Department of Physiology

Equilibrium Potentials

Why bother with equilibrium potentials?

The equilibrium potential was developed to describe a very special circumstance: an ionic concentration gradient across a membrane permeable to only one ion. Since biological membranes are generally permeable to large numbers of ions, at first glance this special situation can appear to be an irrelevancy. Not so!

There are two important reasons the ability to quantify equilibrium potentials is very valuable:

There are some circumstances when a biological membrane becomes very permeable to one ion, so permeable that the permeabilities to other ions become relatively unimportant, and the membrane behaves as if it was a single ion-selective membrane. The equilibrium potential for the ion involved then becomes useful in predicting membrane potential.
Even under ordinary circumstances when the membrane is permeable to many ions, comparison of membrane potential and a particular ion equilibrium potential can allow us to assess whether or not an ion is at equilibrium across the membrane.

So read on!

The Nernst Equilibrium

Conceptually the equilibrium described first by Nernst is quite simple. Consider the following 2 compartment system:

Both compartments contain KCl, but compartment 1 is at a higher concentration. If the membrane allowed KCl to cross, KCl, or more specifically its constituent ions K⁺ and Cl^- ions, would diffuse from compartment 1 to compartment 2.

Suppose the membrane is permeable only to K⁺ ions. K⁺ will tend to diffuse from compartment 1 to compartment 2, but Cl^- ions cannot because the membrane is not permeable to them. As soon as this happens there will be a net transfer of positive charge from compartment 1 to 2 (carried by the K⁺ ions) and compartment 2 will become electrically positive with respect to compartment 1.

As soon as this happens, the electrical gradient will tend to push K⁺ ions from compartment 2 to compartment 1. Very quickly, an equilibrium will be established in which the electrical difference will be just large enough to move K⁺ ions to the left at the same rate as they tend to diffuse to the right due to the concentration gradient. The electrical potential difference at which this happens is called the Nernst potential or equilibrium potential.

The Equilibrium Potential is Predictable - The Nernst Equation

The equilibrium described above is predictable with the Nernst equation, which here is given in a form applicable to cell membranes:

where

E_x is the Nernst potential for ion X (measured as for membrane potentials - inside with respect to outside)
[X]_o is the concentration of X outside the cell
[X]_i is the concentration of X inside the cell
z_x is the valence of ion X
R is the gas constant
T is the absolute temperature
F is Faraday's constant

The ability to relate the equilibrium potential and concentration gradient for a particular ion has practical benefits. For example it allows the measurement of pH using what is essentially a voltmeter measuring the equilibrium potential of protons between a reference solution on one side of a proton-permeable glass, and of an unknown concentration of protons in a test solution on the other side. But the Nernst potential is more valuable in the study of cells for two reasons:

If we know the concentrations of an ion inside and outside of a cell, we can calculate the Nernst potential. This calculation tells us what potential would exist if the membrane were selectively permeable to only this ion, and if the ion movement due to the concentration were matched by opposite movement due to the electrical gradient (as described above). But once we note that this description involves only the question of the concentration gradient and the electrical gradient for this one ion, we can see that the same relationship must apply for a membrane which might also be permeable to some other ions, provided the concentrations are not running down. So in a cell with steady concentrations of ions inside and out, we can use the Nernst potential to ask whether the ion is at equilibrium, i.e. whether movements due to concentration gradients are balanced by movements due to the electrical gradient by merely comparing the membrane potential (E_m) and the Nernst potential. Only if E_m = E_x can we conclude that the ion is at equilibrium. If they are not equal the ion must be subject to net movement. If the concentrations are not changing, there must be some mechanism countering this movement; a mechanism we term an ion pump.
The second use of the Nernst potential is quite different. If a membrane were to suddenly become very permeable to a particular ion (e.g. through the opening of a population of ion selective channels), and that permeability were to be very large, the membrane potential that must result is that predicted by the Nernst equation for the concentration gradient that applied for the particular ion, for the the membrane is approximating a single ion selective one. Thus the Nernst potential predicts the membrane potential that will be approximated if this ion's permeability becomes very large. For example if a membrane becomes very permeable to Na⁺ ions, the membrane potential will tend to approach E_Na. The latter is usually significantly positive, so the result will be a substantial depolarisation. If the membrane becomes very permeable to K⁺ ions, E_m will approach E_K which is more negative than the normal membrane potential, i.e. the membrane will be hyperpolarised.

The tendency for ions to move in response to permeability changes when the ion is not at equilibrium that has just been qualitatively described, can be quantified using the Nernst potential and a measure of permeability. The measure is of ionic current, since the movement of ions carries charge and hence is an electrical current.

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