Optimization methods provide systematic means for studying the relationship between the parameters and the solutions in mathematical models. In renal systems the models involve a large number of parameters and, when measurements exist, they are associated with some uncertainty. Further, the experimental data is often indirect, in that the measured variable is seldom the actual parameter, but is normally a functional variable that is dependent upon the parameters and is measurable. Once a model of a renal process is formulated, optimization methods can be used to validate the model by searching for sets of reasonable model parameters that result in model behavior consistent with measured responses. Further, optimization analysis can reveal synergism between parameters that yield optimal functional behaviors, such as maximal energy efficiency. However, application of optimization methods to complex biological models is often difficult because of the large numbers of parameters, and because the problem may be ill-posed. In this application we aim to develop strategies and approaches for the use of optimization methods in renal physiology, and to use these methods to investigate two fundamental problems. The first concerns the determinants of urine concentrating ability of the renal countercurrent system. The second focuses on the function and binding sequence configuration of different co transporters in renal epithelial cells. These studies will provide new insights into the renal countercurrent system, and optimal function and structure of co transporters in epithelial cells. They will also provide new insight into the best approaches for application of optimization methods to study renal function. Because the resultant optimal models of the co transporters will be made available as part of a toolbox through the world wide web, these studies will provide renal epithelial physiologists with simulation tools for experimental design and data analysis. If successful, the studies will provide a means to extract addition information about renal system function from existing data. Because the renal countercurrent system and the co transporters in epithelial cells are both involved in the regulation of renal water and salt excretion, these studies may eventually facilitate progress in understanding the renal role in hypertension and in diseases associated with defects in urine concentration.
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