Equilibrium Potentials




Nerve and muscle cells encode information through changes in their membrane potentials. As we analyze the basis for such changes, an essential tool will be the concept of an equilibrium potential. Let's approach this topic by first looking at the concentrations of ions inside and outside cells and then at a simple system in which an electric potential difference develops.

Ionic Concentrations Inside and Outside Cells

The figure to the right illustrates the relative concentrations of the important ions inside and outside cells. Considerable energy is expended by cells to move Na+ and K+ actively so that they have the relative concentrations shown. The Cl- then adjusts passively in response to the resulting electrical potential difference.

The X- shown represents negative ions inside the cell that cannot cross the membrane. Many proteins are negatively charged, as are phosphate ions. It is tempting to think that the X- has something to do with the negative electrical potential difference across the plasma membrane. But this is fallacious. Negative charges inside the cell are paired with positive charges so that by themselves they do not create an electrical potential difference. The small net separation of charge is right at the membrane. Only a very small number of diffusible ions are involved in charging the membrane to -70 mV.

(But some people, including some biologists, start reasoning that the X- will cause the diffusible ions to readjust across the membrane and that this somehow influences the electrical potential difference. This would be the case if the plasma membrane were rigid. But since it is not, movement of ions by the X- creates an osmotically unstable cell. This is why cells must expend so much energy to keep ions way out of equilibrium. In particular, the abundant Na+ is kept low inside the cell. This is to prevent cells from bursting due to osmotically instability. Here is the correct logic: The presence of X-, which cannot cross the membrane, potentially would create an osmotically unstable situation; Therefore cells expend much energy to keep the diffusible ions completely out of equilibrium; The resulting ionic concentration gradients then create the small net separation of charge across the membrane; It is this small net separation of charge that changes during electrical signalling in neurons.)


It is important to note that the ion concentrations barely change in healthy cells, even during ion movements during electrical signalling in neurons. Ions do move across the membrane, but in amounts that are small relative to the total number of ions inside the cell. Only small numbers of ions need move to change the net separation of charge across the membrane.

One important ion not shown is Ca++. It is kept at very low concentrations inside the cell by active transport. We will deal with it separately. (Also, H+ and -HCO3 are important, but fall in the realm of acid-base balance.)

Development of an Electric Potential Difference

Membrane permeable to both K+ and Na+ Membrane permeable only to K+ Reveal anions at end
Red = K+
Blue = Na+
As you know already, the movements of ions across membranes are influenced by two energetic factors. The first is the concentration gradient. This, of course, is true for uncharged substances as well. However, because ions are charged, they also are influenced by any electrical potential difference across the membrane.

Now refer to the thought experiment to the right. Here we have a high concentration of K+ on the left of the membrane and a high concentration of Na+ on the right of the membrane. This situation is similar, in fact, to cells. The predominate positive ion inside cells is K+, while the predominate positive ion in the extracellular fluid is Na+. For clarity in the figure, the negative ions are masked.

First, we are going to place open ion channels for both K+ and Na+ in the membrane. Select this option and observe that both K+ and Na+ diffuse down their corresponding concentration gradient. But since these are opposing, no significant separation of charge takes place and the membrane potential is about zero.

Second, we are going to place open K+ channels in the membrane and closed Na+ channels in the membrane. This is typical of resting nerve and muscle cells. Select this option and observe that an electrical potential difference begins to develop. This is because only K+ can diffusion down its concentration gradient.

Third, select the last option and observe how the anions match up with the cations.

Thus, an electrical potential difference develops because the ion concentrations are different on the two sides of a membrane and because the membrane is permeable only to one ion.

Reaching Equilibrium

But how long will the above process continue? Will the membrane potential tend to increase indefinitely? Actually, the net diffusion of K+ will stop rather quickly due to the developing electrical potential difference. Ions, because they are charged, are influenced not only by their concentration gradient but also by electrical potential differences.

Observe that as K+ diffuses due to its concentration gradient, it causes the development of an electrical potential difference that acts in the opposite direction on positive ions. Indeed, the diffusion of K+ down its concentration gradient quickly creates an electrical potential difference that completely counterbalances the tendency of K+ to diffuse due to its concentration gradient.

For a specific ion, the electrical potential difference that exactly counterbalances diffusion due to the concentration difference is called the equilibrium potential for that specific ion. In our thought experiment above, the membrane potential becomes equal to the K+ equilibrium potential. This is because only K+ can cross the membrane and influence the electrical potential difference.

Equilibrium Potentials for Various Ions

If the concentration gradient for a given ion is known, the equilibrium potential for that ion can be calculated (using the Nernst Equation). Shown below are the equilibrium potentials calculated for K+, Na+ and Cl- using the ionic concentrations for a typical neuron.

  EQUIL. POT.
K+ -90 mV
Na+ +60 mV
Cl- -70 mV

Notice that the equilibrium potential for Cl- is near the resting membrane potential of the cell. This is because no ATP energy is being expended to keep it out of equilibrium. For this reason, the resting membrane potential of a cell will cause the concentration of Cl- inside the cell to remain at a much lower level so that the concentration gradient (inward) and electrical potential difference (outward) have equal and opposite effects.

Thus, if the membrane potential is at the equilibrium potential for a specific ion, there is no net tendency for that ion to move in or out of the cell. But what if the membrane potential is not at the equilibrium potential for a specific ion, and there are open ion channels that will allow the ion to cross? In that case, the ion will tend to move across the membrane. In the next page, you will see what happens as a consequence.



Quick Quiz

QUESTION: What ion has a high concentration inside cells?
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QUESTION: Given that the Cl- equilibrium potential is -70 mV and the membrane potential is -70 mV, what will happen if Cl- ion channels open?
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QUESTION: Given that the membrane potential is -70 mV, in what direction will the electrical potential difference make K+ move through open K+ channels?
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QUESTION: Given that the membrane potential is -70 mV, in what direction will the concentration gradient make K+ move through open K+ channels?
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QUESTION: Given that the Na+ equilibrium potential is +60 mV and the membrane potential moves from its resting level to 0 mV, in what direction will Na+ now move through any open Na+ channels?
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QUESTION: If the K+ equilibrium potential is -90 mV and the membrane potential is -70 mV, in what direction will K+ move through open K+ channels?
ANSWER