使用统一色噪声近似求解具有波动速率参数的遗传反馈回路的稳态波动
Steady-state fluctuations of a genetic feedback loop with fluctuating rate parameters using the unified colored noise approximation
摘要：
随机自动调节基因表达的常见模型描述了通过协同蛋白质结合、活性状态下的有效蛋白质产生和蛋白质稀释的启动子转换。在这里，我们考虑这个模型的扩展，其中具有短相关时间的有色噪声被添加到反应速率参数中-我们表明，当噪声的大小和时间尺度被适当选择时，它可以解释没有明确建模的快速反应，例如，在没有mRNA描述的模型中，蛋白质产生速率的波动可以解释在真核生物中翻译之前的核mRNA加工的快速多个阶段。我们展示了如何统一的色噪声近似可以用来推导出表达的蛋白质数量分布，这是在很好的协议与随机模拟。我们发现，即使当速率参数中的噪声很小时，我们的模型预测的蛋白质分布也可以与假设恒定反应速率的模型显着不同。
英文摘要：
A common model of stochastic auto-regulatory gene expression describes promoter switching via cooperative protein binding, effective protein production in the active state and dilution of proteins. Here we consider an extension of this model whereby colored noise with a short correlation time is added to the reaction rate parameters -- we show that when the size and timescale of the noise is appropriately chosen it accounts for fast reactions that are not explicitly modelled, e.g., in models with no mRNA description, fluctuations in the protein production rate can account for rapid multiple stages of nuclear mRNA processing which precede translation in eukaryotes. We show how the unified colored noise approximation can be used to derive expressions for the protein number distribution that is in good agreement with stochastic simulations. We find that even when the noise in the rate parameters is small, the protein distributions predicted by our model can be significantly different than models assuming constant reaction rates.
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