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Estimation of Acid‐Base and NH+4 Transport Parameters in a TAL Cell Model Using Inverse Methods

A mathematical model of a medullary thick ascending limb (mTAL) cell was used to study cytosolic pH (pHi) responses to luminal NH4+ perturbations. TAL cells load NH4+ via apical NH4+‐permeable channels and the NKCC2 cotransporter, resulting in a rapid fall in pHi. Our goal was to use our model and published NH4+ perturbation data to estimate parameters associated with pHi regulation using an inverse method. The TAL cell model, which includes NH+4 binding by NKCC2 and NHE, also includes models for Na+,K+‐ATPase, the Cl−‐HCO3− exchanger, KCC1, and trans‐ and paracellular electrodiffusion. A least‐squares problem was formulated and solved to fit the model to the data. First, steady‐state short‐circuit current data was used to estimate parameters important in Na+ transport; this yielded reasonable cytosolic concentrations, membrane PD's and resistances. The model was then fit to time records of NH4+ perturbations, with and without inhibition of NKCC2 or K+ channels, to estimate parameters associated with NH4+ transport. The results show that our TAL cell model, when used with parameter sets obtained from optimization methods, exhibits behaviors consistent with a wide variety of experimental results, including NH4+ perturbations, in isolated perfused TAL segments. This provides validation of the TAL model, which we intend to use in a multi‐cell model of the TAL segment.