Effects of Stochastic Single-Molecule Reactions on Coherent Ensemble Oscillations in the KaiABC Circadian Clock

How do many constituent molecules in a biochemical system synchronize, giving rise to coherent system-level oscillations? One system that is particularly suitable for use in studying this problem is a mixture solution of three cyanobacterial proteins, KaiA, KaiB, and KaiC: the phosphorylation level of KaiC shows stable oscillations with a period of approximately 24 h when these three Kai proteins are incubated with ATP in vitro. Here, we analyze the mechanism behind synchronization in the KaiABC system theoretically by enhancing a model previously developed by the present author. Our simulation results suggest that positive feedback between stochastic ATP hydrolysis and the allosteric structural transitions in KaiC molecules drives oscillations of individual molecules and promotes synchronization of oscillations of many KaiC molecules. Our simulations also show that the ATPase activity of KaiC is correlated with the oscillation frequency of an ensemble of KaiC molecules. These results suggest that stochastic ATP hydrolysis in each KaiC molecule plays an important role in regulating the coherent system-level oscillations. This property is robust against changes in the binding and unbinding rate constants for KaiA to/from KaiC or KaiB, but the oscillations are sensitive to the rate constants of the KaiC phosphorylation and dephosphorylation reactions.