KAUST Grant NumberKUK-C1-013-04
Online Publication Date2014-02-08
Print Publication Date2015-01
Permanent link to this recordhttp://hdl.handle.net/10754/599034
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AbstractIn 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.
CitationKimpton LS, Whiteley JP, Waters SL, Oliver JM (2014) On a poroviscoelastic model for cell crawling. Journal of Mathematical Biology 70: 133–171. Available: http://dx.doi.org/10.1007/s00285-014-0755-1.
SponsorsThis 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.
JournalJournal of Mathematical Biology
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