Parameter Estimation for Mathematical Models of Ion Transport in the Renal System
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Nonlinear optimization approaches were used to compute rate constants for mathematical models of renal sodium-potassium-chloride and potassium-chloride transporters in cell membranes. The optimization consisted in minimizing the distance between model unidirectional fluxes and published experimental fluxes for different forms of these transporters. Two optimization techniques, a descent method and the simulated annealing method, were used. Both found similar optima inside the bounded region. The simulated annealing method requires much more run time. However, it does not require the derivatives of the function being optimized, as the descent method does, and it is easier to implement in different numerical computing environments. It also has the capacity of making a more rigorous search. The obtained models are useful to study the function, regulation, and pathophysiology of renal epithelial cells.