Soft quaternary anticholinergics: Comprehensive quantitative structure-activity relationship (QSAR) with a linearized biexponential (LinBiExp) model

A comprehensive quantitative structure-activity relationship (QSAR) study is presented for quaternary soft anticholinergics including two distinctly different classes designed on the basis of the soft analogue and the inactive metabolite approaches. Because of the clear biphasic (bilinear) nature of the activity data when all structures (n = 76) were considered as a function of molecular size (volume), a nonlinear model had to be used, and a linearized biexponential (LinBiExp) model proved very adequate. LinBiExp can fit activity data that show a maximum (or a minimum) around a given parameter value but tend to show linearity away from this turning point. Contrary to Hansch-type parabolic models, LinBiExp represents a natural extension of linear models, and a direct correspondence between its parameters and those obtained earlier by linear regression on compound subsets covering more limited parameter ranges could be easily established. Stereospecificity was confirmed as important, and the presence of an acid moiety was found to essentially eliminate activity. The consideration of bilinear behavior, which most likely results from size limitations at the binding site, can also explain the embarrassingly low activity found for a relatively large compound predicted as highly active by Lien, Ariens, and co-workers based on their QSAR study.