Nonlinear dynamics and noise actuated by the cycle of gene inactivation in stochastic transcription

Gene transcription is a stochastic process with random switching between gene offand on states. In this paper, we established a cycle of gene inactivation consisting of two off-states. External signals trigger the random transition from the "ground off"(I1) state to the "excited off"(I2) state, which in turn either jumps forward to the on state or recycles back to I1 state. By integrating inactivation cycle with mRNA birth and death processes, we focus on how the recycling efficiency lambda(21) from I2 to I1 influences dynamical mRNA mean m(t) and the stationary noise strength Phi*. We first reveal a bidirectional regulation of lambda(21) on m(t): Increase of lambda(21) can either induce the monotonic dynamics of m(t) to the non-monotonic behavior or suppress non-monotonic dynamics to monotonicity for m(t). For Phi*, we observe two regulation scenarios that the increase of lambda(21) can significantly upregulate Phi* and weaken the non-monotonic dependence of Phi* on the other parameter rates. The robustness of these results is further tested against experimental data in E.coli, yeast and mammalian cells. Taken together, we show that the cycle of gene inactivation can provide a more comprehensive mechanism on gene regulation. (c) 2020 Elsevier B.V. All rights reserved.