Role of the reaction-structure coupling in temperature compensation of the KaiABC circadian rhythm

When the mixture solution of cyanobacterial proteins, KaiA, KaiB, and KaiC, is incubated with ATP in vitro, the phosphorylation level of KaiC shows stable oscillations with the temperature-compensated circadian period. Elucidating this temperature compensation is essential for understanding the KaiABC circadian clock, but its mechanism has remained a mystery. We analyzed the KaiABC temperature compensation by developing a theoretical model describing the feedback relations among reactions and structural transitions in the KaiC molecule. The model showed that the reduced structural cooperativity should weaken the negative feedback coupling among reactions and structural transitions, which enlarges the oscillation amplitude and period, explaining the observed significant period extension upon single amino-acid residue substitution. We propose that an increase in thermal fluctuations similarly attenuates the reaction-structure feedback, explaining the temperature compensation in the KaiABC clock. The model explained the experimentally observed responses of the oscillation phase to the temperature shift or the ADP-concentration change and suggested that the ATPase reactions in the CI domain of KaiC affect the period depending on how the reaction rates are modulated. The KaiABC clock provides a unique opportunity to analyze how the reaction-structure coupling regulates the system-level synchronized oscillations of molecules. Author summary The reconstituted KaiABC circadian clock provides a unique opportunity to analyze how the effects of chemical and structural features of individual molecules determine the system-level oscillations of many molecules. By modeling the coupling of chemical reactions and structural transitions in the KaiC molecule, we showed that reducing the coupling strength enlarges the oscillation amplitude and period, explaining the observed striking change of the period length upon single-residue substitution in KaiC. We propose that thermal fluctuations attenuate the reaction-structure coupling similarly to the residue substitution, explaining the stable temperature compensation observed in the KaiABC clock. The combined experimental and theoretical analyses should open a way to develop techniques to design the system-level molecular oscillations, further providing a basis for understanding circadian clocks in vivo.