Models of the Na-K pump in cardiac muscle predict the wrong intracellular Na+ activity

The Na-K pump in cardiac Purkinje strands has been carefully studied with voltage clamp and Na+-selective microelectrodes. In three of these studies both the rate of change of intracellular Na+ activity, a(Nai), after pump blockade, and the time constant of reduction of a(Nai) after an Na+ load were measured. These two parameters can be employed with a formalism relating pump activity to a(Nai) in order to predict the a(Nai) in the steady state. Several formalisms were tested: (a) a first-order dependence on a(Nai); (b) a model based on the assumption of a single, saturable, Na+-binding site that must be occupied for transport to occur; (c) a model based on n equivalent, saturable, Na+ binding sites per pump molecule all of which must be occupied for transport to occur. The first two models predicted an a(Nai) that is far below the value of about 6 mM that is experimentally obtained. The third model would work for n greater than or equal to 4. These results suggest that either the cardiac Na-K pump is not well described by available Na-K pump models for n less than 4 or that the measured Na+ influx rate, extrusion rate or a(Nai) are in error.