Local conformational perturbations of the DNA molecule in the SG-model

L. A. Krasnobaeva, A. V. Shapovalov

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Within the formalism of the Fokker-Planck equation, the influence of nonstationary external force, random force, and dissipation effects on dynamics local conformational perturbations (kink) propagating along the DNA molecule is investigated. Such waves have an important role in the regulation of important biological processes in living systems at the molecular level. As a dynamic model of DNA was used a modified sine-Gordon equation, simulating the rotational oscillations of bases in one of the chains DNA. The equation of evolution of the kink momentum is obtained in the form of the stochastic differential equation in the Stratonovich sense within the framework of the well-known McLaughlin and Scott energy approach. The corresponding Fokker-Planck equation for the momentum distribution function coincides with the equation describing the Ornstein-Uhlenbek process with a regular nonstationary external force. The influence of the nonlinear stochastic effects on the kink dynamics is considered with the help of the Fokker-Planck nonlinear equation with the shift coefficient dependent on the first moment of the kink momentum distribution function. Expressions are derived for average value and variance of the momentum. Examples are considered which demonstrate the influence of the external regular and random forces on the evolution of the average value and variance of the kink momentum. Within the formalism of the Fokker-Planck equation, the influence of nonstationary external force, random force, and dissipation effects on the kink dynamics is investigated in the sine-Gordon model. The equation of evolution of the kink momentum is obtained in the form of the stochastic differential equation in the Stratonovich sense within the framework of the well-known McLaughlin and Scott energy approach. The corresponding Fokker-Planck equation for the momentum distribution function coincides with the equation describing the Ornstein-Uhlenbek process with a regular nonstationary external force. The influence of the nonlinear stochastic effects on the kink dynamics is considered with the help of the Fokker-Planck nonlinear equation with the shift coefficient dependent on the first moment of the kink momentum distribution function. Expressions are derived for average value and variance of the momentum. Examples are considered which demonstrate the influence of the external regular and random forces on the evolution of the average value and variance of the kink momentum.

Original languageEnglish
Title of host publicationNew Operational Technologies, NEWOT 2015: Proceedings of the 5th International Scientific Conference "New Operational Technologies"
PublisherAmerican Institute of Physics Inc.
Volume1688
ISBN (Electronic)9780735413351
DOIs
Publication statusPublished - 17 Nov 2015
Externally publishedYes
Event5th International Scientific Conference on New Operational Technologies, NEWOT 2015 - Tomsk, Russian Federation
Duration: 29 Sep 201530 Sep 2015

Conference

Conference5th International Scientific Conference on New Operational Technologies, NEWOT 2015
CountryRussian Federation
CityTomsk
Period29.9.1530.9.15

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ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

Krasnobaeva, L. A., & Shapovalov, A. V. (2015). Local conformational perturbations of the DNA molecule in the SG-model. In New Operational Technologies, NEWOT 2015: Proceedings of the 5th International Scientific Conference "New Operational Technologies" (Vol. 1688). [030020] American Institute of Physics Inc.. https://doi.org/10.1063/1.4936015