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Non-Stochastic and Stochastic Atom-Based 3D-Chiral Linear Indices and Their Applications to Central Chirality Codification
* 1, 2 , 2, 3
1  Applied Chemistry Research Center, Central University of Las Villas, Santa Clara, 54830, Villa Clara, Cuba
2  Department of Pharmacy, Faculty of Chemical-Pharmacy and Department of Drug Design, Chemical Bioactive Center, Central University of Las Villas, Santa Clara, 54830, Villa Clara, Cuba
3  Institut Universitari de Ciència Molecular, Universitat de València, Dr. Moliner 50, E-46100 Burjassot, València, Spain

Abstract: 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 linear indices to distinguish s-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 s-stereoisomers combinatorial library. Two linear discriminant analysis models, using non-stochastic and stochastic linear indices, were obtained. The models shown 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(Rcan 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 s-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 (scv = 0.186) and q2 = 0.90 (scv = 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 provide a powerful alternative to 3D-QSAR.
Keywords: non-stochastic and stochastic 3D-chiral linear indices; 3D-QSAR; angiotesinconverting enzyme inhibitors; s-receptor antagonists; binding affinity of steroids