School of Mathematics and Computers, Wuhan Textile University, Wuhan 430200, People's Republic of China.
Key Laboratory of Computational Mathematics, School of Mathematics, Sun Yat-sen University, Guangdong Province, Guangzhou 510275, People's Republic of China.
Phys Rev E. 2020 Jan;101(1-1):012405. doi: 10.1103/PhysRevE.101.012405.
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.
除了内在的随机可变性外，基因表达还涉及到由异质性和波动过程引起的随机反应延迟，这会影响反应物（例如 mRNA 或蛋白质）探索其环境的效率。与前者受到广泛研究不同，后者对基因表达的影响仍不完全清楚。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效于引入负反馈，而稳定的蛋白质分布仅取决于延迟的均值，而与分布无关。我们通过数值模拟表明，随机反应延迟总是略微放大平均蛋白质水平，但显著降低蛋白质噪声（通过方差与平均平方的比值来量化）。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。
