Download The Mechanical and Electrical Dynamics of Gel

The Mechanical and Electrical Dynamics of Gel Electrophoresis
The term "electrophoresis" refers simply to the movement of particles by an electric force. The first
electrophoresis experiments were carried out on molecules in a conductive buffer solution, where the only
force acting on the sample was the electric field. The vast majority of current laboratory techniques are
performed in a matrix perfused by an aqueous solution of buffer salts. The addition of a matrix (or gel)
stabilizes the system against solution turbulence, and extends the range of geometries available to the user.
The primary purpose of the matrix, however, is to introduce a sieving action which allows separations based
on molecular size. Our discussion will focus on this type of electrophoresis design.
Sample Mobility
Within an electrophoresis gel, a protein or nucleic acid molecule experiences electric force proportional to
its effective charge, Q, and the electric field strength, E. The biomolecule will move with a constant velocity
because the electric force on the molecule is met by an opposite force due to the frictional resistance, ƒ, of
the matrix.
If electrophoresis occurred in free solution, rather than within a gel, the force of frictional resistance, ƒ, upon
biomolecules would follow Stokes' law:
ƒ = 6(pi)rvn
where r is the radius of the particle moving with velocity v through a medium of viscosity n. The
electromotive force on a molecule, proportional to its charge, is thus opposed by the frictional force ƒ,
proportional to its mass. Mobility in free solution would then be the same for molecules of the same charge
to mass ratio. Stokes' law, however, is not sufficient to describe the frictional force within a gel matrix. In
addition to the viscosity of the medium, also determining frictional resistance are the density and effective
"pore size" of the matrix. The result of this combination of factors is that among molecules of the same
charge to mass ratio, larger molecules move more slowly in gel electrophoresis and electrophoretic
separation occurs by size. In techniques such as denaturing DNA or RNA electrophoresis or SDS-PAGE
protein electrophoresis, conditions are maintained so that the charge to mass ratio is virtually equal among
sample molecules and separation occurs in a predictable manner based on the size of the molecules.
The gel electrophoresis of samples having identical charge to mass ratios results in fractionation by size.
Although experiencing greater electric force because of their greater charge, the larger molecules reach force
equilibrium with the opposing frictional resistance at a slower speed, thus their lower electrophoretic
mobility.
Two additional factors determining sample mobility are the ionic strength of the surrounding solution and
the temperature of the gel. To maintain physiological pH and control the net charge on biological molecules
in electrophoresis, the solution perfusing the gel matrix contains buffer ions. The ionic strength of this buffer
will have a strong effect on the migration of sample molecules. Higher ionic strength in the solution reduces
the effective charge of the sample molecules. Therefore, low ionic strength solutions generally correspond to
high rates of migration. Electrophoresis in higher ionic strength solutions generally gives slower rates of
migration but produces sharper bands. A problem occurs, however, with high ionic strength buffers, when
excessive power generation causes the gel temperature to increase. This temperature increase leads to a
decrease in the viscosity of the medium, which then leads to increased current and further heating. Buffer
evaporation, sample denaturation, and convective mixing are typical problems which can result in this
scenario.
Electrophoresis System Dynamics
The apparatus in gel electrophoresis constitutes an electrical/thermodynamic system. The apparatus receives
energy from the power source and releases energy as heat. The figure below shows a stylized representation
of a typical vertical slab gel apparatus. The gel, perfused with buffer solution and held between two glass
plates, has been clamped in position, its upper end is immersed in the buffer solution of the upper electrode
chamber. The lower end of the gel is immersed in the lower electrode chamber, which contains buffer
solution as well.
A gel electrophoresis apparatus is essentially a resistor (the gel) connected to a voltage source, creating a
simple DC circuit. The voltage drop across the gel provides the motive force which drives the buffer and
sample ions through the gel.
After samples are introduced into the sample wells at the top of the matrix, the electric field between the
electrode chambers causes them to migrate toward the lower chamber. The electrophoresis apparatus can be
viewed as a simple DC circuit composed of one voltage source and three resistors in series, the resistors
being the upper chamber, the gel, and the lower chamber. Because the cross-section of each electrode
chamber is much greater than the cross-section of the gel slab, and because the chambers are shorter in
length as well, the vast majority of the resistance in the circuit derives from the gel slab. For this reason it is
sufficient to consider the gel slab as the only resistor in the circuit, where the vast majority of power is
expended. An exception to this rule occurs if buffer salts are inadvertently absent from one or both of the
electrode chambers.
Ohm's Law: Relationships between electrical parameters
Ohm's law describes the relationship between the voltage, V, the current, I, and the resistance, R, in a DC
circuit. A greater voltage produces a greater proportional current through a given resistor:
V = IR
A variation of Ohm's law describes how small changes in electrical current can produce large changes in the
expenditure of power, P:
P = IV = I2R
Although the electrical current through the gel consists of both migrating buffer ions and sample molecules,
the vast majority of the current is represented by the buffer ions. As voltage is applied, the cations in
solution migrate toward the negative electrode in the upper chamber, and the anions (and negatively charged
sample molecules) migrate toward the positive electrode in the lower chamber.
Several factors must be in balance for gel electrophoresis to proceed toward good results. Of major concern
is the management of the heat generated by current flow. While small buffer ions, for example, might be
more effective in preventing interactions among sample molecules, very mobile ions create a much more
conductive buffer. Excessive current flow will be accompanied by excessive heat generation, which can
cause convection currents, solution evaporation, or in the case of agarose electrophoresis the melting of the
matrix itself. The management of heat is a major reason for the choice of bulky, organic ions, such as Tris
base or glycine. (The following section treats the buffer system in more detail.)
Because temperature regulation is especially critical in both polyacrylamide and agarose electrophoresis of
DNA and RNA, this type of electrophoresis is most often carried out under conditions of constant power (or
constant current with agarose electrophoresis, for historical reasons). In denaturing PAGE electrophoresis, a
relatively high temperature must be established and maintained to prevent the renaturation of sample
molecules, but the temperature cannot be allowed to get too high. Constant power conditions (or constant
current) provide the most precise regulation of heat generation. A small variation in buffer concentration can
be managed under conditions of constant power but would lead to a total failure under conditions of constant
voltage.
Constant voltage conditions, however, are generally employed in the SDS-PAGE electrophoresis of
proteins. Here, the generally smaller apparatus has less difficulty exchanging heat with the environment, and
sample denaturation is not nearly as temperature sensitive. In this scenario, the advantages of directly
controlling the field strength via constant voltage conditions outweigh those of directly controlling the
power generation.
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