On a poroviscoelastic model for cell crawling

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

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

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.
Original languageEnglish (US)
Pages (from-to)133-171
Number of pages39
JournalJournal of Mathematical Biology
Volume70
Issue number1-2
DOIs
StatePublished - Feb 8 2014
Externally publishedYes

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