Freesolution Electrophoresis

A. Conventional Procedures

Until the late 1950s electrophoretic experiments were carried out in columns of aqueous solutions. The equipment was, in principle, that given in Fig. 1, but, in practice, it consisted of a glass U-tube having a square cross-section and constructed from three sections (divided across the channel of the U). Each section carried parts of both limbs of the U-tube, and they were designed so that each could slide across the others in a plane set normal to the direction of the channels in the U-tube. The top section had outlets from the U-tube in order to connect the limbs to separate electrode vessels, while the bottom section was essentially a connector to complete the bottom part of the U-tube. The middle section was the optical component, and it could be divided into two sections, but it is more con venient to describe the action as though the middle were a single section. The middle carried the optical windows on two sides of each channel, and it was usual to monitor the movement of the boundary through these windows by non-invasive optical methods. The experiment was performed by first introducing the solvent into the cell while all the sections were connected. Then one would slide the center section plus the top section across the bottom, so isolating the bottom section. The solvent was removed from one of the limbs in the U-tube and replaced by the solution (dialyzed if the experiment involved macroions). The top section was then moved back, leaving all the sections isolated from the one limb and replaced by solvent before the connection was made to the electrode vessels. The whole assembly was mounted on a mechanical support, and the solvent was added in order to fill the electrode vessels and top of the cell. Saturated KCl solution was added to the bottom of each electrode vessel after the electrodes were inserted. The complete unit was placed in a thermostatted bath having optical windows for examining the center section from outside the bath. When it was equilibrated for temperature, the middle section was moved across to complete the channel through the U-tube. This operation produced a boundary between solution and solvent at the two interfaces between top, middle, and bottom sections. During the experiment, the movement of the boundary was observed by a variety of methods of which the most popular wer schlieren and interference optics. Thepatterns were recorded on films, which were eventually measured to calculate velocities and boundary profiles. Considerable care was taken before the experiment began to equalize the column heights, thus reducing hydrostatic distrubance. The electrodes were made from silver wire and coated with AgCl, so when the electrodes were immersed in the saturated KCl solution at the bottom of the electrode vessels the major current was transported by Cl-. Electrolysis did not occur, provided that the solution under investigation contained K+ and Cl-. The assembly was vertically mounted, and the densities of the solutions had to increase from the top to the bottom in order to minimize mechanical mixing of the boundaries.

Electrical heating of the solution occurred during the experiment, and the resulting density changes could cause convection, which would modify the boundaries and in extreme cases destroy them. To reduce this convection, experiments were normally made at the temperature of maximum density of water (~277°C) while the current was kept low by employing organic solutes to buffer the pH when solutions of polyampholytes were examined. Despite all these precautions, considerable experience was required in setting up the experiments and interpreting the results. This equipment (colloquially called the Tiselius apparatus) was used extensively by biophysical chemists when

TABLE I Examples of Mobilities u of Several Proteins Measured in Solutions Having Ionic Strengths of ~0.1 M

Isoelectric

u X 10-9

Protein

point

pH

(m2 sec-1 V-1)

Ovalbumin

4.58

6.8

-6.1

a-Lactoglobulin A

5.09

5.3-6.0

-0.63

a-Lactoglobulin B

5.23

5.3-6.0

-0.12

a-Casein

4.1

8.6

-6.7

Serum albumin

4.7

8.6

-6.7

studying mixtrues of proteins. Information from these experiments was obtained on the role of charges in stabilizing macroions in solutions. Some selected results of mobilities and isoelectric points are given in Table I in order to gauge the magnitudes of the mobilities as well as illustrate the values of typical isoelectric points (where zero mobility would be observed) for these proteins.

It should be pointed out that results from free-solution electrophoresis were tested against models used to generate Eqs. (6)—(12), and these comparisons showed that no general model could be proposed to describe adequately the properties of charged macroions in solution. When this conclusion is combined with the technical problems of interpreting incompletely separated boundaries and the difficulties of covering wide-ranging conditions for the experiments, it is clear why the use of the Tiselius apparatus declined during the 1960s and hydrodynamic properties were studied by ultracentrifugal analyses. The ultracentrifuge had a built-in stabilizing force that reduced convection, and it could be used to study neutral molecules as well as charged molecules in a wide variety of solvents and temperatures. Possibly because of its unique features, electrophoresis did not disappear but evolved into a qualitative tool through the use of stabilizing gels. This made the technique one of the most widely applied procedures in biochemical studies (see Section III). As for small ions, the understanding of the conductance of ionic solutions has not been seriously pursued in recent times, so the need to develop new experimental procedures that use boundaries has not been present.

B. Electrophoretic Light Scattering

A development in light scattering in the 1970s made it possible to study the electrophoretic movement of macroions without forming boundaries. The physical principle behind the technique was to measure molecular motions through the Doppler shift in the frequency of scattered light relative to the incident beam. The measurements were made using a single-mode laser as the source of light. When light is scattered from a stationary object, its fre quency is the same as the incident light, but in solutions the molecules become stationary only when the temperature is absolute zero. At higher temperatures molecules show the random motion known as Brownian motion, and light scattered from these is shifted to higher or lower frequencies depending on the relative direction the molecules were moving at the time of scatter. This is called quasi-elastic light scattering (QEL) in order to contrast it with the situation where no change in frequency of the light occurs during scattering, which is called elastic scattering. The frequency shift is less than 1 MHz for macroions and becomes smaller as the size of the molecule increases. Experimentally, the problem was to determine this small shift relative to the incident light frequency of about 1015 Hz.

Measuring small shifts in frequency of light can best be achieved by interferometric methods in which the scattered light is mixed with the incident light at the surface of a detecter (e.g., a photomultiplier cathode). The resulting signal has a frequency that equals the difference between the two frequencies. Two basic procedures have been developed for recording these beat frequencies: heterodyne and homodyne detection. The heterodyne method requires either a direct mixing of the incident light with the scattered light (after reduction of the incident intensity) on the detecter surface or the positioning of a stationary scat-terer in the solution (e.g., a captive polystyrene sphere of considerably larger dimensions than the macroions being investigated) and recording the resultant signal. In homo-dyne experiments the scattered light at time t is autocorre-lated with that recorded a short time later (t + t). Unlike conventional light scattering, where the light intensity is recorded and which requires high incident light levels, the intensity of scattered light for QEL must be sufficiently low that the photons arriving at the detecter can be counted. When counting is employed it is possible to sample the flux of photons temporally, and using statistical procedures of autocorrelation the counts are processed to produce a relaxation curve with an exponential decay of the first-order correlation function with time. The time constant of the curve is related to the diffusion constant of the scattering macroions and therefore provides a measure of the diffusion of the ions. These measurements are obtained from a solution that is at true equilibrium, and no separation occurs during the experiment.

Electrophoretic applications of this method depend on the known inverse relationship between the first-order correlation function and the power spectrum. (They are a Fourier transform pair.) With random motion the frequencies of the scattered light spread about the incident light, producing a Lorentzian distribution (the center being at the frequency of the incident light; the spectrum is known as a Rayleigh line to distinguish it from other spectral lines such as Raman lines). If an external, polarized electric field is applied to the solution, the molecules drift in the fixed direction as well as diffuse. In the Fourier transform this is equivalent to multiplying the transform by the transform of a uniform linear motion, which happens to be a single sine function. The result in QEL is to replace the constantly decaying relaxation curve by a peak about which the relaxation occurs. The amount this peak is displaced from the zero time of the autocorrelation time scale is a measure of the constant velocity (or its period) of the scattering ions, while from the relaxation time the diffusion coefficient and hence the frictional coefficient can be estimated. Since the time required to collect the autocorrelation data following a single electrical pulse can be as low as 1 msec, this means that short repetitive pulses of relatively high voltage can be applied across the solution and synchronized with the autocorrelation of the scattered photons. Often, in this technique platinum electrodes are used to apply the voltage rather than reversible electrodes. Naturally, with these electrodes, electrolysis of the solvent occurs, and this generates a pH gradient between the electrodes. This effect can be reduced if the polarity of the electrodes is reversed between pulses, but more reliable results could be obtained if reversible silver/silver chloride electrodes were used. The fact that reversing the polarity reverses the movement does not affect the analysis, provided that the voltages of the pulses remain constant and movement is across the incident light beam. If the angle between the incident light and scattered light is decreased, the transport vector decreases in magnitude until at full-forward scattering only the diffusion is important. It is thus possible to discriminate between the two effects by measuring the correlation function at a range of angles.

Few results on the use of this procedure for macroions having relative masses of less than a million have been reported. This is because smaller biological macroions have relatively small scattering cross, sections, and a lengthy experiment is required to obtain a statistically significant result. For small molecules the repetitive pulsing has to extend over many minutes, and in this time extraneous effects, such as the accumulation of electrolysis products (if platinum electrodes must be used) or of gas bubbles, dis-trub the result. The technique is ideal for simultaneously studying diffusion and charge on a macroion, because diffusion can be converted directly to a frictional coefficient, which means that charge can be correctly calculated from the mobility [see Eq. (6)]. Examples of suitable macroions are viruses and particles from biological cells. Another advantage of the heterodyne method is that it is possible to define a "frequency window" for the analysis of a given size of molecule, so that specific ions can be followed even when present in a mixture of smaller or very much larger ions.

III. ELECTROPHORESIS IN A STATIONARY MATRIX

Despite the decline in the application of free-solution electrophoresis to physical chemistry, the results from this work showed that electrophoresis has a unique place in studies of biological macroions. Thus, attempts were made to reduce the technical problems associated with elec-trophoresing mixtures of macroions. Efforts were directed at reducing the convective distrubances of the moving boundaries by introducing a neutral but physically inert matrix to support the solutions. Initially, paper saturated with suitable buffers was used, and a spot of the solution of macroion was placed on the paper before the electric field was applied across the strip. The positions of the bands at the end of the experiment were found by selective staining. This was reasonably successful for some applications, but because particles moved in a solvent that was adsorbed to the surface of the cellulose fibers in the paper, there were inconsistencies in the overall conduction of the ions. Heating in regions of low electrical resistance dried the paper unevenly even in a saturated atmosphere.

For these reasons paper was replaced by starch gels, and here the proportion of free solvent to inert matrix was considerably higher than could be achieved with paper. These gels are stabilized by weak intermolecular forces (hydrogen bonding and van der Waals dispersion forces). Thus, they require a backing plate for transferring the gel to a staining medium, and this disturbed the gels during handling. Furthermore, untreated starch has a number of free phosphate groups covalently linked to the carbohydrate chains, and these cause undesirable pumping of water (electroosmosis) when an electric field is applied across the starch strips. These difficulties prompted workers to search for gels that were electrically neutral as well as physically strong enough to be handled without distro-tion. This led to the development of modern polyacry-lamide gels. These gels form the matrix for most present-day electrophoretic analyses.

A. Polyacrylamide Gel Electrophoresis

Acrylamide has the chemical structure given in Fig. 4a, and it is the opening of the double (n) bond that leads to the polymerization. It is necessary to activate this

FIGURE 4 Chemical structures of (a) acrylamide and (b) N,N'-methylenebisacrylamide (bisacrylamide).

FIGURE 4 Chemical structures of (a) acrylamide and (b) N,N'-methylenebisacrylamide (bisacrylamide).

polymerization by one of a variety of procedures, all of which produce free radicals in solution. These radicals are produced by hydrolysis of water, either photochem-ically using riboflavin phosphate as a catalyst or chemically using chemical catalysts. Once the initiation has occurred, the acrylamide crosslinks with itself, with the evolution of heat to produce linear chains that are terminated when the activated chain ends are neutralized by collision with other free radicals from the solvent. The product is a stable gel containing only a few percentage points (by weight) of polyacrylamide. Gels formed from only acrylamide have many undesirable properties (e.g., they are glutinous and stick to glass), and the pore sizes are illdefined. A more satisfactory gel was formed by including a small proportion of the bifunctional acrylamide (Fig. 4b) in the mixture. This forms random cross-links between the linear chains during polymerization. The average size of the pores formed by this mixture is determined by the proportion of bisacrylamide (Fig. 4b) to the normal acrylamide in the original solution. The mechanical stability of the gel decreases with increased proportion of crosslinking, and for some purposes the bisacry-lamide is replaced by N,N'-diallyltartardiamide. The latter produces a gel that is more restrictive to macroions than bisacrylamide at high proportions of cross-linker, but in turn it is more manageable. The solvent is held in these pores, and the whole gel can be handled without mechanical supports, despite the fact that it consists of up to 95% (by weight) of solvent.

Polyacrylamide gel electrophoresis (PAGE) is carried out using simple equipment. The gels are cast either in glass tubes or as slabs supported on nonconducting plates, which can themselves be thermostatted. Because the gels are generally thin, they have low electrical conductance, so relatively high voltages can be applied without excessive heating (say, 1000 V across a 15-cm tube, 2-mm diameter).

Along with the developments of PAGE were the production of a variety of organic ions that would buffer pH without producing solutions of high conductivity. High conductivity arises because of high mobilities of ions, and this is inversely proportional to the van der Waals radius of an ion [Eq. (6); the frictional coefficient is proportional to this radius]. Organic ions have larger radii than inorganic ions such as phosphates, and so their conductivity is less.

B. Molecular Properties Important for Polyacrylamide Gel Electrophoresis

When ions are transported through the pores of the gel, their relative mobilities can be used to determine their sizes, provided that they are not excluded from the pores of the gel. The radii of the transporting ions are not simple to define because for both the stationary matrix and the diffusible ions there are layers of solvent that are trans ported with the ion (or remain stationary on the gel), therefore making their radii different from that expected from crystallographic models. In general the penetrating ions move through the pores with mobilities commensurate with those measured in free solution. It is usually difficult to measure these mobilities because the path length taken by the ion is unknown, although it is certainly greater than the simple linear distance measured macroscopically along the gel. This means that PAGE cannot yield physico-chemical data on absolute charges of diffusible ions; only relative mobilities can be obtained and estimated by reference to standards electrophoresed in the same gel.

In the case of macroions the relationship between relative mobilities and charge is complicated by the possibility that selective retardation of the ions occurs as a result of physical impedence by the gel matrix and adsorption onto the stationary polyacrylamide. Contributions from both occur with all ions, but for proteins the adsorption is less important than the filtering. At the simplest level this filtering would be described through frictional coefficients [Eq. (6)], which for a fixed pore size increase in proportion to the cube root of the mass. Thus, the velocity is proportional to M-1/3, and the relative position of macroions on a gel at the end of an experiment are a function of charge and mass (that is, proportional to Q/M1/3), which means that the charge cannot be measured independently of the mass. Because of this proportional dependence of relative positions on the two dependent parameters, one must be fixed before the other can be estimated using relative mobilities. Thus, if Q were constant for the macroions in a mixture, the effective van der Waals radii could be estimated for each from its relative mobility, and if the shape of the ions were constant (that is, all spheres), this would give relative masses M.

These criteria have been used extensively for measuring relative masses of proteins and nucleic acids by including in a separate channel a mixture of standard proteins or nucleic acids of known relative masses; the masses are estimated in advance using absolute procedures such as that involving the analytical ultracentrifuge. It is usually not possible to measure charge this way, because a range of macroions are not usually available having a fixed mass but carrying a range of charges. It is possible to generate such a standard by progressive carbamylation of amino groups (easily achieved by cautions warming of a protein with urea solutions) to produce secondary amines that are not charged at neutral pH. If the carbamylation is not allowed to go to completion for all the side chains, this will produce a mixture of molecules of relatively constant mass (the carbamyl group has a relative mass of 60, so even adding 10 groups to one macroion will not significantly increase the mass). This standard mixture can be used to determine relative charges of the unknowns; then if the original absolute charge and amino acid composition are known (required to give the number of amines substituted), it is possible to calculate the number of charges on the unknown protein. Inaccuracies are introduced into these calculations because the amount of adsorption of the charged macroions to the polyacrylamide is dependent on the charge, so the position of the polyampholyte after car-bamylation does not remain a simple function of charge.

This brief definition of the molecular parameters that affect rates of transport in PAGE illustrates the important assumptions made in converting relative positions to molecular parameters for the procedures discussed in the following sections.

C. Estimation of Relative Masses Using Polyacrylamide Gel Electrophoresis

Most of the charge of a biological macroion comes from dissociation of the intrinsic chemical groups. In the case of many of the nonparticulate and soluble proteins, these groups have isoelectric points in the pH range 4-5, which means that at neutral pH they are negatively charged. The absolute charge is not independent of mass, because the capacity to carry more amino acids bearing charged side chains is greater the larger the mass, while the composition is determined by genetic factors. This means the ratio Q/M1/3 is not constant for all proteins, so that separations between individual proteins can be obtained experimentally. In the case of nucleic acids the total charge is generally related to mass for a given type of nucleic acid, because here each nucleoside (the effective monomer of nucleic acids) carries free phosphates that are equally ionized at neutral pH. Thus, the relative positions after PAGE can be related to size. As a result, masses determined by a single PAGE experiment with native proteins are less readily interpreted in terms of van der Waals radii than those made with nucleic acids (but see the later discussion of the Ferguson plot). It has been found, however, that when a protein is mixed with certain charged detergents [the most popular being sodium dodecyl sulfate (SDS)] the quantity of detergent associated with a gram of protein is relatively constant. The result of this association is a spheroidal micelle having a charge and frictional coefficient proportional to the relative mass of the protein [see Eq. (6)]. The addition of SDS dissociates multisubunit proteins into their respective components, so although adding SDS produces a macroion whose mass can be estimated from PAGE (the intrinsic charge of the protein is swamped by the added charge from the SDS), the native biologically active units cannot be examined in the detergent. Despite this deficiency, SDS-PAGE has become the most popular method of determining relative masses of protein subunits and has displaced the ultracentrifuge in routine investigations. Another attraction is that the detergent solubilizes otherwise insoluble proteins and peptides, making it possible to study otherwise insoluble mixtures.

When a highly charged macroion is produced, the aggregate moves rapidly in the gel matrix under a moderate potential gradient. Their relative velocities are related to size, but since these macroions still carry some residual shape from the native molecule, the frictional coefficient is not always equal to the expected sphere. Hence, it is important to use reference standards whose overall original shape is similar to the unknown proteins if reasonable estimates are to be obtained. (The absolute accuracy is seldom better than ±10%, although reproducibility is much higher.) To reduce the contribution from variable shapes it is usual to perform several experiments in gels formed from various concentrations of acrylamide and bisacry-lamide. Plotting the logarithm of the relative mobility against the concentration of acrylamide gives a straight line whose slope can be related to the molecular size, while the intercept on the ordinate (infinite dilution of acrylamide and bisacrylamide) is a measure of the mobility of the SDS-protein in free solution (Ferguson plot). These plots can be used to determine relative masses of native proteins, because the slope is a measure of the effective ratio of charge to mass at unit charge. Proteins that contain a significant amount of covalently linked carbohydrate can still give anomalous results in this plot because the randomly arranged carbohydrate chains change the overall shape of the ellipsoid from that given by standards using purer proteins. Another factor to be considered is the dependence on the amount of detergent bound per unit weight of peptide. Although this is generally constant, there are notable exceptions where the equilibrium between free SDS and that bound does not follow the expected relationship. To overcome this problem, high concentrations of SDS (say, 10% solutions) may be required in some cases, and this has its own limitations.

The bands or spots produced by SDS-PAGE are widened by diffusion of the micelles within the pores of the polyacrylamide, but since the electrophoretic mobilities of the bands are unidirectional and are greater than those produced by diffusion, the leading edge of the band is sharper than that expected from a simple diffusional model [Eq. (9)]. The concentration of the micelles at the leading edge is an advantage when small amounts of a macroion are being studied. Some experimental procedures enhance this sharpening by enlisting the Kohlrausch regulating function [T±/C, Eq. (4)]. To produce sharp bands this ratio must be unequal on the two sides of an interface, and to achieve this the salt concentrations (and pH for polyampholytes) must be different across the interface. Practically, this is achieved by layering a thin band of gel containing different buffers on top of the main gel and electrophoresing the protein through this band before entering the main gel. More elaborate arrangements of different salt concentrations and pH have been used to produce stacking of native proteins by varying their relative charges in a plane in the gel. This changes the relative mobilities, so that T±/C for each protein is not equal to that in the next plane (called isotachophoresis).

Procedures similar to those used for proteins can be used for nucleic acids. Here, the gels not only act as stable supports for mechanical handling, but also as separate mixtures according to mass. No additional detergents are required because the structure of nucleic acids in solution is essentially a random coil formed from highly charged polyelectrolytes.

For technical reasons gels containing less than 2% (by weight) of acrylamide are unmanageable, and yet even at that concentration the pore sizes are too small to admit large macroions (radii >10 nm). To handle these ions, gels must be formed from polysaccharides. The most common is agarose, a polymer of galactose. Agarose is a fraction from agar, a seaweed polysaccharide, which is partly sul-fonated so the charged parts must be removed for use in electrophoresis. These gels are mechanically fragile but can be partly stabilized if a few covalent bonds are formed between some of the galactose units.

D. Isoelectric Focusing and Isotachophoresis

The procedures described for PAGE employ the charges only as a means of electrically driving the macroions along the gel in a fixed direction in order to separate mixtures and estimate relative masses. These procedures yield little information on the charge of the protein or utilize the unique pH where polyampholytes have no net charge (see Section II.D) in order to separate a complex mixture. A stationary boundary forms at this pH, but since the object of the experiment is to both separate and concentrate proteins into narrow bands, a stable pH gradient must be generated. To do this the solution containing the monomeric acrylamide must contain ampholyte buffers that when electrophoresed move more rapidly than the polyampholytes and settle at their respective isoelectric points where they buffer the pH. If a wide-ranging mixture of ampholytes, themselves having many different isoelectric points, is used, the result is a stable pH gradient, which can be made approximately linear with distance between the electrodes.

A pH gradient can be formed if water is electrolyzed— acid at the anode and alkaline at the cathode—but the buffering capacity of water is negligible and the gradient is easily swamped by the protein when they are included. To make a stable gradient a variety of organic ampholines have been synthesized, with various proportions of acidic and basic groups in the heterogeneous mixture of ampho-lines. When these are included in the polyacrylamide gel as free solutes, a pH gradient can be generated by elec-

trophorsing the slab for a period before adding the protein. This pre-electrophoresing settles the ampholines at their varied isoelectric points. Because ampholines contain many functional groups,1 they possess greater buffering capacity than a similar mass of peptides, and so the gradient is not disturbed by the presence of the protein.

In these experiments the current is very low after the initial removal of excess charged diffusible ions because the only remaining transportable ions in the system are H+ and OH—. The focused boundaries follow the approximate shape described by Eq. (21) and are stationary within the gel for long periods. True equilibrium, where the position is independent of very long times, is rarely achieved because the transport of the H+ and OH— continues, and this slowly drags the ampholines with them, eventually destroying the gradient. Ampholines have been developed that can be copoymerized into the polyacrylamide gel to prevent their movement, and when these are used the pH gradient is formed mechanically before the acrylamide is polymerized.

With this technique it is possible to focus individual proteins from a mixture into bands that are fractions of a millimeter wide and have effective concentrations exceeding the solubility of the protein. At these high concentrations the protein "steals" the water from the polyacrylamide chains, and this weakens the matrix, making the columns fragile at this point. The technique can be applied to the study of native or denatured proteins. In the latter case a charged detergent (e.g., SDS) is displaced from the protein during electrophoresis because the unassociated detergent moves to the anode, therefore forcing the micelles to dissociate in order to maintain chemical equilibrium between associated and free detergent. Eventually, all the adsorbed SDS is stripped away from the peptide, leaving it with its native intrinsic charge (and possible insolubility).

For preparative procedures where relatively high concentrations of a mixture of polyampholytes are applied initially to the pH gradient, it is often uneconomic to employ supporting ampholines in the gel. In these cases a pH gradient is generated during preparation of the gel column using conventional buffers. The object of an experiment is to isolate one polyampholyte selectively by stacking it at an interface between two zones using the Kohlrausch regulating function as an underlying theoretical guide (see Section I.A). In order to apply the technique it is necessary to have studied the protein using analytical PAGE in order to ascertain its relative charge and mass. The latter is required in order to adjust the properties of the supporting polyacrylamide gel in isotachophoresis so that it does not

1They can be likened to polyacrylic acid, where each monomer exposes a charged carboxylic group, but in the ampholines each monomer exposes a basic and an acidic group, so by producing a mixture of oligomers from the ampholines a wide range of isoelectric points can be produced.

restrict the movement of the polyampholyte. Then a series of buffer zones must be inserted, and both the type and the concentrations of these buffers must be controlled so that a pH gradient is generated yet the ionic strength in the stacking regions is low. Then after electrophoresing of the polyampholytes, the selected few that produce equality for the regulating function across the phases produce sharp boundaries at these interfaces. The selection depends on the charge of the polyampholyte (which is dependent on pH in the zone) as well as the buffer concentration. Ideally, the polyampholyte should be the major transporter of the current rather than the buffer ions. Computer programs exist that optimize the buffering conditions for these experiments. The procedure is often known as steady-state stacking and multiphasic zone electrophoresis. Although these procedures have much in common with isotachophore-sis, there are experimental variations between them which might distinguish them for some applications.

E. Two-Dimensional Polyacrylamide Gel Electrophoresis

Present applications of electrophoresis are far removed from the early physical work where the technique provided the only means of measuring charges on particles. Now electrophoresis has become an empirical tool for separat ing complex biological mixtures of macroions. In this evolution, attempts were made to expand to two-dimensional separations, but only recently has this procedure been successful. The method illustrates the resolving power produced by combining isoelectric focusing in one direction with separations according to van der Waals radii in the second. In order to carry out the experiment the protein mixture is first separated according to the isoelectric points of the components (see Section III.D). At the end of this experiment these gels are placed on top of a slab of poly-acrylamide, usually formed as a gradient in concentration of acrylamide and increasing in concentration away from the isoelectrically focused gel. This combination is then electrophoresed by SDS-PAGE (Section II.C) before the separated peptides in the gel are visualized by selective staining or autoradiogaphy. Combining the two orthogonal properties of proteins produces the typical result shown in Fig. 5 for a mixture taken from a rat's liver. The procedure does not lend itself to inclusion of reference standards in the gel, while prior denaturation of the proteins with SDS yields a valuable map of the gene products, as in Fig. 5. It is helpful in genetic studies if the disulfide crosslinks between the subunits have been destroyed by adding mercapto compunds to the original preparations. These maps are reproducible provided that the experimental procedures are rigorously controlled, making it possible to

FIGURE 5 Two-dimensional separation of a mixture of denatured peptides from a rat's liver. The separation horizontally is by isoelectric focusing (Section III.D) with the low pH to the left. The vertical separation was made by SDS-PAGE according to size, the largest at the top. (The upper limit of relative mass is ~105 and the lower limit is -15,000.)

locate unique peptides affected by biological experiments through direct superposition of many maps on top of one another. As many as 2000 peptides have been resolved in one map from a single mixture, and individual variations can be noted by suitable computer analyses of the digitized maps.

Two-dimensional maps of nucleic acid fragments are also made during sequencing procedure in order to read gene codes. These maps are different in format from those prepared from protein mixtures because the radioactively labeled and partially hydrolyzed nucleic acids are separated in one direction according to size, while the second dimension contains parallel "ladders" formed from replicate experiments in which the nucleic acids are hydrolyzed by different enzymes. The result is a series of bands that can be correlated with other bands in order to produce the correct sequence of nucleotides in the original nucleic acid. These gels are usually much longer than those used for protein separations, and the visualization is generally carried out after labeling with radioactive isotopes or covalently linked fluorescent dyes.

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