Optimal Mathematical Models of Renal Transport Processes

描述(申请人提供)：最优化方法为研究数学模型中参数和解之间的关系提供了系统的手段。在肾脏系统中，模型涉及大量参数，当测量存在时，它们与一些不确定性相关。此外，实验数据通常是间接的，因为被测量的变量很少是实际参数，而通常是依赖于参数并且是可测量的函数变量。一旦制定了肾脏过程的模型，就可以使用优化方法来验证模型，方法是搜索一组合理的模型参数，这些参数导致模型行为与测量的响应一致。此外，优化分析可以揭示产生最佳功能行为的参数之间的协同作用，例如最大能效。然而，由于复杂生物模型的参数较多，而且问题可能是不适定的，因此将优化方法应用于复杂的生物模型往往是困难的。 在这项应用中，我们的目标是开发在肾脏生理学中使用最优化方法的策略和方法，并使用这些方法来研究两个基本问题。第一个涉及肾脏逆流系统尿液浓缩能力的决定因素。第二个重点是肾上皮细胞中不同共转运蛋白的功能和结合序列构型。 这些研究将提供对肾脏逆流系统的新见解，以及上皮细胞中共转运体的最佳功能和结构。它们还将为应用最优化方法研究肾功能提供新的见解。由于得到的联合转运蛋白的最佳模型将作为工具箱的一部分通过万维网提供，这些研究将为肾上皮生理学家提供用于实验设计和数据分析的模拟工具。 如果成功，这些研究将提供一种从现有数据中提取有关肾脏系统功能的附加信息的方法。由于肾脏逆流系统和上皮细胞共转运体都参与调节肾脏水和盐的排泄，这些研究最终可能有助于了解肾脏在高血压和与尿液浓度缺陷相关的疾病中的作用。

DESCRIPTION (provided by applicant): 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.