An Electric Model for Flat Simple Epithelial Cells with Low Resistive Junctional Membranes. A Mathematical Supplement

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Abstract
A theoretical model, Heaviside's `Bessel cable', for flat simple epithelial cells with low resistive junctional membranes was already discussed in another paper in relation to the electric properties of the amphibian gut epithelium. This paper is intended to supplement the mathematical side of the theory. The differential equations for potential and current distribution associated with the radial spread of a current injected into a thin membrane-bounded layer of cytoplasm are formulated. The steady-state and more general solutions are derived with application of the Laplace transformation technique. An asymptotic expansion of the transient solution is also presented, which might be useful for estimation of the cell membrane capacitance.

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