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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 Ψ-RNA packaging region

Abstract:

A new set of nucleotide-based bio-macromolecular descriptors are presented. This novel approach to bio-macromolecular design from a linear algebra point of view is relevant to nucleic acids quantitative structure-activity relationship (QSAR) studies. These bio-macromolecular indices are based on the calculus of bilinear maps on ℜn [b<inf>mk</inf> (over(x, -)<inf>m</inf>, over(y, -)<inf>m</inf>) : ℜn × ℜn → 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, M<inf>m</inf>k and s M<inf>m</inf>k, respectively. That is to say, the kth non-stochastic and stochastic nucleic acid's bilinear indices are calculated using M<inf>m</inf>k and s M<inf>m</inf>k 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 ε{lunate}<inf>260</inf> at 260 nm and pH=7.0, first (Δ E<inf>1</inf>) and second (Δ E<inf>2</inf>) single excitation energies in eV, and first (f<inf>1</inf>) and second (f<inf>2</inf>) 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 Ψ-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 non-stochastic bilinear indices explains about 91% of the variance of the experimental Log K (R=0.95 and s=0.08×10-4 M-1) as long as the best stochastic bilinear indices-based equation account for 93% of the Log K variance (R=0.97 and s=0.07×10-4 M-1). The leave-one-out (LOO) press statistics, evidenced high predictive ability of both models (q2=0.86 and s<inf>cv</inf>=0.09×10-4 M-1 for non-stochastic and q2=0.91 and s<inf>cv</inf>=0.08×10-4 M-1 for stochastic bilinear indices). The nucleic acid's bilinear indices-based models compared favorably 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 far-reaching (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. © 2009 Elsevier Ltd. All rights reserved.