Simulation of a kink movement in homogeneous and heterogeneous DNA sequences taking into account the dissipation

Abstract

The problem of modelling the movement of a nonlinear conformational perturbation (i.e., kink) along a DNA molecule is considered taking into account the dissipation. The study of movement peculiarities is performed using a homogeneous sequence of nucleotides and a heterogeneous one consisting of two homogeneous parts separated by a boundary. Using analytic and numerical methods, it is shown that the effect of dissipation leads to a decrease of the energy of kink E, its velocity v, and the mass M. It is also shown that the consideration of the dissipation near the boundary leads to a smoothing of kink motion trajectories in the plane {z, t} in comparison with trajectories calculated without taking into account the dissipation and characterized by a sharp bend on the boundary caused by effects of reflection from the boundary or by a passage through the boundary with an increase or decrease of motion velocity.

DNA Breathers and Cell Dynamics

“…This potential does not contribute to the total energy of the system (vanishes) only when the base pairs form a spiral. Substituting (2), (3), (4) and (5) (6) where m is the nucleotide mass, F n (t) is an external stochastic force. For the convenience of studying the model, the dimensionless Hamilton function is obtained.…”

“…It is a complex dynamic system consisting of many atoms and has a quasi-one-dimensional structure with specific symmetry, multiple degrees of freedom, and many types of movements and a special distribution of internal interactions [1]. These functions of DNA are discussed in some DNA models to investigate the relationship of structural-dynamic and functional properties of the molecule [2][3][4][5][6][7][8][9][10][11][12][13]. A comprehensive review on the DNA properties can be found in the work [14].…”