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Oscillator death in coupled biochemical oscillators

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Abstract

Circadian rhythm, cell division and metabolic oscillations are rhythmic cellular behaviors that must be both robust but also to respond to changes in their environment. In this work, we study emergent behavior of coupled biochemical oscillators, modeled as repressilators. While more traditional approaches to oscillators synchronization often use phase oscillators, our approach uses switching systems that may be more appropriate for cellular networks dynamics governed by biochemical switches. We show that while one-directional coupling maintains stable oscillation of individual repressilators, there are well-characterized parameter regimes of mutually coupled repressilators, where oscillations stop. In other parameter regimes, joint oscillations continue. Our results may have implications for the understanding of condition-dependent coupling and un-coupling of regulatory networks.

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Acknowledgements

We acknowledge the Indigenous nations and peoples who are the traditional owners and caretakers of the land on which this work was undertaken at the Montana State University.

Funding

This research was partially supported by NSF Grant DMS-1839299 and NIH Grant 5R01GM126555-01.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Montana State University, Bozeman, MT, 59715, USA

    Tomáš Gedeon & Breschine Cummins

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  1. Tomáš Gedeon
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  2. Breschine Cummins
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Correspondence to Tomáš Gedeon.

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This paper is dedicated to Eduardo Sontag on the occasion of his 70th birthday.

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Gedeon, T., Cummins, B. Oscillator death in coupled biochemical oscillators. Math. Control Signals Syst. 35, 781–801 (2023). https://doi.org/10.1007/s00498-023-00348-3

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