## Equilibrium Potentials for Sodium Potassium and Chloride

If the permeability of the cell membrane to sodium is not zero, then the resting membrane potential of the cell must have a contribution from Na+ as well as from K+ and Cl-. This is true even though the sodium pump eventually removes any sodium that leaks into the cell. There are two reasons for this. First, recall that electrical force per particle is much stronger than concentra-tional force per particle; therefore, even a tiny trickle of sodium that would cause a negligible change in internal concentration could produce large changes in membrane potential. Because the sodium pump responds only to changes in the bulk concentration of sodium inside the cell, it could not detect and respond to the tiny changes that would occur for even large changes in membrane potential. Second, even though sodium that leaks in is eventually pumped out, the efflux of sodium through the pump is coupled with an influx of potassium. Thus, there is a net transfer of positive charge into the cell associated with leakage of sodium.

Application of the Nernst equation to the concentrations of sodium, potassium, and chloride in the ICF and ECF of a typical mammalian cell (Table 2-1) shows that the membrane potential cannot possibly be simultaneously at the equilibrium potentials of all three ions. As we calculated in Chapter 4, EK = ECl = about -80 mV (actually a bit greater than -81 mV, given the values in Table 2-1). But with [Na+]o = 120 mM and [Na+] = 12 mM, ENa would be

+58 mV. The membrane potential, Em, cannot simultaneously be at -80 mV and +58 mV. The actual value of membrane potential will fall somewhere between these two extreme values. If the sodium permeability of the membrane were in fact zero, Em would be determined solely by EK and ECl and would be -80 mV. Conversely, if chloride and potassium permeability were zero, Em would be determined only by sodium and would lie at ENa, +58 mV. Because the permeabilities of all three ions are nonzero, there will be a struggle between Na+ on the one hand, tending to make Em equal +58 mV, and K+ and Cl- on the other, tending to make Em equal -80 mV. Two factors determine where Em will actually fall: (1) ion concentrations, which determine the equilibrium potentials for the ions; and (2) relative ion permeabilities, which determine the relative importance of a particular ion in governing where Em lies. Before expressing these relations quantitatively, it will be useful to consider the mechanism of ionic permeability in more detail.

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