Origins of binary gene expression in post-transcriptional regulation by microRNAs

MicroRNA-mediated regulation of gene expression is characterised by some distinctive features that set it apart from unregulated and transcription-factor-regulated gene expression. Recently, a mathematical model has been proposed to describe the dynamics of post-transcriptional regulation by microRNAs. The model explains the observations made in single-cell experiments quite well. In this paper, we introduce some additional features into the model and consider two specific cases. In the first case, a noncooperative positive feedback loop is included in the transcriptional regulation of the target gene expression. In the second case, a stochastic version of the original model is considered in which there are random transitions between the inactive and active expression states of the gene. In the first case we show that bistability is possible in a parameter regime, due to the presence of a nonlinear protein decay term in the gene expression dynamics. In the second case, we derive the conditions for obtaining stochastic binary gene expression. We find that this type of gene expression is more favourable in the case of regulation by microRNAs as compared to the case of unregulated gene expression. The theoretical predictions relating to binary gene expression are experimentally testable.