An Overview of the Circadian Clock in the Frame of Chronotherapy: From Bench to Bedside.

Most living organisms in both the plant and animal kingdoms have evolved processes to stay in tune with the alternation of day and night, and to optimize their physiology as a function of light supply. In mammals, a circadian clock relying on feedback loops between key transcription factors will thus control the temporally regulated pattern of expression of most genes. Modern ways of life have highly altered the synchronization of human activities with their circadian clocks. This review discusses the links between an altered circadian clock and the rise of pathologies. We then sum up the proofs of concept advocating for the integration of circadian clock considerations in chronotherapy for health care, medicine, and pharmacotherapy. Finally, we discuss the current challenges that circadian biology must face and the tools to address them.

HEXIM1 Diffusion in the Nucleus Is Regulated by Its Interactions with Both 7SK and P-TEFb.

How nuclear proteins diffuse and find their targets remains a key question in the transcription field. Dynamic proteins in the nucleus are classically subdiffusive and undergo anomalous diffusion, yet the underlying physical mechanisms are still debated. In this study, we explore the contribution of interactions to the generation of anomalous diffusion by the means of fluorescence spectroscopy and simulation. Using interaction-deficient mutants, our study indicates that HEXIM1 interactions with both 7SK RNA and positive transcription elongation factor b are critical for HEXIM1 subdiffusion and thus provides evidence of the effects of protein-RNA interaction on molecular diffusion. Numerical simulations allowed us to establish that the proportions of distinct oligomeric HEXIM1 subpopulations define the apparent anomaly parameter of the whole population. Slight changes in the proportions of these oligomers can lead to significant shifts in the diffusive features and recapitulate the modifications observed in cells with the various interaction-deficient mutants. By combining simulations and experiments, our work opens new prospects in which the anomaly α coefficient in diffusion becomes a helpful tool to infer alterations in molecular interactions.

Entraining Oscillations in the NF-κB Signaling System: With a Little Help from Noise.

Two studies show that noise is a key ingredient of new mechanisms for entraining the NF-κB system.

A Mathematical Model of the Liver Circadian Clock Linking Feeding and Fasting Cycles to Clock Function.

To maintain energy homeostasis despite variable energy supply and consumption along the diurnal cycle, the liver relies on a circadian clock synchronized to food timing. Perturbed feeding and fasting cycles have been associated with clock disruption and metabolic diseases; however, the mechanisms are unclear. To address this question, we have constructed a mathematical model of the mammalian circadian clock, incorporating the metabolic sensors SIRT1 and AMPK. The clock response to various temporal patterns of AMPK activation was simulated numerically, mimicking the effects of a normal diet, fasting, and a high-fat diet. The model reproduces the dampened clock gene expression and NAD+ rhythms reported for mice on a high-fat diet and predicts that this effect may be pharmacologically rescued by timed REV-ERB agonist administration. Our model thus identifies altered AMPK signaling as a mechanism leading to clock disruption and its associated metabolic effects and suggests a pharmacological approach to resetting the clock in obesity.

Probing entrainment of Ostreococcus tauri circadian clock by green and blue light through a mathematical modeling approach.

Most organisms anticipate daily environmental variations and orchestrate cellular functions thanks to a circadian clock which entrains robustly to the day/night cycle, despite fluctuations in light intensity due to weather or seasonal variations. Marine organisms are also subjected to fluctuations in light spectral composition as their depth varies, due to differential absorption of different wavelengths by sea water. Studying how light input pathways contribute to circadian clock robustness is therefore important. Ostreococcus tauri, a unicellular picoplanktonic marine green alga with low genomic complexity and simple cellular organization, has become a promising model organism for systems biology. Functional and modeling approaches have shown that a core circadian oscillator based on orthologs of Arabidopsis TOC1 and CCA1 clock genes accounts for most experimental data acquired under a wide range of conditions. Some evidence points at putative light input pathway(s) consisting of a two-component signaling system (TCS) controlled by the only two histidine kinases (HK) of O. tauri. LOV-HK is a blue light photoreceptor under circadian control, that is required for circadian clock function. An involvement of Rhodopsin-HK (Rhod-HK) is also conceivable since rhodopsin photoreceptors mediate blue to green light input in animal circadian clocks. Here, we probe the role of LOV-HK and Rhod-HK in mediating light input to the TOC1-CCA1 oscillator using a mathematical model incorporating the TCS hypothesis. This model agrees with clock gene expression time series representative of multiple environmental conditions in blue or green light, characterizing entrainment by light/dark cycles, free-running in constant light, and resetting. Experimental and theoretical results indicate that both blue and green light can reset O. tauri circadian clock. Moreover, our mathematical analysis suggests that Rhod-HK is a blue-green light receptor and drives the clock together with LOV-HK.

Minimal model of transcriptional elongation processes with pauses.

Fundamental biological processes such as transcription and translation, where a genetic sequence is sequentially read by a macromolecule, have been well described by a classical model of nonequilibrium statistical physics, the totally asymmetric exclusion principle (TASEP). This model describes particles hopping between sites of a one-dimensional lattice, with the particle current determining the transcription or translation rate. An open problem is how to analyze a TASEP where particles can pause randomly, as has been observed during transcription. In this work, we report that surprisingly, a simple mean-field model predicts well the particle current for all values of the average pause duration, using a simple description of blocking behind paused particles.

Stochastic oscillations induced by intrinsic fluctuations in a self-repressing gene.

Biochemical reaction networks are subjected to large fluctuations attributable to small molecule numbers, yet underlie reliable biological functions. Thus, it is important to understand how regularity can emerge from noise. Here, we study the stochastic dynamics of a self-repressing gene with arbitrarily long or short response time. We find that when the mRNA and protein half-lives are approximately equal to the gene response time, fluctuations can induce relatively regular oscillations in the protein concentration. To gain insight into this phenomenon at the crossroads of determinism and stochasticity, we use an intermediate theoretical approach, based on a moment-closure approximation of the master equation, which allows us to take into account the binary character of gene activity. We thereby obtain differential equations that describe how nonlinearity can feed-back fluctuations into the mean-field equations to trigger oscillations. Finally, our results suggest that the self-repressing Hes1 gene circuit exploits this phenomenon to generate robust oscillations, inasmuch as its time constants satisfy precisely the conditions we have identified.

Transcriptional versus non-transcriptional clocks: a case study in Ostreococcus.

Circadian rhythms are ubiquitous on earth from cyanobacteria to land plants and animals. Circadian clocks are synchronized to the day/night cycle by environmental factors such as light and temperature. In eukaryotes, clocks rely on complex gene regulatory networks involving transcriptional regulation but also post-transcriptional and post-translational regulations. In multicellular organisms clocks are found at multiple levels from cells to organs and whole organisms, making the study of clock mechanisms more complex. In recent years the picoalga Ostreococcus has emerged as a new circadian model organism thanks to its reduced gene redundancy and its minimalist cellular organization. A simplified version of the "green" plant clock, involving the master clock genes TOC1 and CCA1, has been revealed when the functional genomics and mathematical model approaches were combined. Specific photoreceptors such as a blue light sensing LOV histidine kinase mediate light input to the Ostreococcus clock. Non-transcriptional redox rhythms have also been identified recently in Ostreococcus and human red blood cells. This review highlights the progress made recently in the understanding of circadian clock architecture and function in Ostreococcus in the context of the marine environment.

Circadian clocks in changing weather and seasons: lessons from the picoalga Ostreococcus tauri.

Daylight is the primary cue used by circadian clocks to entrain to the day/night cycle so as to synchronize physiological processes with periodic environmental changes induced by Earth rotation. However, the temporal daylight pattern is not the same every day due to erratic weather fluctuations or regular seasonal changes. Then, how do circadian clocks operate properly in varying weather and seasons? In this paper, we discuss the strategy unveiled by recent studies of the circadian clock of Ostreococcus tauri, the smallest free-living eukaryotic organism. It combines mechanisms controlling light inputs and clock sensitivity, shaping both the dynamics of the core circadian oscillator and its forcing by light so as to ensure stable and precise synchronization in all weather and seasons.

Spectral quantification of nonlinear behaviour of the nearshore seabed and correlations with potential forcings at Duck, N.C., U.S.A.

Local bathymetric, quasi-periodic patterns of oscillation are identified from 26 years of monthly profile surveys taken at two shore-perpendicular transects at Duck, North Carolina, USA. The data cover both the swash and surf zones. Singular Spectrum Analysis (SSA) and Multi-channel Singular Spectrum analysis (MSSA) methods are applied, on the shoreface, to three potential forcings: the monthly wave heights, the monthly mean water levels and the large scale atmospheric index known as the North Atlantic Oscillation. The patterns within these forcings are compared to the local bathymetric patterns; it is found that the patterns extracted using SSA and MSSA agree well with previous patterns identified using wavelets and confirm the highly non-stationary behaviour of beach levels at Duck. This is followed by analysis of potential correlations between the local bathymetry (at the two transects) and hydrodynamic and atmospheric patterns. The study is then extended to all measured bathymetric profiles, covering an area of 1100 m (alongshore) by 440 m (cross-shore). MSSA showed no collective inter-annual patterns of oscillations present in the bathymetry and the three potential forcings. Annual and semi-annual cycles within the bathymetry are found to be strongly correlated with the monthly wave height, in agreement with the SSA findings. Other collective intra-annual cycles besides the semi-annual were identified; they were all correlated with the North Atlantic Oscillation.

Robust and flexible response of the Ostreococcus tauri circadian clock to light/dark cycles of varying photoperiod.

The green microscopic alga Ostreococcus tauri has recently emerged as a promising model for understanding how circadian clocks, which drive the daily biological rhythms of many organisms, synchronize to the day/night cycle in changing weather and seasons. Here, we analyze translational reporter time series data for the central clock genes CCA1 and TOC1 for a wide range of daylight durations (photoperiods). The variation of temporal expression profiles with day duration is complex, with the two protein peaks tracking different times of the day. Nevertheless, all profiles are accurately reproduced by a simple two-gene transcriptional loop model whose parameters depend on light only through the photoperiod value. We show that this non-intuitive behavior allows the circadian clock to combine flexibility and robustness with respect to daylight fluctuations.

A dynamical model of oocyte maturation unveils precisely orchestrated meiotic decisions.

Maturation of vertebrate oocytes into haploid gametes relies on two consecutive meioses without intervening DNA replication. The temporal sequence of cellular transitions driving eggs from G2 arrest to meiosis I (MI) and then to meiosis II (MII) is controlled by the interplay between cyclin-dependent and mitogen-activated protein kinases. In this paper, we propose a dynamical model of the molecular network that orchestrates maturation of Xenopus laevis oocytes. Our model reproduces the core features of maturation progression, including the characteristic non-monotonous time course of cyclin-Cdks, and unveils the network design principles underlying a precise sequence of meiotic decisions, as captured by bifurcation and sensitivity analyses. Firstly, a coherent and sharp meiotic resumption is triggered by the concerted action of positive feedback loops post-translationally activating cyclin-Cdks. Secondly, meiotic transition is driven by the dynamic antagonism between positive and negative feedback loops controlling cyclin turnover. Our findings reveal a highly modular network in which the coordination of distinct regulatory schemes ensures both reliable and flexible cell-cycle decisions.

Robust entrainment of circadian oscillators requires specific phase response curves.

The circadian clocks keeping time in many living organisms rely on self-sustained biochemical oscillations entrained by external cues, such as light, to the 24-h cycle induced by Earth's rotation. However, environmental cues are unreliable due to the variability of habitats, weather conditions, or cue-sensing mechanisms among individuals. A tempting hypothesis is that circadian clocks have evolved so as to be robust to fluctuations in the signal that entrains them. To support this hypothesis, we analyze the synchronization behavior of weakly and periodically forced oscillators in terms of their phase response curve (PRC), which measures phase changes induced by a perturbation applied at different times of the cycle. We establish a general relationship between the robustness of key entrainment properties, such as stability and oscillator phase, on the one hand, and the shape of the PRC as characterized by a specific curvature or the existence of a dead zone, on the other hand. The criteria obtained are applied to computational models of circadian clocks and account for the disparate robustness properties of various forcing schemes. Finally, the analysis of PRCs measured experimentally in several organisms strongly suggests a case of convergent evolution toward an optimal strategy for maintaining a clock that is accurate and robust to environmental fluctuations.

Robustness of circadian clocks to daylight fluctuations: hints from the picoeucaryote Ostreococcus tauri.

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 the 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 the 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 intriguing 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.

A robust two-gene oscillator at the core of Ostreococcus tauri circadian clock.

The microscopic green alga Ostreococcus tauri is rapidly emerging as a promising model organism in the green lineage. In particular, recent results by Corellou et al. [Plant Cell 21, 3436 (2009)] and Thommen et al. [PLOS Comput. Biol. 6, e1000990 (2010)] strongly suggest that its circadian clock is a simplified version of Arabidopsis thaliana clock, and that it is architectured so as to be robust to natural daylight fluctuations. In this work, we analyze the time series data from luminescent reporters for the two central clock genes TOC1 and CCA1 and correlate them with microarray data previously analyzed. Our mathematical analysis strongly supports both the existence of a simple two-gene oscillator at the core of Ostreococcus tauri clock and the fact that its dynamics is not affected by light in normal entrainment conditions, a signature of its robustness.

Cooperative oscillation of nondegenerate transverse modes in an optical system: multimode operation in parametric oscillators.

We show experimentally that parametric interaction can induce a cooperative oscillation of non-simultaneously resonant transverse modes in an optical parametric oscillator. More generally, this effect is expected to occur in any spatially extended system subjected to boundary conditions where nonlinear wave mixing of two nonresonant spatial modes can generate a resonant oscillation.

Oscillations in the expression of a self-repressed gene induced by a slow transcriptional dynamics.

We revisit the dynamics of a gene repressed by its own protein in the case where the transcription rate does not adapt instantaneously to protein concentration but is a dynamical variable. We derive analytical criteria for the appearance of sustained oscillations and find that they require degradation mechanisms much less nonlinear than for infinitely fast regulation. Deterministic predictions are confirmed by stochastic simulations of this minimal genetic oscillator.

Topological characterization of deterministic chaos: enforcing orientation preservation.

The determinism principle, which states that dynamical state completely determines future time evolution, is a keystone of nonlinear dynamics and chaos theory. Since it precludes that two state space trajectories intersect, it is a core ingredient of a topological analysis of chaos based on a knot-theoretic characterization of unstable periodic orbits embedded in a strange attractor. However, knot theory can be applied only to three-dimensional systems. Still, determinism applies in any dimension. We propose an alternative framework in which this principle is enforced by constructing an orientation-preserving dynamics on triangulated surfaces and find that in three dimensions our approach numerically predicts the correct topological entropies for periodic orbits of the horseshoe map.

Embeddings of low-dimensional strange attractors: topological invariants and degrees of freedom.

When a low-dimensional chaotic attractor is embedded in a three-dimensional space its topological properties are embedding-dependent. We show that there are just three topological properties that depend on the embedding: Parity, global torsion, and knot type. We discuss how they can change with the embedding. Finally, we show that the mechanism that is responsible for creating chaotic behavior is an invariant of all embeddings. These results apply only to chaotic attractors of genus one, which covers the majority of cases in which experimental data have been subjected to topological analysis. This means that the conclusions drawn from previous analyses, for example that the mechanism generating chaotic behavior is a Smale horseshoe mechanism, a reverse horseshoe, a gateau roulé, an S -template branched manifold, etc., are not artifacts of the embedding chosen for the analysis.