Sasai, M.; Fujishiro, S.

When three cyanobacterial proteins--KaiA, KaiB, and KaiC--are incubated with ATP in vitro, the phosphorylation level of KaiC exhibits stable circadian oscillations. Biochemical and structural analyses have shown that KaiC's ATPase activity is crucial for these oscillations, leading to the hypothesis that ATP-consuming dynamics function as a molecular clock, determining the oscillation period of individual molecules. Moreover, these molecular clocks synchronize with one another, resulting in collective oscillations at the ensemble level. In this study, we develop a theoretical model to test this molecular clockwork hypothesis. Our model clarifies the relationship between the oscillation period and ATPase activity, explaining the significant changes in the period induced by amino-acid substitutions near the CI-CII domain boundary of the KaiC hexamer. Furthermore, the model addresses the physical basis for temperature compensation concerning both the oscillation period and ATPase activity. Thus, the molecular clockwork perspective provides a framework for understanding the atomic design behind collective oscillations.