Negative Autoregulation Controls size Scaling in Confined Gene Expression Reactions

Gene expression via transcription-translation is the most fundamental reaction to sustain biological systems, and complex reactions such as this one occur in a small compartment of living cells. Transcriptional feedback that controls gene expression during mRNA synthesis is a vital mechanism that regulates protein synthesis in cells. There is increasing evidence that the cellular compartment induces steric effects in gene expression reactions. However, the finite-size effect of spatial constraints on feedback regulation is not well understood. Here, we study the confinement effect on transcriptional negative feedback regulation of gene expression reactions using a theoretical model. We find that negative feedback regulation alters the scaling relation of gene expression level on compartment volume, approaching the regular scaling relation without the steric effect. Our findings suggest that negative autoregulatory feedback at the transcription step can dampen the size-dependence of protein expression levels in heterogeneous cell populations.