双噪声激励下的基因转录调控系统的稳态分析  

Steady-state Analysis of the Gene Transcriptional Regulation System Under the Double-noise Excitation

作　　者：张萌 郭永峰 刘倩茹 ZHANG Meng;GUO Yongfeng;LIU Qianru(School of Mathematical Sciences,Tiangong University,Tianjin 300387,China)

机构地区：[1]天津工业大学数学科学学院,天津300387

出　　处：《复杂系统与复杂性科学》2023年第2期38-42,67,共6页Complex Systems and Complexity Science

基　　金：国家自然科学基金(11672207);天津市自然科学基金(17JCYBJC15700)。

摘　　要：鉴于噪声对生物系统的基因转录调控有着重要的影响作用,研究了乘性高斯白噪声和加性Lévy噪声共同激励下的基因转录调控系统的动力学特性。首先借助Janicki-Weron算法模拟出Lévy噪声,然后利用四阶Runge-Kutta算法计算出蛋白质浓度的稳态概率密度函数,并通过绘制其图像对系统的动力学行为进行稳态分析。研究发现:高斯噪声强度、Lévy噪声强度、稳定性指标、偏斜参数均会诱导蛋白质浓度发生相变现象,且这些参数指标的增大会使基因转录调控系统逐渐从“开启”状态转变为“关闭”状态。Noise is playing an important role in the regulation of gene transcription in biological systems.This paper studies the dynamics of gene transcription regulation system under the effects of multiplicative Gaussian white noise and additive Lévy noise.Firstly,the Lévy noise is simulated with the Janicki-Weron algorithm,and then the fourth-order Runge-Kutta algorithm is used to calculate the steady-state probability density(SPD)function of the protein concentration,then the steady state analysis of the gene transcriptional regulation system is carried out by the SPD figures.The study found that Gaussian noise intensity,Lévy noise intensity,stability index,and skewness parameter all can induce phase transitions in the gene transcription regulation system;At the same time,the increase of these parameters will cause the gene transcription regulation system to gradually the"on"state changes to the"off"state.

关 键 词：基因转录调控系统 Lévy噪声 高斯白噪声 稳态概率密度 相变 

分 类 号：O414.2[理学—理论物理] O415.6[理学—物理]