An important task in the post-gene era is to understand the role of stochasticity in gene regulation. Here, we analyze a cascade model of stochastic gene expression, where the upstream gene stochastically generates proteins that regulate, as transcription factors, stochastic synthesis of the downstream output. We find that in contrast to fast input fluctuations that do not change the behavior of the downstream system qualitatively, slow input fluctuations can induce different modes of the distribution of downstream output and even stochastic focusing or defocusing of the downstream output level, although the regulatory protein follows the same distribution in both cases. This finding is counterintuitive but can have broad biological implications, e.g., slow input rather than fast fluctuations may both increase the survival probability of cells and enhance the sensitivity of intracellular regulation. In addition, we find that input fluctuations can minimize the output noise.

中文翻译：

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快速和慢速输入波动对基因调节输出的不同影响。

后基因时代的一个重要任务是了解随机性在基因调控中的作用。在这里，我们分析了随机基因表达的级联模型，其中上游基因随机产生调节下游输出的随机合成作为转录因子的蛋白质。我们发现，与快速输入波动并不能从质量上改变下游系统行为的相反，缓慢的输入波动可以诱发下游输出分布的不同模式，甚至导致下游输出水平的随机聚焦或散焦，尽管调节蛋白在两种情况下都遵循相同的分布。这一发现是违反直觉的，但可能具有广泛的生物学意义，例如，缓慢的输入而不是快速的波动可能会增加细胞的存活率并增强细胞内调节的敏感性。此外，我们发现输入波动可以将输出噪声降至最低。