In mammals, the circadian pacemaker, which controls daily rhythms, is located in the suprachiasmatic nucleus (SCN). Circadian oscillations are generated in individual SCN neurons by a molecular regulatory network. Cells oscillate with periods ranging from 20 to 28 h, but at the tissue level, SCN neurons display significant synchrony, suggesting a robust intercellular coupling in which neurotransmitters are assumed to play a crucial role. We present a dynamical model for the coupling of a population of circadian oscillators in the SCN. The cellular oscillator, a three-variable model, describes the core negative feedback loop of the circadian clock. The coupling mechanism is incorporated through the global level of neurotransmitter concentration. Global coupling is efficient to synchronize a population of 10,000 cells. Synchronized cells can be entrained by a 24-h light-dark cycle. Simulations of the interaction between two populations representing two regions of the SCN show that the driven population can be phase-leading. Experimentally testable predictions are: 1), phases of individual cells are governed by their intrinsic periods; and 2), efficient synchronization is achieved when the average neurotransmitter concentration would dampen individual oscillators. However, due to the global neurotransmitter oscillation, cells are effectively synchronized.

We use a core molecular model capable of generating circadian rhythms to assess the robustness of circadian oscillations with respect to molecular noise. The model is based on the negative feedback exerted by a regulatory protein on the expression of its gene. Such a negative regulatory mechanism underlies circadian oscillations of the PER protein in Drosophila and of the FRQ protein in Neurospora. The model incorporates gene transcription into mRNA, translation of mRNA into protein, reversible phosphorylation leading to degradation of the regulatory protein, transport of the latter into the nucleus, and repression of gene expression by the nuclear form of the protein. To assess the effect of molecular noise, we perform stochastic simulations after decomposing the deterministic model into elementary reaction steps. The oscillations predicted by the stochastic simulations agree with those obtained with the deterministic version of the model. We show that robust circadian oscillations can occur already with a limited number of mRNA and protein molecules, in the range of tens and hundreds, respectively. Entrainment by light͞dark cycles and cooperativity in repression enhance the robustness of circadian oscillations with respect to molecular noise.circadian clocks ͉ stochastic simulations ͉ model ͉ Drosophila ͉ Neurospora

During blastocyst formation, inner cell mass (ICM) cells differentiate into either epiblast (Epi) or primitive endoderm (PrE) cells, labeled by Nanog and Gata6, respectively, and organized in a salt-and-pepper pattern. Previous work in the mouse has shown that, in absence of Nanog, all ICM cells adopt a PrE identity. Moreover, the activation or the blockade of the Fgf/RTK pathway biases cell fate specification towards either PrE or Epi, respectively. We show that, in absence of Gata6, all ICM cells adopt an Epi identity. Furthermore, the analysis of Gata6 +/− embryos reveals a dose-sensitive phenotype, with fewer PrE-specified cells. These results and previous findings have enabled the development of a mathematical model for the dynamics of the regulatory network that controls ICM differentiation into Epi or PrE cells. The model describes the temporal dynamics of Erk signaling and of the concentrations of Nanog, Gata6, secreted Fgf4 and Fgf receptor 2. The model is able to recapitulate most of the cell behaviors observed in different experimental conditions and provides a unifying mechanism for the dynamics of these developmental transitions. The mechanism relies on the co-existence between three stable steady states (tristability), which correspond to ICM, Epi and PrE cells, respectively. Altogether, modeling and experimental results uncover novel features of ICM cell fate specification such as the role of the initial induction of a subset of cells into Epi in the initiation of the salt-and-pepper pattern, or the precocious Epi specification in Gata6 +/− embryos.

We examine theoretical models for circadian oscillations based on transcriptional regulation in Drosophila and Neurospora. For Drosophila, the molecular model is based on the negative feedback exerted on the expression of the per and tim genes by the complex formed between the PER and TIM proteins. For Neurospora, similarly, the model relies on the feedback exerted on the expression of the frq gene by its protein product FRQ. In both models, sustained rhythmic variations in protein and mRNA levels occur in continuous darkness, in the form of limit cycle oscillations. The effect of light on circadian rhythms is taken into account in the models by considering that it triggers degradation of the TIM protein in Drosophila, and frq transcription in Neurospora. When incorporating the control exerted by light at the molecular level, we show that the models can account for the entrainment of circadian rhythms by light-dark cycles and for the damping of the oscillations in constant light, though such damping occurs more readily in the Drosophila model. The models account for the phase shifts induced by light pulses and allow the construction of phase response curves. These compare well with experimental results obtained in Drosophila. The model for Drosophila shows that when applied at the appropriate phase, light pulses of appropriate duration and magnitude can permanently or transiently suppress circadian rhythmicity. We investigate the effects of the magnitude of light-induced changes on oscillatory behavior. Finally, we discuss the common and distinctive features of circadian oscillations in the two organisms.

The recent increase in the number of microbial time series studies offers new insights into the stability and dynamics of microbial communities, from the world's oceans to human microbiota. Dedicated time series analysis tools allow taking full advantage of these data. Such tools can reveal periodic patterns, help to build predictive models or, on the contrary, quantify irregularities that make community behavior unpredictable. Microbial communities can change abruptly in response to small perturbations, linked to changing conditions or the presence of multiple stable states. With sufficient samples or time points, such alternative states can be detected. In addition, temporal variation of microbial interactions can be captured with time-varying networks. Here, we apply these techniques on multiple longitudinal datasets to illustrate their potential for microbiome research.