Mixtures of opposing phosphorylations within hexamers precisely time feedback in the cyanobacterial circadian clock

Circadian oscillations are generated by the purified cyanobacterial clock proteins, KaiA, KaiB, and KaiC, through rhythmic interactions that depend on multisite phosphorylation of KaiC. However, the mechanisms that allow these phosphorylation reactions to robustly control the timing of oscillations over a range of protein stoichiometries are not clear. We show that when KaiC hexamers consist of a mixture of differentially phosphorylated subunits, the two phosphorylation sites have opposing effects on the ability of each hexamer to bind to the negative regulator KaiB. We likewise show that the ability of the positive regulator KaiA to act on KaiC depends on the phosphorylation state of the hexamer and that KaiA and KaiB recognize alternative allosteric states of the KaiC ring. Using mathematical models with kinetic parameters taken from experimental data, we find that antagonism of the two KaiC phosphorylation sites generates an ultrasensitive switch in negative feedback strength necessary for stable circadian oscillations over a range of component concentrations. Similar strategies based on opposing modifications may be used to support robustness in other timing systems and in cellular signaling more generally.Circadian clocks are biological timing systems that allow organisms to anticipate and prepare for daily changes in the environment. A hallmark of a circadian oscillator is its ability to drive self-sustained rhythms in gene expression and behavior with a period close to 24 h, even in the absence of environmental cues (1). A general challenge for the biochemical machinery that generates rhythms is to precisely define the duration of the day in the face of perturbations, including fluctuations in the cellular abundance of the molecular components. The importance of maintaining precise circadian timing is underscored by experiments showing that mismatch between the clock period and the rhythms in the external environment results in health problems and fitness defects (2, 3).Although circadian clocks are found across all kingdoms of life, the Kai oscillator from cyanobacteria presents a uniquely powerful model system to study the design principles inherent in the molecular interactions that generate rhythms. A mixture of the purified proteins KaiA, KaiB, and KaiC results in stable oscillations in the phosphorylation state of KaiC in vitro that persist for many days and share many of the properties of circadian clocks in vivo (4–6). In particular, the oscillator can successfully generate near–24-h rhythms over a range of concentrations of the clock proteins both in vivo and in vitro (7–9), so fine-tuning of gene expression is not needed to support a functional clock. Much has been learned about the behavior of the isolated Kai proteins, including the determination of high-resolution crystal structures of all three components (10–12). A critical challenge that remains is to understand how the properties of the Kai proteins are integrated together in the full system to generate precisely timed rhythms.KaiC appears to be the central hub of timing information in the oscillator. Each KaiC molecule consists of two AAA+ family ATPase domains that consume the free energy of ATP hydrolysis to drive oscillations. Like many other members of this family, KaiC forms hexamers, and the enzymatic active sites are formed at the subunit interfaces where nucleotides are bound. The C-terminal, or CII, domain of KaiC has additional phosphotransferase activities that are unusual for the AAA+ family: it can phosphorylate and dephosphorylate two residues near the subunit interface, Ser431 and Thr432 (13). KaiC autokinase and autophosphatase activities occur at the same active site (14, 15). In isolation, KaiC has high phosphatase activity, but the enzyme is pushed toward kinase activity by the activator protein KaiA, which interacts directly with the KaiC C-terminal tail (16, 17). Roughly speaking, kinase activity predominates during the day, and phosphatase activity predominates during the night (18). Thus, understanding the feedback mechanisms that generate a precise time delay between these modes is crucial to understanding timing in the oscillator (19).Inactivation of KaiA and a transition from kinase to phosphatase mode occur when KaiB•KaiC complexes form, closing a negative feedback loop by sequestering KaiA in a ternary complex and leaving it unable to act on other KaiC molecules (20, 21). By temporarily removing KaiA molecules from their activating role, this molecular titration mechanism may act to synchronize the activity of all KaiC hexamers in the reaction (20, 22, 23). Phosphorylation and dephosphorylation proceed in a strongly ordered fashion so that in response to a change in KaiA activity, Thr432 is (de)phosphorylated first, followed later by Ser431 (18, 20, 21). It is known that phosphorylated Ser431 is important for allowing the formation of KaiB•KaiC complexes. However, recent work has made it clear that the binding of KaiB involves both KaiC domains—in particular, the slow ATPase activity of the N-terminal CI domain, which is not phosphorylated, is required for KaiB interaction (24, 25).Because of the importance of precisely timing negative feedback via KaiB•KaiC complex formation for generating appropriate rhythms (22), we wanted to understand the role of phosphorylation of the KaiC hexamer in controlling this process. The involvement of both KaiC domains suggests that information about phosphorylation in CII is communicated allosterically through changes in hexamer structure to the CI domain, potentially through ring–ring stacking interactions (24, 26). We therefore hypothesized that the KaiC phosphorylation sites on each subunit might act as allosteric regulators in the context of a hexameric ring so that phosphorylation of one subunit would alter the ability of all other subunits in the ring to engage with KaiA and KaiB, providing a cooperative mechanism to control the timing of these interactions.We conducted a series of biochemical experiments and perturbations to study the effect of altering the status of each phosphorylation site on the KaiC hexamer. To interpret these results, we then developed a mathematical model analogous to classical models of allosteric transitions in multimeric proteins. We constrain the kinetic parameters in this model using experimental measurements of rate constants, allowing us to compare the predictions of the model directly with data. We conclude that maintenance of circadian timing over a range of protein concentrations requires an effectively ultrasensitive switch in each KaiC hexamer from an exclusively KaiA-binding state to a state that can bind to KaiB as phosphorylation proceeds. This effect requires that KaiC hexamers consist of mixtures of differentially phosphorylated subunits, as would be produced by stochastic autophosphorylation of a hexamer. Ultrasensitivity results from opposing effects of phosphorylation on Thr432 and Ser431 in controlling a concerted transition within a given KaiC hexamer. Including this mechanism in the model is necessary to explain the experimentally observed tolerance of the system to altered protein concentrations.