## Resumen

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 ℜ^{n} [b_{mk} (over(x, -)_{m}, over(y, -)_{m}) : ℜ^{n} × 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, M_{m}^{k} and ^{s} M_{m}^{k}, respectively. That is to say, the kth non-stochastic and stochastic nucleic acid's bilinear indices are calculated using M_{m}^{k} and ^{s} M_{m}^{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}_{260} at 260 nm and pH=7.0, first (Δ E_{1}) and second (Δ E_{2}) single excitation energies in eV, and first (f_{1}) and second (f_{2}) 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 (q^{2}=0.86 and s_{cv}=0.09×10^{-4} M^{-1} for non-stochastic and q^{2}=0.91 and s_{cv}=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.

Idioma original | Inglés |
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Páginas (desde-hasta) | 229-241 |

Número de páginas | 13 |

Publicación | Journal of Theoretical Biology |

Volumen | 259 |

N.º | 2 |

DOI | |

Estado | Publicada - 21 jul. 2009 |

Publicado de forma externa | Sí |