[43] Determination of size, molecular weight, and presence of subunits

566

CHARACTERIZATION OF PURIFIED PROTEINS

[43]

[43] D e t e r m i n a t i o n o f Size, M o l e c u l a r W e i g h t , a n d P r e s e n c e of Subunits

By

THOMAS M. LAUE a n d DAVID G. RHODES

The apparent molecular weight of a given protein is perhaps the most often cited distinguishing characteristic of the molecule. This property is at the basis of many fractionation methods and is an easy-to-use descriptor ("the 30K subunit"). Nevertheless, some care is advisable if one intends to obtain accurate estimates of molecular size. In this chapter, size will refer to the physical dimensions of the protein, as opposed to the molecular weight of the protein, which is related to the mass of the protein. This chapter also considers the asymmetry (or axial ratio) of proteins, as this information is intimately involved in the apparent size of the molecule. Many proteins assemble into larger aggregates, with each constituent chain being considered a subunit.l The concept of a subunit, however, must be defined in context by the individual investigator, taking into account the system at hand and the objectives of the work with the system. For the purposes of this discussion, independent subunits will be defined as those protein moieties which do not have a contiguous polypeptide backbone. Thus, disulfide-linked peptide chains as well as segments associated through noncovalent interactions are considered subunits. The methodological approaches to determine the size or molecular weight of a protein can be categorized into three broadly defined areas: chemical analysis, such as composition analysis or the effect of the molecule on the properties (e.g., vapor pressure, freezing and boiling points) of a solvent, the transport of the molecule in response to some applied force (e.g., electrical, centrifugal, mechanical), and scattering of incident radiation (e.g., light, X rays, neutrons). As they are sensitive to different features of the molecule, selection of appropriate methods depends on what one needs to know about the system and with what accuracy. The capabilities, advantages, and limitations of a number of techniques are outlined in Table I. Beyond these criteria, the protein and the method must be compatible with regard to the quantity of protein available, the attainable level of purity, 2 solvent requirements, and peculiarities of the z S. N. Timasheff and G. R. Fasman, (eds.), "Subunits in Biological Systems," Part A. Dekker, New York, 1971. 2 D. G. Rhodes and T. M. Laue, this volume, [42].

METHODS IN ENZYMOLOGY, VOL. 182

Copyright © 1990 by Academic Press, Inc. All rights of reproduction in any form reserved.

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SIZE,

Mr,

AND

PRESENCE

OF SUBUNITS

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CHARACTERIZATION OF PURIFIED PROTEINS

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protein that may interfere with a specific technique. The various approaches are useful probes of other molecular properties as well, and these will be brought out in discussions of individual techniques. In addition, as will be pointed out in the text, many techniques are best used in combination with other techniques (e.g., viscosity and sedimentation, composition and SDS gel electrophoresis). This is not a complete list; many methods not included (such as radiation inactivation and cDNA analysis) may be useful in specific situations. We have selected for detailed discussion those techniques which are most useful and/or most commonly used. Suggested readings for a more complete treatment of other techniques are listed in Table I. Chemical Methods

Composition Overview. Methods that provide molar quantitation of either amino acids and/or specific prosthetic groups may be used to estimate the minimum molecular weight of a protein: Mmin = m/n

(1)

where Mr~n is the molecular weight estimate (g/mol) of the protein, m is the mass of the protein used in the analysis, and n is the number of moles of the protein-related component measured in the analysis. Good quantitation has been achieved using amino acid analyses, 3 end-group analysis, 4 and quantitative analysis for specific prosthetic groups) The quantity of material required for such composition-based molecular weight analyses is most dependent on the sensitivity of the analytical method being used. Since many newer analytical techniques are sensitive in the nanomole to picomole range, only microgram or even smaller quantities of material may be required. The error in the minimum molecular weight estimate will depend on the errors incurred in both the mass estimate and in the analysis for the particular constituent and, therefore, will depend on the methods chosen for these two measurements. By combining data from analyses for several different constituents, the accuracy can be improved. For this reason, independent estimates based on amino acid analyses, quantitative analysis of the end group, or quantitation of nonprotein cofactors are recommended. 3j. Ozols, this volume [44]. 4 p. Matsudaira, this volume [45]. 5 S. Seifter and S. England, this volume [47].

[43]

SIZE, M r , AND PRESENCE OF SUBUNITS

569

Because composition analysis provides only a minimum molecular weight, it is very useful to combine these data with results from other approaches to obtain the mass of the protein. An accurate composition analysis can be combined with techniques that provide only low-accuracy total molecular weights to yield high-accuracy results. Perhaps the most often used example of this approach is the combination of amino acid analysis 3 with SDS gel electrophoresis 6 (see below). One should, in principle, be able to estimate M by determining the smallest integers that could account for the full amino acid composition. In practice, uncertainty in the concentration of all 20 individual amino acid makes this approach quite unreliable by itself. However, an approximate molecular weight from SDS gel electrophoresis can guide in the selection of the appropriate absolute concentrations from the relative concentrations, indicating to the investigator whether to "round up" or "round down" individual values. Method. An estimate of protein mass is made most accurately from a measurement of dry weight when the protein is present in a volatile buffer (e.g., ammonium bicarbonate). Compensation for nonvolatile buffer components can be made from the difference in mass between dried samples of the protein-containing solution and the buffer alone, but is difficult to do with great accuracy and should not be attempted with partially volatile buffers. Alternatively, protein concentration measurements are often used in place of dry weight estimates (the mass value used for analysis simply being the product of mass-concentration and the volume). Concentration estimates can be made refractometrically, spectrophotometrically, or by chemical assay. The accuracy of such measurements often is limited, even though the precision may be reasonable, because standardization is a major problem. This is especially true for glycoproteins, lipoproteins, or other proteins with unusual compositions where the method of analysis may be sensitive only to certain constituents of the protein (e.g., peptide bonds). Of the methods listed, refractometry (or differential refractometry) is the most accurate means of estimating concentration. Amino acid analysis also provides a suitable means of quantitation. 3 Problems and Pitfalls. Composition-based minimum molecular weight analyses are sensitive to sample purity. In general, any contaminant that influences either the mass estimation or the quantitative analysis will affect the accuracy of the determination. Since no fractionation of the starting material is afforded by these analyses, contamination or heterogeneity will cause trouble. Therefore, samples must be purified prior to analysis. The degree of purity required depends on the nature of the

6 D. Garfin, this volume [33].

570

CHARACTERIZATION OF PURIFIED PROTEINS

[43]

contaminant and the sensitivity of the mass estimate or the analytical method to that contaminant. In all of these methods, it must be assumed that there is only one, or an integral number, of moles of the analyzed component per mole of protein. Since no information concerning quaternary structure is available, only a minimum molecular weight is obtained. For example, quantitative analysis of heme iron in either hemoglobin or myoglobin would yield nearly identical apparent molecular weights, despite the fact that the molecular weight of intact hemoglobin is 4-fold greater than that of myoglobin. Colligative P r o p e r t i e s Overview. Dissolution of a solute in a solvent reduces the chemical potential of that solvent and results in a number of observable phenomena known collectively as colligative properties. 7 The relationship at the basis of these phenomena is Id.a - go = R T ln(yaXa)

(2)

where/Xa is the chemical potential of a solute (cal/mol),/z ° is/Xa in the standard state, R is the gas constant (8.3144 x 10 7 cal/mol. K), T is the temperature (K), y is the activity coefficient of a, and Xa is the mole fraction of a. When Xa is less than 1,/xa is less than go. The molecular weight of any solute can, in principle, be determined by the extent to which the solution activity is changed by the presence of a known weight of solute. Thus, the molecular weight of any solute, including proteins, could be determined by measuring freezing point depression, boiling point elevation, osmotic pressure, or vapor pressure. Because changes in freezing temperature or boiling temperature are generally quite small for protein-sized molecules, and occur at extremes of temperature at which the molecules may not be stable, these methods are generally inapplicable for study of protein solutions. On the other hand, both vapor pressure and osmotic pressure have been used for measurement of protein molecular weights, but this will not be discussed in detail here. Vapor pressure osmometers and membrane osmometers are commercially available. The former reliably measure molecular weights in water to approximately 25,000, whereas the latter are used for proteins above 20,000. Protein concentrations on the order of 0.1 to 1 mg/ml and sample volumes of 10 to 200 /zl are required. As with composition methods, accurate determinations of sample mass are necessary for both of these methods. It should also be noted that the molecular weight measured with 7 I. Tinoco, K. Sauer, and J. Wang, "Physical Chemistry," p. 117. Prentice-Hall, Englewood Cliffs, New Jersey, 1985.

[43]

SIZE, Mr, AND PRESENCE OF SUBUNITS

571

any colligative property is a number average and can be severely affected by contaminating low-molecular-weight species. Additional information can be found in Refs. 7 and 8 and in manufacturer's literature.

Transport Methods Sedimentation Equilibrium Overview. Sedimentation equilibrium provides the single most accurate and powerful method for the determination of the native molecular weight of a protein. It is a simple, nondestructive, relatively rapid method. All parameters that describe sedimentation equilibrium are either readily measured or easily estimated. It has several unique capabilities, and can provide quantitative estimates of molecular weights, stoichiometries, and association constants for a wide range of chemical systems. For example, by sedimenting in neutrally buoyant (nonsedimenting) detergents, the native molecular weight of detergent-solubilized proteins may be measured. 8 Many systems not amenable to analysis by any other technique can often be examined profitably by sedimentation equilibrium. However, because sedimentation equilibrium generally requires sophisticated, expensive equipment, and other methods suitable for many purposes are available, this procedure is used much less frequently than in the past. Nevertheless, equilibrium sedimentation provides one of the most powerful methods for the quantitative examination of protein-protein associations, and is irreplaceable for the study of protein systems with weak to moderate association constants. Method. In an equilibrium sedimentation experiment the purpose is to produce a measurable protein concentration gradient along the radial axis of the centrifuge cell. The length of time needed to achieve sedimentation equilibrium depends on the length of the solution column, the value of o(see below), and the diffusion constant. Because the time to reach equilibrium depends on the square of the column length, various cells and techniques have been developed to examine short columns (3 or 0.3 mm long). 9 Using these cells, equilibrium can be reached in a matter of minutes to a few hours. After sedimenting for this time, the concentration distribution is measured at three or four half-hour or 1-hr intervals. Invariance of the distribution over time indicates that equilibrium has been reached. 8 W. W. Fish, in "Methods in Membrane Biology" (E. E. Korn, ed.), Vol. 4, p. 189. Plenum Press, New York, 1978. 9 C. H. Chervenka, " A Manual of Methods for the Analytical Ultracentrifuge." Spinco Div., Beckman Instruments, Palo Alto, California, 1970.

572

CHARACTERIZATION OF PURIFIED PROTEINS

[43]

or is the measured quantity in a sedimentation equilibrium experiment.l° It is defined as o- = M(1

-

Op)to2/RT

(3)

where or is the reduced molecular weight, 0 is the protein's partial specific volume (ml/g, determined as described for sedimentation velocity), p (g/ml) is the solution density (as described for sedimentation velocity), and o92 ( s e c -2) is the square of the rotor's angular velocity (to = rpm. ,r/ 30). or is most frequently determined as the slope of a graph of the natural logarithm of the concentration as a function of r2/2, where r is the radial position in the rotor. The slope may be calculated at each of several radial positions (or, correspondingly, at each of several concentrations). Molecular weights determined in this fashion are weight-average values. Alternatively, o- may be obtained from nonlinear least-squares fitting to equations that describe the concentration distribution (i.e., c as a function of r2/2) that are beyond the scope of this chapter. 11 These equations have been derived from thermodynamic first principles for a variety of models that include association and nonideality of the proteins. The concentration distribution at equilibrium can be determined by any number of means. If a preparative centrifuge 12 or an "airfuge" 13 is being used for the measurement, any assay that is proportional to the concentration of protein may be used following fractionation of the content of the cell. However, it is then necessary to perform several experiments for different lengths of time to ensure that equilibrium has been reached. Also, these techniques suffer a loss of precision due to the collapse of the concentration gradient that occurs as the rotor decelerates and as fractionation of the cell contents is performed. The analytical ultracentrifuge alleviates this problem by permitting the solution contents to be examined optically as the centrifuge is operating and the contents of the cell remain at equilibrium. 9 Currently, there are two optical systems available for the analytical centrifuge, the absorbance scanner and the Rayleigh interferometer. These two systems provide complementary information, with the selectivity and sensitivity of the scanner being useful for some situations, while the precision and accuracy of the Rayleigh system are needed in others. The radius must be calculated with accuracy. The analytical ultracentrifuge provides reference markers, which along with the optical magnifiD. A. Yphantis, Biochemistry 3, 297 (1964). II M. L. Johnson, J. J. Correia, D. A. Yphantis, and H. R. Halvorson, Biophys. J. 36, 575 (1981). 12 A. K. Attri and A. P. Minton, Anal. Biochem. 152, 319 (1986). 13 p. Bock and H. Halvorson, Anal. Biochem. 137, 172 (1983). to

[43]

SIZE, Mr, AND PRESENCE OF SUBUNITS

573

cation factor are used to calculate the radial position in the image. The instrument operating manuals provide good information on how to determine the radius. 9 When using a preparative centrifuge, the radius must be calculated from geometric considerations. The original articles describe how this is done for various rotors and cells. 12,13 P r o b l e m s and Pitfalls. The principal problem in sedimentation equilibrium analysis is obtaining a sufficient quantity of highly purified protein for analysis. This is not as formidable as it seems, since a molecular weight may be measured using the Rayleigh interferometer with just 20/zl of solution at a concentration of 1 mg/ml. This is no more material than is often used for gel electrophoresis. In cases where a preparative centrifuge is being used and a sensitive assay is available, less material may be required, but lower precision can be expected. It should also be realized that equilibrium sedimentation does not afford the extent of fractionation that is seen with gel filtration or gel electrophoresis. Even so, the gravitational field does fractionate the solution to some extent, such that very large particles (e.g., dust, flocculant) are removed from observation. This means that the scrupulous cleanliness of samples necessary for scattering techniques (see below) is not needed for analytical centrifugation. Note that buffer components will also be fractionated in the gravitational field. For this reason, buffers that have a 0 that is near that of the solvent (Op = 1) are preferred. Thus, buffers such as Tris are good choices for sedimentation, while phosphate buffers can pose problems under some circumstances. 1° Problems of buffer sedimentation are minimized by extensive dialysis and careful filling of the cell. Convection can also be a problem. As with sedimentation velocity analysis, it is usually caused by rotor vibration or thermal gradients, and can be minimized by taking precautions to balance the cells carefully and setting the cooling apparatus appropriately. In addition, convection can be minimized by including a sufficient quantity of a buffer component to provide a small, stabilizing density gradient (e.g., 0.1 M NaCI, or small quantities of sucrose). Convection can often be detected in the concentration gradient as a bump on the ordinarily smooth exponential gradient. Alternatively, a " h o o k " in the concentration gradient (either positive or negative) may be present near the meniscus. Many times convection can be detected by examining the difference between two concentration curves made at the same speed, but at different times. Thus, the procedure of making several measurements at a given speed serves two purposes, first to ensure that equilibrium has been reached, and second, to check for convection. Under some circumstances, a sample that exhibits convection in the meniscus region may still provide some useful information if that region of the concentration gradient is omitted from the analysis.

574

CHARACTERIZATION OF PURIFIED PROTEINS

[43]

Tests are available for detecting impurities in a sample being analyzed by sedimentation equilibrium. One is to generate graphs of the apparent molecular weight (determined as the local slope from the graph of In c versus r2/2) as a function of concentration. If the M(c) graphs are independent of rotor speed, one can be quite certain that the sample is pure. More sensitive tests for heterogeneity are outlined in [42] of this volume. Sedimentation Velocity Overview. Sedimentation velocity is a simple, nondestructive technique for the characterization of the hydrodynamic behavior of a protein. It has the advantage over gel chromatography of being a primary technique (not requiring standards) for the determination of hydrodynamic parameters. Because of its roots in first principles, sedimentation analysis can be applied to systems that cannot be analyzed by any other means. The principal result from a sedimentation velocity experiment is the sedimentation coefficient (s), which is a measure of the ratio of the buoyant mass of the protein to its frictional coefficient: s = M(1 - Op)/Nof

(4)

where s is the sedimentation coefficient in Svedberg units (× 10-13 s e c - l ) , No is Avogadro's number, and f is the protein frictional coefficient. The diffusion coefficient, D (cmZ/sec), defined in Eq. (5), also is measurable from boundary spreading in measurements of analytical centrifugation experiments: D = RT/Nof

(5)

The ratio of s/D [Eq. (6)] provides a measure of the molecular weight that is free of any requirements concerning size, shape, or similarity to protein standards: s/D = M(1 - Op)/RT

(6)

Alternatively, if an accurate molecular weight is known, measurement of the sedimentation coefficient allows the frictional coefficient, f, to be determined using Eqs. (6) and (7). The ratio o f f / f ° may then be used to estimate the shape of the protein, where f0 is defined as the frictional coefficient expected for an anhydrous sphere of equal molecular weight and density, f 0 is calculated by writing the Stokes equation for this sphere: fo = 6"n',/rsphere = 6~w/[M03/(4¢rNo)]v3

(7)

where ~/is the viscosity and rsphereis the radius of the equivalent sphere.

[43]

SIZE, Mr, AND PRESENCE OF SUBUNITS

575

This ratio f / f o is then compared to standard and theoretical values to estimate the asymmetry and overall shape of the protein (see below). Method. Sedimentation velocity experiments are best performed in an analytical ultracentrifuge, although methods of reasonable accuracy have been devised for preparative centrifuges. The advantage of the analytical machine is its accuracy (---I-3%), which is nearly an order of magnitude better than can be expected from techniques using preparative machines. Moreover, data are acquired throughout the experiment so that better diagnostics of unusual behavior is afforded. The advantage of the preparative machines is that sensitive or specific assays may be used so that in cases where the purity of the sample is in doubt, a specific assay can identify the component of interest. Detailed methods for using the analytical ultracentrifuge 9 and for using preparative centrifuges 14,15are available. As noted before, the principal measurement in any sedimentation experiment is the concentration as a function of radial position. The sedimentation coefficient is determined from the slope of a graph of the natural logarithm of the distance that the molecules have sedimented as a function of time (d In r/dt): s = (d In r/dt)/to 2

(8)

where r is the distance of the boundary of the molecules from the center of the rotor and t is the time (in seconds) from the start of the experiment (usually taken to be the time at which the rotor is two-thirds its final speed). For experiments where the sample being examined is a thin zone of molecules, r is taken to be the point of maximum concentration. For broad zone or boundary experiments, r is taken to be the midpoint between zero concentration and the plateau concentration. For the schleiren optical system, which provides a measure o f d c / d r (r), r is usually taken to be the maximum of the schlieren peak. For proper interpretation and comparison, the sedimentation coefficient must be corrected to standard conditions of water at 20° and zero protein concentration (s°0,w) using

0

S20'w = S°bserved

(1 1

U20,wDT,b /

t

\a920,w/ ~-~-,w/

(9)

where O, t9, and ~ are the partial specific volume, density, and viscosity at the experimental temperature (T or 20°) and buffer conditions (w, water; b, buffer), respectively. Tabulated values for the viscosity of water are used to correct for the effect of temperature on the sedimentation coefficient. The density is either measured or calculated from tabulated values. 14 D. Freifelder, this series, Vol. 27, p. 140. 15 R. Martin and B. Ames, J. Biol. Chem. 236, 1372 (1961).

576

CHARACTERIZATION OF PURIFIED PROTEINS

[43]

The effect of protein concentration on s is assessed by determining s at each of several protein concentrations. Typically, there is a slight linear decrease in s as the protein concentration is increased. The diffusion coefficient is determined from the spreading of the boundary as it progresses down the analytical cell. A graph is made of [c/ (dc/dr)max] 2, where (dc/dr)m~x is the concentration gradient at the point of maximum gradient, for most cases the midpoint of the boundary 9, as a function of time, and the slope of this line is used to estimate D, the diffusion coefficient:

( l_.L](d{[c/(dc/dr)max]2}.] D = \4¢r/\ dt /

(10)

where D is in centimeters squared per second and c is the protein concentration (arbitrary units). The ratio of s/D provides the reduced molecular weight, M . (l - Or)/ R T so determination of M requires other experimental measurements. The solvent density, p, is readily measured or calculable from tabulated data. The partial specific volume of the protein, 0, can be measured, but more frequently is calculated from its composition using the method of Cohn and Edsall and tabulated values of 0 for the amino acids. 16Values of 0 for carbohydrates may be found in Gibbons 17 and Durschlag. is Values for other common protein-associated components can be found in Steele et al. 19or Reynolds and McCaslin. 2° For more accurate work 0 is adjusted for temperature (over the range 4-40 °) using a coefficient of 4.3 × l0 -4 cm3/g • K, as described by Durschlag. is The effects of pH, the buffer composition, and preferential hydration on O are typically neglected, except in cases where a high concentration of denaturant is used. Special provisions may be made for estimating the isopotential apparent partial specific volume (l-I) of simple proteins in solvents containing 8 M urea and 6 M guanidinium chloride, using the method given by Prakash and Timasheff. 21 Likewise, H may be estimated for simple proteins in solvents containing varying amounts of NaC1, NazSO4, MgSO4, glycine, /3alanine, a-alanine, betaine, and CH3COONa using the method of Arakawa and Timasheff. 22 Neither estimate is very accurate, however, if the 16 T. L. McMeekin and K. Marshall, Science 116, 142 (1952). 17 Ro Ao Gibbons, in "Glycoproteins," Part A (A. Gottschalk, ed.), p. 31. Elsevier, Amsterdam, 1972. ig j. Durschlag, in "Thermodynamic Data for Biochemistry and Biotechnology" (H. Hinz, ed.), p. 46. Springer-Verlag, Berlin, 1986. 19j° H. C. Steele, C. Tanford, and J. A. Reynolds, this series, Vol. 48, p. 18. 20 j. A. Reynolds and D. R. McCaslin, this series, Vol. 117, p. 47. 21 V. Prakash and S. N. Timasheff, this series, Vol. 117, p. 53. 22 T. Arakawa and S. N. Timasheff, this series, Vol. 117, p. 60.

[43]

SIZE, Mr, AND PRESENCE OF SUBUNITS

577

protein contains significant levels (> 10%, w/w) of nonamino acid constituents (e.g., glycoproteins, lipoproteins) or if the axial ratio is greater than 10. Hydrodynamic interpretation of sedimentation data can be made once an accurate molecular weight and 0 estimate are available. First, one calculates f0 using Eq. (7) above. The ratio of the measured frictional coefficient t o f ° (f/fo) will be a value greater than one. Note thatfmust be 0 calculated using S2o,w: f = M(1 - Op)/Nos°o,w

(11)

where the various terms are as described above, and s20,w 0 is determined as described in Eq. (9). There are two reasons that f/fo will be greater than one. First, proteins are " c o a t e d " by a layer of water molecules that move with the protein as it sediments. While these water molecules freely exchange with those in the bulk solvent, the net result of the layer is to increase the effective radius of the protein. As can be seen from Eq. (7), any increase in the effective radius will increase f. Second, the frictional coefficient depends on the surface area of the protein presented to the solvent. For a molecule of given mass and density, a sphere would be the shape that exposes the minimum surface area, so any molecular asymmetry will increase f. The degree of molecular asymmetry is estimated by determining the axial ratio (a/b) of the ellipsoids of revolution, prolate (elongated) or oblate (flattened), that would result in an identical value for f/fo. It should be clear that the asymmetry is being modeled using these ellipsoids of revolution, and that the results may not "look" like the molecule at all. However, if one can measure the asymmetry for the isolated subunits of a multimeric protein, as well as for the intact oligomer, it is possible to use changes in a/b to distinguish between possible arrangements of the subunits. 23 Problems and Pitfalls. The use of sedimentation velocity measurements to determine molecular weights has declined in favor of gel electrophoresis, gel chromatography, or the more accurate method of sedimentation equilibrium. However, sedimentation velocity provides the best and the only primary method for the determination of hydrodynamic parameters available to molecular biologists. Electrophoresis and gel filtration require that standards be used, which places restrictions on the data interpretation. Of all the techniques described in this chapter, the problems and pitfalls of sedimentation analysis are the best documented and most easily overcome. z3 C. R. Cantor and P. R. Schimmel, in "Biophysical Chemistry," Part II, p. 565. Freeman, San Francisco, California, 1980.

578

CHARACTERIZATION OF PURIFIED PROTEINS

[43]

The most demanding aspect of sedimentation is the availability of sufficient material for analysis. If the standard optical systems on the current (Beckman model E) analytical ultracentrifuge are used, 0.5 ml of solution with protein concentrations in the range of 0.1-1 mg/ml is needed to obtain good data. The principal technical difficulty with sedimentation analysis is convection. This problem usually indicates that the drive is vibrating excessively, that the temperature control is not set properly, or that the cell is misaligned or deformed. All of these potential obstacles may be tested for and corrected. The second problem is that the "current" ultracentrifuge is antiquated, and few individuals are well versed in its operation. The techniques are not inherently difficult, but the machinery is ornery. It is expected that a new analytical ultracentrifuge will be available by the 1990s, and that the data acquisition and analysis described above will be automated. The interpretation of sedimentation coefficients for proteins that bind significant levels of buffer components (e.g., detergent-solubilized proteins) is made difficult by the fact that the bound components will contribute to the measured s in four terms: M, 0, p, andf. Of these terms, M, 0, and f are usually the most affected by bound components, and, unlike sedimentation equilibrium (see below), there is no way to "blank out" the contribution of such components. Thus, the measured sedimentation coefficient is for the complex of the protein with the bound component, making it difficult to extract any useful information concerning the protein alone. Another widely used method of estimating molecular weights of proteins is the gradient sedimentation method introduced by Martin and Ames. 15In this method, one creates a linear gradient of sucrose in buffer in a swinging bucket centrifuge tube. The sucrose concentration typically ranges from 5% at the top of the tube to 20% at the bottom; the actual range is less important than the linearity and reproducibility of the gradient. The unknown sample is layered onto a gradient and a set of standard proteins of known molecular weight layered onto an equivalent gradient. The centrifugation proceeds for an appropriate interval (typically 12-24 hr) and the material on the gradients collected as fractions. The protein concentration in these fractions is determined by spectrophotometric, enzymatic, or other assays. The basis of the method is the fact that in a linear sucrose gradient, the distance travelled by a molecule should be a linear function of the time of centrifugation at a specified speed. In addition, the distance will depend linearly on s. The ratio of the distance travelled by an unknown protein to that of a standard will be equal to the ratio of their sedimentation coeffi-

[43]

SIZE, M r , AND PRESENCE OF SUBUNITS

579

cients, which will, in turn be approximated by the ratio of the molecular weights to the 2/3 power. This method yields approximate values of s and M, but is simple, requires no specialized equipment, and can be used to estimate s and M for very small amounts of material if a suitable (e.g., enzymatic) assay is available.

Gel Filtration Chromatography Overview. Gel filtration chromatography is one of the most powerful and simplest methods for the estimates of the molecular weight of proteins. Because of the fractionation afforded by the method, and because assays specific for the protein of interest may be used (e.g., enzymatic, immunological), sample purity does not have to be very high. The method is nondestructive, can be fairly rapid, and has moderate accuracy as long as the protein of interest is roughly the same shape as the protein standards used to calibrate the column. 24 The determination of a molecular weight by gel chromatography relies on the comparison of the elution volume of the unknown with those of several protein standards whose molecular weights are known. The molecular weight of the unknown is estimated from a graph of the logarithm of the molecular weight as a function of elution volume (or Kay, as described below) made using the data from the protein standards. (It is worth noting that the actual dependence is on the logarithm of the effective hydrated radius, or "Stokes radius" of the protein, and that the fit of standard proteins to this variable is better.) The elution volume (Ve) for the standards should cover the range from Vo (the void volume) to Vj (where Vi is the included volume). A column-independent measure of the protein behavior, Kay, is more useful for comparison of results than simply the elution volume: Kav= V e - Vo/(Vt- Vo)

(12)

where Kay is the fraction of the stationary gel volume which is accessible to the protein, and Vt is the total volume of the gel bed. Use of Kay is preferred over V~ since, for a given gel type, values of Kay will vary only slightly from column to column. The methods described below can be used for both native and denatured proteins and, therefore, provide a means for establishing the presence of subunits. However, gel filtration in denaturing solvents typically requires more material than denaturing gel electrophoresis and is thus not used as often. Method. The principle of operation and selection of gel media and gel 24 G. K. Ackers, Ado. Protein Chem. 24, 343 (1970).

580

CHARACTERIZATION OF PURIFIED PROTEINS

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porosity is described in detail elsewhere in this volume. 25 One must choose a gel in which the protein to be examined is partially included. Choice of the gel medium usually is arbitrary, as long as the protein does not bind to the gel matrix. When there is a choice of bead sizes for a given porosity, the smallest bead size should be used, as this improves the column resolution. Check the manufacturer's recommendations for any particular limitations on solvents, but in general, just about any freeflowing aqueous buffer system may be used. It is recommended that buffers of moderate ionic strength be used so that electrostatic interactions between the protein and immobile charges on the gel matrix are minimized. For best results, use a long, narrow column. Preparation of the gel, pouring of the column, and equilibration of the column by washing with buffer should be done according to the manufacturer's specifications. Likewise, flow rates should be chosen in accordance with the manufacturer's specifications. In general, lower flow rates afford better resolution because the solute can fully equilibrate with the gel matrix at all times, but excessive diffusion can limit resolution if a column is run too slowly. For molecular weight estimations, extra care should be exercised in making sure that the "fines" (partially pulverized gel beads) are removed, as these will reduce the column flow rate and reduce the column resolution. All samples should be in the same buffer as that used to equilibrate the column. Sample volumes applied to the column should generally be less than 2% of the column's bed volume. Care should be exercised when applying samples to the column to make sure that the gel bed is not disturbed or that the gel bed does not run dry. In addition, the flow rate of the column should be kept constant throughout all of the analyses, since flow rate dependence of the elution volume can be expected. 24 Elution volume (Ve) is the volume eluted from the column, starting once one-half of the sample has penetrated the top of the gel bed and continuing until the maximum (peak) of the protein of interest has eluted. The void volume (V0) of the column usually can be measured using commercially available, size-graded Blue Dextran (M = 2,000,000), and monitoring the effluent spectrophotometrically at 540 nm (or 280 nm). The included volume can be measured using as a sample some buffer of somewhat different pH or conductivity (extremes should be avoided), or one that contains a small dye (e.g., Bromphenol Blue). Care should be exercised in the choice of the dye, as many aromatic compounds will stick to gel matrices, resulting in anomalously high Kay and Vi values. E. Stellwegen, this volume [25].

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Protein standards should be used that span the full range of sizes that can be analyzed by the gel medium chosen. For best results, a minimum of four different standards should be used. Kits containing prestained proteins are available. Any convenient assay for detecting the presence of the protein being analyzed may be used. If for any reason the column must be repacked, the calibration must be performed again. Use of column chromatography to estimate the molecular weight of denatured proteins poses special problems. 8 This method relies on the shape of the unknown being identical to that of the standards. This means that the protein must be totally denatured, including reduction of disulfide bonds. Buffers should contain a reducing agent or else the sulfhydryls should be alkylated to prevent reformation of any disulfide bonds. Both the standards and the unknown must be analyzed after the same treatment and the same buffer conditions. Calibration proceeds as described above. Problems and Pitfalls. The greatest source of error in gel chromatography comes from the requirement that the unknown be similar in shape and density to the protein standards. Since the protein standards used are almost universally compact, globular proteins, this means that fibrous proteins, or proteins having fibrous regions, can behave anomalously on gel columns. One indication of such molecular asymmetry is if Kay for the unknown increases when analyzed at decreased flow rates, while those for the standards remain unchanged. Since it is the size of the protein and not the molecular weight that is being assessed by this technique, molecular weight estimates for proteins that are complexed with other molecules (e.g., detergent-solubilized proteins, extensively glycosylated proteins) will be unreliable. Finally, if the protein interacts with the gel matrix (e.g., binds or is repelled), inaccuracies will result. This can be tested by determining the molecular weight using two different types of gel matrix (e.g., Sepharose and acrylamide). If Kay > 1, then the molecule is binding to the column, and a different gel matrix should be used. On the other hand, if Kay < 0, the column is "channeling" and must be repoured and recalibrated.

Electrophoresis Overview. The most widely used method of evaluating the size of a protein molecule is electrophoresis. The method is simple, inexpensive, rapid, and reasonably accurate for a very wide range of proteins. For these reasons it is the method of choice for most protein systems, and almost always included in characterization studies. SDS gel electrophoresis is the most widely used method for determining apparent molecular

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weights of denatured proteins (discussed elsewhere in this volume6), but electrophoretic methods for obtaining size, shape, and molecular weight information are not limited to just this approach. Despite its popularity, it is not necessary to include SDS in the gel formulation; native gel electrophoresis of protein samples may be carried out under almost any buffer condition required. In addition, the sensitivity of current staining procedures allows these approaches to be applied to very small amounts of protein. 26 Method. The basic procedures are identical to those described earlier6 for electrophoresis of denatured proteins, except that the buffer composition is left to the discretion of the investigator. There are some restrictions; as with gels under denaturing conditions, the buffer in which the gel is cast cannot contain reducing agents. In addition, because the conditions to which the protein is exposed may affect charge, association, or shape, the composition of the buffer in the gel must be controlled carefully. One must, therefore, be especially cautious about relative proportions of catalyst, so that excess oxidant is not left in the gel. It is often easiest to prerun such gels to remove by-products of polymerization. If the geometry of the gel apparatus allows the slab to be exposed (e.g., a horizontal slab or a vertical slab in which one of two glass plates can be removed and later replaced) the gel can be dialyzed against the buffer of choice prior to running. Because slabs are generally quite thin, dialysis for several hours is generally sufficient. This dialysis procedure can also be used to introduce reducing reagents postpolymerization, or to use a set of gels cast together (and thus, presumably, uniform in porosity) with a variety of buffer conditions. The basis of electrophoretic protein size analysis is based on a simple principle: that a charged particle in an electric field is forced through the surrounding medium by a force proportional to the charge on the particle and the strength of the field, and is subject to a frictional force proportional to the velocity, the radius of the particle, and the viscosity of the medium. As with SDS gel electrophoresis, the investigator may control the frictional coefficient by controlling the porosity of the gel matrix. In addition, under nondenaturing conditions, the mobility can be significantly affected by alterations of the intrinsic charge on the protein due to changes o f p H at which the electrophoresis is carried out. This distinction is important. In SDS gel electrophoresis, the charge is dominated by the negatively charged SDS associated with the protein so the sample is applied to the cathode end of the gel and the sample always moves toward the anode. In nondenaturing electrophoresis, the direction of migration 26 C. R. Merril, this v o l u m e [36].

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will depend on the buffer pH relative to the pI of the protein. If the pI of the protein is unknown (and quantities are too limited to allow experimental determination with isoelectric focusing), a horizontal electrophoresis apparatus may be used, and the starting wells placed in the center of the gel. Otherwise, a "best guess" might be made by using the pI of related proteins. The mobility will also be affected by the chosen buffer condition. Beyond association or conformational changes associated with changing buffer conditions, the relative mobilities of various protein at a given pH will usually be fairly constant. The absolute mobility, however, will be strongly affected by the concentrations of counterions. The analysis of native gel electrophoresis mobility data is analogous to that of SDS gels. The only significant difference is that, in the native system, one cannot assume that the proteins are all in the shape of long rods. One must compare the mobility of the sample to that of a set of standards. 27 Ferguson analysis can also be used to identify the feature(s) (size and/or charge) that distinguish two components and to extrapolate to the mobility expected in the absence of sieving effects. 28 The slope of the Ferguson plot (log of the relative mobility, Rf, vs gel concentration) is proportional to rs, the Stokes radius. Interpolative estimation of an unknown rs is more reliable using this relation than using, for example, the slope of the Ferguson plot with molecular weights of the standards. The analysis simply involves running the unknown and several standards in a set (at least five) of gels of different total concentrations, and plotting log Rf vs the gel concentration for all standards and for the unknown. The slopes for the standards are then plotted as a function of the (known) rs, and the rs of the unknown is derived from this plot and the measured slope. The range of gel concentrations used will depend on the size of the protein under study; at some concentration the protein will be excluded from the gel. A more closely spaced group of gel concentrations covering a lower range should then be used. Problems and Pitfalls. Although electrophoresis under nondenaturing conditions can provide useful information about the physical characteristics of the protein under a number of different conditions, it is important to be aware that this is a zonal method, and that concentration effects (or dilution effects) can be serious. It is probably not generally advisable, for example, to use this approach to study association behavior quantitatively. z7 D. Rodbard and A. Chrambach, Anal. Biochem. 40, 95 (1971). 2s A. T. Andrews, "Electrophoresis: Theory, Techniques, and Biochemical and Clinical Applications." Clarendon Press, Oxford, 1986.

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This is not a primary technique; it depends on selection of appropriate standards. These are generally globular, unmodified, soluble proteins, so that highly asymmetric proteins or proteins with unusual nonprotein "baggage" may yield erroneous results. The Ferguson analysis helps to account for differences in mobility due to charge differences, but exaggerated charge densities may yield anomalous results. Because the buffer conditions in native gel electrophoresis are selected by the individual investigator, and thus may vary widely, one must be aware of the solution components responsible for carrying current. High ionic strength buffers may result in unacceptably slow protein mobilities, and low ionic strength buffers may run properly at surprisingly low currents. Because of this variability and because protein integrity is more important, one must be particularly aware of power dissipation and cautious about efficient removal of heat generated in the gel.

Viscosity The viscosity of a solution depends on a number of variables (T, P, etc.), including the amount and nature of any solute that might be present. The response of a particle in a fluid under shear will depend on the frictional coefficient of the particle (as the "handle" the solution has on the particle) as well as on the mass of the particle (as this will determine the energy required to attain a given movement). 29,3°Because the intrinsic viscosity of a protein depends very strongly on the asymmetry of the molecule, viscosity measurements are sensitive indicators of protein shape. In addition, it is possible to combine viscosity data with sedimentation data to calculate the molecular weight of a protein. Apparatus for rheological measurements vary widely; their use is generally quite simple, but must be performed under rigorously controlled conditions. Scattering Methods Scattering methods are generally used to obtain radii of gyration, but specific scattering methods can provide diffusion coefficients, molecular weight, and thermodynamic parameters. 31,32Details regarding these methods are reviewed elsewhere and will not be treated in depth here. 29 j. T. Yang, Adv. Protein Chem. 16, 63 (1961). 3oj. F. Johnson, J. R. Martin, and R. S. Porter, in "Physical Methods of Chemistry" (A. Weissberger and B. W. Rossiter, eds.), Vol. 1, Part VI. Wiley, New York (1977). 3z S. N. Timasheff and R. Townend, in "Physical Principles and Techniques of Protein Chemistry" (S. J. Leach, ed.), Part B, p. 147. Academic Press, New York, 1970. 32 B. Chu, "Laser Light Scattering." Academic Press, New York, 1974.

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Electron Microscopy Electron microscopy is an appealing approach to determining molecular size and shape for large protein molecules or associated complexes of subunits because it is a direct imaging method. Initial work in this area was used to identify the shape of very large complexes like the hemocyanin aggregates, 33 but more recent work has focused on imaging of crystalline arrays of membrane proteins. 34 This method provides very detailed information about the native size and shape of the molecule for a class of proteins that are incompatible with many other analysis methods. The resolution of the transmission electron microscopy approaches utilizing mathematical filtering and reconstruction methods is quite high; domains of specific subunits can often be resolved. Recent work with ultrathin (one to two atomic layers) coating techniques 35 has allowed individual proteins as small as 100 kDa (-0.5-nm resolution) to be directly visualized with scanning electron microscopy. The rapidly developing direct imaging technologies seem likely to play an ever-increasing role in analysis of macromolecular size and shape analysis. Presence of Subunits

To determine whether subunits are present generally involves characterization of one or more properties of the system under conditions which favor association, followed by analysis under conditions which are likely to favor dissociation. Clearly, this implies that the investigator has some prior knowledge of the conditions under which association should be expected, or that one is willing to investigate a variety of conditions which have been shown in other cases to result in dissociation. On the other hand, a properly planned "search for subunits" will not only reveal their existence but will yield additional information about the nature of the system. Before initiating a wide-ranging search for associating or dissociating conditions, it is worthwhile using a "brute force" test as a preliminary evaluation. One normally carries out one fractionation procedure under some (often physiological) buffer condition and a second under strongly denaturing conditions. One very simple, rapid approach for searching for subunits is to carry out electrophoresis under nondenaturing conditions, using the buffer in which the protein was isolated, followed by a second dimension under 33 E. J. F. vanBruggen and E. H. Wiebenga, J. Mol. Biol. 4, 1 (1962). 34 U. B. Sletyr, P. Messner, D. Pum, and M. SAra, eds., "Crystalline Bacterial Cell Surface Layers." Springer-Verlag, Berlin, 1988. 35 K.-R. Peters, personal communication.

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dissociating or denaturing conditions. The nature of the denaturing conditions may vary depending on the type of subunit and the association one expects to find. For example, one could run the second electrophoresis at extremes of pH, in the presence of urea or SDS, or in the presence or absence of other buffered components like calcium. Changes in mobility due to changes of buffer condition should be accounted for in analyzing the second dimension. That is, analysis should be based on the apparent size of the molecule under associating and possibly dissociating buffer conditions. If one is investigating the possibility that disulfide-linked subunits are present, SDS gel electrophoresis in the absence of reducing agents may be carried out as the first dimension, and SDS gel electrophoresis in the presence of reducing agents may be carried out in the second dimension. (Note: Because in-gel alkylation of disulfides is difficult, it is recommended that mercaptoacetate be included in the second gel running buffer to avoid reoxidation). Differences in the apparent molecular weight or the appearance of ¢nultiple components in the second dimension will indicate that disulfide-linked subunits were present. Differences in apparent molecular weight deduced from nondenaturing electrophoresis compared with the apparent molecular weight based on electrophoresis under completely denaturing conditions (SDS-PAGE) could indicate the presence of subunits, but one must consider the possibility that the electrophoretic behavior of the molecule is anomalous (i.e., extremes of asymmetry or intrinsic charge). In the case of subunits which ard in association/dissociation equilibrium, the definitive approach to determining the presence of subunits requires experimental determination of the apparent size of the molecule under conditions where the equilibrium is shifted to either associating or dissociating conditions. Because the dissociation implies that the samples being studied will be very dilute, very sensitive methotls must be used. Sedimentation equilibrium is very useful for determining the molecular weight of a native protein, and is therefore useful in determining the stoichiometry of the subunits in the final assembly. This is done by comparison of the native molecular weight with that obtained in separate experiments under denaturing conditions, such as by denaturing gel electrophoresis. If the protein is composed of subunits of a single molecular weight, division of the native molecular weight by the denatured molecular weight will provide the subunit stoichiometry. Likewise, for proteins that contain more than one chain, comparison of the native molecular weight to the sum of the monomer molecular weights often will allow the stoichiometry of the different subunits in the native complex to be determined. In cases where there is a wide discrepancy between the subunit

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molecular weights or when the native structure contains a large number of monomers, these estimate are imprecise. While the subject requires too much detail to be presented in full here, it is important to note that equilibrium sedimentation provides one of the most powerful means of determining association constants of mass action-driven macromolecular associations. 1~The method of experimentation is essentially as outlined above, except that experiments are done at concentrations that encompass the range where significant mass changes occur due to association. The association constant may be estimated using graphical means, or more accurately using nonlinear leastsquares analyses. H Gel-permeation chromatography can also be useful in determining the stoichiometry of the subunits in the final assembly. Again, this is done by comparison of the native molecular weight determined by gel filtration with that obtained under denaturing conditions, such as by SDS gel electrophoresis. One can test for association and, in principle, determine stoichiometry using the ratio of the native molecular weight and the denatured molecular weight. Gel chromatography is also useful for diagnosing interacting protein systems. If, for example, the protein of interest is undergoing a rapidly equilibrating assembly/disassembly, the peak shape is skewed, with the leading edge being hypersharp and the trailing edge being diffuse. Likewise, if the Kav increases with increasing protein loading concentration, it usually means that such an interaction is occurring, and that more detailed analyses will be required. 24

[44] A m i n o Acid Analysis

By JURIS OZOLS Amino acid analysis provides an important quantitative parameter in the characterization of isolated protein or peptide samples. Because of the availability of highly sensitive instruments for determining amino acids in the picomole range, the preparation of the sample for analysis is of prime importance in obtaining meaningful results. Analysis of a standard mixture of amino acids can be readily achieved reproducibly down to picomole levels, but obtaining accurate results from a microgram of protein after the necessary transfer and hydrolysis steps, without losses or contamination, is far more difficult.

METHODS IN ENZYMOLOGY, VOL. 182

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