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Bond-Extended Stochastic and Non-Stochastic Bilinear Indices. 1. QSPR/QSAR Applications to the Description of Properties/Activities of Small-Medium Size Organic Compounds
* 1, 2, 3 , 1, 4 , 1 , 3 , 1 , 5
1  Unit of Computer-Aided Molecular “Biosilico” Discovery and Bioinformatic Research (CAMD-BIR Unit), Faculty of Chemistry-Pharmacy. Central University of Las Villas, Santa Clara, 54830, Villa Clara, Cuba
2  Institut Universitari de Ciència Molecular, Universitat de València, Edifici d'Instituts de Paterna, Polígon la Coma s/n, E-46071 Valencia, Spain
3  Unidad de Investigación de Diseño de Fármacos y Conectividad Molecular, Departamento de Química Física, Facultad de Farmacia, Universitat de València, Spain
4  Department of Chemistry, Faculty of Chemistry-Pharmacy. Central University of Las Villas, Santa Clara, 54830, Villa Clara, Cuba
5  Associação para o desenvolvimento da Faculdade de Ciências do Porto, Rua do Campo Alegre, 687, 4169-007, Porto. Portugal

Abstract: Bond-extended stochastic and non-stochastic bilinear indices are introduced in this paper as novel bond-level molecular descriptors (MDs). These novel totals (wholemolecule) MDs are based on a bilinear maps (forms) similar to use defined in linear algebra. The proposed non-stochastic indices try to match molecular structure provided by the molecular topology by using the kth Edge(Bond)-Adjacency Matrix (Ek, designed here as non-stochastic E matrix). The stochastic parameters are computed by using the kth stochastic edge-adjacency matrix, ESk, as matrix operators of bilinear transformations. This new edge (bond)-adjacency relationships can be obtained directly from Ek and can be consider like a new matrix-transformation strategic to obtain new relation for a molecular graph. In both set of MDs, chemical information is codified by using different pair combinations of atomic weightings (in this case four atomic-labels: atomic mass, polarizability, van der Waals volume, and electronegativity). In addition, a local-fragment (bond-type) formalism was also developed. The kth bond-type bilinear indices are calculated by summing the kth bond bilinear indices of all bonds of the same bond type in the molecules. The new set of MDs can be easily and quickly calculate in our in house software TOMOCOMD-CARDD (TOpological MOlecular COMputer Design Computer-Aided –Rational– Drug Design). The reported application and utilization of these MDs for predictive capability correlations of structure with physicochemical and pharmacology properties are reviewed. Three benchmark datasets have been used to evaluate the QSPR/QSAR behavior of the new bond-level TOMOCOMD-CARDD MDs. We developed the QSPR models to describe several physicochemical properties of octane isomers (FIRST CASE) and, to analyze of the boiling point of 28 alkyl-alcohols (SECOND CASE) and to examine of the specific rate constant (log k), the partition coefficient (log P), as well as the antibacterial activity of 34 derivatives of 2-furylethylenes (THIRD CASE). For these three rounds, the quantitative models found are significant from a statistical point of view and permit a clear interpretation of the studied properties in terms of the structural features of molecules. A leave-out-out cross-validation procedure revealed that the regression models had a good predictability. The comparison with other approaches reveals good performance of the method proposed. Therefore, it is clearly demonstrated that this suitability is higher than that shown by other 2D/3D well-known sets of MDs. The approach described here appears to be a very promising structural invariant, useful for QSPR/QSAR studies and shown to provide an excellent alternative or guides for discovery and optimization of new lead compounds, reducing the time and cost of traditional procedure.
Keywords: Octane Isomers, Alkyl-alcohol, 2-Furylethylene, Physicochemical Properties, Antibacterial Activity, QSPR/QSAR Model, Multiple Linear Regression, Linear Drisciminant Analysis, Edge-Adjacency Matrix, Stochastic Edge-Adjacency Matrix, Non-Stochastic and Stochastic Bond-Based Bilinear Indices, TOMOCOMDCARDD Software