## Testing Bernsteins Hypothesis

How would one go about testing Bernstein's hypothesis? If the membrane potential (Vm) is equal to the K+ equilibrium potential (EK), one should be able to substitute the known outside and inside concentrations of K+ into the Nernst equation and determine the equilibrium potential (EK), which should equal the measured membrane potential (Vm). Furthermore, because of the logarithmic relationship in the Nernst equation, if the outside K+ concentration is artificially manipulated by a factor of 10, then the equilibrium potential will change by a factor of 60 mV. If the membrane potential is governed by the K+ equilibrium potential, then the membrane potential should also change by 60 mV.

Figure 4 illustrates one direct experimental test of Bernstein's hypothesis performed by Hodgkin and

Horowicz. A cell was impaled with a microelectrode and the resting potential was measured. The extracellular K+ concentration was systematically varied, and the change in the resting potential was monitored. When the K+ concentration was changed by a factor of 10, the resting potential changed by a factor of 60 mV. The straight line on the plot is the relationship predicted by the Nernst equation (note that it is a straight line because these data are plotted on a semilog scale).

The fit is not perfect, however, and the experimental data deviate from the predicted values when the extracellular K+ concentration is reduced to low levels. If there is a deviation from the Nernst equation, the membrane must be permeable, not only to K+, but to another ion as well. That other ion appears to be Na+. As indicated earlier, Na+ has a high concentration outside the cell and a low concentration inside the cell. If the cell has a slight permeability to Na+, Na+ will tend to diffuse into the cell and produce a charge distribution across the membrane so that the inside of the membrane will be positive with respect to the outside. This slight increase in the positivity on the inside surface of the membrane will tend to reduce the negative charge distribution produced by the diffusion of K+ out of the cell. The slight permeability of the membrane to Na+ will tend, therefore, to make the cell slightly less negative than would be expected were the membrane only permeable to K+. If a membrane is permeable to more than one cation, the Nernst equation cannot be used to predict the resultant membrane potential. However, in such a case the Goldman equation can be used. 