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The Goodwin Oscillator and its Legacy

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Abstract

In the 1960’s Brian Goodwin published a couple of mathematical models showing how feedback inhibition can lead to oscillations and discussed possible implications of this behaviour for the physiology of the cell. He also presented key ideas about the rich dynamics that may result from the coupling between such biochemical oscillators. Goodwin’s work motivated a series of theoretical investigations aiming at identifying minimal mechanisms to generate limit cycle oscillations and deciphering design principles of biological oscillators. The three-variable Goodwin model (adapted by Griffith) can be seen as a core model for a large class of biological systems, ranging from ultradian to circadian clocks. We summarize here main ideas and results brought by Goodwin and review a couple of modeling works directly or indirectly inspired by Goodwin’s findings.

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Acknowledgements

DG would like to thank Albert Goldbeter and Thomas Erneux for numerous discussions about biological oscillators, feedback loops, and Hopf bifurcation. PR would like to acknowledge the stimulating cooperativity he received by Ludger Rensing (Deutsch et al. 2013) when using the Goodwin oscillator in studies of circadian rhythms. The work of DG is supported by the “Fonds National de la Recherche Scientifique” (FNRS, Belgium) [Project CDR J.0076.19].

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Authors and Affiliations

  1. Unité de Chronobiologie Théorique, Service de Chimie Physique CP 231, Université Libre de Bruxelles, Bvd du Triomphe, 1050, Brussels, Belgium

    Didier Gonze

  2. Centre for Organelle Research, University of Stavanger, Richard Johnsens gate 4, 4021, Stavanger, Norway

    Peter Ruoff

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  1. Didier Gonze
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  2. Peter Ruoff
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Correspondence to Didier Gonze.

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The paper is a contribution for a special issue in honor of Brian Goodwin (editor: J. Jaeger).

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Gonze, D., Ruoff, P. The Goodwin Oscillator and its Legacy. Acta Biotheor 69, 857–874 (2021). https://doi.org/10.1007/s10441-020-09379-8

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