Lévy noise induced switch in the gene transcriptional regulatory system.

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.