explain phenomena such as the large difference in activity between
molecules of wildly different structures or between enantiomers. In these cases it is
very useful to combine physical measurements with molecular modelling, molecular
property and spectroscopic data and use multivariate analysis.
For both CNS penetration and gastric absorption many studies show a parabolic
relationship with an optimum Log P value of around 2 ± 1. Evidence for this comes from
a wide variety of experiments in the literature from brain concentration of radiolabelled
compounds to CNS behavioural studies.
Recently more sophisticated analysis of molecular properties such as "Partial Charged
Surface Area" (PSA) and the hydrogen bonding properties of molecules have lead to
better predictions of oral absorption.
Although lipophilicity is just one of many factors involved in biological activity it is
often one of the most influential. In PLS regression of molecular properties vs biological
activity measurements of LogP almost always features in the more important coefficients.
It is also a good idea to add a LogP squared to any regression analysis to take account of
the non linearity mentioned above.
1.8 How are Log P results related to solubility?
Log P’s of neutral immiscible liquids run parallel with their solubilities in water; however
for solids solubility also depends on the energy required to break the crystal lattice.
Bannerjee, Yalkowsky and Valvoni (1980) Envir.Sci.Tech,14,1227 have suggested the
following empirical equation to relate solubility, melting point and Log P:
where S is the solubility in water in micromoles per litre.
It is therefore possible to have compounds with high Log P values which are still soluble
on account of their low melting point. Similarly it is possible to have a low Log P
compound with a high melting point, which is very insoluble.
In cases of precipitation when titrating a basic compound, the solubility of the free base
may be calculated using the equation:
Where:
= solubility at
= solubility of free base
1.9 What do Log P values mean in practice?
From a survey of the literature, it is possible to obtain some general guidelines about the
optimum Log P values for certain classes of drugs. When designing drug molecules some
thought should be given to the following:
Studies have found: (bear in mind these may not apply to your class of chemicals)
•
•
•
•
•
•
Optimum CNS penetration around Log P = 2 +/- 0.7 (Hansch)
Optimum Oral absorption around Log P = 1.8
Optimum Intestinal absorption Log P =1.35
Optimum Colonic absorption LogP = 1.32
Optimum Sub lingual absorption Log P = 5.5
Optimum Percutaneous Log P = 2.6 (& low mw)
Formulation and dosing forms:
•
•
•
•
Low Log P (below 0) Injectable
Medium (0-3) Oral
High (3-4) Transdermal
Very High (4-7) Toxic build up in fatty tissues
Drug Clearance and Toxicity
•
•
Increasing LogD 7.4 above 0 will decrease renal clearance and increase metabolic
clearance.
High Log D7.4 compounds will tend to be metabolised by P450 enzymes in the
liver.
•
•
•
A high degree of ionisation keeps drugs out of cells and decreases systemic
toxicity.
pKa in range 6 to 8 is advantageous for membrane penetration.
Drugs should be designed with the lowest possible Log P, to reduce toxicity,
non-specific binding, increase ease of formulation and bioavailability. Drugs
should also be as low mw as possible to lower the risk of allergic reactions. (See
principle of minimum hydrophobicity)
Physiological pH values:
•
•
•
•
•
Stomach 2
Kidneys 4.2 (variable)
Small Intestine Fed 5.0 Fasted 6.8
Duodenal Mucus 5.5
Plasma 7.4
Principle of minimum hydrophobicity
Taken from the introductory chapter in "Lipophilicity in Drug Action and Toxicology"
VCH 1995 Vol 4 p22-24 Bernard Testa, Vladimir Pliska and Han van de Waterbeemd.
"Both parabolic and bilinear relationships allow one to derive the optimum value of log P for transport to
a given location, within the time of a biological assay. Evidence for an optimum lipophilicity for CNS
depressants was found by 1968. Hancsh was then able to assert that in order for drugs to gain rapid access
to the CNS, they should preferably have a logP value near 2.0. Subsequently, studies on anesthetics,
hypnotics and other CNS agents have lead to the "Principle of Minimum Hydrophobicity in Drug Design"
The thrust of this is to keep drugs out of the CNS, and thereby avoid CNS related side effects such as
depression, weird dreams and sedation, one should design drugs so that logP is considerably lower than
2.0. This ploy has been successful in the new generation of non-sedative antihistamines.
That we require drugs to have lower rather than higher lipophilicity depends also on other observations
made over the past 30 years. Many studies on plants animals, fish various organelles such as liver
microsomes, and enzymes have shown a linear increase in toxicity or inhibitory action in a series of
compounds as LogP or pi increases.
A very high lipophilicity should also be avoided because of adverse effects on protein binding and on drug
absorption, including solubility.
Linear and sometimes parabolic relationships have been found between lipophilicity and drug metabolism,
either in whole animals, in liver microsomes, or by specific enzymes such as cytochrome P450. Metabolism
can be undesirable for two reasons; it may limit drug bioavailability, or it may produce toxic metabolites.
The ideal drug candidate, going into human studies, should have already been designed with the idea of
keeping lipophilicity as low as possible, provided this can be done without loss of affinity to the target
receptor."
Lipinski's "Rule of 5" for Drugs
Chris Lipinski of Pfizer derived an easy to use 'rule of thumb' for drug likeness in
molecules after surveying the worlds marketed drugs.
The rule states that for reasonable absorption
•
•
•
•
Keep H-Bond donors below 5 (sum of OH and NHs)
Keep mW below 500
Log P should be below 5
No more than 10 H bond acceptors (sum of Ns and Os)
Like all rules they are there to be broken and a number of exceptions exist. I have
personally worked on a couple of well-absorbed drugs which broke this rule but as a
general guide it works well. Remember that you may have charge in your molecule so
that LogD(7.4) or LogD(5.5) is really the important parameter rather than Log P. Keeping
LogD(7.4) around 2 seem generally good advice. Manipulating the pKa can be a way of
improving a molecule.
Clarke-Delaney "Guide of 2" for Agrochemicals
Erik Clarke and John Delaney of Syngenta have derived a set of guidelines for
agrochemicals
•
•
•
•
•
•
Mw 200-400
Mpt <200
LogPoct <2
pKa (base) 7+/- 2
Log Sw 2+/-1
Stability alerts <2
For other attempts at rules for agrochemicals see references 19 and 20 Refs
Introduction / pH / Activity / pH measurement / pKa / LogP / Partition Solvents / Use of LogP /
Methods / Refs / Top
2.0 Measurement Strategy
The strategy for measuring pKa and Log P is determined by the solubility of a compound.
The compound must be soluble (and stable) during any procedure to ensure equilibrium
is maintained.
Typically in titration methods the compound is titrated towards the direction of its neutral
form, resulting in a dramatic drop in solubility. Often several experiments are required to
determine the concentration required for the compound to stay in solution. Data collected
while precipitation is occurring produces incorrect results. Sometimes if sufficient data is
collected while the compound is in solution the pKa may still be calculated.
The pKa's of poorly soluble compounds must be measured in aqueous-methanol solution.
If several titrations are carried out with different ratios of Methanol:Water the YesudaShedlovsky equation can reveal the theoretical pKa in purely aqueous solution.
Log P determination of poorly soluble compounds is a problem. Provided the Log P is
high enough the compound may be determined by titration, adding the sample to the
octanol first. The compound will then back partition into the aqueous layer. If this fails
then spectroscopic methods have to be employed since more dilute solutions may be
used.
Substances submitted for pKa and LogP need to be pure, of accurately known
composition and be submitted as free bases or inorganic acid salts. In general no reliable
measurements can be made on organic acid salts.
A good strategy is to submit compounds in a series. The reasons for this are:
•
•
•
•
•
to compare and contrast the properties of a closely related series, using directly
comparable techniques.
to find a common measurement strategy for all the compounds in a series
to identify experimental problems common to the series
to prevent unnecessary measurements, only key members of the series should be
chosen
to ensure reagents with short shelf lives, and apparatus can be prepared
Introduction / pH / Activity / pH measurement / pKa / LogP / Partition Solvents / Use of LogP /
Methods / Refs / Top
3.0 Log P/pKa measurement techniques:
Method
Measures
Advantage
Disadvantage
Conc required
Sample
size
Sirius Potentiometric
pKa/Log P
pKa, Log P,
Rapid, Convenient
Insoluble or neutral
samples cannot be
measured
0.0001M
(0.1mM)
1-5 mg
Log Papp
Sirius YesudaShedlovsky
pKa
pKa for insoluble samples
Takes three or more
titrations
0.0005M
(0.5mM)
5mg
Sirius Ion Pair Log P
LogP, Log P(ip)
Predict Log D more accurately
Takes three or more
titrations
0.0001M
(0.1mM)
3-15 mg
Manual potentiometric
pKa
pKa
Simple, rapid
Not for low or
overlapping pKa's
>0.0025M(2.5mM)
50 mg
pKa by UV
pKa
pKa for poorly soluble or scarce
compounds
Slow
0.000025M(25uM)
6 mg
pKa by Solubility
pKa
pKa for very insoluble
compounds
Slow, Low accuracy
Below
0.0005M
(0.5mM)
10 mg
LogP by Filter Probe
Log P
Log P for poorly soluble
compounds, Reliable > Log P of
0.2.
Messy, Slow to set up,
requires care. Inaccurate
below Log P of 0.2
0.000025M
(25uM)
6 mg
LogD by Filter probe
pKa, Log P, Log
D
Can determine LogP app at any
pH
Only possible with
compounds possessing
Isobestic point
0.000025M
(25uM)
6 mg
Log P by Shake flask
Log P, Log D at
chosen pH
Low Log P values. Can
investigate surface effects
Slow, Tedious, messy
0.000025M
(25uM)
6mg
Log P by HPLC *
Log D at pH 7
Many compounds may be
measured at once. Small sample
size
Inaccurate, generally
only carried out at pH 7
~ 2.5mM
0.5 mg
(* NB: This table is rather out of date. See Sirius Analytical's new high throughput
instruments)
3.1 Aqueous Titration using Sirius Potentiometric Method
This method is the easiest method of pKa and Log P measurement, and provides detailed
information on the partitioning characteristics of a sample at all pH values.
The PCA101 and GLpKa (TM) pKa/LogP analysers are based on a potentiometric titration
method. The basic principle of operation is to determine the pKa by titration followed by
a back titration to determine the apparent pKa in the presence of octanol. Any
partitioning by the compound will shift the equilibrium and cause a change in the
apparent pKa. From this shift the Log P may be calculated. Sophisticated software allows
detailed iterative calculations to be made and values to be carefully refined.
GlpKa (TM)
PCA101
This more recent technique gives an unprecedented amount of information about the
ionisation and partition behaviour of a molecule; however this is accompanied by more
attention to detail in the calculation and interpretation stages. If a sample is soluble and
well behaved, then it is possible to determine all its pKa values, its Log P and the
apparent log P at every pH. In addition log P values of ionised species where they occur
may be calculated.
The technique can be performed on samples at a concentration of 0.0001M or above, the
ideal concentration being 0.0005 M. Using the PCA101 for a well behaved molecule the
analysis time would be 0.5 Day, including calculation time. The newer GLpKa (TM) has an
autosampler and can also do multiple titrations on each sample and recently has much
improved software for semi-automated refinement.
If the sample is very insoluble then the Log P cannot be measured. The pKa however
may be measurable by either partial titration or by a Yesuda Shedlovsky experiment.
3.2 Yesuda Shedlovsky experiment for determination of pKa of insoluble
compounds
This technique requires three titrations in Aqueous-methanol, each with a different
proportion of methanol. From the results a corrected extrapolation gives the theoretical
aqueous value. (ref 4)
The technique can be performed on samples at a concentration of 0.0005M.
3.3 Ion Pair Log P
Ion pair LogPs may be determined by at least two, preferably three titrations in different
ratios of octanol to water. The apparent pKa in the presence of octanol , the poKa, can be
used to determine the presence of ion pair partitioning according to the equations:
Where r = octanol:water ratio
Both the Log P and the LogD values may be severely affected if one or more of the
charged species partitions. Ion pairing effects may be fully determined with the Sirius
Instruments, even in cases of poly-protic compounds where any of the charged or neutral
species may partition.
3.4 pKa by Manual Titration.
This technique has largely been superseded by the Sirius technology, where available. It
is carried out manually using a ROSS pH electrode and a volumetric pipette. The
technique may be carried out on compounds with reasonable aqueous solubilities (>
0.0025 M) and that are available in amounts greater than 30 mg. The method is rapid,
simple and accurate; however very low pKa's (pKa < 3) and overlapping pKa's cannot be
determined. The method is detailed in the book "Measurement of pKa" Albert and
Serjeant (ref 1)
A computer program or spreadsheet to calculate pKa values from the experimental data
can be written to speed up the calculations. Analysis time is about 0.5 Day
3.5 pKa by U.V. Spectroscopy.
In cases of poor solubility or small sample amounts, pKa values are calculated from U.V.
measurements. The method simply relies on the change in U.V. spectra at different pH's
An adaptation of the filter probe method (see later) is used.
Sample concentrations down to 4mg/400ml may be determined (approx. 0.000025M).
A recent advance by Sirius Analytical Instruments is the D-PAS probe which enables
spectrophotometric determinations to be made with the GLpKa(TM) instrument.
3.6 pKa by Solubility Method.
In cases of extreme insolubility pKa values may be measured by the solubility method.
An aqueous solution of a substance is titrated in the direction of its neutral species until
the free base or free acid is precipitated. pKa may then be calculated from the solubility
product.
This method is not very accurate but may be used on very dilute solutions.
3.7 Filter Probe Measurements.
An older method of Log P determinations is the Filter Probe method , first developed by
E. Tomlinson at University of Amsterdam. (ref 9)The experiment is a variation on the
shake flask method, except that it is rapid, and relies on continuous sampling. An
aqueous solution of the sample under test is placed in a reaction vessel and circulated
through a U.V.flow-cell. The absorbance of the aqueous solution is measured before and
after the addition of octanol. A solvent inlet filter prevents any octanol from passing
through to the detector.
The method is rapid and reliable for log P values from around 0.2 upwards; but low log P
values are difficult to measure due to the insignificant change in absorbance which
results. The reason for this is that below a phase volume ratio of 40 (400 ml water/10ml
octanol) the octanol tends to break through the filter. In cases of low Log P the shake
flask method has to be adopted.
Sample concentrations down to 4mg/400ml may be determined (approx. 0.000025M)
3.8 Log D and Log P by Filter Probe Method.
Log D profiles may be obtained by performing the filter probe experiment over a range of
pH values. The critical part of the experiment is to discover whether the compound of
interest has an isobestic point in its U.V. spectrum. If it does not, the experiment cannot
be performed; if it does, both Log P and pKa values may be determined. This method is
similar to the potentiometric method described earlier except the amount of unpartitioned substance is determined by spectroscopy rather than by potentiometry. The
advantage of this method is that only one experiment needs to be performed to yield Log
P, Log P app and pKa's but not all compounds have an isobestic point.
Sample concentrations down to 4mg/400ml may be determined (approx. 0.000025M).
3.9 Log P by Shake Flask.
The shake flask method is the oldest and most tedious way of measuring log P values.
The U.V. absorbance of an aqueous solution is measured before and after being shaken
with a known volume of octanol. The method is messy and smelly but is the only method
that can be used in cases of very low Log P values. One advantage of the method is that
the appearance of compound in the octanol may be checked against the disappearance
from the aqueous phase to see if any surface effects have occurred. Some molecules may
form effective surfactants! It is very important to pre-saturate the solvents in prolonged
shake-flask experiments.
The experiment must be performed over 3 days or more to ensure equilibrium is reached,
although the actual time taken in doing the experiment is about 0.5 Day
3.10 Log P by HPLC.
HPLC may be used to estimate Log P values. Compounds with known Log P's are
injected onto a C18 reverse phase HPLC column and their capacity factors used to create
a calibration curve. Unknown compounds are then injected and their capacity factors
used to predict Log P. Strictly this technique is only valid for neutral molecules. Charged
molecules have a far more complex retention behaviour than simple partition.
Some liq-liq partition experiments have been reported using an octanol saturated column
and an aqueous mobile phase; however the method is messy and requires frequent regeneration of the column.
The chromatographic methods suffer the disadvantage that the retention time is linearly
related to the partition coefficient, i.e. for a doubling of the LogP, there is a tenfold
increase in the retention. This often requires different length columns to be used, short
ones for high LogP values and long ones for low values.
In my experience HPLC log P determinations using C18 columns can be unreliable,
especially with strongly charged molecules However reasonable correlation can be had
with neutral or compounds which are uncharged at pH 7.4 . In cases where the molecule
is charged and the pKa is known a correction factor may be added to correct the Log D
measurement to Log P.
The discrepancies with the HPLC method are probably due to the imperfect nature of
C18-silica columns. Some of the new generation reverse phase materials, such as C18alumina, polymeric C18, ultra-high carbon loaded C18 and porous graphitic carbon may
overcome these problems. A recent development is an immobilised artificial membrane
(IAM) column, which should more closely model biological membranes.
The main advantage of the HPLC method is that a range of compounds may be
determined at the same time. A new rapid technique has been reported where all
compounds and standards are simultaneously injected and the identity of each peak is
determined by mass spectroscopy. Although this means a lot of work for the
spectroscopist, the amount of chromatography is dramatically reduced.
A refinement of this teqnique is the determination of logk'0 This is achieved by measuring
logk' in several different concentrations of aqeous methanol mobile phases and
extrapolating back to 0% methanol. The resultant l logk'0 values have been correlated to
log P values more sucsessfully. The concerns about polar interactions and the charge
present on the analytes still remain.
Introduction / pH / Activity / pH measurement / pKa / LogP / Partition Solvents / Use of LogP /
Methods / Refs / Top
References
1.
A.Albert and E.P.Seargent " The Determination of Ionisation Constants - A laboratory Manual", 3rd Edition, Chapman and Hall
1984 ISBN 0-412-24290-7
2.
Avdeef A "Weighting Scheme for Regression Analysis Using pH data from Acid Base Titrations" Anal.Chim.Acta 1983 148
pp237-244
3.
Avdeef A "pH-Metric LogP 1 Difference plots for determining Ion-Pair Octanol-Water Partition Coefficients of Multiprotic
Substances" Quant.Struct-Act. Relationships 1992 11 pp510-517
4.
Avdeef A, Comer J.E.A, Thomson, S.J. "pH-Metric Logp 3. Glass Electrode Calibration in Methanol-Water Applied to pKa
Determination of Water Insoluble Subatances by Potentiometric Titration "Anal.Chem 1993 65 pp42-49
5.
6.
Leahy D.E et al "QSAR: Rational Approaches to the design of Bioactive Compounds" Elsevier 1991 pp75-82
7.
Ganellin C.R. "Uses of partition coefficients by brain penetration applied to the design of H2-receptor histamine antagonists "
Elsevier 1991 pp103-110
8.
H Heller, M Schaeffer, K Schulten, "Molecular Dynamics simulation of a bilayer of 200 lipids in the gel and in the Liquid-crystal
phases", J Phys Chem 97 1993 pp8343-60,,
9.
Tomlinson E. "Filter Probe Extractor: A tool for the rapid Determination of Oil-Water Partition Coefficients" J.Pharm.Sci 1982 71
602-604
El Tayar et al "Partition of solutes in different solvent systems: the contribution of hydrogen bonding, capacity and polarity
J.Pharm.Sci 80 590-598 & 744-749.1991
10. Clarke F.H. "Ionisation constants by Curve Fitting. Application to the determination of partition coefficients"
J.Pharm.Sci 1984
73 226-230
11. Leo A. Hansch C. Elkins D. Partition Coefficients and their uses Chemical Reviews 71 No.6 December 1971
12. W.Dunn III, J.H.Block, R.S.Pearlman Partition Coefficient Determination and estimation. Pergamon 1986 ISBN 0-08-033649-3
13. Perrin D.D. Dissociation Constants of Organic Bases in Organic Solution Butterworths London 1965
14. Kortum G. Vogel W. Andrussow K. Dissociation Constants of Organic Acids in Aqueous Solution Butterworths 1961 (Reprint of
Pure and Applied Chemistry Vol1 No. 2-3 1961
15. Dissociation Constants of Inorganic Acids Butterworths 1969 ISBN 408-70015-7 (Reprint of Pure and Applied Chemistry Vol 20
No.2 1969)
16. Sirius Analytical Instruments Ltd STAN Sirius Technical Application notes Volume 1 1994
17. Sirius Analytical Instruments Ltd Applications and Theory Guide to pH-Metric pKa and logP determination 1993
18. Christopher A. Lipinski, Franco Lombardo, Beryl W. Dominy, Paul J. Feeney "Experimental and computational approaches to
estimate solubility and permeability in drug discovery and development settings", Adv. Drug Delivery Rev., 1997, 23(1-3), 3-25:
19. C.M.Tice Pest Management Science 2001,57,3-16. "Selecting the right compounds for screening: Does Lipinski's rule of 5 for
pharmaceuticals apply to agrochemicals?
20. G.G.Briggs Agrevo UK. SCI Meeting Dec 1997. Uptake of Agrochemicals & Pharmaceuticals. Predicting uptake and movement of
agrochemicals from physical properties.
Trademarks: The registered trademarks GlPka (TM) and Four-Plus (TM) are used with kind
permission of Sirius Analytical Limited.
Introduction / pH / Activity / pH measurement / pKa / LogP / Partition Solvents / Use of LogP /
Methods / Refs / Top
Appendix 1 - Log P calculations
The following Javascript calculators will help you calculate % ionised or Log D:
Percent Ionised
Log D
Useful Log D formulas:
Log D = Log P - Log[1+10^(-charge * (pH-pKa))]
Log P = Log D + Log[1+10^(-charge * (pH-pKa))]
If Log P(i) is known:
Log D = Log (Log 10^(LogP) + 10^(logPion - charge*(pH-pKa)) - Log[1+10^(-charge *
(pH-pKa))]
Introduction / pH / Activity / pH measurement / pKa / LogP / Partition Solvents / Use of LogP /
Methods / Refs / Top
Appendix 2 - Worked Example Calculations
Please note: I am often asked by students for help in completing chemistry assignments. I
am sorry but I simply do not have the time available to help - sorry for this. Please work
through the examples below and you should have enough knowledge by then to tackle
most pH-related problems. For further reading please look at the references section
above.
Question 1.
An Acid has a pKa of 5.2. What percentage of the acid is ionised at pH 6.0?
The % ionisation of an acid is given by the equation:
hence at pH 6;
% ionised = 100/(1+10(5.2 - 6))
= 100/(1+0.585)
= 86.3 % ionised
Question 2.
A 0.0049 M aqueous solution of Compound X precipitated out of solution at pH 6.3.
Estimate the solubility of the free base in pure water in g/litre. (pKa = 7.6, mw = 435.6)
Solubility of the free base may be calculated using the equation:
Where:
= solubility at
= solubility of free base
0.0049 = So[1+107.6-6.83]
0.0049 = So[6.888]
So = 0.0049/6.888
So=7.113 x 10-4 moles/litre
So=7.113 x 10-4 x 435.6
So = 0.31 g/litre (in de-ionised H20 at 22.7C)
Solubility estimates by this method may be unreliable since precipitation may occur from
super-saturated solutions.
Question 3.
A compound has a Log P of 3.95 and a pKa of 7.3. Estimate the apparent Log P (or
Log D ) at pH 7.4.
The distribution constant may be calculated by the equations:
for acids
for bases
hence :
Log D(7.4) = 3.95 - log [ 1+10(7.3-7.4)]
Log D(7.4) =3.696
Question 4.
What strength Sodium Hydroxide is needed to form the sodium salt of a compound
with a weakly acidic group possessing a Ka of 3.7 x 1011 ?
pKa = -log Ka, hence pKa = -log (3.7x10-11) = 10.43
The compound will only be significantly ionised above its pKa, ideally > 2 units above.
Since Sodium Hydroxide is 100% dissociated, we can calculate the strength of NaOH to
get pH > pKa
pH
%ionised
M NaOH Solution
11
78%
0.001M
11.5
92%
0.003M
12
97%
0.01M
12.5
99%
0.03M
Hence 0.03 M NaOH (aq) should be used to isolate the salt.
Question 6.
Weak acids with pKa's less than 16 will not be detectable as acids at all since the [H+]
they produce will be less than that produced by the autolysis of water. Similarly strong
acids are completely ionised in water and so appear to be the same strength. Suggest
ways in which (i) a weak acid (or strong base) and (ii) a strong acid (or weak base)
could be measured
Non Aqueous measurements can extend the range of pKa measurements:
For a weak acid must provide a stronger base as a solvent than water
For a strong acid must provide a weaker base (stronger acid) as a solvent than water.
Measurements are subject to large errors and involve lengthy and careful calibration.
Example: Urea pKa=0.1 (weak base) determined in Acetic Acid
Question 5.
Consider the following Compounds:
Compound
Type
pKa
Toluene-4-sulphonic acid
Acid
-1.3
Benzoic Acid
Acid
4.2
Thiopental
Acid
7.6
Codeine
Base
8.2
Atropine
Base
10
(a) Which will be best absorbed from the stomach (stomach pH = 2)
(b) Which will be best absorbed from the small intestine ( pH = 4.2)
(c) Which pass most readily from the plasma into the brain (pH of plasma = 7.3)
(d) Which will be eliminated least readily from the kidneys ( urine pH of 4.2 )
Assuming that the Log P of each compound is equivalent:
(a) At pH 2 Toluene sulphonic acid, Codeine and Atropine will be ionised, whereas
Benzoic acid and Thiopental will be non-ionised and will be best absorbed
(b) At pH 6 only Thiopental is non-ionised and so will be the best absorbed
(c) At pH 7.3 Codeine is 11% in the molecular form, whereas Thiopental is 67% nonionised, and so will be absorbed the best. All the other compounds are too highly ionised
to penetrate.
(d) Re-adsorption of substances in the urine by the tubules in the kidneys will be greatest
for un-ionised molecules. Hence the weak acid Thiopental will be re-adsorbed the most
since it is non-ionised at pH4.2. Benzoic acid is only half-ionised, and all the rest are
ionised.