Figure 3.

(a) Comparison between the mRNA content over a single-cell trajectory in time (blue) with the mRNA distribution of a proliferating population (orange). Histograms for both mRNA distributions (right) compare the average of 100 trajectory realizations with the snapshot of a single population at t = 7T. Parameters used are T = 1 , N = 4, W = 2 , $\hat{n}=50$, η = 1. (Inset) Probability distribution π_i of finding a cell at different cell cycle stages for single trajectory (blue) and a proliferating population (orange). Stochastic simulations for π_i (circles) are compared with theoretical results (bars) obtained from equation (4.2) (that for the Erlang case is constant π_i = 1/N) and from equation (5.4). (b,c) Relative error made in the average number of mRNAs (R) and its variance ($R_{\sigma }$) when considering the cell cycle to be deterministic instead of Erlang distributed in a growing proliferative population. Comparison includes theoretical results (lines) and stochastic simulations (circles). Simulations in (b) show the average of 5000 snapshots at a time 10 T and in (c) the average of 25000 snapshots at a time 10 T. Error bars indicate the standard error of the mean.