Gene transcription is a random process in single cells manifested by the observed distribution of mRNA copy numbers in homogeneous cell populations. A central question is to understand how mRNA distribution is modulated under environmental changes. In this work, we initiate a theoretical study on mRNA distribution dynamics for the stochastic transcription model that involves cross-talking signaling pathways to direct gene activation in response to external signals. We first express the distribution in mathematical dynamical formulas under both moderate and high transcriptional upregulations. In each scenario, our further numerical examples display an observed dynamical transition type among three distribution modes for stress genes in yeast. In particular, the intermediate bimodal stage sustains within a certain length of early time and lasts much longer than that generated by the single pathway. This shows the general and robust bimodal transcription regulated by the cross-talk of signaling pathways.

中文翻译：

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通过交叉对话信号通路动态调节mRNA分布。

基因转录是单个细胞中的随机过程，其表现为在均质细胞群体中观察到的mRNA拷贝数分布。一个中心问题是了解在环境变化下如何调节mRNA的分布。在这项工作中，我们启动了有关随机转录模型的mRNA分布动力学的理论研究，该模型涉及串扰信号通路，以响应外部信号指导基因激活。我们首先在中等和高度转录上调下以数学动力学公式表示分布。在每种情况下，我们的其他数值示例都显示了在酵母中应激基因的三种分布模式之间观察到的动态过渡类型。尤其是，中间双峰阶段在早期的一定长度内维持，并且比单途径产生的持续时间长得多。这显示了受信号传导途径的串扰调节的一般和稳健的双峰转录。