Amplitude of circadian oscillations entrained by 24-h light-dark cycles

An intriguing property of circadian clocks is that their free-running period is not exactly 24h. Using models for circadian rhythms in Neurospora and Drosophila, we determine how the entrainment of these rhythms is affected by the free-running period and by the amplitude of the external light-dark cycle. We first consider the model for Neurospora, in which light acts by inducing the expression of a clock gene. We show that the amplitude of the oscillations of the clock protein entrained by light-dark cycles is maximized when the free-running period is smaller than 24h. Moreover, if the amplitude of the light-dark cycle is very strong, complex oscillations occur when the free-running period is close to 24h. In the model for circadian rhythms in Drosophila, light acts by enhancing the degradation of a clock protein. We show that while the amplitude of circadian oscillations entrained by light-dark cycles is also maximized if the free-running period is smaller than 24h, the range of entrainment is centered around 24h in this model. We discuss the physiological relevance of these results in regard to the setting of the free-running period of the circadian clock.     

Modulation of circadian clocks by nutrients and food factors

Daily activity rhythms that are dominated by internal clocks are called circadian rhythms. A central clock is located in the suprachiasmatic nucleus of the hypothalamus, and peripheral clocks are located in most mammalian peripheral cells. The central clock is entrained by light/dark cycles, whereas peripheral clocks are entrained by feeding cycles. The effects of nutrients on the central and peripheral clocks have been investigated during the past decade and much interaction between them has come to light. For example, a high-fat diet prolongs the period of circadian behavior, a ketogenic diet advances the onset of locomotor activity rhythms, and a high-salt diet advances the phase of peripheral molecular clocks. Moreover, some food factors such as caffeine, nobiletin, and resveratrol, alter molecular and/or behavioral circadian rhythms. Here, we review nutrients and food factors that modulate mammalian circadian clocks from the cellular to the behavioral level.     

Transplanted Drosophila excretory tubules maintain circadian clock cycling out of phase with the host

Circadian rhythms in behaviors and physiological processes are driven by conserved molecular mechanisms involving the rhythmic expression of clock genes in the brains of animals [1]. The persistence of similar molecular rhythms in peripheral tissues in vitro [2] [3] suggests that these tissues contain self-sustained circadian clocks that may be linked to rhythmic physiological functions. It is not known how brain and peripheral clocks are organized into a synchronized timing system; however, it has been assumed that peripheral clocks submit to a master clock in the brain. To address this matter we examined the expression of two clock genes, period (per) and timeless (tim), in host and transplanted abdominal organs of Drosophila. We found that excretory organs in tissue culture display free-running, light-sensitive oscillations in per and tim gene activity indicating that they house self-sustained circadian clocks. To test for humoral factors, we monitored cycling of the TIM protein in excretory tubules transplanted into host flies entrained to an opposite light-dark cycle. We show that the clock protein in the donor tubules cycled out of phase with that in the host tubules, indicating that different organs may cycle independently, despite sharing the same hormonal milieu. We suggest that one way to achieve circadian coordination of physiological sub-systems in higher animals may be through the direct entrainment of light-sensitive clocks by environmental signals.     

Stochastic models for circadian rhythms: effect of molecular noise on periodic and chaotic behaviour

Circadian rhythms are endogenous oscillations that occur with a period close to 24 h in nearly all living organisms. These rhythms originate from the negative autoregulation of gene expression. Deterministic models based on such genetic regulatory processes account for the occurrence of circadian rhythms in constant environmental conditions (e.g., constant darkness), for entrainment of these rhythms by light-dark cycles, and for their phase-shifting by light pulses. When the numbers of protein and mRNA molecules involved in the oscillations are small, as may occur in cellular conditions, it becomes necessary to resort to stochastic simulations to assess the influence of molecular noise on circadian oscillations. We address the effect of molecular noise by considering the stochastic version of a deterministic model previously proposed for circadian oscillations of the PER and TIM proteins and their mRNAs in Drosophila. The model is based on repression of the per and tim genes by a complex between the PER and TIM proteins. Numerical simulations of the stochastic version of the model are performed by means of the Gillespie method. The predictions of the stochastic approach compare well with those of the deterministic model with respect both to sustained oscillations of the limit cycle type and to the influence of the proximity from a bifurcation point beyond which the system evolves to stable steady state. Stochastic simulations indicate that robust circadian oscillations can emerge at the cellular level even when the maximum numbers of mRNA and protein molecules involved in the oscillations are of the order of only a few tens or hundreds. The stochastic model also reproduces the evolution to a strange attractor in conditions where the deterministic PER-TIM model admits chaotic behaviour. The difference between periodic oscillations of the limit cycle type and aperiodic oscillations (i.e. chaos) persists in the presence of molecular noise, as shown by means of Poincaré sections. The progressive obliteration of periodicity observed as the number of molecules decreases can thus be distinguished from the aperiodicity originating from chaotic dynamics. As long as the numbers of molecules involved in the oscillations remain sufficiently large (of the order of a few tens or hundreds, or more), stochastic models therefore provide good agreement with the predictions of the deterministic model for circadian rhythms.     

Deterministic Versus Stochastic Models for Circadian Rhythms

Circadian rhythms which occur with a period close to 24 h in nearly all living organisms originate from the negative autoregulation of gene expression.Deterministic models based on genetic regulatory processes account for theoccurrence of circadian rhythms in constant environmental conditions (e.g.constant darkness), for entrainment of these rhythms by light-dark cycles, and for their phase-shifting by light pulses. At low numbers of protein and mRNA molecules, it becomes necessary to resort to stochastic simulations to assess the influence of molecular noise on circadian oscillations. We address the effect of molecular noise by considering two stochastic versions of a core model for circadian rhythms. The deterministic version of this core modelwas previously proposed for circadian oscillations of the PER protein in Drosophila and of the FRQ protein in Neurospora. In the first, non-developed version of the stochastic model, we introduce molecular noise without decomposing the deterministic mechanism into detailed reaction steps while in the second, developed version we carry out such a detailed decomposition. Numerical simulations of the two stochastic versions of the model are performed by means of the Gillespie method. We compare the predictions of the deterministic approach with those of the two stochastic models, with respect both to sustained oscillations of the limit cycle type and to the influence of the proximity of a bifurcation point beyond which the system evolves to a stable steady state. The results indicate that robust circadian oscillations can occur even when the numbers of mRNA and nuclear protein involved in the oscillatory mechanism are reduced to a few tens orhundreds, respectively. The non-developed and developed versions of the stochastic model yield largely similar results and provide good agreement with the predictions of the deterministic model for circadian rhythms.     

Egg-laying rhythm in <Emphasis Type="Italic">Drosophila melanogaster</Emphasis>

Extensive research has been carried out to understand how circadian clocks regulate various physiological processes in organisms. The discovery of clock genes and the molecular clockwork has helped researchers to understand the possible role of these genes in regulating various metabolic processes. In Drosophila melanogaster, many studies have shown that the basic architecture of circadian clocks is multi-oscillatory. In nature, different neuronal subgroups in the brain of D. melanogaster have been demonstrated to control different circadian behavioural rhythms or different aspects of the same circadian rhythm. Among the circadian phenomena that have been studied so far in Drosophila, the egg-laying rhythm is unique, and relatively less explored. Unlike most other circadian rhythms, the egg-laying rhythm is rhythmic under constant light conditions, and the endogenous or free-running period of the rhythm is greater than those of most other rhythms. Although the clock genes and neurons required for the persistence of adult emergence and activity/rest rhythms have been studied extensively, those underlying the circadian egg-laying rhythm still remain largely unknown. In this review, we discuss our current understanding of the circadian egg-laying rhythm in D. melanogaster, and the possible molecular and physiological mechanisms that control the rhythmic output of the egg-laying process.     

Another place, another timer: Marine species and the rhythms of life

The marine ecosystem is governed by a multitude of environmental cycles, all of which are linked to the periodical recurrence of the sun or the moon. In accordance with these cycles, marine species exhibit a variety of biological rhythms, ranging from circadian and circatidal rhythms to circalunar and seasonal rhythms. However, our current molecular understanding of biological rhythms and clocks is largely restricted to solar-controlled circadian and seasonal rhythms in land model species. Here, we discuss the first molecular data emerging for circalunar and circatidal rhythms and present selected species suitable for further molecular analyses. We argue that a re-focus on marine species will be crucial to understand the principles, interactions and evolution of rhythms that govern a broad range of eukaryotes, including ourselves.     

Modeling the emergence of circadian rhythms in a clock neuron network

Circadian rhythms in pacemaker cells persist for weeks in constant darkness, while in other types of cells the molecular oscillations that underlie circadian rhythms damp rapidly under the same conditions. Although much progress has been made in understanding the biochemical and cellular basis of circadian rhythms, the mechanisms leading to damped or self-sustained oscillations remain largely unknown. There exist many mathematical models that reproduce the circadian rhythms in the case of a single cell of the Drosophila fly. However, not much is known about the mechanisms leading to coherent circadian oscillation in clock neuron networks. In this work we have implemented a model for a network of interacting clock neurons to describe the emergence (or damping) of circadian rhythms in Drosophila fly, in the absence of zeitgebers. Our model consists of an array of pacemakers that interact through the modulation of some parameters by a network feedback. The individual pacemakers are described by a well-known biochemical model for circadian oscillation, to which we have added degradation of PER protein by light and multiplicative noise. The network feedback is the PER protein level averaged over the whole network. In particular, we have investigated the effect of modulation of the parameters associated with (i) the control of net entrance of PER into the nucleus and (ii) the non-photic degradation of PER. Our results indicate that the modulation of PER entrance into the nucleus allows the synchronization of clock neurons, leading to coherent circadian oscillations under constant dark condition. On the other hand, the modulation of non-photic degradation cannot reset the phases of individual clocks subjected to intrinsic biochemical noise.     

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 molecular clocks tick along ontogenesis

The circadian system controls the timing of behavioral and physiological functions in most organisms studied. The review addresses the question of when and how the molecular clockwork underlying circadian oscillations within the central circadian clock in the suprachiasmatic nuclei of the hypothalamus (SCN) and the peripheral circadian clocks develops during ontogenesis. The current model of the molecular clockwork is summarized. The central SCN clock is viewed as a complex structure composed of a web of mutually synchronized individual oscillators. The importance of development of both the intracellular molecular clockwork as well as intercellular coupling for development of the formal properties of the circadian SCN clock is also highlighted. Recently, data has accumulated to demonstrate that synchronized molecular oscillations in the central and peripheral clocks develop gradually during ontogenesis and development extends into postnatal period. Synchronized molecular oscillations develop earlier in the SCN than in the peripheral clocks. A hypothesis is suggested that the immature clocks might be first driven by external entraining cues, and therefore, serve as "slave" oscillators. During ontogenesis, the clocks may gradually develop a complete set of molecular interlocked oscillations, i.e., the molecular clockwork, and become self-sustained clocks.     

Circadian Clock-Regulated Expression of Phytochrome and Cryptochrome Genes in Arabidopsis

Many physiological and biochemical processes in plants exhibit endogenous rhythms with a period of about 24 h. Endogenous oscillators called circadian clocks regulate these rhythms. The circadian clocks are synchronized to the periodic environmental changes (e.g. day/night cycles) by specific stimuli; among these, the most important is the light. Photoreceptors, phytochromes, and cryptochromes are involved in setting the clock by transducing the light signal to the central oscillator. In this work, we analyzed the spatial, temporal, and long-term light-regulated expression patterns of the Arabidopsis phytochrome (PHYA to PHYE) and cryptochrome (CRY1 and CRY2) promoters fused to the luciferase (LUC(+)) reporter gene. The results revealed new details of the tissue-specific expression and light regulation of the PHYC and CRY1 and 2 promoters. More importantly, the data obtained demonstrate that the activities of the promoter::LUC(+) constructs, with the exception of PHYC::LUC(+), display circadian oscillations under constant conditions. In addition, it is shown by measuring the mRNA abundance of PHY and CRY genes under constant light conditions that the circadian control is also maintained at the level of mRNA accumulation. These observations indicate that the plant circadian clock controls the expression of these photoreceptors, revealing the formation of a new regulatory loop that could modulate gating and resetting of the circadian clock.     

In vivo monitoring of peripheral circadian clocks in the mouse

The mammalian circadian system is comprised of a central clock in the suprachiasmatic nucleus (SCN) and a network of peripheral oscillators located in all of the major organ systems. The SCN is traditionally thought to be positioned at the top of the hierarchy, with SCN lesions resulting in an arrhythmic organism. However, recent work has demonstrated that the SCN and peripheral tissues generate independent circadian oscillations in Per1 clock gene expression in vitro. In the present study, we sought to clarify the role of the SCN in the intact system by recording rhythms in clock gene expression in vivo. A practical imaging protocol was developed that enables us to measure circadian rhythms easily, noninvasively, and longitudinally in individual mice. Circadian oscillations were detected in the kidney, liver, and submandibular gland studied in about half of the SCN-lesioned, behaviorally arrhythmic mice. However, their amplitude was decreased in these organs. Free-running periods of peripheral clocks were identical to those of activity rhythms recorded before the SCN lesion. Thus, we can report for the first time that many of the fundamental properties of circadian oscillations in peripheral clocks in vivo are maintained in the absence of SCN control.