Membrane Potentials

Every cell in your body is electrically active: to a greater or lesser degree, they all pump ions across the cell membranes to maintain an electrical potential difference across the membrane. There are various reasons for maintaining these "membrane potentials" (also called "rest" potentials); we will examine the propagation of nerve impulses in human motor neurons, where the electrical implications are obvious. But we must first discuss the difference between conductors and "dielectrics".

A "perfect conductor" has free electrons which distribute themselves evenly on the surface in an equilibrium configuration so as to minimize the energy of the charge configuration. The electric field is perpendicular to the conductor since there must be no net forces on the charges in equilibrium. The conductor is an equipotential volume, so the electric field is zero inside, and any excess charge distributes itself on the surface. Many metals are modelled as perfect conductors.

Dielectrics are substances with polar molecules, more tightly bound valence (outer) electrons and hence fewer conductance electrons. A "perfect insulator" has no conductance electrons at all, but still can influence the electric field due to its polar molecules. Having defined perfect conductors and perfect insulators, we must now state that nothing is perfect (as if you didn't know!); there exists a continuum between perfect conductors and perfect insulators.

The cell membrane is a dielectric with a dielectric constant of about 9. We assume that the intracellular and extracellular ("interstitial") fluids are conductors whose charge carriers are "large" ions (relative to individual electrons). The interior of a cell is then an equipotential volume (which implies that the mobile ions are near the membrane on each side during equilibrium). It has an average internal potential about - 70 mV below the interstitial fluid for human motor neurons.

The cell membrane itself is a phosolipid protein bilayer which is highly non-polar, and thus a very good insulator. Ions enter and leave the cell through "ion channels" located in the cell membrane. Some of these channels are "passive", so that ions may freely move diffusively through the channel. Some are "chemically gated", as in the Sodium pumps which pump Sodium (Na) (and some Calcium, Ca) out of the cell, while pumping in Potassium (K) in the ratio of 2 K for every 3 Na pumped out. This not only compensates for leakage through passive channels, but also establishes a concentration gradient; but since K and Na have the same charge, it does not affect the rest potential. Still other channels are "voltage gated", where they remain closed at some potentials and open at others. Typical ion concentrations (millimols / liter) maintained in human motor neurons for the rest potential are:

Interior Na = 15K = 150 Cl = 10 large anions = 65
Exterior Na = 150 K = 5 Cl = 110large anions = .2

("large" means too large to travel through any channels; the membrane is nonpermeable to them.)

The next section is about the action potential.

If you have stumbled on this page, and the equations look funny (or you just want to know where you are!), see the College Physics for Students of Biology and Chemistry home page.

1996, Kenneth R. Koehler. All Rights Reserved. This document may be freely reproduced provided that this copyright notice is included.

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