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Universality in kinetic models of circadian rhythms in \(Arabidopsis\,\,thaliana\)

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Abstract

Biological evolution has endowed the plant Arabidopsis thaliana with genetically regulated circadian rhythms. A number of authors have published kinetic models for these oscillating chemical reactions based on a network of interacting genes. To investigate the hypothesis that the Arabidopsis circadian dynamical system is poised near a Hopf bifurcation like some other biological oscillators, we varied the kinetic parameters in the models and searched for bifurcations. Finding that each model does exhibit a supercritical Hopf bifurcation, we performed a weakly nonlinear analysis near the bifurcation points to derive the Stuart–Landau amplitude equation. To illustrate a common dynamical structure, we scaled the numerical solutions to the models with the asymptotic solutions to the Stuart–Landau equation to collapse the circadian oscillations onto two universal curves—one for amplitude, and one for frequency. However, some models are close to bifurcation while others are far, some models are post-bifurcation while others are pre-bifurcation, and kinetic parameters that lead to a bifurcation in some models do not lead to a bifurcation in others. Future kinetic modeling can make use of our analysis to ensure models are consistent with each other and with the dynamics of the Arabidopsis circadian rhythm.

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Code availibility

The MATLAB code to replicate the calculations in this work is available on GitHub at https://github.com/oshindel/Reductive-Perturbation-Method-A.-thaliana.

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Acknowledgements

The authors would like to thank Harry L. Swinney for a critical reading of the manuscript and helpful conversations. This research was funded by Trinity University with a Murchison Fellowship to Y.X. and start-up funds to O.S.

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Authors and Affiliations

  1. Physics and Astronomy, Trinity University, San Antonio, TX, 78212, USA

    Yian Xu & Orrin Shindell

  2. Physics, University of Colorado Denver, Denver, CO, 80203, USA

    Masoud Asadi-Zeydabadi & Randall Tagg

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  1. Yian Xu
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  2. Masoud Asadi-Zeydabadi
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  3. Randall Tagg
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  4. Orrin Shindell
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Correspondence to Orrin Shindell.

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Xu, Y., Asadi-Zeydabadi, M., Tagg, R. et al. Universality in kinetic models of circadian rhythms in \(Arabidopsis\,\,thaliana\). J. Math. Biol. 83, 51 (2021). https://doi.org/10.1007/s00285-021-01677-0

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  • DOI: https://doi.org/10.1007/s00285-021-01677-0

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