Elucidating the ticking of an in vitro circadian clockwork

Subunit shuffling dynamics in KaiC's central hub reveal the synchronization mechanism of the cyanobacterial circadian clock

Protein complexes are critical for cellular functions, and subunit exchange within these complexes is increasingly recognized as a key regulatory mechanism. In the cyanobacterial circadian clock, subunits shuffling of the core clock protein KaiC is thought to synchronize the clock, though the underlying mechanism remains unclear. We developed a chromatography-based method to monitor the shuffling dynamics of hexamerization domain of KaiC (KaiC-CI) and found that ATPase activity is essential for this process. By analyzing experiment data with quantitative models, we found that KaiC-CI hexamer stochastically disassembles into two oligomers for shuffling after hydrolysis. Further, by assuming a hidden conformation for post-hydrolysis hexamers, we established an ATPase activity-dependent model that quantitatively describes the shuffling dynamics of KaiC-CI hexamers, linking the shuffling rate to ATP hydrolysis and nucleotide exchange rates. Using this model, we estimated the shuffling dynamics of full-length KaiC with indirect experimental data. Our findings suggest that KaiC's phosphorylation states regulate nucleotide exchange rates in the CI domain, thereby modulating ATPase activity and influencing subunit shuffling. This study provides a mechanistic framework for understanding the role of ATPase activity in subunit exchange and its implications for circadian clock regulation.

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

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

Perfecting the Life Clock: The Journey from PTO to TTFL

The ubiquity of biological rhythms in life implies that it results from selection in the evolutionary process. The origin of the biological clock has two possible hypotheses: the selective pressure hypothesis of the oxidative stress cycle and the light evasion hypothesis. Moreover, the biological clock gives life higher adaptability. Two biological clock mechanisms have been discovered: the negative feedback loop of transcription-translation (TTFL) and the post-translational oscillation mechanism (PTO). The TTFL mechanism is the most classic and relatively conservative circadian clock oscillation mechanism, commonly found in eukaryotes. We have introduced the TTFL mechanism of the classical model organisms. However, the biological clock of prokaryotes is based on the PTO mechanism. The Peroxiredoxin (PRX or PRDX) protein-based PTO mechanism circadian clock widely existing in eukaryotic and prokaryotic life is considered a more conservative oscillation mechanism. The coexistence of the PTO and TTFL mechanisms in eukaryotes prompted us to explain the relationship between the two. Finally, we speculated that there might be a driving force for the evolution of the biological clock. The biological clock may have an evolutionary trend from the PTO mechanism to the TTFL mechanism, resulting from the evolution of organisms adapting to the environment.

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.

Overall structure of fully assembled cyanobacterial KaiABC circadian clock complex by an integrated experimental-computational approach

In the cyanobacterial circadian clock system, KaiA, KaiB and KaiC periodically assemble into a large complex. Here we determined the overall structure of their fully assembled complex by integrating experimental and computational approaches. Small-angle X-ray and inverse contrast matching small-angle neutron scatterings coupled with size-exclusion chromatography provided constraints to highlight the spatial arrangements of the N-terminal domains of KaiA, which were not resolved in the previous structural analyses. Computationally built 20 million structural models of the complex were screened out utilizing the constrains and then subjected to molecular dynamics simulations to examine their stabilities. The final model suggests that, despite large fluctuation of the KaiA N-terminal domains, their preferential positionings mask the hydrophobic surface of the KaiA C-terminal domains, hindering additional KaiA-KaiC interactions. Thus, our integrative approach provides a useful tool to resolve large complex structures harboring dynamically fluctuating domains.

The revealed full KaiA₁₂B₆C₆ complex is assembled including the dynamic and asynchronous KaiA N-terminal domains that have been missing in cryo-EM structures.

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.

Exploring cyclic networks of multisite modification reveals origins of information processing characteristics

Multisite phosphorylation (and generally multisite modification) is a basic way of encoding substrate function and circuits/networks of post-translational modifications (PTM) are ubiquitous in cell signalling. The information processing characteristics of PTM systems are a focal point of broad interest. The ordering of modifications is a key aspect of multisite modification, and a broad synthesis of the impact of ordering of modifications is still missing. We focus on a basic class of multisite modification circuits: the cyclic mechanism, which corresponds to the same ordering of phosphorylation and dephosphorylation, and examine multiple variants involving common/separate kinases and common/separate phosphatases. This is of interest both because it is encountered in concrete cellular contexts, and because it serves as a bridge between ordered (sequential) mechanisms (representing one type of ordering) and random mechanisms (which have no ordering). We show that bistability and biphasic dose response curves of the maximally modified phosphoform are ruled out for basic structural reasons independent of parameters, while oscillations can result with even just one shared enzyme. We then examine the effect of relaxing some basic assumptions about the ordering of modification. We show computationally and analytically how bistability, biphasic responses and oscillations can be generated by minimal augmentations to the cyclic mechanism even when these augmentations involved reactions operating in the unsaturated limit. All in all, using this approach we demonstrate (1) how the cyclic mechanism (with single augmentations) represents a modification circuit using minimal ingredients (in terms of shared enzymes and sequestration of enzymes) to generate bistability and oscillations, when compared to other mechanisms, (2) new design principles for rationally designing PTM systems for a variety of behaviour, (3) a basis and a necessary step for understanding the origins and robustness of behaviour observed in basic multisite modification systems.

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.

Real-Time In Vitro Fluorescence Anisotropy of the Cyanobacterial Circadian Clock

Uniquely, the circadian clock of cyanobacteria can be reconstructed outside the complex milieu of live cells, greatly simplifying the investigation of a functioning biological chronometer. The core oscillator component is composed of only three proteins, KaiA, KaiB, and KaiC, and together with ATP they undergo waves of assembly and disassembly that drive phosphorylation rhythms in KaiC. Typically, the time points of these reactions are analyzed ex post facto by denaturing polyacrylamide gel electrophoresis, because this technique resolves the different states of phosphorylation of KaiC. Here, we describe a more sensitive method that allows real-time monitoring of the clock reaction. By labeling one of the clock proteins with a fluorophore, in this case KaiB, the in vitro clock reaction can be monitored by fluorescence anisotropy on the minutes time scale for weeks.

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.

Computational modelling unravels the precise clockwork of cyanobacteria

Precisely timing the regulation of gene expression by anticipating recurring environmental changes is a fundamental part of global gene regulation. Circadian clocks are one form of this regulation, which is found in both eukaryotes and prokaryotes, providing a fitness advantage for these organisms. Whereas many different eukaryotic groups harbour circadian clocks, cyanobacteria are the only known oxygenic phototrophic prokaryotes to regulate large parts of their genes in a circadian fashion. A decade of intensive research on the mechanisms and functionality using computational and mathematical approaches in addition to the detailed biochemical and biophysical understanding make this the best understood circadian clock. Here, we summarize the findings and insights into various parts of the cyanobacterial circadian clock made by mathematical modelling. These findings have implications for eukaryotic circadian research as well as synthetic biology harnessing the power and efficiency of global gene regulation.

Robustness of Clocks to Input Noise

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

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

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

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.

Role of ATP Hydrolysis in Cyanobacterial Circadian Oscillator

A cyanobacterial protein KaiC shows a stable oscillation in its phosphorylation level with approximately one day period when three proteins, KaiA, KaiB, and KaiC, are incubated in the presence of ATP in vitro. During this oscillation, KaiC hydrolyzes more ATP molecules than required for phosphorylation. Here, in this report, a theoretical model of the KaiABC oscillator is developed to elucidate the role of this ATP consumption by assuming multifold feedback relations among reactions and structural transition in each KaiC molecule and the structure-dependent binding reactions among Kai proteins. Results of numerical simulation showed that ATP hydrolysis is a driving mechanism of the phosphorylation oscillation in the present model, and that the frequency of ATP hydrolysis in individual KaiC molecules is correlated to the frequency of oscillation in the ensemble of many Kai molecules, which indicates that the coherent oscillation is generated through the coupled microscopic intramolecular and ensemble-level many-molecular regulations.

Architecture and mechanism of the central gear in an ancient molecular timer

Molecular clocks are the product of natural selection in organisms from bacteria to human and their appearance early in evolution such as in the prokaryotic cyanobacterium Synechococcus elongatus suggests that these timers served a crucial role in genetic fitness. Thus, a clock allows cyanobacteria relying on photosynthesis and nitrogen fixation to temporally space the two processes and avoid exposure of nitrogenase carrying out fixation to high levels of oxygen produced during photosynthesis. Fascinating properties of molecular clocks are the long time constant, their precision and temperature compensation. Although these are hallmarks of all circadian oscillators, the actual cogs and gears that control clocks vary widely between organisms, indicating that circadian timers evolved convergently multiple times, owing to the selective pressure of an environment with a daily light/dark cycle. In S. elongatus, the three proteins KaiA, KaiB and KaiC in the presence of ATP constitute a so-called post-translational oscillator (PTO). The KaiABC PTO can be reconstituted in an Eppendorf tube and keeps time in a temperature-compensated manner. The ease by which the KaiABC clock can be studied in vitro has made it the best-investigated molecular clock system. Over the last decade, structures of all three Kai proteins and some of their complexes have emerged and mechanistic aspects have been analysed in considerable detail. This review focuses on the central gear of the S. elongatus clock and only enzyme among the three proteins: KaiC. Our determination of the three-dimensional structure of KaiC early in the quest for a better understanding of the inner workings of the cyanobacterial timer revealed its unusual architecture and conformational differences and unique features of the two RecA-like domains constituting KaiC. The structure also pinpointed phosphorylation sites and differential interactions with ATP molecules at subunit interfaces, and helped guide experiments to ferret out mechanistic aspects of the ATPase, auto-phosphorylation and auto-dephosphorylation reactions catalysed by the homo-hexamer. Comparisons between the structure of KaiC and those of nanomachines such as F1-ATPase and CaMKII also exposed shared architectural features (KaiC/ATPase), mechanistic principles (KaiC/CaMKII) and phenomena, such as subunit exchange between hexameric particles critical for function (clock synchronization, KaiABC; memory-storage, CaMKII).

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

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

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

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

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

Timing the day: what makes bacterial clocks tick?

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

Systems Biology-Derived Discoveries of Intrinsic Clocks

A systems approach to studying biology uses a variety of mathematical, computational, and engineering tools to holistically understand and model properties of cells, tissues, and organisms. Building from early biochemical, genetic, and physiological studies, systems biology became established through the development of genome-wide methods, high-throughput procedures, modern computational processing power, and bioinformatics. Here, we highlight a variety of systems approaches to the study of biological rhythms that occur with a 24-h period-circadian rhythms. We review how systems methods have helped to elucidate complex behaviors of the circadian clock including temperature compensation, rhythmicity, and robustness. Finally, we explain the contribution of systems biology to the transcription-translation feedback loop and posttranslational oscillator models of circadian rhythms and describe new technologies and "-omics" approaches to understand circadian timekeeping and neurophysiology.

Toward Multiscale Models of Cyanobacterial Growth: A Modular Approach

Oxygenic photosynthesis dominates global primary productivity ever since its evolution more than three billion years ago. While many aspects of phototrophic growth are well understood, it remains a considerable challenge to elucidate the manifold dependencies and interconnections between the diverse cellular processes that together facilitate the synthesis of new cells. Phototrophic growth involves the coordinated action of several layers of cellular functioning, ranging from the photosynthetic light reactions and the electron transport chain, to carbon-concentrating mechanisms and the assimilation of inorganic carbon. It requires the synthesis of new building blocks by cellular metabolism, protection against excessive light, as well as diurnal regulation by a circadian clock and the orchestration of gene expression and cell division. Computational modeling allows us to quantitatively describe these cellular functions and processes relevant for phototrophic growth. As yet, however, computational models are mostly confined to the inner workings of individual cellular processes, rather than describing the manifold interactions between them in the context of a living cell. Using cyanobacteria as model organisms, this contribution seeks to summarize existing computational models that are relevant to describe phototrophic growth and seeks to outline their interactions and dependencies. Our ultimate aim is to understand cellular functioning and growth as the outcome of a coordinated operation of diverse yet interconnected cellular processes.

Using computational models to discover and understand mechanisms

Areas of biology such as cell and molecular biology have been dominated by research directed at constructing mechanistic explanations that identify parts and operations that when organized appropriately are responsible for the various phenomena they investigate. Increasingly the mechanisms hypothesized involve non-sequential organization of non-linear operations and so exceed the ability of researchers to mentally rehearse their behavior. Accordingly, scientists rely on tools of computational modeling and dynamical systems theory in advancing dynamic mechanistic explanations. Using circadian rhythm research as an exemplar, this paper explores the variety of roles computational modeling is playing. They serve not just to determine whether the mechanism will produce the desired behavior, but in the discovery process of hypothesizing mechanisms and in understanding why proposed mechanisms behave as they do.

Evolution of KaiC-Dependent Timekeepers: A Proto-circadian Timing Mechanism Confers Adaptive Fitness in the Purple Bacterium Rhodopseudomonas palustris

Circadian (daily) rhythms are a fundamental and ubiquitous property of eukaryotic organisms. However, cyanobacteria are the only prokaryotic group for which bona fide circadian properties have been persuasively documented, even though homologs of the cyanobacterial kaiABC central clock genes are distributed widely among Eubacteria and Archaea. We report the purple non-sulfur bacterium Rhodopseudomonas palustris (that harbors homologs of kaiB and kaiC) only poorly sustains rhythmicity in constant conditions-a defining characteristic of circadian rhythms. Moreover, the biochemical characteristics of the Rhodopseudomonas homolog of the KaiC protein in vivo and in vitro are different from those of cyanobacterial KaiC. Nevertheless, R. palustris cells exhibit adaptive kaiC-dependent growth enhancement in 24-h cyclic environments, but not under non-natural constant conditions. Therefore, our data indicate that Rhodopseudomonas does not have a classical circadian rhythm, but a novel timekeeping mechanism that does not sustain itself in constant conditions. These results question the adaptive value of self-sustained oscillatory capability for daily timekeepers and establish new criteria for circadian-like systems that are based on adaptive properties (i.e., fitness enhancement in rhythmic environments), rather than upon observations of persisting rhythms in constant conditions. We propose that the Rhodopseudomonas system is a "proto" circadian timekeeper, as in an ancestral system that is based on KaiC and KaiB proteins and includes some, but not necessarily all, of the canonical properties of circadian clocks. These data indicate reasonable intermediate steps by which bona fide circadian systems evolved in simple organisms.

Circadian Clocks: Unexpected Biochemical Cogs

A circadian oscillation can be reconstituted in vitro from three proteins that cycles with a period of ∼ 24 h. Two recent studies provide surprising biochemical answers to why this remarkable oscillator has such a long time constant and how it can switch effortlessly between alternating enzymatic modes.

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.

Structural and biophysical methods to analyze clock function and mechanism

Structural approaches have provided insight into the mechanisms of circadian clock oscillators. This review focuses upon the myriad structural methods that have been applied to the molecular architecture of cyanobacterial circadian proteins, their interactions with each other, and the mechanism of the KaiABC posttranslational oscillator. X-ray crystallography and solution NMR were deployed to gain an understanding of the three-dimensional structures of the three proteins KaiA, KaiB, and KaiC that make up the inner timer in cyanobacteria. A hybrid structural biology approach including crystallography, electron microscopy, and solution scattering has shed light on the shapes of binary and ternary Kai protein complexes. Structural studies of the cyanobacterial oscillator demonstrate both the strengths and the limitations of the divide-and-conquer strategy. Thus, investigations of complexes involving domains and/or peptides have afforded valuable information into Kai protein interactions. However, high-resolution structural data are still needed at the level of complexes between the 360-kDa KaiC hexamer that forms the heart of the clock and its KaiA and KaiB partners.

KaiC intersubunit communication facilitates robustness of circadian rhythms in cyanobacteria

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

The cyanobacterial circadian oscillator comprises an autoregulatory loop that is driven by phosphorylation and dephosphorylation of the hexameric kinase KaiC. Kitayama et al. reveal how interactions between KaiC subunits regulate its catalytic activities and ensure robust circadian behaviour.

Intricate protein-protein interactions in the cyanobacterial circadian clock

The cyanobacterial circadian clock consists of a post-translational oscillator (PTO) and a PTO-dependent transcription-translation feedback loop (TTFL). The PTO can be reconstituted in vitro with the KaiA, KaiB, and KaiC proteins, enabling detailed biochemical and biophysical investigations. Both the CI and the CII halves of the KaiC hexamer harbor ATPases, but only the C-terminal CII ring exhibits kinase and phospho-transferase activities. KaiA stimulates the kinase and KaiB associates with KaiC during the dephosphorylation phase and sequesters KaiA. Recent research has led to conflicting models of the KaiB-KaiC interaction, precluding a clear understanding of KaiB function and KaiABC clock mechanism.

An arginine tetrad as mediator of input-dependent and input-independent ATPases in the clock protein KaiC

A post-translational oscillator (PTO) composed of the proteins KaiA, KaiB and KaiC is at the heart of the cyanobacterial circadian clock. KaiC interacts with KaiA and KaiB over the daily cycle, and CII domains undergo rhythmic phosphorylation/dephosphorylation with a 24 h period. Both the N-terminal (CI) and C-terminal (CII) rings of KaiC exhibit ATPase activity. The CI ATPase proceeds in an input-independent fashion, but the CII ATPase is subject to metabolic input signals. The crystal structure of KaiC from Thermosynechococcus elongatus allows insight into the different anatomies of the CI and CII ATPases. Four consecutive arginines in CI (Arg linker) that connect the P-loop, CI subunits and CI and CII at the ring interface are primary candidates for the coordination of the CI and CII activities. The mutation of linker residues alters the period or triggers arhythmic behavior. Comparison between the CI and CII structures also reveals differences in loop regions that are key to KaiA and KaiB binding and activation of CII ATPase and kinase. Common packing features in KaiC crystals shed light on the KaiB-KaiC interaction.

Systems-level characterization of the kernel mechanism of the cyanobacterial circadian oscillator

Circadian clock is an essential molecular regulatory mechanism that coordinates daily biological processes. Toward understanding the design principles of the circadian mechanism in cyanobacteria, the only prokaryotes reported to possess circadian rhythmicity, mathematical models have been used as important tools to help elucidate the complicated biochemical processes. In this study, we focus on elucidating the underlying systems properties that drive the oscillation of the cyanobacterial clockwork. We apply combined methods of time scale separation, phase space analysis, bifurcation analysis and sensitivity analysis to a model of the in vitro cyanobacterial circadian clock proposed by us recently. The original model is reduced to a three-dimensional slow subsystem by time scale separation. Phase space analysis of the reduced subsystem shows that the null-surface of the Serine-phosphorylated state (S-state) of KaiC is a bistable surface, and that the characteristic of the phase portrait indicates that the kernel mechanism of the clockwork behaves as a relaxation oscillator induced by interlinked positive and negative feedback loops. Phase space analysis together with perturbation analysis supports our previous viewpoint that the S-state of KaiC is plausibly a key component for the protein regulatory network of the cyanobacterial circadian clock.

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.

CryoEM and molecular dynamics of the circadian KaiB-KaiC complex indicates that KaiB monomers interact with KaiC and block ATP binding clefts

The circadian control of cellular processes in cyanobacteria is regulated by a posttranslational oscillator formed by three Kai proteins. During the oscillator cycle, KaiA serves to promote autophosphorylation of KaiC while KaiB counteracts this effect. Here, we present a crystallographic structure of the wild-type Synechococcus elongatus KaiB and a cryo-electron microscopy (cryoEM) structure of a KaiBC complex. The crystal structure shows the expected dimer core structure and significant conformational variations of the KaiB C-terminal region, which is functionally important in maintaining rhythmicity. The KaiBC sample was formed with a C-terminally truncated form of KaiC, KaiC-Δ489, which is persistently phosphorylated. The KaiB-KaiC-Δ489 structure reveals that the KaiC hexamer can bind six monomers of KaiB, which form a continuous ring of density in the KaiBC complex. We performed cryoEM-guided molecular dynamics flexible fitting simulations with crystal structures of KaiB and KaiC to probe the KaiBC protein-protein interface. This analysis indicated a favorable binding mode for the KaiB monomer on the CII end of KaiC, involving two adjacent KaiC subunits and spanning an ATP binding cleft. A KaiC mutation, R468C, which has been shown to affect the affinity of KaiB for KaiC and lengthen the period in a bioluminescence rhythm assay, is found within the middle of the predicted KaiBC interface. The proposed KaiB binding mode blocks access to the ATP binding cleft in the CII ring of KaiC, which provides insight into how KaiB might influence the phosphorylation status of KaiC.

Nuclear magnetic resonance spectroscopy of the circadian clock of cyanobacteria

The most well-understood circadian clock at the level of molecular mechanisms is that of cyanobacteria. This overview is on how solution-state nuclear magnetic resonance (NMR) spectroscopy has contributed to this understanding. By exciting atomic spin-½ nuclei in a strong magnetic field, NMR obtains information on their chemical environments, inter-nuclear distances, orientations, and motions. NMR protein samples are typically aqueous, often at near-physiological pH, ionic strength, and temperature. The level of information obtainable by NMR depends on the quality of the NMR sample, by which we mean the solubility and stability of proteins. Here, we use examples from our laboratory to illustrate the advantages and limitations of the technique.

A circadian clock nanomachine that runs without transcription or translation

The biochemical basis of circadian timekeeping is best characterized in cyanobacteria. The structures of its key molecular players, KaiA, KaiB, and KaiC are known and these proteins can reconstitute a remarkable circadian oscillation in a test tube. KaiC is rhythmically phosphorylated and its phospho-status is a marker of circadian phase that regulates ATPase activity and the oscillating assembly of a nanomachine. Analyses of the nanomachines have revealed how their timing circuit is ratcheted to be unidirectional and how they stay in synch to ensure a robust oscillator. These insights are likely to elucidate circadian timekeeping in higher organisms, including how transcription and translation could appear to be a core circadian timer when the true pacemaker is an embedded biochemical oscillator.

Loop-loop interactions regulate KaiA-stimulated KaiC phosphorylation in the cyanobacterial KaiABC circadian clock

The Synechococcus elongatus KaiA, KaiB, and KaiC proteins in the presence of ATP generate a post-translational oscillator that runs in a temperature-compensated manner with a period of 24 h. KaiA dimer stimulates phosphorylation of KaiC hexamer at two sites per subunit, T432 and S431, and KaiB dimers antagonize KaiA action and induce KaiC subunit exchange. Neither the mechanism of KaiA-stimulated KaiC phosphorylation nor that of KaiB-mediated KaiC dephosphorylation is understood in detail at present. We demonstrate here that the A422V KaiC mutant sheds light on the former mechanism. It was previously reported that A422V is less sensitive to dark pulse-induced phase resetting and has a reduced amplitude of the KaiC phosphorylation rhythm in vivo. A422 maps to a loop (422-loop) that continues toward the phosphorylation sites. By pulling on the C-terminal peptide of KaiC (A-loop), KaiA removes restraints from the adjacent 422-loop whose increased flexibility indirectly promotes kinase activity. We found in the crystal structure that A422V KaiC lacks phosphorylation at S431 and exhibits a subtle, local conformational change relative to wild-type KaiC. Molecular dynamics simulations indicate higher mobility of the 422-loop in the absence of the A-loop and mobility differences in other areas associated with phosphorylation activity between wild-type and mutant KaiCs. The A-loop-422-loop relay that informs KaiC phosphorylation sites of KaiA dimer binding propagates to loops from neighboring KaiC subunits, thus providing support for a concerted allosteric mechanism of phosphorylation.

Nature of KaiB-KaiC binding in the cyanobacterial circadian oscillator

In the cyanobacteria Synechococcus elongatus and Thermosynechococcus elongatus, the KaiA, KaiB and KaiC proteins in the presence of ATP generate a post-translational oscillator (PTO) that can be reconstituted in vitro. KaiC is the result of a gene duplication and resembles a double doughnut with N-terminal CI and C-terminal CII hexameric rings. Six ATPs are bound between subunits in both the CI and CII ring. CI harbors ATPase activity, and CII catalyzes phosphorylation and dephosphorylation at T432 and S431 with a ca. 24-h period. KaiA stimulates KaiC phosphorylation, and KaiB promotes KaiC subunit exchange and sequesters KaiA on the KaiB-KaiC interface in the final stage of the clock cycle. Studies of the PTO protein-protein interactions are convergent in terms of KaiA binding to CII but have led to two opposing models of the KaiB-KaiC interaction. Electron microscopy (EM) and small angle X-ray scattering (SAXS), together with native PAGE using full-length proteins and separate CI and CII rings, are consistent with binding of KaiB to CII. Conversely, NMR together with gel filtration chromatography and denatured PAGE using monomeric CI and CII domains support KaiB binding to CI. To resolve the existing controversy, we studied complexes between KaiB and gold-labeled, full-length KaiC with negative stain EM. The EM data clearly demonstrate that KaiB contacts the CII ring. Together with the outcomes of previous analyses, our work establishes that only CII participates in interactions with KaiA and KaiB as well as with the His kinase SasA involved in the clock output pathway.

CmpR is important for circadian phasing and cell growth

In the cyanobacterium Synechococcus elongatus PCC 7942, the circadian clock entrains to a daily light/dark cycle. The transcription factor Pex is abundant under dark conditions and represses kaiA transcription to fine-tune the KaiC-based core circadian oscillator. The transcription of pex also increases during exposure to darkness; however, its mechanism is unknown. We performed a molecular genetic study by constructing a pex expression bioluminescent reporter and screening for brightly luminescent mutants by random insertion of a drug resistance gene cassette in the reporter genome. One mutant contained an insertion of an antibiotic resistance cassette in the cmpR locus, a transcriptional regulator of inorganic carbon concentration. Insertions of the cassette in the remaining two mutant genomes were in the genes encoding flavodoxin and a putative partner of an ABC transporter with unknown function (ycf22). We further analyzed the cmpR mutant to examine whether CmpR directly or indirectly targeted pex expression. In the cmpR mutant, the pex mRNA level was 1.8-fold that of the wild type, and its circadian peak phase in bioluminescence rhythm occurred 5 h later. Moreover, a high-light stress phenotype was present in the colony. The abnormalities were complemented by ectopic induction of the native gene. However, the cmpR/pex double mutation partly suppressed the phase abnormality (2.5 h). In vitro DNA binding analysis of CmpR showed positive binding to the psbAII promoter, but not to any pex DNA. We postulate that the phenotypes of cmpR-deficient cells were attributable mainly to a feeble metabolic and/or redox status.

Quantifying the rhythm of KaiB-C interaction for in vitro cyanobacterial circadian clock

An oscillator consisting of KaiA, KaiB, and KaiC proteins comprises the core of cyanobacterial circadian clock. While one key reaction in this process--KaiC phosphorylation--has been extensively investigated and modeled, other key processes, such as the interactions among Kai proteins, are not understood well. Specifically, different experimental techniques have yielded inconsistent views about Kai A, B, and C interactions. Here, we first propose a mathematical model of cyanobacterial circadian clock that explains the recently observed dynamics of the four phospho-states of KaiC as well as the interactions among the three Kai proteins. Simulations of the model show that the interaction between KaiB and KaiC oscillates with the same period as the phosphorylation of KaiC, but displays a phase delay of ∼8 hr relative to the total phosphorylated KaiC. Secondly, this prediction on KaiB-C interaction are evaluated using a novel FRET (Fluorescence Resonance Energy Transfer)-based assay by tagging fluorescent proteins Cerulean and Venus to KaiC and KaiB, respectively, and reconstituting fluorescent protein-labeled in vitro clock. The data show that the KaiB∶KaiC interaction indeed oscillates with ∼24 hr periodicity and ∼8 hr phase delay relative to KaiC phosphorylation, consistent with model prediction. Moreover, it is noteworthy that our model indicates that the interlinked positive and negative feedback loops are the underlying mechanism for oscillation, with the serine phosphorylated-state (the "S-state") of KaiC being a hub for the feedback loops. Because the kinetics of the KaiB-C interaction faithfully follows that of the S-state, the FRET measurement may provide an important real-time probe in quantitative study of the cyanobacterial circadian clock.

Systems biology of cellular rhythms

Rhythms abound in biological systems, particularly at the cellular level where they originate from the feedback loops present in regulatory networks. Cellular rhythms can be investigated both by experimental and modeling approaches, and thus represent a prototypic field of research for systems biology. They have also become a major topic in synthetic biology. We review advances in the study of cellular rhythms of biochemical rather than electrical origin by considering a variety of oscillatory processes such as Ca++ oscillations, circadian rhythms, the segmentation clock, oscillations in p53 and NF-κB, synthetic oscillators, and the oscillatory dynamics of cyclin-dependent kinases driving the cell cycle. Finally we discuss the coupling between cellular rhythms and their robustness with respect to molecular noise.

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.

Dephosphorylation of the core clock protein KaiC in the cyanobacterial KaiABC circadian oscillator proceeds via an ATP synthase mechanism

The circadian clock of the cyanobacterium Synechococcus elongatus can be reconstituted in vitro from three proteins, KaiA, KaiB, and KaiC in the presence of ATP, to tick in a temperature-compensated manner. KaiC, the central cog of this oscillator, forms a homohexamer with 12 ATP molecules bound between its N- and C-terminal domains and exhibits unusual properties. Both the N-terminal (CI) and C-terminal (CII) domains harbor ATPase activity, and the subunit interfaces between CII domains are the sites of autokinase and autophosphatase activities. Hydrolysis of ATP correlates with phosphorylation at threonine and serine sites across subunits in an orchestrated manner, such that first T432 and then S431 are phosphorylated, followed by dephosphorylation of these residues in the same order. Although structural work has provided insight into the mechanisms of ATPase and kinase, the location and mechanism of the phosphatase have remained enigmatic. From the available experimental data based on a range of approaches, including KaiC crystal structures and small-angle X-ray scattering models, metal ion dependence, site-directed mutagenesis (i.e., E318, the general base), and measurements of the associated clock periods, phosphorylation patterns, and dephosphorylation courses as well as a lack of sequence motifs in KaiC that are typically associated with known phosphatases, we hypothesized that KaiCII makes use of the same active site for phosphorylation and dephosphorlyation. We observed that wild-type KaiC (wt-KaiC) exhibits an ATP synthase activity that is significantly reduced in the T432A/S431A mutant. We interpret the first observation as evidence that KaiCII is a phosphotransferase instead of a phosphatase and the second that the enzyme is capable of generating ATP, both from ADP and P(i) (in a reversal of the ATPase reaction) and from ADP and P-T432/P-S431 (dephosphorylation). This new concept regarding the mechanism of dephosphorylation is also supported by the strikingly similar makeups of the active sites at the interfaces between α/β heterodimers of F1-ATPase and between monomeric subunits in the KaiCII hexamer. Several KaiCII residues play a critical role in the relative activities of kinase and ATP synthase, among them R385, which stabilizes the compact form and helps kinase action reach a plateau, and T426, a short-lived phosphorylation site that promotes and affects the order of dephosphorylation.

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.

Biochemical frequency control by synchronisation of coupled repressilators: an in silico study of modules for circadian clock systems

Exploration of chronobiological systems emerges as a growing research field within bioinformatics focusing on various applications in medicine, agriculture, and material sciences. From a systems biological perspective, the question arises whether biological control systems for regulation of oscillatory signals and their technical counterparts utilise similar mechanisms. If so, modelling approaches and parameterisation adopted from building blocks can help to identify general components for frequency control in circadian clocks along with gaining insight into mechanisms of clock synchronisation to external stimuli like the daily rhythm of sunlight and darkness. Phase-locked loops could be an interesting candidate in this context. Both, biology and engineering, can benefit from a unified view resulting from systems modularisation. In a first experimental study, we analyse a model of coupled repressilators. We demonstrate its ability to synchronise clock signals in a monofrequential manner. Several oscillators initially deviate in phase difference and frequency with respect to explicit reaction and diffusion rates. Accordingly, the duration of the synchronisation process depends on dedicated reaction and diffusion parameters whose settings still lack to be sufficiently captured analytically.