title: A continuum model for coupled cells.
abstract: 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.
mesh_terms: D000818:Animals; D001692:Biological Transport; D004058:Diffusion; D007365:Intercellular Junctions / Q000502:physiology*; D008433:Mathematics; D008954:Models, Biological; D010539:Permeability