Fig. 6

A method we propose to distinguish the slow, intermediate and fast regimes. (a) 50,000 sample points are selected randomly according to the invariant distribution solved from the CME, i.e. 50,000 cells are selected randomly from a cell population. Then the cells are classified by the number of proteins. We call the cells with large number of proteins (n>400) as P+ cells, and the cells with small number of proteins (n≤400) as P- cells. We define the fraction of P+ cells in a cell group as P+ fraction. b, c We simulate the evolution of the two groups for a long time with Gillespie’s algorithm. The change of P+ fractions are recorded in solid lines and the final values of P+ fractions are drawn in dashed lines. It is obvious that cells of the intermediate regime have shorter memory, for they rapidly recover to the origin unsorted state (invariant distribution). d, e, f If we perturb κ (through changing d _G and keeping the ratios d _G /k _G , d _G /k _G0 and other parameters unchanged), the lines of P+ fractions are shifted in different ways with respect to different regimes. In the slow regime (κ=0.001), P+ fraction changes more quickly when κ increases, whereas in the relative fast regime (κ=2, 50), the time spent for cells to recover to the invariant distribution is longer or unchanged when κ increases. g The evolution of distributions in the view of protein molecules. These are detailed data of subfigure B which illustrate our thought clearly. h Comparison of the slow, intermediate and fast regimes. Using this method, we successfully distinguish the three regimes. The parameters are the same with Fig. 5 in all the figures above