Quantitative Structureactivity Relationships And Drug Design

JOHN C.DEARDEN and tKENNETH C.JAMES

CONTENTS

5.1 INTRODUCTION 168

5.2 HYDROPHOBICITY PARAMETERS 169

5.2.1 Hydrophobic (Hansch) substituent constants 170

5.2.2 Hydrophobic fragmentai constants 171

5.2.3 Chromatographic hydrophobicity values 172

5.2.4 Aqueous solubility 173

5.3 ELECTRONIC PARAMETERS 173

5.3.1 Hammett constants 174

5.3.2 Inductive substituent constants 177

5.3.3 Taft's substituent constants 178

5.3.4 Hydrogen bonding parameters 178

5.3.5 Whole molecule parameters 179

5.4 STERIC PARAMETERS 179 5.4.1 Substituent parameters 179

5.4.1.1 Taft's steric substituent constants 179

5.4.1.2 Van der Waals dimensions 181

5.4.1.3 Charton's steric constants 181

5.4.1.4 Sterimol parameters 182

5.4.1.5 Molar refractivity 182

5.4.2 Whole molecule parameters 182

5.4.2.1 Relative molecular mass (RMM) 182

5.4.2.2 Molecular volume 183

5.4.2.3 Surface area 183

5.4.2.4 The kappa index 183

5.4.2.5 Minimal steric difference 183

5.4.2.6 Molecular shape analysis 184

5.4.2.7 Molecular similarity 184

5.4.2.8 3-D parameters

5.5 TOPOLOGICAL PARAMETERS

5.6 BIOLOGICAL RELATIONSHIPS

5.6.1 Ferguson effect

5.6.2 Hansch analysis

5.6.2.1 Correlation coefficient

5.6.2.2 Regression coefficients

5.6.2.3 Standard error of the estimate

5.6.2.4 Standard deviation of the coefficient

5.6.2.6 Optimal partition coefficient

5.6.2.7 The bilinear relationship

5.6.2.8 Comparison of slopes and intercepts

5.6.3 Free-Wilson analysis

5.7 SOME LIMITATIONS AND PITFALLS OF QSAR

5.8 MULTIVARIATE ANALYSIS

5.8.1 Pattern recognition methods

5.9 NEURAL NETWORKS

5.10 SUMMARY

FURTHER READING

5.1 INTRODUCTION

Medicinal chemists have tried to quantify relationships between chemical structure and biological activity since before the turn of the century. However, it was not until the early 1960s, through the efforts of Corwin Hansch and his co-workers, that a workable methodology was developed and the subject that was to become known as quantitative structure-activity relationships (QSAR) was born. Since then, thousands of research papers, articles and reviews on QSAR have emerged, with unfamiliar symbols and parameters, and with results which are expressed in a format different from that of traditional medicinal chemistry. It is the object of this chapter to explain these methods of expression, what they are meant to convey, and how the technique may be used in drug design.

The traditional method of searching for new medicinal compounds has sometimes been described as chemical roulette. A chemical structure, known to have a particular biological activity, is chosen, and attempts are made to improve it by modifications based on chemical intuition and isosteric considerations (see Section 5.2), until a highly active compound with minimal side-effects is produced. A plan of the probable receptor site is built up as the number of compounds synthesized and tested increases, and the selection of further new compounds becomes progressively more rational. Beckett's work on analgesics is a classical example of this procedure. By carefully choosing his compounds, he was able to chart a map of the analgesic receptor site (since modified), which is reproduced in Figure 5.1. It can be seen that there is a hollow which will accommodate a protruding group, a flat area which will fit a similar flat surface, and a negatively charged site. Methadone ((5.1) X=H) will fit this receptor; it also has a phenyl group which can lie

Figure 5.1 Analgesic receptor site (as proposed by Beckett, A.H. (1956) Analgesics and their antagonists: some steric and chemical considerations. Part 1. The dissociation constants of some tertiary amines and synthetic analgesics; the conformation of methadone compounds. Journal of Pharmacy and Pharmacology 8, 848-859.

Figure 5.1 Analgesic receptor site (as proposed by Beckett, A.H. (1956) Analgesics and their antagonists: some steric and chemical considerations. Part 1. The dissociation constants of some tertiary amines and synthetic analgesics; the conformation of methadone compounds. Journal of Pharmacy and Pharmacology 8, 848-859.

on the flat surface, and an alkyl chain which will occupy the hollow. Using this approach, one is able to anticipate the shapes of biologically active molecules, and speculate on the types and positions of groups which will bring about the optimal stereochemistry required for activity. Molecular mapping of receptor sites is now carried out with the aid of computer graphics (see Chapter 3).

The quantitative structure-activity approach uses parameters which have been assigned to the various chemical groups that can be used to modify the structure of a drug. The parameter is a measure of the potential contributions of its group to a particular property of the parent drug. In the present situation, a steric parameter, which assesses the bulkiness of the group occupying the hollow on the drug receptor, would be appropriate. In a typical procedure, a series of related compounds are examined, and the relevant parameters of their substituent groups compared with the biological activities of the compounds and then, by mathematical procedures, the structures of the most promising derivatives are predicted. Parameters governing several different properties can be employed, but the three most commonly used are steric and electronic parameters and parameters related to partitioning.

5.2 HYDROPHOBICITY PARAMETERS

Drugs move through an organism, from the site of administration to the site of action, largely by a process of partitioning through lipid membranes. It follows that the partition coefficient (P) of a drug greatly affects the rate at which it reaches the site of action. (It should be remembered that although P is an equilibrium constant, it is defined from the law of mass action as the ratio of the forward and reverse partitioning rate constants.) As P is logarithmically related to free energy, it should be possible to split log P into parameters characteristic of the chemical groups that make up the molecule.

Most of the partitioning work in quantitative structure-activity relationships has been based on the 1-octanol-water system. This is because 1-octanol is considered to be a reasonable model of a lipid, in that it has a polar head-group and a long hydrocarbon chain.

5.2.1 Hydrophobic (Hansch) substituent constants

The difference in log P between a compound containing a substituent group X and the substituted parent compound (X=H) was defined by Hansch as the hydrophobic substituent constant n, i.e. n=log PX-log PH=log(PX/PH). The subscript H represents the unsubstituted compound and the subscript X represents the derivative in which hydrogen has been replaced by the group X.

Values can be used to calculate 1-octanol-water partition coefficients in the same way as Hammett constants can be used to estimate dissociation constants. Thus, the log P value of butan-2-one between 1-octanol and water is 0.32, therefore the log Pfor hexan-2-one in the same system should be 0,32 + 0.52 x 2 = 1.36 (lic^ = 0,52) Values may also be correlated directly with biological activities to give a quantitative structure-activity relationship (QSAR), as will be discussed later.

Collander showed that partition coefficients in one solvent system (P1) are related to those in another (P2) by:

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