title: On a poroviscoelastic model for cell crawling.
abstract: In 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.
authors: Mathematical Institute, University of Oxford, Radcliffe Observatory Quarter, Woodstock Road, Oxford , OX2 6GG, UK.
authors: L S
authors: LS
authors: Kimpton
authors: J P
authors: JP
authors: Whiteley
authors: S L
authors: SL
authors: Waters
authors: J M
authors: JM
authors: Oliver
mesh_terms: D008841:Actin Cytoskeleton / Q000502:physiology; D000818:Animals; D001696:Biomechanical Phenomena; D002448:Cell Adhesion / Q000502:physiology; D002465:Cell Movement / Q000502:physiology*; D003198:Computer Simulation; D004548:Elasticity; D006801:Humans; D055641:Mathematical Concepts; D008954:Models, Biological; D009218:Myosins / Q000502:physiology; D017711:Nonlinear Dynamics; D016062:Porosity; D012212:Rheology; D014783:Viscosity
chemical_list: D009218:Myosins