Bordyugov Grigory, Abraham Ute, Granada Adrian, Rose Pia, Imkeller Katharina, Kramer Achim, Herzel Hanspeter
Institute for Theoretical Biology, Charité Universitätsmedizin Berlin, Berlin, Germany
Laboratory of Chronobiology, Charité Universitätsmedizin Berlin, Berlin, Germany.
J R Soc Interface. 2015 Jul 6;12(108):20150282. doi: 10.1098/rsif.2015.0282.
The circadian clock coordinates daily physiological, metabolic and behavioural rhythms. These endogenous oscillations are synchronized with external cues ('zeitgebers'), such as daily light and temperature cycles. When the circadian clock is entrained by a zeitgeber, the phase difference ψ between the phase of a clock-controlled rhythm and the phase of the zeitgeber is of fundamental importance for the fitness of the organism. The phase of entrainment ψ depends on the mismatch between the intrinsic period τ and the zeitgeber period T and on the ratio of the zeitgeber strength to oscillator amplitude. Motivated by the intriguing complexity of empirical data and by our own experiments on temperature entrainment of mouse suprachiasmatic nucleus (SCN) slices, we present a theory on how clock and zeitgeber properties determine the phase of entrainment. The wide applicability of the theory is demonstrated using mathematical models of different complexity as well as by experimental data. Predictions of the theory are confirmed by published data on Neurospora crassa strains for different period mismatches τ - T and varying photoperiods. We apply a novel regression technique to analyse entrainment of SCN slices by temperature cycles. We find that mathematical models can explain not only the stable asymptotic phase of entrainment, but also transient phase dynamics. Our theory provides the potential to explore seasonal variations of circadian rhythms, jet lag and shift work in forthcoming studies.
昼夜节律时钟协调每日的生理、代谢和行为节律。这些内源性振荡与外部线索（“授时因子”）同步，如每日的光照和温度周期。当昼夜节律时钟被一个授时因子所调节时，时钟控制节律的相位与授时因子的相位之间的相位差ψ对于生物体的适应性至关重要。调节相位ψ取决于内在周期τ与授时因子周期T之间的失配以及授时因子强度与振荡器振幅的比率。受经验数据的有趣复杂性以及我们自己关于小鼠视交叉上核（SCN）切片温度调节的实验的启发，我们提出了一个关于时钟和授时因子特性如何决定调节相位的理论。该理论的广泛适用性通过不同复杂程度的数学模型以及实验数据得到了证明。该理论的预测通过关于不同周期失配τ - T和不同光周期的粗糙脉孢菌菌株的已发表数据得到了证实。我们应用一种新颖的回归技术来分析温度周期对SCN切片的调节作用。我们发现数学模型不仅可以解释调节的稳定渐近相位，还可以解释瞬态相位动态。我们的理论为在未来研究中探索昼夜节律的季节性变化、时差反应和轮班工作提供了可能性。
