Tensor algebra-based geometric methodology to codify central chirality on organic molecules

A novel mathematical procedure to codify chiral features of organic molecules in the QuBiLS-MIDAS framework is introduced. This procedure constitutes a generalization to that commonly used to date, where the values 1 and −1 (correction factor) are employed to weight the molecular vectors when each atom is labelled as R (rectus) or S (sinister) according to the Cahn–Ingold–Prelog rules. Therefore, values in the range [−3,3] with steps equal to 0.25 may be accounted for. The atoms labelled R or S can have negative and positive values assigned (e.g. −3 for an R atom and 1 for an S atom, or vice versa), opposed values (e.g. −3 for an R atom and 3 for an S atom, or vice versa), positive values (e.g. 3 for an R atom and 1 for an S atom) or negative values (e.g. −3 for an R atom and −1 for an S atom). These proposed Chiral QuBiLS-MIDAS 3D-MDs are real numbers, non-symmetric and reduced to ‘classical’ (non-chiral) QuBiLS-MIDAS 3D-MDs when symmetry is not codified (correction factor equal to zero). In this report, only the factors with opposed values were considered with the purpose of demonstrating the feasibility of this proposal. From QSAR modelling carried out on four chemical datasets (Cramer’s steroids, fenoterol stereoisomer derivatives, N-alkylated 3-(3-hydroxyphenyl)-piperidines, and perindoprilat stereoisomers), it was demonstrated that the use of several correction factors contributes to the building of models with greater robustness and predictive ability than those reported in the literature, as well as with respect to the models exclusively developed with QuBiLS-MIDAS 3D-MDs based on the factor 1 | −1. In conclusion, it can be stated that this novel strategy constitutes a suitable alternative to computed chirality-based descriptors, contributing to the development of good models to predict properties depending on symmetry.