Desenvolvimento de modelos mesoscópicos assimétricos para oligonucleotídeos e sua aplicação a defeitos tipo single-bulges em RNAs

Abstract

There is a growing understanding of the biological role of non-canonical RNAs such as mismatches, bulges, triple bases, internal loops hairpins and pseudo-knots, and the nonlinear behavior associated with these processes. In particular, structures containing bulges are important for RNA-RNA interactions, RNA ligands and specic sites of protein bondings. Several physical models are being used for this kind of study. The most frequently used thermodynamic model for non-canonical RNAs of this kind is the nearest-neighbor model (NN model). However, despite the large number of studies using this model they do not obtain a physical relationship between the thermodynamic energies and the structural properties that these molecules assume. Therefore, it is necessary to nd alternative models for a better understanding these kind of defects. The mesoscopic models such as the Peyrard-Bishop (PB) model have not been used in the study of bulges. The PB model can describe in an intuitive way the interactions contained in these duplexes. In the last few years, several variants of this model were used in dierent physical applications and achieved important results with respect to the thermodynamic properties of canonical duplexes. However, the PB model has not been applied to asymmetric structures before. In this work, we show that it is possible to use the Peyrard-Bishop model in asymmetric structures of DNA and RNA containing single-bulges. In the rst part of this work, we adapted the Hamiltonian of the Peyrard-Bishop model to describe the stacking of dierent monomers. We show through the algebraic treatment that the PB model with harmonic stacking describes asymmetrical structures with an eective elastic constant, similar to harmonic oscillators in series. The partition function of this system can be solved numerically by the transfer integral (TI) method, as in the original model. We tried the same treatment with the Hamiltonian with an anharmonic stacking. In this case however, we obtained a Fredholm equation of the second type, that makes it impossible to use the TI technique. For the solution of the Fredholm equation of the second type, we suggest the use of two-dimensional block pulse functions (2D-BPFs) and we apply these functions to the original model for a polymer of the DNA 7 containing only CG base pairs. After that, we apply successfully the asymmetry results to the study of Group I single-bulges in RNA molecules. For this purpose, we created a pseudo-base to describe the absence of the base in the opposite direction of the bulge and divide the local interactions into subgroups of parameters. The parameters of each subgroup were calculated through the minimization between the predicted and experimental temperatures. For a better understanding of the results, we study the opening proles of the experimental sequences and we found a strong perturbation of the guanosine bulges in the sequences that were not related before. The calculations for the experimental sequences containing adenosine and uridine bulges are in agreement with the nuclear magnetic resonance (NMR) measurements. As in the experiment, we note a preference of the uridine bulges for a ipped out conguration. The results found here in the study of bulges showed the correlation of thermodynamic properties with the structural properties of these molecules.