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:
So read on!
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.
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,
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:
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:
Ex 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
zx is the valence of ion X
R is the gas constant
T is the absolute temperature
F is Faraday's constant
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
(Em) and the Nernst potential. Only if
Em = Ex
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 ENa. The latter
is usually significantly positive, so the result will be a substantial
depolarisation. If the membrane becomes very permeable to K+ ions,
Em will approach EK 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.
Department of Physiology,
University of Sydney
Last updated 10 April 2002