Abstract
Many experiments show that the concentrations of protein and mRNA fluctuate but on average are constant in growing cells, independent of the genome copy number. However, models of stochastic gene expression often assume constant gene expression rates that are proportional to the gene copy numbers, which are therefore incompatible with experiments. Here, we construct a minimal gene expression model to fill this gap. We show that (1) because the ribosomes translate all proteins, the concentrations of proteins are regulated in an exponentially growing cell volume; (2) the competition between genes for the RNA polymerases makes the gene expression rate independent of the genome number; (3) the fluctuations in ribosome level and cell density can generate a global extrinsic noise in protein concentrations; (4) correlations between mRNA and protein levels can be quantified.