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Circadian rhythms are acquired through evolution to increase the chances for survival through synchronizing with the daylight cycle. Reliable synchronization is realized through two trade-off properties: regularity to keep time precisely, and entrainability to synchronize the internal time with daylight. We found by using a phase model with multiple inputs that achieving the maximal limit of regularity and entrainability entails many inherent features of the circadian mechanism. At the molecular level, we demonstrate the role sharing of two light inputs, phase advance and delay, as is well observed in mammals. At the behavioral level, the optimal phase-response curve inevitably contains a dead zone, a time during which light pulses neither advance nor delay the clock. We reproduce the results of phase-controlling experiments entrained by two types of periodic light pulses. Our results indicate that circadian clocks are designed optimally for reliable clockwork through evolution.

This article is from Frontiers in Molecular Neuroscience , volume 6 . Abstract Time-Place learning (TPL) refers to the ability of animals to remember important events that vary in both time and place. This ability is thought to be functional to optimize resource localization and predator avoidance in a circadian changing environment. Various studies have indicated that animals use their circadian system for TPL. However, not much is known about this specific role of the circadian system in cognition. This review aims to put TPL in a broader context and to provide an overview of historical background, functional aspects, and future perspectives of TPL. Recent advances have increased our knowledge on establishing TPL in a laboratory setting, leading to the development of a behavioral paradigm demonstrating the circadian nature of TPL in mice. This has enabled the investigation of circadian clock components on a functional behavioral level. Circadian TPL (cTPL) was found to be Cry clock gene dependent, confirming the essential role of Cry genes in circadian rhythms. In contrast, preliminary results have shown that cTPL is independent of Per genes. Circadian system decline with aging predicts that cTPL is age sensitive, potentially qualifying TPL as a functional model for episodic memory and aging. The underlying neurobiological mechanism of TPL awaits further examination. Here we discuss some putative mechanisms.

Physiological rhythms are central to life. Mammalian behavior and metabolism are organized around the day and night by the regulated action of cell-autonomous clocks that exist throughout our bodies. At the core of this molecular clockwork are multiple coupled feedback loops that generate sustained circadian rhythms in gene expression to ultimately orchestrate mammalian physiology. In this work we provide evidence for the role of metabolism in regulating the core clock. We present genes involved in energetic and redox pathways which we identified to be essential for the robustness of cellular timekeepers to temperature fluctuations. We developed the first computational model for circadian redox oscillations that contributes to the understanding of how cellular redox balance might adjust circadian rates in response to perturbations and convey timing information to the core molecular oscillator. Moreover, we show that our mathematical model can be coupled with prior published models of the transcriptional clockwork resulting in 1:1 entrainment. This experimental-theoretical approach exemplifies the need of a dynamic analysis at the system level to understand complex biological processes and provides insights into how basic timekeeping mechanisms are integrated into cellular physiology. Such knowledge might highlight new ways by which functional consequences of circadian timekeeping can be explored in the context of human health and disease.

This article is from BMC Developmental Biology , volume 14 . Abstract Background: Circadian clocks have been postulated to regulate development time in several species of insects including fruit flies Drosophila melanogaster. Previously we have reported that selection for faster pre-adult development reduces development time (by ~19 h or ~11%) and clock period (by ~0.5 h), suggesting a role of circadian clocks in the regulation of development time in D. melanogaster. We reasoned that these faster developing flies could serve as a model to study stage-specific interaction of circadian clocks and developmental events with the environmental light/dark (LD) conditions. We assayed the duration of three pre-adult stages in the faster developing (FD) and control (BD) populations under a variety of light regimes that are known to modulate circadian clocks and pre-adult development time of Drosophila to examine the role of circadian clocks in the timing of pre-adult developmental stages. Results: We find that the duration of pre-adult stages was shorter under constant light (LL) and short period light (L)/dark (D) cycles (L:D = 10:10 h; T20) compared to the standard 24 h day (L:D = 12:12 h; T24), long LD cycles (L:D = 14:14 h; T28) and constant darkness (DD). The difference in the duration of pre-adult stages between the FD and BD populations was significantly smaller under the three LD cycles and LL compared to DD, possibly due to the fact that clocks of both FD and BD flies are driven at the same pace in the three LD regimes owing to circadian entrainment, or are rendered dysfunctional under LL. Conclusions: These results suggest that interaction between light regimes and circadian clocks regulate the duration of pre-adult developmental stages in fruit flies D. melanogaster.

This article is from PLoS ONE , volume 9 . Abstract Circadian clocks in the peripheral tissues of mice are known to be entrained by pulse stimuli such as restricted feeding, novel wheel running, and several other agents. However, there are no reports on high temperature pulse-mediated entrainment on the phase-shift of peripheral clocks in vivo. Here we show that temperature treatment of mice for two days at 41°C, instead of 37°C, for 1–2 h during the inactive period, using a temperature controlled water bath stimulated phase-advance of peripheral clocks in the kidney, liver, and submandibular gland of PER2::LUCIFERASE mice. On the other hand, treatment for 2 days at 35°C ambient room temperature for 2 h did not cause a phase-advance. Maintenance of mice at 41°C in a water bath, sustained the core body temperature at 40–41°C. However, the use of 37°C water bath or the 35°C ambient room temperature elevated the core body temperature to 38.5°C, suggesting that at least a core body temperature of 40–41°C is necessary to cause phase-advance under light-dark cycle conditions. The temperature pulse stimulation at 41°C, instead of 37°C water bath for 2 h led to the elevated expression of Per1 and Hsp70 in the peripheral tissue of mice. In summary, the present study demonstrates that transient high temperature pulse using water bath during daytime causes phase-advance in mouse peripheral clocks in vivo. The present results suggest that hot water bath may affect the phase of peripheral clocks.

This article is from PLoS ONE , volume 9 . Abstract Circadian clocks in the peripheral tissues of mice are known to be entrained by pulse stimuli such as restricted feeding, novel wheel running, and several other agents. However, there are no reports on high temperature pulse-mediated entrainment on the phase-shift of peripheral clocks in vivo. Here we show that temperature treatment of mice for two days at 41°C, instead of 37°C, for 1–2 h during the inactive period, using a temperature controlled water bath stimulated phase-advance of peripheral clocks in the kidney, liver, and submandibular gland of PER2::LUCIFERASE mice. On the other hand, treatment for 2 days at 35°C ambient room temperature for 2 h did not cause a phase-advance. Maintenance of mice at 41°C in a water bath, sustained the core body temperature at 40–41°C. However, the use of 37°C water bath or the 35°C ambient room temperature elevated the core body temperature to 38.5°C, suggesting that at least a core body temperature of 40–41°C is necessary to cause phase-advance under light-dark cycle conditions. The temperature pulse stimulation at 41°C, instead of 37°C water bath for 2 h led to the elevated expression of Per1 and Hsp70 in the peripheral tissue of mice. In summary, the present study demonstrates that transient high temperature pulse using water bath during daytime causes phase-advance in mouse peripheral clocks in vivo. The present results suggest that hot water bath may affect the phase of peripheral clocks.

The development of systemic approaches in biology has put emphasis on identifying genetic modules whose behavior can be modeled accurately so as to gain insight into their structure and function. However most gene circuits in a cell are under control of external signals and thus quantitative agreement between experimental data and a mathematical model is difficult. Circadian biology has been one notable exception: quantitative models of the internal clock that orchestrates biological processes over the 24-hour diurnal cycle have been constructed for a few organisms, from cyanobacteria to plants and mammals. In most cases, a complex architecture with interlocked feedback loops has been evidenced. Here we present first modeling results for the circadian clock of the green unicellular alga Ostreococcus tauri. Two plant-like clock genes have been shown to play a central role in Ostreococcus clock. We find that their expression time profiles can be accurately reproduced by a minimal model of a two-gene transcriptional feedback loop. Remarkably, best adjustment of data recorded under light/dark alternation is obtained when assuming that the oscillator is not coupled to the diurnal cycle. This suggests that coupling to light is confined to specific time intervals and has no dynamical effect when the oscillator is entrained by the diurnal cycle. This intringuing property may reflect a strategy to minimize the impact of fluctuations in daylight intensity on the core circadian oscillator, a type of perturbation that has been rarely considered when assessing the robustness of circadian clocks.

Circadian oscillation provides selection advantages through synchronization to the daylight cycle. However, a reliable clock must be designed through two conflicting properties: entrainability to synchronize internal time with periodic stimuli such as sunlight, and regularity to oscillate with a precise period. These two aspects do not easily coexist because better entrainability favors higher sensitivity, which may sacrifice the regularity. To investigate conditions for satisfying the two properties, we analytically calculated the optimal phase-response curve with a variational method. Our result indicates an existence of a dead zone, i.e., a time period during which input stimuli neither advance nor delay the clock. A dead zone appears only when input stimuli obey the time course of actual solar radiation but a simple sine curve cannot yield a dead zone. Our calculation demonstrates that every circadian clock with a dead zone is optimally adapted to the daylight cycle.

This article is from Frontiers in Aging Neuroscience , volume 6 . Abstract Alzheimer’s disease (AD) is a global epidemic. Unfortunately, we are still without effective treatments or a cure for this disease, which is having devastating consequences for patients, their families, and societies around the world. Until effective treatments are developed, promoting overall health may hold potential for delaying the onset or preventing neurodegenerative diseases such as AD. In particular, chronobiological concepts may provide a useful framework for identifying the earliest signs of age-related disease as well as inexpensive and noninvasive methods for promoting health. It is well reported that AD is associated with disrupted circadian functioning to a greater extent than normal aging. However, it is unclear if the central circadian clock (i.e., the suprachiasmatic nucleus) is dysfunctioning, or whether the synchrony between the central and peripheral clocks that control behavior and metabolic processes are becoming uncoupled. Desynchrony of rhythms can negatively affect health, increasing morbidity and mortality in both animal models and humans. If the uncoupling of rhythms is contributing to AD progression or exacerbating symptoms, then it may be possible to draw from the food-entrainment literature to identify mechanisms for re-synchronizing rhythms to improve overall health and reduce the severity of symptoms. The following review will briefly summarize the circadian system, its potential role in AD, and propose using a feeding-related neuropeptide, such as ghrelin, to synchronize uncoupled rhythms. Synchronizing rhythms may be an inexpensive way to promote healthy aging and delay the onset of neurodegenerative disease such as AD.

This article is from Diabetes , volume 62 . Abstract None

The cyanobacterium Synechococcus elongatus uses both a protein phosphorylation cycle and a transcription-translation cycle to generate circadian rhythms that are highly robust against biochemical noise. We use stochastic simulations to analyze how these cycles interact to generate stable rhythms in growing, dividing cells. We find that a protein phosphorylation cycle by itself is robust when protein turnover is low. For high decay or dilution rates (and co mpensating synthesis rate), however, the phosphorylation-based oscillator loses its integrity. Circadian rhythms thus cannot be generated with a phosphorylation cycle alone when the growth rate, and consequently the rate of protein dilution, is high enough; in practice, a purely post-translational clock ceases to function well when the cell doubling time drops below the 24 hour clock period. At higher growth rates, a transcription-translation cycle becomes essential for generating robust circadian rhythms. Interestingly, while a transcription-translation cycle is necessary to sustain a phosphorylation cycle at high growth rates, a phosphorylation cycle can dramatically enhance the robustness of a transcription-translation cycle at lower protein decay or dilution rates. Our analysis thus predicts that both cycles are required to generate robust circadian rhythms over the full range of growth conditions.

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 non-specific 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 the different phosphoforms, makes the clock less susceptible to perturbations in protein synthesis; and the presence of multiple, asynchronously replicating copies of the same chromosome diminishes the effect of replicating any single copy of a gene.

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 complex clocks.

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 complex clocks.

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 complex clocks.

Autonomous circadian clocks drive daily rhythms in physiology and behaviour. A network of coupled neurons, the suprachiasmatic nucleus (SCN), serves as a robust self-sustained circadian pacemaker. Synchronization of this timer to the environmental light-dark cycle is crucial for an organism's fitness. In a recent theoretical and experimental study it was shown that coupling governs the entrainment range of circadian clocks. We apply the theory of coupled oscillators to analyse how diffusive and mean-field coupling affects the entrainment range of interacting cells. Mean-field coupling leads to amplitude expansion of weak oscillators and, as a result, reduces the entrainment range. We also show that coupling determines the rigidity of the synchronized SCN network, i.e. the relaxation rates upon perturbation. %(Floquet exponents). Our simulations and analytical calculations using generic oscillator models help to elucidate how coupling determines the entrainment of the SCN. Our theoretical framework helps to interpret experimental data.

This article is from PLoS ONE , volume 8 . Abstract Dysfunction of circadian clocks exacerbates various diseases, in part likely due to impaired stress resistance. It is unclear how circadian clock system responds toward critical stresses, to evoke life-protective adaptation. We identified a reactive oxygen species (ROS), H2O2 -responsive circadian pathway in mammals. Near-lethal doses of ROS-induced critical oxidative stress (cOS) at the branch point of life and death resets circadian clocks, synergistically evoking protective responses for cell survival. The cOS-triggered clock resetting and pro-survival responses are mediated by transcription factor, central clock-regulatory BMAL1 and heat shock stress-responsive (HSR) HSF1. Casein kinase II (CK2) –mediated phosphorylation regulates dimerization and function of BMAL1 and HSF1 to control the cOS-evoked responses. The core cOS-responsive transcriptome includes CK2-regulated crosstalk between the circadian, HSR, NF-kappa-B-mediated anti-apoptotic, and Nrf2-mediated anti-oxidant pathways. This novel circadian-adaptive signaling system likely plays fundamental protective roles in various ROS-inducible disorders, diseases, and death.

This article is from Journal of the Royal Society Interface , volume 11 . Abstract Circadian oscillation provides selection advantages through synchronization to the daylight cycle. However, a reliable clock must be designed through two conflicting properties: entrainability to synchronize internal time with periodic stimuli such as sunlight, and regularity to oscillate with a precise period. These two aspects do not easily coexist, because better entrainability favours higher sensitivity which may sacrifice regularity. To investigate conditions for satisfying the two properties, we analytically calculated the optimal phase–response curve with a variational method. Our results indicate an existence of a dead zone, i.e. a time period during which input stimuli neither advance nor delay the clock. A dead zone appears only when input stimuli obey the time course of actual solar radiation, but a simple sine curve cannot yield a dead zone. Our calculation demonstrates that every circadian clock with a dead zone is optimally adapted to the daylight cycle.

This article is from The Journal of Endocrinology , volume 222 . Abstract Adaptation to the environment is essential for survival, in all wild animal species seasonal variation in temperature and food availability needs to be anticipated. This has led to the evolution of deep-rooted physiological cycles, driven by internal clocks, which can track seasonal time with remarkable precision. Evidence has now accumulated that a seasonal change in thyroid hormone (TH) availability within the brain is a crucial element. This is mediated by local control of TH-metabolising enzymes within specialised ependymal cells lining the third ventricle of the hypothalamus. Within these cells, deiodinase type 2 enzyme is activated in response to summer day lengths, converting metabolically inactive thyroxine (T4) to tri-iodothyronine (T3). The availability of TH in the hypothalamus appears to be an important factor in driving the physiological changes that occur with season. Remarkably, in both birds and mammals, the pars tuberalis (PT) of the pituitary gland plays an essential role. A specialised endocrine thyrotroph cell (TSH-expressing) is regulated by the changing day-length signal, leading to activation of TSH by long days. This acts on adjacent TSH-receptors expressed in the hypothalamic ependymal cells, causing local regulation of deiodinase enzymes and conversion of TH to the metabolically active T3. In mammals, the PT is regulated by the nocturnal melatonin signal. Summer-like melatonin signals activate a PT-expressed clock-regulated transcription regulator (EYA3), which in turn drives the expression of the TSHβ sub-unit, leading to a sustained increase in TSH expression. In this manner, a local pituitary timer, driven by melatonin, initiates a cascade of molecular events, led by EYA3, which translates to seasonal changes of neuroendocrine activity in the hypothalamus. There are remarkable parallels between this PT circuit and the photoperiodic timing system used in plants, and while plants use different molecular signals (constans vs EYA3) it appears that widely divergent organisms probably obey a common set of design principles.

This article is from Interface Focus , volume 1 . Abstract We present a new approach to understanding how regulatory networks such as circadian clocks might evolve robustness to environmental fluctuations. The approach is in terms of new balance equations that we derive. We use it to describe how an entrained clock can buffer the effects of daily fluctuations in light and temperature levels. We also use it to study a different approach to temperature compensation where instead of considering a free-running clock, we study temperature buffering of the phases in a light-entrained clock, which we believe is a more physiological setting.

This article is from Frontiers in Endocrinology , volume 5 . Abstract None

This article is from Scientific Reports , volume 2 . Abstract Peripheral circadian clocks in mammals are strongly entrained by light-dark and eating cycles. Their physiological functions are maintained by the synchronization of the phase of organs via clock gene expression patterns. However, little is known about the adaptation of peripheral clocks to the timing of multiple daily meals. Here, we investigated the effect of irregular eating patterns, in terms of timing and volume, on their peripheral clocks in vivo. We found that the phase of the peripheral clocks was altered by the amount of food and the interval between feeding time points but was unaffected by the frequency of feeding, as long as the interval remained fixed. Moreover, our results suggest that a late dinner should be separated into 2 half-dinners in order to alleviate the effect of irregular phases of peripheral clocks.

This article is from PLoS Biology , volume 12 . Abstract : Studies in Drosophila circadian neurons reveal a bifurcation in the Pigment Dispersing Factor (PDF) neuropeptide signaling pathway, independently synchronizing circadian clocks via PKA or acutely controlling neuronal excitability via cAMP.

This article is from PLoS Biology , volume 12 . Abstract : Studies in Drosophila circadian neurons reveal a bifurcation in the Pigment Dispersing Factor (PDF) neuropeptide signaling pathway, independently synchronizing circadian clocks via PKA or acutely controlling neuronal excitability via cAMP.

This article is from PLoS Biology , volume 12 . Abstract : Studies in Drosophila circadian neurons reveal a bifurcation in the Pigment Dispersing Factor (PDF) neuropeptide signaling pathway, independently synchronizing circadian clocks via PKA or acutely controlling neuronal excitability via cAMP.