Single-molecular and Ensemble-level Oscillations of Cyanobacterial Circadian Clock

When three cyanobacterial proteins, KaiA, KaiB, and KaiC, are incubated with ATP in vitro, the phosphorylation level of KaiC hexamers shows stable oscillation with approximately 24 h period. In order to understand this KaiABC clockwork, we need to analyze both the macroscopic synchronization of a large number of KaiC hexamers and the microscopic reactions and structural changes in individual KaiC molecules. In the present paper, we explain two coarse-grained theoretical models, the many-molecule (MM) model and the single-molecule (SM) model, to bridge the gap between macroscopic and microscopic understandings. In the simulation results with these models, ATP hydrolysis drives oscillation of individual KaiC hexamers and ATP hydrolysis is necessary for synchronizing oscillations of a large number of KaiC hexamers. Sensitive temperature dependence of the lifetime of the ADP bound state in the CI domain of KaiC hexamers makes the oscillation period temperature insensitive. ATPase activity is correlated to the frequency of phosphorylation oscillation in the single molecule of KaiC hexamer, which should be the origin of the observed ensemble-level correlation between the ATPase activity and the frequency of phosphorylation oscillation. Thus, the simulation results with the MM and SM models suggest that ATP hydrolysis randomly occurring in each CI domain of individual KaiC hexamers is a key process for oscillatory behaviors of the ensemble of many KaiC hexamers.\n\nSignificance StatementCyanobacterial proteins, KaiA, KaiB, and KaiC, can reconstitute a circadian clock when they are incubated with ATP in vitro. In order to understand this prototypical oscillator, we need to analyze both synchronization of a macroscopically large number of oscillating molecules and microscopic reactions in individual molecules. We introduced two theoretical models to unify macroscopic and microscopic viewpoints. Simulation results suggest that ATP hydrolysis is necessary for synchronization and temperature compensation and that ATPase activity is correlated to the oscillation frequency in individual molecules. Thus, ATP hydrolysis randomly occurring in individual molecules should determine important features of the ensemble-level oscillation.