5. Principles of Electrophoresis; Macromolecular Charges in Solution

            Electrophoresis is the forced migration of charged particles, usually macromolecules, in an electric field (Figure 16.18).  If a macromolecule has a net charge q and a constant, uniform external electric field  is applied, there will be a net force  on the molecule given by   In general, the macromolecule will accelerate rapidly and the electric force will be balanced very rapidly by a growing frictional force,  due to collisions with solvent molecules.  After reaching equilibrium, the molecule will migrate in the electric field with a constant velocity, obtained from setting the net force  equal to zero and solving for v,

                                                                                                                      (7)       

The electrophoretic mobility U is defined as the velocity normalized by the applied electric field, and using Equation (7) can be written as

                                                                                                                (8)

Mobility is an intrinsic property of the macromolecule, depending only on its charge and frictional properties.

 

Figure 16.18.  Electric and viscous drag forces acting on a macromolecule.

For a real macromolecule in solution, both the actual net charge q and the frictional factor f will be difficult to ascertain.  If electrophoretic mobility were to be measured, one of these parameters would still need to be obtained independently before the other could be found from the above equation.  This fact, and difficulties in generating a known uniform field, have made electrophoresis complex and little used as an analytical tool to learn about the electrical properties of macromolecules.  However, there are a number of electrophoresis methods in almost daily use in most biomolecular laboratories.  Before considering some of these techniques in a bit of detail in the next Section, we need to gain a basic understanding of the charge on a macromolecule in solution.

 

 

            Figure 16.19  The three different ionic forms of the amino acid alanine.   Proteins, made from hundreds of amino acids, will have large numbers of variable electric charges, depending on the pH of the surroundings

            Unlike isolated ions, such as Na+ or Cl-, that have a definite charge state, macromolecules have a variable net charge that depends on the pH of their local environment.  Macromolecules such as proteins or nucleic acids, consist of many subunits, each with multiple ionizable charged groups that may be neutral, positive or negative, depending on the pH.  The term zwitterion or polyelectrolyte is used to describe such macromolecules with numerous charged groups (Figure 16.19).  By adjusting the pH, the net charge on a macromolecule can thus be made positive, negative or neutral.  That particular pH at which the macromolecule is electrically neutral is called the isoelectric point.  At pH values below the isoelectric point the macromolecule has a net positive charge while at higher pH’s its net charge is negative.

Figure 16.20  A region of a macromolecule with its surrounding cloud of counterions.

            Macromolecules are rarely suspended in pure water.  Almost always they are found with salts, buffers, and often with many other small and large molecules.  While the concentration of ions gives some measure of their effectiveness in electrical shielding, a better measure is the ionic strength I, defined as

                                                                                                              (9)

where the sum is over all ionic species of concentration ci and valence zi. 

It is important to realize that although the Coulomb force is long-range, as we have discussed, normally macromolecules in solution will be effectively electrically shielded unless at very low ionic strengths (Figure 16.20). Because of the electrical attraction of opposite charges, a charged macromolecule in solution will have large numbers of small ions of opposite charge, called counterions, surrounding each of its charged groups.  These counterions form a charge cloud that tends to completely cancel the effects of the macromolecular charge beyond a certain characteristic distance, known as the screening (or Debye) length.  A calculation of the screening length LD finds

                                                                                              (10)

where k is a (dielectric) constant characteristic of the electrical properties of the solvent (water has k = 80), kB is Boltzmann’s constant, and T is the absolute temperature.  Table 16.2 gives the screening lengths for different concentrations of ions in water.  Effectively, at ion concentrations of above about 10 - 100 mM, the macromolecular charges are fully screened and there are no electrical interactions with other large molecules until they come within about 1 nm.  At lower ion concentrations there may be longer range electric interactions between macromolecules.

 

Table 16.2  Screening lengths at different ionic strengths of solution.

Concentration (mM)

Screening length (nm)

for monovalent ions

Screening length (nm)

for divalent ions

0.1

30.4

17.6

1.0

  9.6

  5.6

10

  3.0

  1.8

100

  1.0

  0.6

 

 

6. Modern Electrophoresis Methods

            There is a fundamental problem in using electrophoresis as described in the previous section.  In order to maintain a buffer and solvent system with a typical salt concentration of 0.1 M, even a very modest electric field will create substantial heating of the solution, resulting in convection currents that would completely distort the controlled migration of macromolecules.  We will study this heating phenomenon when we study electric currents, but it is ultimately due to the transformation of kinetic energy into internal energy through collisions and it is a similar effect to that resulting in the heat generated by a toaster, for example.  Early in the history of electrophoresis, the answer to the heating problem was to reduce the ionic strength of the solution; but then, as we have seen, long-range interactions are possible and in some cases the macromolecules may not be stable under those conditions.  Today all electrophoresis is carried out not in solution, but in gels, to avoid overall convection problems due to heating or vibrational disturbances. 

            One of the most important electrophoresis techniques is SDS gel electrophoresis, used to measure molecular weights of proteins.  Since the conformations of proteins are so diverse, substantial information about a protein would be required to know how the friction factor in Equation (8) is related to molecular weight.  Instead, in this technique the proteins are first denatured so that they lose all of their secondary structure and become simply random coil backbone polymers.  Then SDS (sodium dodecyl sulfate), a highly charged reagent that binds to all proteins with a very similar mass of SDS per unit length of protein backbone, and thus a very similar electric charge per unit length of protein, is added to saturate the protein.  These highly charged SDS molecules exert strong internal repulsive forces that tend to stretch out the random coil protein into a rod-like shape.  In essence, all proteins are made to look virtually the same, rods of the same diameter but with lengths that are proportional to the molecular weight of the protein. 

            The technique involves placing a small amount of such denatured SDS-protein mixture (with a colored dye or stain added so that one can see where the fastest migrating protein is located) at the top of a slab or tube of a gel (typically polyacrylamide), and turning on an electric field within the gel using electrodes attached to a power supply (Figure 16.21).  The proteins and dye migrate down the gel at a constant rate that depends on the molecular weight of the protein with the smaller proteins migrating faster.  At a given concentration of gel material and given electric field strength, standards of known molecular weight are used to empirically construct a calibration curve of molecular weight vs electrophoretic mobility (basically determined from the distance traveled down the tube normalized between 0 and 1- see Figure 16.22).  Molecular weights of unknown samples can be determined from their mobilities and such a calibration curve.  Over a limited molecular weight range, the electrophoretic mobility of proteins is found to be proportional to the logarithm of their molecular weight, as shown in the figure.  This technique, known as SDS-PAGE (PolyAcrylamide Gel Electrophoresis), can rapidly and cheaply measure molecular weights with an accuracy of about 5% and can also determine trace amounts of impurities in a sample.  It is one of the most common tools in the study of proteins today.

Figure 16.21  Gel electrophoresis being set up to run.  Plexiglass housing holds a slab gel that is being loaded with a sample

 

Figure 16.22  Example of calibration plot for SDS-polyacrylamide gel electrophoresis.

               Precisely how macromolecules move through the supporting gel material in gel electrophoresis is not well understood.  Our description and the usual analysis of electrophoretic mobility is totally empirical.  For very large macromolecules such as high molecular weight DNAs that tend to get stuck in the pores of even very dilute gels, it has been experimentally discovered that, by using a series of electric field pulses of short duration and varying direction, DNA migration can be enhanced.  These efforts have led to an increased understanding of the migration of macromolecules in gels.  Such knowledge is also applicable to the motion of macromolecules through networks of filamentous proteins within the cytoplasm of a cell.

            Another important gel electrophoresis method, using the ideas developed above on the polyelectrolyte nature of macromolecules, is isoelectric focusing.  Native proteins migrate in an electric field through a gel in which a pH variation has been established.  Proteins migrating in the gel will constantly vary their electric charge as the local pH changes until they arrive at the location corresponding to their isoelectric point (Figure 16.23).  They remain there since, with their net charge equal to zero, they experience no force.  Since the isoelectric point of a protein is an intrinsic property, a detailed map of proteins separated according to isoelectric points can be obtained.

Figure 16.23  Schematic of isoelectric focusing.  Polyelectrolytes move until they reach their isoelectric point and have zero net charge.

            Often isoelectric focusing is combined with SDS-PAGE in two-dimensional gel electrophoresis.  In this case, the native proteins are first run in a pH gradient gel slab along one direction.  When completed, the electric field is set at 90o to its initial direction, a new gel slab saturated with SDS and denaturants is butted against the original gel slab, and the proteins are made to migrate into the new gel.  There they denature, acquire an SDS coat and migrate according to molecular weight along the new direction.  When complete there is a two dimensional map of proteins with isoelectric point along one direction and, by calibration, molecular weight obtainable from the position along the other direction (Figure 16.24).  Proteins with similar isoelectric points or with similar molecular weights can be further separated by this method so long as the other property is distinct.  There are numerous other variations of these techniques in one or two dimensions in current use with new methods being developed.

 

Figure 15.24  Two-dimensional gel electrophoresis of the proteins of the influenza virus.  The vertical scale is molecular weight while the horizontal scale is isoelectric point.