Adaptive temperature compensation in circadian oscillations

A Compensated Clock: Temperature and Nutritional Compensation Mechanisms Across Circadian Systems

Circadian rhythms are ∼24-h biological oscillations that enable organisms to anticipate daily environmental cycles, so that they may designate appropriate day/night functions that align with these changes. The molecular clock in animals and fungi consists of a transcription-translation feedback loop, the plant clock is comprised of multiple interlocking feedback-loops, and the cyanobacterial clock is driven by a phosphorylation cycle involving three main proteins. Despite the divergent core clock mechanisms across these systems, all circadian clocks are able to buffer period length against changes in the ambient growth environment, such as temperature and nutrients. This defining capability, termed compensation, is critical to proper timekeeping, yet the underlying mechanism(s) remain elusive. Here we examine the known players in, and the current models for, compensation across five circadian systems. While compensation models across these systems are not yet unified, common themes exist across them, including regulation via temperature-dependent changes in post-translational modifications.

A mathematical model of melatonin synthesis and interactions with the circadian clock

A new mathematical model of melatonin synthesis in pineal cells is created and connected to a slightly modified previously created model of the circadian clock in the suprachiasmatic nucleus (SCN). The SCN influences the production of melatonin by upregulating two key enzymes in the pineal. The melatonin produced enters the blood and the cerebrospinal fluid and thus the SCN, influencing the circadian clock. We show that the model of melatonin synthesis corresponds well with extant experimental data and responds similarly to clinical experiments on bright light in the middle of the night. Melatonin is widely used to treat jet lag and sleep disorders. We show how the feedback from the pineal to the SCN causes phase resetting of the circadian clock. Melatonin doses early in the evening advance the clock and doses late at night delay the clock with a dead zone in between where the phase of the clock does not change.

Temperature compensation through kinetic regulation in biochemical oscillators

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

A circadian-like gene network programs the timing and dosage of heterochronic miRNA transcription during C. elegans development

Development relies on the exquisite control of both the timing and the levels of gene expression to achieve robust developmental transitions. How cis- and trans-acting factors control both aspects simultaneously is unclear. We show that transcriptional pulses of the temporal patterning microRNA (miRNA) lin-4 are generated by two nuclear hormone receptors (NHRs) in C. elegans, NHR-85 and NHR-23, whose mammalian orthologs, Rev-Erb and ROR, function in the circadian clock. Although Rev-Erb and ROR antagonize each other to control once-daily transcription in mammals, NHR-85/NHR-23 heterodimers bind cooperatively to lin-4 regulatory elements to induce a single pulse of expression during each larval stage. Each pulse's timing, amplitude, and duration are dictated by the phased expression of these NHRs and the C. elegans Period ortholog, LIN-42, that binds to and represses NHR-85. Therefore, during nematode temporal patterning, an evolutionary rewiring of circadian clock components couples the timing of gene expression to the control of transcriptional dosage.

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

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

A Unified Model for Entrainment by Circadian Clocks: Dynamic Circadian Integrated Response Characteristic (dCiRC)

Circadian rhythms are ubiquitous and are observed in all biological kingdoms. In nature, their primary characteristic or phenotype is the phase of entrainment. There are two main hypotheses related to how circadian clocks entrain, parametric and non-parametric models. The parametric model focuses on the gradual changes of the clock parameters in response to the changing ambient condition, whereas the non-parametric model focuses on the instantaneous change of the phase of the clock in response to the zeitgeber. There are ample empirical data supporting both models. However, only recently has a unifying model been proposed, the circadian integrated response characteristic (CiRC). In the current study, we developed a system of ordinary differential equations, dynamic CiRC (dCiRC), that describes parameters of circadian rhythms and predicts the phase of entrainment in zeitgeber cycles. dCiRC mathematically extracts the underlying information of velocity changes of the internal clock that reflects the parametric model and the phase shift trajectory that reflects the non-parametric model from phase data under entraining conditions. As a proof of concept, we measured clock parameters of 26 Neurospora crassa ecotypes in both cycling and constant conditions using dCiRC. Our data showed that the morning light shortens the period of the clock while the afternoon light lengthens it. We also found that individual ecotypes have different strategies of integrating light effects to accomplish the optimal phase of entrainment, a model feature that is consistent with our knowledge of how circadian clocks are organized and encoded. The unified model dCiRC will provide new insights into how circadian clocks function under different zeitgeber conditions. We suggest that this type of model may be useful in the advent of chronotherapies.

Thermogenetics: Applications come of age

Temperature is a ubiquitous physical cue that is non-invasive, penetrative and easy to apply. In the growing field of thermogenetics, through beneficial repurposing of natural thermosensing mechanisms, synthetic biology is bringing new opportunities to design and build robust temperature-sensitive (TS) sensors which forms a thermogenetic toolbox of well characterised biological parts. Recent advancements in technological platforms available have expedited the discovery of novel or de novo thermosensors which are increasingly deployed in many practical temperature-dependent biomedical, industrial and biosafety applications. In all, the review aims to convey both the exhilarating recent technological developments underlying the advancement of thermosensors and the exciting opportunities the nascent thermogenetic field holds for biomedical and biotechnology applications.

Collective Oscillations in Coupled-Cell Systems

We investigate oscillations in coupled systems. The methodology is based on the Hopf bifurcation theorem and a condition extended from the Routh–Hurwitz criterion. Such a condition leads to locating the bifurcation values of the parameters. With such an approach, we analyze a single-cell system modeling the minimal genetic negative feedback loop and the coupled-cell system composed by these single-cell systems. We study the oscillatory properties for these systems and compare these properties between the model with Hill-type repression and the one with protein-sequestration-based repression. As the parameters move from the Hopf bifurcation value for single cells to the one for coupled cells, we compute the eigenvalues of the linearized systems to obtain the magnitude of the collective frequency when the periodic solution of the coupled-cell system is generated. Extending from this information on the parameter values, we further compute and compare the collective frequency for the coupled-cell system and the average frequency of the decoupled individual cells. To compare these scenarios with other biological oscillators, we perform parallel analysis and computations on a segmentation clock model.

Robust oscillations in multi-cyclic Markov state models of biochemical clocks

Organisms often use cyclic changes in the concentrations of chemical species to precisely time biological functions. Underlying these biochemical clocks are chemical reactions and transport processes, which are inherently stochastic. Understanding the physical basis for robust biochemical oscillations in the presence of fluctuations has thus emerged as an important problem. In a previous paper [C. del Junco and S. Vaikuntanathan, Phys. Rev. E 101, 012410 (2020)], we explored this question using the non-equilibrium statistical mechanics of single-ring Markov state models of biochemical networks that support oscillations. Our finding was that they can exploit non-equilibrium driving to robustly maintain the period and coherence of oscillations in the presence of randomness in the rates. Here, we extend our work to Markov state models consisting of a large cycle decorated with multiple small cycles. These additional cycles are intended to represent alternate pathways that the oscillator may take as it fluctuates about its average path. Combining a mapping to single-cycle networks based on first passage time distributions with our previously developed theory, we are able to make analytical predictions for the period and coherence of oscillations in these networks. One implication of our predictions is that a high energy budget can make different network topologies and arrangements of rates degenerate as far as the period and coherence of oscillations are concerned. Excellent agreement between analytical and numerical results confirms that this is the case. Our results suggest that biochemical oscillators can be more robust to fluctuations in the path of the oscillator when they have a high energy budget.

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.

Resonant Behavior in a Periodically Forced Nonisothermal Oregonator

Nonisothermal chemical oscillators are poorly studied systems because chemical oscillations are conventionally studied under isothermal conditions. Coupling chemical reactions with heat generation and removal in a nonisothermal oscillatory system can lead to a highly nontrivial nonlinear dynamic behavior. For the current study, we considered the three-variable Oregonator model with the temperature incorporated as a variable (not a parameter), thus adding an energy balance to the set of equations. The effect of temperature on reaction rates is included through the temperature-dependent reaction rate coefficients (Arrhenius law). To model a continuous operation in a laboratory environment, the system was subjected to external forcing through the coolant temperature and infrared irradiation. By conducting numerical simulations and parametric studies, we found that the system is capable of a resonant behavior exhibiting induced oscillations. Our findings indicate that an external source of heat (e.g., via an infrared light emitting diode) can be used to induce a Hopf bifurcation under resonant conditions in an experimental Belousov-Zhabotinsky reactor.

An Inactivation Switch Enables Rhythms in a Neurospora Clock Model

Autonomous endogenous time-keeping is ubiquitous across many living organisms, known as the circadian clock when it has a period of about 24 h. Interestingly, the fundamental design principle with a network of interconnected negative and positive feedback loops is conserved through evolution, although the molecular components differ. Filamentous fungus Neurospora crassa is a well-established chrono-genetics model organism to investigate the underlying mechanisms. The core negative feedback loop of the clock of Neurospora is composed of the transcription activator White Collar Complex (WCC) (heterodimer of WC1 and WC2) and the inhibitory element called FFC complex, which is made of FRQ (Frequency protein), FRH (Frequency interacting RNA Helicase) and CK1a (Casein kinase 1a). While exploring their temporal dynamics, we investigate how limit cycle oscillations arise and how molecular switches support self-sustained rhythms. We develop a mathematical model of 10 variables with 26 parameters to understand the interactions and feedback among WC1 and FFC elements in nuclear and cytoplasmic compartments. We performed control and bifurcation analysis to show that our novel model produces robust oscillations with a wild-type period of 22.5 h. Our model reveals a switch between WC1-induced transcription and FFC-assisted inactivation of WC1. Using the new model, we also study the possible mechanisms of glucose compensation. A fairly simple model with just three nonlinearities helps to elucidate clock dynamics, revealing a mechanism of rhythms' production. The model can further be utilized to study entrainment and temperature compensation.

Non-sinusoidal Waveform in Temperature-Compensated Circadian Oscillations

Time series of biological rhythms are of various shapes. Here, we investigated the waveforms of circadian rhythms in gene-protein dynamics using a newly developed, to our knowledge, index to quantify the degree of distortion from a sinusoidal waveform. In general, most biochemical reactions accelerate with increasing temperature, but the period of circadian rhythms remains relatively stable with temperature change, a phenomenon known as "temperature compensation." Despite extensive research, the mechanism underlying this remains unclear. To understand the mechanism, we used transcriptional-translational oscillator models for circadian rhythms in the fruit fly Drosophila and mammals. Given the assumption that reaction rates increase with temperature, mathematical analyses revealed that temperature compensation required waveforms that are more nonsinusoidal at higher temperatures. We then analyzed a post-translational oscillator (PTO) model of cyanobacteria circadian rhythms. Because the structure of the PTO is different from that of the transcriptional-translational oscillator, the condition for temperature compensation would be expected to differ. Unexpectedly, the computational analysis again showed that temperature compensation in the PTO model required a more nonsinusoidal waveform at higher temperatures. This finding held for both models even with a milder assumption that some reaction rates do not change with temperature, which is consistent with experimental evidence. Together, our theoretical analyses predict that the waveform of circadian gene-activity and/or protein phosphorylation rhythms would be more nonsinusoidal at higher temperatures, even when there are differences in the network structures.

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

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

Hidden long evolutionary memory in a model biochemical network

We introduce a minimal model for the evolution of functional protein-interaction networks using a sequence-based mutational algorithm, and apply the model to study neutral drift in networks that yield oscillatory dynamics. Starting with a functional core module, random evolutionary drift increases network complexity even in the absence of specific selective pressures. Surprisingly, we uncover a hidden order in sequence space that gives rise to long-term evolutionary memory, implying strong constraints on network evolution due to the topology of accessible sequence space.

Delay models for the early embryonic cell cycle oscillator

Time delays are known to play a crucial role in generating biological oscillations. The early embryonic cell cycle in the frog Xenopus laevis is one such example. Although various mathematical models of this oscillating system exist, it is not clear how to best model the required time delay. Here, we study a simple cell cycle model that produces oscillations due to the presence of an ultrasensitive, time-delayed negative feedback loop. We implement the time delay in three qualitatively different ways, using a fixed time delay, a distribution of time delays, and a delay that is state-dependent. We analyze the dynamics in all cases, and we use experimental observations to interpret our results and put constraints on unknown parameters. In doing so, we find that different implementations of the time delay can have a large impact on the resulting oscillations.

Complexity of Biochemical and Genetic Responses Reduced Using Simple Theoretical Models

Living systems are known to behave in a complex and sometimes unpredictable manner. Humans, for a very long time, have been intrigued by nature, and have attempted to understand biological processes and mechanisms using numerous experimental and mathematical techniques. In this chapter, we will look at simple theoretical models, using both linear and nonlinear differential equations, that realistically capture complex biochemical and genetic responses of living cells. Even for cases where cellular behaviors are stochastic, as for single-cell responses, randomness added to well-defined deterministic models has elegantly been shown to be useful. The data collectively present evidence for further exploration of the self-organizing rules and laws of living matter.

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.

Robust network topologies for generating oscillations with temperature-independent periods

Nearly all living systems feature a temperature-independent oscillation period in circadian clocks. This ubiquitous property occurs at the system level and is rooted in the network architecture of the clock machinery. To investigate the mechanism of this prominent property of the circadian clock and provide general guidance for generating robust genetic oscillators with temperature-compensated oscillations, we theoretically explored the design principle and core network topologies preferred by oscillations with a temperature-independent period. By enumerating all topologies of genetic regulatory circuits with three genes, we obtained four network motifs, namely, a delayed negative feedback oscillator, repressilator, activator-inhibitor oscillator and substrate-depletion oscillator; hybrids of these motifs constitute the vast majority of target network topologies. These motifs are biased in their capacities for achieving oscillations and the temperature sensitivity of the period. The delayed negative feedback oscillator and repressilator are more robust for oscillations, whereas the activator-inhibitor and substrate-depletion oscillators are superior for maintaining a temperature-independent oscillation period. These results suggest that thermally robust oscillation can be more plausibly achieved by hybridizing these two categories of network motifs. Antagonistic balance and temperature insulation mechanisms for achieving temperature compensation are typically found in these topologies with temperature robustness. In the temperature insulation approach, the oscillation period relies on very few parameters, and these parameters are influenced only slightly by temperature. This approach prevents the temperature from affecting the oscillation period and generates circadian rhythms that are robust against environmental perturbations.

Revealing physical interaction networks from statistics of collective dynamics

Revealing physical interactions in complex systems from observed collective dynamics constitutes a fundamental inverse problem in science. Current reconstruction methods require access to a system's model or dynamical data at a level of detail often not available. We exploit changes in invariant measures, in particular distributions of sampled states of the system in response to driving signals, and use compressed sensing to reveal physical interaction networks. Dynamical observations following driving suffice to infer physical connectivity even if they are temporally disordered, are acquired at large sampling intervals, and stem from different experiments. Testing various nonlinear dynamic processes emerging on artificial and real network topologies indicates high reconstruction quality for existence as well as type of interactions. These results advance our ability to reveal physical interaction networks in complex synthetic and natural systems.

Using Sub-Network Combinations to Scale Up an Enumeration Method for Determining the Network Structures of Biological Functions

Deduction of biological regulatory networks from their functions is one of the focus areas of systems biology. Among the different techniques used in this reverse-engineering task, one powerful method is to enumerate all candidate network structures to find suitable ones. However, this method is severely limited by calculation capability: due to the brute-force approach, it is infeasible for networks with large number of nodes to be studied using traditional enumeration method because of the combinatorial explosion. In this study, we propose a new reverse-engineering technique based on the enumerating method: sub-network combinations. First, a complex biological function is divided into several sub-functions. Next, the three-node-network enumerating method is applied to search for sub-networks that are able to realize each of the sub-functions. Finally, complex whole networks are constructed by enumerating all possible combinations of sub-networks. The optimal ones are selected and analyzed. To demonstrate the effectiveness of this new method, we used it to deduct the network structures of a Pavlovian-like function. The whole Pavlovian-like network was successfully constructed by combining robust sub-networks, and the results were analyzed. With sub-network combination, the complexity has been largely reduced. Our method also provides a functional modular view of biological systems.

The effects of time-varying temperature on delays in genetic networks

Delays in gene networks result from the sequential nature of protein assembly. However, it is unclear how models of gene networks that use delays should be modified when considering time-dependent changes in temperature. This is important, as delay is often used in models of genetic oscillators that can be entrained by periodic fluctuations in temperature. Here, we analytically derive the time dependence of delay distributions in response to time-varying temperature changes. We find that the resulting time-varying delay is nonlinearly dependent on parameters of the time-varying temperature such as amplitude and frequency, therefore, applying an Arrhenius scaling may result in erroneous conclusions. We use these results to examine a model of a synthetic gene oscillator with temperature compensation. We show that temperature entrainment follows from the same mechanism that results in temperature compensation. Under a common Arrhenius scaling alone, the frequency of the oscillator is sensitive to changes in the mean temperature but robust to changes in the frequency of a periodically time-varying temperature. When a mechanism for temperature compensation is included in the model, however, we show that the oscillator is entrained by periodically varying temperature even when maintaining insensitivity to the mean temperature.

CRY1 and CRY2 genetic variants in seasonality: A longitudinal and cross-sectional study

Cryptochromes are key components of the circadian clocks that generate and maintain seasonal variations. The aim of our study was to analyze the associations of CRY1 and CRY2 genetic variants with the problematicity of seasonal variations, and whether the problematicity of seasonal variations changed during the follow-up of 11 years. Altogether 21 CRY1 and 16 CRY2 single-nucleotide polymorphisms (SNPs) were genotyped and analyzed in 5910 individuals from a Finnish nationwide population-based sample who had filled in the self-report on the seasonal variations in mood and behavior in the year 2000. In the year 2011, 3356 of these individuals filled in the same self-report on the seasonal variations in mood and behavior. Regression models were used to test whether any of the SNPs associated with the problematicity of seasonal variations or with a change in the problematicity from 2000 to 2011. In the longitudinal analysis, CRY2 SNP rs61884508 was protective from worsening of problematicity of seasonal variations. In the cross-sectional analysis, CRY2 SNP rs72902437 showed evidence of association with problematicity of seasonal variations, as did SNP rs1554338 (in the MAPK8IP1 and downstream of CRY2).

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

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

Temperature compensation and temperature sensation in the circadian clock

All known circadian clocks have an endogenous period that is remarkably insensitive to temperature, a property known as temperature compensation, while at the same time being readily entrained by a diurnal temperature oscillation. Although temperature compensation and entrainment are defining features of circadian clocks, their mechanisms remain poorly understood. Most models presume that multiple steps in the circadian cycle are temperature-dependent, thus facilitating temperature entrainment, but then insist that the effect of changes around the cycle sums to zero to enforce temperature compensation. An alternative theory proposes that the circadian oscillator evolved from an adaptive temperature sensor: a gene circuit that responds only to temperature changes. This theory implies that temperature changes should linearly rescale the amplitudes of clock component oscillations but leave phase relationships and shapes unchanged. We show using timeless luciferase reporter measurements and Western blots against TIMELESS protein that this prediction is satisfied by the Drosophila circadian clock. We also review evidence for pathways that couple temperature to the circadian clock, and show previously unidentified evidence for coupling between the Drosophila clock and the heat-shock pathway.

Effect of Multiple Clock Gene Ablations on the Circadian Period Length and Temperature Compensation in Mammalian Cells

Most organisms have cell-autonomous circadian clocks to coordinate their activity and physiology according to 24-h environmental changes. Despite recent progress in circadian studies, it is not fully understood how the period length and the robustness of mammalian circadian rhythms are determined. In this study, we established a series of mouse embryonic stem cell (ESC) lines with single or multiplex clock gene ablations using the CRISPR/Cas9-based genome editing method. ESC-based in vitro circadian clock formation assay shows that the CRISPR-mediated clock gene disruption not only reproduces the intrinsic circadian molecular rhythms of previously reported mice tissues and cells lacking clock genes but also reveals that complexed mutations, such as CKIδ(m/m):CKIε(+/m):Cry2(m/m) mutants, exhibit an additively lengthened circadian period. By using these mutant cells, we also investigated the relation between period length alteration and temperature compensation. Although CKIδ-deficient cells slightly affected the temperature insensitivity of period length, we demonstrated that the temperature compensation property is largely maintained in all mutants. These results show that the ESC-based assay system could offer a more systematic and comprehensive approach to the genotype-chronotype analysis of the intracellular circadian clockwork in mammals.

Brown fat activity deepens depression: True or false?

Circadian clocks have evolved a slowing-down mechanism. Temperature may be the original and universal time-giver to the organism. Brown adipose tissue generates heat and guides the circadian rhythm of core body temperature. The cryptochrome proteins regulate the temperature entrainability, and their dysfunction may let the activation of brown adipose tissue affect the brain more easily. Therefore, the activity of brown adipose tissue may compromise the slowing-down mechanism and thereby contribute to the emergence of mood disorders and the increase in suicide mortality around the time of puberty.

Evolving phenotypic networks in silico

Evolved gene networks are constrained by natural selection. Their structures and functions are consequently far from being random, as exemplified by the multiple instances of parallel/convergent evolution. One can thus ask if features of actual gene networks can be recovered from evolutionary first principles. I review a method for in silico evolution of small models of gene networks aiming at performing predefined biological functions. I summarize the current implementation of the algorithm, insisting on the construction of a proper "fitness" function. I illustrate the approach on three examples: biochemical adaptation, ligand discrimination and vertebrate segmentation (somitogenesis). While the structure of the evolved networks is variable, dynamics of our evolved networks are usually constrained and present many similar features to actual gene networks, including properties that were not explicitly selected for. In silico evolution can thus be used to predict biological behaviours without a detailed knowledge of the mapping between genotype and phenotype.

Noise induced oscillations and coherence resonance in a generic model of the nonisothermal chemical oscillator

Oscillating chemical reactions are common in biological systems and they also occur in artificial non-biological systems. Generally, these reactions are subject to random fluctuations in environmental conditions which translate into fluctuations in the values of physical variables, for example, temperature. We formulate a mathematical model for a nonisothermal minimal chemical oscillator containing a single negative feedback loop and study numerically the effects of stochastic fluctuations in temperature in the absence of any deterministic limit cycle or periodic forcing. We show that noise in temperature can induce sustained limit cycle oscillations with a relatively narrow frequency distribution and some characteristic frequency. These properties differ significantly depending on the noise correlation. Here, we have explored white and colored (correlated) noise. A plot of the characteristic frequency of the noise induced oscillations as a function of the correlation exponent shows a maximum, therefore indicating the existence of autonomous stochastic resonance, i.e. coherence resonance.

Engineered temperature compensation in a synthetic genetic clock

Synthetic biology promises to revolutionize biotechnology by providing the means to reengineer and reprogram cellular regulatory mechanisms. However, synthetic gene circuits are often unreliable, as changes to environmental conditions can fundamentally alter a circuit's behavior. One way to improve robustness is to use intrinsic properties of transcription factors within the circuit to buffer against intra- and extracellular variability. Here, we describe the design and construction of a synthetic gene oscillator in Escherichia coli that maintains a constant period over a range of temperatures. We started with a previously described synthetic dual-feedback oscillator with a temperature-dependent period. Computational modeling predicted and subsequent experiments confirmed that a single amino acid mutation to the core transcriptional repressor of the circuit results in temperature compensation. Specifically, we used a temperature-sensitive lactose repressor mutant that loses the ability to repress its target promoter at high temperatures. In the oscillator, this thermoinduction of the repressor leads to an increase in period at high temperatures that compensates for the decrease in period due to Arrhenius scaling of the reaction rates. The result is a transcriptional oscillator with a nearly constant period of 48 min for temperatures ranging from 30 °C to 41 °C. In contrast, in the absence of the mutation the period of the oscillator drops from 60 to 30 min over the same temperature range. This work demonstrates that synthetic gene circuits can be engineered to be robust to extracellular conditions through protein-level modifications.

The circadian clock in murine chondrocytes regulates genes controlling key aspects of cartilage homeostasis

ObjectiveTo characterize the circadian clock in murine cartilage tissue and identify tissue-specific clock target genes, and to investigate whether the circadian clock changes during aging or during cartilage degeneration using an experimental mouse model of osteoarthritis (OA).

MethodsCartilage explants were obtained from aged and young adult mice after transduction with the circadian clock fusion protein reporter PER2::luc, and real-time bioluminescence recordings were used to characterize the properties of the clock. Time-series microarrays were performed on mouse cartilage tissue to identify genes expressed in a circadian manner. Rhythmic genes were confirmed by quantitative reverse transcription–polymerase chain reaction using mouse tissue, primary chondrocytes, and a human chondrocyte cell line. Experimental OA was induced in mice by destabilization of the medial meniscus (DMM), and articular cartilage samples were microdissected and subjected to microarray analysis.

ResultsMouse cartilage tissue and a human chondrocyte cell line were found to contain intrinsic molecular circadian clocks. The cartilage clock could be reset by temperature signals, while the circadian period was temperature compensated. PER2::luc bioluminescence demonstrated that circadian oscillations were significantly lower in amplitude in cartilage from aged mice. Time-series microarray analyses of the mouse tissue identified the first circadian transcriptome in cartilage, revealing that 615 genes (∼3.9% of the expressed genes) displayed a circadian pattern of expression. This included genes involved in cartilage homeostasis and survival, as well as genes with potential importance in the pathogenesis of OA. Several clock genes were disrupted in the early stages of cartilage degeneration in the DMM mouse model of OA.

ConclusionThese results reveal an autonomous circadian clock in chondrocytes that can be implicated in key aspects of cartilage biology and pathology. Consequently, circadian disruption (e.g., during aging) may compromise tissue homeostasis and increase susceptibility to joint damage or disease.

The Goodwin model: behind the Hill function

The Goodwin model is a 3-variable model demonstrating the emergence of oscillations in a delayed negative feedback-based system at the molecular level. This prototypical model and its variants have been commonly used to model circadian and other genetic oscillators in biology. The only source of non-linearity in this model is a Hill function, characterizing the repression process. It was mathematically shown that to obtain limit-cycle oscillations, the Hill coefficient must be larger than 8, a value often considered unrealistic. It is indeed difficult to explain such a high coefficient with simple cooperative dynamics. We present here molecular models of the standard Goodwin model, based on single or multisite phosphorylation/dephosphorylation processes of a transcription factor, which have been previously shown to generate switch-like responses. We show that when the phosphorylation/dephosphorylation processes are fast enough, the limit-cycle obtained with a multisite phosphorylation-based mechanism is in very good quantitative agreement with the oscillations observed in the Goodwin model. Conditions in which the detailed mechanism is well approximated by the Goodwin model are given. A variant of the Goodwin model which displays sharp thresholds and relaxation oscillations is also explained by a double phosphorylation/dephosphorylation-based mechanism through a bistable behavior. These results not only provide rational support for the Goodwin model but also highlight the crucial role of the speed of post-translational processes, whose response curve are usually established at a steady state, in biochemical oscillators.

Generation of oscillating gene regulatory network motifs

Using an improved version of an evolutionary algorithm originally proposed by François and Hakim [Proc. Natl. Acad. Sci. USA 101, 580 (2004)], we generated small gene regulatory networks in which the concentration of a target protein oscillates in time. These networks may serve as candidates for oscillatory modules to be found in larger regulatory networks and protein interaction networks. The algorithm was run for 10(5) times to produce a large set of oscillating modules, which were systematically classified and analyzed. The robustness of the oscillations against variations of the kinetic rates was also determined, to filter out the least robust cases. Furthermore, we show that the set of evolved networks can serve as a database of models whose behavior can be compared to experimentally observed oscillations. The algorithm found three smallest (core) oscillators in which nonlinearities and number of components are minimal. Two of those are two-gene modules: the mixed feedback loop, already discussed in the literature, and an autorepressed gene coupled with a heterodimer. The third one is a single gene module which is competitively regulated by a monomer and a dimer. The evolutionary algorithm also generated larger oscillating networks, which are in part extensions of the three core modules and in part genuinely new modules. The latter includes oscillators which do not rely on feedback induced by transcription factors, but are purely of post-transcriptional type. Analysis of post-transcriptional mechanisms of oscillation may provide useful information for circadian clock research, as recent experiments showed that circadian rhythms are maintained even in the absence of transcription.

Hypothesis: Cryptochromes and Brown Fat are Essential for Adaptation and Affect Mood and Mood-Related Behaviors

Solar radiation and ambient temperature have acted as selective physical forces among populations and thereby guided species distributions in the globe. Circadian clocks are universal and evolve when subjected to selection, and their properties contribute to variations in fitness within specific environments. Concerning humans, as compared to the remaining, the "evening owls" have a greater deviation from the 24 h cycle, are under a greater pressure to circadian desynchrony and more prone to a cluster of health hazards with the increased mortality. Because of their position in the hierarchy and repressive actions, cryptochromes are the key components of the feedback loops on which circadian clocks are built. Based on the evidence a new hypothesis is formulated in which brown adipocytes with their cryptochromes are responsive to a broad range of physical stimuli from the habitat and through their activity ensure adaptation of the individual. The over-activated brown adipose tissue with deficient cryptochromes might induce disrupted thermoregulation and circadian desynchrony, and thereby contribute to lowered mood and pronounced depressive behaviors.