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

A topological mechanism for robust and efficient global oscillations in biological networks

Long and stable timescales are often observed in complex biochemical networks, such as in emergent oscillations. How these robust dynamics persist remains unclear, given the many stochastic reactions and shorter time scales demonstrated by underlying components. We propose a topological model that produces long oscillations around the network boundary, reducing the system dynamics to a lower-dimensional current in a robust manner. Using this to model KaiC, which regulates the circadian rhythm in cyanobacteria, we compare the coherence of oscillations to that in other KaiC models. Our topological model localizes currents on the system edge, with an efficient regime of simultaneously increased precision and decreased cost. Further, we introduce a new predictor of coherence from the analysis of spectral gaps, and show that our model saturates a global thermodynamic bound. Our work presents a new mechanism and parsimonious description for robust emergent oscillations in complex biological networks.

Investigating the Roles for Essential Genes in the Regulation of the Circadian Clock in Synechococcus elongatus Using CRISPR Interference

Circadian rhythms are found widely throughout nature where cyanobacteria are the simplest organisms, in which the molecular details of the clock have been elucidated. Circadian rhythmicity in cyanobacteria is carried out via the KaiA, KaiB, and KaiC core oscillator proteins that keep ~24 h time. A series of input and output proteins-CikA, SasA, and RpaA-regulate the clock by sensing environmental changes and timing rhythmic activities, including global rhythms of gene expression. Our previous work identified a novel set of KaiC-interacting proteins, some of which are encoded by genes that are essential for viability. To understand the relationship of these essential genes to the clock, we applied CRISPR interference (CRISPRi) which utilizes a deactivated Cas9 protein and single-guide RNA (sgRNA) to reduce the expression of target genes but not fully abolish their expression to allow for survival. Eight candidate genes were targeted, and strains were analyzed by quantitative real-time PCR (qRT-PCR) for reduction of gene expression, and rhythms of gene expression were monitored to analyze circadian phenotypes. Strains with reduced expression of SynPCC7942_0001, dnaN, which encodes for the β-clamp of the replicative DNA polymerase, or SynPCC7942_1081, which likely encodes for a KtrA homolog involved in K+ transport, displayed longer circadian rhythms of gene expression than the wild type. As neither of these proteins have been previously implicated in the circadian clock, these data suggest that diverse cellular processes, DNA replication and K+ transport, can influence the circadian clock and represent new avenues to understand clock function.

Timed material self-assembly controlled by circadian clock proteins

Active biological molecules present a powerful, yet largely untapped, opportunity to impart autonomous regulation to materials. Because these systems can function robustly to regulate when and where chemical reactions occur, they have the ability to bring complex, life-like behavior to synthetic materials. Here, we achieve this design feat by using functionalized circadian clock proteins, KaiB and KaiC, to engineer time-dependent crosslinking of colloids. The resulting material self-assembles with programmable kinetics, producing macroscopic changes in material properties, via molecular assembly of KaiB-KaiC complexes. We show that colloid crosslinking depends strictly on the phosphorylation state of KaiC, with kinetics that are synced with KaiB-KaiC complexing. Our microscopic image analyses and computational models indicate that the stability of colloidal super-structures depends sensitively on the number of Kai complexes per colloid connection. Consistent with our model predictions, a high concentration stabilizes the material against dissolution after a robust self-assembly phase, while a low concentration allows circadian oscillation of material structure. This work introduces the concept of harnessing biological timers to control synthetic materials; and, more generally, opens the door to using protein-based reaction networks to endow synthetic systems with life-like functional properties.

Determining subunit-subunit interaction from statistics of cryo-EM images: observation of nearest-neighbor coupling in a circadian clock protein complex

Biological processes are typically actuated by dynamic multi-subunit molecular complexes. However, interactions between subunits, which govern the functions of these complexes, are hard to measure directly. Here, we develop a general approach combining cryo-EM imaging technology and statistical modeling and apply it to study the hexameric clock protein KaiC in Cyanobacteria. By clustering millions of KaiC monomer images, we identify two major conformational states of KaiC monomers. We then classify the conformational states of (>160,000) KaiC hexamers by the thirteen distinct spatial arrangements of these two subunit states in the hexamer ring. We find that distributions of the thirteen hexamer conformational patterns for two KaiC phosphorylation mutants can be fitted quantitatively by an Ising model, which reveals a significant cooperativity between neighboring subunits with phosphorylation shifting the probability of subunit conformation. Our results show that a KaiC hexamer can respond in a switch-like manner to changes in its phosphorylation level.

KidA, a multi-PAS domain protein, tunes the period of the cyanobacterial circadian oscillator

The cyanobacterial clock presents a unique opportunity to understand the biochemical basis of circadian rhythms. The core oscillator, composed of the KaiA, KaiB, and KaiC proteins, has been extensively studied, but a complete picture of its connection to the physiology of the cell is lacking. To identify previously unknown components of the clock, we used KaiB locked in its active fold as bait in an immunoprecipitation/mass spectrometry approach. We found that the most abundant interactor, other than KaiC, was a putative diguanylate cyclase protein predicted to contain multiple Per-Arnt-Sim (PAS) domains, which we propose to name KidA. Here we show that KidA directly binds to the fold-switched active form of KaiB through its N-terminal PAS domains. We found that KidA shortens the period of the circadian clock both in vivo and in vitro and alters the ability of the clock to entrain to light-dark cycles. The dose-dependent effect of KidA on the clock period could be quantitatively recapitulated by a mathematical model in which KidA stabilizes the fold-switched form of KaiB, favoring rebinding to KaiC. Put together, our results show that the period and amplitude of the clock can be modulated by regulating the access of KaiB to the fold-switched form.

Regulation mechanisms of the dual ATPase in KaiC

KaiC, a core clock protein in the cyanobacterial circadian clock system, hydrolyzes adenosine triphosphate (ATP) at two distinct sites in a slow but ordered manner to measure the circadian timescale. We used biochemical and structural biology techniques to characterize the properties and interplay of dual-adenosine triphosphatase (ATPase) active sites. Our results show that the N-terminal and C-terminal ATPases communicate with each other through an interface between the N-terminal and C-terminal domains in KaiC. The dual-ATPase sites are regulated rhythmically in a concerted or opposing manner dependent on the phase of the circadian clock system, controlling the affinities of KaiC for other clock proteins, KaiA and KaiB.

KaiC is a dual adenosine triphosphatase (ATPase), with one active site in its N-terminal domain and another in its C-terminal domain, that drives the circadian clock system of cyanobacteria through sophisticated coordination of the two sites. To elucidate the coordination mechanism, we studied the contribution of the dual-ATPase activities in the ring-shaped KaiC hexamer and these structural bases for activation and inactivation. At the N-terminal active site, a lytic water molecule is sequestered between the N-terminal domains, and its reactivity to adenosine triphosphate (ATP) is controlled by the quaternary structure of the N-terminal ring. The C-terminal ATPase activity is regulated mostly by water-incorporating voids between the C-terminal domains, and the size of these voids is sensitive to phosphoryl modification of S431. The up-regulatory effect on the N-terminal ATPase activity inversely correlates with the affinity of KaiC for KaiB, a clock protein constitutes the circadian oscillator together with KaiC and KaiA, and the complete dissociation of KaiB from KaiC requires KaiA-assisted activation of the dual ATPase. Delicate interactions between the N-terminal and C-terminal rings make it possible for the components of the dual ATPase to work together, thereby driving the assembly and disassembly cycle of KaiA and KaiB.

Elucidation of master allostery essential for circadian clock oscillation in cyanobacteria

Spatiotemporal allostery is the source of complex but ordered biological phenomena. To identify the structural basis for allostery that drives the cyanobacterial circadian clock, we crystallized the clock protein KaiC in four distinct states, which cover a whole cycle of phosphor-transfer events at Ser⁴³¹ and Thr⁴³². The minimal set of allosteric events required for oscillatory nature is a bidirectional coupling between the coil-to-helix transition of the Ser⁴³¹-dependent phospho-switch in the C-terminal domain of KaiC and adenosine 5'-diphosphate release from its N-terminal domain during adenosine triphosphatase cycle. An engineered KaiC protein oscillator consisting of a minimal set of the identified master allosteric events exhibited a monophosphorylation cycle of Ser⁴³¹ with a temperature-compensated circadian period, providing design principles for simple posttranslational biochemical circadian oscillators.

A Night-Time Edge Site Intermediate in the Cyanobacterial Circadian Clock Identified by EPR Spectroscopy

As the only circadian oscillator that can be reconstituted in vitro with its constituent proteins KaiA, KaiB, and KaiC using ATP as an energy source, the cyanobacterial circadian oscillator serves as a model system for detailed mechanistic studies of day-night transitions of circadian clocks in general. The day-to-night transition occurs when KaiB forms a night-time complex with KaiC to sequester KaiA, the latter of which interacts with KaiC during the day to promote KaiC autophosphorylation. However, how KaiB forms the complex with KaiC remains poorly understood, despite the available structures of KaiB bound to hexameric KaiC. It has been postulated that KaiB-KaiC binding is regulated by inter-KaiB cooperativity. Here, using spin labeling continuous-wave electron paramagnetic resonance spectroscopy, we identified and quantified two subpopulations of KaiC-bound KaiB, corresponding to the "bulk" and "edge" KaiBC sites in stoichiometric and substoichiometric KaiBiC6 complexes (i = 1-5). We provide kinetic evidence to support the intermediacy of the "edge" KaiBC sites as bridges and nucleation sites between free KaiB and the "bulk" KaiBC sites. Furthermore, we show that the relative abundance of "edge" and "bulk" sites is dependent on both KaiC phosphostate and KaiA, supporting the notion of phosphorylation-state controlled inter-KaiB cooperativity. Finally, we demonstrate that the interconversion between the two subpopulations of KaiC-bound KaiB is intimately linked to the KaiC phosphorylation cycle. These findings enrich our mechanistic understanding of the cyanobacterial clock and demonstrate the utility of EPR in elucidating circadian clock mechanisms.

Evolution of the repression mechanisms in circadian clocks

BACKGROUND

Circadian (daily) timekeeping is essential to the survival of many organisms. An integral part of all circadian timekeeping systems is negative feedback between an activator and repressor. However, the role of this feedback varies widely between lower and higher organisms.

RESULTS

Here, we study repression mechanisms in the cyanobacterial and eukaryotic clocks through mathematical modeling and systems analysis. We find a common mathematical model that describes the mechanism by which organisms generate rhythms; however, transcription's role in this has diverged. In cyanobacteria, protein sequestration and phosphorylation generate and regulate rhythms while transcription regulation keeps proteins in proper stoichiometric balance. Based on recent experimental work, we propose a repressor phospholock mechanism that models the negative feedback through transcription in clocks of higher organisms. Interestingly, this model, when coupled with activator phosphorylation, allows for oscillations over a wide range of protein stoichiometries, thereby reconciling the negative feedback mechanism in Neurospora with that in mammals and cyanobacteria.

CONCLUSIONS

Taken together, these results paint a picture of how circadian timekeeping may have evolved.

Reconstitution of an intact clock reveals mechanisms of circadian timekeeping

[Figure: see text].

Monitoring Protein-Protein Interactions in the Cyanobacterial Circadian Clock in Real Time via Electron Paramagnetic Resonance Spectroscopy

The cyanobacterial circadian clock in Synechococcus elongatus consists of three proteins, KaiA, KaiB, and KaiC. KaiA and KaiB rhythmically interact with KaiC to generate stable oscillations of KaiC phosphorylation with a period of 24 h. The observation of stable circadian oscillations when the three clock proteins are reconstituted and combined in vitro makes it an ideal system for understanding its underlying molecular mechanisms and circadian clocks in general. These oscillations were historically monitored in vitro by gel electrophoresis of reaction mixtures based on the differing electrophoretic mobilities between various phosphostates of KaiC. As the KaiC phospho-distribution represents only one facet of the oscillations, orthogonal tools are necessary to explore other interactions to generate a full description of the system. However, previous biochemical assays are discontinuous or qualitative. To circumvent these limitations, we developed a spin-labeled KaiB mutant that can differentiate KaiC-bound KaiB from free KaiB using continuous-wave electron paramagnetic resonance spectroscopy that is minimally sensitive to KaiA. Similar to wild-type (WT-KaiB), this labeled mutant, in combination with KaiA, sustains robust circadian rhythms of KaiC phosphorylation. This labeled mutant is hence a functional surrogate of WT-KaiB and thus participates in and reports on autonomous macroscopic circadian rhythms generated by mixtures that include KaiA, KaiC, and ATP. Quantitative kinetics could be extracted with improved precision and time resolution. We describe design principles, data analysis, and limitations of this quantitative binding assay and discuss future research necessary to overcome these challenges.

Mutation of alanine-422 in KaiC leads to a low amplitude of rhythm in the reconstituted cyanobacterial circadian clock

The cyanobacterial circadian oscillator can be reconstituted by mixing the purified clock proteins KaiA, KaiB, and KaiC with ATP in vitro, leading to a 24-h oscillation of KaiC phosphorylation. The cyanobacterial mutant pr1 carrying valine instead of alanine at position 422 of KaiC (KaiC-A422V) lost the ability to shift the phase of the circadian rhythm. In this study, we analyzed KaiC-A422V to investigate the effect of this single-residue substitution on the in vitro reconstitution of KaiC oscillation. KaiC-A422V exhibited low amplitude oscillations of phosphorylation with a smaller amount of Kai complex than wild-type KaiC (KaiC-WT). Although KaiA can stimulate KaiC phosphorylation, the phosphorylation level of KaiC-A422V is much lower than that of KaiC-WT even at higher KaiA concentrations. It has been suggested that monomer shuffling of KaiC is involved in entraining the in vitro rhythm. To examine whether KaiC-A422V has the capacity for monomer shuffling, we used the difference in the amplitude of the phosphorylation rhythms between KaiC-WT and KaiC-A422V as the indicator of monomer shuffling. When KaiC-A422V and KaiC-WT were mixed, the amplitude of the phosphorylation rhythm changed according to the mixing ratio. This suggests that KaiC-A422V has a reduced ability to shuffle monomers in hexameric KaiC. In addition, the A422V mutation resulted in a change of the stability of the KaiC protein.

Bayesian modeling reveals metabolite-dependent ultrasensitivity in the cyanobacterial circadian clock

Mathematical models can enable a predictive understanding of mechanism in cell biology by quantitatively describing complex networks of interactions, but such models are often poorly constrained by available data. Owing to its relative biochemical simplicity, the core circadian oscillator in Synechococcus elongatus has become a prototypical system for studying how collective dynamics emerge from molecular interactions. The oscillator consists of only three proteins, KaiA, KaiB, and KaiC, and near-24-h cycles of KaiC phosphorylation can be reconstituted in vitro. Here, we formulate a molecularly detailed but mechanistically naive model of the KaiA-KaiC subsystem and fit it directly to experimental data within a Bayesian parameter estimation framework. Analysis of the fits consistently reveals an ultrasensitive response for KaiC phosphorylation as a function of KaiA concentration, which we confirm experimentally. This ultrasensitivity primarily results from the differential affinity of KaiA for competing nucleotide-bound states of KaiC. We argue that the ultrasensitive stimulus-response relation likely plays an important role in metabolic compensation by suppressing premature phosphorylation at nighttime.

Damped circadian oscillation in the absence of KaiA in Synechococcus

Proteins KaiA, KaiB and KaiC constitute a biochemical circadian oscillator in the cyanobacterium Synechococcus elongatus. It has been reported kaiA inactivation completely abolishes circadian oscillations. However, we show here that kaiBC promoter activity exhibits a damped, low-amplitude oscillation with a period of approximately 24 h in kaiA-inactivated strains. The damped rhythm resonates with external cycles with a period of 24–26 h, indicating that its natural frequency is similar to that of the circadian clock. Double-mutation experiments reveal that kaiC, kaiB, and sasA (encoding a KaiC-binding histidine kinase) are all required for the damped oscillation. Further analysis suggests that the kaiA-less damped transcriptional rhythm requires KaiB-KaiC complex formation and the transcription-translation feedback loop, but not the KaiC phosphorylation cycle. Our results provide insights into mechanisms that could potentially underlie the diurnal/circadian behaviors observed in other bacterial species that possess kaiB and kaiC homologues but lack a kaiA homologue.

Proteins KaiA, KaiB and KaiC constitute a biochemical circadian oscillator in Synechococcus cyanobacteria. Here, Kawamoto et al. show that kaiBC promoter activity exhibits a damped, low-amplitude circadian oscillation in the absence of KaiA, which could explain the circadian rhythms observed in other bacteria that lack a kaiA homologue.

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.

ATP hydrolysis by KaiC promotes its KaiA binding in the cyanobacterial circadian clock system

ATP hydrolysis in the KaiC hexamer triggers the exposure of its C-terminal segments into the solvent so as to capture KaiA, providing mechanistic insights into the circadian periodicity regulation.

The cyanobacterial clock is controlled via the interplay among KaiA, KaiB, and KaiC, which generate a periodic oscillation of KaiC phosphorylation in the presence of ATP. KaiC forms a homohexamer harboring 12 ATP-binding sites and exerts ATPase activities associated with its autophosphorylation and dephosphorylation. The KaiC nucleotide state is a determining factor of the KaiB–KaiC interaction; however, its relationship with the KaiA–KaiC interaction has not yet been elucidated. With the attempt to address this, our native mass spectrometric analyses indicated that ATP hydrolysis in the KaiC hexamer promotes its interaction with KaiA. Furthermore, our nuclear magnetic resonance spectral data revealed that ATP hydrolysis is coupled with conformational changes in the flexible C-terminal segments of KaiC, which carry KaiA-binding sites. From these data, we conclude that ATP hydrolysis in KaiC is coupled with the exposure of its C-terminal KaiA-binding sites, resulting in its high affinity for KaiA. These findings provide mechanistic insights into the ATP-mediated circadian periodicity.

The Kai-Protein Clock-Keeping Track of Cyanobacteria's Daily Life

Life has adapted to Earth's day-night cycle with the evolution of endogenous biological clocks. Whereas these circadian rhythms typically involve extensive transcription-translation feedback in higher organisms, cyanobacteria have a circadian clock, which functions primarily as a protein-based post-translational oscillator. Known as the Kai system, it consists of three proteins KaiA, KaiB, and KaiC. In this chapter, we provide a detailed structural overview of the Kai components and how they interact to produce circadian rhythms of global gene expression in cyanobacterial cells. We discuss how the circadian oscillation is coupled to gene expression, intertwined with transcription-translation feedback mechanisms, and entrained by input from the environment. We discuss the use of mathematical models and summarize insights into the cyanobacterial circadian clock from theoretical studies. The molecular details of the Kai system are well documented for the model cyanobacterium Synechococcus elongatus, but many less understood varieties of the Kai system exist across the highly diverse phylum of Cyanobacteria. Several species contain multiple kai-gene copies, while others like marine Prochlorococcus strains have a reduced kaiBC-only system, lacking kaiA. We highlight recent findings on the genomic distribution of kai genes in Bacteria and Archaea and finally discuss hypotheses on the evolution of the Kai system.

Molecular dynamics simulations of nucleotide release from the circadian clock protein KaiC reveal atomic-resolution functional insights

The cyanobacterial clock proteins KaiA, KaiB, and KaiC form a powerful system to study the biophysical basis of circadian rhythms, because an in vitro mixture of the three proteins is sufficient to generate a robust ∼24-h rhythm in the phosphorylation of KaiC. The nucleotide-bound states of KaiC critically affect both KaiB binding to the N-terminal domain (CI) and the phosphotransfer reactions that (de)phosphorylate the KaiC C-terminal domain (CII). However, the nucleotide exchange pathways associated with transitions among these states are poorly understood. In this study, we integrate recent advances in molecular dynamics methods to elucidate the structure and energetics of the pathway for Mg·ADP release from the CII domain. We find that nucleotide release is coupled to large-scale conformational changes in the KaiC hexamer. Solvating the nucleotide requires widening the subunit interface leading to the active site, which is linked to extension of the A-loop, a structure implicated in KaiA binding. These results provide a molecular hypothesis for how KaiA acts as a nucleotide exchange factor. In turn, structural parallels between the CI and CII domains suggest a mechanism for allosteric coupling between the domains. We relate our results to structures observed for other hexameric ATPases, which perform diverse functions.

Robustness of Clocks to Input Noise

To estimate the time, many organisms, ranging from cyanobacteria to animals, employ a circadian clock which is based on a limit-cycle oscillator that can tick autonomously with a nearly 24 h period. Yet, a limit-cycle oscillator is not essential for knowing the time, as exemplified by bacteria that possess an "hourglass": a system that when forced by an oscillatory light input exhibits robust oscillations from which the organism can infer the time, but that in the absence of driving relaxes to a stable fixed point. Here, using models of the Kai system of cyanobacteria, we compare a limit-cycle oscillator with two hourglass models, one that without driving relaxes exponentially and one that does so in an oscillatory fashion. In the limit of low input noise, all three systems are equally informative on time, yet in the regime of high input-noise the limit-cycle oscillator is far superior. The same behavior is found in the Stuart-Landau model, indicating that our result is universal.

Revealing circadian mechanisms of integration and resilience by visualizing clock proteins working in real time

The circadian clock proteins KaiA, KaiB, and KaiC reconstitute a remarkable circa-24 h oscillation of KaiC phosphorylation that persists for many days in vitro. Here we use high-speed atomic force microscopy (HS-AFM) to visualize in real time and quantify the dynamic interactions of KaiA with KaiC on sub-second timescales. KaiA transiently interacts with KaiC, thereby stimulating KaiC autokinase activity. As KaiC becomes progressively more phosphorylated, KaiA's affinity for KaiC weakens, revealing a feedback of KaiC phosphostatus back onto the KaiA-binding events. These non-equilibrium interactions integrate high-frequency binding and unbinding events, thereby refining the period of the longer term oscillations. Moreover, this differential affinity phenomenon broadens the range of Kai protein stoichiometries that allow rhythmicity, explaining how the oscillation is resilient in an in vivo milieu that includes noise. Therefore, robustness of rhythmicity on a 24-h scale is explainable by molecular events occurring on a scale of sub-seconds.

High protein copy number is required to suppress stochasticity in the cyanobacterial circadian clock

Circadian clocks generate reliable ~24-h rhythms despite being based on stochastic biochemical reactions. The circadian clock in Synechococcus elongatus uses a post-translational oscillator that cycles deterministically in a test tube. Because the volume of a single bacterial cell is much smaller than a macroscopic reaction, we asked how clocks in single cells function reliably. Here, we show that S. elongatus cells must express many thousands of copies of Kai proteins to effectively suppress timing errors. Stochastic modeling shows that this requirement stems from noise amplification in the post-translational feedback loop that sustains oscillations. The much smaller cyanobacterium Prochlorococcus expresses only hundreds of Kai protein copies and has a simpler, hourglass-like Kai system. We show that this timer strategy can outperform a free-running clock if internal noise is significant. This conclusion has implications for clock evolution and synthetic oscillator design, and it suggests hourglass-like behavior may be widespread in microbes.

Circadian clocks must maintain their fidelity despite stochasticity arising from finite protein copy numbers. Here, the authors show that a small cyanobacterium relies on an environmentally driven timer likely because its low protein copy numbers cannot support an accurate free-running clock.

Conformational rearrangements of the C1 ring in KaiC measure the timing of assembly with KaiB

KaiC, the core oscillator of the cyanobacterial circadian clock, is composed of an N-terminal C1 domain and a C-terminal C2 domain, and assembles into a double-ring hexamer upon ATP binding. Cyclic phosphorylation and dephosphorylation at Ser431 and Thr432 in the C2 domain proceed with a period of approximately 24 h in the presence of other clock proteins, KaiA and KaiB, but recent studies have revealed a crucial role for the C1 ring in determining the cycle period. In this study, we mapped dynamic structural changes of the C1 ring in solution using a combination of site-directed tryptophan mutagenesis and fluorescence spectroscopy. We found that the C1 ring undergoes a structural transition, coupled with ATPase activity and the phosphorylation state, while maintaining its hexameric ring structure. This transition triggered by ATP hydrolysis in the C1 ring in specific phosphorylation states is a necessary event for recruitment of KaiB, limiting the overall rate of slow complex formation. Our results provide structural and kinetic insights into the C1-ring rearrangements governing the slow dynamics of the cyanobacterial circadian clock.

Structure, function, and mechanism of the core circadian clock in cyanobacteria

Circadian rhythms enable cells and organisms to coordinate their physiology with the cyclic environmental changes that come as a result of Earth's light/dark cycles. Cyanobacteria make use of a post-translational oscillator to maintain circadian rhythms, and this elegant system has become an important model for circadian timekeeping mechanisms. Composed of three proteins, the KaiABC system undergoes an oscillatory biochemical cycle that provides timing cues to achieve a 24-h molecular clock. Together with the input/output proteins SasA, CikA, and RpaA, these six gene products account for the timekeeping, entrainment, and output signaling functions in cyanobacterial circadian rhythms. This Minireview summarizes the current structural, functional and mechanistic insights into the cyanobacterial circadian clock.

Period Robustness and Entrainability of the Kai System to Changing Nucleotide Concentrations

Circadian clocks must be able to entrain to time-varying signals to keep their oscillations in phase with the day-night rhythm. On the other hand, they must also exhibit input compensation: their period must remain approximately one day in different constant environments. The posttranslational oscillator of the Kai system can be entrained by transient or oscillatory changes in the ATP fraction, yet is insensitive to constant changes in this fraction. We study in three different models of this system how these two seemingly conflicting criteria are met. We find that one of these (our recently published Paijmans model) exhibits the best tradeoff between input compensation and entrainability: on the footing of equal phase-response curves, it exhibits the strongest input compensation. Performing stochastic simulations at the level of individual hexamers allows us to identify a new, to our knowledge, mechanism, which is employed by the Paijmans model to achieve input compensation: at lower ATP fraction, the individual hexamers make a shorter cycle in the phosphorylation state space, which compensates for the slower pace at which they traverse the cycle.

The cyanobacterial circadian clock follows midday in vivo and in vitro

Circadian rhythms are biological oscillations that schedule daily changes in physiology. Outside the laboratory, circadian clocks do not generally free-run but are driven by daily cues whose timing varies with the seasons. The principles that determine how circadian clocks align to these external cycles are not well understood. Here, we report experimental platforms for driving the cyanobacterial circadian clock both in vivo and in vitro. We find that the phase of the circadian rhythm follows a simple scaling law in light-dark cycles, tracking midday across conditions with variable day length. The core biochemical oscillator comprised of the Kai proteins behaves similarly when driven by metabolic pulses in vitro, indicating that such dynamics are intrinsic to these proteins. We develop a general mathematical framework based on instantaneous transformation of the clock cycle by external cues, which successfully predicts clock behavior under many cycling environments.

Structural basis of the day-night transition in a bacterial circadian clock

Circadian clocks are ubiquitous timing systems that induce rhythms of biological activities in synchrony with night and day. In cyanobacteria, timing is generated by a posttranslational clock consisting of KaiA, KaiB, and KaiC proteins and a set of output signaling proteins, SasA and CikA, which transduce this rhythm to control gene expression. Here, we describe crystal and nuclear magnetic resonance structures of KaiB-KaiC,KaiA-KaiB-KaiC, and CikA-KaiB complexes. They reveal how the metamorphic properties of KaiB, a protein that adopts two distinct folds, and the post-adenosine triphosphate hydrolysis state of KaiC create a hub around which nighttime signaling events revolve, including inactivation of KaiA and reciprocal regulation of the mutually antagonistic signaling proteins, SasA and CikA.

A thermodynamically consistent model of the post-translational Kai circadian clock

The principal pacemaker of the circadian clock of the cyanobacterium S. elongatus is a protein phosphorylation cycle consisting of three proteins, KaiA, KaiB and KaiC. KaiC forms a homohexamer, with each monomer consisting of two domains, CI and CII. Both domains can bind and hydrolyze ATP, but only the CII domain can be phosphorylated, at two residues, in a well-defined sequence. While this system has been studied extensively, how the clock is driven thermodynamically has remained elusive. Inspired by recent experimental observations and building on ideas from previous mathematical models, we present a new, thermodynamically consistent, statistical-mechanical model of the clock. At its heart are two main ideas: i) ATP hydrolysis in the CI domain provides the thermodynamic driving force for the clock, switching KaiC between an active conformational state in which its phosphorylation level tends to rise and an inactive one in which it tends to fall; ii) phosphorylation of the CII domain provides the timer for the hydrolysis in the CI domain. The model also naturally explains how KaiA, by acting as a nucleotide exchange factor, can stimulate phosphorylation of KaiC, and how the differential affinity of KaiA for the different KaiC phosphoforms generates the characteristic temporal order of KaiC phosphorylation. As the phosphorylation level in the CII domain rises, the release of ADP from CI slows down, making the inactive conformational state of KaiC more stable. In the inactive state, KaiC binds KaiB, which not only stabilizes this state further, but also leads to the sequestration of KaiA, and hence to KaiC dephosphorylation. Using a dedicated kinetic Monte Carlo algorithm, which makes it possible to efficiently simulate this system consisting of more than a billion reactions, we show that the model can describe a wealth of experimental data.

Circadian clocks are biological timekeeping devices with a rhythm of 24 hours in living cells pertaining to all kingdoms of life. They help organisms to coordinate their behavior with the day-night cycle. The circadian clock of the cyanobacterium Synechococcus elongatus is one of the simplest and best characterized clocks in biology. The central clock component is the protein KaiC, which is phosphorylated and dephosphorylated in a cyclical manner with a 24 hr period. While we know from elementary thermodynamics that oscillations require a net turnover of fuel molecules, in this case ATP, how ATP hydrolysis drives the clock has remained elusive. Based on recent experimental observations and building on ideas from existing models, we construct the most detailed mathematical model of this system to date. KaiC consists of two domains, CI and CII, which each can bind ATP, yet only CII can be phosphorylated. Moreover, KaiC can exist in two conformational states, an active one in which the phosphorylation level tends to rise, and an inactive one in which it tends to fall. Our model predicts that ATP hydrolysis in the CI domain is the principal energetic driver of the clock, driving the switching between the two conformational states, while phosphorylation in the CII domain provides the timer for the conformational switch. The coupling between ATP hydrolysis in the CI domain and phosphorylation in the CII domain leads to novel testable predictions.

Timing the day: what makes bacterial clocks tick?

Chronobiological studies of prokaryotic organisms have generally lagged far behind the study of endogenous circadian clocks in eukaryotes, in which such systems are essentially ubiquitous. However, despite only being studied during the past 25 years, cyanobacteria have become important model organisms for the study of circadian rhythms and, presently, their timekeeping mechanism is the best understood of any system in terms of biochemistry, structural biology, biophysics and adaptive importance. Nevertheless, intrinsic daily rhythmicity among bacteria other than cyanobacteria is essentially unknown; some tantalizing information suggests widespread daily timekeeping among Eubacteria and Archaea through mechanisms that share common elements with the cyanobacterial clock but are distinct. Moreover, the recent surge of information about microbiome-host interactions has largely neglected the temporal dimension and yet daily cycles control important aspects of their relationship.

Structural characterization of the circadian clock protein complex composed of KaiB and KaiC by inverse contrast-matching small-angle neutron scattering

The molecular machinery of the cyanobacterial circadian clock consists of three proteins: KaiA, KaiB, and KaiC. Through interactions among the three Kai proteins, the phosphorylation states of KaiC generate circadian oscillations in vitro in the presence of ATP. Here, we characterized the complex formation between KaiB and KaiC using a phospho-mimicking mutant of KaiC, which had an aspartate substitution at the Ser431 phosphorylation site and exhibited optimal binding to KaiB. Mass-spectrometric titration data showed that the proteins formed a complex exclusively in a 6:6 stoichiometry, indicating that KaiB bound to the KaiC hexamer with strong positive cooperativity. The inverse contrast-matching technique of small-angle neutron scattering enabled selective observation of KaiB in complex with the KaiC mutant with partial deuteration. It revealed a disk-shaped arrangement of the KaiB subunits on the outer surface of the KaiC C1 ring, which also serves as the interaction site for SasA, a histidine kinase that operates as a clock-output protein in the regulation of circadian transcription. These data suggest that cooperatively binding KaiB competes with SasA with respect to interaction with KaiC, thereby promoting the synergistic release of this clock-output protein from the circadian oscillator complex.

Conversion between two conformational states of KaiC is induced by ATP hydrolysis as a trigger for cyanobacterial circadian oscillation

The cyanobacterial circadian oscillator can be reconstituted in vitro by mixing three clock proteins, KaiA, KaiB and KaiC, with ATP. KaiC is the only protein with circadian rhythmic activities. In the present study, we tracked the complex formation of the three Kai proteins over time using blue native (BN) polyacrylamide gel electrophoresis (PAGE), in which proteins are charged with the anionic dye Coomassie brilliant blue (CBB). KaiC was separated as three bands: the KaiABC complex, KaiC hexamer and KaiC monomer. However, no KaiC monomer was observed using gel filtration chromatography and CBB-free native PAGE. These data indicate two conformational states of KaiC hexamer and show that the ground-state KaiC (gs-KaiC) is stable and competent-state KaiC (cs-KaiC) is labile and degraded into monomers by the binding of CBB. Repeated conversions from gs-KaiC to cs-KaiC were observed over 24 h using an in vitro reconstitution system. Phosphorylation of KaiC promoted the conversion from gs-KaiC to cs-KaiC. KaiA sustained the gs-KaiC state, and KaiB bound only cs-KaiC. An E77Q/E78Q-KaiC variant that lacked N-terminal ATPase activity remained in the gs-KaiC state. Taken together, ATP hydrolysis induces the formation of cs-KaiC and promotes the binding of KaiB, which is a trigger for circadian oscillations.

Discrete gene replication events drive coupling between the cell cycle and circadian clocks

Many organisms possess both a cell cycle to control DNA replication and a circadian clock to anticipate changes between day and night. In some cases, these two rhythmic systems are known to be coupled by specific, cross-regulatory interactions. Here, we use mathematical modeling to show that, additionally, the cell cycle generically influences circadian clocks in a nonspecific fashion: The regular, discrete jumps in gene-copy number arising from DNA replication during the cell cycle cause a periodic driving of the circadian clock, which can dramatically alter its behavior and impair its function. A clock built on negative transcriptional feedback either phase-locks to the cell cycle, so that the clock period tracks the cell division time, or exhibits erratic behavior. We argue that the cyanobacterium Synechococcus elongatus has evolved two features that protect its clock from such disturbances, both of which are needed to fully insulate it from the cell cycle and give it its observed robustness: a phosphorylation-based protein modification oscillator, together with its accompanying push-pull read-out circuit that responds primarily to the ratios of different phosphoform concentrations, makes the clock less susceptible to perturbations in protein synthesis; the presence of multiple, asynchronously replicating copies of the same chromosome diminishes the effect of replicating any single copy of a gene.