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, mathematical models, which may be used in the interpretation of experimental data. Comparison of the approximate analytical models with the detailed computer simulation is used to assess the range of applicability of the simpler models. The major aim for the next period of investigation is the completion of a model of the proximal nephrovascular unit - including proximal tubule, glomerulus, and peritubular capillary. The model tracks the concentrations and fluxes of Na+, K+, H+, C1-, carbonate ion, secondary hydrogen phosphate ion, primary hydrogen phosphate ion, glucose and urea. The primary focus of this simulation is the study of the proximal tubule sodium reabsorption: the transepithelial pathways and driving forces of sodium transport and the mechanisms by which physical factors modulate this reabsorption. In particular, this is an effort to quantify the effects of luminal and peritubular factors which mediate the balance between glomerular filtration and proximal reabsorption. The second focus is the representation of proximal tubule bicarbonate reabsorption: mechanisms of transport defined in cell membrane systems are to be examined in the context of a tubule model, in simulations of the acid-base disturbances. Of particular interest is the role of the proximal nephron in the maintenance of metabolic alkalosis - defining the interplay of decreased glomerular filtration rate, extracellular volume depletion, and increased peritubular pH.
A second aim for the next investigational period is the representation of the cortical collecting tubule. This model will be developed in a step-wise fashion from simulations of toad and turtle urinary bladder. It will be used to explore the interaction of tubule flow, acid-base states, and sodium avidity on potassium transport by this nephron segment.
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