Díaz Humberto González, de Armas Ronal Ramos, Molina Reinaldo
Department of Drug Design, CBQ, Central University of 'Las Villas', Las Villas 54830, Cuba.
Bull Math Biol. 2003 Nov;65(6):991-1002. doi: 10.1016/s0092-8240(03)00064-8.
The design of novel anti-HIV compounds has now become a crucial area for scientists working in numerous interrelated fields of science such as molecular biology, medicinal chemistry, mathematical biology, molecular modelling and bioinformatics. In this context, the development of simple but physically meaningful mathematical models to represent the interaction between anti-HIV drugs and their biological targets is of major interest. One such area currently under investigation involves the targets in the HIV-RNA-packaging region. In the work described here, we applied Markov chain theory in an attempt to describe the interaction between the antibiotic paromomycin and the packaging region of the RNA in Type-1 HIV. In this model, a nucleic acid squeezed graph is used. The vertices of the graph represent the nucleotides while the edges are the phosphodiester bonds. A stochastic (Markovian) matrix was subsequently defined on this graph, an operation that codifies the probabilities of interaction between specific nucleotides of HIV-RNA and the antibiotic. The strength of these local interactions can be calculated through an inelastic vibrational model. The successive power of this matrix codifies the probabilities with which the vibrations after drug-RNA interactions vanish along the polynucleotide main chain. The sums of self-return probabilities in the k-vicinity of each nucleotide represent physically meaningful descriptors. A linear discriminant function was developed and gave rise to excellent discrimination in 80.8% of interacting and footprinted nucleotides. The Jackknife method was employed to assess the stability and predictability of the model. On the other hand, a linear regression model predicted the local binding affinity constants between a specific nucleotide and the antibiotic (R(2)=0.91, Q(2)=0.86). These kinds of models could play an important role either in the discovery of new anti-HIV compounds or the study of their mode of action.
