Time delay-accelerated transition of gene switch and -enhanced stochastic resonance in a bistable gene regulatory model

The roles of time delay on gene switch and stochastic resonance are systematically explored based on a famous gene transcriptional regulatory model with noises. Our theoretical results show that the time delay can induce the switch, i.e., the TF-A monomer concentration shifts from the high concentration state to the low concentration state (“on”→“off”), and can further accelerate the transition from “on” to “off”. Moreover, it is found that the stochastic resonance can be enhanced by the time delay and the correlated noise intensity. However, the additive noise original from the synthesis rate restrains the stochastic resonance. It is very interesting that the resonance bi-peaks structure appears for the large value of the additive noise intensity. The theoretical results by using small-delay time-approximation approach are consistent well with our numerical simulation.