  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.
