The movement of charged substances across the plasma membrane is governed not only by the concentration gradient across the membrane but also by the electrical potential across the membrane. Equilibrium for an ion across the membrane is reached when the electrical gradient exactly balances the concentration gradient for that ion. The equation that expresses this equilibrium condition quantitatively is the Nernst equation, which gives the value of membrane potential that will exactly balance a given concentration gradient.

If more than one ion can cross the cell membrane, both can be at equilibrium only if the Nernst, or equilibrium, potentials for both ions are the same. This requirement leads to the defining properties of the Donnan, or Gibbs-Donnan, equilibrium, which applies simultaneously to two permeant ions. By working through a series of examples, we saw how it is possible to build a model cell that is at equilibrium and that has ICF, ECF, and membrane potential like that of real animal cells.

Real cells, however, were found to be permeable to sodium ions. This removed an important cornerstone of the equilibrated model cell, and forced a change in viewpoint about the relation between animal cells and their environment. Real cells must expend metabolic energy, in the form of ATP, in order to "pump" sodium out against its concentration and electrical gradients and thus to maintain osmotic balance. In the next chapter, we will consider what effect the sodium permeability of the plasma membrane might have on the electrical membrane potential. We will see how the membrane potential depends not only on the concentrations of ions on the two sides of the membrane, as in the Nernst equation, but also on the relative permeability of the membrane to those ions.

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