Interaction effects of DNA, RNA-polymerase, and cellular fluid on the local dynamic behaviors of DNA

In view of the complex structure and environment, the dynamic analysis on deoxyribonucleic acid (DNA) is a challenge in the biophysics field. Considering the local interaction with ribonucleic acid (RNA)-polymerase as well as the dissipative effect of cellular fluid, a coupling sine-Gordon-type dynamic model is used to describe the rotational motions of the bases in DNA. First, the approximate symmetric form is constructed. Then, the wave form and the wave velocity of the kink solution to the proposed dynamic model are investigated by a Runge-Kutta structure-preserving scheme based on the generalized multi-symplectic idea. The numerical results indicate that, the strengthening of the local interaction between DNA and RNA-polymerase described by the coupling potential makes the form of the kink solution steep, while the appearance of the friction between DNA and cellular fluid makes the form of the kink solution flat. In addition, the appearance of the friction decreases the velocities of both the symplectic configuration and the anti-symplectic configuration with different degrees. The above findings are beneficial to comprehend the DNA transcription mechanism.