The membrane potential difference

The membrane potential of -10, -15 mV given by the Donnan equilibrium represents the minimum potential energy content of the cell. Certainly, the functions that this low amount of energy is able to activate are limited. In order to increase the potential energy and, as a consequence, the possibility to perform work, the electrochemical potential must be increased by the electrogenic transport of the Na⁺/K⁺ ATPase, which continuously contributes to maintaining the electrochemical gradients between the inside and outside of the cell.

In addition, the resting permeabilities of each ion able to cross the membrane must be sufficiently low so that the gradients do not disperse too quickly across the membrane.

Active ion transport such as the electrogenic work of the Na⁺/K⁺ ATPase, contributes to the increase in potential energy by maintaining the chemical gradients of sodium and potassium and the electrical gradients, to stabilize the membrane potential. Membrane potential, in each cell, changes according to the activity of specific ionic permeabilities.

If it is assumed that the only ions involved are sodium and potassium and that both have an equal probability of moving freely through the phospholipid bilayer, the potential across the membrane approximates the mathematical average of the equilibrium potentials of the two ions. The potential difference would be at -16 mV, an intermediate value between the equilibrium potentials of potassium, -87.6 mV, and sodium, +57.1 mV (tab. 3.2).

If, on the other hand, the permeability for the sodium ion is very low, i.e., the probability of the specific pores being open is practically zero, the potential difference across the membrane matches the value of the potassium equilibrium potential, i.e., around -80 mV. In practice, potassium ions continue to move through their specific pores until the membrane potential coincides with the potassium equilibrium potential.

At this value of membrane potential, even if the specific pores are open, the net flux of potassium is null (paragraph 3.2.8). Similarly, but with an opposite situation, i.e., a high probability that the specific pores for the sodium ion are open and a high probability that those for potassium are closed, the membrane potential becomes stable at the sodium equilibrium potential, i.e., around +50 mV.

Supremacy in the decision of the membrane potential value belongs to the most permeable ion, which forces the membrane potential to be close to its equilibrium potential. However, all other permeable ions contribute to set the membrane potential value of a cell. The influence of each ion is directly proportional to its permeability level.

It therefore can be stated that in the presence of specific pores for sodium and potassium ions and a membrane dividing two environments at different solute concentrations (Table 3.2), there will be different values for the membrane potential, but in any case within the range delimited by E_Na and E_K, the equilibrium potentials of the ions involved.

The membrane potential of a cell depends on the equilibrium potential of all the ions capable of crossing the plasma membrane through specific pores. The contribution of each ion is the tendency to bring this potential towards the value of its own equilibrium potential, taking into account the extent of the permeability and the electrochemical gradient of each individual ion.

This behavior is fully described by the Goldmann equation which takes into account the Nernst equation for the different ions involved in the determination of the membrane potential and their respective membrane permeabilities.