### Аннотация

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.

Язык оригинала | Английский |
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Заголовок главной публикации | New Operational Technologies, NEWOT 2015: Proceedings of the 5th International Scientific Conference "New Operational Technologies" |

Издатель | American Institute of Physics Inc. |

Том | 1688 |

ISBN (электронная версия) | 9780735413351 |

DOI | |

Статус публикации | Опубликовано - 17 ноя 2015 |

Опубликовано для внешнего пользования | Да |

Событие | 5th International Scientific Conference on New Operational Technologies, NEWOT 2015 - Tomsk, Российская Федерация Длительность: 29 сен 2015 → 30 сен 2015 |

### Конференция

Конференция | 5th International Scientific Conference on New Operational Technologies, NEWOT 2015 |
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Страна | Российская Федерация |

Город | Tomsk |

Период | 29.9.15 → 30.9.15 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Цитировать

*New Operational Technologies, NEWOT 2015: Proceedings of the 5th International Scientific Conference "New Operational Technologies"*(Том 1688). [030020] American Institute of Physics Inc.. https://doi.org/10.1063/1.4936015