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J. Fischbarg, F.P. J. Diecke; A Mathematical Model of Electrolyte and Fluid Transport Across Corneal Endothelium . Invest. Ophthalmol. Vis. Sci. 2005;46(13):2207.
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© ARVO (1962-2015); The Authors (2016-present)
Purpose: 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. Methods: To construct a model, 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 5 of 11 parameters. The remaining 6 parameter values are calculated assuming cellular steady–state and developing a set of 11 simultaneous equations which are solved using algebraic software. With that as a 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 (∼1700 lines of code) that monitors temporal changes in chemical and electrical driving forces across cell membranes and the paracellular pathway. Results: The program reproduces quite well the behaviors experimentally observed for the translayer electrical potential difference and rate of fluid transport. It predicts a decrease in fluid transport observed after inhibition of apical Na channels by phenamil, after inhibition of Cl– channels, after inhibition of Na–bicarbonate cotransporters and anion exchangers with DIDS, and after replacing ambient bicarbonate by Cl–. It also predicts the dependence of transendothelial electrical potential difference on ambient bicarbonate and Na+ concentrations. Lastly, it predicts the behavior of intracellular pH seen experimentally when apical and basolateral membranes are exposed to bicarbonate and CO2– free solutions and to low bicarbonate solutions at constant CO2. In addition, we have used it to compare predictions of translayer fluid transport by two competing theories, electro–osmosis and local osmosis. Conclusions: We have developed a mathematical model which reproduces changes in transendothelial potential difference, fluid transport and intracellular pH upon experimental manipulations. Only predictions using electro–osmosis fit all the experimental data.
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