A continuum model for coupled cells

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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.

Original languageEnglish (US)
Pages (from-to)351-369
Number of pages19
JournalJournal of Mathematical Biology
Issue number3
StatePublished - Jul 1983


  • Averaging
  • Coupled cells
  • Reaction-diffusion equations


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