Nonparametric entrainment of the in vitro circadian phosphorylation rhythm of cyanobacterial KaiC by temperature cycle

Evolutionary origins of self-sustained Kai protein circadian oscillators in cyanobacteria

Light-dark cycles affect photosynthetic efficiency in autotrophic cyanobacteria; therefore, determining whether ancient cyanobacteria possessed a self-sustained circadian clock when oxygenic photosynthetic systems were established is an important issue in chronobiology. Here we examine the oscillation of the clock protein KaiC in modern cyanobacteria, as well as the function and structure of ancestral Kai proteins, to determine the evolutionary origin of the self-sustained Kai-protein oscillators. The results show that the oldest double-domain KaiC in ancestral bacteria lacks the factors functionally and structurally essential for rhythmicity. The ancestral Kai proteins have acquired these factors through molecular evolution that occurred around Global Oxidation and Snowball Earth events, and are eventually inherited as a self-sustained circadian oscillator by the most recent common ancestor of cyanobacteria capable of oxygenic photosynthesis. This autonomous Kai protein oscillator is further inherited by most freshwater and marine cyanobacteria present today as an autotrophic basis for time-optimal acquisition and consumption of energy from oxygenic photosynthesis.

Self-sustained rhythmic behavior of Synechocystis sp. PCC 6803 under continuous light conditions in the absence of light-dark entrainment

Circadian clocks regulate biological activities, providing organisms with a fitness advantage under diurnal conditions by enabling anticipation and adaptation to recurring external changes. Three proteins, KaiA, KaiB, and KaiC, constitute the circadian clock in the cyanobacterial model Synechococcus elongatus PCC 7942. Several techniques established to measure circadian output in Synechococcus yielded comparably weak signals in Synechocystis sp. PCC 6803, a strain important for biotechnological applications. We applied an approach that does not require genetic modifications to monitor the circadian rhythms in Synechococcus and Synechocystis. We placed batch cultures in shake flasks on a sensor detecting backscattered light via noninvasive online measurements. Backscattering oscillated with a period of ∼24 h around the average growth. Wavelet and Fourier transformations are applied to determine the period's significance and length. In Synechocystis, oscillations fulfilled the circadian criteria of temperature compensation and entrainment by external stimuli. Remarkably, dilution alone synchronized oscillations. Western blotting revealed that the backscatter was ∼6.5 h phase-delayed in comparison to KaiC3 phosphorylation.

Noise-induced entrainment of the circadian clock by thermoperiods in tomato: A computational approach

The endogenous circadian rhythm (approximately 24 h) allows plants to adapt to daily light and temperature variations. Although the mechanism of photoperiod entrainment has been studied extensively, entrainment to diurnal temperature rhythms remains poorly understood. Here we investigate the stochastic entrainment of the circadian clock in the model crop tomato, subject to different thermoperiods. We first proposed the deterministic model of the thermoresponsive circadian clock. The expressions of the circadian clock genes under constant warm temperature (29 ℃) were quantified by RT-qPCR for basal parameters estimation through minimizing the cost function. Model simulations by the stochastic simulation algorithm showed warm temperatures resulting in an advanced phase for approximately 3-4 h. A few hundred molecules for the system size of the stochastic model were sufficient to engage the robust oscillations. Multiple temperature inputs and abnormal temperature cycles similarly showed the invariant robustness of the oscillations. In addition, phases of the core circadian elements were remarkably correlated linearly with periods under temperature cycles. Whereas, the phases were correlated with the duration of daily warm temperature stimuli in a polynomial mode.

Temperature compensation through kinetic regulation in biochemical oscillators

Nearly all circadian clocks maintain a period that is insensitive to temperature changes, a phenomenon known as temperature compensation (TC). Yet, it is unclear whether there is any common feature among different systems that exhibit TC. From a general timescale invariance, we show that TC relies on the existence of certain period-lengthening reactions wherein the period of the system increases strongly with the rates in these reactions. By studying several generic oscillator models, we show that this counterintuitive dependence is nonetheless a common feature of oscillators in the nonlinear (far-from-onset) regime where the oscillation can be separated into fast and slow phases. The increase of the period with the period-lengthening reaction rates occurs when the amplitude of the slow phase in the oscillation increases with these rates while the progression speed in the slow phase is controlled by other rates of the system. The positive dependence of the period on the period-lengthening rates balances its inverse dependence on other kinetic rates in the system, which gives rise to robust TC in a wide range of parameters. We demonstrate the existence of such period-lengthening reactions and their relevance for TC in all four model systems we considered. Theoretical results for a model of the Kai system are supported by experimental data. A study of the energy dissipation also shows that better TC performance requires higher energy consumption. Our study unveils a general mechanism by which a biochemical oscillator achieves TC by operating in parameter regimes far from the onset where period-lengthening reactions exist.

Weak and strong phase response curves of the onion fly circadian clock at temperature changes of 1 °C and 4 °C

With increasing soil depth, the amplitude and phase of the daily temperature cycle decreases and is delayed, respectively. The onion fly, Delia antiqua, which pupates at a soil depth of 2-20 cm, advances the eclosion phase of its circadian clock as the temperature amplitude decreases. This "temperature-amplitude response" compensates for the depth-dependent phase delay of the temperature change and ensures eclosion in the early morning. To clarify the physiological mechanisms that induce a temperature-amplitude response, we performed phase-resetting experiments using a 12-h high- or low-temperature pulse with an amplitude of 1 °C or 4 °C. Based on the results obtained, four phase transition curves and four phase response curves were constructed. These curves show that the phase of the eclosion clock shifted more as the magnitude of the temperature change increased. The 24-h temperature cycle delayed, rather than advanced, the phase of the D. antiqua circadian eclosion rhythm. Therefore, we propose that a small phase delay is caused by a small temperature amplitude at a deep site in the soil and a large phase delay is caused by a large temperature amplitude at a shallow site, leading to the temperature-amplitude response exhibited by D. antiqua.

Protocols for in vitro reconstitution of the cyanobacterial circadian clock

Circadian clocks are intracellular systems that orchestrate metabolic processes in anticipation of sunrise and sunset by providing an internal representation of local time. Because the ~24-h metabolic rhythms they produce are important to health across diverse life forms there is growing interest in their mechanisms. However, mechanistic studies are challenging in vivo due to the complex, that is, poorly defined, milieu of live cells. Recently, we reconstituted the intact circadian clock of cyanobacteria in vitro. It oscillates autonomously and remains phase coherent for many days with a fluorescence-based readout that enables real-time observation of individual clock proteins and promoter DNA simultaneously under defined conditions without user intervention. We found that reproducibility of the reactions required strict adherence to the quality of each recombinant clock protein purified from Escherichia coli. Here, we provide protocols for preparing in vitro clock samples so that other labs can ask questions about how changing environments, like temperature, metabolites, and protein levels are reflected in the core oscillator and propagated to regulation of transcription, providing deeper mechanistic insights into clock biology.

Structure-function relationship of KaiC around dawn

KaiC is a multifunctional enzyme functioning as the core of the circadian clock system in cyanobacteria: its N-terminal domain has adenosine triphosphatase (ATPase) activity, and its C-terminal domain has autokinase and autophosphatase activities targeting own S431 and T432. The coordination of these multiple biochemical activities is the molecular basis for robust circadian rhythmicity. Therefore, much effort has been devoted to elucidating the cooperative relationship between the two domains. However, structural and functional relationships between the two domains remain unclear especially with respect to the dawn phase, at which KaiC relieves its nocturnal history through autodephosphorylation. In this study, we attempted to design a double mutation of S431 and T432 that can capture KaiC as a fully dephosphorylated form with minimal impacts on its structure and function, and investigated the cooperative relationship between the two domains in the night to morning phases from many perspectives. The results revealed that both domains cooperate at the dawn phase through salt bridges formed between the domains, thereby non-locally co-activating two events, ATPase de-inhibition and S431 dephosphorylation. Our further analysis using existing crystal structures of KaiC suggests that the states of both domains are not always in one-to-one correspondence at every phase of the circadian cycle, and their coupling is affected by the interactions with KaiA or adjacent subunits within a KaiC hexamer.

The circadian clock of the bacterium B. subtilis evokes properties of complex, multicellular circadian systems

Circadian clocks are pervasive throughout nature, yet only recently has this adaptive regulatory program been described in nonphotosynthetic bacteria. Here, we describe an inherent complexity in the Bacillus subtilis circadian clock. We find that B. subtilis entrains to blue and red light and that circadian entrainment is separable from masking through fluence titration and frequency demultiplication protocols. We identify circadian rhythmicity in constant light, consistent with the Aschoff's rule, and entrainment aftereffects, both of which are properties described for eukaryotic circadian clocks. We report that circadian rhythms occur in wild isolates of this prokaryote, thus establishing them as a general property of this species, and that its circadian system responds to the environment in a complex fashion that is consistent with multicellular eukaryotic circadian systems.

Recent research advances on non-linear phenomena in various biosystems

All biological phenomena can be classified as open, dissipative and non-linear. Moreover, the most typical phenomena are associated with non-linearity, dissipation and openness in biological systems. In this review article, four research topics on non-linear biosystems are described to show the examples from various biological systems. First, membrane dynamics of a lipid bilayer for the cell membrane is described. Since the cell membrane separates the inside of the cell from the outside, self-organizing systems that form spatial patterns on membranes often depend on non-linear dynamics. Second, various data banks based on recent genomics analysis supply the data including vast functional proteins from many organisms and their variable species. Since the proteins existing in nature are only a very small part of the space represented by amino acid sequence, success of mutagenesis-based molecular evolution approach crucially depends on preparing a library with high enrichment of functional proteins. Third, photosynthetic organisms depend on ambient light, the regular and irregular changes of which have a significant impact on photosynthetic processes. The light-driven process proceeds through many redox couples in the cyanobacteria constituting chain of redox reactions. Forth topics focuses on a vertebrate model, the zebrafish, which can help to understand, predict and control the chaos of complex biological systems. In particular, during early developmental stages, developmental differentiation occurs dynamically from a fertilized egg to divided and mature cells. These exciting fields of complexity, chaos, and non-linear science have experienced impressive growth in recent decades. Finally, future directions for non-liner biosystems are presented.

Role of the reaction-structure coupling in temperature compensation of the KaiABC circadian rhythm

When the mixture solution of cyanobacterial proteins, KaiA, KaiB, and KaiC, is incubated with ATP in vitro, the phosphorylation level of KaiC shows stable oscillations with the temperature-compensated circadian period. Elucidating this temperature compensation is essential for understanding the KaiABC circadian clock, but its mechanism has remained a mystery. We analyzed the KaiABC temperature compensation by developing a theoretical model describing the feedback relations among reactions and structural transitions in the KaiC molecule. The model showed that the reduced structural cooperativity should weaken the negative feedback coupling among reactions and structural transitions, which enlarges the oscillation amplitude and period, explaining the observed significant period extension upon single amino-acid residue substitution. We propose that an increase in thermal fluctuations similarly attenuates the reaction-structure feedback, explaining the temperature compensation in the KaiABC clock. The model explained the experimentally observed responses of the oscillation phase to the temperature shift or the ADP-concentration change and suggested that the ATPase reactions in the CI domain of KaiC affect the period depending on how the reaction rates are modulated. The KaiABC clock provides a unique opportunity to analyze how the reaction-structure coupling regulates the system-level synchronized oscillations of molecules.

Controllable Biological Rhythms and Patterns

One of the goals of soft robotics is to implement intelligent functions capable of processing complex information in soft materials. This is a noble goal, and we already have a familiar example, albeit not an artificial one, in a living organism. We believe that the intelligent biological elements acquired through the evolutionary process, which do not require an electricity supply or CPU, can be used for soft robotics. In this letter, we introduce three biological elements: proteins, squid, and nematodes, which show temporal or special patterns. We then discuss an attempt to apply them to soft robotics.

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.

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.

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.

Design principles for enhancing phase sensitivity and suppressing phase fluctuations simultaneously in biochemical oscillatory systems

Biological systems need to function accurately in the presence of strong noise and at the same time respond sensitively to subtle external cues. Here we study design principles in biochemical oscillatory circuits to achieve these two seemingly incompatible goals. We show that energy dissipation can enhance phase sensitivity linearly by driving the phase-amplitude coupling and increase timing accuracy by suppressing phase diffusion. Two general design principles in the key underlying reaction loop formed by two antiparallel pathways are found to optimize oscillation performance with a given energy budget: balancing the forward-to-backward flux ratio between the two pathways to reduce phase diffusion and maximizing the net flux of the phase-advancing pathway relative to that of the phase-retreating pathway to enhance phase sensitivity. Experimental evidences consistent with these design principles are found in the circadian clock of cyanobacteria. Future experiments to test the predicted dependence of phase sensitivity on energy dissipation are proposed.

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.

Low temperature nullifies the circadian clock in cyanobacteria through Hopf bifurcation

Cold temperatures lead to nullification of circadian rhythms in many organisms. Two typical scenarios explain the disappearance of rhythmicity: the first is oscillation death, which is the transition from self-sustained oscillation to damped oscillation that occurs at a critical temperature. The second scenario is oscillation arrest, in which oscillation terminates at a certain phase. In the field of nonlinear dynamics, these mechanisms are called the Hopf bifurcation and the saddle-node on an invariant circle bifurcation, respectively. Although these mechanisms lead to distinct dynamical properties near the critical temperature, it is unclear to which scenario the circadian clock belongs. Here we reduced the temperature to dampen the reconstituted circadian rhythm of phosphorylation of the recombinant cyanobacterial clock protein KaiC. The data led us to conclude that Hopf bifurcation occurred at ∼19 °C. Below this critical temperature, the self-sustained rhythms of KaiC phosphorylation transformed to damped oscillations, which are predicted by the Hopf bifurcation theory. Moreover, we detected resonant oscillations below the critical temperature when temperature was periodically varied, which was reproduced by numerical simulations. Our findings suggest that the transition to a damped oscillation through Hopf bifurcation contributes to maintaining the circadian rhythm of cyanobacteria through resonance at cold temperatures.

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.

Direct Repression of Evening Genes by CIRCADIAN CLOCK-ASSOCIATED1 in the Arabidopsis Circadian Clock

The circadian clock is a biological timekeeping system that provides organisms with the ability to adapt to day-night cycles. Timing of the expression of four members of the Arabidopsis thaliana PSEUDO-RESPONSE REGULATOR(PRR) family is crucial for proper clock function, and transcriptional control of PRRs remains incompletely defined. Here, we demonstrate that direct regulation of PRR5 by CIRCADIAN CLOCK-ASSOCIATED1 (CCA1) determines the repression state of PRR5 in the morning. Chromatin immunoprecipitation followed by deep sequencing (ChIP-seq) analyses indicated that CCA1 associates with three separate regions upstream of PRR5 CCA1 and its homolog LATE ELONGATED HYPOCOTYL (LHY) suppressed PRR5 promoter activity in a transient assay. The regions bound by CCA1 in the PRR5 promoter gave rhythmic patterns with troughs in the morning, when CCA1 and LHY are at high levels. Furthermore,ChIP-seq revealed that CCA1 associates with at least 449 loci with 863 adjacent genes. Importantly, this gene set contains genes that are repressed but upregulated incca1 lhy double mutants in the morning. This study shows that direct binding by CCA1 in the morning provides strong repression of PRR5, and repression by CCA1 also temporally regulates an evening-expressed gene set that includes PRR5.

Reciprocity Between Robustness of Period and Plasticity of Phase in Biological Clocks

Circadian clocks exhibit the robustness of period and plasticity of phase against environmental changes such as temperature and nutrient conditions. Thus far, however, it is unclear how both are simultaneously achieved. By investigating distinct models of circadian clocks, we demonstrate reciprocity between robustness and plasticity: higher robustness in the period implies higher plasticity in the phase, where changes in period and in phase follow a linear relationship with a negative coefficient. The robustness of period is achieved by the adaptation on the limit cycle via a concentration change of a buffer molecule, whose temporal change leads to a phase shift following a shift of the limit-cycle orbit in phase space. Generality of reciprocity in clocks with the adaptation mechanism is confirmed with theoretical analysis of simple models, while biological significance is discussed.

Loss of Drosophila melanogaster TRPA1 Function Affects “Siesta” Behavior but Not Synchronization to Temperature Cycles

To maintain synchrony with the environment, circadian clocks use a wide range of cycling sensory cues that provide input to the clock (zeitgebers), including environmental temperature cycles (TCs). There is some knowledge about which clock neuronal groups are important for temperature synchronization, but we currently lack knowledge on the temperature receptors and their signaling pathways that feed temperature information to the (neuronal) clock. Since TRPA1 is a well-known thermosensor that functions in a range of temperature-related behaviors, and it is potentially expressed in clock neurons, we set out to test the putative role of TRPA1 in temperature synchronization of the circadian clock. We found that flies lacking TRPA1 are still able to synchronize their behavioral activity to TCs comparable to wild-type flies, both in 16°C : 25°C and 20°C : 29°C TCs. In addition, we found that flies lacking TRPA1 show higher activity levels during the middle of the warm phase of 20°C : 29°C TCs, and we show that this TRPA1-mediated repression of locomotor activity during the “siesta” is caused by a lack of sleep. Based on these data, we conclude that the TRPA1 channel is not required for temperature synchronization in this broad temperature range but instead is required to repress activity during the warm part of the day.

Circadian rhythms. Atomic-scale origins of slowness in the cyanobacterial circadian clock

Circadian clocks generate slow and ordered cellular dynamics but consist of fast-moving bio-macromolecules; consequently, the origins of the overall slowness remain unclear. We identified the adenosine triphosphate (ATP) catalytic region [adenosine triphosphatase (ATPase)] in the amino-terminal half of the clock protein KaiC as the minimal pacemaker that controls the in vivo frequency of the cyanobacterial clock. Crystal structures of the ATPase revealed that the slowness of this ATPase arises from sequestration of a lytic water molecule in an unfavorable position and coupling of ATP hydrolysis to a peptide isomerization with high activation energy. The slow ATPase is coupled with another ATPase catalyzing autodephosphorylation in the carboxyl-terminal half of KaiC, yielding the circadian response frequency of intermolecular interactions with other clock-related proteins that influences the transcription and translation cycle.

A protocol for preparing nucleotide-free KaiC monomer

The hexameric form of the KaiC protein is a core of the cyanobacterial biological clock, and its enzymatic activities exhibit circadian periodicity. The instability of the monomeric form of nucleotide-free KaiC has precluded its storage and detailed analyses of the activities of the reassembled hexamer. Here, we provide a protocol for preparing nucleotide-free KaiC monomer that is stable in solution and for triggering its reassembly into intact KaiC hexamer by the addition of ATP. A phosphate buffer containing glutamic acid and arginine enhanced the stability of KaiC monomer considerably. In addition, we found that reassembled KaiC hexamer was functionally active as the intact hexamer. This protocol provides a methodological basis for further analyses of first-turnover events of the ATPase/autokinase/autophosphatase activities of the KaiC hexamer.

Metabolic compensation and circadian resilience in prokaryotic cyanobacteria

For a biological oscillator to function as a circadian pacemaker that confers a fitness advantage, its timing functions must be stable in response to environmental and metabolic fluctuations. One such stability enhancer, temperature compensation, has long been a defining characteristic of these timekeepers. However, an accurate biological timekeeper must also resist changes in metabolism, and this review suggests that temperature compensation is actually a subset of a larger phenomenon, namely metabolic compensation, which maintains the frequency of circadian oscillators in response to a host of factors that impinge on metabolism and would otherwise destabilize these clocks. The circadian system of prokaryotic cyanobacteria is an illustrative model because it is composed of transcriptional and nontranscriptional oscillators that are coupled to promote resilience. Moreover, the cyanobacterial circadian program regulates gene activity and metabolic pathways, and it can be manipulated to improve the expression of bioproducts that have practical value.

Insight into cyanobacterial circadian timing from structural details of the KaiB-KaiC interaction

Circadian timing in cyanobacteria is determined by the Kai system consisting of KaiA, KaiB, and KaiC. Interactions between Kai proteins change the phosphorylation status of KaiC, defining the phase of circadian timing. The KaiC-KaiB interaction is crucial for the circadian rhythm to enter the dephosphorylation phase but it is not well understood. Using mass spectrometry to characterize Kai complexes, we found that KaiB forms monomers, dimers, and tetramers. The monomer is the unit that interacts with KaiC, with six KaiB monomers binding to one KaiC hexamer. Hydrogen-deuterium exchange MS reveals structural changes in KaiC upon binding of KaiB in both the CI and CII domains, showing allosteric coupling upon KaiB binding. Based on this information we propose a model of the KaiB-KaiC complex and hypothesize that the allosteric changes observed upon complex formation relate to coupling KaiC ATPase activity with KaiB binding and to sequestration of KaiA dimers into KaiCBA complexes.

Entrainment of spontaneously hypertensive rat fibroblasts by temperature cycles

The functional state of the circadian system of spontaneously hypertensive rats (SHR) differs in several characteristics from the functional state of normotensive Wistar rats. Some of these changes might be due to the compromised ability of the central pacemaker to entrain the peripheral clocks. Daily body temperature cycles represent one of the important cues responsible for the integrity of the circadian system, because these cycles are driven by the central pacemaker and are able to entrain the peripheral clocks. This study tested the hypothesis that the aberrant peripheral clock entrainment of SHR results from a compromised peripheral clock sensitivity to the daily temperature cycle resetting. Using cultured Wistar rat and SHR fibroblasts transfected with the circadian luminescence reporter Bmal1-dLuc, we demonstrated that two consecutive square-wave temperature cycles with amplitudes of 2.5°C are necessary and sufficient to restart the dampened oscillations and entrain the circadian clocks in both Wistar rat and SHR fibroblasts. We also generated a phase response curve to temperature cycles for fibroblasts of both rat strains. Although some of the data suggested a slight resistance of SHR fibroblasts to temperature entrainment, we concluded that the overall effect it too weak to be responsible for the differences between the SHR and Wistar in vivo circadian phenotype.

Cooperative KaiA-KaiB-KaiC interactions affect KaiB/SasA competition in the circadian clock of cyanobacteria

The circadian oscillator of cyanobacteria is composed of only three proteins, KaiA, KaiB, and KaiC. Together, they generate an autonomous ~24-h biochemical rhythm of phosphorylation of KaiC. KaiA stimulates KaiC phosphorylation by binding to the so-called A-loops of KaiC, whereas KaiB sequesters KaiA in a KaiABC complex far away from the A-loops, thereby inducing KaiC dephosphorylation. The switch from KaiC phosphorylation to dephosphorylation is initiated by the formation of the KaiB-KaiC complex, which occurs upon phosphorylation of the S431 residues of KaiC. We show here that formation of the KaiB-KaiC complex is promoted by KaiA, suggesting cooperativity in the initiation of the dephosphorylation complex. In the KaiA-KaiB interaction, one monomeric subunit of KaiB likely binds to one face of a KaiA dimer, leaving the other face unoccupied. We also show that the A-loops of KaiC exist in a dynamic equilibrium between KaiA-accessible exposed and KaiA-inaccessible buried positions. Phosphorylation at the S431 residues of KaiC shift the A-loops toward the buried position, thereby weakening the KaiA-KaiC interaction, which is expected to be an additional mechanism promoting formation of the KaiABC complex. We also show that KaiB and the clock-output protein SasA compete for overlapping binding sites, which include the B-loops on the CI ring of KaiC. KaiA strongly shifts the competition in KaiB's favor. Thus, in addition to stimulating KaiC phosphorylation, it is likely that KaiA plays roles in switching KaiC from phosphorylation to dephosphorylation, as well as regulating clock output.

Adaptive temperature compensation in circadian oscillations

A temperature independent period and temperature entrainment are two defining features of circadian oscillators. A default model of distributed temperature compensation satisfies these basic facts yet is not easily reconciled with other properties of circadian clocks, such as many mutants with altered but temperature compensated periods. The default model also suggests that the shape of the circadian limit cycle and the associated phase response curves (PRC) will vary since the average concentrations of clock proteins change with temperature. We propose an alternative class of models where the twin properties of a fixed period and entrainment are structural and arise from an underlying adaptive system that buffers temperature changes. These models are distinguished by a PRC whose shape is temperature independent and orbits whose extrema are temperature independent. They are readily evolved by local, hill climbing, optimization of gene networks for a common quality measure of biological clocks, phase anticipation. Interestingly a standard realization of the Goodwin model for temperature compensation displays properties of adaptive rather than distributed temperature compensation.

Structural and dynamic aspects of protein clocks: how can they be so slow and stable?

KaiC is a core protein of the cyanobacterial Kai oscillator, which persists without transcription-translation feedback. In the presence of KaiA and KaiB, KaiC reveals rhythmic activation/inactivation of its ATPase and autokinase/autophosphotase activities over approximately 24 h. Since the in vitro reconstruction of the Kai oscillator, the structures and functions of the Kai proteins have been studied extensively. Each protein's crystal structure and low-resolution views of Kai complexes have been reported. In addition, newer data are emerging on dynamic aspects such as assembly/disassembly of the Kai components and a ticking motion of KaiC, which is probably coupled to its slow, temperature-compensated ATPase activity. The accumulated evidence offers an ideal opportunity to revisit a fundamental question regarding biological circadian clocks: what determines the temperature-compensated 24 h period? In this review, I summarize the current understanding of the Kai oscillator's molecular mechanism and discuss emerging ideas on protein clocks.

Generic temperature compensation of biological clocks by autonomous regulation of catalyst concentration

Circadian clocks--ubiquitous in life forms ranging from bacteria to multicellular organisms--often exhibit intrinsic temperature compensation; the period of circadian oscillators is maintained constant over a range of physiological temperatures, despite the expected Arrhenius form for the reaction coefficient. Observations have shown that the amplitude of the oscillation depends on the temperature but the period does not; this suggests that although not every reaction step is temperature independent, the total system comprising several reactions still exhibits compensation. Here we present a general mechanism for such temperature compensation. Consider a system with multiple activation energy barriers for reactions, with a common enzyme shared across several reaction steps. The steps with the highest activation energy rate-limit the cycle when the temperature is not high. If the total abundance of the enzyme is limited, the amount of free enzyme available to catalyze a specific reaction decreases as more substrates bind to the common enzyme. We show that this change in free enzyme abundance compensates for the Arrhenius-type temperature dependence of the reaction coefficient. Taking the example of circadian clocks with cyanobacterial proteins KaiABC, consisting of several phosphorylation sites, we show that this temperature compensation mechanism is indeed valid. Specifically, if the activation energy for phosphorylation is larger than that for dephosphorylation, competition for KaiA shared among the phosphorylation reactions leads to temperature compensation. Moreover, taking a simpler model, we demonstrate the generality of the proposed compensation mechanism, suggesting relevance not only to circadian clocks but to other (bio)chemical oscillators as well.

Fluorescence correlation spectroscopy to monitor Kai protein-based circadian oscillations in real time

Dynamic protein-protein interactions play an essential role in cellular regulatory systems. The cyanobacterial circadian clock is an oscillatory system that can be reconstituted in vitro by mixing ATP and three clock proteins: KaiA, KaiB, and KaiC. Association and dissociation of KaiB from KaiC-containing complexes are critical to circadian phosphorylation and dephosphorylation of KaiC. We developed an automated and noninvasive method to monitor dynamic complex formation in real time using confocal fluorescence correlation spectroscopy (FCS) and uniformly labeled KaiB as a probe. A nanomolar concentration of the labeled KaiB for FCS measurement did not interfere with the oscillatory system but behaved similarly to the wild-type one during the measurement period (>5 days). The fluorescent probe was stable against repeated laser exposure. As an application, we show that this detection system allowed analysis of the dynamics of both long term circadian oscillations and short term responses to temperature changes (∼10 min) in the same sample. This suggested that a phase shift of the clock with a high temperature pulse occurred just after the stimulus through dissociation of KaiB from the KaiC complex. This monitoring method should improve our understanding of the mechanisms underlying this cellular circadian oscillator and provide a means to assess dynamic protein interactions in biological systems characterized by rates similar to those observed with the Kai proteins.

The cyanobacterial circadian system: from biophysics to bioevolution

Recent studies have unveiled the molecular machinery responsible for the biological clock in cyanobacteria and found that it exerts pervasive control over cellular processes including global gene expression. Indeed, the entire chromosome undergoes daily cycles of topology/compaction! The circadian system comprises both a posttranslational oscillator (PTO) and a transcriptional/translational feedback loop (TTFL). The PTO can be reconstituted in vitro with three purified proteins (KaiA, KaiB, and KaiC) and ATP. These are the only circadian proteins for which high-resolution structures are available. Phase in this nanoclockwork has been associated with key phosphorylations of KaiC. Structural considerations illuminate the mechanism by which the KaiABC oscillator ratchets unidirectionally. Models of the complete in vivo system have important implications for our understanding of circadian clocks in higher organisms, including mammals. The conjunction of structural, biophysical, and biochemical approaches to this system has brought our understanding of the molecular mechanisms of biological timekeeping to an unprecedented level.

Cell autonomy and synchrony of suprachiasmatic nucleus circadian oscillators

The suprachiasmatic nucleus (SCN) of the hypothalamus is the site of the master circadian pacemaker in mammals. The individual cells of the SCN are capable of functioning independently from one another and therefore must form a cohesive circadian network through intercellular coupling. The network properties of the SCN lead to coordination of circadian rhythms among its neurons and neuronal subpopulations. There is increasing evidence for multiple interconnected oscillators within the SCN, and in this review we will highlight recent advances in our knowledge of the complex organization and function of the cellular and network-level SCN clock. Understanding the way in which synchrony is achieved between cells in the SCN will provide insight into the means by which this important nucleus orchestrates circadian rhythms throughout the organism.

Vasoactive intestinal polypeptide requires parallel changes in adenylate cyclase and phospholipase C to entrain circadian rhythms to a predictable phase

Circadian oscillations in the suprachiasmatic nucleus (SCN) depend on transcriptional repression by Period (PER)1 and PER2 proteins within single cells and on vasoactive intestinal polypeptide (VIP) signaling between cells. Because VIP is released by SCN neurons in a circadian pattern, and, after photic stimulation, it has been suggested to play a role in the synchronization to environmental light cycles. It is not known, however, if or how VIP entrains circadian gene expression or behavior. Here, we tested candidate signaling pathways required for VIP-mediated entrainment of SCN rhythms. We found that single applications of VIP reset PER2 rhythms in a time- and dose-dependent manner that differed from light. Unlike VIP-mediated signaling in other cell types, simultaneous antagonism of adenylate cyclase and phospholipase C activities was required to block the VIP-induced phase shifts of SCN rhythms. Consistent with this, VIP rapidly increased intracellular cAMP in most SCN neurons. Critically, daily VIP treatment entrained PER2 rhythms to a predicted phase angle within several days, depending on the concentration of VIP and the interval between VIP applications. We conclude that VIP entrains circadian timing among SCN neurons through rapid and parallel changes in adenylate cyclase and phospholipase C activities.

Temperature as a universal resetting cue for mammalian circadian oscillators

Environmental temperature cycles are a universal entraining cue for all circadian systems at the organismal level with the exception of homeothermic vertebrates. We report here that resistance to temperature entrainment is a property of the suprachiasmatic nucleus (SCN) network and is not a cell-autonomous property of mammalian clocks. This differential sensitivity to temperature allows the SCN to drive circadian rhythms in body temperature, which can then act as a universal cue for the entrainment of cell-autonomous oscillators throughout the body. Pharmacological experiments show that network interactions in the SCN are required for temperature resistance and that the heat shock pathway is integral to temperature resetting and temperature compensation in mammalian cells. These results suggest that the evolutionarily ancient temperature resetting response can be used in homeothermic animals to enhance internal circadian synchronization.

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

The circadian KaiABC oscillator is driven by a sequestration feedback, which is biochemically realized by a strong affinity of KaiA to exclusively serine phosphorylated KaiBC complexes.

A highly non-linear feedback model explains the time courses of the phosphorylation states and the robustness under concerted changes of all Kai proteins.

Native mass spectrometry reveals the existence of two KaiA binding sites on KaiC, confirming the theoretical predictions.

Temperature entrainment arises from a temperature-dependent change in the abundance of KaiAC and KaiBC complexes.

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 (Nakajima et al, 2005). Although the three component oscillator is apparently simple, it is highly precise and shows in-phase oscillations over several days (Mihalcescu et al, 2004). If we assume that cyanobacteria gain an evolutionary advantage from predicting the time of maximal sunlight intensity in a very reliable way, a highly robust but entrainable oscillator is likely the optimal solution. To elucidate the mechanism of the opposing properties of the clockwork—robustness and tenability—a mathematical modeling approach is necessary. The model must account for both the measured invariance of the phosphorylation level under concerted concentration changes of all Kai proteins (Kageyama et al, 2006) and for the experimentally observed temperature entrainment (Yoshida et al, 2009).

Here, we show by mathematical modeling, in combination with the measurements of the KaiABC complex formation dynamics from native mass spectrometry, that oscillations in the Kai system are a consequence of KaiA sequestration by KaiC hexamers and KaiBC complexes. Our in vitro model includes the characteristic KaiC phospho-form cycle, originating from two KaiC residues, serine (431) and threonine (432) (Nishiwaki et al, 2000). We allow for three pools that represent different forms of the KaiC complex. Together with the four phosphorylation states of KaiC, this gives a 3 × 4-dimensional model. We used data from the time course experiments of the O'Shea laboratory (Rust et al, 2007) to determine the unknown parameters of the KaiABC system. A global optimization algorithm is used to scan a large range of parameter values, resulting in a mathematical quantitative model of the KaiABC clockwork, see Figure 5. The KaiB response experiment (Rust et al, 2007) turned out to be crucial for identifying the mechanism by which individual KaiC hexamers can be synchronized in their phosphorylation dynamics. Importantly, the dephosphorylation phase can only be explained by a highly non-linear dependency of the KaiBC complex formation on the actual phosphorylation state. This can be realized by allowing only KaiBC complexes with exclusively serine phosphorylated KaiC, [S–KaiBC]₆, to inactivate KaiA with a high efficiency.

This theoretical prediction is confirmed by native mass spectrometry, generating semi-quantitative time courses of the KaiABC complex formation dynamics. Our experiments show the existence of two different KaiC binding sites to KaiA. The constant sequestration of free KaiA by the KaiA₂C₆ complexes is the molecular realization of the dynamic invariance condition because it requires most of the KaiA to be inactive at every instant of time, regardless of the phosphorylation state. The second binding site KaiA₄C₆ reflects the KaiA-binding domain at the catalytic active center of the KaiC hexamer. This hypothesis is confirmed by comparison of the mass spectrometry signal for KaiA₄C₆ with predictions from the mathematical model (Figure 7A and B). In the late phosphorylation phase, KaiBC complexes rapidly build up and sequestrate KaiA (Figure 7C), which represent an additional binding site. The relative amount of KaiA₆B₆C₆ confirms the sequestration hypotheses and corresponds to the theoretically estimated amount of sequestrated KaiA. The time of maximum sequestration—as defined by the appearance of the largest observed sequestration complex KaiA₁₀B₆C₆ (Figure 7E)—agrees with the theoretical expected sequestration maximum (Figure 7F) where [S-KaiBC]₆ is maximal.

To test further the predictive power of the mathematical model, we reproduced the observed phase synchronization dynamics on entrainment by temperature cycles. The response to a sudden temperature change results in a phase shift of phospho-KaiC, whereas the circadian period does not show any temperature dependency within a physiologically relevant range (Yoshida et al, 2009). As phosphorylation and dephosphorylation dynamics of KaiC alone and incubated with KaiA do not show significant temperature dependence (Tomita et al, 2005), phase entrainment is likely a consequence of temperature-induced changes in binding constants associated with the various KaiABC complexes. From thermodynamic arguments, we expect that an increasing temperature will enhance dissociation of KaiA and KaiB from KaiC. Indeed, a reduction in the net complex formation rate for S-KaiBC, D-KaiBC, and for KaiAC on temperature increase results in the experimentally observed differences in phase response, which compensate during the circadian cycle to assure temperature invariance of the ciracadian period.

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.

The molecular clockwork of a protein-based circadian oscillator

The circadian clock of the cyanobacterium Synechococcus elongatus PCC 7942 is governed by a core oscillator consisting of the proteins KaiA, KaiB, and KaiC. Remarkably, circadian oscillations in the phosphorylation state of KaiC can be reconstituted in a test tube by mixing the three Kai proteins and adenosine triphosphate. The in vitro oscillator provides a well-defined system in which experiments can be combined with mathematical analysis to understand the mechanism of a highly robust biological oscillator. In this Review, we summarize the biochemistry of the Kai proteins and examine models that have been proposed to explain how oscillations emerge from the properties of the oscillator's constituents.

Circadian clocks and phosphorylation: Insights from computational modeling

Circadian clocks are based on a molecular mechanism regulated at the transcriptional, translational and post-translational levels. Recent experimental data unravel a complex role of the phosphorylations in these clocks. In mammals, several kinases play differential roles in the regulation of circadian rhythmicity. A dysfunction in the phosphorylation of one clock protein could lead to sleep disorders such as the Familial Advanced Sleep Phase Disorder, FASPS. Moreover, several drugs are targeting kinases of the circadian clocks and can be used in cancer chronotherapy or to treat mood disorders. In Drosophila, recent experimental observations also revealed a complex role of the phosphorylations. Because of its high degree of homology with mammals, the Drosophila system is of particular interest. In the circadian clock of cyanobacteria, an atypical regulatory mechanism is based only on three clock proteins (KaiA, KaiB, KaiC) and ATP and is sufficient to produce robust temperature-compensated circadian oscillations of KaiC phosphorylation. This review will show how computational modeling has become a powerful and useful tool in investigating the regulatory mechanism of circadian clocks, but also how models can give rise to testable predictions or reveal unexpected results.