Electrophoresis is used widely in biomedical research. It’s an example of physics applied to biology that is not discussed in Intermediate Physics for Medicine and Biology. In Random Walks in Biology, Howard Berg describes electrophoresis.
If a particle carries an electric charge, then one can exert a force on it with an electric field. An ion carrying a charge q (esu) in an electric field of intensity E (statvolts/cm) experiences a force in the direction of the field Eq (dynes). [Sorry about the cgs units.] Unfortunately, q is not easy to define. Particles of biological interest contain a variety of ionizable groups whose charges depend strongly on pH. These charges are shielded by counter-ions attracted from the medium in which the particles are suspended. The effectiveness of the shielding depends on the ionic strength. So you do not hear much about particles that have specified electrophoretic drift rates per unit field (as you do, for example, about 30, 50, or 70 S ribosomes [S is a parameter commonly used in centrifuge work, corresponding to velocity per unit acceleration and measured insvedbergs, 1 Sv = 10^−13 seconds]). Nevertheless, electrophoretic methods of separating and characterizing biological materials are extremely useful. In practice, they are remarkably simple.
I like the comparison of electrophoresis to centrifugation. Both are examples of diffusion with drift; the physics is nearly the same. Berg continues
…One layers a mixture of particles at the top of a medium designed to suppress convective stirring and passes an electrical current through that, generating patterns analogous to those shown at the bottom of Fig. 4.7… The relative displacement of the … [bands] increases linearly with time, while the spreading increases as the square-root of time; so the separation improves as the square-root of time….
The bottom of Berg’s Fig. 4.7 looks like this:
As noted earlier, convective stirring is suppressed in the ultracentrifuge by the use of density gradients, e.g., of sucrose or CsCl. In an electrophoresis experiment, it is more convenient to use a gel, e.g., polyacrylamide or agarose. At the end of the experiment the bands can be precipitated into the gel and/or stained, e.g., with colored or fluorescent dyes, or the gel can be dried down and exposed to X-ray film to reveal components that are radioactive…
Gels not only suppress convective stirring, they act as molecular sieves. The rate of migration of a particle through the gel is strongly dependent on size. A particle that is small compared with the pores in the gel can diffuse through it, almost as if the gel were not there. Particles of intermediate size get through with varying degrees of difficulty. Particles that move through a dilute aqueous medium at roughly the same rate move through the gel at rates that decrease exponentially with size; as a result, an estimate of size (or mass) can be made from a measurement of the logarithm of the displacement. Pieces of DNA and RNA are routinely sorted in this way, as are proteins dissolved in ionic detergents, such as sodium dodecyl sulfate. It is easy to distinguish gels of this kind, because the faster moving bands always are broader; the molecules that drift more rapidly are smaller and have larger diffusion constants.
In a later chapter, Berg develops the analogy between electrophoresis and centrifugation further.
An analogous situation [to density-gradient sedimentation] arises in electrophoresis when the experiment is run in a pH gradient. At equilibrium, a protein will form a band centered at the pH at which it is electrically neutral, i.e., at its isoelectric point. A particle at a more acid pH is positively charged and moves toward the cathode; a particle at a more basic pH is negatively changed and moves toward the anode. Thus, the pH gradient must be acidic near the anode and basic near the cathode.