# Nernst Equation

There is another way to look at the equilibrium potential: it is the membrane potential that would exactly balance the diffusion gradient and prevent the net movement of a particular ion. Since the diffusion gradient depends on the difference in concentration of the ion, the value of the equilibrium potential must depend on the ratio of the concentrations of the ion on the two sides of the membrane. The Nernst equation allows this theoretical equilibrium potential to be calculated for a particular ion when its con-

Intracellular electrode ^¡ji Voltmeter

Voltmeter

Extracellular electrode

Electrical attraction

Diffusion

■ Figure 6.22 Potassium equilibrium potential. If K+ were the only ion able to diffuse through the plasma membrane, it would distribute itself between the intracellular and extracellular compartments until an equilibrium was established. At equilibrium, the K+ concentration within the cell would be higher than outside the cell because of the attraction of K+ for the fixed anions. Not enough K+ would accumulate within the cell to neutralize these anions, however, so the inside of the cell would be -90 millivolts compared to the outside of the cell. This membrane voltage is the equilibrium potential (EK) for potassium.

centrations are known. The following simplified form of the equation is valid at a temperature of 37° C:

where

Ex = equilibrium potential in millivolts (mV) for ion x Xo = concentration of the ion outside the cell Xi = concentration of the ion inside the cell z = valence of the ion (+1 for Na+ or K+)

Note that, using the Nernst equation, the equilibrium potential for a cation has a negative value when Xi is greater than Xo. If we substitute K+ for X, this is indeed the case. As a hypothetical example, if the concentration of K+ were ten times higher inside compared to outside the cell, the equilibrium potential would be 61 mV (log 1/10) = 61 x (-1) = -61 mV. In reality, the concentration of K+ inside the cell is actually thirty times greater than outside (150 mEq/L inside compared to 5 mEq/L outside). Thus,

This means that a membrane potential of 90 mV, with the inside of the cell negative, would be required to prevent the diffusion of K+ out of the cell.

If we wish to calculate the equilibrium potential for Na+, different values must be used. The concentration of Na+ in the

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Chapter Six extracellular fluid is 145 mEq/L, whereas its concentration inside cells is only 12 mEq/L. The diffusion gradient thus promotes the movement of Na+ into the cell, and, in order to oppose this diffusion, the membrane potential would have to have a positive polarity on the inside of the cell. This is indeed what the Nernst equation would provide. Thus,

This means that a membrane potential of 60 mV, with the inside of the cell positive, would be required to prevent the diffusion of Na+ into the cell. 