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Modelling non-local cell-cell adhesion: a multiscale approach.

Anna Zhigun1, Mabel Lizzy Rajendran2

  • 1School of Mathematics and Physics, Queen's University Belfast, University Road, Belfast, BT7 1NN, Northern Ireland, UK. A.Zhigun@qub.ac.uk.

Journal of Mathematical Biology
|April 3, 2024
PubMed
Summary

This study introduces a multiscale model for cell migration, combining deterministic adhesion and stochastic movement. The model captures how cell adhesion influences population dynamics and movement patterns in biological systems.

Keywords:
Cadherin bindingCell adhesion molecule bindingCell movementCell-cell adhesionDiffusion-adhesion equationsHyperbolic scalingKinetic transport equationsMultiscale modellingMyopic diffusionNon-local modelsParabolic scaling

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Area of Science:

  • Mathematical Biology
  • Biophysics
  • Computational Biology

Background:

  • Cell-cell adhesion is crucial for multicellular organism development and maintenance.
  • It regulates cell migration, essential for processes like embryogenesis and cancer progression.

Purpose of the Study:

  • To develop a versatile multiscale modeling approach for self-adhesive cell populations.
  • To integrate microscopic adhesion mechanisms with mesoscopic stochastic processes.

Main Methods:

  • A multiscale approach combining deterministic microscopic adhesion with stochastic mesoscopic velocity-jump processes.
  • Derivation of mesoscopic kinetic transport equations with multiple non-localities.
  • Application of parabolic and hyperbolic scalings to obtain macroscopic models.

Main Results:

  • The model yields kinetic transport equations with non-local adhesion and myopic diffusion.
  • Simulations demonstrate the combined effects of adhesion and stochastic motion on cell population dynamics.
  • A novel non-linear integral equation coupled to the cell density equation captures microscopic adhesion effects on a macroscale.

Conclusions:

  • The developed multiscale approach provides a robust framework for modeling cell migration influenced by adhesion.
  • The model effectively links subcellular adhesion molecule binding to macroscopic population behavior.
  • This work offers insights into the complex dynamics of cell populations in biological contexts.