is very useful, saving much time and effort in the synthesis and testing of new drugs.
Hundreds of examples of such analyses are available in the literature; many show pos-
itive predictive values for drug activity, whereas some other drug series cannot be inter-
preted by this method.
Regression analysis is currently the most widely used correlative method in drug
design. This is because it simplifies problems within a set of compounds by using a lim-
ited number of descriptors, notably the Hansch hydrophobic constant π, Hammet con-
stants, or other electronic characteristics of substituents, and the Taft steric constant ES.
Nevertheless, there are several difficulties and pitfalls in using the Hansch method.
First, the inherent disadvantage of regression analysis is that one can obtain good fits
(r^2 >0.9) simply by manipulating the constants. Therefore, curve fitting must be done
for a relatively large number of compounds to ensure that all predictors are considered.
Second, the mode of action may change for drugs within a seemingly continuous series,
invalidating the comparison of some compounds in the series with the predictor com-
pounds. The Hansch method cannot anticipate such a change.
Other problems with the Hansch method are that biological systems are often too
crude as models for its application, or the electronic effects operative in a drug mole-
cule are not sufficiently understood or precise. Finally, the method requires consider-
able time and expense, even in the hands of an expert. Difficulties notwithstanding, the
Hansch approach took both chemists and pharmacologists out of the dark age of pure
empiricism and allowed them to consider simultaneously the effects of a large number
of variables of drug activity—a feat unattainable with classical methods.
Nevertheless, Hansch analysis revolutionized drug molecule optimization and
directly led to two other strategies for molecule optimization: the Free–Wilson method
and the Topliss decision tree.
The Free–Wilson Method.This method also assumes that biological activity can be
described by the additive properties of the substituents on a basic molecular structure.
In the Fujita–Ban modification of this method
whereCis the drug concentration for a standardized effect,aiis the group contribution
of the ith substituent to the pharmacological activity of the substituted molecule,Xis
unity if substituent iis present and zero otherwise, and μ 0 = 1 /Cfor the parent com-
pound. Regression analysis is used to determine aiandμ. In the Fujita–Ban modifica-
tion of the Free–Wilson method, no assumptions are made about the relevance of the
model parameters to the biological activity of the molecule. The effect of each sub-
stituent is considered to be independent of any other, and each makes a constant con-
tribution to the overall activity of the molecule. Therefore the method is applicable to
compounds with more than one variable group. The result is a data matrix that shows
the contribution of each substituent in each position to the overall biological effect of the
molecule. The Free–Wilson equation bears close similarities to the linear Hansch equa-
tion, and the results of the two can be comparable. The Free–Wilson method, however,
cannot predict the activities of compounds that have substituents not included in the
matrix. Consequently, this method has found only limited application in drug series
where many close analogs are already available but physicochemical data are lacking.
142 MEDICINAL CHEMISTRY
log 1/C=∑
aiXi+μ 0 (3.4)