Soft Quaternary Anticholinergics:  Comprehensive Quantitative Structure−Activity Relationship (QSAR) with a Linearized Biexponential (LinBiExp) Model

Abstract

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, Ariëns, and co-workers based on their QSAR study.

The time-profile of cell growth in fission yeast: model selection criteria favoring bilinear models over exponential ones

“…This was also made possible by extending a recently-introduced linearized biexponential model (LinBiExp) [21] to allow fitting of general bilinear-type data with a single, unified model. Originally, LinBiExp was introduced to describe quantitative structure-activity relationship (QSAR) data such as toxicities, antimicrobial activities and receptor-binding affinities that have a maximum or a minimum, but are essentially linear sufficiently far away from the zone of the turning point (the zone of the extreme value) [21,22]. However, by extending its parameter-range, LinBiExp can easily be generalized to describe not only data that show a maximum or a minimum, but also data that show only a rate-change between two essentially linear portions, such as those presented here and related to cell growth.…”

Activity-Limiting Role of Molecular Size: Size-Dependency of Maximum Activity for P450 Inhibition as Revealed by qHTS Data

“…For QSAR-type analyses, we found LinBiExp to be most useful in fitting decimal log-scaled concentration data (e.g., log 1/IC 50 , log 1/ED 50 , log 1/K d ) as a function of molecular size (Buchwald, 2005(Buchwald, , 2008Buchwald and Bodor, 2006;Buchwald and Yamashita, 2014). While we found molecular volume (V) as a particularly useful three-dimensional size descriptor and used it in various previous bilinear-type fittings, here we used the more convenient and readily available molecular weight as the independent variable (i.e., x = MW in eq.…”

“…Our approach is based on the linearized biexponential (LinBiExp) model that allows bilinear dependence on two sides of a smooth transition region positioned at a turning point (Buchwald, 2005(Buchwald, , 2007. Such an approach already proved useful in a much more limited quantitative structure-activity relationship (QSAR) for CYP3A4 (Buchwald and Yamashita, 2014), as well as in modeling several other pharmaceutically relevant activities (Buchwald, 2005(Buchwald, , 2008Buchwald and Bodor, 2006). This approach allowed development of a QSAR equation that accounted for close to 65% of the variability in the CYP3A4-inhibitory activity of more than 70 structurally diverse compounds with only two main descriptors, molecular size and an indicator variable for the presence of triazole/imidazole moieties (Buchwald and Yamashita, 2014).…”

Retrometabolism‐Based Drug Design and Targeting

“…Because of its hydrolytic deactivation in mammals, malathion (92) is much less toxic than other organophosphates such as phorate (90) or parathion (91) as illustrated by the corresponding LD 50 values. our laboratories [298,299]. Several new molecules synthesized were found to be potent anticholinergics both in vitro and in vivo, but in contrast to their hard analogs they had no systemic anticholinergic activity following topical administration.…”

“…Recently, we were able to put together a retrospective, comprehensive quantitative structure-activity relationship (QSAR) study for all quaternary soft anticholinergics (n ¼ 76) discussed here from these two distinctly different classes, which were designed on the basis of the soft analog and the inactive metabolite approaches, respectively [299]. Modeled activity data included pA 2 values (the negative logarithm of the molar concentration of the antagonist that produces a twofold right-shift in the concentration-response curve of the agonist) measured using the in vitro guinea pig ileum assay and receptor binding pK i values measured with cloned muscarinic receptors (M 3 subtype).…”