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

Circadian clocks tick a rhythm with a nearly 24-hour period in a variety of organisms. In the clock proteins of cyanobacteria, KaiA, KaiB, and KaiC, known as a minimum circadian clock, the slow KaiB-KaiC complex formation is essential in determining the clock period. This complex formation, occurring when the C1 domain of KaiC hexamer binds ADP molecules produced by the ATPase activity of C1, is considered to be promoted by accumulating ADP molecules in C1 through inhibiting the ADP/ATP exchange (ADP release) rather than activating the ATP hydrolysis (ADP production). Significantly, this ADP/ATP exchange inhibition accelerates the complex formation together with its promotion, implying a potential role in the period robustness under environmental perturbations. However, the molecular mechanism of this simultaneous promotion and acceleration remains elusive because inhibition of a backward process generally slows down the whole process. In this article, to investigate the mechanism, we build several reaction models of the complex formation with the pre-binding process concerning the ATPase activity. In these models, six KaiB monomers cooperatively and rapidly bind to C1 when C1 binds ADP molecules more than a given threshold while stabilizing the binding-competent conformation of C1. Through comparison among the models proposed here, we then extract three requirements for the simultaneous promotion and acceleration: the stabilization of the binding-competent C1 by KaiB binding, slow ADP/ATP exchange in the binding-competent C1, and relatively fast ADP/ATP exchange occurring in the binding-incompetent C1 in the presence of KaiB. The last two requirements oblige KaiC to form a multimer. Moreover, as a natural consequence, the present models can also explain why the binding of KaiB to C1 reduces the ATPase activity of C1.Author summary: Circadian clocks tick a rhythm with a nearly 24-hour period in various organisms. The cyanobacterial circadian clock, composed of only three proteins, KaiA, KaiB, and KaiC, has attracted much attention because of its simplicity. The slow KaiB-KaiC complex formation is essential in determining the clock period in this system. Significantly, this complex formation is accelerated together with its promotion, implying a potential role in the period-keeping mechanism. However, this simultaneous promotion and acceleration is theoretically exceptional because this complex formation is promoted by inhibiting a backward process, which generally slows down the whole process. In this article, we investigate the molecular mechanism of this phenomenon by building mathematical models to find that the binding of KaiB to C1 must lower the ADP/ATP exchange of the C1 domain of KaiC via stabilizing the binding-competent conformation of C1. The present results would be of benefit for future investigations on functional roles of the simultaneous promotion and acceleration in the KaiABC oscillator.