Abstract
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 in the CI domain of KaiC hexamers drives oscillation of individual KaiC hexamers and the 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 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 stochastically occurring in each CI domain of individual KaiC hexamers is a key process for oscillatory behaviors of the ensemble of many KaiC hexamers.