Parameter estimation for mathematical models of a nongastric H+(Na+)-K(+)(NH4+)-ATPase

The role of nongastric H(+)-K(+)-ATPase (HKA) in ion homeostasis of macula densa (MD) cells is an open question. To begin to explore this issue, we developed two mathematical models that describe ion fluxes through a nongastric HKA. One model assumes a 1H(+):1K(+)-per-ATP stoichiometry; the other assumes a 2H(+):2K(+)-per-ATP stoichiometry. Both models include Na+ and NH4+ competitive binding with H+ and K+, respectively, a characteristic observed in vitro and in situ. Model rate constants were obtained by minimizing the distance between model and experimental outcomes. Both 1H(+)(1Na(+)):1K(+)(1NH4 (+))-per-ATP and 2H(+)(2Na(+)):2K(+)(2NH4 (+))-per-ATP models fit the experimental data well. Using both models, we simulated ion net fluxes as a function of cytosolic or luminal ion concentrations typical for the cortical thick ascending limb and MD region. We observed that (1) K+ and NH4+ flowed in the lumen-to-cytosol direction, (2) there was competitive behavior between luminal K+ and NH4+ and between cytosolic Na+ and H+, 3) ion fluxes were highly sensitive to changes in cytosolic Na+ or H+ concentrations, and 4) the transporter does mostly Na+ / K+ exchange under physiological conditions. These results support the concept that nongastric HKA may contribute to Na+ and pH homeostasis in MD cells. Furthermore, in both models, H+ flux reversed at a luminal pH that was <5.6. Such reversal led to Na+ / H+ exchange for a luminal pH of <2 and 4 in the 1:1-per-ATP and 2:2-per-ATP models, respectively. This suggests a novel role of nongastric HKA in cell Na+ homeostasis in the more acidic regions of the renal tubules.