Computational modeling and dynamical analysis for B. subtilis competence genic regulation circuit with multiple time delays and external noisy regulation

Bacillus subtilis (B. subtilis), a bacterium known to enter a competent state spontaneously, has garnered significant attention due to its intricate internal regulatory mechanisms. This study proposes a six-dimensional continuous delay differential equation (DDE) model incorporating two-time delays and a stochastic model that accounts for noise, aimed at delving deeper into the dynamic behaviors of the B. subtilis competence gene regulation circuit. Our investigation reveals that time delays play a crucial role in inducing oscillatory behavior within the continuous DDE model. Analyzing the dynamics of multiple time delays proves to be more intricate than studying a single delay. Furthermore, certain parameter adjustments significantly influence the system's dynamic characteristics. The introduction of noise also triggers oscillations, with the irregular oscillation patterns closely aligning with real-world observations. Intriguingly, the effects of parameters and noise regulation undergo significant changes when time delays are jointly considered. This analysis offers a fresh perspective on understanding B. subtilis competence and provides essential theoretical support for subsequent experimental endeavors in this domain of biomathematics.