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

• Published in: American journal of physiology. Renal physiology 2015-09, Vol.309 (5), p.F434-F446
• Main Authors: Nadal-Quirós, Mónica, Moore, Leon C, Marcano, Mariano
• Format: Article
• Language: English
• Subjects: Adenosine triphosphatase; H(+)-K(+)-Exchanging ATPase - metabolism; Homeostasis; Homeostasis - physiology; Humans; Kidney Tubules, Distal - metabolism; Loop of Henle - metabolism; Mathematical models; Models, Biological; Parameter estimation; Physiology
• ISSN: 1931-857X; 1522-1466
• DOI: 10.1152/ajprenal.00539.2014

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