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Nucleotide’s Bilinear Indices: Novel Bio-Macromolecular Descriptors for Bioinformatics Studies of Nucleic Acids. I. Prediction of Paromomycin’s Affinity Constant with HIV-1 ?-RNA Packaging Region
* 1, 2, 3 , 1, 4 , 1 , 5 , 5 , 6 , 2 , 3
1  Unit of Computer-Aided Molecular “Biosilico” Discovery and Bioinformatic Research (CAMDBIR 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, Poligon 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 Physiology, Medical School “Faustino Pérez Hernández”, Km # 3 Circumvallation, Sancti-Spíritus, Cuba
5  Laboratorio de Electrónica Molecular, Departamento de Química, Modulo II, grano de Oro, Facultad Experimental de Ciencias, La Universidad del Zulia (LUZ), Venezuela
6  Bioinformatics Group, Informatics Research Center (CEI), Faculty of Mathematics, Physics and Computer Science. Central University of Las Villas, Santa Clara, 54830, Villa Clara, Cuba

Abstract: A new set of nucleotide-based biomacromolecular descriptors are presented. This novel approach to biomacromolecular design from a linear algebra point of view is relevant to nucleic acids QSAR (Quantitative Structure-Activity Relationship) studies. These biomacromolecular indices are based on the calculus of bilinear maps on Rn [ mk ( m , m ) b x y : R n x R n ?R ] in canonical basis. Nucleic acid’s bilinear indices are calculated from kth power of non-stochastic and stochastic nucleotide’s graph–theoretic electronic-contact matrices, km M and km sM , respectively. That is to say, the kth non-stochastic and stochastic nucleic acid’s bilinear indices are calculated using km M and km sM as matrix operators of bilinear transformations. Moreover, biochemical information is codified by using different pair combinations of nucleotide-base properties as weightings (experimental molar absorption coefficient 260 ? at 260 nm and PH = 7.0, first ( 1 ?E ) and second ( 2 ?E ) single excitation energies in eV, and first (f1) and second (f2) oscillator strength values (of the first singlet excitation energies) of the nucleotide DNA-RNA bases. As example of this approach, an interaction study of the antibiotic Paromomycin with the packaging region of the HIV-1 ?-RNA have been performed and it have been obtained several linear models in order to predict the interaction strength. The best linear model obtained by using nonstochastic bilinear indices explains about 91% of the variance of the experimental Log K (R = 0.95 and s = 0.08x10-4M-1) as long as the best stochastic bilinear indices-based equation account for 89% of the Log K variance (R = 0.94 and s = 0.10 x10-4M-1). The Leave-One-Out (LOO) press statistics, evidenced high predictive ability of both models (q2 = 0.86 and scv = 0.09×10-4M-1 for non-stochastic and q2 = 0.79 and scv = 0.11 x10-4M-1 for stochastic bilinear indices). The nucleic acid’s bilinear indices based models compared favourably with other nucleic acid’s indices based approaches reported nowadays. These models also permit the interpretation of the driving forces of the interaction process. In this sense, developed equations involve short-reaching (k = 3), middle-reaching (4 < k < 9) and farreaching (k = 10 or greater) nucleotide’s bilinear indices. This situation points to electronic and topologic nucleotide’s backbone interactions control of the stability profile of Paromomycin-RNA complexes. Consequently, the present approach represents a novel and rather promising way to theoretical-biology studies.
Keywords: TOMOCOMD-CANAR software, Nucleic Acid and Nucleotide Bilinear Indices, HIV-1 ?-RNA Packaging Region, Paromomycin, Footprinting, QSPR, Linear Multiple Regression