Longitudinal displacements of base pairs in DNA and effects on the dynamics of nonlinear excitations

A model of the DNA is proposed and studied analytically and numerically. The model is an extension of a well known model and describes the double helix as two chains of pendula (each pendulum representing a base). Each base (or pendulum) can rotate and translate along the helix axis. In the continuum limit the system is described by the perturbed Sine-Gordon equation describing the twist of the bases and by a nonlinear partial differential equation (PDE) describing the longitudinal displacements of the bases. This coupled system of PDEs was studied analytically using different approaches and the corresponding results were tested through numerical simulations. It was found that if the coupling parameters satisfy a well defined relationship, then there exist bounded travelling wave solutions.