Nernst Equation Background

Determining whether and how much of some material moves into or out of a cell depends solely on the free energy of the material inside the cell (Gin) compared to its free energy outside the cell (G out) at equilibrium (i.e. when there is no net change in amounts). Or, in other words, movement across the membrane depends on

(out-in).

So, when = 0, no energy was expended to obtain the equilibrium situation; if is a positive value, then energy is stored in the gradient, and if it is a negative value, then energy is required to form the gradient.

For our considerations, G can be expressed simply as:

(#1)

Where:

c=concentration (moles)
E=potential (volts. Note: is the membrane potential)
z=charge or valence (if any) of the transported substance

The other symbols are constants:

R=gas constant (8.3143 Joules/mole/degree)
T=temperature (298 degrees kelvin)
F=Faraday (96490 Joules/mole/volt)

In other words, G is equal to the sum of a concentration term plus an electrical term. Since we want to find Gout - Gin (that is ), all we have to do is arrange equation 1 in the following way:

(#2)

Which simplifies to:

(#3)

If =0 in equation 3, i.e. no energy is needed to account for the equilibrium values, then the equation reduces to:

(#4)

Equation 4 is called the Nernst equation and it is extremely useful for analyzing ion movements through channels where no direct expenditure of energy is needed.

Revised 9/26/96 Brewer