Isoform switching facilitates period control in the Neurospora crassa circadian clock

Abundant clock proteins point to missing molecular regulation in the plant circadian clock

Understanding the biochemistry behind whole-organism traits such as flowering time is a longstanding challenge, where mathematical models are critical. Very few models of plant gene circuits use the absolute units required for comparison to biochemical data. We refactor two detailed models of the plant circadian clock from relative to absolute units. Using absolute RNA quantification, a simple model predicted abundant clock protein levels in Arabidopsis thaliana, up to 100,000 proteins per cell. NanoLUC reporter protein fusions validated the predicted levels of clock proteins in vivo. Recalibrating the detailed models to these protein levels estimated their DNA-binding dissociation constants (Kd). We estimate the same Kd from multiple results in vitro, extending the method to any promoter sequence. The detailed models simulated the Kd range estimated from LUX DNA-binding in vitro but departed from the data for CCA1 binding, pointing to further circadian mechanisms. Our analytical and experimental methods should transfer to understand other plant gene regulatory networks, potentially including the natural sequence variation that contributes to evolutionary adaptation.

Data-driven modelling captures dynamics of the circadian clock of Neurospora crassa

Eukaryotic circadian clocks are based on self-sustaining, cell-autonomous oscillatory feedback loops that can synchronize with the environment via recurrent stimuli (zeitgebers) such as light. The components of biological clocks and their network interactions are becoming increasingly known, calling for a quantitative understanding of their role for clock function. However, the development of data-driven mathematical clock models has remained limited by the lack of sufficiently accurate data. Here we present a comprehensive model of the circadian clock of Neurospora crassa that describe free-running oscillations in constant darkness and entrainment in light-dark cycles. To parameterize the model, we measured high-resolution time courses of luciferase reporters of morning and evening specific clock genes in WT and a mutant strain. Fitting the model to such comprehensive data allowed estimating parameters governing circadian phase, period length and amplitude, and the response of genes to light cues. Our model suggests that functional maturation of the core clock protein Frequency causes a delay in negative feedback that is critical for generating circadian rhythms.

Circadian rhythms are endogenous autonomous clocks that emancipate daily rhythms in physiology and behavior. Lately, a large body of research has contributed to our understanding of clocks’ genetic and mechanistic basis across kingdoms of life, i.e., mammals, fungi, plants, and bacteria. Several mathematical models have made key contributions to our current understanding of the design principles of the Neurospora crassa circadian clock and conditions for self-sustained oscillations. However, previous models uncovered and described the principle properties of the clock in generic manner due to a lack of experimental data. In this study, we developed a mathematical model based on systems of differential equations to describe the core clock components and estimated model parameters from luciferase data that capture experimental observations. We demonstrate the model predictive control simulation emphasizing the importance of functional maturation of the core clock protein Frequency in generating circadian rhythms.

Temperature robustness in Arabidopsis circadian clock models is facilitated by repressive interactions, autoregulation, and three-node feedbacks

The biological interactions underpinning the Arabidopsis circadian clock have been systematically uncovered and explored by biological experiments and mathematical models. This is captured by a series of published ordinary differential equation (ODE) models, which describe plant clock dynamics in response to light/dark conditions. However, understanding the role of temperature in resetting the clock (entrainment) and the mechanisms by which circadian rhythms maintain a near-24 h period over a range of temperatures (temperature compensation) is still unclear. Understanding entrainment and temperature compensation may elucidate the principles governing the structure of the circadian clock network. Here we explore the design principles of the Arabidopsis clock and its responses to changes in temperature. We analyse published clock models of Arabidopsis, spanning a range of complexity, and incorporate temperature-dependent dynamics into the parameters of translation rates in these models, to discern which regulatory patterns may best explain clock function and temperature compensation. We additionally construct three minimal clock models and explore what key features govern their rhythmicity and temperature robustness via a series of random parameterisations. Results show that the highly repressive interactions between the components of the plant clock, together with autoregulation patterns and three-node feedback loops, are associated with circadian function of the clock in general, and enhance its robustness to temperature variation in particular. However, because the networks governing clock function vary with time due to light and temperature conditions, we emphasise the importance of studying plant clock functionality in its entirety rather than as a set of discrete regulation patterns.

It's about time: Analysing simplifying assumptions for modelling multi-step pathways in systems biology

Thoughtful use of simplifying assumptions is crucial to make systems biology models tractable while still representative of the underlying biology. A useful simplification can elucidate the core dynamics of a system. A poorly chosen assumption can, however, either render a model too complicated for making conclusions or it can prevent an otherwise accurate model from describing experimentally observed dynamics. Here, we perform a computational investigation of sequential multi-step pathway models that contain fewer pathway steps than the system they are designed to emulate. We demonstrate when such models will fail to reproduce data and how detrimental truncation of a pathway leads to detectable signatures in model dynamics and its optimised parameters. An alternative assumption is suggested for simplifying such pathways. Rather than assuming a truncated number of pathway steps, we propose to use the assumption that the rates of information propagation along the pathway is homogeneous and, instead, letting the length of the pathway be a free parameter. We first focus on linear pathways that are sequential and have first-order kinetics, and we show how this assumption results in a three-parameter model that consistently outperforms its truncated rival and a delay differential equation alternative in recapitulating observed dynamics. We then show how the proposed assumption allows for similarly terse and effective models of non-linear pathways. Our results provide a foundation for well-informed decision making during model simplifications.

A simplified modelling framework facilitates more complex representations of plant circadian clocks

The circadian clock orchestrates biological processes so that they occur at specific times of the day, thereby facilitating adaptation to diurnal and seasonal environmental changes. In plants, mathematical modelling has been comprehensively integrated with experimental studies to gain a better mechanistic understanding of the complex genetic regulatory network comprising the clock. However, with an increasing number of circadian genes being discovered, there is a pressing need for methods facilitating the expansion of computational models to incorporate these newly-discovered components. Conventionally, plant clock models have comprised differential equation systems based on Michaelis-Menten kinetics. However, the difficulties associated with modifying interactions using this approach-and the concomitant problem of robustly identifying regulation types-has contributed to a complexity bottleneck, with quantitative fits to experimental data rapidly becoming computationally intractable for models possessing more than ≈50 parameters. Here, we address these issues by constructing the first plant clock models based on the S-System formalism originally developed by Savageau for analysing biochemical networks. We show that despite its relative simplicity, this approach yields clock models with comparable accuracy to the conventional Michaelis-Menten formalism. The S-System formulation also confers several key advantages in terms of model construction and expansion. In particular, it simplifies the inclusion of new interactions, whilst also facilitating the modification of regulation types, thereby making it well-suited to network inference. Furthermore, S-System models mitigate the issue of parameter identifiability. Finally, by applying linear systems theory to the models considered, we provide some justification for the increased use of aggregated protein equations in recent plant clock modelling, replacing the separate cytoplasmic/nuclear protein compartments that were characteristic of the earlier models. We conclude that as well as providing a simplified framework for model development, the S-System formalism also possesses significant potential as a robust modelling method for designing synthetic gene circuits.

Heat the Clock: Entrainment and Compensation in Arabidopsis Circadian Rhythms

The circadian clock is a biological mechanism that permits some organisms to anticipate daily environmental variations. This clock generates biological rhythms, which can be reset by environmental cues such as cycles of light or temperature, a process known as entrainment. After entrainment, circadian rhythms typically persist with approximately 24 hours periodicity in free-running conditions, i.e. in the absence of environmental cues. Experimental evidence also shows that a free-running period close to 24 hours is maintained across a range of temperatures, a process known as temperature compensation. In the plant Arabidopsis, the effect of light on the circadian system has been widely studied and successfully modelled mathematically. However, the role of temperature in periodicity, and the relationship between entrainment and compensation, are not fully understood. Here we adapt recent models to incorporate temperature dependence by applying Arrhenius equations to the parameters of the models that characterize transcription, translation, and degradation rates. We show that the resulting models can exhibit thermal entrainment and temperature compensation, but that these phenomena emerge from physiologically different sets of processes. Further simulations combining thermal and photic forcing in more realistic scenarios clearly distinguish between the processes of entrainment and compensation, and reveal temperature compensation as an emergent property which can arise as a result of multiple temperature-dependent interactions. Our results consistently point to the thermal sensitivity of degradation rates as driving compensation and entrainment across a range of conditions.

Temperature-amplitude coupling for stable biological rhythms at different temperatures

Most biological processes accelerate with temperature, for example cell division. In contrast, the circadian rhythm period is robust to temperature fluctuation, termed temperature compensation. Temperature compensation is peculiar because a system-level property (i.e., the circadian period) is stable under varying temperature while individual components of the system (i.e., biochemical reactions) are usually temperature-sensitive. To understand the mechanism for period stability, we measured the time series of circadian clock transcripts in cultured C6 glioma cells. The amplitudes of Cry1 and Dbp circadian expression increased significantly with temperature. In contrast, other clock transcripts demonstrated no significant change in amplitude. To understand these experimental results, we analyzed mathematical models with different network topologies. It was found that the geometric mean amplitude of gene expression must increase to maintain a stable period with increasing temperatures and reaction speeds for all models studied. To investigate the generality of this temperature-amplitude coupling mechanism for period stability, we revisited data on the yeast metabolic cycle (YMC) period, which is also stable under temperature variation. We confirmed that the YMC amplitude increased at higher temperatures, suggesting temperature-amplitude coupling as a common mechanism shared by circadian and 4 h-metabolic rhythms.

Molecular Mechanisms Regulating Temperature Compensation of the Circadian Clock

An approximately 24-h biological timekeeping mechanism called the circadian clock is present in virtually all light-sensitive organisms from cyanobacteria to humans. The clock system regulates our sleep–wake cycle, feeding–fasting, hormonal secretion, body temperature, and many other physiological functions. Signals from the master circadian oscillator entrain peripheral clocks using a variety of neural and hormonal signals. Even centrally controlled internal temperature fluctuations can entrain the peripheral circadian clocks. But, unlike other chemical reactions, the output of the clock system remains nearly constant with fluctuations in ambient temperature, a phenomenon known as temperature compensation. In this brief review, we focus on recent advances in our understanding of the posttranslational modifications, especially a phosphoswitch mechanism controlling the stability of PER2 and its implications for the regulation of temperature compensation.

Stochastic models of cellular circadian rhythms in plants help to understand the impact of noise on robustness and clock structure

Rhythmic behavior is essential for plants; for example, daily (circadian) rhythms control photosynthesis and seasonal rhythms regulate their life cycle. The core of the circadian clock is a genetic network that coordinates the expression of specific clock genes in a circadian rhythm reflecting the 24-h day/night cycle. Circadian clocks exhibit stochastic noise due to the low copy numbers of clock genes and the consequent cell-to-cell variation: this intrinsic noise plays a major role in circadian clocks by inducing more robust oscillatory behavior. Another source of noise is the environment, which causes variation in temperature and light intensity: this extrinsic noise is part of the requirement for the structural complexity of clock networks. Advances in experimental techniques now permit single-cell measurements and the development of single-cell models. Here we present some modeling studies showing the importance of considering both types of noise in understanding how plants adapt to regular and irregular light variations. Stochastic models have proven useful for understanding the effect of regular variations. By contrast, the impact of irregular variations and the interaction of different noise sources are less well studied.

Light and circadian regulation of clock components aids flexible responses to environmental signals

The circadian clock measures time across a 24 h period, increasing fitness by phasing biological processes to the most appropriate time of day. The interlocking feedback loop mechanism of the clock is conserved across species; however, the number of loops varies. Mathematical and computational analyses have suggested that loop complexity affects the overall flexibility of the oscillator, including its responses to entrainment signals. We used a discriminating experimental assay, at the transition between different photoperiods, in order to test this proposal in a minimal circadian network (in Ostreococcus tauri) and a more complex network (in Arabidopsis thaliana). Transcriptional and translational reporters in O. tauri primarily tracked dawn or dusk, whereas in A. thaliana, a wider range of responses were observed, consistent with its more flexible clock. Model analysis supported the requirement for this diversity of responses among the components of the more complex network. However, these and earlier data showed that the O. tauri network retains surprising flexibility, despite its simple circuit. We found that models constructed from experimental data can show flexibility either from multiple loops and/or from multiple light inputs. Our results suggest that O. tauri has adopted the latter strategy, possibly as a consequence of genomic reduction.

Interaction of light and temperature signalling

Light and temperature are arguably two of the most important signals regulating the growth and development of plants. In addition to their direct energetic effects on plant growth, light and temperature provide vital immediate and predictive cues for plants to ensure optimal development both spatially and temporally. While the majority of research to date has focused on the contribution of either light or temperature signals in isolation, it is becoming apparent that an understanding of how the two interact is essential to appreciate fully the complex and elegant ways in which plants utilize these environmental cues. This review will outline the diverse mechanisms by which light and temperature signals are integrated and will consider why such interconnected systems (as opposed to entirely separate light and temperature pathways) may be evolutionarily favourable.

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.

The Neurospora photoreceptor VIVID exerts negative and positive control on light sensing to achieve adaptation

Light adaptation in Neurospora is mediated by the photoreceptor VIVID, which exerts both a negative and positive effect on light sensing. These apparently paradoxical roles of VIVID are explained by the dynamics of a network motif that utilizes futile cycling.

The fungus Neurospora detects relative changes in light intensity by adapting to the ambient light level and remaining responsive to increases in light intensity.

Both the downregulation of the acute light response and maintained responsiveness are mediated by the photoreceptor VIVID (VVD).

Data-based mathematical modeling shows that this paradoxical function of VVD can be realized by a futile-cycle network motif that turns feedback inhibition into sensory adaptation.

The light response in Neurospora is mediated by the photoreceptor and circadian transcription factor White Collar Complex (WCC). The expression rate of the WCC target genes adapts in daylight and remains refractory to moonlight, despite the extraordinary light sensitivity of the WCC. To explain this photoadaptation, feedback inhibition by the WCC interaction partner VIVID (VVD) has been invoked. Here we show through data-driven mathematical modeling that VVD allows Neurospora to detect relative changes in light intensity. To achieve this behavior, VVD acts as an inhibitor of WCC-driven gene expression and, at the same time, as a positive regulator that maintains the responsiveness of the photosystem. Our data indicate that this paradoxical function is realized by a futile cycle that involves the light-induced sequestration of active WCC by VVD and the replenishment of the activatable WCC pool through the decay of the photoactivated state. Our quantitative study uncovers a novel network motif for achieving sensory adaptation and defines a core input module of the circadian clock in Neurospora.

Unraveling the circadian clock in Arabidopsis

The circadian clock is an endogenous timing system responsible for coordinating an organism's biological processes with its environment. Interlocked transcriptional feedback loops constitute the fundamental architecture of the circadian clock. In Arabidopsis, three feedback loops, the core loop, morning loop and evening loop, comprise a network that is the basis of the circadian clock. The components of these three loops are regulated in distinct ways, including transcriptional, post-transcriptional and posttranslational mechanisms. The discovery of the DNA-binding and repressive activities of TOC1 has overturned our initial concept of its function in the circadian clock. The alternative splicing of circadian clock-related genes plays an essential role in normal functioning of the clock and enables organisms to sense environmental changes. In this review, we describe the regulatory mechanisms of the circadian clock that have been identified in Arabidopsis.

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.

Digital clocks: simple Boolean models can quantitatively describe circadian systems

The gene networks that comprise the circadian clock modulate biological function across a range of scales, from gene expression to performance and adaptive behaviour. The clock functions by generating endogenous rhythms that can be entrained to the external 24-h day–night cycle, enabling organisms to optimally time biochemical processes relative to dawn and dusk. In recent years, computational models based on differential equations have become useful tools for dissecting and quantifying the complex regulatory relationships underlying the clock's oscillatory dynamics. However, optimizing the large parameter sets characteristic of these models places intense demands on both computational and experimental resources, limiting the scope of in silico studies. Here, we develop an approach based on Boolean logic that dramatically reduces the parametrization, making the state and parameter spaces finite and tractable. We introduce efficient methods for fitting Boolean models to molecular data, successfully demonstrating their application to synthetic time courses generated by a number of established clock models, as well as experimental expression levels measured using luciferase imaging. Our results indicate that despite their relative simplicity, logic models can (i) simulate circadian oscillations with the correct, experimentally observed phase relationships among genes and (ii) flexibly entrain to light stimuli, reproducing the complex responses to variations in daylength generated by more detailed differential equation formulations. Our work also demonstrates that logic models have sufficient predictive power to identify optimal regulatory structures from experimental data. By presenting the first Boolean models of circadian circuits together with general techniques for their optimization, we hope to establish a new framework for the systematic modelling of more complex clocks, as well as other circuits with different qualitative dynamics. In particular, we anticipate that the ability of logic models to provide a computationally efficient representation of system behaviour could greatly facilitate the reverse-engineering of large-scale biochemical networks.

Alternative splicing mediates responses of the Arabidopsis circadian clock to temperature changes

Alternative splicing plays crucial roles by influencing the diversity of the transcriptome and proteome and regulating protein structure/function and gene expression. It is widespread in plants, and alteration of the levels of splicing factors leads to a wide variety of growth and developmental phenotypes. The circadian clock is a complex piece of cellular machinery that can regulate physiology and behavior to anticipate predictable environmental changes on a revolving planet. We have performed a system-wide analysis of alternative splicing in clock components in Arabidopsis thaliana plants acclimated to different steady state temperatures or undergoing temperature transitions. This revealed extensive alternative splicing in clock genes and dynamic changes in alternatively spliced transcripts. Several of these changes, notably those affecting the circadian clock genes late elongated hypocotyl (LHY) and pseudo response regulator7, are temperature-dependent and contribute markedly to functionally important changes in clock gene expression in temperature transitions by producing nonfunctional transcripts and/or inducing nonsense-mediated decay. Temperature effects on alternative splicing contribute to a decline in LHY transcript abundance on cooling, but LHY promoter strength is not affected. We propose that temperature-associated alternative splicing is an additional mechanism involved in the operation and regulation of the plant circadian clock.

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.

Multiple light inputs to a simple clock circuit allow complex biological rhythms

Circadian clocks are biological timekeepers that allow living cells to time their activity in anticipation of predictable environmental changes. Detailed understanding of the circadian network of higher plants, such as Arabidopsis thaliana, is hampered by the high number of partially redundant genes. However, the picoeukaryotic alga Ostreococcus tauri, which was recently shown to possess a small number of non-redundant clock genes, presents an attractive alternative target for detailed modelling of circadian clocks in the green lineage. Based on extensive time-series data from in vivo reporter gene assays, we developed a model of the Ostreococcus clock as a feedback loop between the genes TOC1 and CCA1. The model reproduces the dynamics of the transcriptional and translational reporters over a range of photoperiods. Surprisingly, the model is also able to predict the transient behaviour of the clock when the light conditions are altered. Despite the apparent simplicity of the clock circuit, it displays considerable complexity in its response to changing light conditions. Systematic screening of the effects of altered day length revealed a complex relationship between phase and photoperiod, which is also captured by the model. The complex light response is shown to stem from circadian gating of light-dependent mechanisms. This study provides insights into the contributions of light inputs to the Ostreococcus clock. The model suggests that a high number of light-dependent reactions are important for flexible timing in a circadian clock with only one feedback loop.

Circadian clock parameter measurement: characterization of clock transcription factors using surface plasmon resonance

To refine mathematical models of the transcriptional/translational feedback loop in the clockwork of Arabidopsis thaliana, the investigators sought to determine the affinity of the transcription factors LHY, CCA1, and CHE for their cognate DNA target sequences in vitro. Steady-state dissociation constants were observed to lie in the low nanomolar range. Furthermore, the data suggest that the LHY/CCA1 heterodimer binds more tightly than either homodimer and that DNA binding of these complexes is temperature compensated. Finally, it was found that LHY binding to the evening element in vitro is enhanced by both molecular crowding effects and by casein kinase 2-mediated phosphorylation.

Circadian oscillators in eukaryotes

The biological clock, present in nearly all eukaryotes, has evolved such that organisms can adapt to our planet's rotation in order to anticipate the coming day or night as well as unfavorable seasons. As all modern high-precision chronometers, the biological clock uses oscillation as a timekeeping element. In this review, we describe briefly the discovery, historical development, and general properties of circadian oscillators. The issue of temperature compensation (TC) is discussed, and our present understanding of the underlying genetic and biochemical mechanisms in circadian oscillators are described with special emphasis on Neurospora crassa, mammals, and plants.

Robustness from flexibility in the fungal circadian clock

BACKGROUND

Robustness is a central property of living systems, enabling function to be maintained against environmental perturbations. A key challenge is to identify the structures in biological circuits that confer system-level properties such as robustness. Circadian clocks allow organisms to adapt to the predictable changes of the 24-hour day/night cycle by generating endogenous rhythms that can be entrained to the external cycle. In all organisms, the clock circuits typically comprise multiple interlocked feedback loops controlling the rhythmic expression of key genes. Previously, we showed that such architectures increase the flexibility of the clock's rhythmic behaviour. We now test the relationship between flexibility and robustness, using a mathematical model of the circuit controlling conidiation in the fungus Neurospora crassa.

RESULTS

The circuit modelled in this work consists of a central negative feedback loop, in which the frequency (frq) gene inhibits its transcriptional activator white collar-1 (wc-1), interlocked with a positive feedback loop in which FRQ protein upregulates WC-1 production. Importantly, our model reproduces the observed entrainment of this circuit under light/dark cycles with varying photoperiod and cycle duration. Our simulations show that whilst the level of frq mRNA is driven directly by the light input, the falling phase of FRQ protein, a molecular correlate of conidiation, maintains a constant phase that is uncoupled from the times of dawn and dusk. The model predicts the behaviour of mutants that uncouple WC-1 production from FRQ's positive feedback, and shows that the positive loop enhances the buffering of conidiation phase against seasonal photoperiod changes. This property is quantified using Kitano's measure for the overall robustness of a regulated system output. Further analysis demonstrates that this functional robustness is a consequence of the greater evolutionary flexibility conferred on the circuit by the interlocking loop structure.

CONCLUSIONS

Our model shows that the behaviour of the fungal clock in light-dark cycles can be accounted for by a transcription-translation feedback model of the central FRQ-WC oscillator. More generally, we provide an example of a biological circuit in which greater flexibility yields improved robustness, while also introducing novel sensitivity analysis techniques applicable to a broader range of cellular oscillators.

Weather and seasons together demand complex biological clocks

The 24-hour rhythms of the circadian clock [1] allow an organism to anticipate daily environmental cycles, giving it a competitive advantage [2, 3]. Although clock components show little protein sequence homology across phyla, multiple feedback loops and light inputs are universal features of clock networks [4, 5]. Why have circadian systems evolved such a complex structure? All biological clocks entrain a set of regulatory genes to the environmental cycle, in order to correctly time the expression of many downstream processes. Thus the question becomes: What aspects of the environment, and of the desired downstream regulation, are demanding the observed complexity? To answer this, we have evolved gene regulatory networks in silico, selecting for networks that correctly predict particular phases of the day under light/dark cycles. Gradually increasing the realism of the environmental cycles, we have tested the networks for the minimal characteristics of clocks observed in nature: oscillation under constant conditions, entrainment to light signals, and the presence of multiple feedback loops and light inputs. Realistic circadian gene networks are found to require a nontrivial combination of conditions, with seasonal differences in photoperiod as a necessary but not sufficient component.

A role for casein kinase 2 in the mechanism underlying circadian temperature compensation

Temperature compensation of circadian clocks is an unsolved problem with relevance to the general phenomenon of biological compensation. We identify casein kinase 2 (CK2) as a key regulator of temperature compensation of the Neurospora clock by determining that two long-standing clock mutants, chrono and period-3, displaying distinctive alterations in compensation encode the beta1 and alpha subunits of CK2, respectively. Reducing the dose of these subunits, particularly beta1, significantly alters temperature compensation without altering the enzyme's Q(10). By contrast, other kinases and phosphatases implicated in clock function do not play appreciable roles in temperature compensation. CK2 exerts its effects on the clock by directly phosphorylating FREQUENCY (FRQ), and this phosphorylation is compromised in CK2 hypomorphs. Finally, mutation of certain putative CK2 phosphosites on FRQ, shown to be phosphorylated in vivo, predictably alters temperature compensation profiles effectively phenocopying CK2 mutants.

Circadian clocks can take a few transcriptional knocks

A thought-provoking study in this issue of The EMBO Journal shows that the circadian clock in mouse fibroblasts is surprisingly insensitive to the inhibition of total cellular mRNA production. The authors go on to show intriguing parallels between compensation of period to changes in temperature and global transcription rate.

Closing the circadian negative feedback loop: FRQ-dependent clearance of WC-1 from the nucleus

In Neurospora crassa, a transcription factor, WCC, activates the transcription of frq. FRQ forms homodimers as well as complexes with an RNA helicase, FRH, and the WCC, and translocates into the nucleus to inactivate the WCC, closing the time-delayed negative feedback loop. The detailed mechanism for closing this loop, however, remains incompletely understood. In particular within the nucleus, the low amount of FRQ compared with that of WC-1 creates a conundrum: How can the nuclear FRQ inactivate the larger amount of WCC? One possibility is that FRQ might function as a catalytic component in phosphorylation-dependent inhibition. However, in silico experiments reveal that stoichiometric noncatalytic binding and inhibition can generate a robust oscillator, even when nuclear FRQ levels are substantially lower than nuclear WCC, so long as there is FRQ-dependent clearance of WC-1 from the nucleus. Based on this model, we can predict and now demonstrate that WC-1 stability cycles, that WC-1 is stable in the absence of FRQ, and that physical binding between FRQ and WCC is essential for closure of the negative feedback loop. Moreover, and consistent with a noncatalytic clearance-based model for inhibition, appreciable amounts of the nuclear FRQ:WCC complex accumulate at some times of day, comprising as much as 10% of the nuclear WC-1.