Ring-shaped multimeric structure enables the acceleration of KaiB-KaiC complex formation induced by the ADP/ATP exchange inhibition

Circadian clocks tick a rhythm with a nearly 24-hour period in various organisms. The clock proteins of cyanobacteria, KaiA, KaiB, and KaiC, compose a minimum circadian clock. The slow KaiB-KaiC complex formation, which is essential in determining the clock period, occurs when the C1 domain of KaiC binds ADP produced by ATP hydrolysis. KaiC is considered to promote this complex formation by inhibiting the backward process, ADP/ATP exchange, rather than activating the forward process, ATP hydrolysis. Remarkably, although inhibition of backward process, in general, decelerates the whole process, KaiC oppositely accelerates the complex formation. In this article, by building a novel reaction model, we investigate the molecular mechanism of the simultaneous promotion and acceleration of the complex formation, which may play a significant role in keeping the period invariant under environmental perturbations. Based on several experimental results, we assume in this model that six KaiB monomers cooperatively and rapidly binds to C1 with the stabilization of the binding-competent conformation of C1 only when C1 binds six ADP. We find the cooperative KaiB binding effectively separates the pre-binding process of C1 into a fast transformation to binding-competent C1 requiring multiple ATP hydrolyses and its slow backward transformation. Since the ADP/ATP exchange retards the forward process, its inhibition results in the acceleration of the complex formation. We also find that, in a simplified monomeric model where KaiB binds to a KaiC monomer independently of the other monomers, the ADP/ATP exchange inhibition cannot accelerate the complex formation. In summary, we conclude that the ring-shaped hexameric form of KaiC enables the acceleration of the complex formation induced by the backward process inhibition because the cooperative KaiB binding arises from the structure of KaiC. Author summary Circadian clocks tick a rhythm with a nearly 24-hour period in various organisms. The cyanobacterial circadian clock has attracted much attention because of its simplicity, composed of only three proteins, KaiA, KaiB, and KaiC. The rate of the slow KaiB-KaiC complex formation, which plays an essential role in the period determination, is mainly regulated by the ATP hydrolysis (forward process) and the ADP/ATP exchange (backward process) of KaiC. KaiC promotes the complex formation by inhibiting the backward process rather than activating the forward process. Remarkably, although inhibition of backward process, in general, slows down the whole process, KaiC oppositely accelerates the complex formation. In this article, we investigate the molecular mechanism of this acceleration by building a novel mathematical model based on several significant experimental results. We find the cooperative binding of six KaiB to a KaiC hexamer, which arises from the ring-shaped hexameric structure of KaiC, effectively separates the pre-binding process into a fast transformation to the binding-competent KaiC requiring multiple ATP hydrolyses and its slow backward transformation. Since the ADP/ATP exchange retards the forward process, its inhibition results in the acceleration of the complex formation.