Global parameter search reveals design principles of the mammalian circadian clock

Suprachiasmatic nucleus: cell autonomy and network properties

The suprachiasmatic nucleus (SCN) is the primary circadian pacemaker in mammals. Individual SCN neurons in dispersed culture can generate independent circadian oscillations of clock gene expression and neuronal firing. However, SCN rhythmicity depends on sufficient membrane depolarization and levels of intracellular calcium and cAMP. In the intact SCN, cellular oscillations are synchronized and reinforced by rhythmic synaptic input from other cells, resulting in a reproducible topographic pattern of distinct phases and amplitudes specified by SCN circuit organization. The SCN network synchronizes its component cellular oscillators, reinforces their oscillations, responds to light input by altering their phase distribution, increases their robustness to genetic perturbations, and enhances their precision. Thus, even though individual SCN neurons can be cell-autonomous circadian oscillators, neuronal network properties are integral to normal function of the SCN.

Quantification of circadian rhythms in single cells

Bioluminescence techniques allow accurate monitoring of the circadian clock in single cells. We have analyzed bioluminescence data of Per gene expression in mouse SCN neurons and fibroblasts. From these data, we extracted parameters such as damping rate and noise intensity using two simple mathematical models, one describing a damped oscillator driven by noise, and one describing a self-sustained noisy oscillator. Both models describe the data well and enabled us to quantitatively characterize both wild-type cells and several mutants. It has been suggested that the circadian clock is self-sustained at the single cell level, but we conclude that present data are not sufficient to determine whether the circadian clock of single SCN neurons and fibroblasts is a damped or a self-sustained oscillator. We show how to settle this question, however, by testing the models' predictions of different phases and amplitudes in response to a periodic entrainment signal (zeitgeber).

How to achieve fast entrainment? The timescale to synchronization

Entrainment, where oscillators synchronize to an external signal, is ubiquitous in nature. The transient time leading to entrainment plays a major role in many biological processes. Our goal is to unveil the specific dynamics that leads to fast entrainment. By studying a generic model, we characterize the transient time to entrainment and show how it is governed by two basic properties of an oscillator: the radial relaxation time and the phase velocity distribution around the limit cycle. Those two basic properties are inherent in every oscillator. This concept can be applied to many biological systems to predict the average transient time to entrainment or to infer properties of the underlying oscillator from the observed transients. We found that both a sinusoidal oscillator with fast radial relaxation and a spike-like oscillator with slow radial relaxation give rise to fast entrainment. As an example, we discuss the jet-lag experiments in the mammalian circadian pacemaker.

Circadian clocks and phosphorylation: Insights from computational modeling

Circadian clocks are based on a molecular mechanism regulated at the transcriptional, translational and post-translational levels. Recent experimental data unravel a complex role of the phosphorylations in these clocks. In mammals, several kinases play differential roles in the regulation of circadian rhythmicity. A dysfunction in the phosphorylation of one clock protein could lead to sleep disorders such as the Familial Advanced Sleep Phase Disorder, FASPS. Moreover, several drugs are targeting kinases of the circadian clocks and can be used in cancer chronotherapy or to treat mood disorders. In Drosophila, recent experimental observations also revealed a complex role of the phosphorylations. Because of its high degree of homology with mammals, the Drosophila system is of particular interest. In the circadian clock of cyanobacteria, an atypical regulatory mechanism is based only on three clock proteins (KaiA, KaiB, KaiC) and ATP and is sufficient to produce robust temperature-compensated circadian oscillations of KaiC phosphorylation. This review will show how computational modeling has become a powerful and useful tool in investigating the regulatory mechanism of circadian clocks, but also how models can give rise to testable predictions or reveal unexpected results.

Free-running period of neurons in the suprachiasmatic nucleus: Its dependence on the distribution of neuronal coupling strengths

The suprachiasmatic nucleus (SCN) pacemaker shows a free-running period ranging from 20 to 28 h for different species, which was usually explained from the angle of coupling strength. Based on the assumption of nonidentical coupling strengths in SCN, we find an alternative mechanism that the diversity of free-running period can be also caused by the distribution of coupling strengths. The free-running period is proportional to the average coupling strength and inverse proportional to the dispersion of couplings. Moreover, we present an analytic phase model to confirm our finding, which shows a solid foundation of our finding and opens a window to study the collective behaviors of SCN oscillators.

Neurotransmitter-Mediated Collective Rhythms in Grouped Drosophila Circadian Clocks

Over the past decades, fly Drosophila melanogaster has being used as a premier model organism to study molecular and genetic bases of circadian rhythms. Here the authors propose a multicellular heterogeneous model for which the network of Drosophila circadian oscillators consists of two groups, the self-sustained lateral neurons (LNs) communicating to each other and the damped dorsal neurons (DNs) receiving neurotransmitters only from the LNs without interaction within this group. By simulating different experimental conditions, the authors find that the proposed model, except for being capable of reproducing some known experimental results well, also can predict some interesting phenomena: 1) The DNs need neuronal projections from the LNs to be rhythmic and to synchronize; 2) the effect of communication on mean amplitude and mean period of two oscillatory groups is different; 3) communication delay can facilitate the network synchronization of the LNs; and 4) only the LNs lose rhythmicity under constant light conditions. These results reveal the mechanism of an integrated pacemaker that would govern behavioral and physiological rhythmicity of the model organism.