Cell polarisation in a bulk-surface model can be driven by both classic and non-classic Turing instability
Johannes Borgqvist1, Adam Malik1, Carl Lundholm1
1Department of Mathematical Sciences, Chalmers University of Technology and the University of Gothenburg, Gothenburg, Sweden.
NPJ Systems Biology and Applications
|February 27, 2021
Summary
Cell polarization relies on Cdc42 accumulation. This study models Cdc42 dynamics, revealing Turing instability drives polarization, with reaction strength and diffusion determining pole size and timing.
Area of Science:
- Cell Biology
- Biophysics
- Mathematical Biology
Background:
- GTPase Cdc42 regulates eukaryotic cell polarization, with its active form accumulating at membrane poles.
- Cdc42 accumulation is thought to result from activation-inactivation reactions and diffusion.
- Mathematical modeling suggests diffusion-driven instability, akin to Turing's model, underlies this process.
Purpose of the Study:
- To develop, analyze, and validate a 3D bulk-surface model for Cdc42 dynamics.
- To investigate the conditions under which classic and non-classic Turing instability occur in Cdc42 polarization.
- To predict key polarization parameters like pole size and time to polarization using simulations.
Main Methods:
- Development and analysis of a 3D bulk-surface mathematical model for Cdc42.
- Derivation of conditions for classic and non-classic Turing instability.
- Three-dimensional spatio-temporal simulations to predict polarization dynamics.
Main Results:
- The model demonstrates both classic and non-classic Turing instability.
- Non-classic Turing instability can be considered a limit case of classic diffusion-driven instability.
- Simulation results indicate reaction strength primarily drives cell polarization, while relative diffusion determines pole size.
Conclusions:
- The developed 3D model accurately represents Cdc42 dynamics and cell polarization.
- Turing instability is a key mechanism driving cell polarization.
- Reaction strength and diffusion rates are critical parameters influencing polarization outcomes.
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