Quantitative structure-activity relationships. IV. Non-linear dependence of biological activity on hydrophobic character: a new model.

A new model is derived for the dependence of biological activity on hydrophobic character from a simple hypothetical system. Unlike the parabolic Hansch model this model can explain the peculiar effect that for homologous series of compounds the logarithms of biological activities of the lower homologs are linearly dependent on hydrophobic character, while for the higher homologs the relationship between biological activities and hydrophobic character changes to a parabola. Although these relationships are known and several appropriate models were proposed, the bilinear model presented in this paper is the first which can be described by a simple and generally valid equation: log 1/C = a log P--b log (beta - P + 1) + c While the parameters a, b and c can be calculated by linear multiple regression analysis, the non-linear term beta must be derived by a stepwise iteration process or ty Taylor series iteration. Examples are given for comparison of the bilinear model and the parabolic Hansch model.