Abstract
In this paper, we will explore the stochastic exit problem for the gene regulatory circuit in B. subtilis affected by colored noise. The stochastic exit problem studies the state transition in B. subtilis (from competent state to vegetative state in this case) through three different quantities: the probability density function of the first passage time, the mean of first passage time, and the reliability function. To satisfy the Markov nature, we convert the colored noise system into the equivalent white noise system. Then, the stochastic generalized cell mapping method can be used to explore the stochastic exit problem. The results indicate that the intensity of noise and system parameters have the effect on the transition from competent to vegetative state in B. subtilis. In addition, the effectiveness of the stochastic generalized cell mapping method is verified by Monte Carlo simulation.
Highlights
B. subtilis, which is a single-celled creature, is simpler and easier than multicellular creature [1]
Once sporulation forms, B. subtilis maintains this state until the environment improves [2]. e competent cell can switch to vegetative state with a certain probability. e state transition can be attributed to the excitability in the gene regulatory circuit
We study the stochastic exit problem for the gene regulatory circuit in B. subtilis with colored noise through the above three different quantities
Summary
B. subtilis, which is a single-celled creature, is simpler and easier than multicellular creature [1]. Kohar and Lu studied the effect of both the intrinsic and extrinsic noises and parameters on the dynamics of gene regulatory circuits through the randomization-based approach [6]. E stochastic exit problem is usually used to analyze such state transition through three quantities: the probability density function of first passage time (PDF of FPT), the mean of first passage time (MFPT), and the reliability function [10, 11]. The FPT refers to the time that B. subtilis takes to finish the transition from the stable competent state to stable vegetative state in this paper. We study the stochastic exit problem for the gene regulatory circuit in B. subtilis with colored noise through the above three different quantities.
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