Apart from intrinsic stochastic variability, gene expression also involves stochastic reaction delay arising from heterogeneity and fluctuation processes, which can affect the efficiency of reactants (e.g., mRNA or protein) in exploring their environments. In contrast to the former that has been extensively investigated, the impact of the latter on gene expression remains not fully understood. Here, we analyze a non-Markovian model of bursty gene expression with general delay distribution. We analytically find that the effect of stochastic reaction delay is equivalent to the introduction of negative feedback, and stationary protein distribution only depends on the mean of the delay and is independent of its distribution. We numerically show that the stochastic reaction delay always slightly amplifies the mean protein level but remarkably reduces the protein noise (quantified by the ratio of the variance over the squared average). Our analysis indicates that stochastic reaction delay is an important factor affecting gene expression.

中文翻译：

---

随机反应延迟对基因表达的显式影响。

除了固有的随机变异性外，基因表达还涉及由异质性和波动过程引起的随机反应延迟，这可能会影响反应物（例如，mRNA或蛋白质）探索其环境的效率。与已经被广泛研究的前者相反，后者对基因表达的影响仍然没有被完全理解。在这里，我们分析了具有一般延迟分布的突发基因表达的非马尔可夫模型。我们通过分析发现，随机反应延迟的影响等同于负反馈的引入，而固定蛋白的分布仅取决于延迟的平均值，而与延迟的分布无关。我们从数值上显示出，随机反应延迟总是会略微放大平均蛋白质水平，但会显着降低蛋白质噪音（通过方差与平方平均值之比进行量化）。我们的分析表明，随机反应延迟是影响基因表达的重要因素。