Oscillation dynamic mechanism driven by time delays in the competent gene regulatory circuit of B. subtilis

Bacillus subtilis with competent states absorbs DNA and may improve the growth of bacteria by integrating new genetic material. Therefore, it is important to clarify how the genes interact in the circuit so that cells enter into a competent state or return to a vegetative state. The gene regulatory circuit consists of two positive feedback loops and one negative feedback loop. In this paper, a mathematical model is developed by considering transcription time delays to further study dynamic behavior of the B. subtilis competent gene regulatory network. Combined with theoretical calculation and numerical simulation, it is verified that the time delay in indirect transcription inhibition indeed has the effect of inducing the periodic oscillation of the B. subtilis competent system. In addition, some important chemical reaction rates can also regulate system dynamic behavior. However, under the control of time delay, the effects of the important chemical reaction rates have changed significantly. In particular, the time delay can advance critical value of the important chemical reaction rates where vibration occurs and can also weaken or even eliminate the effect of the important chemical reaction rates. These results will help us to analyze the competent state of B. subtilis.