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

Abstract

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. * koda@ims.ac.jp † shinji@ims.ac.jp Circadian clocks are biological timing systems embedded in most living organisms and enable the organisms to anticipate daily changes in the environment and to adjust their biological activities. The simplest circadian clock is that of cyanobacteria, where the core oscillator is composed of only three proteins, KaiA, KaiB, and KaiC[1]. Interestingly, this circadian rhythm can be reconstituted in a test tube just by mixing the three proteins with ATP, which results in a nearly 24-hour periodic oscillation of phosphorylation of KaiC[2]. In addition to this self-sustaining oscillation, the KaiABC oscillator possesses several fundamental functions as a biological clock. For example, the period of the oscillator is robust against environmental perturbations such as temperature[2] and concentrations of the proteins[3]. The oscillator is further entrained by various periodic environmental changes, including temperature[4] and ATP/ADP ratio in buffer[5]. This simple yet functional system has thus attracted considerable interests in elucidating the molecular origins of circadian rhythm. KaiC is the central component in the KaiABC oscillator, and in the presence of ATP, forms a homohexamer with two ring-shaped domains, C1 and C2[6, 7]. Both C1 and C2 have ATPase activities. C2 also has autokinase and autophosphatase activities, where two residues near the ATP binding site in C2, Ser431 and Thr432, are phosphorylated and dephosphorylated. With the help of KaiA and KaiB, (de)phosphorylation occurs in the following order: ST → SpT → pSpT → pST → ST[8, 9], where S/pS and T/pT are the unphosphorylated/phosphorylated states of Ser431 and Thr432, respectively. KaiA promotes phosphorylation of KaiC[10, 11] by acting on the C-terminal tail of C2[12-15]. It facilitates the exchange of bound ADP with exogenous ATP[16], suggesting that the enhanced ADP/ATP exchange supplies abundant phosphate for phosphorylation reactions in the form of ATP, and shifts the equilibrium of phosphorylation reactions toward phosphorylated states.KaiB, on the other hand...