A mathematical model of electrolyte and fluid transport across corneal endothelium.

To predict the behavior of a transporting epithelium by intuitive means can be complex and frustrating. As the number of parameters to be considered increases beyond a few, the task can be termed impossible. The alternative is to model epithelial behavior by mathematical means. For that to be feasible, it has been presumed that a large amount of experimental information is required, so as to be able to use known values for the majority of kinetic parameters. However, in the present case, we are modeling corneal endothelial behavior beginning with experimental values for only five of eleven parameters. The remaining parameter values are calculated assuming cellular steady state and using algebraic software. With that as base, as in preceding treatments but with a distribution of channels/transporters suited to the endothelium, temporal cell and tissue behavior are computed by a program written in Basic that monitors changes in chemical and electrical driving forces across cell membranes and the paracellular pathway. We find that the program reproduces quite well the behaviors experimentally observed for the translayer electrical potential difference and rate of fluid transport, (a) in the steady state, (b) after perturbations by changes in ambient conditions HCO3-, Na+, and Cl- concentrations), and (c) after challenge by inhibitors (ouabain, DIDS, Na+- and Cl(-)-channel inhibitors). In addition, we have used the program to compare predictions of translayer fluid transport by two competing theories, electro-osmosis and local osmosis. Only predictions using electro-osmosis fit all the experimental data.