Effect of post-transcriptional feedback on the stochastic effect in gene expression

The post-transcriptional feedback mediated by microRNA is ubiquitous in a wide range of biological organisms, but how it impacts the dynamic of gene expression remains to be fully explored. A qualitative understanding the effect of the post-transcriptional feedback requires analysis of the corresponding stochastic models, the exact analytic results of which have not been obtained so far. Here, we analyzed a model of gene expression with post-transcriptional and feedback regulation and obtain exact results for the corresponding mRNA steady-state distribution. The results obtained provide new insights into the role of post-transcriptional regulation and feedback in controlling noise and stochastic deviation. We demonstrate that the effect of post-transcriptional feedback on noise depends on the time scale of enzyme switching and the reference model. Our results also indicate that deviation in post-transcriptional feedback can be decomposed into two parts: deviation caused by enzyme fluctuation and deviation caused by feedback and intrinsic noise. More importantly, we show that the gain in stochastic deviation is generally obtained at the cost of large noise. Our results provide insight into the role of post-transcriptional regulation in controlling the dynamic of gene expression.