Concepts Related to Understanding Membrane Potentials

Diffusion across membranes

It is important to have a firm understanding of the physical basis for biological events, otherwise a point is reached at which one is unable to make sense of the event. Why do molecules of solute move across semipermeable membranes from a compartment with higher concentration to one of lower concentration? First, molecules in solution are not stationary. They diffuse because of molecular vibrations, a property of any material that is above absolute zero. On a much larger scale you can see evidence of such vibrations in the light microscope, as Brownian motion. For example, nonmotile bacterial cells appear to move because they are so small, the vibrations of their component molecules randomly produce net forces that result in translational motion.

Brownian motion is random, of course, so why is there net diffusion in one direction? Consider a semipermeable membrane to have a limited number of channels through which a molecule may travel. As a result of random motion, molecules occasionally bounce though a channel. If they are more concentrated on one side of a membrane, the probability of a molecule moving from the side with greater concentration to the side with lower concentration is greater than the probability of the opposite happening. However, molecules do move in both directions, even at equilibrium, under which condition movement in one direction equals movement in the other direction.

Net diffusion in one direction is therefore a result of the probability of a greater number of successful translocations on one side of a membrane than the other. Consider that however small the number, there is a finite probability that there will be net diffusion from a side of smaller concentration to the side with greater concentration!

Did the concentration change?

One of the most valuable models for studying membrane potentials is the giant squid axon, with typical diameter of 1 mm. Instead of using artificial compartments, let one compartment be a section of giant squid axon with total surface area of 1 square cm. The axoplasm within 1 square cm of cell membrane will contain 3 x 10^-5 moles of potassium ion. To produce a 77 mV transmembrane potential, 8 x 10^-13 ions must be translocated, which amounts to one displaced ion for every 3.8 x 10^7 ions in solution. For practical purposes, such a change is undetectable (Aidley, 1998).

Keeping the same proportions, the concentration of compartment A in the example would be reduced by 2.6 x 10^-6 mM (0.0000026 mM) to obtain a 77 mV potential difference.

The manner in which a measurement or other piece of numerical data is presented provides important information. In the example, the concentrations of potassium ions are written as 100 mM and 5 mM respectively. A 5 mM concentration means "greater than 4.5 mM and less than 5.5 mM." Assuming that the ion concentration in compartment A was determined to the same level of accuracy (and the zeroes are not merely placeholders), then 100 mM really means "greater than or equal to 99.5 mM and less than or equal to 100.5 mM."

Take the expected concentration change, substract it from 100 mM, and what do you get? If you said "100 mM," then you get the grand prize. If you said "99.9999974 mM," then you need to read about error analysis and significant figures.

Created by David R. Caprette (caprette@rice.edu), Rice University 1 Jun 01
Updated 18 Jul 05
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