Modelling cell motility and chemotaxis with evolving surface finite elements

Charles M. Elliott, Bjoern Stinner, Chandrasekhar Venkataraman*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

102 Citations (Scopus)

Abstract

We present a mathematical and a computational framework for the modelling of cell motility. The cell membrane is represented by an evolving surface, with the movement of the cell determined by the interaction of various forces that act normal to the surface. We consider external forces such as those that may arise owing to inhomogeneities in the medium and a pressure that constrains the enclosed volume, as well as internal forces that arise from the reaction of the cells' surface to stretching and bending. We also consider a protrusive force associated with a reaction-diffusion system (RDS) posed on the cell membrane, with cell polarization modelled by this surface RDS. The computational method is based on an evolving surface finite-element method. The general method can account for the large deformations that arise in cell motility and allows the simulation of cell migration in three dimensions. We illustrate applications of the proposed modelling framework and numerical method by reporting on numerical simulations of a model for eukaryotic chemotaxis and a model for the persistent movement of keratocytes in two and three space dimensions. Movies of the simulated cells can be obtained from http://homepages.warwick.ac.uk/similar to maskae/CV_Warwick/Chemotaxis.html.

Original languageEnglish
Pages (from-to)3027-3044
Number of pages18
JournalJournal of the Royal Society Interface
Volume9
Issue number76
DOIs
Publication statusPublished - 7 Nov 2012

Keywords

  • cell motility
  • chemotaxis
  • surface finite elements
  • reaction-diffusion systems
  • WILLMORE FLOW
  • MOVEMENT
  • ORIENTATION
  • ALGORITHM
  • EQUATIONS
  • MIGRATION
  • SYSTEMS
  • MOTION
  • ROLES

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