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 基因调控网络在调节细胞增殖-静止转变中起核心作用。基于Gillespie的化学Langevin方法，提出了随机双稳态Rb-E2F基因的时滞调控网络。发现在中等强度的内部噪声下，Cyclin E合成速率的延迟可以大大增加E2F的平均浓度值。当在两个与 E2F 相关的正反馈回路中都考虑延迟时，在特定的延迟范围 (3-13) hr 内，E2F 的平均表达显着增加。此外，这个范围在董等人实验给出的范围内。[65]。通过分析不同延迟时间的准电位曲线，仿真结果表明延迟通过以下方式调节系统的动态行为：小延迟稳定双稳态系统；中等延迟有利于高稳态，使系统在高稳态附近波动；大延迟会引起高稳态和低稳态之间的近似周期性转换。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，以应对不同的情况。这些发现可以解释一些与细胞周期相关的复杂实验结果。细胞本身可以控制E2F的表达水平以应对不同的情况。这些发现可以解释一些与细胞周期相关的复杂实验结果。细胞本身可以控制E2F的表达水平以应对不同的情况。这些发现可以解释一些与细胞周期相关的复杂实验结果。