Effects of promoter leakage on dynamics of gene expression

Quantitative analysis of simple molecular networks is an important step forward understanding fundamental intracellular processes. As network motifs occurring recurrently in complex biological networks, gene auto-regulatory circuits have been extensively studied but gene expression dynamics remain to be fully understood, e.g., how promoter leakage affects expression noise is unclear. In this work, we analyze a gene model with auto regulation, where the promoter is assumed to have one active state with highly efficient transcription and one inactive state with very lowly efficient transcription (termed as promoter leakage). We first derive the analytical distribution of gene product, and then analyze effects of promoter leakage on expression dynamics including bursting kinetics. Interestingly, we find that promoter leakage always reduces expression noise and that increasing the leakage rate tends to simplify phenotypes. In addition, higher leakage results in fewer bursts. Our results reveal the essential role of promoter leakage in controlling expression dynamics and further phenotype. Specifically, promoter leakage is a universal mechanism of reducing expression noise, controlling phenotypes in different environments and making the gene produce generate fewer bursts.