Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710072, China.
Chaos. 2013 Mar;23(1):013110. doi: 10.1063/1.4775758.
The study of random fluctuations in a gene transcriptional regulatory system is extended to the case of non-Gaussian Lévy noise, which can describe unpredictable jump changes of the random environment. The stationary probability densities are given to explore the key roles of Lévy noise in a gene transcriptional regulatory system. The results demonstrate that the parameters of Lévy noise, including noise intensity, stability index, and skewness parameter, can induce switches between distinct gene-expression states. A further concern is the switching time (from the high concentration state to the low concentration one or from the low concentration state to the high concentration one), which is a random variable and often referred to as the mean first passage time. The effects of Lévy noise on expression and degradation time are studied by computing the mean first passage time in two directions and a number of different peculiarities of non-Gaussian Lévy noise compared with Gaussian noise are observed.
研究随机波动的基因转录调控系统扩展到非高斯 Lévy 噪声的情况，该噪声可以描述随机环境的不可预测的跳跃变化。给出了稳态概率密度以探讨 Lévy 噪声在基因转录调控系统中的关键作用。结果表明，Lévy 噪声的参数，包括噪声强度、稳定指数和偏度参数，可以诱导不同基因表达状态之间的转换。进一步关注的是转换时间（从高浓度状态到低浓度状态或从低浓度状态到高浓度状态），这是一个随机变量，通常称为平均首次通过时间。通过计算两个方向的平均首次通过时间来研究 Lévy 噪声对表达和降解时间的影响，观察到与高斯噪声相比，非高斯 Lévy 噪声的许多不同特性。
