The cell membrane is covered with protein complexes called Na+@K+ pumps. Each pump moves 3Na+ ions from the intracellular space to the extracellular milieu for every 2K+ ions it moves into the cell. During normal function, the pumps work constantly. Under normal conditions, there is a gradient of
Na + and K+ ions between the cell and the extracellular space; the concentrations of these ions in these spaces can be found in Table 3.13. Since the ions are pumped against their respective gradients, energy in the form of ATP is required.
An experiment is conducted using ouabain, which blocks Na+9K+ pumps in cells. During this time, the gradient collapses; the intracellular Na+ con-centration becomes 80 mM and the intracellular K+ concentration 72.5 mM. After the experiment, ouabain is removed from the cells by rinsing with PBS (phosphate buffered saline). The pumps begin to operate again to reestablish the gradients. The recovery phase of the experiment lasts 4.0 hr, during which time the cells work to regain the previous ion balance. Model the ion pumps on a cell membrane during the recovery phase. Assume that the volume of the cell is 65.4mm3. Assume that there are 1.0*105 ion pumps per cell. Assume that the pumping rate is constant (i.e., it is not dependent on the gradient of the ions). Assume that there is no diffusion of Na+ or K+ ions across the cell membrane and that no other ion pumps or channels are active.
(a) Calculate the Na+ pumping rate for one cell (molecules/(pump.s)) needed to reestablish the intracellular Na+ concentration in 4.0 hr without consideration of the K+ pumping rate.
(b) Calculate the K+ pumping rate for one cell (molecules/(pump.s)) needed to reestablish the intracellular K+ concentration in 4.0 hr without consideration of the Na+ pumping rate.
(c) Will the cell be able to reestablish the ion balance for both Na+ and K+ to the equilibrium intracellular concentrations listed in with just the described Na+@K+ pump? Why or why not?
(d) In a different experiment, you calculate a Na+ pumping rate of 1.6molecules/(pump.s). What intracellular K+ concentration (mM) can be established in 3.0 hr? Assume the collapsed intracellular conditions above as the starting point for the recovery phase.