General Principles
When an electric field is applied to a solution, solute molecules with a net positive charge migrate toward the cathode, and mole-cules with a net negative charge move toward the anode. This migration is called electrophoresis. The velocity of the molecules depends on two factors. Driving the motion is the force q~ exerted by the electric field on the particle, where q is the mole-cule’s charge (in coulombs) and ~ is the electrical field strength (in volts per meter). Resisting the motion is the frictional force fv exerted on the particle by the medium, where v is the velocity of the particle and f is the frictional coefficient, which depends on the size and shape of the molecules. Large or asymmetric mole-cules encounter more frictional resistance than small or compact ones and consequently have larger frictional coefficients.
When the electric field is turned on, the molecule quickly accelerates to a velocity at which these forces balance and then moves steadily at this rate. The steady velocity is determined by the balance of forces:
(2A.1) We can rewrite this equation as v/~ = q/f in order to express the rate of motion per unit of field strength, v/~. This ratio is called the electrophoretic mobility of the molecule:
(2A.2) On the right-hand side of this equation, we have expressed the charge on the molecule as the product of the unit of electron (or proton) charge (e) times the number of unit charges, Z (a positive or negative integer). Because f depends on molecular size and shape, Equation 2A.1 tells us that the mobility of a molecule depends on its charge and on the molecular dimensions.*
m = v
~= q f = Ze
f (m) fv = q~
Because ions and macroions differ in both respects, their behav-ior in an electric field provides a powerful way of separating them. Electrophoretic separation is one of the most widely used methods in biochemistry.
Paper Electrophoresis and Gel Electrophoresis
Although electrophoresis can be carried out free in solution, it is more convenient to use some kind of supporting medium. The two most commonly used supporting media, paper and gel, are shown in Figures 2A.1 and 2A.2. Paper electrophoresis (Figure 2A.1) can be used for separating mixtures of small charged molecules. A piece of filter paper, moistened with a buffer solution to control the pH, is stretched between two elec-trode vessels. A drop of the mixture to be analyzed is placed on the paper, and the electric current is turned on. After the molecules have migrated for a sufficient time—usually several hours—the paper is removed, dried, and stained with a dye that colors the sub-stances to be examined. Each kind of charged molecule in the mix-ture will have migrated a certain distance toward either the anode or the cathode, depending on its charge and dimensions, and will show up as a stained spot on the paper at the new position. Usually the spots can be identified by comparison with a set of standards run on the same paper. If the unknown substances are radioactive, the spots can be cut out and their radioactivity measured by scintil-lation counting (see Tools of Biochemistry 12A).
Gel electrophoresis (Figure 2A.2) is a technique commonly used with proteins and nucleic acids. A gel containing the appro-priate buffer solution is cast as a thin slab between glass plates.
Common gel-forming materials are polyacrylamide, a water-soluble, cross-linked polymer, and agarose, a polysaccharide. The
ELECTROPHORESIS AND ISOELECTRIC FOCUSING
55
Anode Cathode
Buffer Upper
electrode vessel
Lower electrode vessel Tracking dye Separated
components Gel cast between glass
plates. Notches are cast in the top of the gel to receive samples.
Solutions initially layered here
Buffer
FIGURE 2A.2 Gel electrophoresis.
slab is placed between electrode compartments, with the bottom selected as anode or cathode, depending on whether anions or cations are being separated. A small amount of a solution of each sample is carefully pipetted into one of several precast notches, called “wells”, on top of the gel. Usually glycerol and a water-solu-ble cationic or anionic “tracking” dye (e.g., bromophenol blue) are added to the sample. The glycerol makes the sample solution dense so that it sinks into the well and does not mix into the buffer solution in the upper electrode chamber. The dye migrates faster than most macroions, so the experimenter is able to follow the progress of the experiment. The current is turned on until the tracking dye band is near the bottom of the slab. The gel is then removed from between the glass plates and is usually stained with a dye that binds to proteins or nucleic acids. At this point, a photo-graph is taken of the gel for a permanent record. Because the pro-tein or nucleic acid mixture was applied as a narrow band at the top of the gel, components migrating with different mobilities appear as narrow bands on the gel, although the bands may be broadened somewhat by diffusion. Certain techniques (see Tools of Biochemistry References) make it possible to sharpen the bands even further so that individual types of macroions appear as nar-row lines on the gel; Figure 2A.3 shows an example of separation of DNA fragments by this method. The relative mobility of each component is calculated from the distance it has moved relative to the tracking dye.
Principles of Separation in Gel Electrophoresis
When electrophoresis is carried out in a gel or other supporting medium, the mobility is lower than would be expected from Equation 2A.1 because the gel or other matrix exhibits a molec-ular sieving effect. This can be seen by graphing mobility as a function of the concentration of the gel-forming material (Figure 2A.4a). A graph of log versus weight-percent gel com-position is usually linear; this is called a Ferguson plot. The lim-iting mobility approached as percent gel approaches zero is called the free mobility; it should be given (approximately) by
m
Equation 2A.1. The steepness of the Ferguson plot depends on the size and shape of the macroion, for it reflects the difficulty the macroion experiences in passing through the molecular mesh of the gel.
As a result of these several factors, different kinds of mole-cules can exhibit widely different behaviors in gel electrophoresis (Figure 2A.4b). However, certain simple cases are of great impor-tance. Polyelectrolytes like DNA or polylysine have one unit charge on each residue, so each molecule has a charge (Ze) pro-portional to its molecular length. But the frictional coefficient ( f ) also increases with molecular length, so to a first approximation, a macroion whose charge is proportional to its length has a free mobility almost independent of its size. In a mixture of such molecules, the molecular sieving effect determines the relative mobilities at any given gel concentration (Figure 2A.4c), and the
Top of gel
Molecular weight of DNA
Electrophoresis
+
-FIGURE 2A.3
Gel showing separation of DNA fragments. Following electrophoretic separa-tion of the different length DNA molecules, the gel is mixed with ethidium bro-mide, a fluorescent dye that binds DNA (page 1078). The unbound dye is then washed off and the stained DNA molecules are visualized under ultraviolet light.
Courtesy of David Helfman.
56
CHAPTER 2 THE MATRIX OF LIFE: WEAK INTERACTIONS IN AN AQUEOUS ENVIRONMENTLog relative mobility,m
0% (w/v) polyacrylamide in gel
% (w/v) polyacrylamide in gel
% (w/v) polyacrylamide in gel
Log relative mobility,m
0
Log relative mobility,m
0
LogMW
0 Mobility at a given gel concentration, i.e., at red line in (c) (a) Ferguson plot: mobility of a single
type of molecule
(b) Representative Ferguson plot for different kinds of molecules
(c) Ferguson plot observed when charge is proportional to length
(d) Relationship between molecular weight (M W ) and mobility, at a given gel concentration for molecules like those shown in (c) 1
1 2
2 3
3
4
4 Four
particles with charges proportional to length
Small particle, high charge Small particle, low charge Big particle, high charge Big particle, low charge Free mobility at 0% gel
FIGURE 2A.4
Mobility of the particles in gel electrophoresis.The mobility of the particles varies with the concentration of the gel. A Ferguson plot graphs the log of the relative mobility against the percent gel in the matrix. (a) Ferguson plot for a single type of molecule. Extending the plot to 0% gel gives the theoretical free mobility of the mole-cule. (b) Ferguson plot for four molecules of different size and charge. Note that free mobilities depend more on charge than on size but the slope depends mainly on size.
(c) Ferguson plot for molecules with charges proportional to their lengths. The molecules are numbered in order of increasing length and charge. The free mobilities of such molecules are almost the same, but the longer the molecule, the more it is slowed by increasing gel concentration. (d) Plot of the relationship between molecular weight and mobility. The log of the molecular weight (MW) of the four molecules shown in (c) is plotted against their mobilities at a single gel concentration. When this type of graph is prepared from standards, it can be used to determine the molecular weights of separated molecules.
(m)
sieving effect is proportional to molecular length or molecular weight. This means that we can neatly separate molecules of this kind on the basis of size alone by gel electrophoresis, as shown in Figure 2A.3. For extended molecules like nucleic acids, the rela-tive mobility is often approximately a linear function of the loga-rithm of the molecular weight (Figure 2A.4d). Usually, standards of known molecular weight are electrophoresed in one or more lanes on the gel. The molecular weight is then read from a graph like that in Figure 2A.4d prepared from the standards. For pro-teins, a similar sieving effect is achieved by coating the denatured molecule with the anionic detergent sodium dodecylsulfate (SDS) before electrophoresis. This important technique is dis-cussed further in Tools of Biochemistry 6B.
Isoelectric Focusing
Yet another gel electrophoresis technique allows separation of molecules purely on the basis of their charge characteristics. A polyampholyte will migrate in an electric field like other ions if it has a net positive or negative charge. At its isoelectric point, how-ever, its net charge is zero, and it is attracted to neither the anode nor the cathode. If we use a gel with a stable pH gradient covering a wide pH range, each polyampholyte molecule migrates to the position of its isoelectric point and accumulates there. We can
establish such a gradient by using a mixture of low-molecular-weight ampholytes as the gel buffer. This method of separation, called isoelectric focusing, produces distinct bands of accumu-lated polyampholytes and can resolve molecules with very small dif-ferences in isoelectric point (Figure 2A.5). Because the pH of each portion of the gel is known, isoelectric focusing can also be used to determine the isoelectric point of a particular polyampholyte.
What we have presented here is only a brief overview of a widely applied technique. For further information on gel elec-trophoresis, consult the references.
Capillary Electrophoresis
The term “capillary electrophoresis” (CE) broadly defines several related techniques that achieve high efficiency separations of ions, including macroions. The techniques all employ narrow-bore capillaries (20-200 inner diameter) in which the ions are separated as they migrate from one buffer chamber, past a detec-tor, to a destination buffer chamber (see Figure 2A.6). The equip-ment required to perform CE is more expensive than, and there-fore not as accessible as, that required for gel electrophoresis. In spite of this, for analysis of biomolecules, CE offers many advan-tages over traditional electrophoresis. The requirement to use low potentials (e.g., 25 V/cm) to avoid heat damage to the sample is a
mm
ELECTROPHORESIS AND ISOELECTRIC FOCUSING
57
7.0 7.2 7.4 7.6
Cathode
Position in gel Accumulation
of protein
pH of the gel
pl 7.46
pl 7.64 pl 7.44 pl 7.30 pl 7.36 pl 7.23
Anode 7.8
8.0
pH Protein concentration
+
−
FIGURE 2A.5
Isoelectric focusing of polyampholytes. A mixture of variants of the polyampholyte hemoglobin is placed on a gel with a pH gradient. When an electric field is applied, each variant protein migrates to its own iso-electric point.
Buffer Anode
Source vial Sample vial
Capillary
Detector
Destination vial
Cathode Integrator or
computer
Buffer
−
High-voltage power supply +
+
FIGURE 2A.6
A simple capillary electrophoresis experiment. Sample is introduced into the capillary from the sample vial. The capillary end with the sample is then placed in the source vial and high voltage is applied. The sample components will separate as they migrate toward the destination vial.
major limitation to the efficiency of separations achieved by the gel electrophoresis methods described above. Because CE capillar-ies have a large surface area to volume ratio, heat is efficiently dis-sipated and much higher potentials can be used (e.g., 500 V/cm).
The efficiency of separations is dramatically increased. Analysis times (typically 5–30 minutes) are short, only 10–100 nL of sam-ple is required, and detection is immediate and easily automated.
For these reasons, CE has been used as an analytical technique in genomics studies to achieve rapid sequence analysis of large DNA molecules (discussed further in Chapter 4).
The simplest CE experiments use fused silica capillaries filled with an appropriate buffer and the cathode as the destination electrode (see Figure 2A.6). Capillaries with different coatings, as well as gel-filled capillaries, allow for more sophisticated experiments, including isoelectric focusing and SDS polyacrylamide gel CE.
References
Hames, B. D., and D. Rickwood, eds. (1981) Gel Electrophoresis of Proteins. IRL Press, Oxford, Washington, D.C.; and Rickwood, D., and B. D. Hames, eds. (1982) Gel Electrophoresis of Nucleic Acids. IRL Press, Oxford, Washington, D.C. These two volumes are extremely useful laboratory manuals for gel electrophoresis techniques.
Osterman, L. A. (1984) Methods of Protein and Nucleic Acids Research, Vol. 1, Parts 1 and 2. Springer-Verlag, New York. A comprehensive summary of electrophoresis and isoelectric focusing.
Schmitt-Kopplin, P., ed. (2008) Capillary Electrophoresis: Methods and Protocols. Humana Press, Totowa, N.J. An introduction to many meth-ods of CE analysis, geared toward newcomers to the field.
van Holde, K. E., W. C. Johnson, and P. S. Ho (2006) Principles of Physical Biochemistry (2nd ed.). Prentice Hall, Upper Saddle River, N.J. Chapter 5 contains a more detailed discussion than given here.
A living cell is a dynamic structure.
It grows, it moves, it synthesizes complex macromolecules, and it selectively shuttles substances in and out and between compartments. All of this activity requires energy, so every cell and every organ-ism must obtain energy from its surroundings and expend it as efficiently as pos-sible. Plants gather radiant energy from sunlight; animals use the chemical energy stored in plants or other animals that they consume. The processing of this energy to do the things necessary for a cell or organism to maintain the living state is what much of biochemistry is about. Much of the elegant molecular machinery that exists in every cell is dedicated to this task.Because of the central role of energy in life, it is appropriate that we begin a study of biochemistry with an introduction to bioenergetics—the quantitative analysis of how organisms capture, transform, store, and utilize energy. Bioenergetics may be regarded as a special part of the general science of energy transformations, which is called thermodynamics. In this chapter we shall review just a bit of that field, focus-ing attention on fundamental concepts, such as enthalpy, entropy, and free energy, that are important to the biochemist or biologist.
We will introduce in this chapter the basic approaches for determining changes in free energy in biochemical systems. In subsequent chapters these basic approaches will be discussed further in the context of processes such as protein folding, transport of ions across membranes, and extraction of chemical energy from nutrients to make ATP.
Energy, Heat, and Work
A word we shall often use in our discussion is system. In this context, a system is any part of the universe that we choose for study. It can be a single bacterial cell, a Petri dish containing nutrient and millions of cells, the whole laboratory in which this dish rests, the earth, or the entire universe. A system must have defined boundaries, but otherwise there are few restrictions. Anything not defined as part of the system