Coupling governs entrainment range of circadian clocks

Circadian clock oscillator properties that are crucial for synchronization with the environment (entrainment) are studied in experiment and theory.The ratio between stimulus (zeitgeber) strength and oscillator amplitude, and the rigidity of the oscillatory system (relaxation rate upon perturbation) determine entrainment properties. Coupling among oscillators affects both qualities resulting in increased amplitude and rigidity.Uncoupled lung clocks entrain to extreme zeitgeber cycles, whereas the coupled oscillator system in the suprachiasmatic nucleus (SCN) does not; however, when coupling in the SCN is inhibited, larger ranges of entrainment can be achieved

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

Human chronotypes from a theoretical perspective.

The endogenous circadian timing system has evolved to synchronize an organism to periodically recurring environmental conditions. Those external time cues are called Zeitgebers. When entrained by a Zeitgeber, the intrinsic oscillator adopts a fixed phase relation ψ to the Zeitgeber. Here, we systematically study how the phase of entrainment depends on clock and Zeitgeber properties. We combine numerical simulations of amplitude-phase models with predictions from analytically tractable models. In this way we derive relations between the phase of entrainment ψ to the mismatch between the endogenous and Zeitgeber period, the Zeitgeber strength, and the range of entrainment. A core result is the "180° rule" asserting that the phase ψ varies over a range of about 180° within the entrainment range. The 180° rule implies that clocks with a narrow entrainment range ("strong oscillators") exhibit quite flexible entrainment phases. We argue that this high sensitivity of the entrainment phase contributes to the wide range of human chronotypes

Circadian desynchronization

The suprachiasmatic nucleus (SCN) coordinates via multiple outputs physiological and behavioural circadian rhythms. The SCN is composed of a heterogeneous network of coupled oscillators that entrain to the daily light–dark cycles. Outside the physiological entrainment range, rich locomotor patterns of desynchronized rhythms are observed. Previous studies interpreted these results as the output of different SCN neural subpopulations. We find, however, that even a single periodically driven oscillator can induce such complex desynchronized locomotor patterns. Using signal analysis, we show how the observed patterns can be consistently clustered into two generic oscillatory interaction groups: modulation and superposition. In seven of 17 rats undergoing forced desynchronization, we find a theoretically predicted third spectral component. Combining signal analysis with the theory of coupled oscillators, we provide a framework for the study of circadian desynchronization

Sinusoidal phase response curve (PRC) and associated phase transition curves (PTCs) according to Eq. (5).

<p>Applying -periodic pulses, stationary entrainment phases are given by the intersections of the PTC with the diagonal <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0059464#pone.0059464-Glass1" target="_blank">[15]</a>. Upper graphs: Vanishing frequency mismatch leads to a stable entrainment phase h. Lower graphs: Period mismatches correspond to the borderlines of the entrainment range. The corresponding entrainment phases of 18 h and 6 h are associated to the extrema of the sine-function and are 12 h (or 180° ) apart.</p

Phases of entrainment within the entrainment regions.

<p>Left: Numerical simulations of amplitude-phase model. Right: Entrainment phases from Eq. (2) derived from the Kuramoto phase equation. In both cases the entrainment phase varies from −6 h to 6 h between the borderlines of entrainment. Note that the lines with h are very close to those with h and are not marked separately for the sake of clarity of the graphical representation.</p

Phase response curves of strong (left) and weak (right) oscillators.

<p>The extrema marked by A and B are related to the borders of the entrainment range (compare <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0059464#pone-0059464-g001" target="_blank">Figure 1</a>) as explained in the text.</p

Flexibility of entrainment phases due to small variations of the endogenous period.

<p>The inserts show normally distributed periods with a standard deviation of 0.2 h. Simulations of amplitude-phase models illustrate the flexibility of entrainment phases for strong oscillators (left) compared to weak oscillators (right).</p

Dependences of entrainment phase on period mismatch between endogenous and Zeitgeber periods.

<p>Left: strong oscillator with narrow entrainment range resulting in high sensitivity of the entrainment phase on mismatch. Right: weak oscillator with wide entrainment range and smaller slope of the function .</p