Abstract
In addition to being endogenous, a circadian system must be able to communicate with the outside world and align its rhythmicity to the environment. As a result of such alignment, external Zeitgebers can entrain the circadian system. Entrainment expresses itself in coinciding periods of the circadian oscillator and the Zeitgeber and a stationary phase difference between them. The range of period mismatches between the circadian system and the Zeitgeber that Zeitgeber can overcome to entrain the oscillator is called an entrainment range. The width of the entrainment range usually increases with increasing Zeitgeber strength, resulting in a wedge-like Arnold tongue. This classical view of entrainment does not account for the effects of photoperiod on entrainment. Zeitgebers with extremely small or large photoperiods are intuitively closer to constant environments than equinoctial Zeitgebers and hence are expected to produce a narrower entrainment range. In this paper, we present theoretical results on entrainment under different photoperiods. We find that in the photoperiod-detuning parameter plane, the entrainment zone is shaped in the form of a skewed onion. The bottom and upper points of the onion are given by the free-running periods in DD and LL, respectively. The widest entrainment range is found near photoperiods of 50%. Within the onion, we calculated the entrainment phase that varies over a range of 12 h. The results of our theoretical study explain the experimentally observed behavior of the entrainment phase in dependence on the photoperiod.
Highlights
In analogy to common Zeitgeber signals under laboratory conditions, we investigate the entrainment of the Poincaré Oscillator to square-wave cycles
If the system synchronizes at all and in such case the phase of entrainment (POE) will generally be dependent on the intrinsic properties of the circadian system as well as the waveform, intensity, and period of the Zeitgeber signal
Biochemically motivated models aim to shed light on the interlocking of the circadian clockwork’s cogs and levers in a specific biological context, simple and rather abstract conceptual oscillator models can be used to understand generic features of the circadian system [26]. Following this tradition of modeling in the field of chronobiology [9, 27,28,29,30,31], we describe the dynamical properties of the circadian clock by means of a generic amplitude–phase oscillator, see Section 2.1 for details
Summary
One can expect that Zeitgebers with very short or very long light phase should be less potent in entraining the circadian system than a Zeitgeber with a LD ratio close to 12 h:12 h In this manuscript, we quantify this intuition and compare it to previously published data on entrainment under different seasonal conditions [3, 14, 15]. Arnold Onion Our main result is the existence of the onion-shaped entrainment zone on the photoperiod-detuning parameter plane, compare Figure 1B Both tips of the entrainment onion point to freerunning periods in complete darkness τ DD or constant light τ LL. Even for a constant mismatch τ − T, i.e., for vertical cross-sections of the Arnold onion, large variations of entrainment phases are found
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