The equilibrium potential

The equilibrium potential

The electrical potential difference across the cell membrane that exactly balances the concentration gradient for an ion is known as the equilibrium potential. Because the system is in equilibrium, the membrane potential will tend to stay at the equilibrium potential. For a cell where there is only one permeant ionic species (only one type of ion that can cross the membrane), the resting membrane potential will equal the equilibrium potential for that ion.

The steeper the concentration gradient is, the larger the electrical potential that balances it has to be. You can get an intuitive feeling for this by imagining the ion concentrations on either side of the membrane as hills of different sizes and thinking of the equilibrium potential as the force you'd need to exert to keep a boulder from rolling down the slopes between them.

Left panel: Two compartments separated by a semi-permeable membrane, labeled A and B. There is a voltmeter between A and B. The ion of interest is much more concentrated in A than in B, and the voltmeter with electrodes in A and B registers a large negative voltage. The voltage is analogous to the force we would have to exert to keep a boulder from rolling from a very high place down a hill to a very low place.

Right panel: Same setup, but with A and B having a much slighter difference in concentration of the ion of interest (B slightly less concentrated than A). In this case, the voltage is only slightly negative. This is analogous to the case where we have a very high place and a slightly lower place and are exerting a force to keep a boulder from rolling down this not-very-steep hill.

If you know the $\text{K}^+$start text, K, end text, start superscript, plus, end superscript concentration on both sides of the cell membrane, then you can predict the size of the potassium equilibrium potential.

Does membrane potential equal $\text K^+$start text, K, end text, start superscript, plus, end superscript equilibrium potential?

In glial cells, which are the support cells of the nervous system, the resting membrane potential is equal to the $\text K^+$start text, K, end text, start superscript, plus, end superscript equilibrium potential.

In neurons, however, the resting membrane potential is close but not identical to the $\text K^+$start text, K, end text, start superscript, plus, end superscript equilibrium potential. Instead, under physiological conditions (conditions like those in the body), neuron resting membrane potentials are slightly less negative than the $\text K^+$start text, K, end text, start superscript, plus, end superscript equilibrium potential.

What does that mean? In a neuron, other types of ions besides $\text K^+$start text, K, end text, start superscript, plus, end superscript must contribute significantly to the resting membrane potential.

$\text K^+$start text, K, end text, start superscript, plus, end superscript$\text {K}^+$start text, K, end text, start superscript, plus, end superscript

$\text K^+$start text, K, end text, start superscript, plus, end superscript$\text K^+$start text, K, end text, start superscript, plus, end superscript$\text K^+$start text, K, end text, start superscript, plus, end superscript

Graph depicting membrane potential (mV) on the Y-axis and extracellular [K+] (mM) on the X-axis.

The potassium equilibrium potential forms a straight diagonal line with a positive slope on this graph.

The actual membrane potential of an neuron follows the potassium equilibrium potential in most of the graph. However, it deviates at low K+ concentrations in that it is higher (less negative) than the potassium equilibrium potential.

This discrepancy tells us that ions other than K+ are also involved.

Both $\text K^+$start text, K, end text, start superscript, plus, end superscript and $\text {Na}^+$start text, N, a, end text, start superscript, plus, end superscript contribute to resting potential in neurons

As it turns out, most resting neurons are permeable to $\text {Na}^+$start text, N, a, end text, start superscript, plus, end superscript and $\text{Cl}^-$start text, C, l, end text, start superscript, minus, end superscript as well as $\text K^+$start text, K, end text, start superscript, plus, end superscript. Permeability to $\text{Na}^+$start text, N, a, end text, start superscript, plus, end superscript, in particular, is the main reason why the resting membrane potential is different from the potassium equilibrium potential.

Let’s go back to our model of a cell permeable to just one type of ion and imagine that $\text{Na}^+$start text, N, a, end text, start superscript, plus, end superscript (rather than $\text K^+$start text, K, end text, start superscript, plus, end superscript) is the only ion that can cross the membrane. $\text{Na}^+$start text, N, a, end text, start superscript, plus, end superscript is usually present at a much higher concentration outside of a cell than inside, so it will move down its concentration gradient into the cell, making the interior of the cell positive relative to the outside.

Because of this, the sodium equilibrium potential—the electrical potential difference across the cell membrane that exactly balances the $\text{Na}^+$start text, N, a, end text, start superscript, plus, end superscript concentration gradient—will be positive. So, in a system where $\text{Na}^+$start text, N, a, end text, start superscript, plus, end superscript is the only permeant ion, the membrane potential will be positive.

Starting state:

Zero voltage across the membrane, as measured by a voltmeter with one electrode inside and one electrode outside the cell. The inside of the cell has a low concentration of sodium ions, and the outside of the cell has a higher concentration of sodium ions. Each sodium ion is counterbalanced by an anion that is found on the same side of the membrane as the sodium ion. There are sodium channels in the membrane, but they are initially closed.

The channels open and Na+ can move through them.

At equilibrium:

The voltmeter now registers a positive voltage equal to the sodium equilibrium potential for this particular pair of sodium concentrations.. The Na+ ions have moved down their concentration gradient until their further movement is opposed by a countervailing electrical potential difference across the membrane. There are extra positive charges on the inside of the cell in the form of Na+ ions, and these Na+ ions line up along the membrane. On the opposite side of the membrane, there are extra anions (the former partners of the Na+ ions, which are unable to cross), which also line up at the membrane.

In a resting neuron, both $\text{Na}^+$start text, N, a, end text, start superscript, plus, end superscript and $\text{K}^+$start text, K, end text, start superscript, plus, end superscript are permeant, or able to cross the membrane.

• $\text{Na}^+$start text, N, a, end text, start superscript, plus, end superscript will try to drag the membrane potential toward its (positive) equilibrium potential.
• $\text{K}^+$start text, K, end text, start superscript, plus, end superscript will try to drag the membrane potential toward its (negative) equilibrium potential.

You can think of this as being like a tug-of-war. The real membrane potential will be in between the $\text{Na}^+$start text, N, a, end text, start superscript, plus, end superscript equilibrium potential and the $\text{K}^+$start text, K, end text, start superscript, plus, end superscript equilibrium potential. However, it will be closer to the equilibrium potential of the ion type with higher permeability (the one that can more readily cross the membrane).