# Equilibrium Potentials

An equilibrium potential is a theoretical voltage that would be produced across a plasma membrane if only one ion were able to diffuse through the membrane. Since the membrane is most permeable to K+, we can construct a theoretical approximation by determining what would happen if K+ were the only ion able to cross the membrane. If this were the case, K+ would diffuse until its concentration inside and outside of a cell became stable, thus establishing an equilibrium. In this condition, if a certain amount of K+ were to move inside the cell (by electrical attraction for the fixed anions), an identical amount of K+ would diffuse out of the cell (down its concentration gradient). At equilibrium, the forces of electrical attraction and of the diffusion gradient are equal and opposite.

At this equilibrium, the concentration of K+ would be higher inside the cell than outside the cell; a concentration difference would exist across the plasma membrane that was stabilized by the attraction of K+ to the fixed anions. At this point we could ask, Are the fixed anions neutralized ... are the charges balanced? The answer depends on how much K+ gets into the cell, which in turn depends on the K+ concentration in the extracellular fluid. At the K+ concentrations that are, in fact, found in the body, the answer to our question is no. Not enough K+ is present in the cell to neutralize the fixed anions (fig. 6.22).

At equilibrium, therefore, the inside of the cell membrane would have a higher concentration of negative charges than the outside of the membrane. There is a difference in charge, as well as a difference in concentration, across the membrane. The magnitude of the difference in charge, or potential difference, on the two sides of the membrane under these conditions is 90 millivolts (mV). A sign (+ or -) placed in front of this number indicates the polarity within the cell. This is shown with a negative sign (as -90 mV) to indicate that the inside of the cell is the negative pole. The potential difference of -90 mV, which would be developed if K+ were the only diffusible ion, is called the K+ equilibrium potential (abbreviated EK). 