Little定律在基因表达随机模型中的应用
Applications of Little's Law to stochastic models of gene expression
摘要：
基因表达的内在随机性可导致细胞群体中蛋白质水平的巨大变化。为了解释这种变异性，在基因表达的随机模型中提出了mRNA波动的不同来源（“泊松”和“电报”过程）。泊松和电报情景模型解释了蛋白质表达的“爆发”方面的蛋白质水平的噪声的实验观察。相应地，人们对建立基因表达一般随机模型的突发和稳态蛋白质分布之间的关系非常感兴趣。在这项工作中，我们解决这个问题，考虑随机模型之间的映射基因表达和问题的兴趣在遗传理论。通过应用一般定理，小的法律，我们推导出精确的关系，连接突发和稳态分布的方式与任意等待时间分布的mRNA和蛋白质的到达和降解的模型。导出的关系有影响的方法来量化的转录爆发的程度，从而区分不同来源的内在噪声在基因表达。为了说明这一点，我们考虑了一个模型的小RNA的蛋白质表达的突发调节。对于广泛的参数，我们推导出的平均蛋白质水平的分析表达式（随机模拟验证）的调节小RNA的水平不同。所获得的结果表明，转录爆发的程度，原则上，可以确定从平均稳态蛋白质水平的一般随机模型的基因表达的变化。
英文摘要：
The intrinsic stochasticity of gene expression can lead to large variations in protein levels across a population of cells. To explain this variability, different sources of mRNA fluctuations ('Poisson' and 'Telegraph' processes) have been proposed in stochastic models of gene expression. Both Poisson and Telegraph scenario models explain experimental observations of noise in protein levels in terms of 'bursts' of protein expression. Correspondingly, there is considerable interest in establishing relations between burst and steady-state protein distributions for general stochastic models of gene expression. In this work, we address this issue by considering a mapping between stochastic models of gene expression and problems of interest in queueing theory. By applying a general theorem from queueing theory, Little's Law, we derive exact relations which connect burst and steady-state distribution means for models with arbitrary waiting-time distributions for arrival and degradation of mRNAs and proteins. The derived relations have implications for approaches to quantify the degree of transcriptional bursting and hence to discriminate between different sources of intrinsic noise in gene expression. To illustrate this, we consider a model for regulation of protein expression bursts by small RNAs. For a broad range of parameters, we derive analytical expressions (validated by stochastic simulations) for the mean protein levels as the levels of regulatory small RNAs are varied. The results obtained show that the degree of transcriptional bursting can, in principle, be determined from changes in mean steady-state protein levels for general stochastic models of gene expression.
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