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Local and Global Bifurcations in a Mechanochemical ODE Model for Cell Behavior

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Abstract

We study the dynamics of a two-variable mechanochemical model for GTPase signaling and cell tension using numerical bifurcation analysis, providing insight to the dynamics throughout parameter space. The model exhibits a wide range of local and global bifurcations, including three codimension-two bifurcations occurring along a locus of homoclinics. We use numerical bifurcation analysis and simulation to investigate these bifurcations. This analysis provides evidence for two rarely seen bifurcations: a neutral saddle homoclinic bifurcation and a non-central saddle-node homoclinic bifurcation. We expand the understanding of the dynamics of the mechanochemical model and provide a pedagogically useful example of a realistic but relatively simple model that exhibits a wide range of bifurcations.

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Data Availability

All code used to produce the figures is available as a GitHub repository at https://www.github.com/zmurchok/GTPase-tension-bifurcation.

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Acknowledgements

CZ was partially supported by a Postdoctoral Fellowship Award from the Natural Sciences and Engineering Research Council (NSERC) of Canada and by a National Science Foundation (NSF), United States grant DMS1562078. MS was supported by an Undergraduate Student Research Award (USRA) from NSERC of Canada. WN and ENC are supported by NSERC of Canada.

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Authors and Affiliations

  1. Department of Physics and Astronomy, Vanderbilt University, Nashville, TN, USA

    Cole Zmurchok

  2. Department of Mathematics, The University of British Columbia, Vancouver, BC, Canada

    Matthew Sahota, Wayne Nagata & Eric N Cytrynbaum

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  1. Cole Zmurchok
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Correspondence to Cole Zmurchok.

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Zmurchok, C., Sahota, M., Nagata, W. et al. Local and Global Bifurcations in a Mechanochemical ODE Model for Cell Behavior. Differ Equ Dyn Syst (2023). https://doi.org/10.1007/s12591-023-00636-z

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