On the dynamics of DNA molecules with an-harmonics potential in the normal and damaged states

Abstract

DNA damage 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. We propose a discrete model to describe the nonlinear dynamics DNA molecule with inharmonic potential. We consider two physical situations, the ideal or homogeneous state, and the inhomogeneous or damage state. The problem of the homogeneous (normal) case with ANHP was considered in the literature, but the dynamics of DNA molecules were not inspected. Here, our objective is to distinguish between the dynamics of DNA in the normal and damaged states. The novelty of the present work stems from a conjuncture that the DNA state can be depicted from the dynamics of the molecules. The unified and extended unified methods are used to find the exact solutions of the systems in both cases, respectively. Numerically, it is found that, in the ideal case, the motion of DNA molecules is periodic and stable. Considering the inhomogeneous case due to damage, the small or moderate values of the backbone rigidity make the motion of the molecule periodic and stable, but for high values, the motion becomes aperiodic and unstable. But for small or moderate values of the backbone rigidity, the motion becomes periodic and stable. These results are of interest in vulgarizing the physical properties of DNA molecules.