Optimal switching paths of a non-Markovian model of gene bursty expression

Abstract

Gene expression usually involves multiple biochemical reactions, resulting into the probability of waiting time between consecutive reaction steps is a non-exponential probability distribution, and creating molecular memory. Besides, some experiments indicate that burst of gene expression and positive feedback loops play important roles in gene expression and phenotypic variation. However, how molecular memory and the burst together affect metastable states in gene expression is still open, as far as our knowledge. In this paper, we build a generalized chemical master equation of gene bursty expression with a self-regulatory positive feedback. Using the Wentzel-Kramers-Brillouin (WKB) method, we study optimal paths of switching between bistable states of gene expression under the combination of molecular memory and the burst. Through theoretical analysis and numerical simulations, we find that the burst and molecular memory can change the metastable state structure of the mean-field system of our model, and that the burst can prolong optimal paths of switching from the high state of gene expression to the low state, and shorten optimal paths of switching from the low state to the high state, but molecular memory has the opposite effect on the optimal switching paths. This result is the further improvement on our previous work (Yin et al., 2021).