Projected roles of Na depletion and Na/K pump inactivation with (A and B) and without (B) patch clamp. (A) Simulation of Na/K pump currents, the fraction of pumps that are actively pumping (Factive), and cytoplasmic Na concentrations in a cell model with instantaneous ion diffusion (Fig. 2) and Na/K pumps that inactivate (Fig. 3). Inactivation occurs from all E1 conformations, whereas recovery occurs only when three Na ions are bound to inactive states. The simulation reproduces well the corresponding experiments with different cytoplasmic Na concentrations (Lu et al., 2016). Current decay involves both inactivation and Na depletion with the contributions depicted in the central panel for inactivation and in the right panel for Na concentration changes. (B) Representative long-duration experiment with 60 mM cytoplasmic Na. In the central panel, pump current decay records are shown from the initial (1) and late (2) portions of the experiment. Initially (1), pump current decays in a biphasic fashion. The initial phase has a τ of ∼1 s and amounts to 10% to 20% of peak current magnitude. The slow phase develops with a lag, continues over 40 s, and merges with the usual slow run-down of pump current that occurs in these experiments. After 30 min (2), run-down of pump current has progressed so that peak currents are ∼30% of initial peak currents, and current decay amounts to ∼90% during a 20s application of extracellular K. The right panel reproduces these pump current decay records using slightly modified model parameters. The initial fast current decay in record “1” corresponds largely to inactivation, and the latter decay phase in 1 corresponds largely to Na depletion. Because Na depletion promotes inactivation, however, the processes are interdependent, and the model can develop small oscillations via this feedback. (C) Simulated function of the inactivation process when Na load is changed in a cardiac myocyte that is not patch clamped. Using the same simulation parameters as in A, C depicts model function when Na influx is increased and decreased. The initial Na influx is equivalent to a 20 pA current. It is then increased for 100 s to 100 pA and decreased again to 20 pA. From left to right, the three panels show cytoplasmic Na currents with (blue) and without (red) the simulated Na/K pump inactivation mechanism, cytoplasmic Na concentration changes, and changes of the active state probability of the pump. In summary, the inactivation mechanism promotes the pump to minimize, relatively, cytoplasmic Na changes in the face of Na influx changes. Importantly, cytoplasmic Na concentrations approach a steady state markedly faster (τ ∼90 and ∼200 s with and without inactivation) than the actual turnover of the mean cytoplasmic Na ion to the extracellular space (τ ∼700 s).
