Monti Michele, Lubensky David K, Ten Wolde Pieter Rein
AMOLF, Science Park 104, 1098 XE Amsterdam, The Netherlands.
Department of Physics, University of Michigan, Ann Arbor, Michigan 48109-1040, USA.
Phys Rev E. 2018 Mar;97(3-1):032405. doi: 10.1103/PhysRevE.97.032405.
Circadian clocks are biochemical oscillators that allow organisms to estimate the time of the day. These oscillators are inherently noisy due to the discrete nature of the reactants and the stochastic character of their interactions. To keep these oscillators in sync with the daily day-night rhythm in the presence of noise, circadian clocks must be coupled to the dark-light cycle. In this paper, we study the entrainment of phase oscillators as a function of the intrinsic noise in the system. Using stochastic simulations, we compute the optimal coupling strength, intrinsic frequency, and shape of the phase-response curve, that maximize the mutual information between the phase of the clock and time. We show that the optimal coupling strength and intrinsic frequency increase with the noise, but that the shape of the phase-response curve varies nonmonotonically with the noise: in the low-noise regime, it features a dead zone that increases in width as the noise increases, while in the high-noise regime, the width decreases with the noise. These results arise from a tradeoff between maximizing stability-noise suppression-and maximizing linearity of the input-output, i.e., time-phase, relation. We also show that three analytic approximations-the linear-noise approximation, the phase-averaging method, and linear-response theory-accurately describe different regimes of the coupling strength and the noise.
昼夜节律时钟是一种生化振荡器，它使生物体能够估算一天中的时间。由于反应物的离散性质及其相互作用的随机性，这些振荡器本质上是有噪声的。为了在存在噪声的情况下使这些振荡器与昼夜的日常节律保持同步，昼夜节律时钟必须与明暗周期相耦合。在本文中，我们研究了相位振荡器的同步情况，它是系统中固有噪声的函数。通过随机模拟，我们计算出了最佳耦合强度、固有频率和相位响应曲线的形状，这些参数能使时钟相位与时间之间的互信息最大化。我们表明，最佳耦合强度和固有频率会随着噪声的增加而增加，但相位响应曲线的形状会随着噪声非单调变化：在低噪声 regime 中，它有一个死区，随着噪声增加，死区宽度会增大，而在高噪声 regime 中，死区宽度会随着噪声减小。这些结果源于在最大化稳定性（噪声抑制）和最大化输入 - 输出（即时间 - 相位）关系的线性之间的权衡。我们还表明，三种解析近似方法——线性噪声近似、相位平均方法和线性响应理论——能够准确描述耦合强度和噪声的不同 regime。
