Coarse-grained models coupling cell cycle and gene expression*

During a cell cycle, cells grow and divide. Recent single-cell experiments show that gene expression levels depend on the cell cycle. Particularly important is the proportion of the number of mRNA and protein to the cell volume. It is not clear how cells maintain a constant mRNA and protein concentration as the cells grow. Here we propose a coarse-grained gene expression model incorporating ribosomes and RNA polymerases, which captures the exponential growth of mRNA and protein number. We show that the homeostasis of mRNA and protein concentrations during the cell cycle can be achieved in a robust manner independent of cell shape. Furthermore, we show that the fluctuations in ribosome and polymerase numbers do not propagate to protein concentrations while the fluctuation in cell density does. Furthermore, our model reconciles the discrepancy between theexperimentally observed negligible correlations between mRNA and protein levels, and the predicted positive correlations from previous models