Consequences of mRNA transport on stochastic variability in protein levels

Homogeneous cell populations can exhibit considerable cell-to-cell variability in protein levels arising from the stochastic nature of the gene-expression process. In particular, transcriptional bursting of mRNAs from the promoter has been implicated as a major source of stochasticity in the expression of many genes. In eukaryotes, transcribed pre-mRNAs have to be exported outside the nucleus and in many cases, export rates can be slow and comparable to mRNA turnover rates. We investigate whether such export processes can be effective mechanisms in buffering protein levels from transcriptional bursting of pre-mRNAs in the nucleus. For a stochastic gene-expression model with both transcriptional bursting and export, we derive an exact solution of the steady-state probability-generating function for both the nuclear and the cytoplasmic mRNA levels. These formulas reveal that decreasing export rates can dramatically reduce variability in cytoplasmic mRNA levels. However, our results also show that decreasing export rates enhance mRNA autocorrelation times, which function to increase heterogeneity in protein levels. Our overall analysis concludes that under physiologically relevant parameter regimes, a pre-mRNA export step can decrease steady-state variability at the mRNA level but not at the protein level. Finally, we reinforce previous observations that saturation in the pre-mRNA transport machinery can be an important mechanism in suppressing protein variability from underlying transcriptional bursts.