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Atom-based Stochastic and non-Stochastic 3D-Chiral Bilinear Indices and their Applications to Central Chirality Codification
* 1, 2 , 2, 3 , 3 , 4
1  Applied Chemistry Research Center. Central University of Las Villas, Santa Clara, 54830,Villa Clara, Cuba
2  Unit of Computer-Aided Molecular “Biosilico” Discovery and Bioinformatic Research (CAMD-BIR Unit), Department of Pharmacy, Faculty of Chemistry-Pharmacy and Department of Drug Design, Chemical Bioactive Center. Central University of Las Villas, Santa Clar
3  Institut Universitari de Ciència Molecular, Universitat de València, Edifici d'Instituts de Paterna, P. O. Box 22085, 46071 Valencia, Spain
4  Mediscovery, Inc. Suite 1050, 601 Carlson Parkway, Minnetonka, MN 55305, USA

Abstract: Non-stochastic and stochastic 2D bilinear indices have been generalized to codify chemical structure information for chiral drugs, making use of a trigonometric 3D-chirality correction factor. In order to evaluate the effectiveness of this novel approach in drug design we have modeled the angiotensin-converting enzyme inhibitory activity of perindoprilate’s σ-stereoisomers combinatorial library. Two linear discriminant analysis models, using nonstochastic and stochastic linear indices, were obtained. The models had shown an accuracy of 95.65% for the training set and 100% for the external prediction set. Next the prediction of the σ-receptor antagonists of chiral 3-(3-hydroxyphenyl)piperidines by multiple linear regression analysis was carried out. Two statistically significant QSAR models were obtained when non-stochastic (R2 = 0.953 and s = 0.238) and stochastic (R2 = 0.961 and s = 0.219) 3D-chiral bilinear indices were used. These models showed adequate predictive power (assessed by the leave-one-out cross-validation experiment) yielding values of q2 = 0.935 (scv = 0.259) and q2 = 0.946 (scv = 0.235), respectively. Finally, the prediction of the corticosteroid-binding globulin binding affinity of steroids set was performed. The obtained results 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 a very interesting alternative to other more common 3D-QSAR descriptors.
Keywords: non-Stochastic and Stochastic 3D-Chiral Bilinear Indices, 3D-QSAR, Angiotensin-converting Enzyme Inhibitor, σ-Receptor Antagonist, Steroid Binding Affinity, Discriminant Analysis, Multiple Linear Regression