Sensitivity analysis of circadian entrainment in the space of phase response curves

Sensitivity analysis is a classical and fundamental tool to evaluate the role of a given parameter in a given system characteristic. Because the phase response curve is a fundamental input--output characteristic of oscillators, we developed a sensitivity analysis for oscillator models in the space of phase response curves. The proposed tool can be applied to high-dimensional oscillator models without facing the curse of dimensionality obstacle associated with numerical exploration of the parameter space. Application of this tool to a state-of-the-art model of circadian rhythms suggests that it can be useful and instrumental to biological investigations.Comment: 22 pages, 8 figures. Correction of a mistake in Definition 2.1. arXiv admin note: text overlap with arXiv:1206.414

Network Dynamics Mediate Circadian Clock Plasticity

A circadian clock governs most aspects of mammalian behavior. Although its properties are in part genetically determined, altered light-dark environment can change circadian period length through a mechanism requiring de novo DNA methylation. We show here that this mechanism is mediated not via cell-autonomous clock properties, but rather through altered networking within the suprachiasmatic nuclei (SCN), the circadian “master clock,” which is DNA methylated in region-specific manner. DNA methylation is necessary to temporally reorganize circadian phasing among SCN neurons, which in turn changes the period length of the network as a whole. Interruption of neural communication by inhibiting neuronal firing or by physical cutting suppresses both SCN reorganization and period changes. Mathematical modeling suggests, and experiments confirm, that this SCN reorganization depends upon GABAergic signaling. Our results therefore show that basic circadian clock properties are governed by dynamic interactions among SCN neurons, with neuroadaptations in network function driven by the environment

Emergence of Noise-Induced Oscillations in the Central Circadian Pacemaker

Computational modeling and experimentation explain how intercellular coupling and intracellular noise can generate oscillations in a mammalian neuronal network even in the absence of cell-autonomous oscillators

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 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

Feedback Loops of the Mammalian Circadian Clock Constitute Repressilator

Mammals evolved an endogenous timing system to coordinate their physiology and behaviour to the 24h period of the solar day. While it is well accepted that circadian rhythms are generated by intracellular transcriptional feedback loops, it is still debated which network motifs are necessary and sufficient for generating self-sustained oscillations. Here, we systematically explore a data-based circadian oscillator model with multiple negative and positive feedback loops and identify a series of three subsequent inhibitions known as “repressilator” as a core element of the mammalian circadian oscillator. The central role of the repressilator motif is consistent with time-resolved ChIP- seq experiments of circadian clock transcription factors and loss of rhythmicity in core clock gene knockouts

Synchronization and entrainment of coupled circadian oscillators

Circadian rhythms in mammals are controlled by the neurons located in the suprachiasmatic nucleus of the hypothalamus. In physiological conditions, the system of neurons is very efficiently entrained by the 24-hour light-dark cycle. Most of the studies carried out so far emphasize the crucial role of the periodicity imposed by the light dark cycle in neuronal synchronization. Nevertheless, heterogeneity as a natural and permanent ingredient of these cellular interactions is seemingly to play a major role in these biochemical processes. In this paper we use a model that considers the neurons of the suprachiasmatic nucleus as chemically-coupled modified Goodwin oscillators, and introduce non-negligible heterogeneity in the periods of all neurons in the form of quenched noise. The system response to the light-dark cycle periodicity is studied as a function of the interneuronal coupling strength, external forcing amplitude and neuronal heterogeneity. Our results indicate that the right amount of heterogeneity helps the extended system to respond globally in a more coherent way to the external forcing. Our proposed mechanism for neuronal synchronization under external periodic forcing is based on heterogeneity-induced oscillators death, damped oscillators being more entrainable by the external forcing than the self-oscillating neurons with different periods.Comment: 17 pages, 7 figure

Pacemaker Heterogeneity in the Suprachiasmatic Nucleus: Origins and Network Implications

In mammals, the suprachiasmatic nuclei: SCN) in the ventral hypothalamus function as a circadian pacemaker, controlling daily rhythms in behavior and physiology. Together the SCN contain approximately 20,000 neurons that maintain rhythms in firing rate and gene expression. Previous studies led to the assumption that single SCN neurons are capable of self-sustained circadian rhythms. Whether and which SCN neurons can maintain cell-autonomous daily oscillations has not been extensively tested. We measured PERIOD2::LUCIFERASE expression in isolated SCN neurons over multiple days to determine if all SCN neurons were circadian. We then examined neuropeptide content of the recorded neurons. We found that when isolated physically or with a blocker of cell-cell communication, SCN neurons expressed a range of circadian periods, amplitudes, and abilities to sustain cycling. Surprisingly, most cells were sloppy oscillators, switching from rhythmic to arrhythmic or vice versa throughout their lifetime. We also found no evidence for a class of circadian-pacemaker neurons in the SCN based on neuropeptide expression. We conclude that while all SCN neurons are capable of cell-autonomous rhythms, they are intrinsically sloppy with network interactions dramatically increasing the number of circadian neurons. We next used a mathematical model of the mammalian circadian clock to determine whether rates of gene transcription, protein translation, degradation or phosphorylation might explain the ability of SCN neurons to switch between circadian and arrhythmic behaviors. We found that rhythmicity was more sensitive to the rates of protein translation and degradation. We next tested what effect having neurons with different intrinsic circadian behaviors would have on population synchrony. We simulated cells of known circadian phenotypes: e.g. arrhythmic, damped, or self-sustained) in a pattern defined by small-world network properties and varied the positions and proportions of each oscillator type. We found that increasing the number of damped oscillators or placing them in highly connected locations within the network both augmented the rate at which the network synchronized. We conclude that the SCN likely benefit from a heterogeneous population of oscillators, especially when recovering from an environmental perturbation that causes desynchrony. Finally, we generated and characterized two independent lines of transgenic mice to test the role of vasoactive intestinal polypeptide: VIP) neurons in circadian rhythmicity. These mice express Yellow Fluorescent Protein: YFP) under the control of a fragment of the VIP promoter in VIP neurons of the SCN, neocortex, olfactory bulbs, and enteric nervous system. We crossed these mice to generate a line in which VIP neurons are targeted for deletion using Cre-mediated recombination upon addition of tamoxifen. We observed successful deletion of VIP neurons in cultured SCN explants, but have no evidence to date for deletion of SCN neurons in vivo using a variety of protocols. We conclude that our construct is faithfully expressed in VIP neurons and that in vitro experiments show promising results for further study

Modeling Light Adaptation in Circadian Clock: Prediction of the Response That Stabilizes Entrainment

Periods of biological clocks are close to but often different from the rotation period of the earth. Thus, the clocks of organisms must be adjusted to synchronize with day-night cycles. The primary signal that adjusts the clocks is light. In Neurospora, light transiently up-regulates the expression of specific clock genes. This molecular response to light is called light adaptation. Does light adaptation occur in other organisms? Using published experimental data, we first estimated the time course of the up-regulation rate of gene expression by light. Intriguingly, the estimated up-regulation rate was transient during light period in mice as well as Neurospora. Next, we constructed a computational model to consider how light adaptation had an effect on the entrainment of circadian oscillation to 24-h light-dark cycles. We found that cellular oscillations are more likely to be destabilized without light adaption especially when light intensity is very high. From the present results, we predict that the instability of circadian oscillations under 24-h light-dark cycles can be experimentally observed if light adaptation is altered. We conclude that the functional consequence of light adaptation is to increase the adjustability to 24-h light-dark cycles and then adapt to fluctuating environments in nature