Methods in Enzymology, Volume 4: Special Techniques for the Enzymologist

PREFACE The first three volumes of this series have dealt with the commonly employed methods for the preparation and assay of enzymes, coenzymes, and substrates. The present volume deals with certain special techniques which are considered to be of interest to those in the field of enzymology. Descriptions of many of these procedures are available in monographs dealing respectively with the physical chemistry of the proteins, with specialized methods for the measurement of metabolism, or with procedures for the synthesis, degradation, and measurement of isotopically labeled compounds. It nevertheless appeared worthwhile to have these descriptions written with the special problems of the enzymologist in mind and to have them brought together in a single volume. With the publication of this volume we bring to completion our original plans for a treatise on Methods in Enzymology. It has been our policy to select a recognized authority for the description of each laboratory procedure, with the aim of obtaining a reliable collection of reproducible methods. For the extent to which we have succeeded in this aim, ,we are grateful to all those investigators who have contributed. It would of course have been desirable that all procedures described in these four volumes be checked in an independent laboratory prior to publication. However, it is obvious that with such a system of checking, the publication of an organized treatise of this scope would have been impossible within any reasonable time period. Users of these volumes will undoubtedly find that certain articles are already in need of revision and that certain important new subjects are not covered at all. In an attempt to correct these unavoidable deficiencies, an organized single supplementary volume is planned, which will include material not heretofore covered, as well as revised procedures, to supplement all four of the published volumes. We welcome any suggestions concerning the content of this supplementary volume, which will be published approximately two years from this date.

Baltimore, June 1~, 1957

SIDNEY P. COLOWlCK NATHAN O. KAPLAN

Contributors to Volume IV Article numbers are

s h o w n in parentheses following the n a m e s Affiliations Listed are current.

S. ABRAHAM(22), University of California,

Berkeley, California I-I. S. ANKER (32), University of Chicago, Chicago, Illinois CAMILLO ARTOM (33), Bowman-Gray School of Medicine, Wake Forest College, Winston-Salem, North Carolina A. A. BENSON (36), Pennsylvania State University, State College, Pennsylvania I. A. BERNSTEIN (23), University of Michigan, Ann Arbor, Michigan M. BIER (5), Fordham University, New York, New York ](. BLOCH (29), Harvard University, Cambridge, Massachusetts R. It. BVRRIS (16), University of Wisconsin, Madison, Wisconsin M. CALVIN (36), University of California, Berkeley, California I. L. CHAIKOFF (35), University of California, Berkeley, California BRITTON CHANCE (12), University of Pennsylvania, Philadelphia, Pennsylvania MILDRED COHN (37), Washington University, St. Louis, Missouri S. P. COLOWICX (34), The Johns Hopkins University, Baltimore, Maryland F. H. C. CRICK (4), Cambridge University, Cambridge, England H. FRAENKEL-CONRAT (ll), University of California, Berkeley, California GEORGE GOMORI* (18), Palo Alto Medical Research Foundation, Palo Alto, California ])AVID M. GREENBERG (28), University of California, Berkeley, California W. Z. HASSID (22), University of California, Berkeley, California ROGER ~ . ]-~ERRIOTT (8), The Johns Hopkins University, Baltimore, Maryland N. O ]~-APLAN (34), Brandeis University, Waltham, Massachusetts

of contributors.

EDWARD D. KORN (26), National Insti-

tutes of Health, Bethesda, Maryland A. HELGE F. LAURELL (1A), University of

Uppsala, Uppsala, Sweden DONALD J. R. LAURENCE (7), Chester

Beatty Research Institute, London, England M. LEvY (10), New York University, New York, New York KATHARINE F. LEWIS (25), Lankenau Research Institute, Philadelphia, Pennsylvania OLIVER H. LOWRY (17), Washington University, St. Louis, Missouri WILFRIED F. H. M. MOMMAERTS (6),

School of Medicine, University of California, Los Angeles, California R. R. PORTER (9), The National Institute for Medical Research, London, England J. H. QUASTEL (13, 14), McGill-Montreal General Hospital Research Institute, Montreal, Canada MORTON ROTHSTEIN (28), University of California, Berkeley, California ANTHONY SAN PIETRO (21), The Johns Hopkins University, Baltimore, Maryland ]~. K. SCHACHMAN (2}, University of California, Berkeley, California P. G. SCHOLEFIELD (14), McGill-Montreal General Hospital Research Institute, Montreal, Canada DAVID SHEMIN (27), Columbia University, New York, New York FRITIOF S. SJOSTRAND (19), Karolinska Institute, Stockholm, Sweden DANIEL STEINBERG (20), National Institutes of Health, Bethesda, Maryland J. A. STEKOL (30), Lankenau Hospital Research Institute, Philadelphia, Pennsylvania It. E. SwIM (24), Western Reserve University, Cleveland, Ohio

* Deceased. vii

° . .

Vlll

CONTRIBUTORS TO VOLUME IV

University of California, Berkeley, California ALVIN TAUROG (35), University of California, Berkeley, California ARNE TISELIUS (1), University of Uppsala, Uppsala, Sweden SIDNEY UDENFRIEND (20), National Institutes of Health, Bethesda, Maryland M. F. UTTER (24), Western Reserve University, Cleveland, Ohio HAROLD TARVER (31),

WOLF VISHNIAC (15), Yale University,

New Haven, Connecticut Lankenau Research Institute, Philadelphia, Pennsylvania P. W. WILSON (16), University of Wisconsin, Madison, Wisconsin D. L. WOOD (3), Bell Telephone Laboratories Inc., Murray Hill, New Jersey HARLAND G. WOOD (23), Western Reserve University, Cleveland, Ohio SIDNEY WEINHOUSE (25),

Outline

of Volumes

I, II, III,

VOLUME PREPARATION Section I. General Preparative

AND

IV, and V

I

ASSAY

OF ENZYMES

Procedures

A. TissueSliceTechnique. B. TissueHomogenates.

C. Fractionation of Cellular Components. D. Methods of Extraction of Enzymes. E. Protein Fractionation. F. Preparation of Buffers.

Section II. Enzymes of Carbohydrate

Metabolism

A. Polysaccharide Cleavage and Synthesis. B. Disaccharide, Hexozide, and Glucuronide Metabolism. C. Metabolism of Hexoses. D. Metabolism of Pentoses. E. Metabolism of Three-Carbon Compounds. F. Reactions of Two-Carbon Compounds. G. Reactions of Formate.

Section III. Enzymes of Lipid Metabolism A. Fatty Acid Oxidation. B. Acyl Activation D. Phospholipid and Steroid Enzymes.

and Transfer. C. fipases and E&erases.

Section IV. Enzymes of Citric Acid Cycle VOLUME PREPARATION

AND

II

ASSAY

OF ENZYMES

Section I. Enzymes of Protein Metabolism A. Protein Hydrolyzing Enzymes. B. Enzymes in Amino Acid Metabolism (General). C. Specific Amino Acid Enzymes. D. Peptide Bond Synthesis. E. Enzymes in Urea Synthesis. F. Ammonia Liberating Enzymes. G. Nitrate Metabolism.

Section II. Enzymes of Nucleic Acid Metabolism A. Nucleases. B. Nucleosidases. C. Deaminazes. D. Oxidases. E. Nucleotide Synthesis.

Section III. Enzymes in Phosphate Metabolism A. Phozphomonoesterases. B. Phosphodiesteraaes. C. Inorganic Pyro- and Poly-phosphatazes. D. ATPases. E. Phosphate-Transferring Systems.

Section IV. Enzymes in Coenzyme and Vitamin

Metabolism

A. Synthesis and Degradation of Vitamins. B. Phozphorylation zyme Synthesis and Breakdown.

Section V. Respiratory

of Vitamins. C. Coen-

Enzymes

A. Pyridine Nucleotide-Linked, Enzymes. D. Unclassified.

Including Flavoproteina. B. Iron-Porphyrins. xi

C. Copper

xii

OUTLINE

OF

VOLUMES

I,

II,

VOLUME

PREPARATION AND

III,

IV,

AND

V

III

ASSAY

OF SUBSTRATES

Section I. Carbohydrates A. Polysaccharides. B. Monosaccharides. C. Sugar Phosphates and Related Compounds. D. Unphosphorylated Intermediates and Products of Fermentation and Respiration.

Section II. Lipids and Steroids A, Isolation and Determination of Lipids and Higher Fatty Acids. B. Preparation and Analysis of Phospholipids and Derivatives. C. Fractionation Procedures for Higher and Lower Fatty Acids. D. Preparation and Assay of Cholesterol and Ergosterol.

Section III.

Citric Acid Cycle Components

A. Chromatographic Compounds.

Analyses of Organic Acids. B. Specific Procedures for Individual

Section IV. Proteins and Derivatives A. General Procedures for Determination of Proteins and Amino Acids. B. General Procedures for Preparation of Peptides and Amino Acids. C. Specific Procedures for Isolation and Determination of Individual Amino Acids.

Section V. Nucleic Acids and Derivatives A. Determination, Isolation, and Characterization of Nucleic Acids. B. Determination, Isolation, Characterization, and Synthesis of Nucleotides and Nucleosides.

Section VI. Coenzymes and Related Phosphate Compounds A. General Procedures for Isolation, Determination, and Characterization of Phosphorus Compounds. B. Specific Procedures for N-Phosphates and Individual Coenzymes.

Section VII. Determination

of Inorganic Compounds

VOLUME SPECIAL

TECHNIQUES

IV

FOR THE

ENZYMOLOGIST

Section I. Techniques for Characterization of Proteins (Procedures and Interpretations) A. Electrophoresis; Macro and Micro. B. Ultracentrifugation and Related Techniques (Diffusion, Viscosity) for Molecular Size and Shape. C. Infra-red Spectrophotometry. D. X-ray Diffraction. E. Light Scattering Measurements. F. Flow Birefringence. G. Fluorescence Polarization and Other Fluorescence Techniques. H. The Soluhility Method for Protein Purity. I. Determination of Amino Acid Sequence in Proteins. J. Determination of Essential Groups for Enzyme Activity.

OUTLINE

OF

VOLUMES

Section II. Techniques for Metabolic

I,

II,

III,

IV,

AND

V

... x111

Studies

A. Measurement of Rapid Reaction Rates; Techniques and Applications, Including Determination of Spectra of Cytochromes and Other Electron Carriers in Respiring Cells. B. Use of Artificial Electron Acceptors in the Study of Dehydrogenases. C. Use of Percolation Technique for the Study of the Metabolism of Soil Microorganisms. D. Methods for Study of the Hill Reaction. E. Methods for Measurement of Nitrogen Fixation. F. Cytochemistry.

Section III. Techniques for Isotope Studies A. The Measurement of Isotopes. B. The Synthesis and Degradation of Labeled Compounds (Including Application to Metabolic Studies) : Monosaccharides and Polysaccharides; Citric Acid Cycle Intermediates; Glycolic, Glyoxylic and Oxalic Acids; Purines and Pyrimidines; Porphyrins; Amino Acids and Proteins; Steroids; Methylated Compounds and Derivatives; Sulfur Compounds; Fatty Acids; Phospholipids; &enzymes; Iodinated Compounds; Intermediates of Photosynthesis; On-Labeled Phosphorus Compounds.

VOLUME PREPARATION

Section I. General Preparative

AND

V

ASSAY

OF ENZYMES

Procedures

A. Column Chromatography of Proteins. B. Preparative Electrophoresis. C. Preparation and Solubilization of Particles (Bacterial, Mammalian, and Higher plant). D. Mammalian Cell Culture. E. Protoplasm.

Section II. Enzymes of Carbohydrate

Metabolism

A. Polysaccharide Cleavage and Synthesis. B. Disaccharide, Hexoside and Glucuronide Metabolism. C. Metabolism of Hexoses, Pentoses and 3-Carbon Compounds. D. Hexosamine and Sialic Acid Metabolism. E. Aromatic Ring Synthesis.

Section III. Enzymes of Lipid Metabolism A. Fatty Acid Synthesis and Breakdown. B. Acid Activating Enzymes. C. Phospholipid Synthesis and Breakdown. D. Steroid Metabolism.

Section IV. Enzymes of Citric Acid Cycle A. Krebs Cycle. B. Krebs-Kornberg Cycle. C. Related Enzymes.

Section V. Enzymes of Protein Metabolism Proteolytic Enzymes. B. Amino Acid Dehydrogenases and Transaminases. C. Amino Acid Activating Enzymes. D. Other Enzymes of Amino Acid Breakdown and Synthesis. E. Enzymes of Sulfur Metabolism. A.

xiv

Erratum P. 140, line 3: should read “19.21

for Volume I

g.” instead of “21.01

Erratum

g.”

for Volume II

P. 432, line 2: should read “6.0 ml.” instead of “60 ml.”

Errata for Volume III P. P. P. P.

663, line 3: should read “0.35 y” instead of “35 7.” 843, line 2 from bottom: should read “KH2POr” instead of “K2HPOd.” 948, line 6: should read “31” instead of “0.031.” 1055, entry in author index: Abraham, S., 64.

[1]

ELECTROPHORESIS

[1]

3

Electrophoresis

By ARNE TISELIUS Enzymes, as well as proteins in general, are ampholytes, and therefore their electrochemical properties in relation to the pH of the medium are useful for their characterization. The mobility in an electric field at defined pH values and particularly the pH value at which the migration is zero (the isoelectric point) are widely used for this purpose, as these properties can be determined accurately and conveniently with the methods now available. The name electrophoresis for such phenomena used to refer chiefly to colloids and substances of large molecular weight. However, as the methods gradually have been extended also to low molecular weight material, the new term of "ionophoresis" has been introduced for this case. As it is very difficult to draw a limit here, and as the phenomena involved and the experimental methods applied are practically the same, the author has preferred to use the term electrophoresis throughout this paper. A particularly interesting and valuable feature of electrophoresis is that the differences in rates of migration for the various constituents of a mixture lead to a certain separation, each component migrating at its own characteristic rate. Thus an electrophoretic analysis is possible which can give valuable information concerning the composition of complex mixtures in solution and the homogeneity or purity of a preparation. Another advantage is that this separation is such a gentle procedure, as it involves only the migration in a medium of approximately constant composition. For preparative purposes this may be very important, especially the recent developments in this field which have provided some very useful methods with many possible applications in enzymology as well in protein chemistry in general. A considerable experience collected during the past twenty years shows that the electrophoretic mobility is a highly specific property, and thus even closely similar proteins often may be differentiated by electrophoresis. This is true, however, only if a not too narrow range of pH is investigated, as in certain pH regions mobilities of different substances may differ very little. It should also be noted that the method, on account of its gentleness, will not resolve complexes of different substances unless they are extensively dissociated in solution under the conditions of the experiment. Many cases are known in which enzymes or other proteins, even after repeated crystallization, give inhomogeneous electrophoretic diagrams. Protein crystals tend to adsorb foreign material, but this phenomenon is probably less marked in electro-

4

TECHNIQUES FOR CHARACTERIZATION OF PROTEINS

[1]

phoretic separation where all components are in solution. Thus positively and negatively charged proteins may migrate almost independently of each other in buffered solutions. This is by no means universally true, however, and cases are known where interaction occurs. 1-3 Fairly stable complexes may be formed between dyes and proteins in solution, and these are not separated by electrophoresis. The demonstration of the existence of such complexes may, however, be of great interest from an entirely different point of view, if they are found in extracts of biological material which have not been subject to drastic operations. They give an indication of the presence of such associates in the original material which for many problems in enzyme chemistry may be significant. Complex formation may also be utilized to aid in the separation. The bestknown example is perhaps the electrophoretic fractionation of uncharged carbohydrates which have been complexed with boric acid (Consden and Stanier4). No doubt there are many interesting possibilities of increasing the specificity of electrophoretic analysis by such methods (see also Cann et al.4~). With methods which depend on differBOUNDARY ZONE ential migration through a medium it is SEPARATION SEPARATION convenient to distinguish between boundFIG. 1. Boundary and z o n e ary methods and zone methods, as entirely separation. different techniques are used (Fig. 1). In boundary separation the migration of the boundaries is observed, and the experiment is usually performed in a U-shaped tube where the protein solution is layered under a buffer solution. Thus the system is stabilized by the density differences, and the migration can take place in free solution without the addition of a stabilizing medium. In this case, however, only the fastest and slowest components can be isolated in substance. Intermediate components overlap, but although their separation is observed it cannot easily be utilized for a real isolation. In this respect zone separation is superior. A zone of the sample will, during its migration, split up into as many different zones as it contains differently migrating components, each zone consisting of a single component, which is easily isolated. As the zones have a higher density than the medium, however, 1L. G. Longsworthand D. A. MaeInnes, J. Gen. Physiol. 25, 507 (1942). W. Grassmann, in "The Chemical Structure of Proteins" (Wolstenholme and Cameron, eds.), pp. 55, 195. Churchill, London, 1953. s IV[.Lautout and M. de Serge, Compt. rend. 240, 1282 (1955). R. Consden and W. M. Stanier, Nature 169, 783 (1952). ~"J. R. Cann, J. G. Kirkwood, R. A. Brown, and O. J. Plescia, J. Am. Chem. Soc. 71, 1603_(1949).

/[:

[1]

ELECTROPHORESIS

5

they are not stable, and the important advantage of zone methods has to be gained at the price of stabilizing the system by using a suitable filling material, such as cellulose, starch powder, filter paper, or a density gradient. This introduces a new factor which may influence mobilities and isoelectric points in a way which is difficult to predict. But if the separation is the main purpose, these methods are very useful and have found many applications during the last years. Paper strip electrophoresis has become particularly popular as a micro-method and will be discussed in the following section by Dr. H. Laurell (Vol. IV [1A]). Zone electrophoresis in packed columns has recently been developed to a high degree of perfection. It bears the same relation to paper strip electrophoresis as column chromatography does to paper chromatography, and it allows the separation of considerable quantities of material. This method will therefore also be discussed in some detail. There are some special modifications of electrophoretic analysis without a clear-cut zone or boundary separation which have gained preparative importance. This is particularly true of the electrophoresis convection method and of methods depending on electrophoresis through membranes. The literature on electrophoresis is very extensive. A selection of references to books or articles of a more general interest is given below. 1. General principles and boundary methods. 5-~9 2. Theory. ~4,2° 5 H. A. Abramson, L. S. Moyer, and M. H. Gorin, "Electrophoresis of Proteins." Reinhold Publishing Corp., New York, 1942. 5 H. A. Abramson, E. J. Cohn, B. D. Davis, F. L. Horsfall, L. G. Longsworth, D. A. MacInnes, H. Mueller, and K. Stein, Ann. N . Y . Acad. Sei. 39, 105 (1939). 7 H. J. Antweiler, " D i e quantitative Elektrophorese in der Medizin." SpringerVerlag, Berlin, 1952. 8 D. R. Briggs, in "Biophysical Research M e t h o d s " (F. M. Uber, ed.), pp. 271-300. Interscience Publishers, New York, 1950. 9 H. B. Bull, "Physical Biochemistry," 2nd ed., pp. 161-190. John Wiley & Sons, New York, 1951. 10 L. G. Longsworth and D. A. MacInnes, Chem. Revs. 24, 271 (1939). n L. G. Longsworth, Chem. Revs. 30, 323 (1942). 1, j . A. Luetscher, Physiol. Revs. 27, 621 (1947). 13 K. G. Stern and M. Reiner, Yale J. Biol. and Med. 19, 67 (1946). 14 It. Svensson, Arkiv Kemi Mineral. Geol. 22A (1946). 15 E. Wiedemann, Scientia Pharm. 17, 45 (1949). 16 A. Tiselius, Scientia 45, 163 (1951). 17 A. Tiselius, Naturwissenschaften 37, 25 (1950). Is A. Tiselius, Trans. Faraday Soc. 35, 524 (1937). 19 A. Tiselius, Nova Acta Regiae Soc. Sci. Upsaliensis [4]7, No. 4 (1930). 25 L. G. Longsworth and D. A. MacInnes, J. Am. Chem. Soc. 62, 705 (1940).

6

TECHNIQUES FOR CHARACTERIZATION OF PROTEINS

[l]

3. Zone methods in general and preparative electrophoresis. 21-25 4. Paper electrophoresis (see Vol. IV [1A]).

Boundary Electrophoresis For boundary electrophoresis experiments a U-shaped tube is generally used in which the sample, dissolved in a suitable buffer solution, is allowed to form a layer under a buffer solution of the same composition, so that the boundaries will migrate in a medium of approximately constant composition. The electric current is introduced with reversible electrodes, separated from the boundaries by a sufficient volume of buffer solution to prevent changes in the composition produced at the electrodes to reach the boundaries. The boundaries are stabilized by the differences in density, and thus no special stabilizing medium is required as in zone electrophoresis. Consequently the " f r e e " electrophoretic migration of the components can be measured, and the true mobilities can be calculated directly from the experiments. To secure a sufficient stability the concentrations should not be too low, and it is generally difficult to obtain reliable results at concentrations below 0.01% (protein) unless special precautions are taken (low current). The heat produced by the current may cause convections, and when studying systems of high conductivity (e.g., serum) or low protein concentration it is essential to minimize this disturbance by running the experiment at a temperature just above 0 °. 18As water has a density maximum around -~4 °, the density differences produced by temperature changes in this region are very much smaller than at room temperature, for example. As low temperature is of advantage for other reasons in protein and enzyme work, most experiments of this type are nowadays being performed in refrigerated baths. To facilitate optical observation of the boundaries by the methods described below, the electrophoresis cell is given a rectangular cross section. The U-tube is assembled by one or several such cells, mounted with plane-parallel plates which are greased so that they can slide horizontally a sufficient distance to cut the contents of the tube into a number of fractions. This sliding arrangement is also used when the boundaries 21 H. G. Kunkel, in " M e t h o d s of Biochemical Analysis," Vol. I, pp. 141-170. Interscience Publishers, New York, 1954. 22 H. J. McDonald, "Ionography. Electrophoresis in Stabilized Media." Year Book

Publishers, Chicago, 1955. 23H. Svensson, Advances in Protein Chem. 4, 252 (1948). ~4R. L. M. Synge, in "General Methods of Separation: Electrical Transport Methods in Modern Methods of Plant Analysis, I" (Paech and Tracey, eds.), pp. 55-65. Springer-Verlag, Berlin, 1956. 25A. Tiselius and P. Flodin, Advances in Protein Chem. 8~ 461 (1955).

[1]

ELECTROPHORESIS

7

are to be formed at the beginning of the experiment. Most modern equipment of this type is provided with a "compensation device" which allows a slow and accurately controlled injection of buffer solution into one or the other of the electrode tubes during the experiment. Thus the boundaries may be displaced to any desired position in the tube, and fast-moving boundaries may be kept in the observation field much longer than would otherwise be possible.

FIG. 2. Schematic drawing of an apparatus (manufactured by LKB-Produkter Fabriks AB, Stockholm) for boundary electrophoresis, showing the composite U-tube and the electrodes. Cells 2, 3, and 4 are filled with the sample, and ceils 1 and 5 as well as the electrode vessels with buffer solution. Figure 2 shows a diagrammatic representation of a boundary electrophoresis apparatus with a composite U-tube. Although optical observation of the boundary migration is usually preferred in this type of work, it should be noted that electrophoretic mobilities may also be determined analytically in this apparatus ("transference method"). If cells 2, 3, and 4 in Fig. 2 at the start contain the sample, of known concentration (for example, nitrogen, or any enzymatic activity), and cells 1 and 5 contain only buffer, the experiment is allowed to run until cell 1 is partially filled with migrating material and cell 4 partially emptied. If the bottom cell (cell 3) composition does not change, the increase on one side must

8

TECHNIQUES FOR CHARACTERIZATION OF PROTEINS

[1]

be equal to the decrease on the other. If this difference is Am, the original concentration is c (in the same unit), and the cross-section area of the tube is q, the distance of migration is hm/cq. The quantity Am is determined by taking out the contents from each cell and analyzing at the end of the experiment. It should be noted that this method is applicable also when c and m refer to enzymatic activities and thus may be useful when the actual enzyme concentration in the sample is too low to make optical observation possible. In complicated systems valuable information may also be obtained by combining this procedure with optical observation of the boundaries, and it may be possible this way to determine which of the observed boundaries refers to the enzyme or other material with measurable biological activity which is being studied. Direct optical observation (by photography) of the migration of the boundaries is most commonly used, however, and has the great advantage that it offers a convenient way of studying the heterogeneity of the sample, as each differently migrating component usually will give rise to a separate boundary. The optical methods also allow a quantitative estimation of the relative amount of the different components present (electrophoretic analysis). As substances to be studied generally are colorless, refractive index or ultraviolet light absorption methods are usually preferred. One may distinguish between concentration and concentration-gradient methods, the latter being most suitable for heterogeneity studies. In the author's early experiments 19 the ultraviolet absorption method introduced by Svedberg and Nichols :6 for ultracentrifugation measurements was used. The electrophoresis U-tube is made of quartz and is photographed in transmitted ultraviolet light from a quartz mercury vapor lamp, the light being filtered through quartz cells containing bromine and chlorine. In later work when this method has been used for studying protein chromatography we have found that the somewhat troublesome chlorine-bromine filters may be replaced by a solution of cobalt and nickel sulfate, according to Kasha. 2~ As this method is not sensitive enough to analyze composite boundaries, the author 28 in 1937 introduced refractive index observation, based on the well-known Toepler schlieren method, which depends on gradients rather than on concentrations. The ultraviolet method has the advantage of being more specific than refractive index methods, however, and may perhaps deserve renewed attention, even though it requires the introduction of an all quartz system. Interferometric observation also records concentrations and has been introduced lately by several authors (see, ~6 T. Svedberg and J. B. Nichols, J. Am. Chem. Soc. 48, 3081 (1926). ~ M. Kasha, J. Opt. Soc. Amer. 88, 929 (1948). 28 A. Tiselius, Trans. Faraday Soc. 35, 524 (1937).

[1]

ELECTROPHORESIS

9

for example, Svensson 29 and Svensson and Forsberg~°). These methods are highly sensitive and are often useful, but the evaluation of the diagrams is perhaps somewhat more laborious than with the gradient methods. The former are particularly useful for determinations of relative amounts of the components, the latter for high resolution of boundary composition. A combination of both is probably most valuable. So far most results published have been obtained by gradient methods, and these will therefore be discussed in more detail. They are based on the deviation which a light beam suffers if it passes through a refractive index (that is, a concentration) gradient. Thus if the beam is made to pass horizontally through an electrophoresis tube containing a boundary, it will be deviated downward in those parts of the tube where the boundary is located. If a camera is focused on the tube and if the camera lens is provided with a horizontal edge diaphragm, light from all parts of the tube will be able to pass into the camera except from those levels where the boundary is situated, the light from these parts being deviated below the diaphragm edge. Thus on the image the boundary will come out as a black band. Each setting of the diaphragm corresponds to a certain deviation--that is, to a certain value of the refractive index gradient. As Longsworth ~1 first showed, a complete recording of the gradient throughout the boundary region as a function of the vertical distance in the electrophoresis tube may be obtained by coupling the movement of the edge with a movement of the photographic plate. The same result may also be obtained by a purely optical arrangement introduced by Philpot 32 and further developed by Svensson, ~3 where no movable parts are required and the recording is achieved by the aid of a cylindrical lens combined with a special diaphragm (Fig. 3). For details the reader is referred to the literature recommended in footnotes 5 to 15. The diagrams obtained give the refractive index gradient, d n / d x , as a function of the distance of migrating in the cell. Thus, by integration, the total n v a l u e - - t h a t is, the concentration--can be computed for each sufficiently well-separated component. Typical gradient diagrams are shown in Fig. 4. Both these procedures work satisfactorily and have found extensive use. In addition, mention should be made of the highly accurate "scale m e t h o d " by Lamm 34 which has found wide application especially in 59H. Svensson, Acta Chem. Scan& 3, 1170 (1949). 30H. Svensson and R. Forsberg, J. Opt. Soc. Amer. 44, 414 (1954). al L. G. Longsworth, J. Am. Chem. Soc. 61, 529 (1939). 3~j. S. L. Philpot, Nature 141, 283 (1938). a3H. Svensson, Kolloid-Z. 87, 181 (1939); see also ref. 14. 34O. Lamm, Z. physik. Chem. A138, 313 (1928).

10

TECHNIQUES FOR CHARACTERIZATION OF PROTEINS

Ill

ultracentrifugation and diffusion work but does not seem to have come into general use in electrophoresis, probably because the evaluation of the diagrams is somewhat laborious. Detailed instructions for working with the different types of commercially available electrophoresis apparatus are provided with the instruments and will not be discussed further here. Some general remarks about the procedure may, however, be useful to readers who have no previous experience in electrophoresis work. Boundary electrophoresis, including transference measurements (see p. 7), is so far the most accurate and Op//CO/ S~/s/ern

A

B

C

D

E

f

G

H

Fro. 3. Optical system for boundary observation in eleetrophoresis. The dashed beams . . . . and pass through the cell, C, outside the boundary region and are therefore not deviated but are focused at the upper end of the inclined slit, E. They pass through the cylindrical lens, G, without horizontal deviation and give rise to the "base line" in the curve on the film, H. The beam passes through the boundary in t h e cell, C, and is deviated to the lower end of the inclined slit, E, which gives rise to a horizontal deviation in the cylindric lens, G, resulting in an image point near the peak of the curve on the film, H. [From H. Svensson, Tek. Tidskr, $7, 1952.]

least objectionable method of determining mobilities and isoelectric points for proteins and other large molecular weight substances with a pronounced electrochemical character. It should always be observed that, even if these characteristics are sharply defined and very useful for the characterization of such substances, they depend markedly on other ions present, so that the buffer used and its concentration always should be stated. The other application is the study of homogeneity, and electrophoretic analysis is often used as a sensitive criterion on purity. One must remember, however, that differences may exist which are not reflected in the electrophoretic behavior, and under all conditions the analysis should be made at a number of different pH values before any conclusions are drawn. The possibility of complexes which are too weakly dissociated to be separated into their constituents by electrophoresis should also be kept in mind (cf. p. 4). There are some complications inherent in the method which often

[1]

ET.ECTI~OPHORESm

11

A scend;n9

J

j

~

AIo.

Descer~/n 9

t . 6lob. A

B FIG. 4. Typical boundary electrophoresis diagrams, as obtained by the apparatus and optical arrangement in Figs. 2 and 3. (A) Human pathological serum, showing the main protein components: albumin and a-, f~-, and -y-globulins. (B) Crystalline lactic dehydrogenase, containing two components. Descending pattern in phosphate buffer, pH 5.7, ionic strength 0.1. [According to J. B. Neilands, S c i e n c e 115, 143 (1952).]

12

TECHNIQUES FOR CHARACTERIZATION OF PROTEINS

[1]

puzzle research workers in this field and which have been given the common name of "boundary anomalies." Thus, one finds frequently that descending and ascending boundaries of the same substance and in the same experiment move at somewhat different rates. "False" boundaries, which are due to discontinuities in the buffer medium and thus do not represent new components, are sometimes observed, especially in concentrated solutions, as the well-known ~-boundary in serum experiments. As a rule these disturbances are much reduced if the protein concentration is lowered. The anomalies are more marked, however, with substances of lower molecular weight, and they make it generally impossible to study by this method the migration of amino acids, for example. The general problem of the migration boundaries in electrolyte solutions is a very complex one, but the theory has been worked out in detail (see, for example, Longsworth and MacInnes, 2° Dole, 35 and Svensson~4). Moving boundary electrophoresis of proteins and similar substances is to be regarded as a limiting case, in which one component (the protein) contributes relatively little to the electrolytic conductivity of the system, although it is present in an appreciable concentration. Thus the migration of the protein does not change appreciably the distribution of the potential gradient, and it moves in a medium of practically constant composition and therefore in a constant electric field. This is generally only approximately true, however. If substances are studied for which the ratio conductivity:weight is higher and approaches that value for the buffer ions used, the anomalies dominate the phenomenon and make the interpretation of the results very difficult The decisive factor is thus not the molecular size but the conductivity per unit weight of the substance to be studied The methods of zone electrophoresis to be described below have the advantage of showing a much greater latitude toward boundary anomalies and thus permit the study of substances which previously could not be subject to electrophoresis.

Zone Electrophoresis in Packed Columns and Similar Media (Except Paper Strip Electrophoresis) The development in this field has been particularly rapid during the last few years, and no attempt will be made here to present the historical development. The author has preferred to review the present situation with particular emphasis on procedures of which he has had personal experience. The apparatus required for zone electrophoresis is comparatively simple. Optical observation is not necessary (although in some cases it a~ V. P. Dole, J. Am. Chem. Soc. 67, 1119 (1945).

[l]

ELECTROPtIORESIS

13

would no doubt be of advantage). The zones are localized by analytical or by staining methods. The crucial problem is the filling material necessary for the stabilization of the zones. Proteins and other substances to be studied are often adsorbed to finely divided powders. This tends to give rise to tailing phenomena which greatly interfere with the separation. Thus sometimes the mobility may be reduced to practically zero. The stabilizer should be hydrophilic but insoluble. If it is a powder it should be easy to pack into homogeneous columns which contain a sufficient amount of the solvent medium. There will always be some electrical transport of the solvent through the stabilizer during the experiment (electroendosmosis). This will not interfere with the separation as it only moves the system of zones in the direction of electroosmotic flow, but experience shows that it is important to keep this flow as low as possible. Among powdered materials cellulose and starch have been most widely used so far. In the author's laboratory Flodin and Kupke 3~have found that cellulose powder prepared from cotton by alcoholysis is superior to ordinary cellulose, and this material is now preferred in all our zone electrophoresis investigations. It is advisable, however, to test the material for its adsorption properties on the system to be studied by running a zone through a small column without c u r r e n t - - t h a t is a chromatographic experiment. Gels are often permeable enough also to large protein molecules to make them suitable as stabilizing media for zone electrophoresis. They have the advantage of giving sufficient stabilization at low dry weight, and thus adsorption phenomena are less disturbing. They often give beautiful zones which may be observed optically if the gel is translucent. Silica gel was used by Consden et al.'~7 in their " i o n o p h o r e t i c " separations of peptides and amino acids, but this gel appears to be less suitable for proteins. Agar gel has been used with success by Gordon et al., 3~ and recently Grabar et al. '39 have made extensive electrophoretic investigations by this technique, also combining it with the Oudin serological precipitation method which makes possible a very sensitive identification of different antigens (immuno-clectrophoresis). Smithies t° has obtained very beautiful separations of proteins in starch gels. A disadvantage of the gels is that it is difficult to elute the zones quantitatively without contamination. In this respect powdered stabi36p. Flodin and D. W. Kupke, Biochim. et Biophys. Acta 21, 368 (1956). 37R. Consden, A. H. Gordon, and A. J. P. Martin, Bioehem. J. 40, 33 (1946). a8A. H. Gordon, B. Keil,' and K. Sebesta, Nature 164, 418 (1949). ~9p. Grabar, C. A. Williams, Jr., and J. Courcon, Biochim. et Biophys. Acta 17, 67 (1955). 400. Smithies, Biochem. J. 61, 629 (1955).

[1]

ELECTROPHORESIS

15

-:-4 D4

---2 -_w

-----

--A,

z----.--

----AJ

~_w_

0

_.--__ -

--2-

~.-

--_--.

--_--.

Fu~. 5. Large t y p e of zone c o l u m n electrophoresis a p p a r a t u s according to J. P o r a t h

[Biochim. et Biophys. Acta 22~ 151 (1956)]. Details in the text.

16

TECHNIQUES FOR CHARACTERIZATION OF PROTEINS

[1]

.c. .j

~5

!1 ~o

2b

~o

~0

~

60

7o

'

~o

9o

Tube r~m~er

~o

A Fro. 6A. Mixture of "neutral" amino acids in I N acetic acid resolved by 61 hours of electrophoresis at 30 ma. (2300 v.) in a column 2 X 250 cm. packed with cellulose powder. E is the extinction as determined by the ninhydrin reaction. Each amino acid, 2 mg. [J. Porath, Biochim. et Biophys. Acta 22, 151 (1956).]

.~

~70

~,a.~

~

0

,~ I I

~

~ 11

~0

~00

I,/

//

thO

"~"

I1

H

200 250 [itlcft~e, rd vol~jrn~,ml

B FTO. 6B. Mixture of vitamin B~ components in acetate buffer, p H 5,1, ionic strength 0.05, resolved by 14 hours of electrophoresisat 18 ma. in a column 3 X 50 cm. packed with starch. Each component 2.6 mg. [From N. Siliprandi, D. Siliprandi, and H. Lis, Biochim. et Biophys. Acta 14, 212 (1954).]

[1]

ELECTROPHORESIS

17

l a r g e c o l u m n s t h e c a p a c i t y is c o n s i d e r a b l e . T h u s on c o l u m n s of 150-cm. l e n g t h a n d 6.5-cm. d i a m e t e r as m u c h as 20 to 30 g. of p r o t e i n c a n be s e p a r a t e d a n d s e r u m s a m p l e s c o r r e s p o n d i n g t o 200 ml. u n d i l u t e d s e r u m h a v e b e e n f r a c t i o n a t e d . P e p t i d e s , a m i n o acids, a n d o t h e r low m o l e c u l a r w e i g h t m a t e r i a l l e n d t h e m s e l v e s v e r y well to t h i s k i n d of s e p a r a t i o n . F i g u r e s 6 A - C s h o w s o m e e x a m p l e s of r e s u l t s o b t a i n e d w i t h y e a s t enolase, 2.0

2.0

o

~I,5

1.5

2

~ I.0

1.0

O

~0.5

0.5 5"

20

30

40

FRACTION NUMBER

C Fro. 6C. Cellulose column electrophoresis of yeast enolase. Column dimensions: 1.8 cm., diameter; 70 cm., length. Buffer: 0.0154 M NaH~P04, 0.0115 M Na:B4OT, pH 8.2, # = 0.05. Current: 15 ma. Time: 45 hr. The experiment was performed in a cold room (4°). The protein concentration (O) of the fractions was determined by measuring the optical density at 280 m# in a Beckman DU spectrophotometer using 1-cm. cells, 1 rag. per milliliter giving a value of 0.895. The activity (A) was estimated as the change in optical density at 240 m~ per minute (&D.~40/min.) at 22 ° when 10 p]. of a fraction was added to I ml. of substrate solution (2.4 X 10-3 M DL-2-phosphoglycerate and l0 -3 M mg. ++ in tris(hydroxymethyl)aminomethane-HC1 buffer, pH 7.4, ~ = 0.05) in a 1-cm. cell. [Experiments by Dr. B. Malmstr6m, Uppsala, to be published.[ t h e d a t a b e i n g g i v e n in t h e figure legend. W h e n s e p a r a t i n g low m o l e c u l a r w e i g h t s u b s t a n c e s v o l a t i l e buffers as r e c o m m e n d e d b y P o r a t h 48 a r e v e r y useful, as d i a l y s i s c a n n o t be u s e d in t h i s case to g e t r i d of t h e e l e c t r o l y t e s c o n t a i n e d in t h e f r a c t i o n s i s o l a t e d . P r e c i s e m o b i l i t y m e a s u r e m e n t s c a n n o t be m a d e in zone m e t h o d s w h e r e s t a b i l i z i n g m e d i a a r e used. I t a p p e a r s , h o w e v e r , t h a t t h e d i f f e r e n t c o m p o n e n t s e m e r g e f r o m t h e c o l u m n in t h e o r d e r t o be e x p e c t e d f r o m t h e i r m o b i l i t i e s in free s o l u t i o n . K o l i n , 49 S v e n s s o n a n d V a l m e t , 5° a n d 48j. Porath, Nature 174, 478 (1955). 49 A. Kolin, Proc. Natl. Acad. Sci. U.S. 41, 101 (1955). 5o H. Svensson and E. Vahnet, Science Tools 2, 11 (1955).

[1]

ELECTROPHORESIS

19

vessel and will therefore flow as a narrow vertical zone through the medium and leave the cell through one or a few of the bottom outlets. If a horizontal electric field is applied, however, the zone will split up as shown in the figure, and separated fractions may be collected at suitable outlets. In principle, it should be possible to fractionate very large quantities by such procedures, and the method may even gain industrial application. Maintaining constant conditions of flow and a constant current is very essential for obtaining good resolution. Brattsten 56-5~ has recently published a detailed study of the method and has described its application to serum protein fractionation. For smaller quantities sheets of filter paper may be used which simplifies the apparatus. Further information about this method may also be found in a review by Durrum et al. 59 So far, the capacity does not seem to surpass what can be conveniently handled in a zone column apparatus of the type described above (pp. 14-15), which also has the advantage of simpler construction and more easily controlled manipulation. For still larger capacities the continuous zone electrophoresis no doubt offers promise.

Other Methods of Preparative Electrophoretic Separation The above methods have in common that they allow a control of the separation by observation of boundaries or zones either in the electrophoresis tube itself or in the elution diagrams from the columns. There are some other methods where this is not possible (at least not directly) but which have proved to be quite useful in preparative work. This is particularly true of the "electrophoresis convection" method first proposed by Kirkwood 6° and experimentally realized by Nielsen and Kirkwood. 6~ A description of the apparatus is given in papers by Cann el al. 4~ and Timasheff et al. 82 The latter paper describes a semicontimlou~ modification of the method and gives further references. The method is based on the layering phenomenon sometimes observed in electrodialysis of proteins between vertical membranes. The proteins are concentrated by migration toward one membrane and tend to form a layer, which on account of its higher density will be transported by 5~ I. Brattsten, Arkiv Kemi 4~ 503 (1952). 57 I. Brattsten, Arkiv Kemi 8, 205, 227, 347 (1955). 5a I. Brattsten, Continuous Zone Electrophoresis by Crossed Velocity Fields in a Supporting Medium, Dissertation, Uppsala, 1955. ~ R. J. Block, E. L. Durrum, and G. Zweig, " A Manual of Paper Chromatography and Paper Electrophoresis," pp. 380-390. Academic Press, New York, 1955. s 0 j. E. Kirkwood, J. Chem. Phys. 9, 878 (1941). e~L. E. Nielsen and J. G. Kirkwood, J. Am. Chem. Soc. 68, 181 (1946). 6~ S. N. Timasheff, J. B. Shumaker, Jr., and J. G. Kirkwood, Arch. Biochem. and Biophys. 47, 455 (1953).

20

TECHNIQUES FOR CHARACTERIZATION OF PROTEINS

[l]

convection to the bottom of the cell. Several sharp horizontal boundaries, separating layers of different composition, may thus often be obtained. The Kirkwood apparatus consists essentially of a flat rectangular cell, separated by large surface membranes from the electrode compartments, through which a suitable buffer solution is circulated. The membranes should be semipermeable, thus allowing the buffer ions but not the protein material to pass freely. In the course of the experiment the fastest migrating substances are collected toward the bottom and the slowest at the top. The method is in principle analogous to the well-known Clusius thermodiffusion method for separation of gases. It has been applied with notable success to the fractionation of serum proteins and insulin, for example, and should be easy to adopt for large-scale work. Multimembrane apparatus where the material to be separated is migrating through the membranes has found some use for the electrophoretic separation of peptides and amino acids. With suitable membranes proteins and other large molecular weight material also may be fractionated. The apparatus required is of the same type as a common electrodialyzer and thus quite simple. The membranes serve to keep the separated components apart, but also have a very marked effect on the course of the separation. The result depends largely on the rates of migration within the membranes, which may differ quite considerably both absolutely and relatively from m0bilities in free solution, as the membrane charge and other specific effects have a decisive influence. Thus it is usually necessary to combine membranes of different kinds. Specific effects can naturally be utilized to improve the separation. A detailed discussion of methods of this type has been given by Svensson. 28 Mould and Synge 63 have had some success in attempts to separate substances according to molecular size by migrating them in collodion strips with the aid of electroosmotic transport of the solvent (electrokinetic ultrafiltration). In part the effects obtained seem to be due to adsorption , but the method appears to have interesting possibilities, also in zone separation. t3 D. L. Mould and R. L. M. Synge, Biochem. J. 58, 571 (1954).

32

TECHNIQUES FOR CHARACTERIZATION OF PROTEINS

[2]

[2] Ultracentrifugation, Diffusion, and Viscometry B y H. K. SCHACHMAN

I. Introduction Theoretical and experimental advances which have been made in recent years in ultraeentrifugation, diffusion, and viscometry have resulted in the availability of powerful methods for the determination both of the degree of purity of a given preparation of a protein and of the size and shape of the macromolecules. It is of importance, therefore, that enzymologists be aware of these methods, their potentialities, and their limitations. In addition to considerations of purity and molecular size we will also discuss in this chapter some applications of diffusion and sedimentation methods which possess special appeal to the enzymologist. Techniques are available, although infrequently used, whereby the sedimentation and diffusion of a biologically active material can be studied, even in impure preparations and with only microgram quantities of material, as long as there is a sensitive and accurate biological assay specific for the entity under investigation. With these methods, reasonably accurate values of the molecular weight of an enzyme can be obtained even before purification of the enzyme is achieved. Some of the methods we will discuss are rapid, and the techniques can be performed at low temperature so that labile enzymes can be studied without danger of inactivation. In most cases, a fairly complete study can be performed with as little as 10 to 20 mg. of material, and in special circumstances microgram quantities will suffice. The same methods are equally applicable to the examination of molecules smaller than most proteins and can be used therefore in studies of coenzymes and substrates or the products of proteolytic enzymes or nueleases. In this way, these physical methods can be used to study the mechanism of enzymatic action on large substrate molecules. Ultracentrifugation, in particular, is of use in the study of interaction of enzyme molecules with themselves as in association equilibria or in interaction of enzyme molecules with other molecules such as DPN. For all the work described in this chapter there is now available commercial apparatus which, though expensive and complicated, is generally installed by the manufacturer ready for operation. The detailed description and explanation of the working parts of this equipment will be omitted from our discussion as will be those operating procedures generally supplied by the manufacturer in technical manuals. Only special

[9.]

ULTRACENTRIFUG&TION'~ DIFFUSION, AND VISCOMETRY

33

parts of the experimental procedures common to all different makes of apparatus and requiring techniques developed through experience will be elaborated upon in this discussion.

II. Ultracentrifugation Introduction Ultracentrifuges can be used either to study the velocity of sedimentation of macromolecules through a solution under the influence of a centrifugal field or to study the distribution of the macromolecules in a centrifuge cell which is rotating at much lower speeds so that the molecules obtain equilibrium positions throughout the cell. The former method is known as the sedimentation velocity method and has to date been the more widely used. In a sedimentation velocity experiment the ultracentrifuge is operated at speeds up to 60,000 r.p.m. so that the solute molecules which initially were uniformly distributed throughout the solution in the ultracentrifuge cell are caused to settle toward the periphery of the cell. This migration of the solute molecules leaves a region containing only solvent molecules (if the solute molecules are more dense than the solvent, then the newly created solvent region will be near the meniscus; for solutes which are less dense than the solvent, such as lipoproteins in concentrated salt solutions, the solute will float, leading to a region of pure solvent at the bottom of the cell) in addition to the region in the cell where the concentration of solute is uniform. Between the supernatant and the solution of uniform concentration, known as the plateau region, there is a transition zone in which the co~centration varies with distance from the axis of rotation. This transition zone is called the boundary; and the sedimentation velocity method is based on observations, by optical methods, of the movement of the boundary which in turn is a measure of the movement of the solute molecules in the plateau region. Figure 1A shows schematic drawings of the concentration of solute as a function of distance in the cell at different times. Since the more commonly used optical systems do not record concentration, but rather the change in concentration with distance, the corresponding curves are drawn in Fig. lB. It is such diagrams, as illustrated in Fig. 1B, which are used to study the purity of a given preparation and to determine the sedimentation coefficient, s, of the sedimenting material. It should be noted that the sedimentation velocity method permits the direct measurement of sedimentation coefficients which are related to the size and shape of the sedimenting molecules, but other independent data are needed for the evaluation of molecular weights. In the second application of the ultracentrifuge, known as the sedimen-

34

T E C H N I Q U E S FOR CHARACTERIZATION OF P R O T E I N S

[2]

tation equilibrium method, the ultracentrifuge is operated at relatively low speeds (about 8000 r.p.m, for a protein with a molecular weight of 69,000). Under these conditions the transport of solute in a centrifugal direction due to sedimentation is sufficiently slow as to be counterbalanced by transport in a centripetal direction by the diffusion resulting FROM M E N I S C U S ( C M )

DISTANCE 0

I

I00 Z 0

oi8

I

I

I

,.2

S

1-.IZ w ¢_) z

o ¢3

oi4

50-

J z (.9 ¢e o

/ 0 '

I

B

I-Z tl.I

£9, Z 0 I.n,F.z hi (...) Z 0 U I

I

6.O 6,4 6~8 L2 DISTANCE FROM AXIS OF ROTATION (CM)

Fro. 1. Plot of concentration (A) and concentration gradient (B) versus distance from the axis of rotation during a sedimentation velocity experiment. Sedimentation is to the right.

from the concentration gradient created by the partial sedimentation of the macromolecules. During the first stages of a sedimentation equilibrium run, the concentration decreases at the meniscus and increases at the bottom of the cell, owing to sedimentation. As a consequence of back diffusion, however, a region devoid of solute is not created as in the sedimentation velocity method. Instead the concentration will remain finite at the meniscus as long as the centrifuge is not operated at too high a speed. Under ideal circumstances the concentration at the meniscus

[9.]

ULTRA.CENTRIFUGATION',

DIFFUSION,

AND

VISCOMETRY

35

will approach a value about one-half its initial value. Similarly, sedimentation plus back diffusion at the bottom of the cell leads to a region in which the concentration is higher than the original concentration. In the sedimentation velocity method, where the role of diffusion is much less important, this region of high concentration is restricted to a very thill

O z

DISTANCE FROMMENISCUS(CM) 0.4 0.8 1.2 i ~

o_ I-< n-I-z ~A Z 0°

IO0

Z 0 ~

A

kz hi

B

Z

_o i.n,i-.z

~

4j

Z 0u

g i

i

6.0 6.4 6.8 7.2 DISTANCE FROMA X I S O F R O T A T I O N ( C M ) Fla. 2. Plot of concentration (A) and concentration gradient (B) versus distance from the axis of rotation during a sedimentation equilibrium experiment. Centrifugal direction is toward the right. layer on the cell bottom where the sedimented material is packed as a gel-like pellet. In the center of the cell, during the early stages of a sedimentation equilibrium study, the concentration is independent of position in the cell and practically the same as the initial concentration. As the run proceeds, the plateau region disappears and there is only one position in the cell having a concentration equal to the initial concentration. Finally, after a considerable period of time an equilibrium state is reached after which no further changes in concentration occur with time. These changes in concentration with distance as a function of time are

36

TECHNIQUES FOR CHARA.CTERIZA.TION" OF PROTEIN'S

[2]

visualized in Fig. 2A, and the corresponding gradient curves are illustrated in Fig. 2B. In cont-rast to the sedimentation velocity method, measurements of the concentration distribution at sedimentation equilibrium give directly the molecular weight of the sedimenting macromolecules (both methods require knowledge of the partial specific volume of the macromolecule, and this will be discussed later). Despite this obvious advantage and the additional factor that the theoretical foundations for the equilibrium method are more firm than those for the sedimentation velocity method, there are few recorded examples of the application of the sedimentation equilibrium method to the study of enzymes. This seemingly anomalous situation has arisen both because of the lack of apparatus capable of sustained, continuous use for the long periods (days in the case of proteins) required before equilibrium is reached, and because many proteins are not sufficiently stable to withstand such experiments. A commercial apparatus is now available which is capable of continuous operation even at low temperatures, but it is of greater importance to the enzymologist that considerable theoretical advances have been made which enable us now to determine molecular weights in times as short as one hour. Owing largely to the theoretical work of Archibald I and certain technical improvements especially with regard to optical methods, it seems safe to predict that measurements during the approach to sedimentation equilibrium will become as routine as those by the currently more popular sedimentation velocity method. Because of the importance of these developments we will present in this chapter the method involving the approach to sedimentation equilibrium despite the knowledge that the method is still in its infancy and further refinements both in theory and technique may render the discussion obsolete. We are here using the term "approach to sedimentation equilibrium" rather loosely, since this title leads to the implication that the experiments are conducted for times almost sufficient to attain complete equilibrium. Actually for the use of the equations of Archibald there are no restrictions that the system be near equilibrium. There might be serious objection then to our inclusion of this method under the section entitled "sedimentation equilibrium," especially since this method is clearly not a thermodynamic one. To some extent our classification is arbitrary although it can be justified operationally. If the experiments are designed so as to measure most accurately the velocity of transport of material through the cell as by the proper choice of the centrifugal field for the system under investigation, then the experiments can be classified as sedimentation velocity studies. If, alternatively, the experimental condi1 W. J. Archibald, J. Phys. & Colloid Chem. 51, 1204 (1947).

[9.]

ULTRACENTRIFUGATION, DIFFUSION~ AND VISCOMETRY

37

tions are selected so as to measure precisely the distribution of matter throughout the cell, then the experiments are of the sedimentation equilibrium type. Most ultracentrifuge work done at present is performed in the Model E ultracentrifuge manufactured by the Spinco Division, Beckman Instruments, Inc., Belmont, California. This instrument is completely equipped with the necessary accessories for a variety of ultracentrifuge studies. The majority of the work is performed with the schlieren optical system for viewing and photographing the movement of sedimenting materials. Some special applications, however, can be better performed by absorption techniques using either ultraviolet light or visible light of the appropriate wavelength. A brief description of applications using light absorption techniques will be presented in a later section. A variety of ultracentrifuge cells in optical thicknesses from 1.5 ram. to 30 ram. are available, and the choice of cell depends to some extent on the type of study. For very dilute solutions the cells with the longer optical path are desirable, even though they require larger volumes of solution and even a special rotor. The smaller cells require even less than 0.2 ml. of solution; but, of course, optical registration of the boundary suffers unless high concentrations are used. Cells can be either 4 ° sectors or 2 ° sectors; the latter require longer exposure times and more care in alignment of the cell in the rotor, but they have the decided advantage of requiring smaller volumes of solution. Cells should always be cleaned and dried at the conclusion of the run because salt solutions can cause etching of the cells. Filling needles should have their tips ground flat so as to remove sharp points, and special caution is needed to avoid scratching of the cells. For alkaline or acid solutions, cells with a plastic centerpiece made of Kel-F or epoxy are recommended, and the quality of the latter is so high that they may prove to be the cell of greatest practicality and economy. With plastic cells, no gaskets are required between the centerpiece and the windows, so that assembly of the cells is facilitated. Doublesector cells are available in which one section can be filled with the solution and the other with the solvent. Although the patterns are not so distinct with these double cells, they furnish a base line superimposed on the pattern containing the sedimenting protein, and they can be of use in sedimentation velocity studies. Also special optical selectors facilitate the simultaneous recording of more than one ultracentrifugal analysis in a special rotor containing two or more cells. For equilibrium runs the special one-third speed attachment for the ultracentrifuge is necessary. The optical systems have for years had a bar as the schlieren diaphragm, but it is clear that a phase plate, now commercially available,

38

T E C H N I Q U E S FOR CHARkCTERIZATION OF PROTEINS

[2]

gives much better results and is strongly recommended for all types of work and especially for sedimentation equilibrium. The phase plate can be mounted on the optical track in place of the bar. Since it has been found in recent years that the rotor cools about 0.8 ° on stretching, owing to the high speeds, there has been a growing need for a continuously reading indicator of the temperature of the rotor during the run. This is now available, and the same unit can also control the temperature by activating a heater in the vacuum chamber. For long runs, especially at low temperatures, this is a valuable addition to the ultracentrifuge. Most of the patterns are photographed with Kodak spectroscopic plates, Type I-D(2), with a yellow filter in the optical system, but higher resolution photographs can be obtained with either Kodak M or Kodak Metallographic plates. These are slower plates and longer exposure times are needed, but this disadvantage is largely offset by the replacement of the half-surfaced viewing mirror with the newly developed swing-out mirror. For colored materials like hemoglobin, the yellow filter is replaced by a red filter, and red-sensitive I-N plates are used.

Sedimentation Equilibrium Principle. Although the time required for attainment of equilibrium may be as long as 4 days for a protein of molecular weight about 60,000, Archibald has shown how molecular weights can be calculated from data obtained during the early stages of the run. He pointed out that solute does not leave the centrifuge cell either at the meniscus or the bottom of the cell and that, therefore, the conditions for equilibrium (transport of solute by sedimentation equals transport by diffusion) are fulfilled at these two places in the cell at all times of the run. The equation describing this condition is identical to that which holds elsewhere in the cell when equilibrium is attained, and we can write for a homogeneous material M -

RT (1 -

?p)~2

(dc/dx)m _ x~cm

RT (1 -

~p)~2

(dc/dX)b

(1)

XbCb

In equation 1, M and I~ are the anhydrous molecular weight and the partial specific volume of the solute, R is the gas constant, 8.314 X 107 ergs/mole/degree, T is the absolute temperature, p is the density of the solution, (o is the angular velocity of the centrifuge rotor in radians per second, (r.p.m.) (27r)/60, and cm and (dc/dx)m are the concentration and concentration gradient at the position x~, which is the distance from the axis of rotation to the meniscus. The corresponding quantities with the subscript b refer to the bottom of the cell. The procedure requires knowledge of the concentration gradients, (dc/dx)m and (dc/dX)b, and the concentrations, c~ and Cb. The former can

[2]

ULTRACENTRIFUGATION, DIFFUSION~ AND VISCOMETRY

39

be obtained directly from the photographic plates after suitable corrections for optical constants or with the aid of an auxiliary sedimentation run, data from which obviate measurement of the optical constants both of the apparatus and the solution. As shown in Fig. 2A, cm and cb are, respectively, less and greater than Co, the initial concentration; if the measurements are made early in the run, cm and cb are almost equal to Co. Corrections for the change in concentration at the meniscus and bottom of the cell are made with the equations derived by Klainer and Kegeles: ~ em ~

Co

- -m 2 X

and cb = co d- xb ~1

x2(dc/dx)dx

//

(2) x2(de/dx)d x

where X refers to a position in the plateau region ( d c / d x equals zero). It should be emphasized that the method as presented here, employing equation 2, is that proposed by Klainer and Kegeles, and it requires that the ultracentrifuge run be of limited duration such that there is still a region in the cell in which the concentration is independent of position, i.e., some plateau region still exists. This is clearly evident from the photographic plates, since the plateau region produces the fiat portion of the curve (usually known as the base line) in the optical system commonly employed. If the run is continued for longer times so that there is no longer a fiat portion of the curve seen on the photographic plates, then equation 2 is not applicable and cm and Cb must be evaluated in a manner different from that proposed by Klainer and Kegeles. Since accurate results can be obtained in the shorter runs, we will emphasize in our discussion the evaluation of molecular weights from equations 1 and 2. When the greatest accuracy is desired and experimental factors such as the lability of the enzyme do not preclude runs of long duration, it is advantageous to continue the ultracentrifuge runs for longer times, even after the plateau region is lost. The calculations then become laborious unless complete equilibrium throughout the cell is attained, in which case there is a minimum of calculations. In order to demonstrate the procedures, a sample calculation is included. Whenever such long runs are contemplated it is advisable to fill the ultracentrifuge cell to only about one third of its normal capacity. This reduction in the height of the liquid column, in a radial direction, will materially reduce the length of time required for attainment of equilibrium. E x p e r i m e n t a l Procedure. About 0.8 ml. of solution of enzyme at a concentration between 0.5 and 1.0% is required for the measurements. 2 S. M, Klainer and G, Kegeles, J. Phys. Chem. 59, 952 (1955).

40

TECHNIQUES FOR CHARACTERIZATION OF PROTEINS

[2]

Knowledge of the exact concentration of the protein is not necessary despite the fact that co appears in equation 2. If the protein is available in a dried form devoid of impurities, then dissolution of the protein in the desired buffer will suffice; otherwise it is necessary to dialyze the protein solution against the buffer to equilibrate the two liquids. An additional small amount of the dialyzate or buffer used to dissolve the enzyme is also necessary. Buffers with ionic strengths of 0.1 are desired in order to minimize electrostatic effects caused by the sedimentation of charged macromolecules. Two and possibly three ultracentrifuge runs are required, and these will now be discussed in the order in which they are customarily performed. For the first, the sedimentation equilibrium run, a conventional 12-mm. ultracentrifuge cell is required. In general, 4 ° sector centerpieces are used, but if material is in short supply a 2° sector cell will work well and some saving of material can be effected by its use. Before filling the cell with the solution, 0.1 ml. of Dow-Corning No. 555 silicone fluid is introduced into the cell by means of a 0.25-ml. syringe with a No. 22 needle. The solution of protein is then added to the cell, which will hold about 0.6 ml. if the 4 ° centerpiece is used. The layer of silicone fluid serves a double purpose. First, it creates a base for the aqueous solution which has the contour of an arc drawn from the center of rotation. This eliminates the convective disturbances which result when the aqueous solution is placed directly in the cell, the bottom of which does not have the proper shape. Second, it provides a dense, transparent medium for the bottom so that the bottom of the aqueous phase is clearly visible on the photographic plate. Thickening of the line between the two phases during the run is a good indication of the presence of aggregated or denatured material. Without this dense, transparent layer in the bottom of the cell, the values of xb, cb, and (dc/dx)b are not so readily measurable because of the arrangement of the optical system in existing equipment and the deviation of light due to the concentration gradient at the bottom of the cell. The use of silicone fluids or any noninteracting dense liquid effects a considerable saving in calculations plus increased precision in the evaluation of cb and (dc/dx)b. After the cell is sealed in the conventional manner and aligned properly in the rotor, the rotor is fastened onto the coupling of the drive shaft and the temperature of the rotor is measured by means of the external thermocouple supplied with the instrument. The vacuum chamber is then closed, the vacuum pumps turned on, and after a vacuum of about 1.0 ~ is reached the centrifuge is accelerated to the desired speed. For satisfactory work the ultracentrifuge rotor should be operated at a speed such that the concentration at the bottom of the cell, at equilibrium, is about five times that at the meniscus. If the

[9.]

ULTRACENTRIFUGATION, DIFFUSION, AND VISCOMETRY

41

molecular weight is known approximately, then a satisfactory speed in revolutions per minute can be calculated from [5 X 1 0 n / M ( 1 - Vp)]~, but it should be emphasized t h a t good results can be obtained even at speeds quite far removed from such calculated speeds. In the case of proteins varying in molecular weight from 10,000 to 200,000, speeds from 15,000 to 3000 r.p.m, will be ideal. As soon as the centrifuge rotor attains the desired operating speed, pictures are taken at various angles of the schlieren diaphragm. If the concentration of enzyme is in the neighborhood of 1%, then angles of 80 °, 70 °, and 60 ° are recommended. For more dilute solutions, 70 °, 60 °, and 50 ° are preferred; and for very dilute solutions an early picture at 40 ° is desirable. The optical system of the ultracentrifuge requires only the modification t h a t the bar in the standard instrument be replaced b y a phase plate. This replacement of the bar by a phase plate effects a considerable sharpening of the curve of concentration gradient versus distance on the photographic plates. As a consequence, values proportional to dc/dx can be obtained with high precision. The early photographs are obtained so as to have available a base line for later measurements. After experience with the method is gained, some of the initial photographs at various angles (optical sensitivity) can be omitted, and only those taken which correspond to the angles used later in the run. Pictures during the run should be taken every 8 to 16 minutes at angles of the schlieren diaphragm such that, at the meniscus and b o t t o m of the cell, the deviation of the curve above the base line is 2 to 3 ram. on the photographic plate. Deviations much greater than that are difficult to measure because of the steepness of the curves at the meniscus and b o t t o m of the cell; deviations much less than about 2 ram. are too small for precise measurements (unless plates are to be read on a microcomparator). Operation of the ultracentrifuge for 1 or 2 hours (five to ten pictures at 16-minute intervals) will yield sufficient data for the precise determination of molecular weights. If the material is unstable, however, the length of the run can be reduced. F r o m longer runs additional data can be obtained which will yield greater precision especially in the detection of inhomogeneity. After the requisite number of pictures are taken, the centrifuge rotor is decelerated, the vacuum chamber opened, and the temperature measured. The contents of the cell can be recovered by means of a syringe, and the cell should then be dismantled and cleaned with detergent solution, rinsed with distilled water, dried, and reassembled for subsequent runs. The second ultracentrifuge run performed in a synthetic boundary cell 3 provides the value of co, in equation 2, in arbitrary units, and it also 3 E. G. Pickels, W. F. Harrington, and H. K. Schachman, Proc. Natl. Acad. Sci. U.S. 38, 943 (1952).

42

TECHNIQUES FOR CHARACTERIZATION OF PROTEINS

[2]

furnishes a calibration of the optical system so that the values of (dc/dx) can be determined readily. Cells of various designs and sector angles (2 ° , 3° or 4 °) can be used for this run, but the optical path or centerpiece thickness must be the same as in the cell used for the sedimentation equilibrium run. Almost invariably this will be 12 ram. Another basic requirement is that there should be no mixing as the contents from the upper reservoir or cup empty into the sectoral cavity to form the boundary. About 0.3 ml. of the same enzyme solution used in the previous run is introduced into the sectoral cavity. This is the bottom solution. If the synthetic boundary cell manufactured by the Spinco Division, Beckman Instruments, Inc., is used, the cup is placed into the cell with an orientation such that the pinhole opening in the bottom of the cup is superimposed over the rubber plug which is in the hole drilled into the shoulder of the centerpiece. Then the trap door gasket is placed around the cup. By means of a 1-ml. pipet or a syringe, about 0.2 ml. of solvent is placed in the cup, and then the trap door is placed on the cell which is then ready for insertion into the rotor. If the cell designed by Kegeles4 is used, the solvent is placed into each of the upper reservoir holes before the window is placed on the centerpiece. Then the cell is assembled in the conventional way, and the enzyme solution (bottom solution) is introduced with a syringe as in the conventional cell. The cell is then sealed just as in the sedimentation equilibrium run. After the cell is placed in the rotor and the rotor coupled to the drive shaft, the vacuum chamber is closed without measurement of temperature which is unnecessary for this run. It is advisable, especially in the case of the synthetic boundary cell containing a cup, to start the rotor spinning at low speed (with about 3 to 6 amperes of driving current) without waiting for the chamber to be evacuated. This forces the solution to the bottom of the cell and minimizes possibilities of mixing of solution and solvent prior to the actual formation of the boundary. After the rotor is spun for about 5 minutes with the low driving current, the drive voltage is raised and maintained at a value necessary to provide about 6 to 8 amperes of drive current. This produces a slow acceleration of the rotor, leading to sharp, symmetrical boundaries. In the synthetic boundary cell with the cup, the contents of the cup begin to empty at about 5000 r.p.m., but slight variations in this break-through speed do occur, depending on the age of the rubber plug. The rotor should be accelerated slowly with the drive current raised to about 10 amperes. Frequently, the cup is not entirely emptied before reaching a speed equal to that utilized in the equilibrium run, and it is therefore advisable to use a higher speed setting so that the braking mechanism will not be brought into operation. 4 G. Kegeles, J. Am. Chem. Soc. 74, 5532 (1952).

[9.1

ULTRACENTRIFUGATION, DIFFUSION, AND VISCOMETRY

43

It is not necessary that this run be at the exact speed of the equilibrium run, since the run is used only to provide area measurements which serve as a calibration of the optical system and a measure of the concentration and refractive index increment of the solution. After the boundary has spread sufficiently so t ha t the entire curve is visible, which requires about 5 minutes for proteins, pictures are taken at different angles of the schlieren diaphragm corresponding to those used in the sedimentation equilibrium run. Caution should be exercised that the angles in the second run reproduce faithfully those of the first run. To avoid errors due to backlash in the remote control mechanism for adjusting the angle of the schlieren diaphragm, the desired angular setting should always be approached from the same direction, i.e., clockwise or counterclockwise. This run with the synthetic boundary cell should only co~lsume a shor~ time, sufficient for photographs at each angle used in the sedimentatioH equilibrium run. A period of 20 minutes allows the boundary to spread sufficiently by diffusion for accurate measurements of the area. The centrifuge can then be stopped and the sample recovered, if desired. These two runs will generally suffice for the determination of the molecular weight of enzymes, but for small molecules in salt solutions it is necessary to perform still a third run. Before describing this run, it should be pointed out that the second run (in the synthetic boundary cell) may be omitted if it is certain that the sedimenting material is homogeneous with respect to molecular weight. This will be illustrated later when the calculations are presented. The third run performed with the pure solvent provides the base line necessary for the calculations made from the sedimentation equilibrium run. If one is dealing with a coenzyme, a substrate, or even a protein of molecular weight much below 10,000, then the centrifugal force required for the equilibrium study will be sufficient to cause some redistribution of the buffer ions in the solution. Thus the curvature of the (dc/dx) versus x curve in the sedimentation equilibrium run would be due in part to changes in the salt concentration, and corrections must be made for this effect. At speeds of about 10,000 r.p.m, the sedimentation of the salt is so little and its diffusion so great that the salt concentration is uniform throughout the cell. Under those conditions the base line is obtained as already indicated in the discussion of the sedimentation equilibrimn run. If the centrifuge is run at higher speeds, then a separate run of the solvent (or dialyzate) is necessary, and this should be performed in a manner identical to that used for the solution. This requires not only that the speed and bar angles of the pictures be the same, but also that the same cell should be used with extra precautions to ensure filling to the same extent. Reproducing the volumes in the cell can be performed most conveniently by weighing

[9.]

ULTRACENTRIFUGATION, DIFFUSIOST, AND VISCOMETRY

45

run in the ultracentrifuge and in the calibration run with the synthetic boundary cell. The sample was ribonuclease at a concentration of 1%, and the centrifuge was operating at 11,150 r.p.m. Shortly after reaching speed, the first picture was taken in order to give a base line. The second, third and fourth pictures show how the picture changes during the first 3 hours. In order to show the pattern after the base line (plateau region) is lost, the last pictures were taken after 7 and 26 hours of operation. These pictures are photographic prints of the original centrifuge plates, with the white vertical bands at each side of the pictures corresponding to the holes in the reference cell; thus on each photograph there are two points whose distances from the axis of rotation are readily determined from the construction of the rotor and reference cell. The right-hand

~: ~

i

.... :i

FIG. 4. Ultracentrifuge patterns from a run in the synthetic boundary cell for the determination of the concentration required for a study during the approach to equilibrium.

edge of the black band on the left part of each photograph from most ultraeentrifuges lies at a distance 5.70 em. from the axis of rotation. This should be determined for each instrument. Acceleration of the rotor produces some stretching, and this line then corresponds to a distance 5.72 em. from the axis of rotation at speeds of 60,000 r.p.m. Once this position is known, all measurements on the photographic plate, or an enlargement of it, can be related directly to distances from the axis of rotation. The photographic plates are placed in an enlarger, emulsion side up, and the. curves such as those shown in Fig. 3 for ribonuclease are traced at a magnification of about fivefold. It has been found that tracing the curves on thin, unruled paper is most desirable. To facilitate tracing the necessary parts of the photograph, the vertical lines corresponding to the inner edges of the two reference cell holes, the air-solution meniscus, and the solution-silicone fluid interface are drawn first with the aid of a ruler. Then the horizontal lines through the reference holes, the lines through the air phase and the silicone solution, and finally that through the solution are drawn. In drawing the curved line corresponding to the concentration gradient near the meniscus and the bottom of the cell, it is advisable to draw those regions as if the vertical lines were not present, almost as if one could imagine those curves pro-

46

TECHNIQUES FOR CHARACTERIZATION OF PROTEINS

[2]

jected a slight distance beyond each of the vertical lines. This represents the most difficult part of the tracing, and it is especially difficult when low angles of the schlieren diaphragm are used so that the curves are very steep at the ends of the cell. It is for that reason that angles of 80 ° and 70 ° are preferred, as long as there is sufficient gradient to allow measurements. As the run proceeds, the curvature extends over a greater region in the cell and, as a consequence, tracing is somewhat easier. After the curves are drawn, the tracings are placed on a light box, and graph paper with centimeter and millimeter divisions is superimposed on the original tracings in such a manner that the vertical line corresponding to the air-solution meniscus lies on one of the heavy centimeter divisions. If possible, the flat part of the curve corresponding to the plateau region should also be placed under one of the heavy ruled divisions of the graph paper. In this way, the tracing can be transferred to graph paper. For experiments in which the centrifugal force is sufficiently low that no redistribution of electrolyte occurs and a separate ultracentrifuge run of the buffer can be neglected, it is sufficient to continue the straightline portion of the curve in both directions (toward top and bottom of the cell) until it intersects the vertical lines corresponding to the liquidair and solution-silicone fluid interfaces. This is illustrated in Fig. 5, which also shows some of the symbols used in the detailed calculations. For runs in which the speed is so great that salt redistribution occurs, then the corrections must be made as discussed later. At millimeter intervals starting with the meniscus, called n = 0, the vertical distances between the curved and the extrapolated straight-line portions are recorded. These distances, labeled z~, are proportional to dc/dx with the proportionality constant including optical constants of the apparatus, the concentration of the solute, the refractive index increment of the solute, and the magnification factor of the enlarger. In view of the fact that the same factors are involved in the last picture of Fig. 4, which is a representative photograph from the ultracentrifuge run with the synthetic boundary cell, their evaluation is unnecessary. Tables IA and IB show a sample calculation from the sedimentation equilibrium run. In column 1 are listed the values of n, i.e., the number of the interval. Column 2, labeled R~, gives the distance in centimeters from the reference mark to the interval in question. This distance is next converted into a real distance within the centrifuge cell, and the values are listed in column 3 under R,,/F, where F is the magnification factor relating distances in the cell to distances on the enlargement. This is readily evaluated, since the tracing includes the inner edges of the reference holes in the counterbalance cell. These edges are 1.60 cm. apart in the cell, and F is, therefore, RR/1.60. In the next column the distances R,,/F are con-

[2]

ULTRKCEINTTRIFUGATION~ DIFFUSION~ AND VISCOMETRY

47

verted to values of x,, which are the distances from the axis of rotation (xn = R , / F + 5.70). Column 5 contains the square of these values, and column 6 contains the z~ values. In column 7 are listed the values of .~.r,~z~, and the sum of these values, at the b o t t o m of the column, gives a

RTR

B

M

RBR

iJ-'F m"*l

x\\

Rb \\\

\\\

Rn In: tOO)

x\\

\\\

\\\

(n:lOOl /Z b

Z n (n:3)

\\\

Zn " ~ - ~

m~/

9'0 1001104

,\\\

I \\\

RTR RBR

,k\\ REE AIR REE SILICONE HOLE LAYER LAYER HOLE FIG. 5. Schematic diagram for illustrating the calculations of molecular weight from run during the approach to equilibrium. This corresponds to a print of the original ultracentrifuge pattern. The cross hatched regions and all black lines would be white on the original plates. Also on the original plate would be two horizontal lines corresponding to the image of the phase plate border at the reference holes. These are omitted in the above sketch but should be used in tracing of the curves and in the microcomparator since they furnish a good reference for all measurements in the vertical direction. measure of the integrals in equation 2. To obtain the exact value of the integral in the proper units, this sum must be multiplied by O.1/F, which is the horizontal width of each segment of the summation. The first part of the table contains the data obtained at the top of the cell and, according to equation 2, the value of the summation must be multiplied

48

TECHNIQUES FOR CHARACTERIZATION OF PROTEINS

[2]

b y 1 / x , , 2. T h i s n u m b e r is t h e n s u b t r a c t e d f r o m co t o g i v e cm. T a b l e I B g i v e s t h e d a t a f r o m t h e b o t t o m r e g i o n of t h e cell; t h e s u m m a t i o n h e r e is m u l t i p l i e d b y 1 / x b ~, a n d t h e r e s u l t a n t is a d d e d t o co t o g i v e cb. T h e v a l u e T A B L E IA SEDIMENTATION EQUILIBRIUM OF RIBONUCLEASE

Calculations at the Meniscus (Time = 38 minutes, F = 12.19, 17 = 0.709 cc./g., T = 298.9 °, ~2 = 1.3633 X 106) 1

2

3

4

5

n

R~ cm.

R, F cm.

x~ (5.70 + R , , / F ) cm.

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4.0

0.181 0.189 0.197 0.205 0.213 0.222 0.230 0.238 0.246 0.254 0.263 0.271 0.279 0.287 0.295 0.304 0.312 0.320 0.328

5.881 5.889 5.897 5.905 5.913 5.922 5.930 5.938 5.946 5.954 5.963 5.971 5.979 5.987 5.995 6.004 6.012 6.020 6.028

6

7

x,, "~

z,~

x,,2z,~

cm. ~

em.

em. 8

1.41 1.30 1.20 1.08 0.99 0.88 0.77 0.66 0.57 0.50 0.42 0.35 0~28 0.19 0.13 0.10 0.08 0.04 0.02

48.766 45.084 41.730 37.659 34.614 30.862 27.077 23.272 20.152 17.725 14.934 12.479 10.009 6.810 4.672 3.605 2.892 1.450 0.727

34.586 34.680 34.775 34.869 34.964 35.070 35.165 35.260 35.355 35.450 35.557 35.653 35.748 35.844 35.940 36.048 36.144 36.240 36.337

384.519 nx

cm = co

= 18

x,,, ~ F

x"~zn;

"dx ,, =

1.41

n0~0

1 0.1 c~ = 1.2167 -- 34.58~ ' 19.5/1.6 (384.519) = 1.1255 Mr, _

RT

(1

--

F'p)~

(dc/dx),~

_

6.3636 • 104 ' (0 lz~)"-.---"-.~---" ~ l ) 1.41 (l

13,600

x,,,c,,,

of Co is o b t a i n e d f r o m a n e n l a r g e m e n t of t h e p a t t e r n o b t a i n e d i n t h e r u n u t i l i z i n g t h e s y n t h e t i ~ b o u n d a r y cell. T h e m a g n i f i c a t i o n of t h e e n l a r g e r m u s t , of c o u r s e , b e t h e s a m e i n b o t h t r a c i n g s . F o r t h e c o m p u t a t i o n of co t h e b a s e l i n e is d r a w n u n d e r t h e p e a k f r o m t h e s t r a i g h t - l i n e r e g i o n s o n

[2]

49

ULTRACENTRIFUGATION'j DIFFUSION~ AND VISCOMETR¥

e i t h e r side of t h e p e a k a n d t h e a r e a e v a l u a t e d . T h i s c a n b e d o n e e i t h e r b y m e a n s of a p l a n i m e t e r g i v i n g r e s u l t s in s q u a r e c e n t i m e t e r s or b y s u m m i n g t h e o r d i n a t e s , z~, a t 0.1-cm. i n t e r v a l s a n d t h e n m u l t i p l y i n g t h e r e s u l t a n t b y 0.1. I t h a s b e e n f o u n d t h a t t h e p l a n i m e t e r o p e r a t i o n is less tedious, but both methods give comparable accuracy. The value obtained TABLE IB SEDIMENTATION EQUILIBRUM OF RIBONUCLEASE

Calculations at the Cell Bottom 1

2

3

4

Rn

xn

n

R, cm.

F cm.

(5.70 -t- R,,/F) cm.

116 118 120 122 124 126 128 130 132 134 136 138 140 142

13.8 14.0 14.2 14.4 14.6 14.8 15.0 15.2 15.4 15.6 15.8 16.0 16.2 16.4

1.132 1.149 1.165 1.182 1.198 1.214 1.231 1.247 1.264 1.280 1.296 1.313 1.329 1.346

6.832 6.849 6.865 6.882 6.898 6.914 6.931 6.947 6.964 6.980 6.996 7.013 7.029 7.046

5

6

7

x,~2

z,~

x,,2z,,

cm. ~

cm.

cm?

46.676 4fi.909 47.128 47.362 47.582 47.803 48.039 48.261 48.497 48.720 48.944 49.182 49.407 49.646

0.01 0.03 0.06 0.09 0.12 0.18 0.26 0.42 0.60 0.82 1.05 1.35 1.68 2.06

0.467 1.407 2.828 4.263 5.710 8.605 12.490 20.270 29.098 39.950 51.391 66.396 83.004 102.271 428.150

nb= 142 cb = co + zb---1 2 dX.F ~

x,Yz.; ( d=e2)"b0 6 d x x

nx=ll6 1 0.2 cb = 1.2167 + 49.64-~6 " 19.5/1.6 (428.150) = 1.3582

Mb -

I?T

(1 - ~p)~2

(dc/dx)b _ 6.3636. 104. 2.06 Xbcb (7.046)(1.3582)

13,700

b y e i t h e r of t h e s e t w o m e t h o d s is t h e n m u l t i p l i e d b y 1 / F t o c o r r e c t for m a g n i f i c a t i o n in t h e x d i r e c t i o n , a n d t h e r e s u l t a n t v a l u e is Co. A t t h e b o t t o m of T a b l e s I A a n d I B a r e s h o w n t h e final c a l c u l a t i o n s . Since t h e t e m p e r a t u r e of t h e , r o t o r is k n o w n , i t is c o n v e r t e d i n t o a b s o l u t e t e m p e r a ture, a n d t h e m o l e c u l a r w e i g h t is c a l c u l a t e d f r o m e q u a t i o n 1. W h e n one is d e a l i n g w i t h s m a l l e r m o l e c u l e s a n d u t i l i z i n g h i g h e r c e n t r i f u g a l fields, t h e s o l v e n t is r u n s e p a r a t e l y a n d p i c t u r e s a t t i m e s a n d

[2]

51

ULTRACENTRIFUGATION~ DIFFUSION~ AND VISCOMETRY

T A B L E II SEDIMENTATION EQUILIBRIUM OF RIBONUCLEASE Calculations throughout the entire cell after loss of plateau region* (Time = 63 hours, F = 1.882, V = 0.0709 cc./g., 7' = 296 °, o~2 = 1.3633 × 10 ~) 1

2

n

n ~°

0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80 84 88 92 96 100 104 105.7

3

5

4

R,~"°

x,~~

cm.

cm.

6

(z,~2)~'o cm.

2

z,, ~ ° ell1.

2 6 10 14

1.447 1.487 1.527 1.567

6.469 6.490 6.512 61533

41.8415 42.1200 42.3995 42.6735

0.0774 0.0794 0.0817 0.0838

18 22 26 30 34 38 42 46 50 54 58 62 66 70 74 78 82 86 90 94 98 102 104.8

1.607 1.647 1.687 1.727 1.767 1.807 1.847 1.887 1.927 1.967 2.007 2.047 2.087 2.127 2.167 2.207 2.247 2.287 2.327 2.367 2.407 2.447 2.475

6.554 6.576 6.597 6.618 6.639 6.661 6.682 6.703 6.724 6.746 6.767 6.788 6.809 6.831 6.852 6.873 6.894 6.916 6.937 6.958 6.979 7.001 7.016

42.9550 43.2370 43.5135 43.7910 44.0765 44.3625 44.6425 44.9235 45.2120 45.5020 45.7860 46.0705 46.3625 46.6555 46.9430 47.2315 47.5275 47.8240 48.1150 48.4070 48.7065 49.0070 49.2240

0.0861 0.0889 0.092l 0.0957 0.0997 0.1039 0.1080 0.1121 0.1164 0.1209 0.1259 0.1307 0.1354 0.1410 0.1471 0.1527 0.1584 0.1646 0.1706 0.1771 0.1836 0.1901 0.1959

c,a =

Co -~" Xb 2

-- X,n~ L J x ~

1

Ff

dx

xz dc

7

8

c~ cm.

x 2

cHI.

9

z,,

10 I dc

xc dx

cm.

0.05158 0.05313 0.05491

6.458 6.479 6.501

0.0766 0.230 0.0782 0.227 0.0806 0.226

0.05665 0.05843 0.06026 0.06215 0.06411 0.06614 0.06826 0.07047 0.07277 0.07515 0.07762 0.08019 0.08287 0.0~565 0.08853 0.09153 0.09465 0.09790 0.1013 0.1048 0.1084 0.1122 0.1161 0.1201 0.1219

6.522 6.543 6.565 6.586 6.607 6.628 6.650 6.671 6.692 6.713 6.735 6.756 6.777 6.798 6.820 6.841 6.862 6.883 6.905 6.926 6.947 6.968 6.990 7.011 7.020

0.0828 0.0847 0.0874 0.0904 0.0938 0.0976 0.1018 0.1060 0.1100 0.1141 0.1186 0.1232 0.1286 0.1328 0.1380 0.1440 0.1502 0.1552 0.1616 0.1676 0.1736 0.1806 0.1866 0.1936 0.1981

-zb2

x~ dc

fx

m dxx

0.223 0.222 0.221 0.221 0.222 0.223 0.224 0.226 0.226 0.226 0.227 0.227 0.229 0.228 0.229 0.230 0.231 0.230 0.231 0.231 0.231 0.231 0.230 0.230 0.231

dx]

n = 105.7

fxz~ dC dx = dx m dxx ~-

~ n=O

z~ -- (2.126 × 10-2)(3.223) + (0.925 × 10-2)(0.1959) = 7.033 X 10 -2

n = 105.7

~xb m

dc _ dx x ~ --,- clx =

~

xn2z,, = (2.126 X 10-2)(148.19) -~ (0.925 X 10-2)(9.641) = 3.240 (3.240 -- (49.280)(7.033 X 10 -2) c,, = 0.08148 -b 49.280 -- 41.706 = 0.05158 * The centrifuge plate for this calculation was measured with a microcomparator, and the n intervals are in t e n t h s of millimeters. ax

n=O

52

TECHNIQUES FOR CHARACTERIZATION OF PROTEINS

indeed a plot of this data as log ( 1 / x ) ( d c / d x ) pletely straight.

[2]

versus x 2 is almost com-

Sedimentation Velocity I n t r o d u c t i o n . The primary function of this method is the determina* tion of the sedimentation rate of molecules, but it should be stressed that another powerful application of the method lies in its ability to furnish, often in a simple experiment of short duration, information about the purity of the material under investigation. In this latter regard, sedimentation velocity studies are like electrophoresis experiments, since each of the techniques causes the partial separation of different types of molecules, depending on their physical chemical properties. As a result several boundaries may be observed, or one broad boundary which clearly indicates inhomogeneity of the particles. Thus the sedimentation velocity method can indicate, within limits, of course, whether one or more molecular species is present in solution, provided these different molecules show variations in molecular size and shape. With sufficient research, precise information can be obtained about the amount of each species present in a solution, and thus the ultracentrifuge is an extremely valuable guide in studies aimed at the isolation and purification of an enzyme. Solute molecules in a solvent of different density are caused to move under the influence of a high centrifugal field, and the rate at which they move is a function both of the molecular weight of the solute and of the frictional resistance which the molecules or particles experience as they move through the solvent. Sedimentation velocity measurements of themselves do not yield molecular weights without recourse to other data, such as diffusion coefficients. The equation describing the relationship between the sedimentation rate and the properties of the molecule is

M(1 s -

Nf

Cp)

(4)

where s is the sedimentation coefficient, M is the anhydrous molecular weight of the sedimenting substance, l? is the partial specific volume of the solute, p is the density of the solution, N is Avogadro's number, 6.02 X 1038, and f is the frictional factor which is a function of the size, shape, and hydration of the sedimenting molecules. Movement of individual molecules is followed by examination of the boundary between solvent and solution, as illustrated in Fig. 1. For most purposes, if the boundary is symmetrical, movement of the maximum ordinate of the peak is a sufficiently accurate indicator of the movement of individual molecules. Actually it is the second moment of the gradient curve which

[2]

ULTRACENTRIFUGATION, DIFFUSION, AND VISCOMETRY

53

gives a true picture of the movement of the molecules, but calculations of this second moment are very laborious and often unnecessary. The sedimentation coefficient is defined as the velocity of the sedimenting molecules per unit field, as shown in equation 5, s

-

1 dx ~ x dt

(5)

where x is the distance of the boundary in centimeters from the axis of rotation, t is the time in seconds, and ~ is the angular velocity in radians per second. Generally, sedimentation coefficients lie in the range of 0.25 to 500 X 10-13 cm./sec./dyne/g., or 0.25 to 500 X 10-'a second, and the unit 1 X 10-'3 second has been termed 1 S. where S. is the Svedberg. Determination of Sedimentation Coe~icients. For proteins of molecular weight below about 250,000 the ultracentrifuge should be operated at the top speed of 59,780 r.p.m. ; and for larger molecules the speed should be adjusted so that the boundary moves across the cell in a period of several hours. Photographs are taken at periodic intervals, depending oil the rate of movement of the boundary. It is always advisable to examine the pattern through the viewing screen during the acceleration of the rotor in case material present in the solution sediments across the cell before the rotor attains the desired operating speed. If the substance under investigation has a sedimentation coefficient below 3 S., the use of the synthetic boundary cell is recommended. To damp out charge effects with proteins, ultracentrifuge runs are generally made in salt solutions at an ionic strength of 0.1 or greater. The temperature before and after the run is recorded if the external contact thermocouple is still in use; if the new temperature indicator is available, then the temperature can be recorded during the run. It should be stressed, for the former case, that the temperature of the rotor during a run at 60,000 r.p.m, is about 0.8 ° less than the average of the temperatures obtained from the contact thermocouple. Photographs can be read in a variety of ways, depending on the accuracy desired. For routine work with materials which sediment as relatively sharp boundaries, we have employed a simple light box containing a calibration plate which permits direct reading of boundary positions in centimeters from the axis of rotation. The calibration plate is made by photographing the ruled glass disk supplied by the manufacturer for the determination of the magnification factor of the different lenses. The lines on the resulting photograph will be from 1.8 to 2.2 mm. apart, depending on the particular instrument. With this plate fastened onto the frosted-glass top of a light box, a grid is available whose lines

[9.]

ULTRACENTRIFUGATION, DIFFUSION, AND VISCOMETRY

55

sedimentation coefficients for each time interval and correct them indep e n d e n t l y for temperature, assuming a linear change in temperature. For m a x i m u m use of the data, the averaging of the resulting sedimentation coefficients should be performed in the manner suggested b y Kegeles and G u t t e r ! Alternatively, the times between photographs can be corrected for the variation of the viscosity of water with temperature, as suggested b y Oncley, 9 and then log x can be plotted against the corrected times. log x

x (cml~

~t

Temo:23.7" c,( 20) :0 0.82600

(-~o)

6.700

=1.0065, ~] =0.709CC

solv

/ 0.81800

o/° D/" S = 2.503d

Iogx/dt (60)( ,,02)

6.580 =

(slope)(2.3 0 3 / 6 0 [( 2"rr)(, ,j59780 . . ~ - - - ~]2

)

S = 1.98 x 10"13sec. = 1.98 S 6.520 t , I t o t6 52 Time in m{nutes FIG. 6. D e t e r m i n a t i o n of sedimentation coefficient of ribonuelease from a plot of log x (x is the distance of b o u n d a r y to axis of rotation) versus t (t is the time in minutes). 0.81400 .....

,

Sedimentation coefficients are generally reported as s20.~, the value the material would have in a solvent with the density and viscosity of water at 20 ° . Corrections of the observed sedimentation coefficient, sob,., to this standard state are made according to the equation

where (nt/n20) is the principal correction factor corresponding to the viscosity of water at t ° relative to t h a t at 20 ° , (n/no) is the relative viscosity of the solvent to t h a t of water, and p20.~ and pt are the densities of water at 20 ° and the solvent at t °, respectively. The term pt can be calculated readily from (P/Po)Pt,w. I t is implicitly assumed t h a t V in the reference solvent is the same as in the actual solvent used in the experi9 j . L. Oncley, Ann. N. Y. Acad. ~ci. 41, 121 (1941).

56

TECHNIQUES FOR CHARACTERIZATION OF PROTEINS

[9.]

ment. For the experimental d a t a presented in Fig. 6, calculation of s20.w according to equation 6 leads to the result 820.~ = (1.98)(0.9147)(1.024)(1.0139) = 1.88 S. We have used p, as the density of the solvent, although some workers recommend use of the density of the solution. I t is clear t h a t the density of the solution is correct for sedimentation equilibrium; but there is no corresponding theoretical basis for the density t e r m in sedimentation velocity. In a n y case the difference between solution and solvent density is generally very small, and further, data should be extrapolated to infinite dilution so t h a t no significant error can result from the use of either density. For slowly sedimenting materials in high salt concentrations, formation of the b o u n d a r y between solvent and solution near the center of the cell is especially useful, since it virtually eliminates the need for a reference run of solvent alone. This run is ordinarily necessary as a " b a s e l i n e " run, since the sedimentation of salts causes refractive index gradients at the meniscus and b o t t o m of the cell. The observed p a t t e r n would then be the sum of t h a t due to the material of interest plus t h a t due to the salt. If a conventional cell is used, then a reference run of solvent is made under identical conditions, and the patterns from this run are subtracted from the corresponding patterns in the run of the solution. When the synthetic b o u n d a r y cell is used, the rate of acceleration of the rotor should not be so great as to cause convection which leads to poor boundaries. After the cup containing the solvent is completely emptied, the drive current should be adjusted to about 10 amperes until the operating speed is achieved. For m a n y substances the sedimentation coefficient depends on concentration, and runs at different concentrations are necessary to enable extrapolation of the data to infinite dilution. T h e data can be plotted in a variety of ways, but it is preferable to plot 1Is versus concentration. If viscosity data for the solutions at different concentrations are available, then a plot of s versus c and (v/~o)s versus c (c is concentration) on the same scale provides two curves which should extrapolate to the same value. This greatly facilitates the determination of s at infinite dilution. Measurement of Concentration. The area under the curves shown in Fig. 1 gives a measure of the concentration of the sedimenting material, and the m e t h o d of evaluating the area from synthetic b o u n d a r y cell runs has already been discussed. With a microcomparator and patterns obtained with the phase plate as the schlieren diaphragm these areas can be reproduced with a precision of b e t t e r t h a n 1%. Areas from runs at high speeds in a conventional cell cannot be obtained so accurately. For the

[2]

ULTR&CENTRIFUGATION, DIFFUSION, AND VISCOMETRY

57

latter, it is essential that a "base-line" run be made with pure solvent. This corrects not only for the gradients of refractive index due to sedimentation of salts but also for cell distortion. If possible, this "base-line" run should be made without taking the cell apart, and the volume of solvent in the cell should be the same as in the run with solution. The plastic, double sector ultracentrifuge cell permits the superposition on the photographic plate of the pattern due to the solution and the solvent. With this cell both solvent and solution are run simultaneously and the area of a sedimenting boundary can be determined with great precision since the superposition of the base line on the pattern of the moving boundary eliminates the uncertainties in construction of the base line from separate ultracentrifuge runs. Small amounts of both more rapidly and more slowly sedimenting material can be readily detected by the deviation of the solvent pattern from that of the solution in the region of the cell in front of or behind the principal boundary. In using this cell special efforts should be made to fill both halves of the cell equally so that the menisci are at the same distance from the axis of rotation. The syringe, 0.5 ml., which is first used for transferring the solution into the cell can then be rinsed and used for the solvent. Before using the cell for concentration determinations it should be tested by running solvent in both halves to be certain that cell distortion does not preclude superposition of the base lines from each sector. Since there is some loss of contrast on the photographic plates due to overlapping of the patterns from the two halves of the cell, high contrast photographic plates, such as the 5~etallographic plates, should be used. Whenever concentration determinations are to be made, either on purified components or in the analysis of mixtures, it is recommended that the double sector cell be employed. The solvent and solution patterns should be superimposed either from tracings of enlarged patterns (5X) made with a photographic enlarger or arithmetically if the areas are obtained by summing ordinates measured with a two-dimensional comparator. For this superposition of the patterns, use is made of the images corresponding to the reference holes in the counterbalance. After the base line is drawn under the peak, the area can be measured. The concentration of sedimenting material ill per cent, co, is obtained from the equation Atan~

(x) 2

co = a b m x m ~ A n E ~

where A is the measured area, a is the cell thickness in centimeters (along the optical path), b is the optical lever arm in centimeters (this value is supplied by the manufacturer and is equal to the focal length of the upper

58

TECHNIQUES FOR CHARACTERIZATION OF PROTEINS

[9.]

collimating lens or the distance from this lens to the plane of the schlieren diaphragm), Ois the angle of the schlieren diaphragm as read directly on the ultracentrifuge, mx and mc are the magnification factors of the camera and cylindrical lenses, respectively (these are evaluated according to the manufacturer's instructions with the aid of the ruled glass disk supplied with the ultracentrifuge), and E is the magnification of the enlarger (this is unity if a comparator is used). The term (X/Xo) 2, where x0 is the position of the boundary at zero time and x is the position at a time corresponding to the pattern subject to analysis, is the correction factor to account for the dilution of the contents of the plateau region as a result of the sector shape of the cell and the variation of centrifugal field with distance. To obtain the concentration in weight per cent, An, which is the specific refractive increment, must also correspond to weight per cent. It is equal to the difference in refractive index between a solvent and a solution at a concentration of 1%. For many proteins, An is about 0.00186. If a pure protein is available, the synthetic boundary cell can be used to calibrate the optical system by forming a boundary between solvent and a solution of known concentration. Also, there is available from the manufacturer a special calibration cell which is very useful for checking or determining the optical constants of the ultracentrifuge. Determination of Homogeneity. The minimum requirement for homogeneity of a given sedimenting substance is that the material sediment across the cell as a single, symmetrical boundary without too much broadening of the boundary. This is, of course, a qualitative statement; detailed quantitative measurements can be and, indeed, must be made if homogeneity is to be demonstrated. It should be emphasized that it is extremely dangerous and often incorrect to conclude that a material is homogeneous just because the boundary remains symmetrical and sharp. Frequently boundaries are artificially sharp because of the dependence of sedimentation coefficient on concentration, and tests for homogeneity should be made on dilute solutions and, if possible, as a function of concentration to enable extrapolation to infinite dilution. This is also important in the analyses of mixtures in terms of the relative concentrations of the different components, because of the ultracentrifuge anomaly which causes the slower component to appear to be present in greater concentration than the true concentration. 1°,11 For materials with a sedimentation coefficient below about 1 S., the boundary cannot traverse the whole cell becatlse of the present limitations in rotor speed. Thus the great potential of the ultracentrifuge in resolving different molecular 10 j. p. Johnston and A. G. Peston, Trans. Faraday Soc. 42, 789 (1946). 11 W. F. Harrington and H. K. Schachman, J. Am. Chem. Soc. 75, 3533 (1953).

60

TECHNIQUES FOR CHARACTERIZATION OF PROTEINS

[2]

employing conventional optical techniques, and recourse is made to the so-called analytical method which is based on the determination of the quantity of substance sedimenting across a fixed plane in a centrifuge cell. This method requires a special ultracentrifuge cell called the separation or partition cell which is so constructed as to effect a separation of the contents of the cell into two parts at the conclusion of the run. The amount sedimenting across the partition is determined by the difference between the total amount of material originally in the cell and that which is left above (or centripetal to) the separating plate at the conclusion of the ultracentrifuge experiment. Also required for the method is, of course, a specific and sensitive analysis for the material in question. This may be a bioassay, a chemical analysis, or a physical-chemical measurement such as radioactivity or ultraviolet absorption. As will be seen shortly, the analyses need be only relative so that measurement at the conclusion of the run of the number of units of activity in the upper solution relative to the number in the original solution gives a value of the sedimentation coefficient. The separation cell affords still another important advantage to biochemists interested in a specific biologically active substance. Frequently in the isolation and purification of a given substance two or more boundaries are observed optically in the ultracentrifuge, and it is important to determine which, if either of these corresponds to the material of interest. As long as there is a specific biological test available, the sedimentation coefficient of the substance can be determined even in the presence of much larger quantities of other components. Even when only one component is observed optically and the material is thought to be purified, it may be profitable to measure the sedimentation rate by activity measurements to see if there is a correlation between the physical property of the bulk constituent and the component with the biological activity. For some time there has been available only the partition cell of Tiselius et al., 12 but very recently a cell designed from quite a different point of view has been introduced by Yphantis and Waugh. 1~ Both of these cells are now available commercially from the Spinco Division, Beckman Instruments Inc., Belmont, California, and they are both made by modification of standard 12-mm. 4 ° centerpieces. In the cell of the type proposed by Tiselius et al., slots are made in the walls of the centerpiece at a position approximately two-thirds of the distance from the top. Into these slots fits a thin perforated plate containing about twenty three holes drilled through it, each hole being about 0.28 mm. in 1, A. Tiselius, K. O. Pedersen, and T. Svedberg, Nature 140, 848 (1937). 13 D. A. Yphantis and D. F. Waugh, J. Phys. Chem. 60, 623, 630 (1956).

[2]

ULTRACENTRIFUGATION, DIFF~ISION, AND VISCOMETRY

(}l

diameter. In operation, a piece of Whatman No. 50 filter paper, 12 mm. long and about 0.5 mm. narrower than the porous plate, is overlaid on the plate and they are inserted into the centerpiece. It is implicitly assumed that neither the filter paper nor the perforated plate interferes with the process of sedimentation and, further, that the sedimentation process is convection-free as in the standard ultracentrifuge cells. The function of the barrier is to prevent mixing of the upper and lower solutions at the conclusion of the experiment. In the cell designed by Yphantis and Waugh the separating plate is actually movable and rests on two thin synthetic rubber strips which serve as a spring. Since the plate and rubber are more dense than the liquids customarily employed for analysis, the plate sinks to the bottom of the cell during acceleration of the rotor and the cell simulates a conventional ultracentrifuge cell. On deceleration, at 2000 to 3000 r.p.m., the centrifugal force on the plate is no longer sufficient to counteract the lifting action of the rubber springs, and the plate rises very slowly until it rests against specially constructed stops in the centerpiece. If the cell and movable partition are made and assembled correctly so that there is a precise fit when the plate is in the rest position, the solutions in the two compartments can be effectively separated from each other with little risk of mixing. Surprising as it may seem, the slow movement of the partition from the bottom of the cell to its rest position causes little or no generalized stirring of the contents of the cell. This has been the subject of careful experimentation by Yphantis and Waugh, 13 who, in experiments in which the rotor was decelerated and accelerated, showed that the movement of the partition back and forth through a boundary caused only a little distortion of the boundary. This is true even with solid partitions, so that the liquid must flow around the partition when it is Caused to move in the cell. The success of this technique depends, as in the case of the synthetic boundary cell, on the stability resulting from magnification of small density gradients under the influence of a centrifugal field. Whereas stirring of stratified layers of solution differing in density by only 0.001 g./ml, will occur readily at one gravity, such stirring will not take place in a centrifugal field in which the force on the liquid is many hundreds of times that of gravity. Static experiments with a dye indicator present in the centrifugal compartment and absent in the centripetal part showed that there was little mixing of the liquids when the cell was handled in a fashion simulating a typical ultracentrifuge experiment. Thus the two separation cells functioning in quite different ways achieve, to more or less the desired extent, the same purpose. There is not as yet sufficient experience with the movable partition cell for a detailed comparison with the older cell, but it appears that the

62

TECHNIQUES FOR CHARACTERIZATION OF PROTEIN'S

[2]

newer cell will function better for proteins and low molecular weight materials, whereas the partition cell of Tiselius et al. does interfere with sedimentation and there is a partial disintegration of the sedimenting boundary as it approaches the partition from above. Furthermore, a second boundary forms just centrifugal to the barrier. This probably results from a temporary pile-up of some sedimenting material on the filter paper. Whatever the cause, convection does occur and this may lead to erroneous results. Epstein and Lauffer14 circumvented this effect of the barrier by adding a small amount of sucrose to the solution below the barrier, thereby causing this solution, even if there is some removal of solute by sedimentation, to be heavier than the solution centripetal to the partition. In this manner the disturbance in the upper liquid can be effectively eliminated. In terms of operating procedure there are only minor differences, depending on which cell is used. With the old cell, complete filling in one step is almost impossible. The top portion of the cell is filled by means of a 1-ml. syringe equipped with a No. 22 stainless steel needle the tip of which is ground fiat. This liquid is forced into the bottom compartment by centrifuging at a speed of about 2000 to 3000 r.p.m, for about 1 minute. Then the upper compartment can be filled. This intermediate step can be eliminated in the use of the Yphantis-Waugh cell, since the tip of the needle can be used to depress the platform during the filling of the entire cell. It is a good idea to weigh the filled cell before the ultracentrifuge run and then again at the conclusion of the run, before and after removing the contents of the upper compartment. This is useful, since small leaks in the cell can be detected, and also the weight of the sample removed is determined readily. For this weighing, a small plastic block with a hemicylindrical cavity in the top serves as a stand for proper orientation of the cell with the filling hole pointing upward. Unlike most ultracentrifuge studies, the exact time of the run is important, and it is therefore necessary to record the speed of the rotor at different times on the way up to speed and then at the conclusion of the run during the deceleration period. Generally it will be found that acceleration of the rotor under the influence of 12 to 14 amperes will be linear and, to a very good approximation, the time of acceleration to the desired speed is equivalent to one-third of that period at the final operating speed. Thus one-third of the acceleration and deceleration times must be added to the time that the rotor is at speed for the computation of the sedimentation time. Special precautions are needed in the deceleration of the rotor, since rapid deceleration leads to convective disturbances, as evidenced by the formation of hypersharp spurious boundaries. Yphantis 14 H. T. Epstein and M. A. Lauffer, Arch. Biochem. and Biophys. 35, 371 (1952).

64

TECHNIQUES FOR CHARACTERIZATION OF PROTEINS

[2]

Several runs should be made for different periods of time such that

ct/co varies from about 0.8 to about 0.1. For most enzymes, runs of a duration sufficient to produce a lowering of the average concentration in the upper solution to about 10% of the original will take only 2 or 3 hours at top speed, and the equation presented above is valid. If the molecules being studied are smaller, say about 2000 in molecular weight, then the plateau region will vanish in a 3-hour period and equation 9 is no longer applicable. Yphantis and Waugh 13 have shown, however, that it is possible to obtain both sedimentation coefficients and diffusion coefficients from experiments in which the plateau region is lost and the reader is directed to their papers for this important new development. Application of Absorption Optics to Ultracentrifugation. Many substances of interest to enzymologists have such high extinction coefficients either in a particular region of the visible spectrum or in the ultraviolet that the sedimentation of these materials is more readily examined by absorption techniques than by customary schlieren methods. For example, the amount of ultraviolet light transmitted through a solution of deoxyribonucleic acid at a concentration of 0.001% is only about half the light transmission of the solvent. This difference is readily recorded as variations in the degree of blackening of photographic plates. In contrast, the difference in refractive index between such a solution and the solvent is so small as to be virtually indetectahle by present schlieren methods. Thus ultracentrifugal analysis of materials at such great dilutions is dependent on the availability of absorption methods. Also many substances, the main features of whose absorption spectra are known, such as the cytochromes or hemoglobin, can be studied specifically, even in crude mixtures, by the use of light of the appropriate wavelength. Therefore, it seems likely that there will be a return to the absorption method originally developed and employed by Svedberg and his co-workers. 15 Techniques at present are still in a state of flux, and only very general comments will be made here. A special ultraviolet absorption optical system is now available commercially and can be incorporated in existing ultracentrifuges. This employs light of 254 m~ and can be used for materials which, at that wavelength, have an optical density of 0.2 (in a 1-cm. cuvette). For absorption work at wavelengths in the visible, the schlieren system can be used as an absorption system through the use of appropriate filters to isolate the desired wavelengths. Interference filters are very useful for this purpose. If the absorption method is to give accurate information concerning 15T. Svedberg and K. O. Pedersen, " T h e Ultracentrifuge," Oxford University Press, New York, 1940.

[9.]

ULTRACENTRIFUGATION', DIFFUSION, AN'D VISCOMETRY

65

the change in concentration of the absorbing material as a function of the position in the ultracentrifuge cell, the blackening of the photographic plate must give a faithful record of the intensity of light striking it. Thus, the blackening of the plate must be inversely related to the optical density of the solution in the cell. Further, this blackening must be measured in some type of photodensitometer. For this purpose use is made of the modified Analytrol, manufactured by the Spinco Division, Beckman Instruments, Inc. With suitable precautions and some calculations this instrument in conjunction with the photographic plates gives a curve relating concentration of the absorbing substance as a function of distance from the axis of rotation. This will be recognized as the integral of the patterns given by schlieren methods. From these curves at different times, sedimentation coefficients are readily calculated. Also analysis of the boundary spreading to determine the diffusion coefficient and polydispersity of the sedimenting material is readily achieved by the use of absorption patterns. For strongly absorbing materials like cytochromes or nucleic acids, a detailed analysis can be performed, with the aid of the synthetic boundary cell, on only about 10 ~ of material.

Partial Specific Volume The use of ultracentrifuge data from either sedimentation equilibrium or sedimentation velocity studies requires the evaluation of the term (1 - Vp). Since the partial specific volume, V, of proteins is generally between 0.70 and 0.75 ml./g., and the density, p, is normally close to unity, errors in the determination of 17 are essentially multiplied by a factor of 3 in the final calculation of molecular weights. As a consequence it is imperative that accurate values of V be obtained, and it is just in this area that detailed experimental studies are lacking. The classical method for determining partial specific volumes involves density measurements both on solutions of known concentrations and oll the solvent. From each solution density, p, paired with the density of the solvent, p0, an apparent specific volume is calculated. It has been found almost invariably for proteins that the apparent specific volume is independent of concentration of the protein, and thus the average value for different concentrations is equal to the partial specific volume. In addition to the classical method of determining partial specific volumes there are two other methods which give a reasonably reliable value for 17, and a brief discussion of them will follow a treatment of the more popular method. There are a variety of procedures for determining densities of solutions, and all of them have been used at one time or another. The most

[9.]

ULTRACENTRIFUGATION~ DIFFUSION, AND VISCOMETRY

67

pycnometers of only 2-ml. capacity can be used although greater precision is attainable with larger volumes. Greater precision in measuring the density of solutions can be obtained either through the use of the density gradient column of Linderstr0mLang and Lanz 16 or by means of the magnetic float method developed by MacInnes et al. 17 The former method requires only very small volumes of solution, whereas the latter requires volumes that in many cases are almost prohibitively large. For the use of the magnetic float method which requires apparatus that is not as yet commercially available, the reader should consult the paper by MacInnes and co-workers, is Density measurements with the gradient column require only simple equipment consisting of a constant-temperature bath, a column of liquid in which the density increases, preferably in a linear manner, from top to bottom and in which aqueous solutions are insoluble, a capillary pipet for the delivery of small drops of protein solution into the column, a method for the precise measurement of the height of the drops in the column, and, finally, a set of reference liquids whose densities are accurately known. In the use of the gradient column, mixtures of c.p. bromobenzene and rectified white kerosene are employed. Two mixtures of these liquids are prepared so that they differ in density by about 0.02 g./ml., and they encompass the density range of the solvent and protein solutions. Each of the bromobenzene-kerosene solutions must be saturated with water by shaking with a dilute solution (about 0.2 M) of potassium bromide fo}lowed by storage overnight. This saturation of the liquids for the gradient column is necessary so that there will be no evaporation of water from the drops of protein solution; otherwise, there would be an increase in concentration of protein in the drops, leading to erroneous results. After separation of the individual solutions from the potassium bromide solution, the gradient column is prepared by the method of Linderstr0m-Lang and Lanz. 16 This involves careful layering of the lighter solution over the heavier one in a long cylindrical column held in the well-controlled constant-temperature bath. The two solutions are then mixed partially by gentle stirring so as to produce a gradual change in composition, and hence in density, from the top to the bottom of the column. The stirring operation is an art, and it takes considerable practice before this operation can be performed in a satisfactory manner. 1~K. LinderstrOm-Langand H. Lanz, Compt. rend. trav. lab. Carlsberg S$r. chim. 21, 315 (1938). 17D. A. MacInnes, M. O. Dayhoff, and B. R. Ray, Rev. Sci. Instr. 9.2, 642 (1951). is M. O. Dayhoff, G. E. Perlmann, and D. A. MacInnes, J. Ant. Chem. Soc. 74, 2515 (1952).

68

TECHNIQUES FOR CHARACTERIZ.~TION OF PROTEINS

[2]

Too little stirring leads to a density gradient of only limited extent with uniform regions above and below the actual density gradient, whereas too much stirring produces a column equally unsatisfactory, since the column is almost uniform in density. The density gradient column is allowed to stand undisturbed for a period of 24 hours so that diffusion can smooth out any abrupt density gradients. Then the appropriate standards made from solutions of analytical-grade recrystallized potassium chloride are added to check the gradient column. If the positions of the drops show that the density gradient is satisfactory, then the column is ready for use. Drops are added by means of a capillary pipet delivering about 0.2 mm. 3, and there should be sufficient standard drops of known density to bracket closely the solutions whose densities are to be determined. Several drops can be measured along with several standards almost simultaneously, and the drops should be added with the most dense being first, then the next dense, and so on. The positions of the drops after they reach equilibrium positions, which requires only about 15 minutes, are most readily determined by a cathetometer, although a scale mounted alongside of the column may suffice, depending on the accuracy desired. The density of a given unknown solution, d, is calculated by interpolation according to the equation h - h, (d2 - dl) d = dl T h~ hi

(10)

where h, hi, and h~ are, respectively, the positions measured from some reference mark near the top of the column to the center of the unknown drop, the lower density standard, dl, and the higher density standard, d2. After each experiment the drops are removed from the column which is then ready for use after several hours of standing. Removal of the drops is achieved either by touching the drops with a thin glass rod onto which the drops will adhere so that they can be transferred to the wall of the column at the top of the liquid or by pouring a small amount of sea sand (obtainable from Merck) through the column. Density measurements can also be achieved by hydrostatic weighing in a commercial apparatus such as a Westphal balance or in a modified analytical balance. Accurate densities can also be achieved by differential density measurements using a pair of similar pycnometers one of which is filled with solution and the other with solvent, and then the solutions are exchanged. 19 After the densities of the solutions and solvent are determined, the 19 For a review see chapter on determination of density by N. Bauer, in "Physical Methods of Organic C h e m i s t r y " (Weissberger, ed.), 2nd ed., Part I, p. 253. Interscience Publishers, New York, 1949.

[9"]

ULTRACENTRIFUGATION, DIFFUSION, AND VISCOMETRY

69

apparent specific volume is determined by substituting in the equations Va,p. = 100/d - (100 - n)/do

(11a)

n

or 1

V~,,. = d0

1 (~odO) x

(llb)

where d and do are the densities of solution and solvent, respectively, n is the percentage concentration of solute by weight, and x is the concentration of protein in grams per milliliter of solution. The concentration (tan be determined in a variety of ways. If the protein is in distilled water, then a weighed aliquot is lyophilized followed by drying in vacuo over P~05 at about 110° until constant weight is achieved. Alternatively, the dry weight can be determined by micro-Kjeldahl analysis for nitrogen if the conversion factor relating nitrogen to protein is known. For proteins which must be maintained in a buffer, it is important to perform a dialysis and then the composition can be determined by the difference in dry weights between solution and dialyzate. Frequently the amount of protein is so small as to preclude measurements both of concentration and of density, and recourse can be made to a method employing the ultracentrifuge. As shown in equation 4, the sedimentation coefficient is proportional to (1 - ITp). Thus determination of the density of a solution in which the sedimentation coefficient is equal to zero gives a measure of l?. Accordingly the sedimentation rate of the protein is measured in a series of solutions of increasing density and the resulting data plotted in a manner to enable extrapolation to the value of p corresponding to zero sedimentation rate. This value for the density of the solution is equal to l/i?. Since the equation is restricted to two component systems, it is not valid to employ any material such as sucrose to increase the density of the solution. It appears, however, that mixtures of D~O and H20 act as a one-component solvent and therefore they can be used for these experiments. Unfortunately, D20 solutions are not sufficiently dense to reduce the sedimentation rate of proteins to zero, and a long extrapolation of the data is necessary. With accurate data, however, this can be performed to yield reliable results, and the method has, therefore, much to offer. The data are plotted as ~s versus p, where v is the viscosity of the solvent in poises, i.e., including the buffer contribution and the D20, s is the measured sedimentation coefficient, and p is the density of the solvent. The best-fitting straight line is obtained by the least squares method, and the equation of this line is then used to calculate the value of p corresponding to zero sedimentation rates. Even if the data are obtained with high precision, there is some

70

TECHNIQUES FOR CHARACTERIZATION OF PROTEINS

[9.]

u n c e r t a i n t y i n t h e final result, n o t o n l y b e c a u s e of t h e h a z a r d o u s e x t r a p o l a t i o n , b u t also b e c a u s e of e x c h a n g e of some of t h e h y d r o g e n s of t h e p r o t e i n m o l e c u l e w i t h d e u t e r i u m i n t h e water. T h i s l a t t e r effect is, however, likely to be a s m a l l one a n d for t h e p r e s e n t c a n be neglected. TABLE I I I CALCULATION OF THE APPARENT SPECIFIC VOLUME OF RIBONUCLEASE FROM ITS AMINO ACID COMPOSITION

Amino acid residue

Number of residues/ molecule~

W~

(% by weight a of residue)

Vi

ViWi

(specific volume of residue)

(% by volume of residue)

Aspartic acid Asparagineb

7 9b

5.69 7.31 b

0.59 0.60

3.36 4.39

Glutamie acid Glutamineb

4 8b

3.63 7.27 b

0.66 0.67

2.40 4.87

1.25 6.12 6.34 1.74 2.30 9.44 7.56 5.95 3.52 3.32 3.13 6.84 3.73 9.22 4.43

0.64 0.74 0.86 0.90 0.90 0.63 0.70 0.63 0.75 0.76 0.77 0.71 0.67 0.82 0.70

0.80 4.53 5.45 1.57 2.07 5.95 5.29 3.75 2.64 2.52 2.41 4.86 2.50 7.56 3.10

Glycine Alanine Valine Leucine Isoleucine Serine Threonine Half cystine Methionine Proline Phenylalanine Tyrosine Histidine Lysine Arginine

3 12 9 2 3 15 10 8 4 5 3 6 4 10 4

Total = 126

NW~ = 98.79

~,W~VI = 70.02

Y,W~V~/F,W~ = V~ = 0.709 cc./g.

a The number of each amino acid residue per molecule of ribonuclease, which gives a molecular weight of 13,895 for this enzyme, was obtained from the data of C. H. W. HiTs, W. H. Stein, and S. Moore, J. Biol. Chem. 211, 94i (1954). b To take into account the seventeen amide groups per molecule of RNase, it was assumed that these were approximately equally distributed between the glutamic and aspartic residues. A p p a r e n t specific v o l u m e s of p r o t e i n s c a n be e s t i m a t e d q u i t e r e l i a b l y f r o m t h e a m i n o acid c o m p o s i t i o n , since it has b e e n f o u n d t h a t t h e v o l u m e s of t h e m a c r o m o l e c u l e s are closely e q u a l t o t h e s u m of t h e i n d i v i d u a l a m i n o acid residues. T h i s p o i n t has b e e n e m p h a s i z e d b y M c M e e k i n a n d

72

TECHNIQUES FOR CHARACTERIZATION OF PROTEINS

[2]

concept, formulated by Fick in 1855, can be written dc

dm = - D A ~ dt

(12)

where dm is the mass of material transported in the time, dr, and A is the cross-sectional area of the diffusion cell. The negative sign is present in this equation because the transport of solute is in the direction of decreasing concentration. Thus, if we think of a vertical cell in which the bottom solution is the more concentrated and the positive direction is downward, then mass is transported in the negative direction. Diffusion coefficients can be measured, by direct application of equation 12, from determinations of the amount of material diffusing across a porous membrane separating a pure solvent from a homogeneous solution of some solute. Such diffusion studies, referred to as diffusion through a porous disk, are dependent on the establishment of a steady state in which the amount of solute diffusing per unit time is constant. This method is particularly useful for biological materials for which a specific bioassay is available. Though the method does not give absolute values for the diffusion coefficient, it is particularly valuable for the enzymologist who can use the method for studies of enzymes which have not been purified. The second, more popular method of studying diffusion, known as the free diffusion method, is based on another equation derived by Fick. This relates the rate of change of concentration with time to the rate at which the concentration gradient is changing with position, x, in the cell, as shown in equation 13. dc d2c d--{ = D ~dx (13) In performing measurements by this method, a sharp boundary is created between the solvent and the solution, and the change in concentration of the solute as a function both of distance and of time is followed by any one of a variety of optical procedures. With modern procedures and in apparatus now commercially available it is possible to obtain absolute diffusion coefficients with an accuracy exceeding 1%. Measurements by this method are also sensitive in the detection of impurities either much larger or smaller than the main component or in the determination of the homogeneity with respect to size of the principal diffusing species. In the free diffusion method great care is required in the design and use of the apparatus to ensure the formation of almost infinitely sharp boundaries and to eliminate any vibrations and resultant convection stemming from inadequacies in the mechanical construction or temperature control. For porous disk diffusion experiments, however, most of

[2]

ULTRACENTRIFUGATION, DIFFUSION, AND VISCOMETRY

73

these difficulties are nonexistent because the diaphragm with its extremely fine pores effectively prevents convective transport of liquid from the upper solution to the lower. Meanwhile independent stirring above and below the diaphragm can be used to maintain the homogeneity of each of the two solutions. Solute molecules in a homogeneous solution are in constant motion due to thermal energy, and such motion, known as Brownian movement, has been related to diffusion by Einstein and Smoluchowski. In fact, if we were able to measure precisely the random movements of a given macromolecule in solution over a long period of time (or, alternatively, the motions of many particles at a specific time), we could calculate its diffusion coefficient from an equation derived by these workers. The driving force for such movement is the thermal energy, kT, where k is the Boltzmann constant, 1.38 X 10- ~ erg/degree, and T is the absolute temperature. These randomly moving macromolecules experience a resistance to motion caused by the viscosity of the medium, and this resistance is characterized by a frictional coefficient, f, which is related to the size and shape of the kinetic unit. For particles of any shape which are large compared to the solvent molecules, D-

kT f

(14)

and therefore determination of the diffusion coefficient gives a direct measure of the frictional coefficient which also appears in the equation relating the sedimentation coefficient to molecular weight. Diffusion Through a Porous Disk

This method, introduced by Northrup and Anson 2~ and applied by them and others to the measurement of the diffusion of enzymes, is elegantly simple. Despite numerous limitations it should be employed whenever approximate results are desired for a specific enzyme, whether the enzyme is pure or not. The method is ideal in the latter situation as long as a sensitive and specific assay is available. Figure 7 shows a bell-shaped glass diffusion cell fitted with a stopcock at the top and with a fiat sintered-glass disk (or diaphragm) at the base. In practice, the cell is filled with the solution containing the diffusing substance and is carefully lowered, by means of an adjustable suspension on a rack and pinion device, until the lower edge of the sintered-glass disk just contacts the upper surface of the solvent contained in the outer vessel. Special efforts are necessary so that the glass diaphragm touches the lower liquid over its entire area. Also, caution should be exercised so ~2j. H. Northrop and M. L. Anson, J. Gen. Physiol. 12, 543 (1929).

74

TECHNIQUES FOR CHARACTERIZATION OF PROTEINS

[2]

that the diaphragm is not below the surface of the outer liquid; otherwise a stagnant layer will develop. The technique then consists in measuring the amount of solute appearing in the outer liquid as a function of time. This gives dm/dt of equation 12. Initially the difference in concentration between the inner and outer solutions is known, and for most experiments the time of diffusion is so short that there is no significant change in these concentrations. For the use of equation 12 we must know the concentration gradient which involves dx, the effective thickness of the diaphragm, and al~o A, the cross-sectional area of the diaphragm. Neither of these can be determined readily, since the diameter and length of the pores in the diaphragm no doubt vary from region to region. This

1

-I---"SOLUTION

FIG. 7. Porous disk diffusioncell. difficulty can be obviated through the determination of the "cell cons t a n t " by studies with a substance of known diffusion coefficient. As the technique was originally devised by Northrup and Anson, the solution, or more dense liquid, is on the top, but the pores of the diaphragm are sufficiently narrow to prevent mass flow of liquid despite the obvious gravitational instability. Thus diffusion of solute molecules through the pores of the sintered-glass disk into the solvent below creates a region just below the diaphragm which is more dense than the solvent further down in the cell. Convective stirring results, and the heavier liquid sinks to the bottom being replaced by fresh solvent. Similarly, just above the diaphragm there is a temporary diminution in concentration which also produces instability so that stirring results. The working basis of the method then rests on the hypothesis that the concentration above the membrane remains the same as the original concentration and that in the lower solution is similarly equal to the original concentration of that liquid. Of cours% after a long period of diffusion both of these concentra-

7(]

TECHNIQUES FOR CttARACTERIZATION OF PROTEINS

[2]

open or single cell to a double cell in which the volumes of both compartments are fixed and neither of the solutions is in contact with air, thereby minimizing difficulties due to evaporation. Several different cells have been suggested, and one which seems to be simple to use and free of some of the disadvantages of the open cell is shown in Fig. 8. 23 This cell also has provision for mechanical stirring of the liquid on either side of the porous membrane, since evidence has been presented showing that the density stirring in the Northrup-Anson cell is not completely effective and that stagnant layers exist in the vicinity of the diaphragm. In the

J

~.

ISOLVENT

--SINTERED GLASS

~

--SOLUTION

FIG. 8. Closed porous disk diffusioncell. cell shown in Fig. 8, the more dense solution is placed in the bottom so that gravity is a stabilizing rather than a disturbing force, thereby lessening bulk flow of liquid because of either a faulty membrane or gravitational instability when high concentrations were used in the upper solution. The cell is made of Pyrex glass with each end having a volume of about 50 ml. The diaphragms are Corning medium-grade or Jena G-4, fritted-glass disks (average pore size 15 #), of about 5-cm. diameter and 2- or 3-mm. thickness. In each compartment is placed a glass-enclosed iron wire about 3 mm. in diameter and of length slightly less than the diameter of the diaphragm. These glass stirrers are so constructed with respect to length of wire and thickness of glass that the one in the upper compartment sinks in the liquid and that in the lower one floats. The stirrers can be made to rotate by surrounding the cell with a rotating ~a R. H. Stokes, J. Am. Chem. Soc. 72, 763, 2243 (1950).

[2]

ULTR/kCElgTRIFUGATIOI% DIFFUSION~ AND VISCOMETRY

77

permanent magnet. With a stirring rate of about 20 r.p.m, it is found that no stagnant layers exist and that the solutions in each compartment are uniform in composition. To reduce difficulties from contamination of the porous disk by stopcock grease, Stokes uses rubber stoppers to seal each compartment. The rubber stoppers are equipped with small capillary tubes so that the liquid in the diaphragm is not disturbed when the stoppers are inserted or withdrawn. The capillary in the upper rubber stopper is open to the air to allow for volume changes during diffusion, and the lower capillary is fused to a small glass stopcock which can be opened prior to removal of the stopper. Although the stopcock is greased lightly, the grease does not readily contaminate the cell if care is exercised. As with the Northrup-Anson cell, the solution and solvent must be degassed and special precautions must be taken that no air is trapped in the pores of the glass disk during the filling operation. First the entire cell and diaphragm are filled with solution, then the solution in the upper compartment is removed by suction, and after several rinses solvent is added to this cell. Diffusion is allowed to occur with stirring for several hours. Again the upper compartment is emptied by suction; rinsing is performed and the liquid replaced by fresh solvent previously brought to the same temperature as the diffusion cell. Stirring is then resumed and the time recorded. Depending on the sensitivity of the assay procedure, one may have to allow a diffusion time of many hours. At an appropriate time the upper compartment is drained, the cell inverted, and finally the lower compartment is drained. The necessary determinations are made, and the diffusion coefficient is then calculated from equation 15. The cell is immediately refilled and the experiment repeated. If the newly determined diffusion coefficient agrees with the first one, then it can be assumed that a steady state had been reached and tl~e experimental values are valid. Thermostats are generally maintained at the desired temperature with variations no greater than _0.01 °. With the cell shown in Fig. 8, there appears to be little, if any, bulk flow of liquid through the diaphragm, and special precautions about leveling of the diaphragm are unnecessary. For calibration purposes it has been found that potassium chloride is an excellent standard. If the diffusion experiment is performed at 25 ° with 0.1 M potassium chloride diffusing into an equal volume of distilled water for a period such that the final concentrations are 0.075 M and 0.025 M for the solution and solvent, respectively, then the diffusion coefficient is 1.867 X 10-5 cm.2/sec. The volumes of the individual compartments of the cell are usually determined by weighing the cell empty and filled with water and then by converting the weight of the water into volume through use of the known density of water.

78

TECHNIQUES FOR CHARACTERIZATION OF PROTEII~S

[2]

This method gives satisfactory results with enzymes, although one must, of course, be certain that the enzyme molecules are not adsorbed on the surface of the diaphragm or that the pore size is not so great as to allow bulk flow. In view of the simplicity of the technique it is advisable to run experiments with different cells so that irregularities or deficiencies in an individual cell are readily detected. Free Diffusion Introduction. In the past ten years, major modifications have occurred in our techniques for the study of free diffusion with the result that today such diffusion studies can be performed routinely, and in commercially available apparatus, with an accuracy greater than that obtainable in the determination of sedimentation coefficients. This tremendous advance in experimental tech~fique was due largely to the rediscovery of interferometric optical methods and their adaptation to diffusion studies, As a consequence of these developments the older, more common procedures used in diffusion measurements of protein are now obsolete. We will therefore omit discussion of the older methods of handling the data obtained through the use of the familiar schlieren optical systems. This seemingly arbitrary decision is justifiable because the newer methods are neither more difficult nor more time consuming than the older methods, and further the accuracy of newer techniques is of the order of 10 times that of the latter. A thorough discussion of diffusion measurements involving schlieren optical systems is presented by Lundgren and Ward, 24 and the research worker who does not have available newer commercial apparatus equipped with interferometric optical systems should turn to that article for a detailed description of the different methods of handling the data. There are now available in this country three different instruments (and in Europe several more), each of which is completely equipped for precise diffusiometry by interferometric methods. Two of these, Model B, American Instrument Company, Inc., Silver Spring, Maryland, and Model H, Spinco Division, Beckman Instruments, Inc., Belmont, California, are versatile in that they possess two different interferometric optical systems in addition to the usual schlieren optical systems. The apparatus, Model 38A, made by the Perkin-Elmer Corporation, Norwalk, Connecticut, possesses one interferometric optical system along with the schlieren system. After many years of experimentation which led to a variety of ingenious designs for diffusion cells, there now seems to be widespread ~4 H. P. Lundgren and W. H. Ward, in "Amino Acids and Proteins" (Greenberg, ed.), Chapter 6. Charles C Thomas~ Springfield, Ill., 1951.

80

TECHNIQUES FOR CHARACTERIZATION OF PROTEINS

[2]

mercial models both the Rayleigh and the Gouy interferometric optical systems, and diffusion coefficients of comparable precision can be obtained by either method. A decision as to which is the method of choice in studying proteins is, at best, somewhat arbitrary; and the use in this laboratory of the Rayleigh method is based largely on convenience and ease of handling the data coupled with the ready availability of tables of probability functions necessary for the calculation of diffusion coefficients. For the Gouy method such detailed tables of the necessary mathematical functions are not yet generally available, and laborious, Enzyme Buffer

U

U

! 2

3

4

FIG. 9. Filling of Tiselius electrophoresis cell for a diffusion experiment. time-consuming interpolations within regions of the existing published tables are necessary. The Gouy method offers an important advantage, since it is very sensitive during the early stages of the diffusion experiment when the boundary is very sharp and the consequent interference fringe pattern is greatly spread. Early in a diffusion experiment the Rayleigh pattern is greatly compressed with a resulting loss in resolution; but the resolution of this method improves as the boundary broadens with time, whereas the resolution of the Gouy method decreases. This difference between the two methods can be decisive if one is dealing with a labile enzyme, since the length of a diffusion experiment using the Gouy method can be appreciably less than that with the Rayleigh method. It should be noted, however, that a long period for dialysis of the protein

[2]

ULTRACENTRIFUGATION, DIFFUSION, AND VISCOMETRY

81

solution against a buffer is required for either method, and the duration of the diffusion experiment itself may not be an overpowering factor. The Rayleigh method requires a reference optical limb with a refractive index close to that of the solvent, whereas the Gouy method requires no reference optical path. With present designs of diffusion cells, this constitutes an advantage for the Gouy method for solvents other than dilute salt solutions. In view of the foregoing brief, comparative comments about the two methods, the decision of the author to emphasize in this discussion the Rayleigh method should not be construed as an indication that it is a superior method but rather that it has been found in this laboratory more

F~G. I0. A representative schlieren and Rayleigh pattern from a diffusionexperiment on ribonuclease. convenient and simpler for work dealing with proteins. Where there is a desire for accuracy of the type desired by workers primarily interested in the theory of diffusion, the worker should examine the elegant studies of Gosting and his collaborators 28 employing the Gouy method and those of Longsworth 2~ with the Rayleigh method. The Rayleigh method can be used as well for electrophoresis, whereas the Gouy method cannot yield information about the position and number of boundaries. It is therefore important that enzymologists presently familiar with schlieren methods should acquaint themselves with the Rayleigh method because of its broad utility. In this regard most of the commercial equipment now gives simultaneous photographs of the schlieren and Rayleigh patterns as shown in Fig. 10 for a peptic digest of ribonuclease. E x p e r i m e n t a l Procedure. It is desirable to perform diffusion experiments at the isoelectric point of the protein, since charge effects there are 2~D. F. Akeley and L. J. Gosting, J. Am. Chem. Soc. 75, 5685 (1953). :7 L. G. Longsworth, J. Am. Chem. Soc. 74, 4155 (1952).

82

TECHNIQUES FOR CHARACTERIZATION OF PROTEINS

[2]

minimal. Frequently other factors such as insolubility or loss of activity preclude this practice, and experiments at other pH values can be performed satisfactorily if there is sufficient electrolyte to damp out charge effects which otherwise would lead to high values for the diffusion coefficient. Well-buffered solutions at an ionic strength of 0.1 suffice for this purpose. For the microcell in use in this laboratory, 3 ml. of protein solution at a concentration of 0.5 g. per 100 ml. and a volume of 300 ml. of solvent are ample. After the protein is dissolved in an aliquot of the buffer, it is dialyzed in the cold for a period of about 24 hours. The number of changes of buffer surrounding the dialysis bag and the length of the dialysis period depend largely on the purity and on other factors such as the stability of the enzyme. In certain cases, such as a study of the peptic digestion of ribonuclease, dialysis of the solution under investigation is precluded because of the permeability of the dialysis tubing to some of the products of the reaction, and diffusion experiments are conducted without dialysis as a means of equilibrating the protein solution against the buffer. For such situations special precautions are taken to subject the buffer to the same treatment as the protein solution so that the content of electrolyte in solution and solvent are as nearly the same as possible. Dialysis is conveniently performed by hanging the dialysis bag containing the solution in an Erlenmeyer flask in which is placed a glass-enclosed magnet and the appropriate solvent. The entire flask can be placed on a magnetic stirrer and stored in a cold room until equilibration is achieved. Dialysis tubing (obtainable from the Visking Corp., 6733 West 65th St., Chicago 38, Illinois) can be obtained in various diameters, and we find that 3~-inch tubing serves well for the small volumes used in this work, since ,it leads to a large surface relative to the volume of the protein solution, thereby ensuring a rapid equilibration. Before filling the diffusion cell it is advisable to centrifuge the solution and solvent for a few minutes at about 3000 r.p.m, to remove lint and any insoluble material such as denatured protein. It is important, before assembly of the cell to form a continuous U-tube as shown in Fig. 9, to lubricate each of the glass end plates of the three sections which slide relative to one another. For this purpose a grease made of two parts of petroleum jelly (Vaseline) and one part of mineral oil proves ideal for most work. The lubricant is readily mixed over a gently boiling water bath, and care should be taken to exclude lint from the grease after it is prepared. Some workers prefer as a lubricant a Dow-Corning silicone fluid, No. 200, of viscosity 7500 to 10,000 centistokes. This is satisfactory, but its removal from the cell at the completion of the experiment is difficult. In lubricating the glass plates, precautions should be observed to prevent the grease from entering the

84

TECHNIQUES FOR CHARACTERIZATION OF PROTEINS

[2]

due to thermal gradients is lower at temperatures near the maximum density of the solvent (ca. 1°). This is not nearly so serious as in electrophoresis, and if the material is stable at higher temperatures then diffusion experiments should be conducted at higher temperatures, since diffusion rates are much higher at 25 ° than at 1°. A 5-ml. syringe equipped with a 14-inch hollow stainless steel needle, No. 17 gage, with a blunt tip is used to transfer the protein solution to the cell. In filling the cell, the rack is tipped to the side so that the bottom section of the U-tube is at an angle and there is little tendency to trap air bubbles in the cell as the liquid is added. In this laboratory, observations of the diffusion process are generally conducted in the left-hand limb of the cell. Accordingly, the rack is tipped toward the right and the syringe needle is placed in the right-hand limb to avoid any contact of the needle with the windows of the diffusion channel. Sufficient solution is added so that the level of the solution in both limbs is about half to two-thirds the way up in the center section. The rack is righted and the needle withdrawn. At this point the cell looks like that illustrated by Fig. 9-1. By means of one of the knobs on the cell rack the bottom section is slid to the right, thereby disconnecting the left- and right-hand limbs of the cell as shown in Fig. 9-2. The syringe needle is again placed in the right-hand limb of the cell, and sufficient protein solution is added to raise the level in that limb just above the glass end plates of the center and top section. Less than 2 ml. of protein solution is involved in filling half of the left-hand section, the bottom section, and the entire right-hand section of the microcell. With the rack in place in the water bath, buffer is very carefully and slowly added down one of the side windows of the left-hand channel by means of a motor-driven syringe with a needle containing a very fine tip. This addition is continued until the buffer level in the lefthand limb corresponds roughly with that in the right-hand limb, as in Fig. 9-2. After a little practice this layering of solvent over solution can be done readily and reproducibly with the formation of rather sharp boundaries between the two liquids. In the microcell with a channel width of only 2 mm. there is little tendency for mixing if the operations are performed with care. The needle is then withdrawn and the center section is moved to the left, dragging with it the bottom section so that the cell sections are arranged as shown in Fig. 9-3. After rinsing of the upper, right-hand section free of protein, solvent is now added to both limbs slowly by means of a 25-ml. pipet whose tip rests against the wall of the extension tubes..This addition is repeated until the level of liquid is above the side arms of the extension tubes. Because of the connection between the two tubes, the level in the two vessels automatically reaches the same value; and there is consequently no danger of flow of liquid

[9.]

ULTRACENTRIFUGATION, DIFFUSION, AND VISCOMETRY

85

when the center section of the cell is moved to the right to form a continuous U-tube, as shown in Fig. 9-4. During the few minutes that have elapsed after the layering of solvent over the protein solution, some diffusion of the protein occurs. Furthermore, the layering itself and the subsequent handling of the cell produce distorted and relatively blurred boundaries so that we now create essentially a new boundary by the siphoning procedure of Kahn and Polson. ~5 This boundary sharpening technique can be performed in a variety of ways with equal success, and the method described here has its origin in the experiences of other workers. ~8 Owing to short supply of some of the diffusing substances, we have imposed the important additional restriction that the method require only a small amount of solution even if there is some sacrifice in the quality and sharpness of the initial boundary. A long, stainless steel needle with a special tip ground to an angle of 45 ° is filled with solvent and lowered into the left limb by means of a rack and pinion until the tip is at the level of the boundary. Care should be taken during this operation in order to prevent contact of the needle with either of the optical windows of the diffusion cell. The needle is 14 inches long, No. 17 gage, and onto its end is soldered a 2-inch length of tubing with inner diameter of 0.012 inch and wall thickness of 0.010 inch. The upper end of the needle is connected to a three-way stopcock either directly or by means of a short length of thick-walled, narrow-bore rubber tubing. If the needle and stopcock are rigidly coupled, extra caution is required in mounting the stopcock on the rack so that the mere turning of the stopcock doesn't impart any movement onto the needle. If there is a short length of flexible tubing between needle and stopcock, then a tubing should be selected which doesn't collapse when suction is applied; also the needle and stopcock must move in unison so that there is no bending of the tubing when the needle is raised or lowered. One end of the stopcock is connected by tubing to a motor-driven syringe of 5-ml. capacity. This tubing, like the other, should have a narrow bore and heavy wall thickness. A length of about 15 inches of Tygon tubing is connected to the third arm of the stopcock. This connection is for convenience in filling the syringe, the stopcock, and the sharpening needle without the risk of introducing air bubbles into the system. We have used a syringe of narrow bore so that linear movement of the plunger of the syringe involves only a small volume change. The motor-driven syringe should be capable of movement in either direction, and the speed of the motor must be adjustable. In connecting the piston of the syringe 28 Thanks are due Drs. H. Hoch, G. Kegeles, T. E. Thompson, and J. L. Oncley for their suggestions regarding different procedures for boundary sharpening in diffusion experiments.

86

TECHI~IQUES FOR CHARACTERIZATION OF PROTEINS

[2]

to the arm driven by the motor, care must be taken that the coupling is flexible so that the plunger won't bind with the barrel of the syringe in case of slight misalignment. This flexible coupling must allow for movement in all directions except that in the direction of movement of the plunger. Here there must be firm, continuous tension at all times with no elasticity as with most rubber connections. Otherwise the movement of the plunger and the liquid will occur in spurts and the boundary sharpening will be difficult to control. Many workers prefer to use a siphon and allow the liquid flow to occur through the sharpening needle under the influence of a fixed pressure head rather than trust a motor-driven syringe to produce smooth action. With the sections of the cell completely aligned to form a U, the needle, the stopcock, and only a small part of the syringe filled with solvent, and the needle in position such that its tip is near the center of the boundary, sharpening is begun. First, the connection between the side arms of the extension tubes is closed by means of a hemostat, and then withdrawal of liquid is started. The motor is adjusted so that the flow is only about 0.1 ml./min. This is continued for about 4 minutes during which time the boundary is considerably sharpened owing to the formation near the tip of the needle of an interface between solvent and solution. The motor is then turned off for a few minutes, and some spreading of the boundary occurs because of diffusion. Again the motor is turned on and another 0.3 ml. of liquid is withdrawn at the same rate of 0.1 ml./min. The withdrawal of liquid is then stopped for a few minutes, and the boundary broadens a little due to diffusion. For the last time the motor-driven syringe is started and liquid is withdrawn for about 3 minutes at 0.1 ml./min. The boundary should be examined during this time to see that the fringes are straight, right up to the position where the boundary is being sharpened. The motor is turned off, the stopcock to the sharpening needle is turned 45 ° to isolate the needle, and the bottom section of the cell is moved to the right in order to break the connection between the left- and right-hand limbs. It is important that these operations be done almost simultaneously, with the aid of another individual if necessary. The time of stopping the flow and moving the bottom section is then recorded as the starting time of diffusion. The needle is withdrawn by careful operation of the rack and pinion. When this is completed, it is advisable to slide the center section to the left, dragging with it the bottom section which will now be in its normal position. The center section of the diffusion cell is now isolated from both upper and lower sections. Thus any dust which falls into the open reservoir tubes or moisture which condenses on the cold extension tubes cannot cause a disturbance of the boundary. As soon as the center

88

TECHI~IQUES FOR CHARACTERIZATION OF PROTEINS

[9.1

symmetrically, and the b o u n d a r y width when sharpening is discontinued should be between 0.3 and 0.4 mm. Calculations. Figure 11 shows a series of typical Rayleigh interference patterns obtained in a diffusion experiment with a peptic digest of ribonuclease. I t should be borne in mind t h a t the observed p a t t e r n is essentially a section of a plot of refractive index versus distance in the cell. Since the refractive index of protein solutions can be considered as varying in a linear fashion with the concentration of solute, the Rayleigh m e t h o d gives a plot of the concentration versus distance in the cell, and if we were

Fzo. 11. Representative Rayleigh interference patterns from a diffusion experiment on a peptic digest of ribonuclease. Pictures from top to bottom were taken at 9, 38, 99, 337 and 1183 rain., respectively, after formation of the boundary. to plot the fringe n u m b e r as a function of fringe position the curve obtained would be the integral of the curves obtained b y schlieren methods. For this reason, the Rayleigh m e t h o d is frequently called the integral fringe method. Thus the total n u m b e r of fringes, J, is a measure of the change in concentration across the boundary, and it is equal to a hn/)~, where a is the cell thickness (along the optical path), An is the difference in refractive index between solvent and solution, and X is the wavelength of light. T o compute the diffusion coefficient from Rayleigh patterns we first must evaluate the total n u m b e r of fringes, J . This is done most readily b y using different photographs. An early picture, before the fringes are completely resolved as in the 9-minute photograph, is used to determine the fractional part of J ; and a later photograph, after the fringes are distinctly separated as in the 337-minute photograph, is used to measure

90

TECHNIQUES FOR CHARACTERIZATION OF PROTEINS

[2]

will be straight except for small regions at the top and bottom of the channel where cementing of the end plates onto the optical glass windows causes some distortion. If the fringes are not straight throughout the entire length of the diffusion cell, it is advisable to choose the best region and to form the boundary at that level. There are a variety of methods of handling the data for the calculation of diffusion coefficients. For example, the equivalent of the wellknown height-area method can be used, since J is a measure of the area and we can readily determine the maximum height (of the gradient curve) by finding the minimum separation of fringes. This method has been used by Svensson ~9 and others, but the method used by Longsworth ~7 is recommended both because of its accuracy and because it uses much more of the experimental data and is therefore capable of detecting deviations from ideal diffusion behavior. Computations by the method of Longsworth involve the assumption that the concentration distribution in the boundary is Gaussian, and therefore we can use the Tables of Probability Functions (Federal Work Agency, Works Project Administration, Superintendent of Documents, Washington, D. C., 1941). These tables are very complete and the calculations with them can be made without the need of interpolation. If the concentration and cell thickness are such that there are about 20 fringes in the boundary, then the position and number of all the fringes are tabulated. The number of the fringe with which the cross hairs coincide outside the boundary is termed the zero'th fringe. If there are as many as 50 fringes in the boundary it is advisable, in order to reduce labor, to record the position and number of every other fringe. The method of calculation is illustrated by Table IV showing data obtained on a peptic digest of ribonuclease. In column 1, headed fl, are listed the number of the different fringes up to a value less than J/2. The second column lists the computed value, jk* = (2jk - J)/J, for each value of jk. As long as j~ is less than J/2, the sign of the computed value, j~*, in column 2 can be ignored. Corresponding to each value of jk there should be a value of jr, where j~ is greater than J/2. The values of jl are listed in column 3, and the computed values, jz* = (2jl - J)/J, are tabulated in column 4. It should be stressed that the pairing of fringes can be done in a variety of ways. Thus the pairing of fringes 2 and 10, 3 and 11, 4 and 12, etc., could be changed to 2 and 11, 3 and 12, 4 and 13, etc., or 1 and .10, 2 and 11, 3 and 12, etc., or to a variety of other combinations. Pairing of the fringes in different ways can furnish valuable information about the homogeneity of the diffusing substance and the dependence of diffusion coefficient on concentration. We usually omit the first and last 29 H. Svensson, Acta Chem. Scand. 5~ 72 (1951).

[9-]

ULTRACENTRIFUGkTIO~ DIFFUSION, AND VISCOMETRY

i <

Z ©

r~

~

×

N t~

N

r~ 0

u~ u~ ~

u~ u~ ue~ u~ U~

Z

u~

O

O

~t

91

92

TECHNIQUES FOR CHARACTERIZATION OF PROTEINS

[2]

fringes, since the accuracy in locating these fringes is low, owing to small curvature of these fringes at the ends of the boundary. The corresponding microcomparator readings for each jk and j~ are listed in columns 5 and 6 as Hk and H~, and the distance in centimeters between paired fringes, Hk -- Hz, is listed in column 7 as AH. The values of jk* and j~* correspond to

2 foe_a,d~ v7 listed in the probability tables in the right-hand column of each page. In the left-hand column are listed the values of x corresponding to each value of the integral. Thus the values of jk* and j~.*are found in the righthand column of the probability tables and the corresponding values of x determined. Since x is equal to h/(4Dt)~, these values are recorded for all values ofjk* and j~* in columns 8 and 9. The symbol h is the cell height and is equal to zero at the center of the boundary, where j = J/2. The values in columns 8 and 9 are added to give Ah/(4Dt) ~ shown in column 10. The values of column 7 are now divided by those in column 10 to give column 11, (4Dt) ~ AH/Ah. AH/Ah is the magnification factor of the camera lens relating distances in the diffusion cell to those on the photographic plate. This factor is determined by photographing an accurately ruled glass scale mounted in the appropriate place on the cell rack and comparing the distance between lines on the photograph and original scale. In our instrument AH/Ah is very close to unity, and the average of the values of column 11 is, therefore, (4Dr) ~, where D is the diffusion coefficient in square centimeters per second, and t is the time in seconds. The calculation of D follows immediately to give the value shown in the bottom of the table. This calculation is repeated for a number of pictures taken at different times. The values of D so obtained may show a slight trend downward with time because the initial boundary was, of course, not infinitely sharp. Correction for this effect can be made by determining the "zero time correction." This is most readily obtained from a plot of the apparent diffusion coefficients versus the reciprocal of time. The intercept of this linear plot at lit = 0, corresponding to infinite time, is the true diffusion coefficient, and the slope is D At, where At is the zero time correction. For small molecules like sucrose the zero time correction is of the order of 20 seconds, whereas for proteins it may be of the order of several minutes. The value of the diffusion coefficient obtained above corresponds to a certain solvent and a certain temperature. It is common practice to report diffusion coefficients, D~o.~, corresponding to a temperature of 20 ° in a solvent with the viscosity of water. Correction of the measured value to

94

TECHNIQUES FOR CHARACTERIZATION OF PROTEINS

[2]

microcomparator are recorded. It should be noted that the positions of the Gouy fringes correspond to the concentration gradients in the diffusion cell. Thus the zero'th fringe corresponds to the peak of the schlieren curve and the J / 2 fringe in the Rayleigh system. Also the top fringes in the Gouy system correspond to the ends of the boundary or the first and last Rayleigh fringes. The position of the undeviated slit image is also recorded. This l~osition can be determined from the fringe pattern resulting from the two horizontal slits in the Gouy mask. These slits are so oriented that light passing through them actually traverses the water bath and not the diffusion cell. In the resulting pattern, the center of the central bright fringe corresponds to the position of the center of the image of the light source. It is frequently found, however, that this bright central fringe is displaced if the same double-slit assembly is located in front of the diffusion cell filled with a homogeneous solution. Account must be taken of this deviation, which probably arises from optical imperfection in the ceil. The position of the undeviated slit image can also be obtained, apparently with sufficient precision, by careful location of the brightest fringe in the Gouy pattern. With the recorded values of the undeviated slit image and all the interference minima, a table of fringe number, j, and fringe distance, Y¢, in centimeters can be constructed. If the photograph is enlarged by the cylinder lens, then these distances on the plate must be divided by the magnification of the cylinder lens. For each value o f j the appropriate value of z~is obtained by adding ~ , i.e., zj = j + 3/~. A more accurate value of z¢ can be obtained by the use of Table 1 in the paper by Gosting and Morris. 3° With the values of z¢, the corresponding values of f(z) are computed for each fringe by the relationship (17) f(z) = jzj These values of f(z) are then used to compute values of e-~2 for each fringe. This is performed through the use of Table 1 in the paper of Kegeles and Gosting/' Since this table is rather abbreviated, considerable interpolation is necessary unless one computes a more extensive table from the equation defining f(z) in terms of e-~'~. With the values of e-*~' and Yj, the corresponding value of Ct can be calculated from the relation C,-

Y~

e-zi2

(18)

For an ideal diffusion curve, Ct should be independent of j. The average a0 L. J. Gosting and M. S. Morris, J. Am. Chem. Soc. 71, 1998 (1949). 31 G. Kegeles and L. J. Gosting, J. Am. Chem. Soc. 69, 2516 (1947).

[9.]

ULTRACEN'TRIFUGATION., DIFFUSION., &N'D VISCOMETRY

95

value of Ct is then used to calculate an apparent diffusion coefficient, D,pp., (Jkb)~ Dap~. - 4~.Ct2t

(19)

In this equation, b is the optical lever arm or the distance between the schlieren lens and the schlieren diaphragm (this value is supplied by the manufacturer), k is the wavelength of the light used, and t is the time in seconds. As in the Rayleigh method, photographs at different times are measured and the apparent diffusion coefficients plotted against 1/t to give the time diffusion coefficient and also the zero time correction.

IV. Viscometry Introduction. Although our theoretical understanding of the viscosity of pure liquids is rather limited at present, much is known about the viscosity of solutions of macromolecules. In conjunction with other physical-chemical data, studies of the viscosity of solutions of large molecules can yield valuable information about the molecular size and shape of the dissolved molecules. The coefficient of viscosity of a liquid is generally considered as a measure of its resistance to flow when the liquid is subjected to a shearing force. It can be shown very readily that the coefficient of viscosity is a direct measure of the amount of energy needed to maintain a given rate of flow in a liquid. If particles or large macromolecules such as a protein are added to the liquid, the normal flow patterns in the liquid are disturbed by these particles and more energy is dissipated in the maintenance of flow. Einstein first showed that the increase in viscosity due to the presence of large, rigid, uncharged, spherical particles was proportional to the volume fraction occupied by the particles. For particles known to be spherical, viscosity measurements provide information about the volume concentration of the dissolved macromolecules. Since the dry weight concentration of the solute is generally known, the viscosity data may, for the particular case of spherical particles, be interpreted in terms of the amount of solvent associated in solution with a gram of dry material. In general, of course, the shape of protein molecules is not known, and it is likely that many of them cannot be approximated by rigid, impermeable spherical particles. Anisometric particles such as rodlike or platelike objects are subjected to Brownian motion in solution, and as a result of the rotation of the particles the effective volume occupied by the particles is much larger than their true geometric volume. As a consequence, anisometric particles which are randomly oriented in solution cause a greater increase in viscosity than do spherical particles. Reliable theories are now available relating the viscosity of solutions of

96

TECHNIQUES FOR CHARACTERIZATION OF PROTEINS

[2]

anisometric particles to both the shape and effective volume of the large particles. Unless some simplifying assumptions are made regarding the macromolecules, viscosity data must be combined with other data to determine both the size and shape of the macromolecules. Experimental Procedure. The determination of the absolute viscosity of a liquid is a difficult experimental problem, and recourse is usually made to comparative studies of different liquids and calibration of instruments through the use of liquids of known viscosity. The most popular viscometer is the so-called capillary viscometer in which measurements are made of the volume rate of flow of the liquid through a capillary of known, length and diameter under the influence of a known pressure head. Poiseuille showed m empirically the interrelationships among the various experimental factors, and theories have now been developed to explain the observed results. If a volume of liquid, v, in milliliters, flows through a capillary of length 1 and radius r, in centimeters, under a pressure head, h, in centimeters, the viscosity can be calculated from

hgpr4t~ -

81v

(20)

where g is 980 cm./sec. ~, p is the density in grams per milliliter and ~ is the viscosity in poises. Since we are interested in comparative results for different liquids, a Fro. 13. second liquid can be introduced into the instrument and C a p ill a r y measurements of the volume rate of flow or outflow time viscometer. can again be made. In general, the instrument is used in a reproducible manner, and the quantities h, g, r, l, and v will be the same for the two liquids. We can write, therefore, .

~/~0 = (t/t0)(p/p0)

(21)

where T0, to, and p0 are the viscosity, outflow time, and density for the reference liquid. Figure 13 shows a capillary viscometer, commonly termed an Ostwald viscometer. A given volume of liquid is placed in the reservoir bulb by means of a pipet. With gentle suction applied at the right-hand limb of the viscometer, the liquid is forced through the capillary into the drainage bulb. Suction is continued until the liquid level is above the line scratched in the glass tube above the drainage bulb. There should be sufficient liquid in the viscometer to fill completely the drainage bulb, the capillary tubing, and part of the reservoir bulb. In the same way as the line is engraved above the drainage bulb so there is also engraved a line below the bulb at a distance about 2 cm. from the

[2]

ULTRACENTRIFUGATION, DIFFUSION, AND VISCOMETRY

97

bulb. After the liquid level is raised above the upper engraved line, the negative pressure is released so that there is atmospheric pressure operating on both sides of the viscometer. The liquid flows due to the hydrostatic head, and the time required for the meniscus to pass between the two engraved lines is the outflow time for the volume of liquid contained in the drainage bulb. With this outflow time, the density of the liquid, and measurements of the physical characteristics of the viscometer--i.e., length and radius of the capillary, volume of liquid contained between the two engraved lines, and the mean hydrostatic head between the drainage and reservoir bulbs--the coefficient of viscosity of the liquid can be calculated according to equation 20. As indicated above, however, it is a better procedure to measure the outflow time and density of the unknown liquid, such as a solution of enzyme of known concentration, and compare these results with those of a known liquid, such as water. In the latter case the relative viscosity is calculated from the relative outflow times and the relative densities according to equation 21. Since the viscosity of water at different temperatures is readily available i~ handbooks, the viscosity of the unknown solution can be calculated. There are many precautions to be exercised in the design, construction, and use of a viscometer of the type shown in Fig. 13. With regard to the use of the viscometer for precise work the obvious requirements are accuracy in measuring the outflow times and the densities of the liquids. To facilitate accurate measurements of the outflow time, we have used fine slits made by scratching through a thin film of black cement which coats the glass, in place of the customary engraved lines above and below the drainage bulb of the viscometer. The passage of the meniscus across the slits causes a bright light flash to be visible, due to internal reflections ill the tube, and thus the time at which the liquid passes a given point can be obtained through reflex responses rather than through the more subiective action of judging when the meniscus reaches an engraved line. With the use of a mechanical stopwatch which makes one revolution every 10 seconds, five successive readings of the outflow time for a given liquid are found to lie within about 0.05 second for total outflow times of the order of 60 seconds. As will be seen later, the use of viscosity data for studies of enzymes requires measurements on dilute solutions for which the outflow time is only slightly larger than that of the solvent. Therefore, extreme accuracy is required for the results to have any validity. In such studies, measurements with an electric timer, such as Model S-1 of the Standard Electric Time Co., which makes one revolution per second are recommended. No~ infrequently, five successive readings of the outflow time for the same sample will show an average deviation of only a few hundredths of a second. Densities of the liquids can be measured

98

TECHNIQUES FOR CHARACTERIZATION OF PROTEINS

[2]

with satisfactory precision by using standard pycnometric procedures. With a pycnometer of 5-ml. capacity the density of a liquid can be measured readily to _+0.0001 g./ml. The density term, p/po, of equation 3 is seldom as great as 1.010, and generally it is in the neighborhood of 1.002. If we measure the viscosity of a solvent such as 0.2 M sodium chloride, then P/POrepresents the density of 0.2 M sodium chloride relative to that of water, and the value of p/po is close to 1.01. When the measurements involve a protein solution, the reference liquid will contain the same inorganic salts and the difference in density between the solution and solvent is attributable only to the protein. In the absence of experimental measurements of the density term, due, for example, to inadequate supply of protein for pycnometric studies, the density term can be calculated with satisfactory precision by assuming additivity of the weights and volumes of the protein and the solvent. Thus a solution of protein in water containing 1 g. per 100 ml. of solution can be considered as being composed of 1/1.35 ml. of solid protein (the density of mosrTj 18.24 0 T6l TD 1 1 1

[9.]

ULTRACENTRIFUGATION~ DIFFUSION~ AND VISCOMETRY

99

flowing back and forth in the viscometer. This can be reduced somewhat if care is exercised so that the liquid flows slowly through the capillary when suction is applied above the drainage bulb. In order to ensure that the hydrostatic head of liquid, h, is the same ~t all times, the viscometer should be placed in a metal frame which ~llows for alignment of the viscometer in a vertical position. Once the viscometer is placed in the frame it should not be removed, even for cleaning, unless restandardization is performed with a known liquid. Care should be exercised so that the frame can be mounted on a support in a reproducible manner and so that vibrations due to the stirring of the water in the bath do not affect the viscometer. Capillary viscometers are subject to several limitations which can be eliminated or at least minimized by careful design. Since the liquid is forced both to enter the capillary tube from the drainage bulb and then to leave the capillary into the reservoir bulb, there will be energy losses in establishing the flow pattern characteristic of the capillary. This effect has been termed the kinetic energy effect, and corrections sometimes need be made. If the design is such that the volume rate of flow of liquid is small, the kinetic energy correction can be reduced sufficiently so as to be negligible. This is most readily accomplished not by reducing the hydrostatic head of liquid which introduces other complications or by reducing the radius of the capillary which makes more troublesome the problem of dust particles, but rather by increasing the length of the capillary. If the reservoir bulb is rather large in cross section, slight errors in pipetting the solutions in the viscometer will cause only a small variation in the mean hydrostatic head. Other corrections such as the drainage correction and the surface tension correction are generally almost negligible, since comparisons are made between dilute protein solutions and the solvent. In this laboratory, the capillary tubing used for viscometers has a diameter of about 0.6 mm. and a length between 50 and 100 cm. The diameter is generally measured by weighing a snlall piece of capillary tubing with and without a small column of mercury in the capillary. From measurement of the length of the mercury column and the weight of the mercury whose density is known, the diameter of the capillary is readily determined. Uniformity of the capillary with respect to diameter is tested by using the whole length of capillary and sliding a small amount of mercury along the inside so that the length of the mercury column can be measured in different positions of the capillary. If the length of this mercury column is independent of position in the capillary, the uniformity of the bore of the capillary is demonstrated. The drainage bulb is generally made of tubing with a diameter about 2 ram. by careful glass

100

TECHNIQUES FOR CHARACTERIZATION OF PROTEINS

[2]

blowing to produce a symmetrical bulb of approximately the volume desired. Since many proteins are in scarce supply, we use a bulb of about 0.7-ml. capacity, the volume of which is determined roughly with mercury. The bulb with several centimeters of 2-mm. tubing on either side of it is then fused to one end of the capillary tubing which is then bent carefully about every 20 cm. so that the over-all size of the instrument is not cumbersome. Care is taken in making the turns in the capillary so as to avoid constricting the capillary. The reservoir bulb with a 25-cm.long glass tube (15-mm. inside diameter) is then fused to the other end of the capillary tubing so that the vertical distance between the drainage bulb and the reservoir bulb is about 15 cm. At. the top of the drainage bulb a small piece of glass tubing of 4-ram. diameter is fused onto the 2-mm. tubing, and then cross braces of glass rods are added at various positions to strengthen the viscometer and reduce the risk of breakage. With an instrument of the type described, the outflow time is about 80 seconds and the kinetic energy correction, pv/8~rlt, which should be subtracted from equation 2 is less than 0.1% of the term h g p r 4 t r / 8 1 v . Once the instrument is constructed, measurements with water are made and the viscosity is calculated according to equation 20. This is done not to measure the absolute viscosity of water at the temperature of the water bath, but rather to show that no unforeseen complications have arisen, such as constriction of the tubing, during the construction of the instrument. If the viscosity calculated in this way is within 10% of the known value, then the instrument can be considered satisfactory for use. C a l c u l a t i o n s . It is the increment in viscosity caused by the addition of a known volume fraction of the solute which is of interest to the biochemist, since this is related to the physical properties of the macromolecule. As Einstein pointed out, the theories require that measurements be made at sufficiently low concentrations in order to minimize hydrodynamic interactions among the macromolecules. Therefore, experiments should be conducted at several different concentrations and the data plotted in a manner which permits extrapolation to infinite dilution. If the viscosity of the solvent is n0, the viscosity of a solution, n, of concentration c can be expressed in the form of a power series, 7/70 = l $

Ac $

Bc ~-~

• • •

(22)

where n / n o is generally written 7,e~., the relative viscosity. The term specific viscosity, 7sp., is used quite frequently and is equal to nr~,. - 1. If the specific viscosity is divided by c, we obtain n,p./c = A + B c +

• • •

(23)

[2]

ULTR~_CEN'TRIFUG~-TION~ DIFFUSION, AND VISCOMETRY

101

where ~,p/c is frequently termed the reduced viscosity. At infinite dilution the second and following terms in the power series become negligible, and we obtain equation 24, where [7] is defined lim (~,,./c)c--,o = A = [~]

(24)

as the intrinsic viscosity. Note t h a t it has the units of reciprocal concentration. If, as is rarely the case, the concentration, c, is in volume units, VISCOSITY OF RIBONUCLEASE

at pH 2.3

16.0

"<)"-0"----~

0

O--

"qsp/C cc/gm 8.0

I

i

I

L

I

heated o heated with HSCH2CH20H

1.160

k080 ql/~lo ~

~

t~.."

1.000 2

6 t0 CONC. IN mg/cc. FIO. 14. Plot of n,p./c and n/n0 versus concentration for ribonuclease treated in different ways. i.e., milliliters of solute per milliliter of solution, then [7] would be dimensionless. If the concentration is in grams per milliliter or grams per 100 ml. the intrinsic viscosity will have the units milliliters per gram or deciliters per gram, respectively. Since it is the intrinsic viscosity which is needed, the q u a n t i t y n,p./c should be plotted against c to give curves such as t h a t shown in Fig. 14. Unfortunately such plots usually show wide scattering of the points, especially at low concentrations, and it is sometimes difficult to extrapolate to a reliable value for the intercept, which is the intrinsic viscosity, [7]. I t is advisable in such cases to plot the d a t a also as m,. versus c, which yields a curve such as t h a t shown in Fig. 14.* To evaluate the intrinsic viscosity from such a curve we must * The plot would be identical to that shown in the lower part of the figure but the ordinates would be decreased by 1.000.

[2]

ULTRACENTRIFUGATION, DIFFUSION, AND VISCOMETRY

103

solution is represented as an impermeable rigid ellipsoid of revolution whose hydrodynamic behavior in solution would be equivalent to that of the protein. This is not to say, of course, that the protein molecule in solution is actually an ellipsoid of revolution, and in fact the size and shape of the actual molecule are likely not to be the same as those calculated for the equivalent particle. It should be stressed that the value of f3 defined by Scheraga and Mandelkern is extremely sensitive to slight experimental errors. Oncley, at a much earlier time, 9 proposed another method for handling the dilemma of evaluating the independent contributions of hydration and shape to the hydrodynamic behavior of protein molecules in solution. In effect, he assumed that the volume of a protein molecule in solution is only slightly greater than that calculated from the partial specific volume, with the slight increase being due to hydration. With an assumed value for the hydration, it is then a straightforward matter to calculate the shape of the kinetic unit. The validity of such an assumption for the volume of a protein molecule in solution is a matter of some controversy; though it may be correct for some native proteins, it is almost certain that the more general approach of Scheraga and Mandelkern is more meaningful for denatured proteins. It is beyond the scope of this article to discuss in detail this difficult problem, and the reader is referred to the above papers and the discussion by EdsalP ~ for the different points of view. For detailed calculations the reader will find useful tables in Cohn and Edsall 2~ which relate the frictional ratio and the intrinsic viscosity to the shape of the hydrodynamic unit. Also the contour plots presented by Oncley for these relationships will be of considerable use. It should be pointed out that molecular weights can be calculated from sedimentation and viscosity data or from diffusion and viscosity data if it is either known or assumed that the molecules in solution do not depart significantly from rigid, impermeable spheres. For these calculations the following equations should be used: M = 4690(s2°'w)~['/]~

(1 M-

-

(26)

?p)~

6.58 X 10-'6 (D20.w)3in]

(27)

In equations 26 and 27 a value of ~ equal to 2.16 X 10s has been employed and will provide reliable results even for materials with axial ratio about 5 to I. The sedimentation coefficientsare in Svedbergs, and the intrinsic viscosityin reciprocal concentrationunits, i.e., (g./I00 ml.)-'. ~ J. T. Edsall, in "The Proteins" (Neurath and Bailey, eds.), Chapter 7. Academic Press, New York, 1953.

[1A]

PAPER ELECTROPHORESIS

21

[IA] Paper Electrophoresis B y A. HELGE F. LAURELL

Introduction T h e basic elements of p a p e r electrophoresis m a y be said to h a v e had forerunners in experiments in which filter p a p e r was soaked in different salt solutions a n d dipped into beakers connected through p l a t i n u m electrodes to the poles of V o l t a ' s pile (see the collected v o l u m e s of F a r a d a y and of Berzelius for references), b u t it was p r o b a b l y not until the end of the nineteenth c e n t u r y t h a t the use of electromigration as a potential separation process was conceived. T h e applicability of the m e t h o d of p a p e r electrophoresis seems to h a v e been realized in 1937 b y KSnig in Brazil, who used it for separating v e n o m toxins. I t was later independently reintroduced in 1948 b y H a u g a a r d and K r o n e r and b y Wieland and Fischer and through the publications in 1950 of D u r r u m , Biserte, G r a s s m a n n and Hannig, T u r b a a a d Enenkel, Cremer and Tiselius, and M c D o n a l d et al.; the m e t h o d is now widely used. No a t t e m p t will be m a d e to give a complete bibliography, as the technique during the last few years has been the subject of several monographs, ~-~ reviews, 6-1~ a n d symposia, ~e-15 to which the reader is referred. T h e applicability 1 C. Wunderly, "Die Papierelektrophorese." Verlag H. R. Sauerli~nder, Frankfurtam-Main, 1954. 2 R. J. Block, E. L. Durrum, and G. Zweig, "A Manual of Paper Chromatography and Paper Eleetrophoresis." Academic Press, New York, 1955. 3 H. J. McDonald, "Ionography. Electrophoresis in Stabilized Media." Year Book Publishers, Chicago, 1955. 4 M. Lederer, "Introduction to Paper Electrophoresis and Related Methods." Elsevier Publishing Co., Amsterdam, 1955. hA. Dittmer, "Papierelektrophorese. Grundlagen-Methodik-Klinische Betrachtungen." Gustav Fischer Verlag, Jena, 1956. 6 W. Grassmann, Naturwissenscha]ten 38, 200 (1951). A. Tiselius and P. Flodin, Advances in Protein Chem. 8, 461 (1953). 8 H. G. Kunkel, "Methods of Biochemical Analysis," Vol. 1, p. 141. Interscience Publishers, New York, 1954. 9F. Turba, "Chromatographische Methoden in der Protein-Chemie," p. 324. Springer-Verlag, Berlin, 1954. 10R. L. M. Synge, "Modern Methods of Plant Analysis," Vol. 1, p. 55. SpringerVerlag, Berlin, 1956. ~1H. J. McDonald, Federation Proc. 14, 733 (1955). 12Symposium Utrecht. Chem. Weekblad 49, 229 (1953). 13 let Colloque du Laboratoire de l'H5pital Saint-Jean a Bruges, Union Chimique Belge S. A., 1953. ~42~. CoUoque du Laboratoire de l'HSpital Saint-Jean ~ Bruges, Editions Arscia, Bruxelles, 1954. 15 Ciba Syrup. on Paper Electrophoresis, London (1956).

22

TECHI~IQUES FOR CHARACTERIZATION OF PROTEINS

[1A]

of the method is in most cases obvious and will only be discussed briefly. Applicability Paper electrophoresis may be used for following the distribution of activity among the different protein fractions in each successive step in the course of fractionations by conventional methods such as extraction, salting out, or adsorption. If, in a certain step of a purification procedure, one intends as an alternative to apply zone electrophoresis in columns, paper electrophoresis may be used to find a suitable pH and buffer in which to perform the separation. It is an advantage that only about 0.5 mg. of protein has to be used in each of the preliminary experiments. In many cases, preparative separations can be carried out on a fairly large scale on thick filter papers (see Schultze and Bie118), but zone electrophoresis in columns is probably to be preferred in most cases because of its greater capacity (up to at least 10 to 20 g. of protein) and because of the possibility of using supporting media which give negligible adsorption in a given case. Relative mobility measurements are made by running, on the same paper, the test sample together with a sample of known mobility. If a homogeneous reference substance is found which is not adsorbed to the paper and which migrates an equal distance as the test sample, the mobility is probably of the same magnitude, especially if this equality in migration should hold over different concentrations of hydrogen ion. The method is not suitable for absolute mobility measurements, however, even though an approximate value for the isoelectric point may be found from data collected at different pH's. Approximate mobility values may be arrived at in certain types of apparatus where the evaporation is prevented by placing the paper between two parallel glass plates, as done by Kunkel and Tiselius.17 It is, however, technically difficult to get good separation patterns in this type of apparatus. If enough material is available, mobility measurements will best be "performed with the moving boundary technique. Wallenfels and Pechmann TM were among the first to apply paper electrophoresis in enzyme studies. These authors detected fractions with amylase, protease, lipase, and phosphatase activities in a commercial enzyme preparation (takadiastase). M a n y different enzymes from various origins have since been studied, such as proteinase,i~9,2°pepsin, 21.52 le H. E. Schultze and H. Biel, Behringwerkmitteilungen 30, 72 (1955). 1TH. G. Kunkel and A. Tiselius, J. Gen. Physiol. 35, 89 (1951). 18K. Wallenfelsand E. Pechmann, Angew. Chem. 63, 44 (1951). lg j. M. Gillespie, M. A. Jermyn, and E. F. Woods, Nature 169, 487 (1952).

[IA]

PAPER ELECTROPHORESIS

23

t r y p s i n , 23 c a t h e p s i n , 2' f i b r i n o k i n a s e , 2° a m i n o p e p t i d a s e , :°,~4 r i b o n u c l e a s e 25 a n d its r e a c t i o n p r o d u c t s , 26 m a l t a s e 27,2s i n v e r t a s e , 27 d e x t r i n a s e , 27 cellulase, 29 sucrase, ~9 amylase,'9,:~, 30 glucuronidase,~9, a~ h y a l u r o n i d a s e , a2 lactase, ~7 l y s o z y m e , 33 aldolase, 34 enolase, 35 p h o s p h o r y l a s e , 38 A T P a s e , 37 p h o s p h o m o n o e s t e r a s e , ~s phosphatases,20,~0.3'. 39-43 cholinesterase,30.44, 4~ lipase,S° peroxidase46,47 dehydrogenases,34.4S~,b a n d c y t o c h r o m e c. 49 T h e a b o v e - m e n t i o n e d references give some e x a m p l e s of d i f f e r e n t t e c h n i q u e s for d e t e c t i n g e n z y m a t i c a c t i v i t y on t h e paper. T h e p a p e r strip n m y be d i v i d e d i n t o t w o e q u i v a l e n t strips, one of which is used for s t a i n ing the p r o t e i n zones a n d t h e o t h e r for d e t e c t i o n of e n z y m a t i c a c t i v i t y . T h i s can be d o n e b y c u t t i n g t h e p a p e r i n t o s e g m e n t s each of which is s u b s e q u e n t l y e l u t e d a n d t e s t e d for a c t i v i t y b y c o n v e n t i o n a l m e t h o d s . I n m a n y cases it is possible to s p r a y t h e s u b s t r a t e d i r e c t l y o n t o the p a p e r - p r e f e r a b l y before t h e p r o t e i n f r a c t i o n s h a v e dried on t h e paper. A f t e r 20 F. Lundquist, T. Thorsteinsson, and O. Buus, Biochem. J. 59, 69 (1955). 2~ W. Grassmann, K. Hannig, R. Merten, and G. Schramm, Z. physiol. Chem. 289, 173 (1952). 22 W. D. Heinrich, Biochem. Z. 323, 469 (1953). 23 E. Nikkilh, K. Ekholm, and H. Silvok, Acta Chem. Scan& 6, 617 (1952L 2~ D. H. Spackman, E. L. Smith, and D. M. Brown, J. Biol. Chem. 212, 255 (1955). 25 A. M. Crestfield and F. W. Allen, J. Biol. Chem. 211, 363 (1954). 26 F. F. Davis and F. W. Alien, J. Biol. Chem. 217, 13 (1955). 27L. R. Wetter and J. J. Corrigal, Nature 174, 695 (1954). 2s L. R. Wetter, Biochim. et Biophys. Acta 18, 321 (1955). 29 M. A. Jermyn, Australian J. Sci. Research B5, 433 (1952). 30 A. Delcourt and R. Delcourt, Compt. rend. soc. biol. 147, 1104 (1953). 3~ G. T. Mills and E. E. B. Smith, Biochem. J. 49, vi (1951). ~2 A. Caputo, Nature 17-% 358 (1954). 33 p. Caselli and H. Schumacher, Z. ges. exptl. Med. 124~ 65 (1954). 34 G. Toschi, Boll. soc. ital. biol. sper. 30, 565 (1954). 35 B. MalmstrSm, Arch. Biochem. and Biophys. 46, 345 (1953). ~6G. Toschi, Boll. soc. ital. biol. sper. 30, 563 (1954). a7 G. Toschi, Boll. soc. ital. biol. sper. 30~ 567 (1954). 38 K. M. MOller, Biochim. et Biophys. Acta 16, 162 (1955). 39 j. Roche and S. Bouchilloux, Bull. soc. chim. biol. 35, 567 (1953). 4o G. Eisfeld and E. Koch, Z. ges. inn. Med. u. ihre Grenzgebiete 9, 519 (1954). 4~R. S. Levy and D. Mazia, Arch. Biochem. and Biophys. 44, 280 (1953). ~ G. Nylander, Scand. J. Clin. Lab. Invest. 7, 254 (1955). ~a R. W. Baker and C. Pellegrino, Scand. J. Clin. Lab. Invest. 6, 94 (1954). 44 p. G. Togni and O. Meier, Experientia 9, 106 (1953). 45 C. A. Zittle, E. S. DellaMonica, J. H. Custer, and R. Krikorian, Arch. Biochem. and Biophys. [i6, 469 (1955). 4~ M. A. Jermyn, Nature 169, 488 (1952). 4~ M. A. Jermyn and R. Thomas, Biochem. J. 56, 631 (1954). ts~ E. Mitidieri, L. P. Ribeiro, O. R. Affonso, and G. G. Villela, Biochim. el Biophys. Acta 17, 587 (1955). 4sb T. Wieland and G. Pfleiderer, Angew. Chem. 69, 199 (1957). 49S. Paleus, Acta Chem. Scand. 6, 969 (1952).

24

TECHNIQUES FOR CHARACTERIZATION OF PROTEINS

[].A]

an incubation period the zones of a c t i v i t y are located. This can be done b y using ultraviolet absorption or a suitable color reaction for either the s u b s t r a t e or the product. I n c o r p o r a t i o n of radioactive isotopes in enzymes or substrates which are studied b y p a p e r electrophoresis greatly facilitates their localization on the paper. This procedure has, for instance, been used for studying the p u r i t y of P32-1abeled hexose phosphates. 50 The fate of intramuscularly injected labeled D F P (diisopropylfluorophosphonate), with special regard to its distribution a m o n g the serum esterases, has also been studied b y this method. 61 The radioactive zones are m a d e visible as r a d i o a u t o g r a p h s or are located b y direct m e a s u r e m e n t or b y a recording a u t o m a t i c scanning device. Techniques for combining p a p e r electrophoresis and p a p e r c h r o m a t o g r a p h y , 1-4,5~ either in one or in two separate operations, 53 are useful in cases of low molecular weight substances. T h e introduction of volatile buffers 54-5s for the first electrophoretic separation has facilitated the subsequent chromatographic procedure 59-6~ which otherwise is a p t to be disturbed b y salt effects. A p p a r a t u s for twodimensional p a p e r electrophoresis is likewise reviewed in the m o n o g r a p h s already mentioned. 1-4 A new construction has recently been described b y Mead. ~ After electromigration in one direction, the p H of the buffer in the p a p e r is changed b y exposure to a certain constant v a p o r pressure of ammonia. Electromigration perpendicular to the previous direction is then initiated at the new pH. F o r special demonstrations p H gradients perpendicular 63 or parallel 64 to the electric field h a v e been introduced; the latter alternative has been used b y H o c h 65 for electrophoretic separations of v e r y dilute protein solutions without prior concentration. 50K. T. Schild and L. Bottenbruch, Z. physiol. Chem. 292, 1 (1953). 51R. Goutier, Biochim. et Biophys. Acta 19, 524 (1956). 59B. KickhOfen and O. Westphal, Z. Naturforsch. 7b, 659 (1952). 53 W. Grassmann, H. Hannig, and M. P15ckl, Z. physiol. Chem. 299, 258 (1955). 54R. Consden, A. It. Gordon, and A. J. P. Martin, Biochem. J. 40, 39 (1946). 55H. Mich], Monatsh. Chem. 82, 490 (1951). 56C. H. W. Hirs, S. Moore, and W. H. Stein, J. Biol. Chem. 195, 669 (1952). 57G. G. F. Newton and E. P. Abraham, Biochem. J. 58, 103 (1954). 5s j. Porath, Nature 175, 478 (1955). 59E. L. Durrum, J. Colloid Sci. 6, 274 (1951). 80G. B. Marini-Bettolo, Gazz chim. ital. 84, 1155 (1954). 61R. J. Block, E. L. Durrum, and G. Zweig, " A Manual of Paper Chromatography and Paper Electrophoresis," p. 379. Academic Press, New York, 1955. 82T. It. Mead, Biochem. J. 59, 534 (1955). 8aH. Michl, Monatsh. Chem. 83, 218 (1952). 84H. J. McDonald and M. B. Williamson, Naturwissenschaften 42, 461 (1955). 85H. Hoch, Science 122, 243 (1955).

[1A]

PAPER ELECTROPHORESIS

25

Different paper electrophoretic techniques have been used for studying interactions among various substances in solution. Grassmann and Hiibner 66 showed the possibilities of the method by demonstrating the formation of weak complexes between dyes by means of their twodimensional method. McDonald et al. 67,6s used a different approach for studying interactions between protein and dyes, and Zilversmit and Hood ~9 developed still another technique for detecting interactions of serum proteins with Y~' and Ca 4~. Maurer and Miiller 7° have clearly pointed out the applicability of labeled molecules and used a most interesting technique for studying different forms of interactions, chiefly among serum proteins. In certain cases, the interaction between, for instance, enzymes and substrates or metal activators may be studied by specially adapted techniques of paper electrophoresis. Differences among a number of competitive inhibitors for a certain enzyme may thus be demonstrated if each of the inhibitors in turn is incorporated in the buffer solution in which the filter paper is soaked and a narrow zone of the purified enzyme is allowed to migrate. The protein zone should be retarded if the inhibitorenzyme complex has a net charge which is less than that of the free enzyme. If the equilibrium between free and bound inhibitor is reached instantaneously, the zone should move as a narrow band; if the equilibrium between the two is reached only slowly, the zone should show a considerable tailing. Among the many different forms of apparatus for paper electrophoresis which have been constructed and which are dealt with in detail in the monographs mentioned, three principal types may be distinguished : for low-voltage gradients, for high-voltage gradients, and for continuous separations. Most of these, at least the recent constructions, are capable of giving satisfactory separations, as judged from published patterns; details of construction are given in the original publications. A discussion of physicochemical aspects in relationship to the design of the apparatus has been given by Svensson. 71 It is felt that a discussion of the factors which favor a good separation might be of more value than a detailed technical manual for the handling of a special apparatus. 66 W. G r a s s m a n n and L. Htibner, Naturwissenschaften 40, 279 (1953). 67 R. H. Spitzer a n d H. J. McDonald, Federation Proc. 14, 285 (1955). 6s H. J. McDonald, E. W. Bermes, a n d R. H. Spitzer, Federation Proc. 14, 733

(1955). 69 D. B. Zilversmit and'S. L. Hood, Proc. Soc. Exptl. Biol. Med. 84, 573 (1953). 70 W. Maurer a n d E. R. Miiller, Biochera. Z. 324, 255 (1953). 7, H. Svensson, Ciba Syrup. on Paper Electrophoresis, London p. 86 (1956).

26

TECHNIQUES FOR CHARACTERIZATION OF PROTEINS

[1A]

Low-Voltage Apparatus It is generally accepted that good separations are easily obtained in appratus of the moist-chamber type with the paper either horizontally 72,73 stretched or more or less vertically TM supported. Most factors to be discussed are relevant to both types of apparatus, and in all types gradients of conductivity and pH are established after a certain time, which are due to evaporation. Each type of apparatus has its own parameters as to time, voltage, ionic strength, etc., for obtaining optimal resolution in a given case.

FIG. 1. Schematic drawing of a paper electrophoresis apparatus.

Series of duplicate analyses of protein solutions, such as serum, give very similar results with both types of apparatus, however. 75-77 With certain filter papers it is difficult to avoid a considerable depression in the paper when it is horizontally stretched in the moist chamber, and in these cases it may be advantageous to support the paper on rows of plastic pins. ~,Ts Figure 1 is a schematic drawing of an apparatus incorporating some features which have been found advantageous when working with the two types of apparatus quoted. ~7,7s The even placing of a moist and fragile sheet of filter paper (A) in the electrophoresis chamber (B) is facilitated by temporarily removing the two outer vertical walls (C). The two electrode vessels (D) are filled and leveled by means of a siphon well above the wall which divides each electrode vessel into two compartments, one of which contains a horizontal electrode (E). To keep the 72 W. Grassmann and K. Hannig, Z. physiol. Chem. 290, 1 (1952). ,a T. Wieland and K. Dose, Biochem. Z. 325, 439 (1954). 74 F. G. Williams, E. G. Pickels, and E. L. Durrum, Science 121, 829 (1955). 76 W. P. Jencks, M. A. Jetton, and E. L. Durrum, Biochem. J. 60, 205 (1955). ,6 W. Grassmann and K. Hannig, Klin. Wochschr. 32, 838 (1954). 7~ C. B. Laurell, S. Laurell, and N. Skoog, Clin. Chem. 2, 99 (1956). ~8 E. Valmet and tt. Svensson, Science Tools 1, 3 (1954).

[1A]

PAPER ELECTROPHORESIS

27

supporting plane of the electrophoresis chamber even, a strong metal plate (F) is permanently screwed the chamber (B). The moist chamber is closed by a lid (G) which fits tightly b y means of a v a c u u m seal (H). I t is i m p o r t a n t to have the supporting plane horizontally adjusted and to avoid draft and direct sunshine on the electrophoretic chamber. The structure of the paper, the a m o u n t of buffer solution and other non-conducting solutes held in the paper, the temperature and the electric current, and any liquid flow through the paper are all factors which in an ideal paper electrophoretic separation should remain constant during the experiment. 71,n These conditions are v e r y seldom fulfilled, but knowledge of how the factors influence the separations is essential for understanding why different types of apparatus m a y produce different separation patterns and also for understanding why different sites of application of the zone m a y produce patterns with unequal resolution even if all other factors remain constant. Structure of the Paper. W h a t m a n No. 1, n W h a t m a n 3MM, 75 Schleicher and Schuell 2043aM, n Schleicher and Schuell 2043a and b, 76 and Macherey and Nagel No. 819 76 have all been recommended for paper electrophoresis. For preparative purposes, thick filter papers, such as Munktell No. 20 79,80 or Schleicher and Schuell 2230 sl are used. T h e latter paper seems to adsorb al-lipoprotein far less than does W h a t m a n No. 1. Recently, Gedin 82 has found t h a t W h a t m a n No. 54 adsorbs less lipoprotein from serum than W h a t m a n No. 1. Differences which are not easily predieted are thus found among different papers, and it is advisable to test the q u a n t i t y of substance adsorbed with different papers prior to electrophoresis. This can be done in a simple chromatographic experiment. In m a n y cases the small n u m b e r of carboxyl groups in the paper m a y account for the adsorption; proteins are generally adsorbed less when they are negatively charged. 8~ In m a n y types of apparatus the filter paper is used in form of strips, but in other constructions there are facilities for applying the paper in form of sheets. T h e latter arrangement makes it easier to compare directly two substances migrating in the same paper under identical conditions. Buffer Solution. A sheet of filter paper is dipped into the buffer solution, and the excess moisture is allowed to drain. I t is better to have the paper a little too d r y rather than too wet when it is placed for equilibra79H. G. Kunkel and R. J. Slater, J. Clin. Invest. 31, 677 (1952). 80A.-B. Laurell, Acta Pathol. Microbiol. Scand. Suppl. 103, 18 (1955). 8xH. E. Schultze and H. Biel, Behringwerkmi~leilungen 30, 74 (1955). 83H. Gedin, unpublished observation. sa A. Tiselius and P. Flodin, Advances in Protein Chem. 8, 471 (1953).

28

TECHNIQUES FOR CHAR~kCTERIZATION OF PROTEINS

[1A]

tion in the m o i s t chamber. I n certain t y p e s of a p p a r a t u s it has been found an a d v a n t a g e to leave the a p p a r a t u s with the current on for some hours before the sample is introduced, b u t as an a l t e r n a t i v e the filter p a p e r can be dipped in a buffer with a b o u t 4 0 % higher ionic strength t h a n the buffer in the electrode vessels. ~7 Buffers with ionic strength less t h a n 0.1 are m o s t l y used. T h e i m p o r t a n c e of choosing n o t only a suitable p H b u t also appropriate buffer salts in a t t e m p t s to separate, for instance, an e n z y m e f r o m impurities is d e m o n s t r a t e d in Fig. 2. T h e figure shows the stained protein

FIa. 2. Paper electrophoresis of crude and purified enolase. A crystalline preparation and a crude fraction, both with enolase activity, were subjected to electrophoresis on filter paper (Whatman No. 1) in two different buffers at pH 8.4, ionic strength = 0.05, 130 volts, 2 ma, for 15 hours. To left, the stained pattern in phosphateborate buffer; right, in barbital buffer. Both cells were allowed to run for 3 hours before the samples were applied. The same amount of the two preparations were used in both eases. The two samples were kindly supplied by Dr. B. MalmstrSm. See text for explanation. p a t t e r n s f r o m two parallel experiments with p h o s p h a t e - b o r a t e and barbital buffer of p H 8.4 and ~ = 0.05. A crystalline p r e p a r a t i o n with enolase activity, shown in the ultracentrifuge to consist of only one b o u n d a r y , except for a 5 % impurity, was used in b o t h experiments. T h e stained p a t t e r n to the left represents an earlier stage in the purification of the enzyme. 84 M a r k e d discrepancies are shown between the resolution of the p a t t e r n s in the two buffer solutions. T h e crystalline enolase preparation in b o t h buffers separates into two components, b o t h of which h a v e enolase a c t i v i t y according to Dr. M a l m s t r S m ' s findings. T h e i m p u r i t y which, according to the centrifuge diagrams, should a m o u n t to 84 Both preparations were kindly supplied by Dr. B. MalmstrSm.

[1A]

rAPZR ELECTROPHORESIS

29

5 % is clearly shown in the original stained patterns. At least six components can be detected in the crude enolase preparation, judging from the stained diagram which was separated in phosphate-borate buffer. Such a separation is not achieved with the barbital buffer. The importance of choosing the appropriate buffer is demonstrated if an a t t e m p t at isolating any of the fast-moving components is to be carried out with zone electrophoresis in columns. For minimizing influences due to oxidation during the migration in the paper of a protein zone, the moist chamber has been filled with an inert gas 8~ such as helium which at the same time increases the heat conduction about five times. Oxidation of SH- groups in cysteine m a y occur during the conditions prevailing in paper electrophoresis and might to some extent be prevented b y adding NaHSO~ to the buffer. 8~ Higher yields of alkaline phosphatase activity is obtained, however, if 0.004% H~O2 is added 86 to the buffer solution. Studies of redox systems involved in inactivation of enzymes m a y thus be i m p o r t a n t for retaining activity during the separation. Sucrose has been added to buffers of low ionic strength for preventing globulins from precipitating, s~ Evaporation. In all moist-chamber apparatus, uncontrolled evaporation more or less limits the strength of the electric field which m a y be used in the paper. The evaporation causes a flow of buffer solution from both electrode vessels into the paper. As a consequence of the evaporation, the buffer solution in the paper becomes more concentrated, which in turn leads to an inhomogenous electric field distribution in the paper. 88 Macheboeuf et al. 8~ have used a special apparatus which permits excessive evaporation for demonstrating a phenomenon of dynamic equilibrium called " e l e c t r o r h e o p h o r e s e " which has been used, for example, for studying dilute solutions. E v a p o r a t i o n m a y be diminished or suppressed if an appropriate a m o u n t of relatively inert substances 78,9°,91 such as glycerol or ethylene glycol is added to the buffer. In the apparatus shown in Fig. 1, strips of filter paper soaked in distilled water are placed on B, without contact with A. 85H. J. McDonald, in "Ionography, Electrophoresis in Stabilized 'Media," p. 52. Year Book Publishers, Chicago, 1955. s6 H. E. Schultze and H. Biel, Behringwerkmitteilungen 30, 92 (1955). s7 H. Laurell, Ciba Syrup. on Paper Electrophoresis, London, p. 123 (1956). ss Z. Pucar, Arhiv Kern 25, 205 (1953). s9 M. Macheboeuf, P. Rebeyrotte, J-M. Dubert, and M. Brunerie, Bull. soc. chim. biol. 35, 334 (1953). 90E. L. Durrum, J. Am. Chem. Soc. 73, 4875 (1951). ,t H. J. McDonald, J. Chem. Educ. 29, 428 (1952).

30

TECHNIQUES FOR CHARACTERIZATION OF PROTEINS

[1A]

Application of the Sample. To obtain good resolutions even of minor c o m p o n e n t s it is advisable to a p p l y 8 to 10 ~l. of a clear b u t concentrated (2 to 4 % ) solution as a thin line onto the paper. This can be done b y m e a n s of special applicators, or b y drawing a pipet sev--7 eral times across the application site, as it is emptied slowly through a v e r y fine orifice. M e t h o d s for sharpening zones in columns 92,~3 m a y be applied to p a p e r electrophoresis. A zone of lower electrolyte concentration m a y be applied behind the initial line b y means of a d r y and a moist thick filter paper. For concentrating dilute protein solutions, m e m b r a n e s according to Mies 94 are recommended. A m e m b r a n e in the f o r m of a tube is suspended in a buffer solution, and a partial v a c u u m of a b o u t 300 m m . H g is applied (~ee Buffer Fig. 3). Depending on several factors, such as the voltage gradient and the e v a p o r a t i o n occurring, a suitable starting line has to be found empirically for each a p p a r a t u s to obtain m a x i m a l resolution. Fixation and Staining. M a n y dyes h a v e been shown useful for staining proteins, b u t for reproducible results it is essential t h a t the stain be a well-defined chemical entity. As is well known, m o s t commercially available stains are mixtures of different components, and one b a t c h usually does not h a v e the same composition as another. A few stains are obtainable in a "chromatographically" pure form, however and a m o n g t h e m bromophenol blue, n a p h t h a l e n e black 12B200 (Amido Black 10B, TM Leverkusen, G e r m a n y ) , and lissamine green 95 h a v e been widely used. A staining m e t h o d which is applicable to amino acids and polypeptides, as well as proteins, is described b y Reindel and H o p p e 2 e As to the staining procedure, a choice m a y be m a d e between certain modifications with due regard to the fact t h a t the cost of the rinse solutions m a y v a r y within wide limits. A detailed investigation of staining with b r o m o p h e n o l blue has been carried out b y D u r r u m . 75 A new modification of G r a s s m a n n ' s Amido Black 10B procedure has

FIG. 3. App a r a t u s for c o n centrating dilute protein solutions. The dilute protein solution is p l a c e d in a tube-formed collodion sack (supplied from Membranengesellschaft, GSttingen) and a pressure of 300 m m . t t g is applied above the buffer solution in which the collodion sack is placed.

99 H. Haglund and A. Tiselius, Acta Chem. Scan& 4, 959 (1950). 98j. Porath, Biochim. et Biophys. Acta 22, 160 (1956). 94H. J. Mies, KEn. Wochschr. $1, 159 (1953). g5 E . M . Abdel-Wahab and D. J. R. Laurence, Biochem J. 60~ xxxv (1955). 96F. Reindel and W. Hoppe, Chem. Ber. 87~ 1103 (1954).

[1A]

PAPER ELECTROPHORESIS

31

recently been described. 73 Although many modifications may be equally satisfactory, the following procedure 77 has been found to give reproducible results and can also be used for semi-quantitative estimations of different fractions. 1. The moist paper sheet is dried at 110 ° for 15 minutes. 2. The dried paper is sewed on a special bent glass rod and suspended for 10 minutes in the staining solution (1% bromophenol blue, 20% w / v HgC12 in methanol). 3. The sheet is transferred and rinsed three times for 10 minutes in 0.5% (v/v) acetic acid (about 6 1. of fresh rinsing solution to each of the rectangular jars). The staining capacity of the bromophenol blue solution is slightly impaired after some months, as its composition is altered by evaporation and the addition of salts. It is thus recommended prior to fixation to apply to the moist paper, with a constriction pipet, 10 ~l. of a 2 % albumin solution as an internal standard. For semiquantitative determinations the paper is cut into pieces corresponding to the fractions seen in the pattern. A piece of paper which has not been in contact with protein fractions is used as a blank. All the dry paper pieces are weighed and transferred to equal volumes of 0.1 N Na2CO3 for elution for 3 hours. The absorbance is read at 575 rap, and due corrections are made for the absorbance per milligram of dry paper found in the blank. Equally satisfactory results may be obtained by direct scanning of the filter paper with the dyed zones, if the apparatus has been properly calibrated.

High-Voltage Apparatus and Apparatus for Continuous Separations Paper electrophoresis apparatus with high-voltage gradients have chiefly been used in connection with separations of low molecular weight substances, and striking results have been obtained. For details the reader is referred to Werner and Westphal2 7,* As to paper electrophoresis apparatus aiming at continuous separations, several modifications 98 have appeared since the pioneer work of Svensson et a l 2 ~ and Grassmann and Hannig. 1°° Both Grassmann's apparatus (Bender & Hobein, Munich) and a construction by Durrum (Spinco Co., Belmont, California) are commercially available. Besides many obvious applications they are most useful in cases where adsorption tends to blur the obtained separations. 97 G. Werner a n d O. Westphal, Angew. Chem. 67, 251 (1955). 9s E. S. Holdsworth, Biochem. J. 59, 340 (1955). 99 H. Svensson and I. B r a t t s t e n , Arkiv Kemi 1, 401 (1949). 100 W. G r a s s m a n n and K. Hannig, Z. physiol. Chem. 292, 32 (1953). * See also 48b.

104

TECHNIQUES FOR CHARACTERIZATION OF PROTEINS

[3]

[3] Infrared Spectrophotometry By D. L. Wood

Introduction The energy of a molecule, according to quantum theory, is not allowed to have a continuum of values. Rather it is required that the total energy at any instant have one of a set of discrete characteristic values. The molecule may change its energy by the absorption or emission of a photon or by collision, but it may only change from certain allowed energy levels to certain others according to well-established selection rules. The absorption or emission of radiant energy which accompanies a molecular energy change is possible only if the radiated or absorbed photon has an energy which exactly fits the difference between two energy levels of the molecule. Thus in absorption or emission a discrete spectrum is observed, made up of radiant energies fitting the allowed energy changes for the particular molecule. Most molecular spectrophotometric studies are concerned with absorption of radiant energy, and consideration will not be given here to infrared emission spectra. Therefore, the term spectrum in this discussion means a plot of the discrete energy absorbed by a sample as a function of the frequency or wavelength. The energy of a molecule is usually considered to be a sum of three terms: one from the energy of motion of the electron cloud, one from the vibrational motion of the constituent atoms, and the third from the energy of pure rotation of the whole molecule. Although some electronic transitions are observed in the infrared, most of the spectra under discussion arise from transitions between vibrational and rotational energy levels. Furthermore, in liquids and solids, where molecular rotation is hindered or impossible, only the vibrational part of the energy remains quantized. Thus, except in the case of gases, the infrared spectrum arises solely from changes in the energy of vibration of molecules. The vibrations of a molecule and the energies associated therewith are very sensitive to the strength of chemical bonding and the particular configuration of atoms comprising the molecule. This strong dependence of the spectrum on even the smallest structural detail makes infrared spectrophotometry a useful tool. The following applications illustrate how the sensitivity of the spectrum to composition, structure, configuration, and environment gives the method widespread utility. 1. It is obvious that if the infrared spectrum is highly characteristic of a particular molecule it may be used in the identification of that molecule in a mixture in much the same way that a fingerprint may be used to

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identify an individual in a group of people. For example, even stereoisomers like trans- and gauche-l,2-dibromoethane ~ have infrared spectra sufficiently different to enable one to distinguish between the two forms. Thus infrared spectra are widely used in characterizing unknown pure compounds and in identifying the components of mixtures or solutions. 2. This is also true of individual groups or chemical bonds in a molecule so that the presence of these groups or bonds in a molecule of unknown structure may be detected by their characteristic absorption bands, and thus considerable information about the molecular structure can be obtained. 3. These aspects of qualitative analysis can also be made quantitative, giving a convenient method for quantitative analysis which is extremely useful, since the sample is not destroyed and only a very small quantity of sample is required. 4. A knowledge of the energy levels of a molecule allows the computation of various thermodynamic data 2 so that the infrared spectrum can be useful in the theoretical side of chemistry. 5. The molecular differences in members of homologous series, the effect of environment on molecular structure (e.g. solvent effects), and the progress of chemical reactions may all be followed by this technique. It is safe to say, therefore, that any change in a molecule, however slight, can usually be studied by means of the accompanying change in the infrared spectrum. Procedures Infrared Absorption Measurements. The recording of spectra for molecular structure studies or analysis involves two phases: the sample preparation, and the measurement of energy absorbed as a function of frequency or wavelength. With regard to the energy measurements the operating procedures usually are described in the manufacturer's instruction book, and these instructions make clear the proper choice of recording time, slit width, amplifier gain, and detecting system response time to give the best possible spectrum for the particular sample. Operating procedures, therefore, will not be discussed as far as they pertain to the recording of data. Useful information supplementing that of manufacturers' handbooks will be found in the articles by Clark 2a and Miller. 2b

J. K. Brown and N. Sheppard, Discussions Faraday Soc. 9, 144 (1950). G. Herzberg, "Infrared and Raman Spectra." Van Nostrand, New York, 19~5. 2~C. Clark, in "Physical Techniques in Biological Research" (Oster and Pollistcr, eds.), Vol. 1, pp. 206-316. Academic Press, New York, 1955. 2bF. A. Miller, in "Organic Chemistry" (H. Gilman, ed.), Vol. 4, pp. 122-158. Wiley, New York, 1953.

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The spectrophotometers in common use fall into two classes, either single beam or double beam. In the single-beam type, the energy passing through the sample is simply recorded as a function of distance on a paper chart. In a double-beam instrument, the paper chart record presents the ratio of energy passing through the sample to the energy passing through an identical optical path with no sample, as a function of frequency or wavelength. The two principal advantages of the double-beam over the single-beam system are that the recording of energy ratios directly in the double-beam system eliminates much tedious processing of data, and that the double-beam system eliminates atmospheric absorption bands. One application of the direct recording of ratios by the double-beam type of spectrophotometer is in the measurement of "differential" or, more properly, "ratio" spectra. 3 Suppose two samples have a common major component but a minor component not in common, and it is desired to record the spectrum of the minor component alone. If the two samples are put into cells of appropriate thickness and one introduced in each beam of the double-beam instrument, the major-component absorption bands will be compensated out, leaving those of the minor component. An obvious example is that of a sample in solution where the solvent absorption may be balanced out, leaving just the solute spectrum. There are difficulties in this method, however, the most important of which is that very strong absorption by the component to be balanced out may render the instrument inoperative over the region of strong absorption. That is, the spectrophotometer requires a certain minimum energy to drive the pen across the chart paper. If this amount of energy is not transmitted by the two samples, the detecting system will have no signals to balance and thus no energy to drive the recording pen. Much information can thus be lost in the very regions in which the method might be expected to be most useful. By opening the monochromator slits or advancing the gain of the detecting system in these regions of strong absorption this effect can be minimized, although the best technique is to use only samples in which the absorptions to be balanced out are not over 80 to 90 % of the incident energy. A special case of "ratio spectra" which has been useful in protein structure work is the recording of dichroism by this method. A sample in which the molecules have been suitably oriented may absorb more strongly when the electric vector of the incident infrared radiation is polarized in some particular direction. This is dichroism, and it gives information about the orientation of the specific molecular groupings or chemical bonds involved in a particular absorption band. If two identical oriented samples are located in the two spectrophotometer beams and 3 D. Z. Robinson, Anal. Chem. 24, 619 (1952).

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the radiation in one beam is polarized at 90° to that of the other, a "ratio spectrum" related to the dichroism of the sample will be recorded. This is particularly useful where the dichroism is weak. The polarization of infrared radiation may be accomplished by the use of reflection4 or transmission polarizers usually made of selenium ~ or silver chloride 6 sheets. The silver chloride transmission polarizers are commercially available. In the choice of ordinate and abscissa for presenting the spectrum, present practice 7 tends toward frequency in cm. -1 (kaiser) as abscissa versus absorbance as ordinate, although wavelength in microns (abscissa) versus % transmission (ordinate) is also widely used. The former is TABLE I PRISM MATERIALS Material Glass *Quartz LiF *CaF2 *NaCI KBr *CsBr KRS-5 (TIBr-TII) CsI

Useful range, era. -~ 8000-12,500 4000-12,500 1600- 4000 1100- 4000 650- 1500 370700 300700 270700 195400

preferable, since line widths are not distorted, although the linear wavelength abscissa gives a more linear representation of the actual resolving power throughout the range of a single prism. Ideally, however, more than one prism is used to cover the whole spectrum, and in this case a more uniform resolving power may be obtained on the linear frequency scale. There is a wide choice of prism materials now available, the most common of which are listed in Table I along with their most useful spectral ranges. The four noted with asterisks make a convenient set giving maximum resolving power throughout the spectrum. In actual practice most spectra are recorded with the NaC1 prism, and the others are used in supplementary experiments. It is possible to use any prism at frequencies higher than the limits indicated in the table, although there will usually be another material available which gives higher resolving power in that region. 4 A. H. Pfund, J. Opt. "Soc. Amer. 37, 558 (1947). A. Elliott, E. J. Ambrose, a n d R. B. Temple, J. Opt. Soc. Amer. 38, 212 (1948). 6 R. N e w m a n a n d R. S. Halford, Rev. Sci. Instr. 19, 270 (1948). 7 W. R. Brode, J. Opt. Soc. Amer. 39, 1022 (1949).

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For very high resolving power an echelette diffraction grating can be used as dispersing agent, and recent developments in instrumentation 7a have brought this type of equipment within the means of most infrared laboratories. The limit of resolution of a grating spectrophotometer is well below 0.5 cm. -1, whereas the limit for a prism spectrophotometer in the most favorable regions of the spectrum is about 2-3 cm. -1. One of the time-consuming operations in single-beam spectrophotometry is the reduction of the records of background, sample, and zero energies versus arbitrary frequency calibration units to graphs of absorbance versus frequency. There are several ways of doing this, some of which involve modification of the recording system. 8-I~ A common practice is to use a mechanical device to compute the ordinate ratios for various frequencies located by means of a paper or plastic strip abscissa calibration.1~ Such mechanical devices are usually based on the fact that one leg of a right triangle can be divided into a number of equal parts by drawing lines parallel to the other leg through equidistant points laid out on the hypotenuse. From the same hypotenuse, any number of shorter lengths can be so divided by constructing the appropriate right triangle and drawing in the lines parallel to the base. 12 S a m p l e Preparation. The proper preparation of infrared samples is of in~portance because the spectrum may be different for different procedures and therefore may affect interpretations. The preparative procedures involve the confining of the sample to a layer with two parallel fiat faces through which the radiation may pass, and for many samples this may be done without complication. Gases are usually confined in cylindrical glass or metal tubes with infrared transmitting windows sealed on the ends with a suitable gasket, wax, or cement. Appropriate outlet and inlet tubes usually are of glass with stopcocks and either glass taper joints or glass ball and socket joints for connecting with the gas handling system. The usual length for pressures of 5 to 76 cm. Hg is 10 cm., though shorter (5 em., 2.5 cm.) and longer (up to 10 meters) 13are sometimes useful. The gas pressure and cell length may be adjusted to suit the sample, if it is remembered that higher pressures broaden the infrared bands. It is sometimes desirable to raise the temperature of the cell to raise the vapor pressure of the sample, and v~R. C. Lord and T. K. McCubbin, Jr., J. Opt. Soc. Amer. 46, 441 (1955). 8 C. E. Zerwekh, Rev. Sci. Instr. 20, 371 (1949). 9 R . M . Fuoss and D. J. 5Mead, Rev. Sci. Instr. 16, 223 (1945). 10R. A. G. Carrington and J. G. Reynolds, J. Sci. Instr. 29, 197 (1952). 11R. W. Foreman and W. Jackson, Jr., Instruments 22, 497 (1949). 12H. A. Willis and A. R. Philpotts, Trans. Faraday Soc. 419 187 (1945). 13j. U. White, J. Opt. Soc. Amer. 32, 285 (1942).

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this m a y easily be done electrically. M a n y low-temperature cells have been described, and these m a y sometimes be used to good advantage. TM There is a wide choice of window materials available for infrared cells. T h e choice is usually made on the basis of the transmission limit and chemical or physical stability. The properties of several materials are listed in Table II. The most commonly used materials are: For the highfrequency region, fused quartz. For the region from 2800 to 400 cm. -1, TABLE II WINDOW MATERIALS

Material Glass SiO2 LiF CaF2 BaF2 As~S~ Se

Useful frequency Water range, cm. -1 stability Down to to to to to to to

3000 2800 1600 1000 900 800 600

NaCl KBr AgCl

to 600 to 400 to 400

CsBr KRS-5(T1Br-TII) CsI Polythene

to to to to

250 250 190 100

Remarks

Excellent Excellent Good Good Excellent Good. Excellent

1.0 mm. thick Strong, durable Cleaves, brittle Cleaves, brittle Cleaves, brittle A deep-red glass, soft Amorphous form only; opaque in visible Poor Brittle, fogs easily Poor Brittle, soft, fogs easily Good Soft, plastic, photosensitive, chemically unstable Poor Plastic, fogs easily Good Slightly plastic, deep red, poisonous Poor Fogs easily Excellent Sheets, absorption bands present

NaC1 or K B r for samples without water, and AgC1 for samples containing water. For the low-frequency region CsBr is good where water is not present, but KRS-5 is b e t t e r where water is present. The other window materials included in the table are useful in special cases. Although windows of these transmitting materials may be obtained commercially, it is often desirable to make or refinish windows, especially those of the water-soluble crystals like NaC1, KBr, CsBr, and CsI. The techniques involved are not difficult, and detailed procedures are given in ref. 14. The AgC1 must be protected from photodegradation, particularly by fluorescent lights. Incandescent lighting requires considerable time (days) to cause objectionable decomposition. More serious than this is the problem of keeping all metals below Ag in the electromotive series away L4R. C. Lord, R. S. McDonald, and F. A. Miller, J. Opt. Soc. Amer. 42, 149 (1952).

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from contact with the AgC1. The decomposition by replacement of the Ag by the metal is very rapid. Silver chloride windows may be polished or flattened by pressing between glass plates in a hydraulic press, or rolling between highly polished rolls. They can also be worked into special shapes by pressing or extrusion and welded together with an incandescent electrically heated platinum wire loop. Cells for holding liquid samples are usually much thinner than those for gases (of the order of 0.1 mm.). Their construction is the same in principle as those for gaseous samples but with shorter spacers. Appropriate thicknesses can be accomplished with shims of lead amalgam or other suitable gasket materials, or by a more elaborate construction involving a screw adjustment for variable thicknesses. 1~-17 The filling and emptying of the cell is accomplished through holes drilled in the windows or shims and connecting with hypodermic syringe adapters. The handling of liquid samples in syringes is very convenient. The thickness of an infrared liquid cell can be measured in any one of several ways. Probably the best method requires measuring the chanael spectrum ~s of the empty cell. Because there is interference between rays passing through the cell with rays reflected twice at the two interfaces of the cell windows, there will be a series of maxima and minima in the spectrum of the empty cell. The separation of two successive maxima in terms of wavelength will give the cell thickness, t, according to the formula t = ~ k ~ / 2 ( ~ 1 - ~ ) where ~ and ks are the wavelengths of the two successive transmission maxima. Other methods involve direct measurement with a micrometer, weighing full and empty, the use of known absorption coefficients19 (e.g. benzene in the ultraviolet), and the use of Talbot's fringes, 19 or of visible interference fringes. A great deal of work with liquid samples is done with solutions of compounds. It is important, of course, that the solvent have no absorption bands in the regions where the sample absorbs. The best solvent, therefore, is the one with fewest absorption bands. Carbon tetrachloride and carbon disulfide are the two most commonly used, and if the sample will go into solution in these solvents they make a useful pair, since each is clear of absorption where the other has bands. For convenience in choosing solvents a chart prepared by the Spectroscopy Laboratory at the Massachusetts Institute of Technology is shown in Fig 1. One other 15j. U. White, Rev. Sci. Instr. 211 629 (1950). 19A. V. Stuart, J. Opt. Soc.,Amer. 43, 212 (1953). 17V. J. Coates, Rev. Sci. Instr. 22, 853 (1951). 18D. C. Smith and E. C. Miller, J. Opt. Soc. Amer. 34~ 130 (1944). 19W. C. Price, Trans. Faraday Soc. 41, 189 (1945).

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useful solvent not included on the chart and whose properties make it desirable for solid sample preparation is hexachlorobutadiene. 2° Besides considering the absorption of a solvent one also should consider the effect it may have on the molecule and therefore the spectrum of the solute. The effects of solvents on the spectrum are discussed later in the chapter, and it is well to bear in mind that such effects may be observed. The preparation of gaseous and liquid samples is relatively straightforward compared to that of solid samples. For convenience the preparative techniques for solids may be divided into those applicable to particulate samples and those applicable to continuuus samples. Particulate samples will not in general yield good spectra if the powder alone is placed in the radiation path of the spectrophotometer. The scattering of the radiation by the particles in the sample render it essentially opaque in much the same way as with visible light. The scattering is avoided, however, if the powder is mixed to a paste or slurry with some liquid having nearly the same refractive index as the sample grains. It is convenient if the liquid used in making the paste or mull has enough viscosity to prevent settling of the grains in the cell. It is also desirable, of course, that the mulling liquid have as few absorption bands as possible. It is common practice to choose complementary liquids, the one being free of absorption where the other absorbs. The most commonly used pair is mineral oil (Nujol) and hexachlorobutadiene, although Nujol and Fluorolube or Fluorokerosene are also a successful combination. Since powder samples are not continuous, the radiation may pass unabsorbed between the grains of the mull if the particles are not small compared to the thickness of the layer. For this reason it is desirable that the particle size be as small as possible. A specific procedure for powder sample preparation consists of several steps. First the sample is ground to as fine a particle size as possible in a mortar, ball mill, or air jet mill. Second, a specific amount is weighed out into a small mulling mortar and ground briefly with a drop or two of the liquid mulling agent. Third, the paste is transferred to a suitable infrared window and squeezed into a uniformly thin layer with a second window. The sandwich of two windows with the mull between is clamped in a cell holder and is ready for the spectrophotometer. The matter of proportions of powder and mulling liquid will be dictated by the results, it being necessary to adjust the flow properties and thickness of the mull to suit the circumstances. The order of magnitude of sample size required is 5 to 10 mg./cm. 2 of window area, depending to some extent on the efficiency of transfer of sample from the mulling mortar to the window. 20 j . S. Ard, Anal. Chem. 25~ 1743 (1953).

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A convenient mulling mortar may be made in the form of a hemispherical cup of Pyrex glass about 6 ram. in diameter with a closely fitting spherical Pyrex pestle ground in with No. 240 Carborundum. A small nickel spatula is convenient for transferring the mull from mortar to window. Another recently introduced method of preparing powder samples is a useful supplement to the mulling method. This is the pressed KBr pellet technique first proposed by Sister M. M. Stimson ~1 and independently by Scheidt. ~ In this method the sample powder is mixed with finely divided KBr powder and pressed in an evacuated die under rather high mechanical pressure until a homogeneous transparent plate is produced. Since pure KBr has no absorption at frequencies higher than 400 cm. -1, the spectrum of the plate will be that of the powder sample. It is obviously a great advantage to reduce scattering without introducing absorption bands due to the suspension medium. Dies appropriate to the method are commonly 0.5 inch in diameter and cylindrical with highly polished ends on the plungers. An exhaust port is provided to remove the air from the powder before compression, and "O"-rings are used to seal the plungers. The hydraulic press may be of modest capacity, 10 tons total force on a 0.5-inch-diameter die being sufficient for pressing times of the order of minutes. Both dies and press are commercially available, or they can be made in a well-equipped machine shop. The specific procedure for making a KBr pellet sample 12 mm. in diameter involves the following steps: The KBr powder which has been previously dried at 120 ° for 4 hours, ground, and sieved through a No. 200 mesh screen is weighed out with the sample to make a mixture of 0.1 to 0.5 % of sample in the KBr. The powder mixture is ground in a mortar with acetone to dryness, with care taken to avoid water condensation due to the cooling of the evaporating acetone. About 200 mg. of mixture is put into the die and evacuated. After the 10 tons of force has been applied to the plunger for 1 to 5 minutes, the pellet is removed from the die and is ready for the spectrophotometer. The pellet should be transparent to visible light and without cracks. Opaque spots may be due to moisture contamination, low pressures, or poor evacuation of the die. It is essential that the sample be finely divided for the same reason that mull powders should be finely divided, namely, that radiation will pass between particles unabsorbed if the particle size is not small compared to the thickness of the plate. It has been reported 23 that, the smaller 21 M. M. Stimson, J. Am. Chem. Soc. 74, 1805 (1952). 22 U. Scheidt and H. Reinwein, Z. Naturforsch. 76, 270 (1952); U. Scheidt, ibid. 78, 66 (1953). 2~Perkin-Elmer Instrument News 4, No. 3 (1953).

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the particle size, the better will be the sharpness and separation of absorption bands in pressed KBr samples. Several other methods besides grinding in a mortar have been suggested for rendering the KBr and sample mixture more homogeneous. The ball mill and sonic vibrators may be useful, but freeze-drying of KBr-sample solutions in a suitable solvent is probably more effective, though more elaborate. Satisfactory dispersions have also been made by spraying a solution of the sample over KBr powder and drying the mixture. Whatever the method, however, it should be recognized that the final particle size of the powder to be pressed can affect the quality of the spectrum greatly. Other techniques have been developed for measuring spectra of powder samples. In one method 24 ammonium stearate is used as a solubilizing or dispersing agent for producing stable suspensions of powders in CS2 or CC14. The ammonium stearate has but one more band than mineral oil and has wide regions of no absorption. Another method 2~ reduces scattering by reducing the particle size to considerably less than one wavelength of the absorbed radiation. The powder is ground to as fine a particle size as possible and suspended in a tall cylinder of alcohol. After settling for a suitable length of time, the top fraction containing the smallest particles is decanted, centrifuged, and decanted again, leaving a concentrated suspension of the finest particles. This suspension is spread on a window and the alcohol evaporated to dryness. The sample is then ready for the spectrophotometer. A third method 26 involves recording spectra not of the material itself but of its pyrolysis products. This has been useful for completely intractible solids, but the interpretation of such spectra may be somewhat involved. Fortunately many solids can be prepared in the form of suitably thin transparent films or plates so that scattering of the radiation is not a problem. Thin films can be made by casting from solution or melt, or by cutting up bulk material. Vacuum evaporation 27 has also proved a useful technique. The two factors of paramount importance are that the film be clear and not scatter the radiation and that it be thin enough for good spectra. The proper thickness may be as small as 0.1 ~ for strong absorption bands. It is likely that many water-soluble proteins as well as polymers and even crystalline compounds will form uniform clear coatings on silver chloride plates if a drop of solution is spread and allowed to dry on the plate. There will be, perhaps, some difficulty in making quantitative 24 M. Dolinsky, J. Assoc. OJ~c. Agr. Chemists 34~ 748 (1951). 26 j . M. Hunt, M. P. Wisherd, and L. C. Bonham, Anal. Chem. 22, 1478 (1950). ~6 D. L. Harms, Anal. Chem. 25, 1140 (1953). 2~ j. E. Tyler and S. A. Ehrhardt, Anal. Chem. 25, 390 (1953).

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measurements on such films unless great care is taken to make the thickness uniform and to determine its magnitude. In some cases the thickness can be followed if the films are first cast on the surface of water or mercury where interference fringes in visible light can be observed. For films thicker t h a n 1 or 2 ~, interference fringes in the infrared m a y be used to determine the thickness b y the same method as for e m p t y liquid cells. Solid films of known thickness can also be prepared b y filling a fixed liquid cell with the melt and allowing it to cool below the melting point. Great care is necessary, however, in heating optical crystal windows because thermal stresses from uneven heating will easily crack such materials. For cutting bulk material or large crystals to make infrared specimens two methods m a y be employed if the material has no convenient cleaYage like mica. Some materials will slice in a microtome sufficiently well to be prepared this way. T h e material is waxed to a wooden block with paraffin or a hard beeswax and rosin mixture and sliced in the usual manner. For hard materials such as fibrous proteins or nylon a knife with a 90 ° cutting angle 2s is v e r y helpful, although the standard knife works better on soft materials. The slice usually rolls up into a tight coil during the cutting, but it can be unrolled easily on the surface of or under water. The water can then be removed in an alcohol b a t h and a n y wax removed by a subsequent bath in xylene. Such a procedure will produce excellent selfsupporting films, 3 ~ thick, of such intractable materials as keratins. The second method for cutting bulk material which the author has found useful requires t h a t a conveniently thin slice be cut with a saw of some kind and the slice cemented or waxed to a glass plate. Optical pitch is a good adhesive. T h e free surface is then worked down with various grades of abrasive paper, either wet or dry, on a wheel or by hand, until the surface is fiat, smooth, and polished. T h e slice is then removed from the glass, turned over, and waxed down again so t h a t the polished face is parallel with that of the glass plate. T h e n the second surface can be worked down until an appropriate thickness is obtained. E v e n the most intractable materials such as the keratins or mineral crystals can be handled this way, although some skill is required for preparing the thinner samples (1 to 30 ~ thick). In m a n y cases where the compound can be easily crystallized in the form of thin plates either from solution or from the melt a great deal more information about molecular structure can be discovered from the spectra, since the molecules in a crystal have certain particular orientations. The growing of large single crystal sections (larger than 5 X 10 ram.) is a very specialized art, but if micro-sampling techniques are available it is often the case t h a t crystals selected from a bulk crystalline sample will be 28 E. J. Ambrose and A. Elliott, Proc. Roy. Soc. A206, 206 (1951).

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ble to the source itself where the dimensions of the radiation beam are smallest. Actually it is the entrance slit of the monochromator or its image which determines the "microcell" dimensions, since the two may be equal for the largest slit width used. This reduces the actual sample size required to the order of 1 X 12 mm., or 24 X 10-8 ml. for a thickness of 20 t~. Such cells are available for most spectrophotometers and are quite convenient. A second reduction may be accomplished by masking the slit height to reduce the necessary sample length. 32~ This can best be done at the entrance slit of the monochromator, since in double-beam spectrophotometers individual masking of sample and reference beams in the sample space usually cannot be done precisely enough to preserve the compensation of one beam with the other. As a result of even a small inequality of masking the atmospheric absorption bands will appear and spoil the record. Masking at the entrance slit avoids the difficulty, since the two beams are superimposed at that point. This procedure reduces the energy passing through the monochromator and results in a loss of resolving power or an increase in recording time. For a reduction by a factor of 4 to 1 × 3 ram. in sample size, however, this objection is not serious for modern instruments, since for liquids and solids the bands are broad enough so that no detail is lost. A similar reduction in sample size may be made in spectrophotometers which are so constructed that a pair of lenses of infrared transmitting material (e.g., AgC1) located one focal length each side of the sample will produce a reduced image of the source (or more important the slit) so that very small samples may be used2 ~ This arrangement makes possible spectrophotometric measurements of samples about 1 X 3 ram. in size without loss in resolving power. The ultimate in small sampling is accomplished by means of a "microspectrometer" attachment, one model of which has recently been made available commercially. 3~ One arrangement of such an attachment is in effect a microscope with totally reflecting condenser and obiective so arranged that the enlarged image of the sample, illuminated by an infrared source, falls on the entrance slit of the monochromator of the spectrophotometer. The radiation from the sample image on the monochromator slit has passed first through the very tiny sample and thus the spectrum is recorded. With such an attachment, spectra have been recorded from fibers about 17 t~ in diameter, 34 though the normal sample size is about 650 × 220 u with a sacrifice in resolving power of considerably ~" D. L. Wood, Rev. Sci. Instr. 26, 787 (1955). 33 D, H Anderson and O. F. Miller, J. Opt. Soc. Amer. 4-% 777 (1953). 3~ V. J. Conies, A. Offner, and E. H. Siegler, J. Opt. Soc. Amer. 43, 984 (1953).

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less than a factor of 2. If a sample could be confined to the small area of the normal sample size it would have a volume of about 3 × 10-7 ml. for a 20-~ thickness. The advantages of such small sampling volumes are obvious.

Interpretations Band Assignments, Qualitative Analysis, and Structure Determination. The infrared region from 10,000 to 250 cm. -1 which embraces the present convenient limits of prism spectrophotometry is divided into two parts according to the origin of the absorption bands found in each part. The low-frequency region (250 to 3700 era. -1) contains primarily the bands d u e to fundamental vibrations, whereas the high-frequency region (3700 to 10,000 cm.-0 contains bands due to overtones or combinations of vibrations whose fundamentals are in the low-frequency region. Although the high-frequency region shows promise of being very useful, 84a,b,° most of the data available on infrared assignments is concerned with the low-frequency fundamentals. The fundamental vibrations giving rise to infrared absorption may be divided into four classes: stretching, or valence vibrations; deformation, or bending vibrations; group vibrations where only the atoms in a particular chemical group are involved in the vibration; and the vibrations of the molecule as a whole. Not all the vibrations of a molecule produce infrared absorption, since the absorption requires a dipole moment change, and the dipole moment may remain constant in certain cases even though the molecule is vibrating. The rules governing this matter are called selection rules, and they can be derived from consideration of the symmetry of the molecule. ~ The stretching, deformation, and group vibrations and their characteristic infrared absorption frequencies are really special cases of vibrations of the molecule as a whole. Only in special cases is it possible to separate and assign a normal vibration to a particular part of the molecule. Indeed, this is never completely true, since the motion of one atom in a molecule will surely have some effect on the motion of every other atom in the molecule. It happens in these special cases, however, that the vibrational motion of one group has only a small effect on those of other atoms in the molecule, and in this sense belongs to that particular group. In other words, although all oscillations belong to the molecule as a whole, in some special cases the motion or more properly the energy of the vibration is not distributed uniformly over the molecule but is 34a W. Kaye, Spectrochim. Acta 6, 257 (1954). 34b W. Kaye, Spectrochim. Acta 7~ 181 (1955). 84~K. T. Hecht and D. L. Wood, Proc. Roy. Soc. A285, 174 (1956).

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concentrated in a particular group. T h e separable frequency is a useful concept, b u t it m u s t be applied with care, since e v e r y frequency involves the whole molecule to some extent. T h e b a n d s in an infrared s p e c t r u m m a y serve to identify certain groups b y the presence or absence of b a n d s assigned to actual vibrations of the group. T h e same kind of identification can be m a d e with bands whose actual vibrations are u n k n o w n b u t which have been found empirically to be associated with certain groups in pure compounds. T h e b a n d s whose exact assignments are known are m u c h more helpful t h a n the empirically correlated b a n d s in structural studies. T h e empirically TABLE I I I CARBON-HYDROGEN VALENCE FREQUENCIES

Type of vibration CH3 CH.CH (tertiary) CH (aromatic)

Frequency 2962 cm. -1 (symmetric) 2926 cm. -~ (symmetric) 2890 cm. -1 3030 cm. -~

2872 cm. -~ (asymmetric) 2853 cm. -1 (asymmetric)

correlated bands are of assistance, however, for analysis and characterization of molecules. I t is possible in the limited space available here to review only rather briefly the large b o d y of information now available 35-3'~ on infrared b a n d correlations and assignments. Consequently only the r u d i m e n t s of b a n d assignment procedure will be discussed and further details m a y be gleaned f r o m the specialized references cited. Of particular interest are the books b y B e l l a m y ~5 and b y Randall e! al. 36 and the chapter b y 5/[iller 37 in G i l m a n ' s text on organic chemistry. Stretching or valence vibrations involving hydrogen are rather high in frequency because of the small mass of the proton. T h e y are essentially separate from other bands and lie in the region near 3000 cm. -1. T h e carbon-hydrogen valence frequencies, some of which are listed in T a b l e I I I , are found in m o s t organic compounds. T h e y are usually close together so t h a t it requires the high resolving power of LiF or CaF2 prisms to record spectra in which these b a n d s can be assigned with confidence. T h e C H b a n d s are not often selected as principal identifying features in a~L. J. Bellamy, "Infrared Spectra of Complex Molecules." Methuen, London, 1953. a6 H. M. Randall, N. Fuson, R. G. Fowler, and J. R. Dangl, "Infrared Determination of Organic Structures." Van Nostrand, New York, 1949. 3~F. A. Miller, in "Organic Chemistry" (H. Gilman, ed.), Vol. 4, pp. 122-158. Wiley, New York, 1953. as N. B. Colthup, J. Opt. Soc. Amer. 40, 397 (1950). a9 R. B. Barnes, R. C. Gore, U. Liddell, and V. Z. Williams, "Infrared Spectroscopy." Reinhold, New York, 1944.

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and nitrogen or oxygen produce absorption bands which are highly characteristic of the bond type because the force constant is higher than that of a single bond. Bands due to double-bond oscillations occur in the region from about 1650 cm. -1 to about 1850 cm. -1. The various environments in which the double bond is found affect its frequency. Thus the acid anhydride carbonyl has a band near 1820 cm. -1, whereas the ketone carbonyl is lower near 1715 cm. -1, and the C ~ N link usually exhibits a band in the region from 1640 to 1690 cm. -1. Carbon-carbon double bonds such as those found in the alkenes also fall in this region, giving bands from 1600 to 1680 cm. -I. It is possible in some cases to differentiate conjugated (near .1600 cm. -1) from unconjugated (1620 to 1680 cm. -1) C ~ C bonds. Triple bonds are equally characteristic in the frequency of their absorption bands. Cyanides, nitriles, and acetylenes all have bands in the region between 2000 and 2400 cm. -~ characteristic of their triple bonds. Few other absorption bands occur in this region, so that these groupings are very easily identified. There are many bands in the spectrum of nearly every compound which do not arise from hydrogenic, double-bond, triple-bond, or group vibrations. These are the vibrations of the molecule as a whole, and because of their origin they are very useful in following subtle changes in molecules. For qualitative analysis or structure determination a procedure may be set up so that in principle any unknown compound or mixture may be identified: 36 First a check of the separable frequencies (hydrogenic, double- and triple-bond, or group frequencies) reveals something about the molecule. Perhaps the fact that many frequencies are not there is most important. Second, the "fingerprint region" is checked with spectra of known compounds until one or a superposition of several will match the unknown spectrum. Again, the consideration of bands missing from the unknown may be just as valuable as consideration of bands present. For both of these steps a correlation chart ~ 9 is very helpful, but in the end it will be desirable to compare the unknown spectrum with that of a pure compound or of a known mixture of pure compounds. It is essential, therefore, to have access to a file of pure compound spectra for qualitative analysis and structure determination. In the past it has been necessary for each laboratory to compile its own file, but this information is beginning to become available from various organizations (e.g., American Petroleum Institute, National Research Council, Samuel P. Sadler & Co.). There are great advantages in the use of punched card sorting for this kind of analysis, ~2 and the commercially available data are tending toward this method of presentation. 42 A. W. Baker, N. Wright, and A. Opler, Anal. Chem. 25, 1457 (1953).

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TECHNIQUES FOR CHARACTERIZATION OF PROTEINS

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Since all proteins have similar spectra it is likely that the infrared method will not be useful in qualitative analysis of enzymes, enzyme mixtures, or large peptides. It will, however, be valuable in analysis of mixtures of the smaller molecules such as amino acids 43 commonly employed in experiments with enzymes. Another drawback of the infrared method is its lack of sensitivity in many cases. Although some examples exist where extremely small concentrations can be detected, it is a general rule that the quantitative determination of components present in concentrations of less than 1 to 10% is unlikely, depending on the strength of the absorption bands in question. Auxiliary fractionation or concentration techniques such as distillation or chromatography will, of course, greatly reduce this threshold. 43~ It should be pointed out that in addition to band positions as an index of molecular constitution, recent work has shown that band intensities 44 may also be used for qualitative analysis. This technique has been applied to analysis of carbonyl types in steroids 45 and may also be helpful elsewhere. Two other techniques may contribute to a knowledge of molecular constitution and structure. These involve the use of isotope substitution and dichroie spectra. When an isotope of different mass but identical chemical properties is substituted for an atom in a molecule, the frequencies in which this particular atom participates will change. A common example is substitution of deuterium for hydrogen. Since the mass changes by a factor of 2, there may be a drastic shift of about V ~ in the hydrogen frequencies to the corresponding deuterium frequencies. If the origin of the hydrogenic frequencies is known, then the knowledge of which hydrogens are affected by deuterium substitution may give information about molecular structure. Conversely, deuterium substitution can be used to assign infrared bands to hydrogenic oscillations by noting which bands shift with the substitution. Other isotopes such as N '5 are useful, although the mass effect is much smaller. Dichroic spectra give information about the relative orientations of various parts of a molecule or of the various molecules in a crystal. This comes about because there can be absorption only for the component of the electric vector of the incident radiation which is parallel to the 4aS. E. Darmon, G. B. B. M. Sutherland, and G. R. Tristram, Biochem. J. 42, 508 (1948). 4~ H. M. Randall and D. M. Smith, J. Opt. Soc. Amer. 43, 1086 (1953). ~4D. A. Ramsay, J. Am. Chem. Soc. 74, 72 (1952). 45R. N. Jones, D. A. Ramsay,