Post-transcriptional regulation tends to attenuate the mRNA noise and to increase the mRNA gain

Post-transcriptional regulation is ubiquitous in prokaryotic and eukaryotic cells, but how it impacts gene expression remains to be fully explored. Here, we analyze a simple gene model in which we assume that mRNAs are produced in a constitutive manner but are regulated post-transcriptionally by a decapping enzyme that switches between the active state and the inactive state. We derive the analytical mRNA distribution governed by a chemical master equation, which can be well used to analyze the mechanism of how post-transcription regulation influences them RNA expression level including them RNA noise. We demonstrate that the mean mRNA level in the stochastic case is always higher than that in the deterministic case due to the stochastic effect of the enzyme, but the size of the increased part depends mainly on the switching rates between two enzyme states. More interesting is that we find that in contrast to transcriptional regulation, post-transcriptional regulation tends to attenuate noise in mRNA. Our results provide insight into the role of post-transcriptional regulation in controlling the transcriptional noise.