Quantitative structure-activity relations. 7. The bilinear model, a new model for nonlinear dependence of biological activity on hydrophobic character

Abstract

The bilinear model, log 1/C = a log P - b log (.beta.P + 1) + c, a new model for nonlinear dependence of pharmaceutical biological activity on hydrophobic character, is applied to 57 data sets of biological activity values in homologous series. From a comparison of the statistical parameters and the residuals obtained with the bilinear model and the parabolic model, the superiority of the bilinear model for a precise quantitative description of both linear and nonlinear parts of structure-activity relationships can be derived; the bilinear model explains the particular effect that in homologous series the relationship between biological activity and hydrophobic character is strictly linear for the lower members while for higher members this relationship is nonlinear.