Multiple travelling-wave solutions in a minimal model for cell motility
KAUST Grant NumberKUK-C1-013-04
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AbstractTwo-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 travellingwave 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. © The Author 2012. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.
CitationKimpton LS, Whiteley JP, Waters SL, King JR, Oliver JM (2012) Multiple travelling-wave solutions in a minimal model for cell motility. Mathematical Medicine and Biology 30: 241–272. Available: http://dx.doi.org/10.1093/imammb/dqs023.
SponsorsThis research was supported in part 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 and J.R.K. for that of the Wolfson Foundation and Royal Society.
PublisherOxford University Press (OUP)
CollectionsPublications Acknowledging KAUST Support
- On a poroviscoelastic model for cell crawling.
- Authors: Kimpton LS, Whiteley JP, Waters SL, Oliver JM
- Issue date: 2015 Jan
- A model for cell motility on soft bio-adhesive substrates.
- Authors: Sarvestani AS
- Issue date: 2011 Feb 24
- Cytoplasm dynamics and cell motion: two-phase flow models.
- Authors: Alt W, Dembo M
- Issue date: 1999 Mar 1
- Crawling toward a unified model of cell mobility: spatial and temporal regulation of actin dynamics.
- Authors: Rafelski SM, Theriot JA
- Issue date: 2004
- Thin-film theories for two-phase reactive flow models of active cell motion.
- Authors: Oliver JM, King JR, McKinlay KJ, Brown PD, Grant DM, Scotchford CA, Wood JV
- Issue date: 2005 Mar