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

doi:10.1007/s10483-020-2595-6

Applied Mathematics and Mechanics (English Edition) ›› 2020, Vol. 41 ›› Issue (4): 623-636.doi: https://doi.org/10.1007/s10483-020-2595-6

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

Weipeng HU^1,2, Zichen DENG³

1. School of Civil Engineering and Architecture, Xi'an University of Technology, Xi'an 710048, China;
2. State Key Laboratory of Eco-Hydraulics in Northwest Arid Region of China, Xi'an University of Technology, Xi'an 710048, China;
3. School of Mechanics, Civil Engineering and Architecture, Northwestern Polytechnical University, Xi'an 710072, China

收稿日期:2019-11-08 修回日期:2020-01-03 发布日期:2020-03-26
通讯作者: Weipeng HU E-mail:wphu@nwpu.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Nos. 11972284 and 11672241), the Fund for Distinguished Young Scholars of Shaanxi Province of China (No. 2019JC-29), and the Open Foundation of State Key Laboratory of Structural Analysis of Industrial Equipment of China (No. GZ19103)

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

Weipeng HU^1,2, Zichen DENG³

1. School of Civil Engineering and Architecture, Xi'an University of Technology, Xi'an 710048, China;
2. State Key Laboratory of Eco-Hydraulics in Northwest Arid Region of China, Xi'an University of Technology, Xi'an 710048, China;
3. School of Mechanics, Civil Engineering and Architecture, Northwestern Polytechnical University, Xi'an 710072, China

Received:2019-11-08 Revised:2020-01-03 Published:2020-03-26
Contact: Weipeng HU E-mail:wphu@nwpu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Nos. 11972284 and 11672241), the Fund for Distinguished Young Scholars of Shaanxi Province of China (No. 2019JC-29), and the Open Foundation of State Key Laboratory of Structural Analysis of Industrial Equipment of China (No. GZ19103)

摘要/Abstract

摘要： 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.

关键词: deoxyribonucleic acid (DNA) dynamics, local interaction, generalized multisymplectic idea, kink solution, Runge-Kutta scheme

Abstract: 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.

Key words: deoxyribonucleic acid (DNA) dynamics, local interaction, generalized multisymplectic idea, kink solution, Runge-Kutta scheme

中图分类号:

Weipeng HU, Zichen DENG. Interaction effects of DNA, RNA-polymerase, and cellular fluid on the local dynamic behaviors of DNA[J]. Applied Mathematics and Mechanics (English Edition), 2020, 41(4): 623-636.

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

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

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