Transcriptional bursting is a major source of noise in gene expression. The telegraph model of gene expression, whereby transcription switches between on and off states, is the dominant model for bursting. Recently, it was shown that the telegraph model cannot explain a number of experimental observations from perturbation data. Here, we study an alternative model that is consistent with the data and which explicitly describes RNA polymerase recruitment and polymerase pause release, two steps necessary for messenger RNA (mRNA) production. We derive the exact steady-state distribution of mRNA numbers and an approximate steady-state distribution of protein numbers, which are given by generalized hypergeometric functions. The theory is used to calculate the relative sensitivity of the coefficient of variation of mRNA fluctuations for thousands of genes in mouse fibroblasts. This indicates that the size of fluctuations is mostly sensitive to the rate of burst initiation and the mRNA degradation rate. Furthermore, we show that 1) the time-dependent distribution of mRNA numbers is accurately approximated by a modified telegraph model with a Michaelis-Menten like dependence of the effective transcription rate on RNA polymerase abundance, and 2) the model predicts that if the polymerase recruitment rate is comparable or less than the pause release rate, then upon gene replication, the mean number of RNA per cell remains approximately constant. This gene dosage compensation property has been experimentally observed and cannot be explained by the telegraph model with constant rates.

中文翻译：

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具有聚合酶募集和暂停释放的基因表达随机模型

转录爆发是基因表达中的主要噪音来源。基因表达的电报模型，即转录在开启和关闭状态之间切换，是爆发的主要模型。最近，表明电报模型无法解释来自扰动数据的许多实验观察结果。在这里，我们研究了与数据一致的替代模型，该模型明确描述了 RNA 聚合酶募集和聚合酶暂停释放，这是信使 RNA (mRNA) 生产所必需的两个步骤。我们推导出 mRNA 数量的精确稳态分布和蛋白质数量的近似稳态分布，它们由广义超几何函数给出。该理论用于计算小鼠成纤维细胞中数千个基因的 mRNA 波动变异系数的相对敏感性。这表明波动的大小对爆发起始率和 mRNA 降解率最敏感。此外，我们表明 1) mRNA 数量的时间依赖性分布可以通过修改后的电报模型准确近似，该模型具有类似 Michaelis-Menten 的有效转录率对 RNA 聚合酶丰度的依赖性，以及 2) 该模型预测，如果聚合酶募集率与暂停释放率相当或低于暂停释放率，然后在基因复制时，每个细胞的平均 RNA 数量保持大致恒定。