Characteristics of mRNA dynamics in a multi-on model of stochastic transcription with regulation

Quantitative analysis of simple models of gene expression is an important step forward understanding cell functions as well as cell-to-cell variability. Here, we systematically study a multi-on gene model at the transcription level, where we assume that the promoter has one inactive state with very low efficient transcription and two active states with different high efficient transcription, and that the promoter region contains two regulatory sites for the binding of transcription factors (TFs) characterized by three distinct mechanisms: recruitment mechanism (RM), stabilization mechanism (SM) and mixture mechanism (MM). We first derive the analytical mRNA distribution for these three mechanisms in a united framework, and then use numerical simulations to analyze the TF-regulated effects on mRNA dynamics. Interestingly, we find the promoter noise mainly determines the characteristics of mRNA distributions. Tuning the total interaction efficiency can generate unimodal, bimodal or multimodal (in fact three-peak) distributions of mRNA. These results reveal the essential role of TF regulation in controlling phenotypic variation which is important for the cells surviving in fluctuating environments.