Fig. 3.

(A and B) Cell-cycle-length variability and its effect on mature mRNA distributions. (A) The Erlang distribution provides a good fit to the experimentally measured cell-cycle time distribution of NIH 3T3 cells in ref. 42. PDF, probability distribution function. (B) The SSA modified such that the cell-cycle times are random variables independently drawn from an Erlang distribution is used to obtain the mature mRNA distributions (for the genes DBP_FRT and Per2_het reported in SI Appendix, Table S1) measured across an ensemble of cells (blue dots; see main text for details). The mature mRNA distributions are accurately predicted by modifying our theory (red solid lines; SI Appendix, section 6, Eq. 26) to take into account the asynchronicity of cell cycles across the population. Note that replication always occurs in the middle of a cell cycle. (C) Relative sensitivity of the cyclo-stationary coefficient of variation of mature mRNA noise averaged over the cell cycle to eight parameters. Box plots indicate the median and the 25% and 75% quantiles, with the mean marked as red dots. The median relative sensitivities are also shown as numbers at the bottom of the plot. The sensitivity analysis is carried out on 567,540 parametric combinations estimated for 1,051 genes of CAST allele data of mouse embryonic stem cells. Our results show that the degradation rate $d$ is the most sensitive parameter, followed by ${\sigma }_{\text{u}}^{-}$, while $\alpha$ is the least sensitive one. Note that there is no dependence of the coefficient of variation of mature mRNA on $k$ in the approximate theory, and, hence, $k$ is not a relevant parameter. See SI Appendix, section 11 for the specific range of parameter choice and their justification.