3D-chiral quadratic indices of the 'molecular pseudograph's atom adjacency matrix' and their application to central chirality codification: classification of ACE inhibitors and prediction of sigma-receptor antagonist activities.
Quadratic indices of the 'molecular pseudograph's atom adjacency matrix' have been generalized to codify chemical structure information for chiral drugs. These 3D-chiral quadratic indices make use of a trigonometric 3D-chirality correction factor. These indices are nonsymmetric and reduced to classical (2D) descriptors when symmetry is not codified. By this reason, it is expected that they will be useful to predict symmetry-dependent properties. 3D-Chirality quadratic indices are real numbers and thus, can be easily calculated in TOMOCOMD-CARDD software. These descriptors circumvent the inability of conventional 2D quadratic indices (Molecules 2003, 8, 687-726. http://www.mdpi.org) and other (chirality insensitive) topological indices to distinguish sigma-stereoisomers. In this paper, we extend our earlier work by applying 3D-chirality quadratic indices to two data sets containing chiral compounds. Consequently, in order to test the potential of this novel approach in drug design we have modelled the angiotesin-converting enzyme inhibitory activity of perindoprilate's sigma-stereoisomers combinatorial library. Two linear discriminant analysis (LDA) models were obtained. The first one model was performed considering all data set as training series and classifies correctly 88.89% of active compounds and 100.00% of nonactive one for a global good classification of 96.87%. The second one LDA-QSAR model classified correctly 83.33% of the active and 100.00% of the inactive compounds in a training set, result that represent a total of 95.65% accuracy in classification. On the other hand, the model classifies 100.00% of these compounds in the test set. Similar predictive behaviour was observed in a leave-one-out cross-validation procedure for both equations. Canonical regression analysis corroborated the statistical quality of these models (R(can) of 0.82 and of 0.76, respectively) and was also used to compute biology activity canonical scores for each compound. Finally, prediction of the biological activities of chiral 3-(3-hydroxyphenyl)piperidines, which are sigma-receptor antagonists, by linear multiple regression analysis was carried out. Two statistically significant QSAR models were obtained (R2=0.940, s=0.270 and R2=0.977, s=0.175). These models showed high stability to data variation in the leave-one-out cross-validation procedure (q2=0.912, scv=0.289 and q2=0.957, scv=0.211). The results of this study compare favourably with those obtained with other chirality descriptors applied to the same data set. The 3D-chiral TOMOCOMD-CARDD approach provides a powerful alternative to 3D-QSAR.