On the dynamics of inhomogeneous short-range DNA interactions at a defect

Abstract

DNA defect is due to any change that introduces a deviation from the usual double helical structure. At this state, the study of the motion of DNA molecules requires novel dynamical models. Recently, a few works in the nonlinear dynamics of DNA at a defect, or the level of bases, have been carried out. We suggest a model which describes the links between the different bases of DNA, by accounting for nth site of bases (or space) dependent and the inverse width and the rigidity of the backbone. Short-range interactions at microscopic scale are considered. We mention that the inter-chain interactions as well as the long-chain interactions may introduce a big change of a comprehensive mapping of DNA. The structural properties depend on the velocity of connected base-pairs pbs. Resonance frequency between pbs like damped oscillatory waves propagation has been predicted . Here, the model presented is based on the in-homogeneity of the medium, due to defect, and non-homogeneity of the localization of bases in the opening motion of DNA. Exact solutions of the model equation are obtained by using the extended unified method. Numerical evaluations of these solutions are carried out. It is found that when the inverse width and the rigidity of the backbone are very high, the motion is not like a wave, while for too small or moderate values, wave motion holds. These results found in this work consolidate those found in the literature as the solutions found here are exact.