KaiC Hexamers Research Articles

Study of non-equilibrium statistical physics of protein machine by cryogenic electron microscopy

A comprehensive description of the protein should include its structure, thermodynamics, and kinetic properties. The recent rise of cryogenic electron microscopy (cryo-EM) provides new opportunities for the thermodynamic and kinetic research of proteins. There have been some researches in which cryo-EM is used not only to resolve the high-resolution structure of proteins but also to analyze the conformational distribution of proteins to infer their thermodynamic properties based on data processing methods. However, whether cryo-EM can be used to directly quantify the kinetics of proteins is still unclear. In this work, an ideal protein system, cyanobacterial circadian clock protein, is selected to explore the potential of cryo-EM used to analyze the non-equilibrium process of proteins. Previous research has illustrated that cryoelectron microscope can be used to infer the thermodynamic information about the KaiC protein such as the inter-subunit interaction within the hexamers. Herein, we extend the equilibrium Ising model of KaiC hexamers to a non-equilibrium statistical physics model, revealing the properties of the non-equilibrium process of KaiC hexamers. According to the non-equilibrium model and previous biochemical research, we find that the intrinsic properties of KaiC protein allow its non-equilibrium conformational distribution to be measured by cryo-EM.

Mechanism of autonomous synchronization of the circadian KaiABC rhythm

The cyanobacterial circadian clock can be reconstituted by mixing three proteins, KaiA, KaiB, and KaiC, in vitro. In this protein mixture, oscillations of the phosphorylation level of KaiC molecules are synchronized to show the coherent oscillations of the ensemble of many molecules. However, the molecular mechanism of this synchronization has not yet been fully elucidated. In this paper, we explain a theoretical model that considers the multifold feedback relations among the structure and reactions of KaiC. The simulated KaiC hexamers show stochastic switch-like transitions at the level of single molecules, which are synchronized in the ensemble through the sequestration of KaiA into the KaiC–KaiB–KaiA complexes. The proposed mechanism quantitatively reproduces the synchronization that was observed by mixing two solutions oscillating in different phases. The model results suggest that biochemical assays with varying concentrations of KaiA or KaiB can be used to test this hypothesis.

The energy cost and optimal design for synchronization of coupled molecular oscillators.

A model of coupled molecular biochemical oscillators is proposed to study nonequilibrium thermodynamics of synchronization. We find that synchronization of nonequilibrium oscillators costs addition energy to drive the exchange reaction (chemical interaction) between individual oscillators. By solving the steady state of the many-body system analytically, we show that the system goes through a nonequilibrium phase transition driven by energy dissipation, and the critical energy dissipation depends on both the frequency and strength of the exchange reaction. Moreover, our study reveals the optimal design for achieving maximum synchronization with a fixed energy budget. We apply our general theory to the Kai system in Cyanobacteria circadian clock and predict a relationship between the KaiC ATPase activity and synchronization of the KaiC hexamers. The theoretical framework can be extended to study thermodynamics of collective behaviors in other extended nonequilibrium active systems.

Single-molecular and ensemble-level oscillations of cyanobacterial circadian clock.

When three cyanobacterial proteins, KaiA, KaiB, and KaiC, are incubated with ATP in vitro, the phosphorylation level of KaiC hexamers shows stable oscillation with approximately 24 h period. In order to understand this KaiABC clockwork, we need to analyze both the macroscopic synchronization of a large number of KaiC hexamers and the microscopic reactions and structural changes in individual KaiC molecules. In the present paper, we explain two coarse-grained theoretical models, the many-molecule (MM) model and the single-molecule (SM) model, to bridge the gap between macroscopic and microscopic understandings. In the simulation results with these models, ATP hydrolysis in the CI domain of KaiC hexamers drives oscillation of individual KaiC hexamers and the ATP hydrolysis is necessary for synchronizing oscillations of a large number of KaiC hexamers. Sensitive temperature dependence of the lifetime of the ADP bound state in the CI domain makes the oscillation period temperature insensitive. ATPase activity is correlated to the frequency of phosphorylation oscillation in the single molecule of KaiC hexamer, which should be the origin of the observed ensemble-level correlation between the ATPase activity and the frequency of phosphorylation oscillation. Thus, the simulation results with the MM and SM models suggest that ATP hydrolysis stochastically occurring in each CI domain of individual KaiC hexamers is a key process for oscillatory behaviors of the ensemble of many KaiC hexamers.

Intersubunit communications within KaiC hexamers contribute the robust rhythmicity of the cyanobacterial circadian clock.

Circadian rhythms, endogenous oscillations with periods of ~24 h, are found in many organisms, and they enhance fitness in alternating day/night environments. In cyanobacteria, three clock proteins, KaiA, KaiB, and KaiC, control the timekeeping mechanism. KaiC, the central component of the system, is a hexameric ATPase that also has autokinase and autophosphatase activities. It has been assumed that KaiC’s hexameric structure was critical for regulation of the circadian clock; however, the underlying molecular mechanism of such regulation has remained unclear. Recently, we elucidated the regulation of KaiC’s activities by its phosphorylation state, in the context of its hexameric structure. We found that local interactions at subunit interfaces regulate KaiC’s activities by coupling the nucleotide-binding states. We also discovered the mechanism of regulation by intersubunit communication in KaiC hexamers. Our observations suggest that intersubunit communication precisely synchronizes KaiC subunits to avoid dephasing, and contributes to the robustness of circadian rhythms in cyanobacteria [Kitayama, Y. et al. Nat. Commun. 4:2897 doi: 10.1038/ncomms3897 (2013)].

KaiC intersubunit communication facilitates robustness of circadian rhythms in cyanobacteria

The cyanobacterial circadian clock is the only model clock to have been reconstituted in vitro. KaiC, the central clock component, is a homohexameric ATPase with autokinase and autophosphatase activities. Changes in phosphorylation state have been proposed to switch KaiC’s activity between autokinase and autophosphatase. Here we analyse the molecular mechanism underlying the regulation of KaiC’s activity, in the context of its hexameric structure. We reconstitute KaiC hexamers containing different variant protomers, and measure their autophosphatase and autokinase activities. We identify two types of regulatory mechanisms with distinct functions. First, local interactions between adjacent phosphorylation sites regulate KaiC’s activities, coupling the ATPase and nucleotide-binding states at subunit interfaces of the CII domain. Second, the phosphorylation states of the protomers affect the overall activity of KaiC hexamers via intersubunit communication. Our findings indicate that intra-hexameric interactions play an important role in sustaining robust circadian rhythmicity.

Revealing a Two-Loop Transcriptional Feedback Mechanism in the Cyanobacterial Circadian Clock

Molecular genetic studies in the circadian model organism Synechococcus have revealed that the KaiC protein, the central component of the circadian clock in cyanobacteria, is involved in activation and repression of its own gene transcription. During 24 hours, KaiC hexamers run through different phospho-states during daytime. So far, it has remained unclear which phospho-state of KaiC promotes kaiBC expression and which opposes transcriptional activation. We systematically analyzed various combinations of positive and negative transcriptional feedback regulation by introducing a combined TTFL/PTO model consisting of our previous post-translational oscillator that considers all four phospho-states of KaiC and a transcriptional/translational feedback loop. Only a particular two-loop feedback mechanism out of 32 we have extensively tested is able to reproduce existing experimental observations, including the effects of knockout or overexpression of kai genes. Here, threonine and double phosphorylated KaiC hexamers activate and unphosphorylated KaiC hexamers suppress kaiBC transcription. Our model simulations suggest that the peak expression ratio of the positive and the negative component of kaiBC expression is the main factor for how the different two-loop feedback models respond to removal or to overexpression of kai genes. We discuss parallels between our proposed TTFL/PTO model and two-loop feedback structures found in the mammalian clock.

Circadian Autodephosphorylation of Cyanobacterial Clock Protein KaiC Occurs via Formation of ATP as Intermediate

The cyanobacterial circadian oscillator can be reconstituted in vitro; mixing three clock proteins (KaiA, KaiB, and KaiC) with ATP results in an oscillation of KaiC phosphorylation with a periodicity of ~24 h. The hexameric ATPase KaiC hydrolyzes ATP bound at subunit interfaces. KaiC also exhibits autokinase and autophosphatase activities, the latter of which is particularly noteworthy because KaiC is phylogenetically distinct from typical protein phosphatases. To examine this activity, we performed autodephosphorylation assays using (32)P-labeled KaiC. The residual radioactive ATP bound to subunit interfaces was removed using a newly established method, which included the dissociation of KaiC hexamers into monomers and the reconstitution of KaiC hexamers with nonradioactive ATP. This approach ensured that only the signals derived from (32)P-labeled KaiC were examined. We detected the transient formation of [(32)P]ATP preceding the accumulation of (32)P(i). Together with kinetic analyses, our data demonstrate that KaiC undergoes dephosphorylation via a mechanism that differs from those of conventional protein phosphatases. A phosphate group at a phosphorylation site is first transferred to KaiC-bound ADP to form ATP as an intermediate, which can be regarded as a reversal of the autophosphorylation reaction. Subsequently, the ATP molecule is hydrolyzed to form P(i). We propose that the ATPase active site mediates not only ATP hydrolysis but also the bidirectional transfer of the phosphate between phosphorylation sites and the KaiC-bound nucleotide. On the basis of these findings, we can now dissect the dynamics of the KaiC phosphorylation cycle relative to ATPase activity.

Synchronization of Circadian Oscillation of Phosphorylation Level of KaiC In Vitro

In recent experimental reports, robust circadian oscillation of the phosphorylation level of KaiC has been reconstituted by incubating three cyanobacterial proteins, KaiA, KaiB, and KaiC, with ATP in vitro. This reconstitution indicates that protein-protein interactions and the associated ATP hydrolysis suffice to generate the oscillation, and suggests that the rhythm arising from this protein-based system is the circadian clock pacemaker in cyanobacteria. The mechanism of this reconstituted oscillation, however, remains elusive. In this study, we extend our previous model of oscillation by explicitly taking two phosphorylation sites of KaiC into account and we apply the extended model to the problem of synchrony of two oscillatory samples mixed at different phases. The agreement between the simulated and observed data suggests that the combined mechanism of the allosteric transition of KaiC hexamers and the monomer shuffling between them plays a key role in synchronization among KaiC hexamers and hence underlies the population-level oscillation of the ensemble of Kai proteins. The predicted synchronization patterns in mixtures of unequal amounts of two samples provide further opportunities to experimentally check the validity of the proposed mechanism. This mechanism of synchronization should be important in vivo for the persistent oscillation when Kai proteins are synthesized at random timing in cyanobacterial cells.

A sequestration feedback determines dynamics and temperature entrainment of the KaiABC circadian clock

The circadian rhythm of the cyanobacterium Synechococcus elongatus is controlled by three proteins, KaiA, KaiB, and KaiC. In a test tube, these proteins form complexes of various stoichiometry and the average phosphorylation level of KaiC exhibits robust circadian oscillations in the presence of ATP. Using mathematical modeling, we were able to reproduce quantitatively the experimentally observed phosphorylation dynamics of the KaiABC clockwork in vitro. We thereby identified a highly non-linear feedback loop through KaiA inactivation as the key synchronization mechanism of KaiC phosphorylation. By using the novel method of native mass spectrometry, we confirm the theoretically predicted complex formation dynamics and show that inactivation of KaiA is a consequence of sequestration by KaiC hexamers and KaiBC complexes. To test further the predictive power of the mathematical model, we reproduced the observed phase synchronization dynamics on entrainment by temperature cycles. Our model gives strong evidence that the underlying entrainment mechanism arises from a temperature-dependent change in the abundance of KaiAC and KaiBC complexes.

Mechanism of Robust Circadian Oscillation of KaiC Phosphorylation In Vitro

By incubating the mixture of three cyanobacterial proteins, KaiA, KaiB, and KaiC, with ATP in vitro, T. Kondo and his colleagues in recent work reconstituted the robust circadian rhythm of the phosphorylation level of KaiC. This finding indicates that protein-protein interactions and the associated hydrolysis of ATP suffice to generate the circadian rhythm. Several theoretical models have been proposed to explain the rhythm generated in this “protein-only” system, but the clear criterion to discern different possible mechanisms was not known. In this article, we discuss a model based on two basic assumptions: the assumption of the allosteric transition of a KaiC hexamer and the assumption of the monomer exchange between KaiC hexamers. The model shows a stable rhythmic oscillation of the phosphorylation level of KaiC, which is robust against changes in concentration of Kai proteins. We show that this robustness gives a clue to distinguish different possible mechanisms. We also discuss the robustness of oscillation against the change in the system size. Behaviors of the system with the cellular or subcellular size should shed light on the role of the protein-protein interactions in in vivo circadian oscillation.

Autonomous synchronization of the circadian KaiC phosphorylation rhythm

The cyanobacterial circadian oscillator can be reconstituted in vitro by mixing three purified clock proteins, KaiA, KaiB and KaiC, with ATP. The KaiC phosphorylation rhythm persists for at least 10 days without damping. By mixing oscillatory samples that have different phases and analyzing the dynamics of their phase relationships, we found that the robustness of the KaiC phosphorylation rhythm arises from the rapid synchronization of the phosphorylation state and reaction direction (phosphorylation or dephosphorylation) of KaiC proteins. We further demonstrate that synchronization is tightly linked with KaiC dephosphorylation and is mediated by monomer exchange between KaiC hexamers during the early dephosphorylation phase. This autonomous synchronization mechanism is probably the basis for the resilience of the cyanobacterial circadian system against quantitative fluctuations in clock components during cellular events such as cell growth and division.

Monomer-shuffling and allosteric transition in KaiC circadian oscillation.

Circadian rhythms in living organisms have long been attributed solely to a transcription-translation loop comprising a negative or positive feedback. The rhythms in cyanobacteria are known to be modulated by kaiC, kaiA and kaiB genes. It was recently shown, however, that their product proteins KaiC, KaiA and KaiB are sufficient to reconstitute the circadian rhythm in the phosphorylation level of KaiC in vitro. It has since been unclear why such an oscillatory behavior can occur in the absence of the apparent transcription-translation feedback. In the meantime, it has been reported that the monomer exchange between KaiC hexamers occurs in a phosphorylation-dependent manner, which suggests that the monomer shuffling is also involved in the circadian rhythm (H. Kageyama et al., Mol. Cell, 23, 161 (2006)). To further clarify the role of the monomer shuffling, we have performed a computational modeling of interactions among Kai proteins assuming the allosteric transition of KaiC hexamer as well as the monomer shuffling. The results show that the existence of both monomer shuffling and allosteric transition can synchronize the phosphorylation level of the KaiC hexamers, and stabilizes its oscillation.

An allosteric model of circadian KaiC phosphorylation

In a recent series of ground-breaking experiments, Nakajima et al. [Nakajima M, Imai K, Ito H, Nishiwaki T, Murayama Y, Iwasaki H, Oyama T, Kondo T (2005) Science 308:414-415] showed that the three cyanobacterial clock proteins KaiA, KaiB, and KaiC are sufficient in vitro to generate circadian phosphorylation of KaiC. Here, we present a mathematical model of the Kai system. At its heart is the assumption that KaiC can exist in two conformational states, one favoring phosphorylation and the other dephosphorylation. Each individual KaiC hexamer then has a propensity to be phosphorylated in a cyclic manner. To generate macroscopic oscillations, however, the phosphorylation cycles of the different hexamers must be synchronized. We propose a novel synchronization mechanism based on differential affinity: KaiA stimulates KaiC phosphorylation, but the limited supply of KaiA dimers binds preferentially to those KaiC hexamers that are falling behind in the oscillation. KaiB sequesters KaiA and stabilizes the dephosphorylating KaiC state. We show that our model can reproduce a wide range of published data, including the observed insensitivity of the oscillation period to variations in temperature, and that it makes nontrivial predictions about the effects of varying the concentrations of the Kai proteins.

Elucidating the Ticking of an In Vitro Circadian Clockwork

A biochemical oscillator can be reconstituted in vitro with three purified proteins, that displays the salient properties of circadian (daily) rhythms, including self-sustained 24-h periodicity that is temperature compensated. We analyze the biochemical basis of this oscillator by quantifying the time-dependent interactions of the three proteins (KaiA, KaiB, and KaiC) by electron microscopy and native gel electrophoresis to elucidate the timing of the formation of complexes among the Kai proteins. The data are used to derive a dynamic model for the in vitro oscillator that accurately reproduces the rhythms of KaiABC complexes and of KaiC phosphorylation, and is consistent with biophysical observations of individual Kai protein interactions. We use fluorescence resonance energy transfer (FRET) to confirm that monomer exchange among KaiC hexamers occurs. The model demonstrates that the function of this monomer exchange may be to maintain synchrony among the KaiC hexamers in the reaction, thereby sustaining a high-amplitude oscillation. Finally, we apply the first perturbation analyses of an in vitro oscillator by using temperature pulses to reset the phase of the KaiABC oscillator, thereby testing the resetting characteristics of this unique circadian oscillator. This study analyzes a circadian clockwork to an unprecedented level of molecular detail.

Functioning and robustness of a bacterial circadian clock

Cyanobacteria are the simplest known cellular systems that regulate their biological activities in daily cycles. For the cyanobacterium Synechococcus elongatus, it has been shown by in vitro and in vivo experiments that the basic circadian timing process is based on rhythmic phosphorylation of KaiC hexamers. Despite the excellent experimental work, a full systems level understanding of the in vitro clock is still lacking. In this work, we provide a mathematical approach to scan different hypothetical mechanisms for the primary circadian oscillator, starting from experimentally established molecular properties of the clock proteins. Although optimised for highest performance, only one of the in silico-generated reaction networks was able to reproduce the experimentally found high amplitude and robustness against perturbations. In this reaction network, a negative feedback synchronises the phosphorylation level of the individual hexamers and has indeed been realised in S. elongatus by KaiA sequestration as confirmed by experiments.

Hourglass model for a protein-based circadian oscillator.

Many organisms possess internal biochemical clocks, known as circadian oscillators, which allow them to regulate their biological activity with a 24-hour period. It was recently discovered that the circadian oscillator of photosynthetic cyanobacteria is able to function in a test tube with only three proteins, KaiA, KaiB, and KaiC, and ATP. Biochemical events are intrinsically stochastic, and this tends to desynchronize oscillating protein populations. We propose that stability of the Kai-protein oscillator relies on active synchronization by (i) monomer exchange between KaiC hexamers during the day, and (ii) formation of clusters of KaiC hexamers at night. Our results highlight the importance of collective assembly or disassembly of proteins in biochemical networks, and may help guide design of novel protein-based oscillators.