Heterogeneous recruitment abilities to RNA polymerases generate nonlinear scaling of gene expression level with cell volume
Many experiments have shown that most genes’ expression levels are typically proportional to cell volumes in growing cells. However, a finite number of genes often exhibit nonlinear scaling of expression levels with cell volume. Their corresponding mRNA and protein concentrations are therefore not constant as the cell volume increases. While these genes with changing concentrations often have important biological functions such as cell cycle regulation, the biophysical mechanism underlying the nonlinear scaling between the gene expression level and the cell volume is still unclear. In this manuscript, we show that the nonlinear scaling is, in fact, a direct consequence of heterogeneous recruitment abilities of promoters to RNA polymerases. Those genes with weaker (stronger) recruitment abilities compared with the average ability spontaneously exhibit superlinear (sublinear) scaling with cell volume. Our model makes predictions in agreement with experimental observations, including a correlation between the expression levels and nonlinear scaling degrees with cell volume among genes.