Biophysical Journal 12: 325-350 (1972)
© 1972 the Biophysical Society

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Mass Transfer in the Cornea

II. Ion Transport and Electrical Properties of a Series Membrane Tissue

ABSTRACT

The electrical and active transport properties of isolated rabbit cornea are investigated by computer experimentation. The tissue is modeled as a series membrane system and the passive ion fluxes through it are described by the frictional formulation of irreversible thermodynamics. From short-circuit current (SCC) data, it is found that the epithelial sodium pump rate (P) is not appreciably changed when much of the sodium in the solution bathing the anterior corneal surface (concentration = c₁₁) is replaced by choline, with choline-free medium posteriorly. Simulations of open-circuited corneas, using the mean P computed from the SCC data, yield corneal and stromal potentials in agreement with experiment. The stromal fluid is calculated to become more hypotonic as c₁₁ is diminished, a result consistent with posttest measurements of the sodium content of experimental stromata. The apparent decrease in "bound sodium" which accompanies the reduction of c₁₁ is a result of the associated changes in steady stromal hydration; the epithelial sodium pump does not contribute to corneal deturgescence. The inclusion of a simple epithelial structure in the computations changes the value of P but affects neither its constancy nor the calculated behavior of the cornea under open-circuit conditions. A general algebraic relation among pump rates and ion fluxes in short-circuited series membrane systems bathed in complex media is derived and used to construct a relation between P and SCC for the cornea. This equation yields pump rates in good agreement with the computer results and is used to show that (a) P is independent of c₁₁ if d(SCC)/dc₁₁ is a constant related to the over-all corneal permeability to sodium, and (b) a Lineweaver-Burke plot of 1/SCC vs. 1/c₁₁ can appear to be linear at constant P.