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A coupled bulk-surface model for cell polarisation.

D Cusseddu1, L Edelstein-Keshet2, J A Mackenzie3

  • 1Department of Mathematics, University of Sussex, Brighton BN1 9QH, UK.

Journal of Theoretical Biology
|September 12, 2018
PubMed
Summary
This summary is machine-generated.

This study generalizes the wave pinning model for cell polarization to three dimensions using coupled bulk-surface partial differential equations. The model explains how surface perturbations trigger reactions that stabilize due to bulk interactions, forming patterns.

Keywords:
Asymptotic and local perturbation theoryBulk-surface finite elementsBulk-surface wave pinning modelCell polarisationCoupled bulk-surface semilinear partial differential equationsReaction-diffusion systems

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Area of Science:

  • Mathematical Biology
  • Cellular Dynamics
  • Biophysics

Background:

  • Cellular activities like migration rely on biochemical networks creating cell polarity, breaking symmetry to establish distinct front and back.
  • The minimal wave pinning model simplifies cell polarization dynamics for mathematical analysis.
  • Existing models often lack the dimensionality and complexity to fully capture protein compartmentalization.

Purpose of the Study:

  • To develop a 3D mathematical framework for cell polarization based on coupled bulk-surface partial differential equations.
  • To investigate how local surface perturbations influence reaction-diffusion dynamics in a polarized cell.
  • To explore the role of geometry in pattern formation during cell polarization.

Main Methods:

  • Formulation of a 3D mathematical model using coupled bulk-surface semilinear partial differential equations.
  • Asymptotic and local perturbation analysis to understand model behavior.
  • Bulk-surface finite element method for numerical simulations on various geometries.

Main Results:

  • Demonstration that local surface perturbations can initiate propagating reactions.
  • Observation that propagating reactions are stabilized by bulk components, leading to stable profiles.
  • Numerical simulations confirm pattern formation driven by propagation and pinning dynamics, influenced by geometry.

Conclusions:

  • The generalized 3D framework naturally incorporates protein compartmentalization.
  • The model successfully reproduces pattern formation through propagation and pinning dynamics.
  • This versatile framework can be extended to study complex biochemical reactions and biomechanical properties in multi-dimensional cell polarization.