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Cell polarisation in a bulk-surface model can be driven by both classic and non-classic Turing instability

Johannes Borgqvist, Adam Malik, Carl Lundholm, Anders Logg, Philip Gerlee, Marija Cvijovic
doi: https://doi.org/10.1101/2020.01.29.925628
Johannes Borgqvist
1Department of Mathematical Sciences, Chalmers University of Technology and the University of Gothenburg, Gothenburg, Sweden
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Adam Malik
1Department of Mathematical Sciences, Chalmers University of Technology and the University of Gothenburg, Gothenburg, Sweden
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Carl Lundholm
1Department of Mathematical Sciences, Chalmers University of Technology and the University of Gothenburg, Gothenburg, Sweden
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Anders Logg
1Department of Mathematical Sciences, Chalmers University of Technology and the University of Gothenburg, Gothenburg, Sweden
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Philip Gerlee
1Department of Mathematical Sciences, Chalmers University of Technology and the University of Gothenburg, Gothenburg, Sweden
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Marija Cvijovic
1Department of Mathematical Sciences, Chalmers University of Technology and the University of Gothenburg, Gothenburg, Sweden
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  • For correspondence: marija.cvijovic@chalmers.se
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Abstract

The GTPase Cdc42 is the master regulator of cell polarisation. During this process the active form of Cdc42 is accumulated at a particular site on the cell membrane called the pole. It is believed that the accumulation of the active Cdc42 resulting in a pole is driven by a combination of activation-inactivation reactions and diffusion. It has been proposed using mathematical modelling that this is the result of diffusion-driven instability, originally proposed by Alan Turing. In this study we develop a 3D bulk-surface model of the dynamics of Cdc42. We show that the model can undergo both classic and non-classic Turing instability. We thoroughly investigate the parameter space for which this occurs. Using simulations we show that the model can be used to simulate polarisation and to predict a number of relevant quantitative measures, including pole size and time to polarisation.

Footnotes

  • ↵† johborgq{at}chalmers.se

  • ↵S1 The spherical case is analogous.

  • ↵S2 The critical point u0 is a local max-point of the function v(u).

  • ↵S3 The (c−1, c2)-space is generated completely analogously.

Copyright 
The copyright holder for this preprint is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under a CC-BY-NC-ND 4.0 International license.
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Posted January 30, 2020.
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Cell polarisation in a bulk-surface model can be driven by both classic and non-classic Turing instability
Johannes Borgqvist, Adam Malik, Carl Lundholm, Anders Logg, Philip Gerlee, Marija Cvijovic
bioRxiv 2020.01.29.925628; doi: https://doi.org/10.1101/2020.01.29.925628
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Cell polarisation in a bulk-surface model can be driven by both classic and non-classic Turing instability
Johannes Borgqvist, Adam Malik, Carl Lundholm, Anders Logg, Philip Gerlee, Marija Cvijovic
bioRxiv 2020.01.29.925628; doi: https://doi.org/10.1101/2020.01.29.925628

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