Stochastic models of gene expression are typically formulated using the chemical master equation, which can be solved exactly or approximately using a repertoire of analytical methods. Here, we provide a tutorial review of an alternative approach based on queueing theory that has rarely been used in the literature of gene expression. We discuss the interpretation of six types of infinite-server queues from the angle of stochastic single-cell biology and provide analytical expressions for the stationary and nonstationary distributions and/or moments of mRNA/protein numbers and bounds on the Fano factor. This approach may enable the solution of complex models that have hitherto evaded analytical solution.

中文翻译：

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使用排队论求解随机基因表达模型：教程回顾


基因表达的随机模型通常使用化学主方程来制定，可以使用一系列分析方法精确或近似地求解该方程。在这里，我们提供了对基于排队论的替代方法的教程回顾，该方法很少在基因表达文献中使用。我们从随机单细胞生物学的角度讨论了六种类型的无限服务器队列的解释，并提供了 mRNA/蛋白质数量和 Fano 因子上界的平稳和非平稳分布和/或矩的分析表达式。这种方法可以解决迄今为止无法解析的复杂模型。