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.
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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 seesection 1.7. to 1.9.
Table of Contents:
- Introduction
- Contents
- Understanding pKa and Log P measurements.
- The pH scale
- Activity
- Practical pH measurement
- pKa or Dissociation Constant
- Log P and Partition Coefficients
- Choice of partition solvent
- How are LogP results related to activity?
- How are LogP results related to solubility?
- What do LogP values mean in practice?
- Measurement strategy
- LogP/pKa measurement techniques
- Aqueous Titration using Sirius instruments
- Yesuda-Shedlovsky experiment
- Ion Pair Log P's
- pKa by Manual Titration
- pKa by U.V. Spectroscopy
- pKa by Solubility Method
- Filter Probe Measurements
- Log D and Log P by Filter Probe Method
- Log P by Shake Flask
- Log P by HPLC
- References
- Appendix 1 - Calculating Log D and % ionised
- Appendix 2 - Worked example calculations
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 =8Zwitterion 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 (H-bonding)
Chloroform
/ proton donor (H-bonding)
PGDP
/ proton acceptor (H-bonding)
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)