3D-chiral atom, atom-type, and total non-stochastic and stochastic molecular linear indices and their applications to central chirality codification

Non-stochastic and stochastic 2D linear indices have been generalized to codify chemical structure information for chiral drugs, making use of a trigonometric 3D-chirality correction factor. These descriptors circumvent the inability of conventional 2D non-stochastic [Y. Marrero-Ponce. J. Chem. Inf. Comp., Sci. l 44 (2004) 2010] and stochastic [Y. Marrero-Ponce, et al. Bioorg. Med. Chem., 13 (2005) 1293] linear indices to distinguish σ-stereoisomers. In order to test the potential of this novel approach in drug design we have modelled the angiotensin-converting enzyme inhibitory activity of perindoprilate's σ-stereoisomers combinatorial library. Two linear discriminant analysis models, using non-stochastic and stochastic linear indices, were obtained. The models showed an accuracy of 100% and 96.65% for the training set; and 88.88% and 100% in the external test set, respectively. Canonical regression analysis corroborated the statistical quality of these models (R^can of 0.78 and of 0.77) and was also used to compute biology activity canonical scores for each compound. After that, the prediction of the σ-receptor antagonists of chiral 3-(3-hydroxyphenyl)piperidines by linear multiple regression analysis was carried out. Two statistically significant QSAR models were obtained when non-stochastic (R² = 0.982 and s = 0.157) and stochastic (R² = 0.941 and s = 0.267) 3D-chiral linear indices were used. The predictive power was assessed by the leave-one-out cross-validation experiment, yielding values of q² = 0.982 (s^cv = 0.186) and q² = 0.90 (S_cv = 0.319), respectively. Finally, the prediction of the corticosteroid-binding globulin binding affinity of steroids set was performed. The best results obtained in the cross-validation procedure with non-stochastic (q² = 0.904) and stochastic (q² = 0.88) 3D-chiral linear indices are rather similar to most of the 3D-QSAR approaches reported so far. The validation of this method was achieved by comparison with previous reports applied to the same data set. The non-stochastic and stochastic 3D-chiral linear indices appear to provide an interesting alternative to other more common 3D-QSAR descriptors.