Abstract
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 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 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 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.
Highlights
The circadian clock possesses two core properties
It has been shown that the mammalian pacemaker, the suprachiasmatic nucleus, is quite resistant to phase resetting
Strong oscillators are characterized by large oscillation amplitudes, fast relaxation of perturbations, and small-amplitude Phase response curves (PRCs) [10]
Summary
The circadian clock possesses two core properties. The first one is the endogeneity of circadian rhythms, and the existence of a well-defined natural period t, which expresses itself under constant environmental conditions. The second property is the capability to synchronize to a periodic external Zeitgeber by establishing a precise phase relation to it. If the strength of the Zeitgeber is capable to overcome the period mismatch t{T, the Zeitgeber enforces the periodicity of 24 h in the clock. This situation is called synchronization or entrainment. The range of the period mismatches t{T for which synchronization occurs is called entrainment range It is the difference of both periods t and T (but not the single periods per se) that determines whether the clock would be synchronized or not for a given Zeitgeber strength
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