Abstract
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.
Highlights
Multimeric structure enables the acceleration of KaiB-KaiC complex formation
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
We focus on the binding rate of KaiB to C1, which determines the time required for the complex formation
Summary
The cyanobacterial circadian clock has attracted much attention because it oscillates without transcription-translation feedback [1] and can be reconstituted in vitro by mixing three proteins, KaiA, KaiB, and KaiC, in the presence of ATP [2]. In the presence of KaiA and KaiB, two amino acid residues near the ATP binding site in C2, Ser431 and Thr432, are periodically phosphorylated and dephosphorylated [5, 6]. During this oscillation, KaiA facilitates the phosphorylation by acting on C2 [7–10]. After C2 is phosphorylated, KaiB, on the other hand, inhibits the KaiA activity on C2 [11, 12] by forming the stable C1-KaiB-KaiA complex [13–15].
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