Journal of Mathematical Biology

, 58:135

Continuum model of cell adhesion and migration


DOI: 10.1007/s00285-008-0179-x

Cite this article as:
Kuusela, E. & Alt, W. J. Math. Biol. (2009) 58: 135. doi:10.1007/s00285-008-0179-x


The motility of cells crawling on a substratum has its origin in a thin cell organ called lamella. We present a 2-dimensional continuum model for the lamella dynamics of a slowly migrating cell, such as a human keratinocyte. The central components of the model are the dynamics of a viscous cytoskeleton capable to produce contractile and swelling stresses, and the formation of adhesive bonds in the plasma cell membrane between the lamella cytoskeleton and adhesion sites at the substratum. We will demonstrate that a simple mechanistic model, neglecting the complicated signaling pathways and regulation processes of a living cell, is able to capture the most prominent aspects of the lamella dynamics, such as quasi-periodic protrusions and retractions of the moving tip, retrograde flow of the cytoskeleton and the related accumulation of focal adhesion complexes in the leading edge of a migrating cell. The developed modeling framework consists of a nonlinearly coupled system of hyperbolic, parabolic and ordinary differential equations for the various molecular concentrations, two elliptic equations for cytoskeleton velocity and hydrodynamic pressure in a highly viscous two-phase flow, with appropriate boundary conditions including equalities and inequalities at the moving boundary. In order to analyse this hybrid continuum model by numerical simulations for different biophysical scenarios, we use suitable finite element and finite volume schemes on a fixed triangulation in combination with an adaptive level set method describing the free boundary dynamics.


Cell migrationAdhesion kineticsKeratinocyteContinuum modelFree boundary dynamicsLevel set method

Mathematics Subject Classification (2000)


Supplementary material

285_2008_179_MOESM1_ESM.mpg (42.6 mb)
Movie 1 (related to Fig. 6 of the article): F-actin pattern formation. F-actin pattern formation starting from a constant concentration in a stationary domain. Coloring indicates the volume fraction of F-actin (red: high F-actin concentration, blue: low). Arrows represent the velocity of the F-actin field. ESM 1 (MPG 43,588 kb)
285_2008_179_MOESM2_ESM.mpg (20.9 mb)
Movie 2 (related to Fig. 7 of the article): Polarization. Polarization of an initially symmetric cell fragment. Coloring indicates the density of actin-and-surface bound integrins (red: high integrin density, blue: low). Arrows represent the velocity of the F-actin field. ESM 2 (MPG 21,385 kb)

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Department of Engineering PhysicsHelsinki University of TechnologyEspooFinland
  2. 2.Universität Bonn, Abteilung Theoretische BiologieBonnGermany