Idea Transcript
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 Winner of ACD Labs "Star Pick" Award
NB: You should have MDL's Chime installed to see these pages at their best! 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 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 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.