  Due to the stochastic nature of biochemical processes, the copy number of any
given type of molecule inside a living cell often exhibits large temporal
fluctuations. Here, we develop analytic methods to investigate how the noise
arising from a bursting input is reshaped by a transport reaction which is
either linear or of the Michaelis-Menten type. A slow transport rate smoothes
out fluctuations at the output end and minimizes the impact of bursting on the
downstream cellular activities. In the context of gene expression in eukaryotic
cells, our results indicate that transcriptional bursting can be substantially
attenuated by the transport of mRNA from nucleus to cytoplasm. Saturation of
the transport mediators or nuclear pores contributes further to the noise
reduction. We suggest that the mRNA transport should be taken into account in
the interpretation of relevant experimental data on transcriptional bursting.
