PMC

Stochastic simulation of clock mutations. (Upper) The standard deviation of the period of the normal model (WT); PER1, PER2, CRY1, and CRY2 knockouts; and PER1/PER2 or CRY1/CRY2 mutants where only one copy of either PER1 and PER2 or CRY1 and CRY2 was present was calculated as in . Removing one copy of both the PER genes or both the CRY genes led to less accurate rhythms. Removing PER1 or PER2 led to less accurate rhythms because two fewer PER genes were available. Removing CRY1 or CRY2 caused more accurate rhythms because the CRY genes are activated more often than the PER genes, and homogeneous CRY leads to larger rhythm amplitudes (see text). (Lower) Unlike deterministic simulations, stochastic simulations of PER2 mutants show rhythmicity.

Comparison between stochastic and deterministic simulations. (Top) Stochastic simulation of the Forger–Peskin mathematical model of the mammalian circadian clock () using the Gillespie direct method (blue trace) were irregular because of the long time between activations of the PER genes (see text for simulation details). When promoter binding and unbinding were increased by a factor of 100, PER genes were activated about every hour, which led to much more robust rhythms (black trace). (Middle) Deterministic simulations of our model (black trace) and our model with the above changes in the rates of promoter interactions (blue trace) are almost identical. (Bottom) There is good agreement between stochastic and deterministic simulations of the model with rapid promoter binding and unbinding. The cell volume was calculated from experimental data (see text).

Stochastic simulations become more robust as more molecules are present. The variables in a deterministic simulation are concentrations. With the volume of a cell we can convert these concentrations to the number of molecules of each molecular species. Simulations of the stochastic version of the model were run scaling the cell volume as well as the rate constants for binding with promoters (see text) for ≈1,000 cycles, and each period was calculated by the up-crossing of a particular concentration level of transcription factors (i.e., CRY1 and CRY2) in the nucleus of the cells. One hundred up-crossing concentrations were tried, and the up-crossing that led to the minimum variance was used. Reported is the standard deviation (SD) of the cycle-to-cycle periods. As the average number of molecules in the cell and promoter interactions increased, the clock became more accurate, obeying the 1/n^0.5 (curve) law discussed in the text.