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

Anna Zhigun*, Mabel Lizzy Rajendran

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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Cell-cell adhesion plays a vital role in the development and maintenance of multicellular organisms. One of its functions is regulation of cell migration, such as occurs, e.g. during embryogenesis or in cancer. In this work, we develop a versatile multiscale approach to modelling a moving self-adhesive cell population that combines a careful microscopic description of a deterministic adhesion-driven motion component with an efficient mesoscopic representation of a stochastic velocity-jump process. This approach gives rise to mesoscopic models in the form of kinetic transport equations featuring multiple non-localities. Subsequent parabolic and hyperbolic scalings produce general classes of equations with non-local adhesion and myopic diffusion, a special case being the classical macroscopic model proposed in Armstrong et al. (J Theoret Biol 243(1): 98–113, 2006). Our simulations show how the combination of the two motion effects can unfold. Cell-cell adhesion relies on the subcellular cell adhesion molecule binding. Our approach lends itself conveniently to capturing this microscopic effect. On the macroscale, this results in an additional non-linear integral equation of a novel type that is coupled to the cell density equation.

Original languageEnglish
Article number55
Number of pages35
JournalJournal of Mathematical Biology
Issue number5
Early online date03 Apr 2024
Publication statusPublished - May 2024


  • 35B27
  • 35Q49
  • 35Q92
  • 45K05
  • 92C17
  • Cadherin binding
  • Cell adhesion molecule binding
  • Cell movement
  • Cell-cell adhesion
  • Diffusion-adhesion equations
  • Hyperbolic scaling
  • Kinetic transport equations
  • Multiscale modelling
  • Myopic diffusion
  • Non-local models
  • Parabolic scaling


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