Membrane Potential - All Other Values of Membrane Potential

All Other Values of Membrane Potential

From the viewpoint of biophysics, the resting membrane potential is merely the membrane potential that results from the membrane permeabilities that predominate when the cell is resting. The above equation of weighted averages always applies, but the following approach may be more easily visualized. At any given moment, there are two factors for an ion that determine how much influence that ion will have over the membrane potential of a cell.

1. That ion's driving force and,
2. That ion's permeability

Intuitively, this is easy to understand. If the driving force is high, then the ion is being "pushed" across the membrane hard (more correctly stated: it is diffusing in one direction faster than the other). If the permeability is high, it will be easier for the ion to diffuse across the membrane. But what are 'driving force' and 'permeability'?

• Driving force: the driving force is the net electrical force available to move that ion across the membrane. It is calculated as the difference between the voltage that the ion "wants" to be at (its equilibrium potential) and the actual membrane potential (E_m). So formally, the driving force for an ion = E_m - E_ion

• For example, at our earlier calculated resting potential of −73 mV, the driving force on potassium is 7 mV : (−73 mV) − (−80 mV) = 7 mV. The driving force on sodium would be (−73 mV) − (60 mV) = −133 mV.

• Permeability: is simply a measure of how easily an ion can cross the membrane. It is normally measured as the (electrical) conductance and the unit, siemens, corresponds to 1 C·s−1·V−1, that is one charge per second per volt of potential.

So in a resting membrane, while the driving force for potassium is low, its permeability is very high. Sodium has a huge driving force, but almost no resting permeability. In this case, potassium carries about 20 times more current than sodium, and thus has 20 times more influence over E_m than does sodium.

However, consider another case—the peak of the action potential. Here permeability to Na is high and K permeability is relatively low. Thus the membrane moves to near E_Na and far from E_K.

The more ions are permeant, the more complicated it becomes to predict the membrane potential. However, this can be done using the Goldman-Hodgkin-Katz equation or the weighted means equation. By simply plugging in the concentration gradients and the permeabilities of the ions at any instant in time, one can determine the membrane potential at that moment. What the GHK equations says, basically, is that at any time, the value of the membrane potential will be a weighted average of the equilibrium potentials of all permeant ions. The "weighting" is the ions relative permeability across the membrane.