Journal of Mathematical Biology

, Volume 70, Issue 1–2, pp 133–171 | Cite as

On a poroviscoelastic model for cell crawling

  • L. S. Kimpton
  • J. P. Whiteley
  • S. L. Waters
  • J. M. Oliver


In this paper a minimal, one-dimensional, two-phase, viscoelastic, reactive, flow model for a crawling cell is presented. Two-phase models are used with a variety of constitutive assumptions in the literature to model cell motility. We use an upper-convected Maxwell model and demonstrate that even the simplest of two-phase, viscoelastic models displays features relevant to cell motility. We also show care must be exercised in choosing parameters for such models as a poor choice can lead to an ill–posed problem. A stability analysis reveals that the initially stationary, spatially uniform strip of cytoplasm starts to crawl in response to a perturbation which breaks the symmetry of the network volume fraction or network stress. We also demonstrate numerically that there is a steady travelling-wave solution in which the crawling velocity has a bell-shaped dependence on adhesion strength, in agreement with biological observation.


Cell motility Two-phase flow Viscoelastic Cell Adhesion 

Mathematics Subject Classification (2000)

92C17 76A10 76T99 



This publication is based on work supported by Award No. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST). S.L.W. is grateful for funding from the EPSRC in the form of an Advanced Research Fellowship.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • L. S. Kimpton
    • 1
  • J. P. Whiteley
    • 2
  • S. L. Waters
    • 1
  • J. M. Oliver
    • 1
  1. 1.Mathematical InstituteUniversity of Oxford, Radcliffe Observatory QuarterOxford UK
  2. 2.Department of Computer ScienceUniversity of OxfordOxford UK

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