244 6.6  Electrical Force Tools

6.6  ELECTRICAL FORCE TOOLS

Electrical forces can be used to control the mobility of molecules (e.g., in gel electrophoresis)

as well as generating stable traps for biological particles (anti-​Brownian electrophoretic/​elec­

trokinetic traps [ABEL traps]) and controlling their rotation (electrorotation). One of the

most important applications of electrical forces is in the measurements of ion fluxes through

nanopores. If a small hole is made in a sheet of electrical insulator surrounded by an ionic

solution and an electrostatic potential difference applied across the sheet, then ions will flow

through the hole. If the hole itself has a length scale of nanometers (i.e., a “nanopore”), then

this simple principle can form the basis of several biophysical detection techniques, most

especially patch clamping.

6.6.1  GEL ELECTROPHORESIS

Gel electrophoresis is one the of most ubiquitous and routine biophysical techniques in

modern biochemical research laboratories, but is still in many ways one of the most useful

for its ability to separate the components of a complex in vitro sample composed of a mix­

ture of several different biomolecules in a simple, relatively fast and cheap way, and to char­

acterize these molecules, on their basis of their size, charge, and shape. Usually, a sample

of a few tens of microliters in volume is injected into a semiporous gel and exposed to an

electric field gradient. The gel is composed of either polyacrylamide (for protein samples) or

agarose (for samples containing nucleic acids), with space for ~10 parallel channels in each

gel so that different samples can be run under the same conditions simultaneously. Gels are

cast with a characteristic concentration that affects the distribution of pore sizes in the gel

matrix. Smaller molecules will therefore diffuse faster through this mesh of pores than larger

molecules.

Equating the electrical force to the drag force indicates that the drift speed vd of a molecule

of net charge q during gel electrophoresis across an electric field E is given by

(6.32)

v

Eq

d = γ

Protein samples may either be first denatured by heating and combined with an ionic surfac­

tant molecule such as sodium dodecyl sulfate (SDS), or may be run in a nondenatured native

state. SDS disrupts noncovalent bonds in the protein and so disrupts the normal molecular

conformation to generate a less globular structure with significantly higher surface negative

charge compared to the native state. Each SDS molecule binds nonspecifically to peptides

with a ratio of roughly one molecule per two amino acid residues, resulting in a large net

negative charge from the sulfate groups of the SDS, which mask smaller surface charges of

the substituent group of each amino acid.

The net charge q is thus roughly proportional to the total number of amino acids in the

peptide.

Proteins in this state electrophoretically migrate in a typically ellipsoidal conformation with

their major axis significantly extended parallel to the electric field, normally oriented vertically.

This elongated conformation bears no necessary resemblance to the original molecular

structure and so the molecular mobility is relatively insensitive to the original molecular

shape, but is sensitive to the molecular weight, that is, the elongation of the charged molecule

during electrophoresis is also roughly proportional to its molecular weight. Thus, Equation

6.32 might appear to suggest that the effects of frictional drag and charge cancel out. This is

largely true when we consider frictional drag in a homogeneous medium, and the fact that

larger molecules electrophoretically migrate more slowly than smaller ones, due primarily to

the complex interaction between the molecule and the pores of the gel matrix (the complex

physics are explored comprehensively in Viovy, 2000). The end result is that a protein molecule

will have traveled a characteristic distance in a given time dependent on its molecular