Gene transcription is a stochastic process with random switching between gene off and 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 λ₂₁ from I2 to I1 influences dynamical mRNA mean m(t) and the stationary noise strength Φ*. We first reveal a bidirectional regulation of λ₂₁ on m(t): Increase of λ₂₁ 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 Φ*, we observe two regulation scenarios that the increase of λ₂₁ can significantly up-regulate Φ* and weaken the non-monotonic dependence of Φ* 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.

基因转录是一个随机过程，在基因关闭和开启状态之间随机切换。在本文中，我们建立了一个由两个关闭状态组成的基因失活周期。外部信号触发从“接地随机过渡断开”（我1）状态到“激发关”（我2）状态，而这又或者向前跳到上状态或再循环回到我1个状态。通过与mRNA的出生和死亡流程集成灭活周期，我们专注于再生利用率如何λ ₂₁从我2到我1影响动态mRNA的平均m（t）和静态噪声强度Φ*。我们首先揭示的双向调节λ ₂₁上米（吨）：增加λ ₂₁可以诱导的单调动力学米（吨），以非单调行为或抑制非单调动力学单调性为米（吨）。对于Φ*，我们观察到两种调节方案是增加λ ₂₁可以显着上调Φ*并减弱Φ*对其他参数速率的非单调依赖性。针对大肠杆菌，酵母和哺乳动物细胞中的实验数据，进一步测试了这些结果的鲁棒性。两者合计，我们表明基因失活的周期可以提供更全面的基因调控机制。