KAUST Grant NumberKUK-C1-013-04
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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
CollectionsPublications Acknowledging KAUST Support
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