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title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð±Ð°ÐºÐ°Ð»Ð°Ð²ÑÐ°
titleType: Subtitle
title: Influence of parameters of the simplest gene networks on noise
Creators: name: ÐÑÐ¾Ð·Ð´Ð¾Ð²Ð°, ÐÐ°ÑÑÑ
Publisher: name: Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³ÑÐºÐ¸Ð¹ Ð¿Ð¾Ð»Ð¸ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ½Ð¸Ð²ÐµÑÑÐ¸ÑÐµÑ ÐÐµÑÑÐ° ÐÐµÐ»Ð¸ÐºÐ¾Ð³Ð¾
Year: 2022
Subjects: Ð³ÐµÐ½ÐµÑÐ¸ÑÐµÑÐºÐ°Ñ ÑÐµÑÑ
Ð¾ÑÐ½Ð¾Ð²Ð½Ð¾Ðµ ÐºÐ¸Ð½ÐµÑÐ¸ÑÐµÑÐºÐ¾Ðµ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ðµ
ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ðµ ÐÐ°Ð½Ð¶ÐµÐ²ÐµÐ½Ð°
Ð¼Ð¾Ð´ÐµÐ»Ñ ÑÐ¾Ð¶Ð´ÐµÐ½Ð¸Ñ-Ð³Ð¸Ð±ÐµÐ»Ð¸
gene system
chemical master equation
Langevin equation
birth-death process

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description: The subject of the graduate qualification work is Â«Influence of parameters of theÂ simplest gene networks on noiseÂ». This paper is devoted to numerical modeling of the Langevin equation. BasedÂ on existing scientific articles, the chemical master equation and its approximation, theÂ Langevin equation, were investigated. As a model for the study, the birth-death modelÂ was chosen, which can be considered as an approximation of the simplest geneticÂ systems. This model was considered in three variations: the simplest birth-death model,Â the birth-death model with negative feedback, and the birth-death model with positiveÂ feedback. The paper contains the results of numerical simulation of the LangevinÂ equation for various parameters of the model. In addition, for the simplest birth-deathÂ model, an exact solution of the basic chemical equation is constructed. Analysis ofÂ the results showed that the Langevin equation approximates the solution of the basicÂ chemical equation well.