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

Common stochastic models of gene expression predict the analytical distribution of the total mRNA level per cell but not at subcellular resolution. Here, for a wide class of models of transcription initiation, we obtain an exact steady-state solution for the joint distribution of nuclear and cytoplasmic mRNA levels per cell. Correcting the solution for extrinsic noise and fitting to single human cell data, we precisely quantify the extent of bursty expression in thousands of genes and associate it with their biological functions.