On a poroviscoelastic model for cell crawling.

نویسندگان

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

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.

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عنوان ژورنال:
  • Journal of mathematical biology

دوره 70 1-2  شماره 

صفحات  -

تاریخ انتشار 2015