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Modeling of Cell Movement on Adhesive Substrates

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Mathematical Modelling and Analysis of Complex Fluids and Active Media in Evolving Domains

Modeling the movement of living motile cells on substrates is a formidable challenge; regulatory pathways are intertwined and forces that influence cell motion on adhesive substrates are not fully quantified. Here, we present a mathematical model coupling cell shape dynamics, treated in the framework of the Ginzburg-Landau-type equation for auxiliary mass density (phase field), to a partial differential equation describing the mean orientation (polarization of actin filaments) of the cell’s cytoskeletal network. In order to maintain the total area of the cell, the phase field equation is subject to a global conservation constraint. Correspondingly, the equation for mean polarization incorporates key elements of cell mechanics: directed polymerization of actin network at the cell membrane, decay of polarization in the bulk of the cell, and formation of actin bundles (stress fibers) in the rear. The model successfully reproduces the primary phenomenology of cell motil ity: discontinuous onset of motion, diversity of cell shapes and shape oscillations, as well as distribution of traction on the surface. The results are in qualitative agreement with recent experiments on the motility of keratocyte cells and cell fragments. The asymmetry of the shapes is captured to a large extent in this simple model, which may prove useful for the interpretation of recent experiments and predictions of cell dynamics under various conditions. We also investigate effects of adhesion and substrate elasticity on the shape and dynamics of moving cells. We demonstrate that on hard adhesive substrates the cells exhibit steady-state motion. A transition to stick-slip motion is observed on soft and weakly adhesive surfaces.

This talk is part of the Isaac Newton Institute Seminar Series series.

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