Switches in a genetic regulatory system under multiplicative non-Gaussian noise.

The non-Gaussian noise is multiplicatively introduced to model the universal fluctuation in the gene regulation of the bacteriophage λ. To investigate the key effect of non-Gaussian noise on the genetic on/off switch dynamics from the viewpoint of quantitative analysis, we employ the high-order perturbation expansion to deduce the stationary probability density of repressor concentration and the mean first passage time from low concentration to high concentration and vice versa. The occupation probability of different concentration states can be estimated from the height and shape of the peaks of the stationary probability density, which could be used to determine the overall expression level. A further concern is the mean first passage time, also referred to as the mean switching time, which can be adopted as an important measure to characterize the adaptability of gene expression to the environmental variation. Through our investigation, it is observed that the non-Gaussian heavy-tailed noise can better induce the switches between distinct genetic expression states and additionally, it accelerates the switching process more evidently compared to the Gaussian noise and the bounded noise.