Sufficiency of unidirectional allostery in KaiC in generating the cyanobacterial circadian rhythm

The clock protein of cyanobacteria KaiC forms a homohexamer with two ring-shaped domains, C1 and C2. These domains undergo several domain-specific conformational transitions and allosterically communicate to generate a circadian rhythm. Interestingly, experiments show a possibility that C2 is independent of C1. However, detailed interplay among them remains elusive. Here we propose a mathematical model, which explicitly considers the interplay. The allostery in KaiC is here modeled to be unidirectional from C2 to C1. We demonstrate that the unidirectional allostery is sufficient for the circadian rhythm by showing the quantitative reproducibility of various experimental data, including temperature dependence of both phosphorylation oscillation and ATPase activity. Based on the present model, we further discuss possible functional roles of the unidirectional allostery particularly in the period robustness against both protein concentration and temperature.