The bistable Rb-E2F gene regulatory network plays a central role in regulating cellular proliferation-quiescence transition. Based on Gillespie's chemical Langevin method, the stochastic bistable Rb-E2F gene's regulatory network with time delays is proposed. It is found that under the moderate intensity of internal noise, delay in the Cyclin E synthesis rate can greatly increase the average concentration value of E2F. When the delay is considered in both E2F-related positive feedback loops, within a specific range of delay (3-13) hr , the average expression of E2F is significantly increased. Also, this range is in the scope with that experimentally given by Dong et al. [65]. By analysing the quasi-potential curves at different delay times, simulation results show that delay regulates the dynamic behaviour of the system in the following way: small delay stabilises the bistable system; the medium delay is conducive to a high steady-state, making the system fluctuate near the high steady-state; large delay induces approximately periodic transitions between high and low steady-state. Therefore, by regulating noise and time delay, the cell itself can control the expression level of E2F to respond to different situations. These findings may provide an explanation of some experimental result intricacies related to the cell cycle.

中文翻译：

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噪声和时间延迟对双稳态Rb-E2F基因调控网络中E2F表达水平的影响。

双稳态Rb-E2F基因调节网络在调节细胞增殖-静止过渡中起着核心作用。基于吉莱斯皮化学朗格文方法，提出了具有时滞的随机双稳态Rb-E2F基因调控网络。发现在中等噪声强度下，Cyclin E合成速率的延迟可以大大提高E2F的平均浓度值。当在两个与E2F相关的正反馈回路中均考虑到延迟时，在特定的延迟范围（3-13）hr内，E2F的平均表达会显着增加。同样，该范围在Dong等人实验给出的范围内。[65]。通过分析不同延迟时间下的准电位曲线，仿真结果表明，延迟通过以下方式调节系统的动态行为：较小的延迟可稳定双稳态系统；中等延迟有利于高稳态，使系统在高稳态附近波动；大的延迟会引起高稳态和低稳态之间的近似周期性过渡。因此，通过调节噪声和时间延迟，细胞本身可以控制E2F的表达水平以响应不同的情况。这些发现可能提供了一些与细胞周期有关的实验结果复杂性的解释。细胞本身可以控制E2F的表达水平以响应不同的情况。这些发现可能提供了一些与细胞周期有关的实验结果复杂性的解释。细胞本身可以控制E2F的表达水平以响应不同的情况。这些发现可能提供了一些与细胞周期有关的实验结果复杂性的解释。