Nonlinear dynamics of DNA with topological constraints

Abstract

The mechanical DNA model is developed to study the nonlinear dynamics, topological constrains of the helicoidal geometry DNA molecule, dissipation effects and influence of the external force. To construct the model of DNA the Peyrard-Bishop-Barbi approach has been applied. We have derived equations of motion for the DNA base pairs in the presence of a damping term and external driving force to follow the Caldirola-Kanai method. The analytical small localized solutions as the discrete breather and the antikink have been obtained by multiple scale expansion method for multicomponent lattices. The impact of the damping effect and external forces on the breather and the antikink propagation has been investigated. The prospects of using the helicoidal model of DNA with the energy dissipation and external force are discussed. The dissipative term and the external force term in the DNA motion equations follow from corresponding Hamiltonian energy representation. The advantage of this approach is the promising way to study both the thermodynamic properties and nonlinear dynamics of DNA system related to the types of the collective modes (breathers, antikinks) as new thermodynamic degrees of freedom. This result allows the formulation of the experimental strategy to analyze the qualitative changes in cell dynamics induced by mentioned collective modes.