A continuum model for coupled cells

A continuum model of diffusion-coupled cells that more accurately reflects the presence of low-permeability gap junctions between cells is analyzed. It is shown by a multi-scale analysis that to lowest order the slow evolution of the mean concentration is described by the usual ordinary differential...

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Bibliographic Details
Published in:Journal of mathematical biology 1983-01, Vol.17 (3), p.351-369
Main Author: Othmer, H G
Format: Article
Language:English
Subjects:
Animals
Biological Transport
Diffusion
Intercellular Junctions - physiology
Mathematics
Models, Biological
Permeability
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Summary:A continuum model of diffusion-coupled cells that more accurately reflects the presence of low-permeability gap junctions between cells is analyzed. It is shown by a multi-scale analysis that to lowest order the slow evolution of the mean concentration is described by the usual ordinary differential equations for a discrete model. Furthermore, stable non-uniform steady solutions are shown to exist in the continuum model of a one component system, whereas this is impossible for the standard reaction-diffusion model of this system. It is also shown how to average the equations in this continuum model to obtain a system of reaction-diffusion equations with constant coefficients.
ISSN:0303-6812
1432-1416
DOI:10.1007/BF00276521