Mathematical models are formulated that represent an epithelium as a system of compartments and bounding membranes and permit the computer simulation of normal and pathological states. This project also undertakes the analysis of simplified, approximate models, which may be used in the interpretation of experimental data. The primary aim of this project remains the development of a mathematical model of proximal tubule, and effort will be focused on acid-base transport. A segmented tubule model will be developed, and the impact of the pH dependence of the Na+/H+ exchanger will be examined in simulations of acid-base disturbances. A second question to be addressed is the role of the luminal Na+/H+ exchanger in mediating glomerulotubular balance. Experimental collaborations are planned which will test previous model predictions regarding the importance of paracellular convective fluxes. A second aim of this project is to develop the theory of isotonic volume regulation during fluctuations of net transport. In the proposed work, an analytical model will be extended to estimate isotonic volume regulation and conditions for dynamical stability will be sought. In electrolyte simulations of principal cells and proximal tubule cells, we will examine the hypothesis that cell pH is a key signal for volume regulation. In particular the behavior of pH-dependent K+ channels, pH- dependent Na+/H+ exchange, and pH-dependent Na+-K+ ATPase will be considered, and the question posed is whether such mechanisms are adequate for the variety of volume challenges. The third effort will be to extend and test the current CCT model. The extension will be the full collecting duct, and will be used to simulate currently available clinical tests of "distal nephron" acidification. The goal of this effort is to see whether these tests can indeed be used to infer such defects as H+-pump failure, enhanced backleak, or voltage defects. This will be the first model of this structure and the first tool to be able to give an estimate of the sensitivity of these tests. Some of the predictions of the CCT model will also be tested in experimental collaborations. In particular the hypothesis to be examined is that alkalosis decreases paracellular Cl- permeability, and thus promotes K+ secretion.