Circadian rhythms. Atomic-scale origins of slowness 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.

Light Wavelength as a Contributory Factor of Environmental Fitness in the Cyanobacterial Circadian Clock

A circadian clock is an essential system that drives the 24-h expression rhythms for adaptation to day-night cycles. The molecular mechanism of the circadian clock has been extensively studied in cyanobacteria harboring the KaiC-based timing system. Nevertheless, our understanding of the physiological significance of the cyanobacterial circadian clock is still limited. In this study, we cultured wild-type Synechococcus elongatus PCC 7942 and circadian clock mutants in day-night cycles at different light qualities and found that the growth of the circadian clock mutants was specifically impaired during 12-h blue light/12-h dark (BD) cycles for the first time. The arrhythmic mutant kaiCAA was further analyzed by photosynthetic measurements. Compared with the wild type, the mutant exhibited decreases in the chlorophyll content, the ratio of photosystem I to II, net O2 evolution rate and efficiency of photosystem II photochemistry during BD cycles. These results indicate that the circadian clock is necessary for the growth and the maintenance of the optimum function of the photosynthetic apparatus in cyanobacteria under blue photoperiodic conditions.

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.

The inner workings of an ancient biological clock

Circadian clocks evolved in diverse organisms as an adaptation to the daily swings in ambient light and temperature that derive from Earth's rotation. These timing systems, based on intracellular molecular oscillations, synchronize organisms' behavior and physiology with the 24-h environmental rhythm. The cyanobacterial clock serves as a special model for understanding circadian rhythms because it can be fully reconstituted in vitro. This review summarizes recent advances that leverage new biochemical, biophysical, and mathematical approaches to shed light on the molecular mechanisms of cyanobacterial Kai proteins that support the clock, and their homologues in other bacteria. Many questions remain in circadian biology, and the tools developed for the Kai system will bring us closer to the answers.

Deficiency of circadian clock gene Bmal1 exacerbates noncanonical inflammasome-mediated pyroptosis and lethality via Rev-erbα-C/EBPβ-SAA1 axis

Circadian arrhythmia has been linked to increased susceptibility to multiple inflammatory diseases, such as sepsis. However, it remains unclear how disruption of the circadian clock modulates molecular aspects of innate immune responses, including inflammasome signaling. Here, we examined the potential role of the circadian clock in inflammasome-mediated responses through myeloid-specific deletion of BMAL1, a master circadian clock regulator. Intriguingly, Bmal1 deficiency significantly enhanced pyroptosis of macrophages and lethality of mice under noncanonical inflammasome-activating conditions but did not alter canonical inflammasome responses. Transcriptome analysis of enriched peritoneal myeloid cells revealed that Bmal1 deficiency led to a marked reduction in Rev-erbα expression at steady state and a significant increase in serum amyloid A1 (SAA1) expression upon poly(I:C) stimulation. Notably, we found that the circadian regulator Rev-erbα is critical for poly(I:C)- or interferon (IFN)-β-induced SAA1 production, resulting in the circadian oscillation pattern of SAA1 expression in myeloid cells. Furthermore, exogenously applied SAA1 markedly increased noncanonical inflammasome-mediated pyroptosis of macrophages and lethality of mice. Intriguingly, our results revealed that type 1 IFN receptor signaling is needed for poly(I:C)- or IFN-β-induced SAA1 production. Downstream of the type 1 IFN receptor, Rev-erbα inhibited the IFN-β-induced association of C/EBPβ with the promoter region of Saa1, leading to the reduced transcription of Saa1 in macrophages. Bmal1-deficient macrophages exhibited enhanced binding of C/EBPβ to Saa1. Consistently, the blockade of Rev-erbα by SR8278 significantly increased poly(I:C)-stimulated SAA1 transcription and noncanonical inflammasome-mediated lethality in mice. Collectively, our data demonstrate a potent suppressive effect of the circadian clock BMAL1 on the noncanonical inflammasome response via the Rev-erbα-C/EBPβ-SAA1 axis.

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.

Studying the Human Microbiota: Advances in Understanding the Fundamentals, Origin, and Evolution of Biological Timekeeping

The recently observed circadian oscillations of the intestinal microbiota underscore the profound nature of the human-microbiome relationship and its importance for health. Together with the discovery of circadian clocks in non-photosynthetic gut bacteria and circadian rhythms in anucleated cells, these findings have indicated the possibility that virtually all microorganisms may possess functional biological clocks. However, they have also raised many essential questions concerning the fundamentals of biological timekeeping, its evolution, and its origin. This narrative review provides a comprehensive overview of the recent literature in molecular chronobiology, aiming to bring together the latest evidence on the structure and mechanisms driving microbial biological clocks while pointing to potential applications of this knowledge in medicine. Moreover, it discusses the latest hypotheses regarding the evolution of timing mechanisms and describes the functions of peroxiredoxins in cells and their contribution to the cellular clockwork. The diversity of biological clocks among various human-associated microorganisms and the role of transcriptional and post-translational timekeeping mechanisms are also addressed. Finally, recent evidence on metabolic oscillators and host-microbiome communication is presented.

Spatial-Temporal Genome Regulation in Stress-Response and Cell-Fate Change

Complex functioning of the genome in the cell nucleus is controlled at different levels: (a) the DNA base sequence containing all relevant inherited information; (b) epigenetic pathways consisting of protein interactions and feedback loops; (c) the genome architecture and organization activating or suppressing genetic interactions between different parts of the genome. Most research so far has shed light on the puzzle pieces at these levels. This article, however, attempts an integrative approach to genome expression regulation incorporating these different layers. Under environmental stress or during cell development, differentiation towards specialized cell types, or to dysfunctional tumor, the cell nucleus seems to react as a whole through coordinated changes at all levels of control. This implies the need for a framework in which biological, chemical, and physical manifestations can serve as a basis for a coherent theory of gene self-organization. An international symposium held at the Biomedical Research and Study Center in Riga, Latvia, on 25 July 2022 addressed novel aspects of the abovementioned topic. The present article reviews the most recent results and conclusions of the state-of-the-art research in this multidisciplinary field of science, which were delivered and discussed by scholars at the Riga symposium.

Common Patterns of Hydrolysis Initiation in P-loop Fold Nucleoside Triphosphatases

The P-loop fold nucleoside triphosphate (NTP) hydrolases (also known as Walker NTPases) function as ATPases, GTPases, and ATP synthases, are often of medical importance, and represent one of the largest and evolutionarily oldest families of enzymes. There is still no consensus on their catalytic mechanism. To clarify this, we performed the first comparative structural analysis of more than 3100 structures of P-loop NTPases that contain bound substrate Mg-NTPs or their analogues. We proceeded on the assumption that structural features common to these P-loop NTPases may be essential for catalysis. Our results are presented in two articles. Here, in the first, we consider the structural elements that stimulate hydrolysis. Upon interaction of P-loop NTPases with their cognate activating partners (RNA/DNA/protein domains), specific stimulatory moieties, usually Arg or Lys residues, are inserted into the catalytic site and initiate the cleavage of gamma phosphate. By analyzing a plethora of structures, we found that the only shared feature was the mechanistic interaction of stimulators with the oxygen atoms of gamma-phosphate group, capable of causing its rotation. One of the oxygen atoms of gamma phosphate coordinates the cofactor Mg ion. The rotation must pull this oxygen atom away from the Mg ion. This rearrangement should affect the properties of the other Mg ligands and may initiate hydrolysis according to the mechanism elaborated in the second article.

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.

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.

Coupling of distant ATPase domains in the circadian clock protein KaiC

The AAA⁺ family member KaiC is the central pacemaker for circadian rhythms in the cyanobacterium Synechococcus elongatus. Composed of two hexameric rings of adenosine triphosphatase (ATPase) domains with tightly coupled activities, KaiC undergoes a cycle of autophosphorylation and autodephosphorylation on its C-terminal (CII) domain that restricts binding of clock proteins on its N-terminal (CI) domain to the evening. Here, we use cryogenic-electron microscopy to investigate how daytime and nighttime states of CII regulate KaiB binding on CI. We find that the CII hexamer is destabilized during the day but takes on a rigidified C₂-symmetric state at night, concomitant with ring-ring compression. Residues at the CI-CII interface are required for phospho-dependent KaiB association, coupling ATPase activity on CI to cooperative KaiB recruitment. Together, these studies clarify a key step in the regulation of cyanobacterial circadian rhythms by KaiC phosphorylation.

Highly Sensitive Tryptophan Fluorescence Probe for detecting Rhythmic Conformational changes of KaiC in the Cyanobacterial Circadian Clock System

KaiC, a core protein of the cyanobacterial circadian clock, consists of an N-terminal CI domain and a C-terminal CII domain, and assembles into a double-ring hexamer upon binding with ATP. KaiC rhythmically phosphorylates and dephosphorylates its own two adjacent residues Ser431 and Thr432 at the CII domain with a period of approximately 24h through assembly and disassembly with the other clock proteins, KaiA and/or KaiB. In this study, to understand how KaiC alters its conformation as the source of circadian rhythm, we investigated structural changes of an inner-radius side of the CII ring using time-resolved Trp fluorescence spectroscopy. A KaiC mutant harboring a Trp fluorescence probe at a position of 419 exhibited a robust circadian rhythm with little temperature sensitivity in the presence of KaiA and KaiB. Our fluorescence observations show a remarkable environmental change at the inner-radius side of the CII ring during circadian oscillation. Crystallographic analysis revealed that a side chain of Trp at the position of 419 was oriented toward a region undergoing a helix-coil transition, which is considered to be a key event to allosterically regulate the CI ring that plays a crucial role in determining the cycle period. The present study provides a dynamical insight into how KaiC generates circadian oscillation.

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.

An Adenosine Triphosphate- Dependent 5'-3' DNA Helicase From sk1-Like Lactococcus lactis F13 Phage

Here, we describe functional characterization of an early gene (gp46) product of a virulent Lactococcus lactis sk1-like phage, vB_Llc_bIBBF13 (abbr. F13). The GP46_F13 protein carries a catalytically active RecA-like domain belonging to the P-loop NTPase superfamily. It also retains features characteristic for ATPases forming oligomers. In order to elucidate its detailed molecular function, we cloned and overexpressed the gp46 gene in Escherichia coli. Purified GP46_F13 protein binds to DNA and exhibits DNA unwinding activity on branched substrates in the presence of adenosine triphosphate (ATP). Size exclusion chromatography with multi-angle light scattering (SEC-MALS) experiments demonstrate that GP46_F13 forms oligomers, and further pull-down assays show that GP46_F13 interacts with host proteins involved in replication (i.e., DnaK, DnaJ, topoisomerase I, and single-strand binding protein). Taking together the localization of the gene and the obtained results, GP46_F13 is the first protein encoded in the early-expressed gene region with helicase activity that has been identified among lytic L. lactis phages up to date.

Multimeric structure enables the acceleration of KaiB-KaiC complex formation induced by ADP/ATP exchange inhibition

Circadian clocks tick a rhythm with a nearly 24-hour period in a variety of organisms. In the clock proteins of cyanobacteria, KaiA, KaiB, and KaiC, known as a minimum circadian clock, the slow KaiB-KaiC complex formation is essential in determining the clock period. This complex formation, occurring when the C1 domain of KaiC hexamer binds ADP molecules produced by the ATPase activity of C1, is considered to be promoted by accumulating ADP molecules in C1 through inhibiting the ADP/ATP exchange (ADP release) rather than activating the ATP hydrolysis (ADP production). Significantly, this ADP/ATP exchange inhibition accelerates the complex formation together with its promotion, implying a potential role in the period robustness under environmental perturbations. However, the molecular mechanism of this simultaneous promotion and acceleration remains elusive because inhibition of a backward process generally slows down the whole process. In this article, to investigate the mechanism, we build several reaction models of the complex formation with the pre-binding process concerning the ATPase activity. In these models, six KaiB monomers cooperatively and rapidly bind to C1 when C1 binds ADP molecules more than a given threshold while stabilizing the binding-competent conformation of C1. Through comparison among the models proposed here, we then extract three requirements for the simultaneous promotion and acceleration: the stabilization of the binding-competent C1 by KaiB binding, slow ADP/ATP exchange in the binding-competent C1, and relatively fast ADP/ATP exchange occurring in the binding-incompetent C1 in the presence of KaiB. The last two requirements oblige KaiC to form a multimer. Moreover, as a natural consequence, the present models can also explain why the binding of KaiB to C1 reduces the ATPase activity of C1.

Circadian clocks tick a rhythm with a nearly 24-hour period in various organisms. The cyanobacterial circadian clock, composed of only three proteins, KaiA, KaiB, and KaiC, has attracted much attention because of its simplicity. The slow KaiB-KaiC complex formation is essential in determining the clock period in this system. Significantly, this complex formation is accelerated together with its promotion, implying a potential role in the period-keeping mechanism. However, this simultaneous promotion and acceleration is theoretically exceptional because this complex formation is promoted by inhibiting a backward process, which generally slows down the whole process. In this article, we investigate the molecular mechanism of this phenomenon by building mathematical models to find that the binding of KaiB to C1 must lower the ADP/ATP exchange of the C1 domain of KaiC via stabilizing the binding-competent conformation of C1. The present results would be of benefit for future investigations on functional roles of the simultaneous promotion and acceleration in the KaiABC oscillator.

Spectres of Clock Evolution: Past, Present, and Yet to Come

Circadian clocks are phylogenetically widespread biological oscillators that allow organisms to entrain to environmental cycles and use their steady-state phase relationship to anticipate predictable daily phenomena – such as the light-dark transitions of a day – and prepare accordingly. Present from cyanobacteria to mammals, circadian clocks are evolutionarily ancient and are thought to increase the fitness of the organisms that possess them by allowing for better resource usage and/or proper internal temporal order. Here, we review literature with respect to the ecology and evolution of circadian clocks, with a special focus on cyanobacteria as model organisms. We first discuss what can be inferred about future clock evolution in response to climate change, based on data from latitudinal clines and domestication. We then address our current understanding of the role that circadian clocks might be contributing to the adaptive fitness of cyanobacteria at the present time. Lastly, we discuss what is currently known about the oldest known circadian clock, and the early Earth conditions that could have led to its evolution.

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.

Reconstitution of an intact clock reveals mechanisms of circadian timekeeping

[Figure: see text].

CHRONO and DEC1/DEC2 compensate for lack of CRY1/CRY2 in expression of coherent circadian rhythm but not in generation of circadian oscillation in the neonatal mouse SCN

Clock genes Cry1 and Cry2, inhibitory components of core molecular feedback loop, are regarded as critical molecules for the circadian rhythm generation in mammals. A double knockout of Cry1 and Cry2 abolishes the circadian behavioral rhythm in adult mice under constant darkness. However, robust circadian rhythms in PER2::LUC expression are detected in the cultured suprachiasmatic nucleus (SCN) of Cry1/Cry2 deficient neonatal mice and restored in adult SCN by co-culture with wild-type neonatal SCN. These findings led us to postulate the compensatory molecule(s) for Cry1/Cry2 deficiency in circadian rhythm generation. We examined the roles of Chrono and Dec1/Dec2 proteins, the suppressors of Per(s) transcription similar to CRY(s). Unexpectedly, knockout of Chrono or Dec1/Dec2 in the Cry1/Cry2 deficient mice did not abolish but decoupled the coherent circadian rhythm into three different periodicities or significantly shortened the circadian period in neonatal SCN. DNA microarray analysis for the SCN of Cry1/Cry2 deficient mice revealed substantial increases in Per(s), Chrono and Dec(s) expression, indicating disinhibition of the transactivation by BMAL1/CLOCK. Here, we conclude that Chrono and Dec1/Dec2 do not compensate for absence of CRY1/CRY2 in the circadian rhythm generation but contribute to the coherent circadian rhythm expression in the neonatal mouse SCN most likely through integration of cellular circadian rhythms.

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.

Rhythmic adenosine triphosphate release from the cyanobacterial circadian clock protein KaiC revealed by real-time monitoring of bioluminescence using firefly luciferase

The cyanobacterial circadian clock is composed of three clock proteins, KaiA, KaiB and KaiC. This KaiABC clock system can be reconstituted in vitro in the presence of adenosine triphosphate (ATP) and Mg²⁺ , and shows circadian rhythms in the phosphorylation level and ATPase activity of KaiC. Previously, we found that ATP regulates a complex formation between KaiB and KaiC, and KaiC releases ATP from KaiC itself (PLoS One, 8, 2013, e80200). In this study, we examined whether the ATP release from KaiC shows any rhythms in vitro. We monitored the release of ATP from wild-type and ATPase motif mutants of KaiC as a bioluminescence in real time using a firefly luciferase assay in vitro and obtained the following results: (a) ATP release from KaiC oscillated even without KaiA and KaiB although period of the oscillation was not 24 hr; (b) ATP was mainly released from the N-terminal domain of KaiC; and (c) the ATP release was enhanced and suppressed by KaiB and KaiA, respectively. These results suggest that KaiC can generate basal oscillation as a core clock without KaiA and KaiB, whereas these two proteins contribute to adjusting and stabilizing the oscillation.

Functional and Regulatory Roles of Fold-Switching Proteins

Fold-switching proteins respond to cellular stimuli by remodeling their secondary structures and changing their functions. Whereas several previous reviews have focused on various structural, physical-chemical, and evolutionary aspects of this newly emerging class of proteins, this minireview focuses on how fold switching modulates protein function and regulates biological processes. It first compares and contrasts fold switchers with other known types of proteins. Second, it presents examples of how various proteins can change their functions through fold switching. Third, it demonstrates that fold switchers can regulate biological processes by discussing two proteins, RfaH and KaiB, whose dramatic secondary structure remodeling events directly affect gene expression and a circadian clock, respectively. Finally, this minireview discusses how the field of protein fold switching might advance.

Tuning the circadian period of cyanobacteria up to 6.6 days by the single amino acid substitutions in KaiC

The circadian clock of cyanobacteria consists of only three clock proteins, KaiA, KaiB, and KaiC, which generate a circadian rhythm of KaiC phosphorylation in vitro. The adenosine triphosphatase (ATPase) activity of KaiC is the source of the 24-h period and temperature compensation. Although numerous circadian mutants of KaiC have been identified, the tuning mechanism of the 24-h period remains unclear. Here, we show that the circadian period of in vitro phosphorylation rhythm of mutants at position 402 of KaiC changed dramatically, from 15 h (0.6 d) to 158 h (6.6 d). The ATPase activities of mutants at position 402 of KaiC, without KaiA and KaiB, correlated with the frequencies (1/period), indicating that KaiC structure was the source of extra period change. Despite the wide-range tunability, temperature compensation of both the circadian period and the KaiC ATPase activity of mutants at position 402 of KaiC were nearly intact. We also found that in vivo and in vitro circadian periods and the KaiC ATPase activity of mutants at position 402 of KaiC showed a correlation with the side-chain volume of the amino acid at position 402 of KaiC. Our results indicate that residue 402 is a key position of determining the circadian period of cyanobacteria, and it is possible to dramatically alter the period of KaiC while maintaining temperature compensation.

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.

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.

Biophysical research in Okazaki, Japan

This commentary summarizes the recent biophysical research conducted at the National Institute for Basic Biology, the National Institute for Physiological Sciences, and the Institute for Molecular Science in Okazaki, Japan.

Casein kinase 1 dynamics underlie substrate selectivity and the PER2 circadian phosphoswitch

Post-translational control of PERIOD stability by Casein Kinase 1δ and ε (CK1) plays a key regulatory role in metazoan circadian rhythms. Despite the deep evolutionary conservation of CK1 in eukaryotes, little is known about its regulation and the factors that influence substrate selectivity on functionally antagonistic sites in PERIOD that directly control circadian period. Here we describe a molecular switch involving a highly conserved anion binding site in CK1. This switch controls conformation of the kinase activation loop and determines which sites on mammalian PER2 are preferentially phosphorylated, thereby directly regulating PER2 stability. Integrated experimental and computational studies shed light on the allosteric linkage between two anion binding sites that dynamically regulate kinase activity. We show that period-altering kinase mutations from humans to Drosophila differentially modulate this activation loop switch to elicit predictable changes in PER2 stability, providing a foundation to understand and further manipulate CK1 regulation of circadian rhythms.

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.

Pressure accelerates the circadian clock of cyanobacteria

Although organisms are exposed to various pressure and temperature conditions, information remains limited on how pressure affects biological rhythms. This study investigated how hydrostatic pressure affects the circadian clock (KaiA, KaiB, and KaiC) of cyanobacteria. While the circadian rhythm is inherently robust to temperature change, KaiC phosphorylation cycles that were accelerated from 22 h at 1 bar to 14 h at 200 bars caused the circadian-period length to decline. This decline was caused by the pressure-induced enhancement of KaiC ATPase activity and allosteric effects. Because ATPase activity was elevated in the CI and CII domains of KaiC, while ATP hydrolysis had negative activation volumes (ΔV^≠), both domains played key roles in determining the period length of the KaiC phosphorylation cycle. The thermodynamic contraction of the structure of the active site during the transition state might have positioned catalytic residues and lytic water molecules favourably to facilitate ATP hydrolysis. Internal cavities might represent sources of compaction and structural rearrangement in the active site. Overall, the data indicate that pressure differences could alter the circadian rhythms of diverse organisms with evolved thermotolerance, as long as enzymatic reactions defining period length have a specific activation volume.

IL-23-producing IL-10Rα-deficient gut macrophages elicit an IL-22-driven proinflammatory epithelial cell response

Cytokines maintain intestinal health, but precise intercellular communication networks remain poorly understood. Macrophages are immune sentinels of the intestinal tissue and are critical for gut homeostasis. Here, we show that in a murine inflammatory bowel disease (IBD) model based on macrophage-restricted interleukin-10 (IL-10) receptor deficiency (Cx3cr1Cre:Il10rafl/fl mice), proinflammatory mutant gut macrophages cause severe spontaneous colitis resembling the condition observed in children carrying IL-10R mutations. We establish macrophage-derived IL-23 as the driving factor of this pathology. Specifically, we report that Cx3cr1Cre:Il10rafl/fl:Il23afl/fl mice harboring macrophages deficient for both IL-10R and IL-23 are protected from colitis. By analyzing the epithelial response to proinflammatory macrophages, we provide evidence that T cells of colitic animals produce IL-22, which induces epithelial chemokine expression and detrimental neutrophil recruitment. Collectively, we define macrophage-specific contributions to the induction and pathogenesis of colitis, as manifested in mice harboring IL-10R deficiencies and human IBDs.

Development and Optimization of Expression, Purification, and ATPase Assay of KaiC for Medium-Throughput Screening of Circadian Clock Mutants in Cyanobacteria

The slow but temperature-insensitive adenosine triphosphate (ATP) hydrolysis reaction in KaiC is considered as one of the factors determining the temperature-compensated period length of the cyanobacterial circadian clock system. Structural units responsible for this low but temperature-compensated ATPase have remained unclear. Although whole-KaiC scanning mutagenesis can be a promising experimental strategy, producing KaiC mutants and assaying those ATPase activities consume considerable time and effort. To overcome these bottlenecks for in vitro screening, we optimized protocols for expressing and purifying the KaiC mutants and then designed a high-performance liquid chromatography system equipped with a multi-channel high-precision temperature controller to assay the ATPase activity of multiple KaiC mutants simultaneously at different temperatures. Through the present protocol, the time required for one KaiC mutant is reduced by approximately 80% (six-fold throughput) relative to the conventional protocol with reasonable reproducibility. For validation purposes, we picked up three representatives from 86 alanine-scanning KaiC mutants preliminarily investigated thus far and characterized those clock functions in detail.

A period without PER: understanding 24-hour rhythms without classic transcription and translation feedback loops

Since Ronald Konopka and Seymour Benzer's discovery of the gene Period in the 1970s, the circadian rhythm field has diligently investigated regulatory mechanisms and intracellular transcriptional and translation feedback loops involving Period, and these investigations culminated in a 2017 Nobel Prize in Physiology or Medicine for Michael W. Young, Michael Rosbash, and Jeffrey C. Hall. Although research on 24-hour behavior rhythms started with Period, a series of discoveries in the past decade have shown us that post-transcriptional regulation and protein modification, such as phosphorylation and oxidation, are alternatives ways to building a ticking clock.

KaiC from a cyanobacterium Gloeocapsa sp. PCC 7428 retains functional and structural properties required as the core of circadian clock system

KaiC, the core protein of the cyanobacterial clock, assembles into a hexamer upon ATP-binding. The hexameric KaiC from a cyanobacterium Synechococcus elongatus PCC 7942 (Se-KaiC) is a multifunctional enzyme with autokinase, autophosphatase and ATPase and these activities show a circadian rhythm in the presence of two other clock proteins, KaiA and KaiB both in vivo and in vitro. While an interplay among three enzymatic activities has been pointed out through studies on Se-KaiC as the basis of circadian rhythmicity in cyanobacteria, little is known about the structure and functions of KaiC from other cyanobacterial species. In this study, we established a protocol to prepare KaiC from Gloeocapsa sp. PCC 7428 (Gl-KaiC) belonging to a distinct genus from Synechococcus and characterized its oligomeric structure and function. The results demonstrate that Gl-KaiC shares the basic properties with Se-KaiC. The present protocol offers practical means for further analysis of structure and function of Gl-KaiC, which would provide insights into diversity and evolution of the clock systems in cyanobacteria.

Circadian oscillator proteins across the kingdoms of life: structural aspects

Circadian oscillators are networks of biochemical feedback loops that generate 24-hour rhythms in organisms from bacteria to animals. These periodic rhythms result from a complex interplay among clock components that are specific to the organism, but share molecular mechanisms across kingdoms. A full understanding of these processes requires detailed knowledge, not only of the biochemical properties of clock proteins and their interactions, but also of the three-dimensional structure of clockwork components. Posttranslational modifications and protein–protein interactions have become a recent focus, in particular the complex interactions mediated by the phosphorylation of clock proteins and the formation of multimeric protein complexes that regulate clock genes at transcriptional and translational levels. This review covers the structural aspects of circadian oscillators, and serves as a primer for this exciting realm of structural biology.

Effects of Stochastic Single-Molecule Reactions on Coherent Ensemble Oscillations in the KaiABC Circadian Clock

How do many constituent molecules in a biochemical system synchronize, giving rise to coherent system-level oscillations? One system that is particularly suitable for use in studying this problem is a mixture solution of three cyanobacterial proteins, KaiA, KaiB, and KaiC: the phosphorylation level of KaiC shows stable oscillations with a period of approximately 24 h when these three Kai proteins are incubated with ATP in vitro. Here, we analyze the mechanism behind synchronization in the KaiABC system theoretically by enhancing a model previously developed by the present author. Our simulation results suggest that positive feedback between stochastic ATP hydrolysis and the allosteric structural transitions in KaiC molecules drives oscillations of individual molecules and promotes synchronization of oscillations of many KaiC molecules. Our simulations also show that the ATPase activity of KaiC is correlated with the oscillation frequency of an ensemble of KaiC molecules. These results suggest that stochastic ATP hydrolysis in each KaiC molecule plays an important role in regulating the coherent system-level oscillations. This property is robust against changes in the binding and unbinding rate constants for KaiA to/from KaiC or KaiB, but the oscillations are sensitive to the rate constants of the KaiC phosphorylation and dephosphorylation reactions.

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.

Non-transcriptional processes in circadian rhythm generation

'Biological clocks' orchestrate mammalian biology to a daily rhythm. Whilst 'clock gene' transcriptional circuits impart rhythmic regulation to myriad cellular systems, our picture of the biochemical mechanisms that determine their circadian (∼24 hour) period is incomplete. Here we consider the evidence supporting different models for circadian rhythm generation in mammalian cells in light of evolutionary factors. We find it plausible that the circadian timekeeping mechanism in mammalian cells is primarily protein-based, signalling biological timing information to the nucleus by the post-translational regulation of transcription factor activity, with transcriptional feedback imparting robustness to the oscillation via hysteresis. We conclude by suggesting experiments that might distinguish this model from competing paradigms.

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.

Design Principles of Phosphorylation-Dependent Timekeeping in Eukaryotic Circadian Clocks

The circadian clock in cyanobacteria employs a posttranslational oscillator composed of a sequential phosphorylation-dephosphorylation cycle of KaiC protein, in which the dynamics of protein structural changes driven by temperature-compensated KaiC's ATPase activity are critical for determining the period. On the other hand, circadian clocks in eukaryotes employ transcriptional feedback loops as a core mechanism. In this system, the dynamics of protein accumulation and degradation affect the circadian period. However, recent studies of eukaryotic circadian clocks reveal that the mechanism controlling the circadian period can be independent of the regulation of protein abundance. Instead, the circadian substrate is often phosphorylated at multiple sites at flexible protein regions to induce structural changes. The phosphorylation is catalyzed by kinases that induce sequential multisite phosphorylation such as casein kinase 1 (CK1) with temperature-compensated activity. We propose that the design principles of phosphorylation-dependent circadian-period determination in eukaryotes may share characteristics with the posttranslational oscillator in cyanobacteria.

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.

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.

The mammalian circadian system: a hierarchical multi-oscillator structure for generating circadian rhythm

The circadian nature of physiology and behavior is regulated by a circadian clock that generates intrinsic rhythms with a periodicity of approximately 24 h. The mammalian circadian system is composed of a hierarchical multi-oscillator structure, with the central clock located in the suprachiasmatic nucleus (SCN) of the hypothalamus regulating the peripheral clocks found throughout the body. In the past two decades, key clock genes have been discovered in mammals and shown to be interlocked in transcriptional and translational feedback loops. At the cellular level, each cell is governed by its own independent clock; and yet, these cellular circadian clocks in the SCN form regional oscillators that are further coupled to one another to generate a single rhythm for the tissue. The oscillatory coupling within and between the regional oscillators appears to be critical for the extraordinary stability and the wide range of adaptability of the circadian clock, the mechanism of which is now being elucidated with newly advanced molecular tools.

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.

Time from Semiosis: E-series Time for Living Systems

We develop a semiotic scheme of time, in which time precipitates from the repeated succession of punctuating the progressive tense by the perfect tense. The underlying principle is communication among local participants. Time can thus be seen as a meaning-making, semiotic system in which different time codes are delineated, each having its own grammar and timekeeping. The four time codes discussed are the following: the subjective time having tense, the objective time without tense, the static time without timekeeping, and the inter-subjective time of the E-series. Living organisms adopt a time code called the E-series, which emerges through the local synchronization among organisms or parts of organisms. The inter-subjective time is a new theoretical dimension resulting from the time-aligning activities of interacting agents. Such synchronization in natural settings consists of incessant mutual corrections and adjustments to one's own punctuation, which is then constantly updated. Unlike the third-person observer keeping the objective time while sitting outside a clock, the second-person negotiators participate in forming the E-series time by punctuating and updating the interface through which different tenses meet at the moment of "now." Although physics allows physicists to be the only interpreters, the semiotic perspective upends the physical perspective by letting local participants be involved in the interpretation of their mutual negotiations to precipitate that which is called time.