Chirality measures of α-amino acids

To measure molecular chirality, the molecule is treated as a finite set of points in the Euclidean R(3) space supplemented by k properties, p(1)((i)), p(2)((i)), ..., p(k)((i)) assigned to the ith atom, which constitute a point in the Property P(k) space. Chirality measures are described as the distance between a molecule and its mirror image minimized over all its arbitrary orientation-preserving isometries in the R(3) × P(k) Cartesian product space. Following this formalism, different chirality measures can be estimated by taking into consideration different sets of atomic properties. Here, for α-amino acid zwitterionic structures taken from the Cambridge Structural Database and for all 1684 neutral conformers of 19 biogenic α-amino acid molecules, except glycine and cystine, found at the B3LYP/6-31G** level, chirality measures have been calculated by a CHIMEA program written in this project. It is demonstrated that there is a significant correlation between the measures determined for the α-amino acid zwitterions in crystals and the neutral forms in the gas phase. Performance of the studied chirality measures with changes of the basis set and computation method was also checked. An exemplary quantitative structure–activity relationship (QSAR) application of the chirality measures was presented by an introductory model for the benchmark Cramer data set of steroidal ligands of the sex-hormone binding globulin.