Joint distribution of nuclear and cytoplasmic mRNA levels in stochastic models of gene expression: analytical results and parameter inference

Stochastic models of gene expression are routinely used to explain large variability in measured mRNA levels between cells. These models typically predict the distribution of the total mRNA level per cell but ignore compartment-specific measurements which are becoming increasingly common. Here we construct a two-compartment model that describes promoter switching between active and inactive states, transcription of nuclear mRNA and its export to the cytoplasm where it decays. We obtain an analytical solution for the joint distribution of nuclear and cytoplasmic mRNA levels in steady-state conditions. Based on this solution, we build an efficient and accurate parameter inference method which is orders of magnitude faster than conventional methods.