Stochastic resonance in gene transcriptional regulatory system driven by Gaussian noise and Lévy noise

Abstract

The impacts of noise parameters and input signal parameters on stochastic resonance are explored in a gene transcriptional regulatory model driven by a combination of multiplicative Gaussian noise and additive Lévy noise. The response time series and signal-to-noise ratios are obtained by numerical simulations to quantify the occurrence of stochastic resonance. It is shown that the Gaussian noise intensity can cause the stochastic resonance, while the Lévy noise intensity can cause both the stochastic resonance and inverse stochastic resonance. The increases of Gaussian noise intensity inhibits these two phenomena and enhances system stability. The changes of the Lévy noise intensity parameter can cause the system to switch between low and high concentration state. In addition, the stability index and skewness parameter of Lévy noise can also result in stochastic resonance. Therefore, the optimum stochastic resonance can be achieved and useful genetic information can be easily acquired by adjusting the noise parameters. Our findings should contribute in the selection of appropriate parameters to achieve stochastic resonance in gene transcriptional regulation models, laying the foundation for the selection of stochastic resonance parameter ranges in actual gene transcriptional engineering.