A mathematical model of rat ascending Henle limb. I. Cotransporter function.

Kinetic models of Na+-K+-2Cl- costransporter (NKCC2) and K+-Cl- cotransporter (KCC4), two of the key cotransporters of the Henle limb, are fashioned with inclusion of terms representing binding and transport of NH4+. The models are simplified using assumptions of equilibrium ion binding, binding symmetry, and identity of Cl- binding sites. Model parameters are selected to be consistent with flux data from expression of these transporters in oocytes, specifically inwardly directed coupled transport of rubidium. In the analysis of these models, it is found that despite the simplifying assumptions to reduce the number of model parameters, neither model is uniquely determined by the data. For NKCC or KCC there are two- or three-parameter families of "optimal" solutions. As a consequence, one may specify several carrier translocation rates and/or ion affinities before fitting the remaining coefficients to the data, with no loss of fidelity in simulating the experiments. Model calculations suggest that with respect to NKCC2 near its operating point, the curve of ion flux as a function of cell Cl- is steep, and with respect to KCC4, its curve of ion flux as a function of peritubular K+ is also steep. The implication is that the kinetics are suitable for these two transporters in series to act as a sensor for peritubular K+, to modulate AHL Na+ reabsorption, with cytosolic Cl- as the intermediate variable. The models also reveal the potential for luminal NH4+ to be a potent catalyst for NKCC2 Na+ reabsorption, provided suitable exit mechanisms for NH4+ (from cell-to-lumen) are operative. It is found that KCC4 is likely to augment the secretory NH4+ flux, with peritubular NH4+ uptake driven by the cell-to-blood K+ gradient.