General linearized biexponential model for QSAR data showing bilinear-type distribution

A major impediment of many QSAR-type analyses is that the data show a maximum or minimum and can no longer be adequately described by linear functions that provide unrivaled simplicity and usually give good description over more restricted ranges. Here, a general linearized biexponential (LinBiExp) model is proposed that can adequately describe data showing bilinear-type distribution as a function of not just often-employed lipophilicity descriptors (e.g., log P) but as a function of any descriptor (e.g., molecular volume). Contrary to Hansch-type parabolic models, LinBiExp allows the natural extension of linear models and fitting of asymmetrical data. It is also more general and intuitive than Kubinyi's model as it has a more natural functional form. It was obtained by a differential equation-based approach starting from very general assumptions that cover both static equilibriums and first-order kinetic processes and that involve abstract processes through which the concentration of the compound of interest in an assumed "effect" compartment is connected to its "external" concentration. Physicochemical aspects placing LinBiExp within the framework of linear free energy relationship (LFER) approaches are presented together with illustrative applications in various fields such as toxicity, antimicrobial activity, anticholinergic activity, and glucocorticoid receptor binding. (c) 2005 Wiley-Liss, Inc. and the American Pharmacists Association J Pharm Sci 94:2355-2379, 2005.