Modeling stochastic gene expression has long relied on Markovian hypothesis. In recent years, however, this hypothesis is challenged by the increasing availability of time-resolved data. Correspondingly, there is considerable interest in understanding how non-Markovian reaction kinetics of gene expression impact protein variations across a population of cells. Here, we analyze a stochastic model of gene expression with arbitrary waiting time distributions, which includes existing gene models as its special cases. We find that stationary probabilistic behavior of this non-Markovian system is exactly the same as that of an equivalent Markovian system. Based on this fact, we derive analytical results, which provide new insights into the roles of feedback regulation and molecular memory (MM) in controlling the protein noise and properties of the steady states, which are inaccessible via existing methodology. Our results also provide quantitative insights into diverse cellular processes involving stochastic sources of gene expression and molecular memory.

中文翻译：

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突变基因表达的非马尔可夫模型的分析结果

建模随机基因表达长期以来一直依赖于马尔可夫假设。但是，近年来，随着时间分辨数据可用性的提高，这一假设受到了挑战。相应地，人们对了解基因表达的非马尔可夫反应动力学如何影响整个细胞群体中蛋白质变异的兴趣很大。在这里，我们分析具有随机等待时间分布的基因表达的随机模型，其中包括现有的基因模型作为特例。我们发现，该非马尔可夫系统的平稳概率行为与等效马尔可夫系统的完全相同。基于这一事实，我们得出分析结果，这些提供了有关反馈调节和分子记忆（MM）在控制蛋白质噪声和稳态特性中的作用的新见解，而现有方法无法访问这些信息。我们的结果还提供了对涉及基因表达和分子记忆的随机来源的各种细胞过程的定量见解。