Activation of a gene is a multistep biochemical process, involving recruitments of transcription factors and histone kinases as well as modification of histones. Many of these intermediate reaction steps would have been unspecified by experiments. Therefore, classical two-state models of gene expression established based on the memoryless (or Markovian) assumption would not well describe the reality in gene expression. Recent experimental data have indicated that the inactive phases of gene promoters are differently distributed, showing strong memory. Here, we use a nonexponential waiting-time distribution to model the complex activation process of a gene, and then analyze a queuing model of stochastic transcription. We successfully derive the analytical expression of the stationary mRNA distribution, which provides insight into the effect of molecular memory created by complex activating events on the mRNA expression. We find that the reduction in the waiting-time noise may result in the increase in the mRNA noise, contrary to the previous conclusion. Based on the derived distribution, we also develop a method to infer the waiting-time distribution from a known mRNA distribution. Data analysis on a realistic example verifies the validity of this method.

中文翻译：

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基因表达的排队模型：分析分布及其他

基因的激活是一个多步骤的生化过程，涉及转录因子和组蛋白激酶的募集以及组蛋白的修饰。许多这些中间反应步骤在实验中是未指定的。因此，基于无记忆（或马尔可夫）假设建立的经典基因表达二态模型不能很好地描述基因表达的现实。最近的实验数据表明，基因启动子的非活动期分布不同，表现出强烈的记忆力。在这里，我们使用非指数等待时间分布来模拟基因的复杂激活过程，然后分析随机转录的排队模型。我们成功推导出平稳 mRNA 分布的解析表达，它提供了对复杂激活事件对 mRNA 表达产生的分子记忆的影响的洞察。我们发现等待时间噪声的减少可能导致 mRNA 噪声的增加，这与之前的结论相反。基于派生的分布，我们还开发了一种从已知 mRNA 分布推断等待时间分布的方法。对一个实际例子的数据分析验证了该方法的有效性。