Attenuation of transcriptional bursting in mRNA transport

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.

💡 Research Summary

The paper addresses how stochastic fluctuations generated by transcriptional bursting are reshaped when mRNA molecules are transported from the nucleus to the cytoplasm. Using analytical methods based on master equations and generating functions, the authors model the bursting input as a Poisson process that produces bursts of average size b at rate λ_b, and they couple this source to two distinct transport mechanisms. The first transport model is linear, with a rate proportional to the nuclear mRNA count (v = k_t N). The second model follows Michaelis–Menten kinetics (v = V_max N/(K_m + N)), capturing saturation of transport mediators such as export complexes or nuclear pores.

For each model the authors derive expressions for the mean and variance of cytoplasmic mRNA, focusing on the output Fano factor F_out = Var(N_out)/⟨N_out⟩ as a quantitative measure of noise. In the linear case, when the transport rate k_t is much slower than the transcription rate k_s, the nuclear burst is “averaged out” during the prolonged export, leading to a dramatic reduction of F_out toward the Poisson limit (F ≈ 1). Conversely, if k_t ≥ k_s, the burst is transmitted almost unchanged, and the cytoplasmic noise remains high (F_out ≈ b). The analytical result F_out ≈ 1 + (b k_s/k_t)(1 − e^{−k_t τ}) explicitly shows how the ratio k_s/k_t controls noise attenuation, with τ representing the average transport delay.

In the Michaelis–Menten scenario, the transport behaves linearly at low nuclear mRNA concentrations (N ≪ K_m) but saturates at V_max when N ≫ K_m. Saturation introduces a nonlinear buffering effect: even large fluctuations in the nuclear pool produce only limited changes in the export flux. Consequently, the output Fano factor drops further as K_m decreases (i.e., the system reaches saturation at lower mRNA numbers) and as V_max is reduced (slower maximal export). Numerical simulations confirm that for realistic parameter ranges the cytoplasmic noise can be reduced to near‑Poisson levels, despite strong bursting at the source.

Biologically, the findings imply that eukaryotic cells can mitigate the impact of transcriptional bursting simply by the kinetic properties of mRNA export. The number of nuclear pores, the concentration of export receptors, and the affinity of the transport machinery all set effective K_m and V_max values. By modulating these parameters, a cell could fine‑tune the degree of noise transmitted to downstream processes such as translation. The authors also point out that experimental measurements of bursting should distinguish nuclear from cytoplasmic mRNA, because the latter may display far less variability than the former. Ignoring the transport step, as many current models do, can lead to overestimation of transcriptional noise and misinterpretation of single‑cell RNA‑seq data.

In summary, the study provides a rigorous theoretical framework showing that slow or saturated nuclear‑cytoplasmic transport acts as a powerful noise filter for transcriptional bursts. This insight expands the conventional view of gene expression noise, highlighting the importance of post‑transcriptional steps in shaping cellular variability and offering new avenues for experimental design and synthetic biology applications where precise control of stochasticity is required.