Heterogeneous recruitment abilities to RNA polymerases generate nonlinear scaling of gene expression with cell volume

While most genes' expression levels are proportional to cell volumes, some genes exhibit nonlinear scaling between their expression levels and cell volume. Therefore, their mRNA and protein concentrations change as the cell volume increases, which often have crucial biological functions such as cell-cycle regulation. However, the biophysical mechanism underlying the nonlinear scaling between gene expression and cell volume is still unclear. In this work, we show that the nonlinear scaling is a direct consequence of the heterogeneous recruitment abilities of promoters to RNA polymerases based on a gene expression model at the whole-cell level. Those genes with weaker (stronger) recruitment abilities than the average ability spontaneously exhibit superlinear (sublinear) scaling with cell volume. Analysis of the promoter sequences and the nonlinear scaling of Saccharomyces cerevisiae's mRNA levels shows that motifs associated with transcription regulation are indeed enriched in genes exhibiting nonlinear scaling, in concert with our model.