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Optimal entrainment of circadian clocks in the presence of noise

Michele Monti1, David K. Lubensky2, and Pieter Rein ten Wolde1

  • 1AMOLF, Science Park 104, 1098 XE Amsterdam, The Netherlands
  • 2Department of Physics, University of Michigan, Ann Arbor, Michigan 48109-1040, USA

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Phys. Rev. E 97, 032405 – Published 12 March, 2018

DOI: https://doi.org/10.1103/PhysRevE.97.032405

Abstract

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.

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Outline

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Phys. Rev. E 97, 032405– Published 12 March, 2018
  • Received 7 June 2017
Article part of CHORUS
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