Gallimore, L. S. and Whiteley, J. P. and Waters, S. L. and King, J. R. and Oliver, J. M. (2011) Nonuniqueness in a minimal model for cell motility. Mathematical Medicine and Biology . (Submitted)
Two–phase flow models have been used previously to model cell motility, however these have rapidly become very complicated, including many physical processes, and are opaque. Here we demonstrate that even the simplest one–dimensional, two–phase, poroviscous, reactive flow model displays a number of behaviours 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 solution that co–exist 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.
|Subjects:||D - G > General|
|Research Groups:||Oxford Centre for Collaborative Applied Mathematics|
|Deposited By:||Peter Hudston|
|Deposited On:||22 Feb 2012 07:54|
|Last Modified:||29 May 2015 19:10|
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