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

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.

Two KaiABC systems control circadian oscillations in one cyanobacterium

The circadian clock of cyanobacteria, which predicts daily environmental changes, typically includes a standard oscillator consisting of proteins KaiA, KaiB, and KaiC. However, several cyanobacteria have diverse Kai protein homologs of unclear function. In particular, Synechocystis sp. PCC 6803 harbours, in addition to a canonical kaiABC gene cluster (named kaiAB1C1), two further kaiB and kaiC homologs (kaiB2, kaiB3, kaiC2, kaiC3). Here, we identify a chimeric KaiA homolog, named KaiA3, encoded by a gene located upstream of kaiB3. At the N-terminus, KaiA3 is similar to response-regulator receiver domains, whereas its C-terminal domain resembles that of KaiA. Homology analysis shows that a KaiA3-KaiB3-KaiC3 system exists in several cyanobacteria and other bacteria. Using the Synechocystis sp. PCC 6803 homologs, we observe circadian oscillations in KaiC3 phosphorylation in vitro in the presence of KaiA3 and KaiB3. Mutations of kaiA3 affect KaiC3 phosphorylation, leading to growth defects under both mixotrophic and chemoheterotrophic conditions. KaiC1 and KaiC3 exhibit phase-locked free-running phosphorylation rhythms. Deletion of either system (∆kaiAB1C1 or ∆kaiA3B3C3) alters the period of the cellular backscattering rhythm. Furthermore, both oscillators are required to maintain high-amplitude, self-sustained backscatter oscillations with a period of approximately 24 h, indicating their interconnected nature.

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.

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.

Temperature compensation and entrainment in cyanobacteria circadian rhythm

Circadian rhythm is an endogenous rhythmic behavior of organisms used to adapt to the external environment. Although most biochemical reactions accelerate with increasing temperature, the period of circadian rhythms remains relatively stable across a range of temperature, a phenomenon known as temperature compensation. Meanwhile, circadian rhythms can be reset by environmental signals, such as daily periodic light or temperature, a phenomenon known as entrainment. Cyanobacteria are the simplest organisms to have circadian rhythms. The effect of light on cyanobacteria circadian rhythm has been widely studied with mathematical models. However, the effect of temperature on cyanobacteria circadian rhythm and the mechanisms of temperature compensation and entrainment are far from clear. In this paper, we apply a recent model to incorporate temperature dependence by Van't Hoff rule. With numerical simulation, we study the temperature compensation and entrainment in detail. The results show that the system can exhibit temperature compensation when the post-transcription process is insensitive to temperature. The temperature compensation is caused by the cancellation of the increase of amplitude and the acceleration of speed, resulting in the stable period, when the temperature rises. The system can also exhibit temperature entrainment in constant light in a very limited temperature range. When the periodic light is added simultaneously to simulate more realistic environment, the temperature range of entrainment is greatly improved. The results also suggest that long-day condition is conducive to entrainment. The findings of this paper provide a theoretical reference for biological research and help us understand the dynamical mechanisms of cyanobacteria circadian rhythm.

RadA, a Key Gene of the Circadian Rhythm of Escherichia coli

Circadian rhythms are present in almost all living organisms, and their activity relies on molecular clocks. In prokaryotes, a functional molecular clock has been defined only in cyanobacteria. Here, we investigated the presence of circadian rhythms in non-cyanobacterial prokaryotes. The bioinformatic approach was used to identify a homologue of KaiC (circadian gene in cyanobacteria) in Escherichia coli. Then, strains of E. coli (wild type and mutants) were grown on blood agar, and sampling was made every 3 h for 24 h at constant conditions. Gene expression was determined by qRT-PCR, and the rhythmicity was analyzed using the Cosinor model. We identified RadA as a KaiC homologue in E. coli. Expression of radA showed a circadian rhythm persisting at least 3 days, with a peak in the morning. The circadian expression of other E. coli genes was also observed. Gene circadian oscillations were lost in radA mutants of E. coli. This study provides evidence of molecular clock gene expression in E. coli with a circadian rhythm. Such a finding paves the way for new perspectives in antibacterial treatment.

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.

Robust, coherent, and synchronized circadian clock-controlled oscillations along Anabaena filaments

Circadian clocks display remarkable reliability despite significant stochasticity in biomolecular reactions. We study the dynamics of a circadian clock-controlled gene at the individual cell level in Anabaena sp. PCC 7120, a multicellular filamentous cyanobacterium. We found significant synchronization and spatial coherence along filaments, clock coupling due to cell-cell communication, and gating of the cell cycle. Furthermore, we observed low-amplitude circadian oscillatory transcription of kai genes encoding the post-transcriptional core oscillatory circuit and high-amplitude oscillations of rpaA coding for the master regulator transducing the core clock output. Transcriptional oscillations of rpaA suggest an additional level of regulation. A stochastic one-dimensional toy model of coupled clock cores and their phosphorylation states shows that demographic noise can seed stochastic oscillations outside the region where deterministic limit cycles with circadian periods occur. The model reproduces the observed spatio-temporal coherence along filaments and provides a robust description of coupled circadian clocks in a multicellular organism.

Simple Kinetic Models in Molecular Chronobiology

Circadian rhythms are constituted by a complex dynamical system with intertwined feedback loops, molecular switches, and self-sustained oscillations. Mathematical modeling supports understanding available heterogeneous kinetic data, highlights basic mechanisms, and can guide experimental research. Here, we introduce the basic steps from a biological question to simple models providing insight into gene-regulatory mechanisms. We illustrate the general approach by three examples: modeling decay processes, clock-controlled genes, and self-sustained oscillations.

For Whom the Clock Ticks: Clinical Chronobiology for Infectious Diseases

The host defense against pathogens varies among individuals. Among the factors influencing host response, those associated with circadian disruptions are emerging. These latter depend on molecular clocks, which control the two partners of host defense: microbes and immune system. There is some evidence that infections are closely related to circadian rhythms in terms of susceptibility, clinical presentation and severity. In this review, we overview what is known about circadian rhythms in infectious diseases and update the knowledge about circadian rhythms in immune system, pathogens and vectors. This heuristic approach opens a new fascinating field of time-based personalized treatment of infected patients.

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

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

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.

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.

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.

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).

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

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

Structures of the cyanobacterial circadian oscillator frozen in a fully assembled state

Cyanobacteria have a robust circadian oscillator, known as the Kai system. Reconstituted from the purified protein components KaiC, KaiB, and KaiA, it can tick autonomously in the presence of adenosine 5'-triphosphate (ATP). The KaiC hexamers enter a natural 24-hour reaction cycle of autophosphorylation and assembly with KaiB and KaiA in numerous diverse forms. We describe the preparation of stoichiometrically well-defined assemblies of KaiCB and KaiCBA, as monitored by native mass spectrometry, allowing for a structural characterization by single-particle cryo-electron microscopy and mass spectrometry. Our data reveal details of the interactions between the Kai proteins and provide a structural basis to understand periodic assembly of the protein oscillator.

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.

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.

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

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

Crystal Structure of the CTP1L Endolysin Reveals How Its Activity Is Regulated by a Secondary Translation Product

Bacteriophages produce endolysins, which lyse the bacterial host cell to release newly produced virions. The timing of lysis is regulated and is thought to involve the activation of a molecular switch. We present a crystal structure of the activated endolysin CTP1L that targets Clostridium tyrobutyricum, consisting of a complex between the full-length protein and an N-terminally truncated C-terminal cell wall binding domain (CBD). The truncated CBD is produced through an internal translation start site within the endolysin gene. Mutants affecting the internal translation site change the oligomeric state of the endolysin and reduce lytic activity. The activity can be modulated by reconstitution of the full-length endolysin-CBD complex with free CBD. The same oligomerization mechanism applies to the CD27L endolysin that targets Clostridium difficile and the CS74L endolysin that targets Clostridium sporogenes. When the CTP1L endolysin gene is introduced into the commensal bacterium Lactococcus lactis, the truncated CBD is also produced, showing that the alternative start codon can be used in other bacterial species. The identification of a translational switch affecting oligomerization presented here has implications for the design of effective endolysins for the treatment of bacterial infections.

Forging patterns and making waves from biology to geology: a commentary on Turing (1952) 'The chemical basis of morphogenesis'

Alan Turing was neither a biologist nor a chemist, and yet the paper he published in 1952, 'The chemical basis of morphogenesis', on the spontaneous formation of patterns in systems undergoing reaction and diffusion of their ingredients has had a substantial impact on both fields, as well as in other areas as disparate as geomorphology and criminology. Motivated by the question of how a spherical embryo becomes a decidedly non-spherical organism such as a human being, Turing devised a mathematical model that explained how random fluctuations can drive the emergence of pattern and structure from initial uniformity. The spontaneous appearance of pattern and form in a system far away from its equilibrium state occurs in many types of natural process, and in some artificial ones too. It is often driven by very general mechanisms, of which Turing's model supplies one of the most versatile. For that reason, these patterns show striking similarities in systems that seem superficially to share nothing in common, such as the stripes of sand ripples and of pigmentation on a zebra skin. New examples of 'Turing patterns' in biology and beyond are still being discovered today. This commentary was written to celebrate the 350th anniversary of the journal Philosophical Transactions of the Royal Society.

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.

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

Circadian oscillations are generated by the purified cyanobacterial clock proteins, KaiA, KaiB, and KaiC, through rhythmic interactions that depend on multisite phosphorylation of KaiC. However, the mechanisms that allow these phosphorylation reactions to robustly control the timing of oscillations over a range of protein stoichiometries are not clear. We show that when KaiC hexamers consist of a mixture of differentially phosphorylated subunits, the two phosphorylation sites have opposing effects on the ability of each hexamer to bind to the negative regulator KaiB. We likewise show that the ability of the positive regulator KaiA to act on KaiC depends on the phosphorylation state of the hexamer and that KaiA and KaiB recognize alternative allosteric states of the KaiC ring. Using mathematical models with kinetic parameters taken from experimental data, we find that antagonism of the two KaiC phosphorylation sites generates an ultrasensitive switch in negative feedback strength necessary for stable circadian oscillations over a range of component concentrations. Similar strategies based on opposing modifications may be used to support robustness in other timing systems and in cellular signaling more generally.

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.

Daily rhythms in the cyanobacterium synechococcus elongatus probed by high-resolution mass spectrometry-based proteomics reveals a small defined set of cyclic proteins

Circadian rhythms are self-sustained and adjustable cycles, typically entrained with light/dark and/or temperature cycles. These rhythms are present in animals, plants, fungi, and several bacteria. The central mechanism behind these "pacemakers" and the connection to the circadian regulated pathways are still poorly understood. The circadian rhythm of the cyanobacterium Synechococcus elongatus PCC 7942 (S. elongatus) is highly robust and controlled by only three proteins, KaiA, KaiB, and KaiC. This central clock system has been extensively studied functionally and structurally and can be reconstituted in vitro. These characteristics, together with a relatively small genome (2.7 Mbp), make S. elongatus an ideal model system for the study of circadian rhythms. Different approaches have been used to reveal the influence of the central S. elongatus clock on rhythmic gene expression, rhythmic mRNA abundance, rhythmic DNA topology changes, and cell division. However, a global analysis of its proteome dynamics has not been reported yet. To uncover the variation in protein abundances during 48 h under light and dark cycles (12:12 h), we used quantitative proteomics, with TMT 6-plex isobaric labeling. We queried the S. elongatus proteome at 10 different time points spanning a single 24-h period, leading to 20 time points over the full 48-h period. Employing multidimensional separation and high-resolution mass spectrometry, we were able to find evidence for a total of 82% of the S. elongatus proteome. Of the 1537 proteins quantified over the time course of the experiment, only 77 underwent significant cyclic variations. Interestingly, our data provide evidence for in- and out-of-phase correlation between mRNA and protein levels for a set of specific genes and proteins. As a range of cyclic proteins are functionally not well annotated, this work provides a resource for further studies to explore the role of these proteins in the cyanobacterial circadian rhythm.

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.

Diversity of KaiC-based timing systems in marine Cyanobacteria

The coordination of biological activities into daily cycles provides an important advantage for the fitness of diverse organisms. Most eukaryotes possess an internal clock ticking with a periodicity of about one day to anticipate sunrise and sunset. The 24-hour period of the free-running rhythm is highly robust against many changes in the natural environment. Among prokaryotes, only Cyanobacteria are known to harbor such a circadian clock. Its core oscillator consists of just three proteins, KaiA, KaiB, and KaiC that produce 24-hour oscillations of KaiC phosphorylation, even in vitro. This unique three-protein oscillator is well documented for the freshwater cyanobacterium Synechococcus elongatus PCC 7942. Several physiological studies demonstrate a circadian clock also for other Cyanobacteria including marine species. Genes for the core clock components are present in nearly all marine cyanobacterial species, though there are large differences in the specific composition of these genes. In the first section of this review we summarize data on the model circadian clock from S. elongatus PCC 7942 and compare it to the reduced clock system of the marine cyanobacterium Prochlorococcus marinus MED4. In the second part we discuss the diversity of timing mechanisms in other marine Cyanobacteria with regard to the presence or absence of different components of the clock.

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.

Network balance via CRY signalling controls the Arabidopsis circadian clock over ambient temperatures

Temperature compensation of the Arabidopsis circadian clock is shown to be mediated by the interaction of light and temperature at the level of the crytochrome photoreceptors. These findings reveal that light and temperature share common input mechanisms to the circadian network.

We provide evidence that blue light signalling via the cryptochromes is important for the temperature-dependent control of circadian period in plants.

Light and temperature converge upon common targets in the circadian network.

We have constructed a temperature-compensated model of the plant circadian clock by adding a temperature effect to a subset of light-sensitive processes.

The model matches experimental data and predicted a temperature-dependent change in the protein level of a key clock gene.

Circadian clocks exhibit ‘temperature compensation', meaning that they show only small changes in period over a broad temperature range. Several clock genes have been implicated in the temperature-dependent control of period in Arabidopsis. We show that blue light is essential for this, suggesting that the effects of light and temperature interact or converge upon common targets in the circadian clock. Our data demonstrate that two cryptochrome photoreceptors differentially control circadian period and sustain rhythmicity across the physiological temperature range. In order to test the hypothesis that the targets of light regulation are sufficient to mediate temperature compensation, we constructed a temperature-compensated clock model by adding passive temperature effects into only the light-sensitive processes in the model. Remarkably, this model was not only capable of full temperature compensation and consistent with mRNA profiles across a temperature range, but also predicted the temperature-dependent change in the level of LATE ELONGATED HYPOCOTYL, a key clock protein. Our analysis provides a systems-level understanding of period control in the plant circadian oscillator.

Revealing a two-loop transcriptional feedback mechanism in the cyanobacterial circadian clock

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

Many organisms possess a true circadian clock and coordinate their activities into daily cycles. Among the simplest organisms harboring such a 24 h-clock are cyanobacteria. Interactions among three proteins, KaiA, KaiB, KaiC, and cyclic KaiC phosphorylation govern the daily rhythm from gene expression to metabolism. Thus, the control of the kaiBC gene cluster expression is important for regulating the cyanobacterial clockwork. A picture has emerged in which different KaiC phospho-states activate and inhibit kaiBC expression. However, the mechanism remains to be solved. Here, we investigated the impact of each KaiC phospho-state on kaiBC expression by introducing a model that combines the circadian transcription/translation rhythm with the KaiABC-protein oscillator. We tested 32 combinations of positive and negative transcriptional regulation. It turns out that the kaiBC expression and KaiC phosphorylation dynamics in wild type and kai mutants can only be described by one mechanism: threonine and double phosphorylated KaiC hexamers activate kaiBC expression and the unphosphorylated state suppresses it. Further, we propose that the activator-to-repressor abundance ratio very likely determines the kaiBC expression dynamics in the simulated kai mutants. Our suggested clock model can be extended by further kinetic mechanisms to gain deeper insights into the various underlying processes of circadian gene regulation.

Biochemical analysis of three putative KaiC clock proteins from Synechocystis sp. PCC 6803 suggests their functional divergence

Cyanobacteria have been shown to have a circadian clock system that consists mainly of three protein components: KaiA, KaiB and KaiC. This system is well understood in the cyanobacterium Synechococcus elongatus PCC 7942, for which robust circadian oscillations have been shown. Like many other cyanobacteria, the chromosome of the model cyanobacterium Synechocystis sp. PCC 6803 contains additional kaiC and kaiB gene copies besides the standard kaiABC gene cluster. The respective gene products differ significantly in their amino acid sequences, especially in their C-terminal regions, suggesting different functional characteristics. Here, phosphorylation assays of the three Synechocystis sp. PCC 6803 KaiC proteins revealed that KaiC1 phosphorylation depends on KaiA, as is well documented for the Synechococcus elongatus PCC 7942 KaiC protein, whereas KaiC2 and KaiC3 autophosphorylate independently of KaiA. This was confirmed by in vivo protein-protein interaction studies, which demonstrate that only KaiC1 interacts with KaiA. Furthermore, we demonstrate that the three different Kai proteins form only homomeric complexes in vivo. As only KaiC1 phosphorylation depends on KaiA, a prerequisite for robust oscillations, we suggest that the kaiAB1C1 gene cluster in Synechocystis sp. PCC 6803 controls circadian timing in a manner similar to the clock described in Synechococcus elongatus PCC 7942.

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.

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.

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

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

Modelling cyanobacteria: from metabolism to integrative models of phototrophic growth

Cyanobacteria are phototrophic microorganisms of global importance and have recently attracted increasing attention due to their capability to convert sunlight and atmospheric CO(2) directly into organic compounds, including carbon-based biofuels. The utilization of cyanobacteria as a biological chassis to generate third-generation biofuels would greatly benefit from an increased understanding of cyanobacterial metabolism and its interplay with other cellular processes. In this respect, metabolic modelling has been proposed as a way to overcome the traditional trial and error methodology that is often employed to introduce novel pathways. In particular, flux balance analysis and related methods have proved to be powerful tools to investigate the organization of large-scale metabolic networks-with the prospect of predicting modifications that are likely to increase the yield of a desired product and thereby to streamline the experimental progress and avoid futile avenues. This contribution seeks to describe the utilization of metabolic modelling as a research tool to understand the metabolism and phototrophic growth of cyanobacteria. The focus of the contribution is on a mathematical description of the metabolic network of Synechocystis sp. PCC 6803 and its analysis using constraint-based methods. A particular challenge is to integrate the description of the metabolic network with other cellular processes, such as the circadian clock, the photosynthetic light reactions, carbon concentration mechanism, and transcriptional regulation-aiming at a predictive model of a cyanobacterium in silico.

Modeling circadian clocks: Roles, advantages, and limitations

Circadian rhythms are endogenous oscillations characterized by a period of about 24h. They constitute the biological rhythms with the longest period known to be generated at the molecular level. The abundance of genetic information and the complexity of the molecular circuitry make circadian clocks a system of choice for theoretical studies. Many mathematical models have been proposed to understand the molecular regulatory mechanisms that underly these circadian oscillations and to account for their dynamic properties (temperature compensation, entrainment by light dark cycles, phase shifts by light pulses, rhythm splitting, robustness to molecular noise, intercellular synchronization). The roles and advantages of modeling are discussed and illustrated using a variety of selected examples. This survey will lead to the proposal of an integrated view of the circadian system in which various aspects (interlocked feedback loops, inter-cellular coupling, and stochasticity) should be considered together to understand the design and the dynamics of circadian clocks. Some limitations of these models are commented and challenges for the future identified.

The cyanobacterial circadian system: from biophysics to bioevolution

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

Combined SAXS/EM based models of the S. elongatus post-translational circadian oscillator and its interactions with the output His-kinase SasA

The circadian clock in the cyanobacterium Synechococcus elongatus is composed of a post-translational oscillator (PTO) that can be reconstituted in vitro from three different proteins in the presence of ATP and a transcription-translation feedback loop (TTFL). The homo-hexameric KaiC kinase, phosphatase and ATPase alternates between hypo- and hyper-phosphorylated states over the 24-h cycle, with KaiA enhancing phosphorylation, and KaiB antagonizing KaiA and promoting KaiC subunit exchange. SasA is a His kinase that relays output signals from the PTO formed by the three Kai proteins to the TTFL. Although the crystal structures for all three Kai proteins are known, atomic resolution structures of Kai and Kai/SasA protein complexes have remained elusive. Here, we present models of the KaiAC and KaiBC complexes derived from solution small angle X-ray scattering (SAXS), which are consistent with previous EM based models. We also present a combined SAXS/EM model of the KaiC/SasA complex, which has two N-terminal SasA sensory domains occupying positions on the C-terminal KaiC ring reminiscent of the orientations adopted by KaiB dimers. Using EM we demonstrate that KaiB and SasA compete for similar binding sites on KaiC. We also propose an EM based model of the ternary KaiABC complex that is consistent with the sequestering of KaiA by KaiB on KaiC during the PTO dephosphorylation phase. This work provides the first 3D-catalogue of protein-protein interactions in the KaiABC PTO and the output pathway mediated by SasA.

Flexibility of the C-terminal, or CII, ring of KaiC governs the rhythm of the circadian clock of cyanobacteria

In the cyanobacterial circadian oscillator, KaiA and KaiB alternately stimulate autophosphorylation and autodephosphorylation of KaiC with a periodicity of approximately 24 h. KaiA activates autophosphorylation by selectively capturing the A loops of KaiC in their exposed positions. The A loops and sites of phosphorylation, residues S431 and T432, are located in the CII ring of KaiC. We find that the flexibility of the CII ring governs the rhythm of KaiC autophosphorylation and autodephosphorylation and is an example of dynamics-driven protein allostery. KaiA-induced autophosphorylation requires flexibility of the CII ring. In contrast, rigidity is required for KaiC-KaiB binding, which induces a conformational change in KaiB that enables it to sequester KaiA by binding to KaiA's linker. Autophosphorylation of the S431 residues around the CII ring stabilizes the CII ring, making it rigid. In contrast, autophosphorylation of the T432 residues offsets phospho-S431-induced rigidity to some extent. In the presence of KaiA and KaiB, the dynamic states of the CII ring of KaiC executes the following circadian rhythm: CII STflexible → CIISpTflexible → CIIpSpTrigid → CIIpSTvery-rigid → CIISTflexible. Apparently, these dynamic states govern the pattern of phosphorylation, ST → SpT → pSpT → pST → ST. CII-CI ring-on-ring stacking is observed when the CII ring is rigid, suggesting a mechanism through which the ATPase activity of the CI ring is rhythmically controlled. SasA, a circadian clock-output protein, binds to the CI ring. Thus, rhythmic ring stacking may also control clock-output pathways.

Model-based inference of biochemical parameters and dynamic properties of microbial signal transduction networks

Because of the inherent uncertainty about quantitative aspects of signalling networks it is of substantial interest to use computational methods that allow inferring non-measurable quantities such as rate constants, from measurable quantities such as changes in protein abundances. We argue that true biochemical parameters like rate constants can generally not be inferred using models due to their non-identifiability. Recent advances, however, facilitate the analysis of parameter identifiability of a given model and automated discrimination of candidate models, both being important techniques to still extract quantitative biological information from experimental data.