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A one-dimensional model for the interaction between cell-to-cell adhesion and chemotactic signalling

Published online by Cambridge University Press:  10 February 2011

K. ANGUIGE
K. ANGUIGE*
Affiliation:
Wolfgang Pauli Institute, Fakultät für Mathematik, Universität Wien, Nordbergstraße 15, 1090 Wien, Austria email: kmpa@hotmail.com
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Abstract

We develop and analyse a discrete, one-dimensional model of cell motility which incorporates the effects of volume filling, cell-to-cell adhesion and chemotaxis. The formal continuum limit of the model is a non-linear generalisation of the parabolic-elliptic Keller–Segel equations, with a diffusivity which can become negative if the adhesion coefficient is large. The consequent ill-posedness results in the appearance of spatial oscillations and the development of plateaus in numerical solutions of the underlying discrete model. A global-existence result is obtained for the continuum equations in the case of favourable parameter values and data, and a steady-state analysis, which, amongst other things, accounts for high-adhesion plateaus, is carried out. For ill-posed cases, a singular Stefan-problem formulation of the continuum limit is written down and solved numerically, and the numerical solutions are compared with those of the original discrete model.

Keywords

Cell-to-cell adhesionchemotaxisStefan problems
Type
Papers
Information
European Journal of Applied Mathematics , Volume 22 , Issue 4 , August 2011 , pp. 291 - 316
Copyright
Copyright © Cambridge University Press 2011

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References

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