# L\'{e}vy noise-induced transitions in gene regulatory networks

## TL;DR

This paper investigates how Lévy noise influences gene expression transitions in a two-dimensional B. subtilis model, revealing optimal noise conditions and the impact on basin stability of the competence state.

## Contribution

It introduces a two-dimensional gene network model incorporating Lévy and Brownian noise, analyzing transition dynamics with new quantitative measures and control strategies.

## Key findings

- Optimal noise conditions enhance transition probability.
- Lévy noise significantly affects basin stability.
- Transition metrics depend on noise strength ratio.

## Abstract

Important effects of noise on a one-dimensional gene expression model involving a single gene have recently been discussed. However, few works have been devoted to the transition in two-dimensional models which include the interaction of genes. Therefore, we investigate here, a quantitative two-dimensional model (MeKS network) of gene expression dynamics describing the competence development in the B. subtilis under the influence of L\'evy as well as Brownian motions, where noises can do the B. subtilis a favor in nutrient depletion. To analyze the transitions between the vegetative and the competence regions therein, two deterministic quantities, the mean first exit time (MFET) and the first escape probability (FEP) from a microscopic perspective, as well as their averaged versions from a macroscopic perspective, are applied. The relative contribution factor (RCF), the ratio of non-Gaussian and Gaussian noise strengths, is adopted to implement optimal control in these transitions. Schematic representations indicate that there exists an optimum choice that makes the transition occurring at the highest probability. Additionally, we use a geometric concept, the stochastic basin of attraction, to exhibit a pictorial comprehension about the influence of the L\'{e}vy motion on the basin stability of the competence state.