Abstract
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.
Highlights
Recent single-cell measurements have generated massive data on the histogram of mRNA copy numbers for the target gene in homogeneous cell populations [1, 2]. is provides a good approximation for data fitting by the probability mass function Pm(t), the probability that there are exactly m mRNA molecules of the gene of our concern at time t in one cell [3, 4]. e distribution profile of Pm(t) contains a panoramic information for distinct cellular phenotypes [5, 6]. e commonly observed modes are the decaying distribution that Pm(t) decreases in m, the unimodal distribution that Pm(t) peaks uniquely at some m > 0, and the bimodal distribution that Pm(t) takes exactly two peaks with the first one at m 0 and the other one at some m > 0
The downstream specific transcription factors (TFs) in one pathway compete with the other TFs in another pathway for binding at their shared promoter sites to direct the formation of the intermediate complex [19, 24]. erefore, the two competitive cross-talking pathways could be generated to activate the target gene
It is reported that the bimodal distribution could help differentiate an isogenic cell population into two dynamically stable groups with distinct phenotypes
Summary
Recent single-cell measurements have generated massive data on the histogram of mRNA copy numbers for the target gene in homogeneous cell populations [1, 2]. is provides a good approximation for data fitting by the probability mass function Pm(t), the probability that there are exactly m mRNA molecules of the gene of our concern at time t in one cell [3, 4]. e distribution profile of Pm(t) contains a panoramic information for distinct cellular phenotypes [5, 6]. e commonly observed modes are the decaying distribution that Pm(t) decreases in m, the unimodal distribution that Pm(t) peaks uniquely at some m > 0, and the bimodal distribution that Pm(t) takes exactly two peaks with the first one at m 0 and the other one at some m > 0. The two-state model (1) implicitly assumes that the gene activation from the off state to the on state is directed by a single signaling pathway. The activation of other genes that are involved in stem cell renewal, development, and immunity is often mediated by two signal transduction pathways [21,22,23] In all these cases, the downstream specific transcription factors (TFs) in one pathway compete with the other TFs in another pathway for binding at their shared promoter sites to direct the formation of the intermediate complex [19, 24]. By integrating competitive cross-talking pathways into the gene activation process [24, 25], the two-state model (1) can be generalized as the following equation: λ1. We shall derive Pm(t) generated by cross-talking pathways in simple mathematical formulas in Section 2, and discuss their dynamical profiles and implications in Section 3. e main conclusion and its discussion are given in the last section
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