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Special Semester on Quantitative Biology analyzed by Mathematical Methods
Linz, October 1, 2007 - January 27, 2008
A one-dimensional model of cell diffusion and aggregation, incorporating volume filling and cell-to-cell adhesion

Workshop on Biomechanics and Chemotaxis, Tue, 11 Dec, 2007

Speaker: Keith Anguige

Abstract

We develop and analyse a discrete model of cell motility in one dimension which incorporates the effects of volume filling and cell-to-cell adhesion. The continuum limit of the model is a nonlinear diffusion equation with a diffusivity which can turn negative if the adhesion coefficient is sufficiently large - this is related to pattern formation in numerical solutions of the discrete model. A combination of stability analysis of the discrete equations and steady-state analysis of the limiting PDE (and higher-order modifications thereof) can be used to shed light on these and other qualitative predictions of the model. The inclusion of chemotactic effects, as well as the extension of the model to two dimensions, will also be discussed briefly.

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