Center for Applied Mathematics, Guangzhou University, Guangzhou, 510006, China.
Department of Mathematics, Michigan State University, East Lansing, Michigan, United States of America.
PLoS Comput Biol. 2019 Apr 29;15(4):e1007017. doi: 10.1371/journal.pcbi.1007017. eCollection 2019 Apr.
Gene transcription is a noisy process, and cell division cycle is an important source of gene transcription noise. In this work, we develop a mathematical approach by coupling transcription kinetics with cell division cycles to delineate how they are combined to regulate transcription output and noise. In view of gene dosage, a cell cycle is divided into an early stage [Formula: see text] and a late stage [Formula: see text]. The analytical forms for the mean and the noise of mRNA numbers are given in each stage. The analysis based on these formulas predicts precisely the fold change r* of mRNA numbers from [Formula: see text] to [Formula: see text] measured in a mouse embryonic stem cell line. When transcription follows similar kinetics in both stages, r* buffers against DNA dosage variation and r* ∈ (1, 2). Numerical simulations suggest that increasing cell cycle durations up-regulates transcription with less noise, whereas rapid stage transitions induce highly noisy transcription. A minimization of the transcription noise is observed when transcription homeostasis is attained by varying a single kinetic rate. When the transcription level scales with cellular volume, either by reducing the transcription burst frequency or by increasing the burst size in [Formula: see text], the noise shows only a minor variation over a wide range of cell cycle stage durations. The reduction level in the burst frequency is nearly a constant, whereas the increase in the burst size is conceivably sensitive, when responding to a large random variation of the cell cycle durations and the gene duplication time.
基因转录是一个嘈杂的过程，细胞分裂周期是基因转录噪声的重要来源。在这项工作中，我们通过将转录动力学与细胞分裂周期耦合，开发了一种数学方法来描绘它们是如何结合起来调节转录输出和噪声的。考虑到基因剂量，一个细胞周期被分为早期阶段[公式：见文本]和晚期阶段[公式：见文本]。在每个阶段都给出了 mRNA 数量的均值和噪声的解析形式。这些公式的分析精确地预测了在一个小鼠胚胎干细胞系中从[公式：见文本]到[公式：见文本]测量的 mRNA 数量的倍变化 r*。当转录在两个阶段遵循相似的动力学时，r缓冲 DNA 剂量变化，r∈（1，2）。数值模拟表明，增加细胞周期持续时间可以以较少的噪声上调转录，而快速的阶段转换会导致高度嘈杂的转录。当通过改变单个动力学速率来实现转录自稳态时，观察到转录噪声的最小化。当转录水平与细胞体积成比例时，无论是通过降低转录爆发频率还是通过增加[公式：见文本]中的爆发大小，噪声在细胞周期阶段持续时间的广泛范围内仅表现出较小的变化。当响应细胞周期持续时间和基因复制时间的大随机变化时，降低爆发频率的水平几乎是恒定的，而增加爆发大小的水平则可能是敏感的。
