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Math Med Biol. 2013 Sep;30(3):241-72. doi: 10.1093/imammb/dqs023. Epub 2012 Jul 11.

Multiple travelling-wave solutions in a minimal model for cell motility.

Author information

1
OCCAM, Mathematical Institute, University of Oxford, 24-29 St. Giles', Oxford OX1 3LB, UK.

Abstract

Two-phase flow models have been used previously to model cell motility. In order to reduce the complexity inherent with describing the many physical processes, we formulate a minimal model. Here we demonstrate that even the simplest 1D, two-phase, poroviscous, reactive flow model displays various types of behaviour relevant to cell crawling. We present stability analyses that show that an asymmetric perturbation is required to cause a spatially uniform, stationary strip of cytoplasm to move, which is relevant to cell polarization. Our numerical simulations identify qualitatively distinct families of travelling-wave solutions that coexist at certain parameter values. Within each family, the crawling speed of the strip has a bell-shaped dependence on the adhesion strength. The model captures the experimentally observed behaviour that cells crawl quickest at intermediate adhesion strengths, when the substrate is neither too sticky nor too slippy.

KEYWORDS:

cell adhesion; cell crawling; poroviscous; reactive; two-phase

PMID:
22789545
DOI:
10.1093/imammb/dqs023
[Indexed for MEDLINE]

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