Mathematical models are formulated that represent a leaky epithelium as a system of compartments and bounding membranes and permit the computer simulation of the experimental maneuvers commonly employed in physiological investigation. Further, this project undertakes the identification and analysis of simplified, or approximate, mathematical models which may be used in the reduction of experimental data. Comparison of the approximate analytical models with the output from the detailed computer simulation is used to assess the range of applicability of the simpler models and to isolate confounding influences.
A specific aim i s the construction of a model of mammalian proximal tubule--a model which will include the four ionic species (Na, K, C1, HCO3) and protein oncotic forces, allow for intraepithelial solute-solvent coupling, and track the changes in concentrations and pressures along the tubule length. This model will simulate experiments in isolated perfused tubules or micropuncture experiments in perfused kidneys in which the peritubular solution is fixed and relatively uniform. It will be the first attempt to model both the internal structure of this epithelium and the changes of the luminal fluid along the tubule length. The dynamics of water transport across proximal tubule (solute-solvent coupling, transport against an adverse osmotic gradient, isotonic transport) will be considered with the framework previously devised for the flat epithelial sheet. Analytic models of water flow across a flat epithelium will be extended to a tubular geometry. A second aspect of this project will be an examination of the predictions of the comprehensive epithelial models in simulations of electrophysiological experiments. In particular, the effect of """"""""electrically silent"""""""" events (ion-ion coupling, cell swelling) may alter intracellular potentials.
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