Exact solution of a model of diffusion in an infinite chain or monolayer of cells coupled by gap junctions

Analytic solutions are found for an infinite chain of cells coupled by gap junctions under two initial conditions: (a) One inner cell initially filled uniformly to a fixed concentration and (b) inner cell maintained indefinitely at constant concentration. The solution can be extended by the product method (Carslaw and Jaeger. 1959. Conduction of Heat in Solids. Oxford University Press.) to monolayers. We can also incorporate leakage through the plasma membrane by the product method. We demonstrate the utility of these results by fitting diffusion data from the septate axon of earthworm and by plots of theoretical profiles from monolayers of cells. Use of these analytic solutions enables one to overcome the limitations of methods that lump the effects of cytoplasmic diffusion and junctional permeability into an effective diffusion coefficient.