The Interpretation Of Hydrogen Ion Titration Curves Of Proteins

THE INTERPRETATION OF HYDROGEN ION TITRATION CURVES OF PROTEINS BY CHARLES TANFORD Department of Biochemistry. Duke University. Durham. North Carolina

I . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . ............................ I1. Dissociation Constants of Appropriate 1 Molecules . . . . . . . . . . . . . . . . . I11. Experimental Titration D a t a . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A . Electrometria Titration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B . Reference Points . . . . . . . . . . ............................ C . Spectrophotometric Titration for Phenolic Groups . . . . . . . . . . . . . . . . . . D . Other Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E . Effect of Solvent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

IV . Counting of Groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . .................... A . Counting Procedure . . . . . . . . . . . . . . . . . . . . . . . . .................... B . Difference Counting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V . Rcversibility; Thermodynamic and Kinetic Analysis . . . . . . . . . . . . . . . . . . . .

A . Reversibility and Time-Dependence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..................... ; . . . . . . . . . . . . . . . . C . Kinetic Analys ....................................... c Analysis . . . . . . . . . . . . . . . . . . . . . 7 . . . . . . VI . Semiempirical The A . The Equation of LinderstrZm-Lang . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B Empirical Procedure., . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C . The Electrostatic Interaction Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . D . Intrinsic pK’s and Their Interpretation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E . Heats and Entropies of Dissociation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V I I More Exact Thermodynamic Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VIII . Volume Changes Accompanying Titration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I X . Miscellaneous Topics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A . Binding of Ions Other Than Hydrogen Ions . . . . . . . . . . . . . . . . . . . . . . . . B . The Isoionic Point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C . Charge Fluctuations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . X . Results for Individual Proteins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A . Chymotrypsinogen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B . Chymotrypsin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C . Collagen Fibrils. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D . Conalbumin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E . a-Corticotropin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . F . Cytochrome c . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . G . Fetuin . . . . . . . . . . . . . . . . . . . . .................................. H . Fibrinogen and Fibrin., . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I . Gelatin . . . . . . . . . . . . . . . . . . . ................................... J Hemoglobin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

.

.

.

69

70 71 76 76 78 80 80 82 82 82 85 90 90

95 99 111 119 121 124 127 127 128 130 131 131 133 133 133 138 138 139 139

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CHARLES TANFORD

K. Insulin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

L. @-Lactoglobulin.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . M. Lysozyme.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . N. Myoglobin.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0. Myosin. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . P. Ovalbumin.. . . . . . . . . . . . . . . . . ................... Q . Papain.. . . . . . . . . . . . . . . . . . . . . .................................. It. Paramyosin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S. Pepsin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T. Peroxidase.. . . . . . ............................................. 6.Ribonuclease., , . . ............................................. V. Serum Albumin.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . W. Thyroglobulin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . X. Trypsinogen, . . . . . . . . . . . . . . . ................................. Y. Trypsin., . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

142 144 147 149

153 153 154 154 154 156 160 160 161 181

I. INTRODUCTION In recent years several reviews have been published on the subject of hydrogen ion titration curves of proteins. Among these there are good general introductions to the subject, which include some description of experimental procedures (Tanford, 1955a; Kenchington, 1960); a review by Linderstrgm-Lang and Nielsen (1959), which gives a lucid introduction to the theoretical treatment of protein titration curves; and a review by Steinhardt and Zaiser (1955), which emphasizes anomalous behavior. A review by Jacobsen et al. (1957) is devoted to use of the pH-stat. Apart from treating that subject in some detail, it contains experimental procedures of general utility in the determination of titration data. More complete developments of the subject may be found in textbooks (Edsall and Wyman, 1958; Tanford, 1961a). The definitive treatment of the mathematical theory, for polyelectrolytes in general, and specifically including proteins, is that of Rice and Nagasawa (1961). The existence of these earlier reviews makes it possible for the present treatment to be limited in scope. It will be sufficient to touch only superficially on experimental techniques and on the theoretical derivation of equations The major objective will be, as the title of the paper implies, to show what one can learn from titration curves that is of general interest to protein chemistry. From this point of view, titration curves do not represent just another way of physically characterizing a protein molecule. More than most other physicochemical methods which are in common use, titration studies tend to emphasize individual differences among proteins, and this is reflected in the organization of this paper. There is a large section, entitled “Results for Individual Proteins,” which contains the many features of

HYDROGEN ION TITRATION CURVES OF PROTEIK

71

titration curves which are unique to individual proteins, and which cannot be described in general terms applicable to all proteins.

11. DISSOCIATION CONSTANTS OF APPROPRIATE SMALL MOLECULES In most common proteins, one out of every three or four amino acid residues contains a titratable acidic or basic group. The number of titratable groups per molecule thus ranges from about 20 to about 250 for the many common proteins with molecular weights below 100,000, and it is even larger for proteins with very high molecular weight. The titratable groups which occur in greatest abundance are the carboxyl groups of glutamic acid and aspartic acid side chains; the amino groups of lysine side chains; the guanidyl groups of arginine side chains; the imidazole groups of histidine side chains; and the phenolic groups of tyrosine side chains. Less frequent are the thiol groups of cysteine side chains and the phosphoric acid groups of phosphoserine or phosphothreonine side chains. Heme proteins contain titratable carboxyl groups attached to the heme, and may also have acidic water molecules attached to the heme iron atom. Acidic water molecules may also be attached to other metalloproteins. Glycoproteins, flavoproteins, and nucleoproteins contain additional titratable groups as part of their non-protein conjugates. Finally, the terminal amino and carboxyl groups of nearly all polypeptide chains are in the free titratable form. The structures of the more common titratable groups are shown in Fig. 1. (Other parts of the protein molecule, such as the peptide group, also possess acidic or basic properties, but they are not titrated within the range of pH 1.5 to 12, within which titration studies are usually confined. Protein molecules tend to become degraded outside this range of pH.) We want to know, before we examine the titration curves of proteins, a t what pH these groups might be expected to become converted from their acidic to their basic form. The simplest initial assumption is that proteins will not behave differently in this respect than do other organic molecules. With this assumption we would expect all effects on the acidic properties, except the effects of electrostatic charge, to be short-range effects. As a first approximation, the pK of the carboxyl group of glutamic acid (apart from the effect of electrostatic charge) could be equated with the pK of acetic acid (4.76) or propionic acid (4.87). To obtain a better estimate we can correct for the fact that the glutamic acid side chain in proteins is in fact under the influence of the polar NH and GO group attached to the third carbon atom from the COOH group. The expected pK might then be set equal to the pK of a compound containing polar groups similarly located, such as monoalkyl glutarate (pK = 4.55). Within an uncertainty of about 0.1 or 0.2 the same expected pK is usually obtained in this way,

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CHARLES TANFORD

regardless of which of several alternative model compounds is chosen. Within an uncertainty of this order the effect of ionic strength within reasonable limits is also negligible, so that, in seeking data of this kind for appropriate model compounds, we need not confine ourselves to experimental data which permit evaluation of the effect of ionic strength. CH-R

a-Amino group

Lo I

I

$H

CH-CH, I

co

y

1

I

CH-CH,--COOH A0

Aspartic acid

Q

OH

I

Glutamic acid

I

NH I

CH--CH~-CH2-CH,--NH-C I

co I Histidine

i

ko 1

-

. .

Lysine

b I

I

NH I CH CH,- SH

’Qrosine

NH CH-CH,-CH,-CH,-CH,-NH: I

I

AH I CH-CH,-CH,-COOH

a

Cysteine

\

Arginine NH,

I

NH 0 I II CH-CH,-0-P-OH I A0 OH I

Phosphoserine

i

NH I CH-R’ AOOH

-Carbowl group

(1

FIG.1. Fortnullts for the most irnportant titratable groups of protein molecules. The model compounds listed in Table I were chosen to reseinble thexc groups it8 closely as possible.

The relation between structure and acidity of organic compounds has been the subject of much study. Those aspects which are of interest in connection with protein titration curves have been reviewed in definitive manner by Edsall and Wyman (1958) and by Edsall (1943), and the reader is referred to these reviews for a discussion of the theoretical and empirical principles which are involved. For the present purpose it is sufficient to extract the data which will lead to the “expected” pK values of the titratable groups of proteins, and this has been done in Table I.

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TABLEI Dissociation Conslants of Model Compounds i n Aqueous Solution at or Near 26'Cn Compound

pK observed

Correction required pK corrected

Compounds resembling a-COOH group CHa-CO-CHe-COOH 3.58 3.6 CHa-CO-NH-CHz-COOH 3.60 3.6 Tetraalanine 3.32* Electrostatic" 3.5 Cysteine Microscopic constantsd 3.8 Glutamic acid Microscopic constantsd 4.3 Tyrosine Microscopic constantsd 4.3 Compounds resembling 8-COOH groiip of aspartic acid side chain CHs-CO- (CHe)e-COOH 4.59 4.6 ROOC-(CHz)z-COOH 4.52 4.5 4.5 HOOC- (CHz)2-COOH 4.24 Statistical factore Compounds resembling Y-COOH group of glutamic acid side chain ROOC- (CHZ)a-COOH 4.55' 4.6 4.7 HOOC- (CHZ)3-COOH 4.36 Statistical factors 4.6 Glutamic acid Microscopic constantsd Compound resembling porphyrin COOH groups C sH 6- (CHI)2-COOH 4.66 4.7 Compound resembling imidaaole group of histidine side chain Poly-histidine 6.150 6.15h Compounds resembling wNH: group HeN-CO-CHZ-NH$ 7.93 7.9 ROOC-CHZ-NH: 7.7 7.7 Leucine ester 7.6 7.63 7.8 Glycylglycine ester 7.75 7.8 Tetraalanine 7.966 ElectrostaticC 7.0 Die thy1 glut amate 7.04 Cysteine 6.8 Microscopic constantsd Tyrosine 7.2 Microscopic constantsd Compounds resembling E-NH: group of lysine side chain 10.4 10.4' ROOC-(CHz) s-NH: 10.4 Lysine 10.79 Electrostaticc Compounds resembling SH group of cysteine side chain 9.5 HO- (CHI)z-SH 9.5 9.1 Cysteine Microscopic constantsd Compounds resembling phenolic group of tyrosine side chain 9.5 9.5j Polyt yrosine 9.7 Tyrosine 10.05 Electrostatic 9.8 Tyrosine Microscopic constantsd Compound resembling guanidyl group of arginine side chain Arginine ca. 12.5 Electrostatic" ca. 12.0 Compounds resembling protein-linked phosphate 1.3 Glycerol-2-phosphate (pKI) 1.34 6.6 Glycerol-2-phosphate (pK2) 6.65 6.5 6.50 Glucose-1-phosphate (pKz) 6.02 Phosphoserine peptides (pKa)

-

-

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CHARLES TANFORD

TABLE I-Continued Most of the data are taken from Edsall (1943) or Edsall and Wyman (1958). b Aversge value for four isomers. c A charged group is present on the model compound a t considerable distance from the acidic group. An estimate for its effect on pK has been made by examining effects of similar charged groups on other acids. d By measurement of the dissociation constants of the amino acids, and of suitable esters and other derivatives. The data have been analyzed by Edsall and co-workers (Edsall and Wyman, 1958; Martin et al., 1958) so as to yield, after suitable assumptions, the twelve microscopic dissociation constants. The ones applicable here are those which refer to dissociation of the group in question from an otherwise uncharged molecule. A molecule with two identical dissociable groups will have a pIi which is twice the value for either group alone. f Interpolated between ROOC-(CH&-COOH and ROOC-(CH&--COOH. c From titration of a polymer with degree of polymerization 15 (Patchornik el al. 1957). h The state of knowledge regarding the titration of imidazole groups is unsatisfactory. The p K of the imidazole group of histidine is 6.0, which is in qualitative agreement with the value listed in the table, since the effects of the two charged groups of histidine should roughly cancel. On the other hand, imidazole itself has a pK = 7.0 and 4-metfhylimidazolehas a pK = 7.5. It is not easy to see why a polar group substitution on the ?-carbon atom (relative t o the nearest nitrogen atom) should produce so large a difference in pK. It should be noted the,t a similar problem is 9.7, whereas that of exists for amino groups. The pK of ROOC-(CH?)a-NH: CHs-(CH&-NH: is 10.7. (Added in proof: Koltun et aE. (1959) obtained pK = 6.42 for carbobenzoxy-Lprolyl-L-histidylglycinamide.) i By extrapolation from data for ROOC-(CH&-NH: with n = 1 to 4. i Essentially t h e observed average pK, for a polymer of average degree of polymerization 30, extrapolated to zero net charge of the polymer (Katchalski and Sela, 1953). k Electrostatic correction computed by the Kirkwood-Westheimer theory. 2 Folsch and Osterberg (1959) determined the pK values of several peptides containing phosphoserine and obtained results in the range of 5.4 t o 6.0. Each peptide carried one positive and one negative charge, and no attempt t o correct for their presence was made.

.

The dissociation of a hydrogen ion from an acidic group changes the charge by one unit. Either the acidic form is charged (as in -NHt) and in that case the basic form is uncharged (-NH2); or the acidic form is uncharged (as in -COOH), leading to a charged basic form (-COO-). One of the groups considered in Fig. 1 and in Table I is slightly more complicated, this being the phosphate group which may lose two hydrogen ions to acquire a double negative charge. The model compounds which are considered in Table I contain only those charges which are an inherent part of the dissociating group. No other charges are present (or, if present, have been corrected for). The pK values listed are therefore those which

HYDROGEN ION TITRATION CURVES O F PROTEIN

75

would be expected if each of the titratable groups were attached alone, without other charged groups, to a protein molecule. An actual protein molecule will contain, as we have pointed out, a large number of acidic groups per molecule. At any pH many of these groups will be in their charged form. Since electrostatic effects are long-range effects, we must expect the course of titration of any one group to be influenced by these other charges which are present. To calculate this effect of electrostatic interactions on protein titration curves has been a major preoccupation of those who have been concerned with the theoretical aspects of protein titration curves. We shall discuss these aspects in Sections VI and VII of this review. For the practical aspects of protein titration which are considered in Sections IV and V, the following qualitative conclusions of the theoretical treatment suffice. (1) It is clear from the pK values of the various dissociating groups that the charges on the protein molecule will be mostly positive at low pH and mostly negative at high pH. At some intermediate pH, positive and negative charges will be present in equal numbers. Since positive charges repel protons, and negative charges attract them, we expect pK’s to be reduced below the values of Table I at relatively low pH, and we expect them to be raised above those values at relatively high pH. The expected magnitude of the effect decreases with increasing ionic strength. For proteins with molecular weight below 100,000, at an ionic strength of 0.1 or above, the normal change in pK due to electrostatic interactions will not exceed a value of 1.5 or so, except as one approaches the extreme ends of the titration curve. Furthermore, electrostatic forces affect all groups alike, so that the pK differences between one type of group and another, at any pH, will be expected to remain the same as the differences given by Table I. (2) When a monobasic acid is titrated, the titration curve is described completely by the pK. We know for instance that, when pH = pK 1.0, 91 % of the molecules will be in the acid form, and, when pH = pK 1.0, 91 % will be in the basic form. These same relations would apply to a particular titratable group on a polybasic acid or on a protein molecule, if all other titratable groups on the same molecule were to remain unaffected. In fact, as the pH is changed, many groups on the same molecule are titrated together. Thus when a particular group on a protein molecule is in its acidic form on most of t,he molecules (pH well below pK), other groups like it will also be in their acidic form, and the net molecular electrostatic charge will be more positive than at a higher pH where this particular group is in its basic form on most of the molecules, and other groups like it are also in their basic form. The effect of electrostatic interaction will thus lead this particular group to have a lower pK at luw degrce of dissociation than at high degree of dissociation. The difference in pH required to

-

+

76

CHARLES TANFORD

go from 9 % dissociation to 91 % dissociation will not be 2.0, as it would be if the pK were independent of pH, but will be larger: the difference in p H could be as large as 3.0 or even more. Conclusion. If protein molecules exhibit no interactions that are not also present on smaller molecules, then the pK values of their titratable groups would be expected to be roughly those of Table I. Electrostatic forces may move them up or down by as much as 1.5 pK units, but relative values will be unaffected thereby. The pK changes during the course of titration, so that the titration curve for any one group will be broader than it would be for a monobasic acid. The assumption that protein molecules do not have unique interactions absent in smaller molecules is of course naive. It is in fact untrue. Special interactions occur and upset the “expectationsJJwith which this section has been concerned. It is the occurrence of such deviations from the expected result which lend interest and importance to the study of protein titration curves.

111. EXPERIMENTAL TITRATION DATA

A . Electrometric Titration The foundation for any study of hydrogen ion dissociation in proteins is the electrometric titration curve. To obtain such a curve, one begins with a protein solution of known concentration, a t an arbitrary reference pH, adds to it varying amounts of a strong acid or a strong base, and then measures the new pH attained. I n a separate experiment, or by means of calculations based on similar experiments, one determines how much acid or base is needed to take a solution which does not contain protein, but other wise has the same initial pH, ionic strength, volume, etc., to the same final pH, ionic strength, volume, etc. The amount of acid or base required for the protein solution is always larger (under most circumstances very much larger) than the amount required for the corresponding solution without protein. The difference between the two amounts is the amount of acid or base which is bound to the protein in going from the reference pH to the final pH: a plot of this quantity versus the final pH is the desired titration curve. In plotting this curve, OH- ions bound are counted as H+ ions dissociated, a procedure which is always permissible in aqueous solutions. A sample plot is shown in Pig. 2. The procedure described in the preceding paragraph will of course measure the number of hydrogen ions bound to or dissociated from all substances which are present in the solution under study. The accuracy of an experimental electrome tric titration curve depends to a considerable degree on the absence of buffers, carbon dioxide, and any other substance, other than the protein of interest, which is capable of acting as an acid or base.

HYDROGEN ION TITRATION CURVES OF PROTEIN

77

Titration studies are nearly always carried out so as to maintain the same ionic strength and protein concentration throughout t,he curve, but this is not essential for all applications. Titration curves are always dependent on ionic strength, and a curve which is not obtained at constant ionic strength can be duplicated only if the ionic strength changes are duplicated. Titration curves are often independent of protein concentration, but will depend on the concentration whenever the possibility of association between protein molecules exists.

-

i scale ZHscole PH FIG.2. Titration curve of 8-lactoglobulin a t ionic strength 0.15 and 25°C. T h e

alkaline branch is time-dependent (cf. Fig. 12), and the figure shows d a t a extrapolated t o the time of mixing ( t = 0) and t o infinite time. The figure also shows how t8hecurve is divided into acid, neutral, and alkaline regions. Three ordinate scales with different reference points are given. (Data of Y. Nozaki.)

Titration curves may sometimes depend on the time which has elapsed, between addition of acid or base and the measurement of pH. (This is true, for instance, of the alkaline part of the curve shown in Fig. 2.) By the same token, the titration curve obtained by addition of successive increments of acid or base to the same protein solution will sometimes differ from the curve obtained by addition of successively larger increments of acid or base, each to a fresh aliquot of the initial protein solution. Some titration curves or parts of titration cruves are independent of the initial pH, i.e., the number of H+ ions which are bound in going from, say, a reference point a t pH 5 to pH 4, is the same as the number bound in

78

CHARLES TANFORD

going from pH 5 to pH 4 after starting at a reference point at pH 7. Likewise, the number of protons dissociated in going from pH 4 to pH 5 may be the same as the number bound in going from pH 5 to pH 4. However, in many instances the situation is not so simple. The titration curve shown in Fig. 2, for example, would be obtained from any initial pH between pH 2 and pH 9.75. A different curve is obtained after exposure to any pH greater than 9.75. (See Section V for further discussion of reversibility.)

B . Reference Points We have described titration curves as records of the number of hydrogen ions attached to a protein molecule at m y pH, relative to the number attached at an arbitrary reference pH. It is advantageous however to choose as reference point a position on the titration curve which has physical significance. There are three such positions: (1) Point of zero net proton charge. If an aqueous protein solution is passed through a mixed-bed ion-exchange resin column (Dintzis, 1952), the solution is freed entirely of all small ions except Hf and OH-. The emerging solution is called isoionic.’ The protein molecules in it usually have a very low average charge, often negligibly different from zero. When a neutral salt is added to such a solution to adjust the ionic strength to whatever value is desired, the net molecular charge may alter because the ions of the salt may be bound. However, only minute numbers of protons are bound or dissociated: the net proton charge, which is defined as the average molecular charge due to bound hydrogen ions, or to the presence of groups from which hydrogen ions have been dissociated, usually remains close to zero. We shall discuss this topic in more detail in Section IX, B. What is important here is that the net proton charge of such a solution can always be calculated exactly from the pH of the solution, as Section IX, B will show. Since the titration curve itself tells us how big a change in pH is needed to bind or dissociate any given number of hydrogen ions, it becomes a simple matter to calculate the pH at which the net proton charge is truly zero. Like all aspects of the titration curve, this pH will usually be dependent on the ionic strength. We have pointed out that the net proton charge of a n isoionic solution 1 The distinction between the isoelectric and isoionic states of a protein was first made in a classic paper by SZrensen et al. (1926). Three definitions of the isoionic point were proposed, one of these being the stoichiometrically defined point which we have called the point of zero net proton charge. The other two were operational definitions (summarized by Linderstr6m-Lang and Nielsen, 1959). The term “isoionic point,” as used here, corresponds t o one of these two operational definitions, chosen because i t always permits calculation of the point of zero net proton charge, which is the only parameter of real interest in the analysis of titration curves. The same choice has been made by Scatchard and Black (1949).

HYDROGEN ION TITRATION CURVES OF PROTEIN

79

is nearly always close to zero. It can be shown from the equations given in Section IX, B that it is in fact negligibly different from zero if (a) the isoionic point falls between pH 5 and pH 9, and ( b ) the protein concentration is 1 gm/100 ml or larger. Under these conditions the isoionic point and the point of zero net proton charge are indistinguishable. (These conditions apply to the p-lactoglobulin curve of Fig. 2, for example.) For this reason the terms “isoionic point” and “point of zero net proton charge” are often used interchangeably. It is important to be aware of the difference when proteins such as lysozyme (isoionic point at pH 11) are being studied, and in general whenever protein solutions of low concentration are being used. It is to be noted that the point of zero net proton charge can be determined only for proteins which can be deionized without precipitation or other change. The point would also have little significance (and probably could not in any event be determined unequivocally) if the pH lies in a region where the titration curve is not behaving reversibly. (2) Point of maximum proton charge. At relatively high ionic strength (0.1 or above) a definite acid end point of the titration curve can nearly always be established, an example being provided by Fig. 2. The point represents a plateau of the titration curve, a range of pH within which the number of hydrogen ions attached to the protein molecule remains unchanged. The number of attached hydrogen ions is effectively a “maximum” number: more could be bound only at much greater acidity, where the integrity of the protein molecule would probably be destroyed. In terms of the “expected” pK values of Table I, the acid end point is the point where all titratable groups listed there, except the phosphate group, are expected to have been converted to their acidic forms. (Considering that most proteins have a large positive charge at the acid end point, the expected pK1 for the phosphate group would be zero or less.) (3) Point of minimum proton charge. The shape of the titration cruve at high pH suggests that a similar end point is being approached there, and we have indicated its probable location by the dashed line of Fig. 2. Unfortunately, the experimental curve usually can not be extended to the vicinity of this end point, because irreversible degradation of the protein molecule sets in when a pH of 12 is approached. Thus the alkaline end point, representing a position of minimum proton charge, can not be defined as precisely by experimental measurement as the acid end point. In terms of the pK values of Table I, the alkaline end point of the titration curve is the point where all titratable groups listed in the table, except guanidyl groups, are expected to have been converted to their basic forms. To change the reference point of a titration curve from an arbitrary reference pH to one of the reference points just defined simply involves a

80

CHARLES TANFORD

change in the zero point of the ordinate scale of the titration curve: the difference between the scale values a t any two pH’s must remain the same regardless of the reference point used. For illustration, Fig. 2 shows three ordinate scales based on three different reference points.

C. Spectrophotometric Titration for Phenolic Groups Electrometric titration is simply a measure of the total number of hydrogeri ions bound to or dissociated from a protein molecule, with no discrimination between the various kinds of acidic or basic groups with which these hydrogen ions may be associated. Thus there is a need for alternative methods which focus specifically on hydrogen ions associated with particlar groups of the protein molecule. One such method which has been used extensively is based on the change in the ultraviolet absorption spectrum which occurs when a tyrosine phenolic group dissociates to a phenolate ion. As was first suggested by Crammer and Neuberger (1943)) this spectral change can be used to follow the progress of the dissociation of hydrogen ions from tyrosine phenolic groups of proteins, by measurement of absorbance a t an appropriate wavelength, usually in the range 290 to 300 mp. The ultraviolet spectroscopy of proteins is reviewed elsewhere in this volume (Wetlaufer, 1962), so that no detailed discussion of this method is required. It should be noted however that indole groups of tryptophan side chains absorb in the same region of the spectrum as phenolic groups, and that there are spectral shifts, both for indole and phenolic groups, which are not related to hydrogen ion dissociation. Furthermore, a general increase in absorbance in the ultraviolet takes place whenever aggregation of protein molecules increases the amount of light which is lost by Rayleigh scattering. These effects, undesirable from the present point of view, can to some extent be separated from the changes ascribable to titration of phenolic groups by measurement of absorbance over a wider wavelength range, and by auxiliary studies of molecular weight and conformation. In general the spectrophotometric titration of phenolic groups will yield more accurate results for proteins which have a low tryptophan content and which undergo no conformational change in the pH region in which phenolic groups are titrated.

D. Other Methods Spectroscopic methods for following the titration of other common titratable groups of protein molecules do not exist. The reason is that the peptide group and the aromatic rings of phenylalanine, tryptophan, and tyrosine side chains absorb strongly in the ultraviolet below 250 mp, making it essentially impossible to observe the relatively small changes in absorb-

HYDROGEN ION TITRATION CURVES OF PROTEIN

81

ance which imidazole, sulfhydryl, and other groups undergo in the ultraviolet when their state of ionization is altered. The use of infrared spectra is prevented by similar reasons: not only the various parts of the protein molecule but also the solvent (at least if it is HzO) have overlapping absorption bands, which reduce titration-induced changes to a small fraction of the total absorbance. It has been suggested (Ehrlich and Sutherland, 1954; Susi et al., 1959) that infrared absorption can be used to follow the titration of carboxyl groups of DzO is used as solvent, but no critical examination of this possibility has been made. Spectroscopic methods can be used to follow the dissociation of hydrogen ions from certain special groups present on prosthetic groups of proteins. An example is the Fe(H20)+group of proteins containing ferriheme. The dissociation of this group to Fe(0H) is accompanied by a well-defined change in the visible spectrum, which has been used to follow the reaction by Austin and Drabkin (1935), and subsequently b y other workers. The reaction is also accompanied by a change in the magnetic susceptibility of the iron atom, and this effect, too, can be used as a measure of the extent of titration (Coryell et al., 1937). A method of an entirely different kind has been proposed for following the dissociation of hydrogen ions from the imidazole groups of histidine side chains (Koltun et al., 1958). It is based on the catalysis of the hydrolysis of p-nitrophenylacetate by uncharged (basic) imidazole groups. The rate constant for this reaction is independent of pH. Moreover, the presence of the p-nitrophenylacetate appears not to affect the equilibrium between the acidic and basic forms of the imidazole group. The observed rate of the catalyzed reaction is thus a direct measure of thc fraction of imidazole groups in the basic form a t any pH. There is so far only a single recorded application of this method to proteins (myoglobin, studied by Breslow and Gurd, 1962). A disadvantage of the method is that uncharged amino groups also catalyze the hydrolysis of p-nitrophenylacetate, so that the method can be used unequivocally a t present only in a region of pH where all amino groups are in the charged acidic form. Mention should be made, finally, of the existence of indirect methods. Changes in some property which is not directly related to the dissociation of an acidic group may be observed to have a pH-dependence which resembles the pH-dependence of hydrogen ion dissociation from a single group. It may then be postulated that the change in this property is an indirect reflection of the dissociation of a single group, and that the dissociation curve and pK of the group can be obtained from it. The commonest example of this procedure involves the use of ultraviolet difference spectra (Wetlaufer, 1962), but optical rotation and other properties can be used as well. An instance of an application of such methods to proteins is provided b y Hermans and Scheraga (1961b).

82

CHARLES TANFORD

E . Effect of Solvent The brief survey of experimental methods which we have given has in general assumed that water or an aqueous salt solution is being used as solvent for the protein. When other solvents are used, two problems arise: (1) The dissociation constants of all acids and bases depend on the solvent being used. The characteristic pK’s of Table I would not apply, for instance, in a dioxane/water mixture. (2) The usual techniques for measuring pH are applicable to aqueous solutions only. The electrolytic cell normally used to measure pH, when standardized by appropriate buffer solutions, yields a value of pH which is not exactly the same as, but is very close to -log aH+as defined by other methods. (Bates, 1954; Tanford 1955a). There is no assurance that this will be true in other solvents. There is a simple way to avoid these problems. One can define a pH scale in a completely arbitrary manner relative to the emf of a suitable cell. One can then relate the pH on this scale to an arbitrarily defined “activity” of hydrogen ions, simply be setting pH = -log aH+. The dissociation constants of model compounds can then be determined in terms of this arbitrary scale. This method has been used by Donovan et al. (1959) for protein titrations in concentrated aqueous solutions of guanidine hydrochloride and of urea, and by Sage and Singer (1962) for titrations in ethylene glycol.

IV. COUNTING OF GROUPS The simplest information gained from titration curves is a count of the number of groups titrated. This count can be useful regardless of whether the titration curve is reversible and regardless of whether the protein remains native throughout the pH range of titration. The most interesting applications of group counting are in fact to situations where the titration curve depends on time, the direction of titration, and similar factors, The differences observed, between one set of conditions and another, often tell directly how the protein differs under the two conditions.

A . Counting Procedure Most titration curves, such as that of Fig. 2, consist of three well-separated parts: a steep portion between the acid end point and about pH 5.5, another steep portion between about pH 9 and the alkaline end point, and a relatively flat portion (relatively few groups titrated per pH unit) in between. It is thus quite generally possible to divide the titration curve into three S-shaped portions, as has been done in Fig. 2, and to count separately the groups which titrate in the acid, neutral, and alkaline re-

HYDROGEN ION TITRATION CURVES OF PROTEIN

83

gions. The separation between the three parts is better a t higher ionic strength, and one can also approach closer to the end points a t higher ionic strength. Thus group counting is usually best conducted at ionic strengths of 0.1 or above. Table I shows that organic molecules which have carboxyl groups that resemble the carboxyl groups of proteins generally have pK values from 3.5 to 4.7,when electrostatic effects of charges elsewhere on the molecule are absent, or have been corrected for. The electrostatic effects expected to arise from other charges on a protein molecule may shift these pK values and will broaden the range of pH within which these groups are titrated. However, the major part of all carboxyl groups should be in their acidic form at pH 2 and in their basic form at pH 6 or slightly higher. Furthermore, no other titratable groups are expected from Table I to have pK’s within 2 pK units of the carboxyl groups. (It should be recalled that electrostatic effects are expected to influence all kinds of groups about equally.) It is logical, therefore, tentatively to identify the groups titrated in the acid part of the electrometric titration curve as “carboxyl” groups, the quotation marks signifying that these groups may not all in fact be carboxyl groups. Similary, the neutral region of the curve may be identified with “imidaeole” and “a-amino” groups, the a-amino groups being the N-terminal groups of the polypeptide chains. The alkaline region, finally, may be taken to represent primarily “side-chain amino” and “phenolic” groups, with a contribution from sulfhydryl groups where these are important. The number of polypeptide chains of a protein molecule is usually known. In most cases each polypeptide chain is terminated by a titratable a-amino group at one end and a titratable a-carboxyl group a t the other end. By subtracting the numbers of these groups from the titration regions in which they are tentatively assumed to occur, we obtain a count of “side-chain carboxyl” groups and of “imidazole” groups, the quotation marks again signifying that the identification rests on an assumption of normal titration characteristics which further investigation may prove to be false. If the phenolic groups have been titrated separately by the spectrophotometric method, then a count of these groups is available. The change in absorbance at 295 mp on ionization of a 1 M solution of tyrosine (1-cm light path) is 2300, and, at the present level of approximation, the same figure may be taken for the phenolic groups of proteins, with the understanding that processes other than phenolic ionization may effect the absorbance at 295 mp (see above). Subtracting the number of phenolic groups from the number of groups titrated in the alkaline region as a whole gives a count of “side-chain amino” groups. If the point of zero net proton charge is known, then a count is available

84

CHARLES TANFORD

of the number of hydrogen ions which must be added to go from that point to the acid elid point (point of maximum net proton charge). Unless the protein contains phosphate groups, or other groups with pK’s well below that of carboxyl groups, only amino, imidazolo, and guanidyl groups (from arginine or homoarginine side chains) will hear charges at the acid end point. Moreover, all of these groups will be positively charged. The number of hydrogen ions required to go from the point of zero net proton charge to the acid end point is then simply a measure of the sum of all these groups, which we shall call EN+ for short. If the number of “imidazole” groups and of both kinds of “amino” groups is known from the counting procedures already described, then this number may be subtracted from 2” to yield the number of “guanidyl” groups. It should be noted here that guanidyl groups are normally in their acidic (charged) form throughout the pH range covered by the titration curve of a protein. The count of these groups as obtained here is essentially a count of the number of carboxyl and other groups which must be titrated to neutralize the positive charge present on guanidyl groups. It should also be noted that any metal ions coordinated to a protein may contribute to the maximum charge. A ferric iron atom coordinated to a heme protein, for example, normally bears a charge of +1 a t low pH. Phosphate groups, as previously mentioned, would have a charge of -1 at the acid end point. These charges, where present, will all make a contribution to ZN+. The division of the titration curve into three parts is subject to some arbitrariness. The uncertainty in the count of groups titrated in the acid and alkaline regions is typically about 5 %. The uncertainty in the count of groups titrated in the neutral p H range is numerically the same, but, since there are generally fewer groups in the neutral region, it represents a larger percentage of the number of groups. One way of refining the division of the titration curve into the three regions is based on the fact that carboxyl groups have a heat of dissociation close to zero, whereas imidazole groups have a heat of dissociation of about 6 kcal/mole. An apparent heat of dissociation may be measured from titration curves a t two or more different temperatures

AH,,,

=

-2.303~R[apH/a(l/T)];

(1)

the pH being measured at the same state of titration (same value of ?, see Fig. 2) a t each temperature. This value of AH,,, will generally be quite close to the true heat of dissociation, and may thus be used to define more sharply the transition from titration of L‘carboxyl’7groups to titration of “imidazole” groups. An example is provided by Fig. 3. The same method cannot be used to define the transition from t)heneutral

HYDROGEN ION TITRATION CURVES O F PROTEIN

85

range to the alkaline range, because a-amino groups (which titrate a t the upper end of the neutral region) would be expected to have the same AH (about 11 kcal/mole) as the €-amino groups of the alkaline region. Also, the phenolic groups of the alkaline region are expected to have AH N 6 kcal/mole, which is similar to the value for imidazole groups. (Heats of dissociation will be considered again in Section VI, E.) Other methods of refinement of the count of groups exist. The most important one occurs as an adjunct to the semiempirical analysis of the shape of each part of the titration curve, to be discussed in Sections VI, B and VI, C . It is often impossible to achieve a self-consistent interpre-

, 0 80

100

No.of groups titrated

120

FIG.3. Apparent heat of dissociation i n serum albumin. The break between

AH = 1 kcal/mole and AH = 7 kcal/mole occurs very close t o P = 100, indicating the presence of a total of 100 carboxyl groups per molecule. (Tanford et al., 1955b.)

tation with the numbers deduced from visual examination of the curve, as described here. A self-consistent interpretation may then be obtained by minor alterations in these numbers. It may be noted finally that more classes of titratable groups than have been discussed so far may be discernible. Figure 4 is a particularly striking example. It shows that the phenolic groups of chymotrypsinogen may, simply on inspection, be divided into three separate classes.

B. Difference Counting Counting of titratable groups is particularly interesting when the titration curve for a protein depends on the conditions under which it is determined, as for instance in the example of Fig. 2, where the titration curve above pH 9.7 depends on time. What is the physical meaning of the

86

CHARLES TANFORD

difference between the zero-time curve of Fig. 2, presumably representing a continuation of the titration curve of the native protein, and the lower curve, which represents the titration after some slow molecular change has gone to completion? Titration curves provide one of the simplest methods of detecting the occurrence of conformational change, and numerous examples will be cited. To avoid cumbersome terminology we shall call striking conformational

PH

FIG.4. Spectrophotometric titration of the phenolic groups of a-chymotrypsino gen (Wilcox, 1961). The native curve was obtained a t 25°C in 0.1 M KCI. The arrows indicate time-dependent data. The upper curve was obtained a t 25°C in 6.4 M urea, containing 0.1 M KCI. Under these conditions the protein R i denatured. The total number of groups titrated is 4, a change in absorbance of about 2000 at 295 m p corresponding to titration of a single phenolic group.

changes of this kind “denaturation,” and shall refer to the altered protein as “denatured.” In most instances a combination of physical and chemical measurements is required to specify precisely the nature of a conformation change, and a detailed description is therefore beyond the scope of this paper, which is limited to information derived from titration curves. The term denaturation is to be taken as covering a variety of possible changes in conformation. Figure 2 is one type of situation in which titration curve differences are observed: in this case it is the difference between a native and a denatured protein. Differences of this kind may also be observed by examining the

HYDROGEN ION TITRATION CURVES OF PROTEIN

87

protein in different solvents, or before and after it has combined with a metal ion, or before and after it has reacted with oxygen, or before and after it has been subjected to the action of an activating enzyme, etc. Titration curve differences may be of three types. (1)The total number of groups titrated has altered, i.e., new titratable groups have appeared. (2) The total count of groups remains the same, but their division into the classes enumerated above has altered, e.g., some “imidazole” groups may have become “carboxyl” groups. (3) The numbers counted in each of the

PH FIQ.5. Difference between titration curves for a given type of group in two differ ent states of a given protein. The difference lies in the number of groups available for titration. The top figure shows the actual titration curves, the lower figure a plot of the difference between them.

classes remains the same, but the shape of the curve is altered. With the first two types of difference, the S-shaped curves representing titration of any one of the classes of groups differ in the way shown in Fig. 5. If it is merely the shape of the curve which differs, then the difference will appear as in Fig. 6. Unfortunately, one cannot always tell which type of difference is involved. The alkaline region of the zero-time titration curve of Plactoglobulin (native protein) shown in Fig. 2 cannot be carried above pH 11, because the rate of denaturation becomes too rapid. The segment which is available shows the titration in the alkaline region of about half as many groups as are titrated altogether in this region after denaturation.

88

CHARLES TANFORD

The curve for the native protein is also less steep. It is not possible, however, to tell whether an extension of this curve would continue with its same moderate slope until the total number of groups titrated became the same as for the denatured protein (analogous to Fig. 5 ) or whether it would level off earlier (analogous to Fig. 6). Titration curve differences may be measured directly by means of a pH-stat (Jacobsen et al., 1957). We begin with the protein in its initial native state a t a particular pH, and then allow denaturation, metal binding,

'!2x f

l -

0 r

PH

FIG.6. Difference between titration curves for a given type of group in two difl'crent states of a given protein. The difference lies in the shape of the curve, the number of groups available being the same. The top figure shows the actual titration curves, the lower figure a plot of the difference between them.

or whatever other reaction we wish to study, to occur. The pH-stat is designed to add acid or base so as to maintain the pH unchanged, and the total amount required between the beginning and end of the reaction is then a measure of the difference between the corresponding titration curves a t that pH. Measurements made a t a series of pH values will then produce difference titration curves such as shown in the lower parts of Figs. 5 and 6. By themselves these difference curves are less informative than the complete titration curves. They may however be more precise, and thus are often useful in conjunction with the complete curves. They also allow measurement of the rate of reaction a t the same time as the total difference is observed (see Section V, C ) .

HYDROGEN ION TITRATION CURVES O F PROTEIN

89

An example of direct difference counting, in a situation where the overall titration curve is not known, is provided by Fig. 7. It shows the difference between the titration curves of active carboxypeptidase A, which contains Zn++,and the inactive zinc-free protein, as determined b y Coleman and Vallee (1961). The measurements were made by the pH-stat method, and confined t o a relatively narrow pH range. The figure shows a difference of two groups per bound Zn++ ion, with pK values of 7.7 m d 9.1. The two groups involved lose their protons when Zn++ is bound. I n the absence of a complete titration curve a completely unequivocal interpretation

-n 0

-

V

I

$ 2.0.-

--&, \

q'

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I

z G 1.5,-

40

z 0 ++ c

1.0,-

N

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5

n

w

\ \

\,

pKt7.7

t\

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0.5 -

'\,

pK;9.1

-I

k!

5-

O.O.,

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I

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(CPD) con" _ taining Zn++, and the zinc-free apoenzyme. The data were obtained with a pH-stat, measuring the amount of base required to maintain constant pH as zinc was added t o apoenxyme. The data are for 2 5 T ,ionic strength 1.0.

cannot be made, but it is reasonable to suppose that Zn++ is chelated to two basic groups which are prevented from combining wit.h hydrogen ions as long as the metal remains attached. When Zn++ is removed, these groups bind hydrogen ions with pK values of 7.7 and 9.1. The experiments were carried out in 1 M NaC1, so that electrostatic effects should be suppressed, and pK values observed should correspond closely to those of Table I. Independent information on the strength of Zn++ion binding, suggests that the ion is chelated to a site containing a basic nitrogen atom and a sulfide group. The observed pK's are compatible with such a binding site, the pK of 7.7 corresponding to an a-amino group (or nn imidazole group), while the pK of 9.1 is the expected value for a thiol group.

90

CHARLES TANFORD

Several other interesting examples will be cited in Section X, where the titration curves of individual proteins will be analyzed. It will be seen from difference counting that the binding site for Zn++ in insulin involves two uncharged imidazole groups, and that the site for iron binding in conalbumin involves three ionized phenolic groups. Difference counting will reveal the presence of anomalous carboxyl groups in native 8-lactoglobulin and lysozyme. It will show that deviations from expected pK values, where they occur, are generally characteristic of the native conformation of a protein and that they disappear on denaturation. (One example is provided by Fig. 4. The three distinguishable classes of phenolic groups of chymotrypsinogen disappear on denaturation.) Difference counting will be seen to provide evidence concerning the action of thrombin on fibrinogen, and concerning the action of acid and base in the liberation of gelatin from collagen. Group counting may be used of course to study any chemical modification of proteins. A recent example is provided by the use of difference counting in a study of the effect of photo-oxidation on proteins (Vodrazka et al., 1961). V. REVERSIBILITY ; THERMODYNAMIC AND KINETICANALYSIS

A . Reversibility and Time-Dependence The dissociation of hydrogen ions from the model compounds discussed in Section I1 is ordinarily a very rapid reversible reaction. Measurements by ordinary methods represent thermodynamic equilibrium. They are independent of time and independent of the direction in which the reaction is carried out. Large sections of protein titration curves are often equally time-independent and reversible, as, for instance, the acid part of the titration curve of P-lactoglobulin shown in Fig. 2. Any such section of the titration curve will again represent thermodynamic equilibrium and it may be subjected to thermodynamic analysis, as outlined in Sections VI and VII. On the other hand, a titration curve may depend on the time between addition of acid or base and the pH measurement (as in the alkaline branch of Fig. 2). When this happens, the curve will also in general be irreversible. A titration curve may appear to be time-independent but irreversible, especially if a continuous titration method is employed in which successive increments of acid or base are added to the same solution for each successive pH measurement. A hypothetical example is shown in Fig. 8. When this situation occurs, a careful rerun of the curve, in which each experimental point is obtained with an entirely fresh solution, will usually show time-dependence, as shown by curves 3,4, and 5 of Fig. 8.

HYDROGEN ION TITRATION CURVES OF PROTEIN

91

In many time-dependent situations a zero-time reversible curve (curve 6 of Fig. 8) may be obtained, i.e., reversed points obtained by keeping a solution a t an extreme pH for various lengths of time, and then extrapolating to zero time of exposure to the extreme pH, may coincide with a forward titration curve, each point of which also represents an extrapolation to zero time. In the same situation, the protein represented by curve 2 of Fig. 8 will usually be different from the native protein by criteria such as optical

End with

Denatyed Protein Start with Native Protein

PH

FIG.8. Hypothetical titration curves illustrating time-dependence and irreversi-

bility. Curve 1 is an apparently time-independent curve, obtained by continuous titration, waiting several minutes for each successive pH reading. Curve 2 is the reverse titration curve, beginning a t t h e acid end point. Curve 3 is the forward titration curve obtained by flow methods, each pH being measured on a freshly mixed solution within seconds of mixing. Curves 4 and 5 are obtained from freshly mixed solutions with longer time intervals between mixing and measurement. Curve 6 is the titration curve which one might speculatively draw t o represent “instantaneous” titration of the native protein.

rotation or ultraviolet absorption spectrum, i.e., it will represent titration of a denatured state of the protein. In some instances, curve 2 itself may be reversible, i.e., the denatured protein may be a stable product in rapid equilibrium with its environment. On the other hand, time-dependent reversion to the native form may occur, or further slow denaturation reactions may take place. The zero-time reversible curve can usually be obtained over a limited range of pH only. I n the hypothetical example of Fig. 8, the molecular change which leads to curve 2 as the observed titration curve would become too rapid for extrapolation to zero time well before the acid end point of

92

CHARLES TANFORD

the curve is reached. It is often possible in such situations to extend the zero-time reversible curve by using a lower temperature, or a different ionic strength, to reduce the rate of denaturation. An example is provided by the titration of ferrihemoglobiii. Figure ‘3 shows the titration data obtained by Steinhardt and Zaiser (1953) a t ionic strength 0.02, a t 25°C. It is not possible to see enough of the native titration curve to decide whether it differs from the back titration curve

PH

FIG.9. The acid region of the titration curve of ferrihemoglobin a t ionic strength 0.02, a t 25°C. The lower curves in the inset represent the difference between the 3-sec curve and the 2- t o 22-hr curve, the dotted line incorporating a correction (discussed in the original paper). The upper curves in the inset are not of interest for the present discussion. From Steinhardt and Zaiser (1953).

chiefly in the number of titratable groups or chiefly in the shape. Figure 10 shows similar data for the cyanide complex of ferrihemoglobin, a t ionic strength 0.3, at 05°C (Steinhardt el al., 1962). A difference in the count of groups is now evident on inspection. Another example is provided by the titration of the phenolic groups of ribonuclease (Tanford et al., 1955a), in 0.15 M KC1. At 25°C the data strongly suggest that only three out of six phenolic groups are titrated in the native protein. At 6°C this conclusion becomes unequivocal (Fig. 11). A summary of information on the reversibility of protein titration curves,

HYDROGEN ION TITRATION CURVES OF PROTEIN

93

obtained from recent detailed studies, is given in Table 11. It is seen that some proteins, like chymotrypsinogen, may be titrated reversibly and instantaneously over a wide range of pH. At the other extreme is pepsin, which undergoes autolysis below pH 5 and becomes denatured above pH 6. The fact that a protein titration curve is reversible over a given range 1.61

,

I

/ 3

I

I

I

I

I

I

Cyonoferri hemoglobin 0.3 m CI Q5.C o Notlve Protein (Flowig)

-

1

I

I

I

4

I

I

a

I

, 6

t

7

PH

FIG.10. Data similar t o those of Fig. 9, but for the cyanide complex of ferrihemoglobin, a t lower temperature and higher ionic strength. The curves without experimental points represent similar data for uncomplexed ferrihernoglobiu, at the same temperature and ionic strength. The inset shows the two difference curves obtained from these data. From Steinhardt et al. (1962).

of pH does not necessarily mean that the protein conformation remains unchanged over the same pH range. Several of the proteins listed in Table I1 undergo conformational change within this pH range. In every example cited, except ovalbumin, the evidence for such change first came from an analysis of titration curves by the methods of Section VI.

B. Thermodynamic Analysis Thermodynamic analysis can be carried out only for reversible portions of a titration curve. The commonly used methods of approach will be

94

CHARLES TANFORD

considered in Sections VI and VII. As indicated above it may be possible, over a limited range of pH, to obtain two reversible curves for analysis, one representing the native conformation of the prot.ein, the other representing a denatured state.

C . Kinetic Analysis Whenever a titration curve depends on time, a kinetic analysis becomes possible. As indicated above, the time-dependence usually reflects a

7' 2

16

1 B

X

P 10

\

1' 1

aC 2

t

48

'E 0

0

6

8

10

12

14

PH Fro. 11. Dissociation of the phenolic groups of ribonuclense at ionic strength 0.15. The dashed lines show regions of time-dependence. Half-filled circles represent measurements after reversal from pH 11.5 (middle curve) and after reversal from pH 12.7 (upper curve). 0--T = 25°C; 0--T = 6°C. From Tanford et al. (1955a).

change in protein conformation, and a kinetic study is then a measure of the rate of change of conformation. As an example, Fig. 12 shows pH-stat records of the uptake of hydroxyl ions by 0-lactoglobulin in the alkaline region (Nozaki and Bunville, 1959). These are a part of the data from which the two alkaline branches of the titration curve of Fig. 2 were constructed. They also provide, however, a measure of the rate of denaturation of the protein. No systematic review of kinetic studies of this kind will be attempted in this paper, since they should logically be considered in conjunction with other methods of following the rate of denaturation.

95

HYDROGEN ION TITRATION CURVES O F PROTEIN

TABLEI1 Reversibilitu of Protein Titration Curves at 26'CU or LLlUIlal

Chymotrypsinogen Conalbumin a-Corticotropin Hemoglobin Insulin 8-Lactoglobulin Lysoa yme Myoglobin Ovalbumin Pepsin Ribonuclease Serum albumin

9.4 6.8 8.6 7.0 5.6 5.3 (1l.l)Q 7.5 4.9 <2 9.6 5.4

2.5-11.8 4.2-11.2 2-12 4.4-11.5 2-12 1.5-9.7 2-12 4.5-11.5 2-12 5-6 2-11.5 2-12

No Yes -e

No No/ Yes No No Yesh No No Yes

References to titration studies of individual proteins are given in Section X. The isoionic pH depends on a variety of factors. For example, i t will be higher for ferrihemoglobin than for ferrohemoglobin. The figures given in the table are intended simply as an indication of the p H were & N 0. The pH range depends on the exact conditions. In many instances there has been no serious effort topin down exactly how far a titration m2ty be carried without irreversible change. The range of pH 2 t o 12 given for several proteins does not mean that irreversible changes are known to occur at pH 2 or 12, but only that no such changes were observed within that range. Minor changes and simple reversible association reactions have not been included. a-Corticotropin does not have a globular compact structure at any pH. f The titration curve can give no information on the subject of reversible conformational change in insulin because there is extensive pH-dependent association between insulin molecules. The absence of other conformational change is indicated by hydrodynamic measurements of Fredericq (1956). 0 The isoionic pH of lysoayme is in doubt. See Section X. A No conformational change is detected by analysis of the titration curve. A distinct change in sedimentation coefficient occurs below pH 4, however. (Charlwood and Ens, 1957.)

VI. SEMIEMPIRICAL THERMODYNAMIC ANALYSIS A . The Equation of Linderstr$m-Lang If a portion of a titration curve represents thermodynamic equilibrium, it may be treated by standard methods of thermodynamic analysis. If, for example, a protein molecule has 100 dissociable hydrogen ions, and if

96

CHARLES TANFORD

its titration curve is reversible from one extreme to the other, one could determine the 100 successive equilibrium constants for the reactions PHloo

+ P H Q Q+ H+

*

+ Hf PHi-1 + H+ ...

P H ~ Q PHm

PHi

PH$P+H+

TIME, MINUTES

FIG.12. The time-dependent uptake of base by p-lactoglohulin a t ionic strerigt,h 0.15 at 25"C, as measilred with a pH-stat. The initial point of each curve (filled circles) represents a measurement on a separate solution, with a flow apparatus c a p ble of determining pH within 1 sec of mixing (Nozaki and Bunville, 1959).

where PHi represents a protein molecule in which i of the hydrogen ions are still bound. The dissociation constants which one obtains in this way are however of limited value. They provide an algebraic representation of the titration curve, but they do not reflect the properties of individual acidic groups because a species designated as PHi is not a single species, but represents a mixture of molecules in each of which the i protons are attached to a different set of basic groups. A much more revealing treatment is one which specifically takes into account the fact that many of the titratable groups of a protein molecule are likely to be intrinsically identical, or very nearly so. Furthermore, it takes into account the one interaction between titratable groups which is

HYDROGEN ION TITRATION CURVES OF PROTEIN

97

known to be of predominant importance, this being the Coulombic interaction between their charges, and introduces suitable theoretical expressions for this interaction into the equation for the titration curve. The first and simplest treatment of this kind was developed by Linderstrgm-Lang (1924). Its basic assumption is that the charge on a protein molecule is evenly smeared over the surface of a sphere. The sphere is assumed impenetrable to the solvent. The electrostatic interaction between charges enters into the theory by virtue of the fact that each hydrogen ion to be added has to increase the molecular charge by one unit, being opposed by the charge already present. As a result, the equilibrium constant K , for dissociation of any one titratable group of type i,

Ki

xiaH+ 1 - xi

= __

where xi is the average degree of dissociation and aH+the thermodynamic activity of hydrogen ions in the solution, becomes dependent on the average charge per protein molecule. This dependence takes an exponential form,

z

Ki

=

Kikl e2w'

(3)

where KM: is the intrinsic dissociation constant for the group in question, this being the value of Ki in the absence of electrostatic interaction, i.e., when 2 is zero. The constant w of Eq. (3) is the same for all titratable groups and is given by the equation 2

DRkT

(4)

where e is the unit of electron charge (4.80 X lo-'' esu), D is the dielectric constant of the solvent, k is Boltzmann's constant, T is the temperature, K is the Debye-Huckel parameter proportional to the square root of the ionic strength (at 25°C in water it is 3.87 X 1071"2, where I is the ionic strength), R is the radius of the sphere which represents the protein molecule, and a is the radial distance of closest approach to the center of this sphere of the center of the average ion of the salt which is being used to create the ionic strength. Generally the distance a will be of the order R 4- 2.5 A. A detailed derivation of Eqs. ( 3 ) and (4) has been given elsewhere (Tanford, 1961a). Combining Eqs. (2) and (3), we get

98

CHARLES TANFORD

or, in logarithmic form, X.

log A 1 - xi

=

pH

- pK:At

+ 0.868~2

(6)

In using these equations we should note that neither K , nor K/fl is a true thermodynamic equilibrium constant because the ratio xi/( 1 - x i ) is a concentration ratio instead of an activity ratio. Ionic strength is however the only factor which should influence its value measurably (see Section VI, D),and K:;: should remain essentially constant over the entire titration curve as long as ionic strength remains constant. It should be noted also that the “pH” which is ordinarily measured in the laboratory is not exactly -log uH+if uH+is to have the meaning assigned to it in Eq. (2). In dilute aqueous solutions, however, the difference must be quite small ( Tanford, 1955a). In using these equations we need to know the average net charge 2 at each pH. The titration curve gives us the major part of this charge, namely the part 2, which is due to hydrogen ions bound to basic groups or dissociated from neutral acidic groups. This quantity is given directly by the titration curve if the reference point for the ordinate is the point of zero net proton charge, i.e., if the isoionic pH has been determined. However, even if the pH of zero net proton charge has not been experimentally measured, it can be calculated after the group counting procedure is completed. If we know the maximum value of 2, at the acid end point of the curve, ( Z H ) m a x , then, at any other pH, ZH

and 2,

=

=

(2H)msx

-

f

(7)

0 at that pH where F =

In the absence of any other information we have no choice but to choose

2 as equal to 2, . However, if the salt ions, which are present in the solu-

tion to maintain a moderately high ionic strength, are known to be bound to the protein, then 2 must be corrected appropriately. If the electrolyte used is KC1, for example,

2 = 2,

+

- acl-

(8 1 where a is the average number of ions of a given type bound to the protein. The D values may be determined in separate experiments (Scatchard et al., 1950, 1957; Carr, 19,55), but these experiments are more difficult than the determination of titration curves and in many cases the a values for the ions are not known. We now introduce the second important feature of the LinderstrgmLang treatment, that many of the titratable groups of any protein molecule are intrinsically identical. In other words, we can divide the titratable rK+

HYDROGEN ION TITRATION CURVES OF PROTEIN

99

groups into a small number of classes: n1 groups of type 1, n2 groups of type 2, etc. All the groups of a given type have the same intrinsic pK, so that each group has the same degree of dissociation at any pH. The total number of groups of type i which are dissociated at any pH is then fj =

with

5, given

ngg

(9)

by Eq. ( 5 ) or (6). The total of all groups dissociated is

the summation extending over all types of dissociable groups. With Eqs. ( 5 ) and (9) the equation for the titration curve as a whole becomes eZwUB/a,+ P=C 1niKjf; + Kiffie2wa/aH+ i

(11)

The derivation of Eq. (11) is based on two assumptions which cannot be far from true for many globular proteins: ( a ) that the titratable groups are located on an approximately spherical particle which is impenetrable to the solvent and to small ions which it may contain, and ( b ) that the most important interaction between the titratable groups is the result of Coulombic forces between their charges. It will be seen in Section VLI however that the Linderstrgm-Lang method of calculating this interaction cannot be correct, although it will also be seen that the error introduced thereby will not be a serious one under favorable circumstances. The more sophisticated treatment of the electrostatic interaction which will be introduced in Section VII cannot be used as the basis of a practical analysis of protein titration curves because it requires precise knowledge of the location of titratable groups on the protein molecule, which is not available. One is therefore compelled to use Eq. (11) as the only available equation for the titration curve, with the understanding that it can be expected to apply only approximately. On the following pages we shall find many experimental deviations from the results predicted by the Linderstrgm-Lang treatment, and shall often use them as evidence that one of the basic assumptions of the treatment is inapplicable : the protein under examination may not be a compact, globular protein, or the interactions between titratable groups may not be purely electrostatic. However it will also be kept in mind that deviations may result from the approximate nature of the dculation, in situations where the lmic assumptions remain true.

R . Empirical Procedure In a practical procedure for applying the Linderstrgm-Lang treatment to experimental data, one modification is made. The electrostatic interac-

100

CHARLES TANFORD

tion factor w is treated as an empirical parameter, not necessarily equal to that calculated by Eq. (4). If necessary, w is considered to be a variable, its value depending on 2. It is generally assumed (tentatively) that all groups which are chemically identical, and fall into the same region of the titration curve, have the same pK i nt . The carboxyl groups of aspartic and glutamic acid are considered identical for this purpose because uncharged model compounds resembling these groups have essentially identical pK values, as shown in Table I. The a-carboxyl groups at the ends of polypeptide chains (if their number is known) are however assigned a different pKint, on the basis of the information of Table I. An exception is made of course if the group counting procedure shows that groups which are chemically alike clearly do not have the same P K ~ ,,, ~ as in the case of the phenolic groups of chymotrypsinogen (Fig. 4). The major terms of Eqs. (10) or (11) are now analyzed separately. The simplest is the term for the phenolic groups, the degree of dissociation of which is obtained independently of other groups by use of spectrophotometric titration. For other kinds of groups, where the electrometric titration curve must be used, we pick a region of pH within which only one of the iiof Eq. (10) is an unknown function of 2. Tn the acid region for example we may tentatively assume that the pKint of the usually small number of a-carboxyl groups is known. Side-chain carboxyl groups are the only other groups which are titrated in this range, so that Eq. (10) becomes F

=

nlxl

+ n2xz

(12)

where subscript 1 refers to a-carboxyl groups and subscript 2 to side-chain carboxyl groups. With x1 calculable, because pK/Ai has been assigned, we obtain x2 as a function of 2. I n general, in a region where groups of type m are the principal groups being titrated, so that variation in x, is the major factor in the change in i with 2, we wiIl have i-m-2

7 =

C

i=l

ni

+ nm--lxm-i+ nmxn+ nm+lxm+l -.

(13)

where groups designated by subscripts 1, 2, , ?n - 2, are known to be completely dissociated, so that xi for these groups is equal to unity, while groups with subscripts m 2, m 3, etc., are still completely in the acidic form, so that xi = 0. The values of xm--l and xpn+l,which make a relatively small contribution to the change in F, may either be known (they may be the phenolic or side-chain carboxyl groups), or they may be tcntatively calculated with assumed values for pKint and w by Eq. (6). The

+

+

HYDROGEN ION TITRATION CURVES OF PROTEIN

net result is that we can get 2% as a function of We can now rearrange Eq. (6)to give pH

- log[xm/(l - x,)]

=

101

zfor any kind of group.

pK!,mt) - 0.868~2

(14)

and plot the left-hand side of the equation versus 2. This will give a value for pK%) as the intercept at 2 = 0, and will show whether w can be considered a constant or whether it must be regarded as variable. The value of w is obtained from the slope if it is a constant, or by calculation using Eq. (14) and the value of pIC!,m,‘ if it is variable. The entire calculation must now be repeated whenever, in an equation of the type of Eq. (13), the calculation depended on tentative values of zm--l and x,+~, New values of these parameters are now used, based on PKint and w values which were obtained from the first round of calculations. By successive approximations of this type, there soon emerge values for each xi as a function of pH which no longer change with further reiteration of the mathematical procedure. Each of these will yield a value for pKi’hl and a single value or a set of values for w. Results obtained in this way will be discussed in the following section. It should be noted that the procedure outlined here often leads to refinement of the values of niwhich were originally obtained by the group counting procedure. If, for example, the successive evaluations of 2% consistently lead to a sharp rise in pH - log[s,/( 1 - z,)] at the high pH end, this suggests that the last one or two of the groups of type m which are being titrated have a higher pK than the rest. At least one possible explanation is that one or two groups which have been counted as being of type m really belong to type m 1. On the other hand, if pH - log [xm/(l z,)] decreases markedly at the high pH end, this suggests that we have counted too small a number of groups as being of type m.

+

+

C. The Electrostatic Interaction Factor The “expected” value of the electrostatic interaction factor w is given by Eq. (4). To estimate the radius R of the sphere representing the protein molecule, we can use an experimental value of the partial specific volume 8 and a reasonable estimate for the bound water, 61 grams per gram of protein (usually 61 0.2 is chosen). The volume per protein molecule becomes (Tanford, 196lb)

-

4 M - 7rR3 = - ( V 3 3t

+ 61~:)

where M is the molecular weight of the protein, 51 is Avogadro’s number, and vy is the specific volume of the solvent, which in the case of water is 1.00 at normal temperatures.

102

CHARLES TANFORD

Ail alt,eriiative procedure is to calculate the radius of a sphere equivalent to the protein molecule from hydrodynamic measurements. The value of R obtained in this way is always larger than that calculated by Eq. (15), even for the native protein conformation, the reason being that protein molecules are in fact never perfectly spherical. The resulting values of w are roughly 20 % less than those obtained with a radius calculated by Eq. (15). Some sample calculations are shown in Table 111. It is seen that w is larger for a smaller sphere and larger at low ionic strength. The data in the table are for 25°C. The effect of temperature, however, is quite small. Figures 13 to 17 show some experimental plots of titration data according to Eq. (14). For some of the examples chosen, ion binding data were available, so that the left-hand side of Eq. (14) could be plotted against 2.

TABLE111 Calculated Values for w at 36%' and Several Ionic Strengths Protein

a-Corticotropin Ribonuclease &Lactoglobulin Serum albumin

I

I

I

Mol. wt.

Calculated radiusa (A)

4541 13,683 35,500 65,000

12.0 17.1 23.7 28.9

Value of w

I

I = 0.01 I = 0.03 Z = 0.15 I = 1.00 0.218 0.137 0.088 0.066

0.186 0.113 0.069 0.051

0.138 0.079 0.046 0.033

0.094 0.051 0.029 0.020

Radius calculated by Eq. (15).

In most instances however only 2, is known, so that this has had to be used as abscissa. Figure 13 shows the data for the three phenolic groups of ribonuclease which ionize reversibly (Tanford et at., 19558), based on spectrophotometric titration curves such as Fig. 11. A straight-line plot is obtained, in agreement with Eq. (14). The values of 20 are 0.112, 0.093, and 0.061, respectively, at ionic strengths 0.01, 0.03, and 0.15. (The salt used to produce the ionic strength was KCI, and there is evidence that neither K+ nor C1is bound to an appreciable extent. The use of 2, as abscissa is therefore presumably acceptable.) Comparison with the calculated values of Table 111 shows that the experimental values are lower than predicted by about 20%. Such a deviation must be considered almost within the error of calculation. [If the radius of the hydrodynamically equivalent sphere (19 A) had been used as the basis of calculation, the calculated values of w would have become 0.119,0.096, and 0.066, respectively.] Another example showing good agreement with the theory is provided

HYDROGEN ION TITRATION CURVES O F PROTEIN

103

by the data for the side-chain carboxyl groups of p-lactoglobulin, shown in Fig. 14. The values of w are 0.072 and 0.039, respectively, at ionic strengths 0.01 and 0.15. Thus they are again somewhat smaller than the calculated values (0.088 and 0.046) given in Table 111. The electrolyte

10.0 CI

10.4

. I ( U

\

n

3 10.2 I

%

10.0 9.8

2

0

-4

-2 Charge

-0

-8

FIG.13. Titration data for the three reversibly titrated phenolic groups of riboiiuclease a t 25°C and a t three ionic strengths, plotted according to Eq. (14) (Tanford et al., 1955a).

n

U

r(

4.6

Y

1

s16

I 4.0

x,

0 0

3.6 -

P

1

30

X

I

20

10

ZH

I

0

- 10

FIG.14. Titration data for the normal aide-chain carboxyl groups of p-lactoglobulin a t 25°C and ionic strengths 0.01 (steeper line) and 0.15, plotted according to Eq. (14) (Nozaki et al., 1959).

104

CHARLES TANFORD

used was again KC1. Both ions of this salt are bound by ,@-lactoglobulin, and very approximate estimates for the extent of binding as a function of

$o. t

9.8

I

8

I

2

-

I

4

I

6

kZ)

I

8

I

10

FIG.15. Titration data for the phenolic groups of or-corticotropin, a t 25°C and ionic strength 0.1, plotted according to Eq. (14) (LBonis and Li,1959).

-

2,

FIG.16. Titration data for the carboxyl groups of lysozyme, a t 25"C, at three ionic strengths ( I ) . Plotted from data of Tanford and Wagner (1954).

pH are known. These indicate that the change in 2 over the acid pH range is about 0.8 of the change in 2, a t ionic strength 0.01 and about 0.67 of the change in 2, at ionic strength 0.15. The corresponding values of w become 0.090 and 0.058. These values are somewhat larger than the cal-

HYDROGEN ION TITRATION CURVES O F PROTEIN

105

culated values of Table 111. They should not be taken seriously because of the poor precision of the binding data, but they do serve to indicate that the difference between 2 and 2, is of such magnitude as to bring w values quite close to the values calculated by Eq. (4). An entirely different] situation exists in the titration of a-corticotropin (LBonis and Li, 1959). Data for the phenolic groups, obtained in 0.1 M KCl, are shown in Fig. 15. A straight line is obtained, but w is only 0.034 instead of the value of 0.16 expected a t that ionic strength from Table 111. This difference is far outside the limits of error of the calculation. The carboxyl groups of lysozyme (Tanford and Wagner, 1954) by con-

n

H

I 4.0

l-l

Y H

8

'

.-(

E

3.5

3.0

60

40

z

20

0

-20

FIG.17. Titration data for the carboxyl groups of bovine serum albumin, a t 25°C and ionic strengths 0.01 (lowest curve), 0.03, 0.08, and 0.15 (upper curve), plotted according t o Eq. (14) (Tanford et al., 1955b).

trast give a value of w much larger than expected. This protein has essentially the same size as ribonuclease, so that the expected values of w at ionic strengths 0.03, 0.15, and 1.00 are 0.11, 0.08, and 0.05, respectively. Experimental plots of pH - log[z/(l - z)] versus 2, , shown in Fig. 16, give the much higher values 0.23, 0.175, and 0.11. Moreover lysozyme is known to bind chloride ion strongly, the extent of binding increasing with increasing 2, , so that the values of w based on 2 would be even higher. Figure 17 shows an even more striking anomaly. It represents the titration of the carboxyl groups of bovine serum albumin (Tanford et aZ., 1955b), and it is seen that a constant value of w will not fit the data at all, the plots of pH - log[z/(l - z)] versus 2 being curved. It should be noted however that the steepest parts of the plots (near 2 = 0) are linear, and that the slopes give w values of 0.054, 0.036, 0.028, and 0.023, respec-

10G

CHARLES TANFORD

tively, at ionic strengths 0.01, 0.03, 0.08,and 0.15. These values are not too far below the calculated values of Table 111. The most interesting aspect of the foregoing results is that they indicate that the Linderstrfim-Lang equations are obeyed in some of the examples cited, whereas quite different results are obtained in other instances. We shall now examine some of the possible reasons for deviations from the Linderstrgim-Lang model. 1 . Trivial Factors It is seen from the discussion of the data for ribonuclease and p-lactoglobulin (Figs. 13 and 14) that two simple factors can lead to w values which are less than those given in Table 111, but only by a small amount. There is uncertainty in the choice of a radius for the sphere used to represent the molecule, and experimental uncertainty as to the relation between 2 and i?, . The uncertainty in the radius can account only for smaller values of w than those of Table 111, because the values in the table are based on what is essentially the minimum possible radius. The uncertainty in 2 can account only for smaller values of w (if 2, is used as abscissa in the logarithmic plots) because any change in i?, will favor the binding of oppositely charged ions, so that increments in i? are less than those in 2, . These two factors, plus the approximate nature of the theory as a whole, suggest that experimental values of w which are up to one-third less than those predicted by Eq. (4)should not be regarded as significant. On the other hand, values larger than those calculated by the equation [with Eq. (15) used for R] are more likely to carry significance. 2'. Unfolding or Swelling of the Protein Molecule

When unfolding or swelling of a protein molecule occurs, permitting the solvent to penetrate into the molecular domain, there is a drastic reduction in w,especially at higher ionic strength (Tanford, 195513, 1961a). As the sample calculation of Table IV shows, a swelling to twice the original radius (eight times the original volume) reduces w to an exceedingly small value at ionic strength 0.15. Unfolding of a globular structure to a random coil would lead to an increase in effective radius which would be of this order of magnitude. This is the most likely explanation for the low values for w which are obtained for a-corticotropin. The titration curve therefore suggests that this molecule exists in water in an unfolded rather than a compact globular conformation. This conclusion is supported by measurement of hydrodynamic properties of a-corticotropin. 3. Rod-Shaped Molecules Electrostatic interaction between charges on a rigid thin rod is also less than interaction between the same number of charges on an impenetrable

107

HYDROGEN ION TITRATION CURVES OF PROTEIN

sphere (Hill, 1955), but the effect of ionic strength is not nearly so great as it is for an unfolded molecule. It is likely that an unequivocal differentiation between a rod and a loose flexible coil could be made on this basis, though no actual examples have been reported.

4. Reversible Transition from Native to Denatured Conformations within the

Titration Region We have already pointed out (Section V, A ) that titration curves can provide evidence for the existence of slow and irreversible changes in conformation. Where such changes occur, two separate curves can often be TABLEIV Theoretical Effect of Swelling, Dissociation, and Aggregation orL the Electrostatic Interaction Factor w at M ° C Value of w

I Impenetrable sphere, R = 25 A Same sphere, swollen by solvent penetration to R = 50 A Impenetrable spheres formed by dissociation to half molecules, R = 25/2'/* = 19.8 A Same, dissociated to quarter molecules, R = 25/4]/3 = 15.7 A Aggregation to impenetrable sphere with R = 25 X 4 '/3= 39.7 A

= 0.01

I = 0.15

0.081 0.027

0.042 0.004

0.056~

0. 031a

0.0380

0.023"

0.1630

0. 074a

a These are the apparent values of w which would be obtained with 2 calculated for the original molecular weight, assuming neither dissociation nor aggregation to take place.

obtained, at least over a limited range of pH, one representing the native and the other the altered conformation. If a change in conformation occurs rapidly and reversibly iL would not be detectable in that way, for a single smooth reversible titration curve would be observed. This curve might, for example, resemble curve 1 of Fig. 8. If the data from such a curve are plotted according to Eq. (14), the plot would initially (high pH end in this case) be that for the native protein, but, in the region of conformational change, the increased uptake or dissociation of hydrogen ions would be reflected by a break in this plot. Separate curves for native and denatured proteins being unavailable in this situation, it will not normally be possible to decide whether the conformational change which occurs is one which involves a change in the number of titratable groups or whether it involves a change in w or pKint without change in group number. If the process is one of unfolding, with-

108

CHARLES TANFORD

out change in the number of groups or in any pKint , then the reversible conformational change would correspond to a change from a curve like the flatter curve of Fig. 6 to the steeper one, the greater steepness being due to the large decrease in w which accompanies unfolding. The logarithmic plots which might correspond to native and unfolded proteins, each stable over a wide range of pH, are shown in Fig. 18, as is the experimental curve which would be obtained if SL transition from one conformation to the other occurs during the titration. This curve resembles the titration curve observed for the carboxyl groups of serum albumin (Fig. 17), and therefore indicates that one possible interpretation of the titration data for serum

+

-

-2-

-

FIG.18. Hypothetical plot of titration data for groups which all have the same pKi,t . The three curves show the data as they might appear for a protein which is native throughout the pH range of titration, for a similar protein which is unfolded throughout the same pH range, and for a protein which undergoes a rapid reversible transition from a compact, native to an unfolded conformation.

albumin is that this protein undergoes reversible unfolding in the region of titration of the carboxyl groups. That such unfolding occurs has in fact been shown be several other techniques (e.g., Yang and Foster, 1954; Tanford et al., 1955c) The curve of Fig. 18 which represents the unfolded protein has been drawn as a curve rather than a straight line because unfolded proteins have a flexible conformation and are expected to expand with increasing charge, with a resulting decrease in w. The titration curves of simple polyelectrolytes, when plotted according to Eq. (14), do not result in linear plots (Tanford, 196la). Although the titration data for the carboxyl groups of serum albumin are qualitatively compatible with the idea that serum albumin undergoes re-

HYDROGEN ION TITRATION CURVES O F PROTEIN

109

versible expansion during their titration, this does not exclude other possibilities. A conformational change which irivolves a change ill tlhe number of titratable carboxyl groups, or in the PI<,,^ of these groups, could lead to experimental data which resemble those shown in Fig. 18. A quantitative explanation of the data of Fig. 17 is in fact not yet available (see Section X). All that the limited discussion given here can really demonstrate is that a conformational change takes place. A detailed understanding of the titration curve requires a study of the conformational change by all available methods. 5. Dissociation and Aggregation Unfolding has been cited as one way to account for electrostatic interaction which is much smaller than expected. Another possibility is dissociation into smaller units without other change, i.e., the smaller units are considered spherical and impenetrable to solvent, and Eq. (4) is assumed applicable to the calculation of w. If Ml is the true molecular weight of the protein, w1the corresponding value of the electrostatic interaction factor, and Zl the corresponding charge at any pH, then, for any titratable group with given pKint, pH - log[z/(l

- x)] = pKint - 0.868wlZ1

(16)

If the observed titration curve is based on a false molecular weight Mz , then the values of 2 which one uses in Eq. (14) are equal to ( M z / M l ) Z l . Thus the term wZ of the equation is equal to w ( M ~ / M ~,)aid, ~ I by comparison with Ey. (16), the apparent value of w becomes

w

= Wl(MljM2)

(17)

The anticipated decrease in w resulting from this effect is shown in Table IV. It is seen that dissociation is less effective than unfolding in reducing w at moderate ionic strengths. Aggregation of proteins will have the opposite effect of dissociation: the apparent value of w, obtained from an analysis which assumes that no aggregation has occurred, will be larger than expected. Since aggregation can proceed to formation of very large aggregates, quite larger increases in w could occur in this way. One experimental titration curve which probably reflects aggregation is that of zinc-free insulin (Tanford and Epstein, 1954). Between pH 4 and pH 7 this protein becomes insoluble, but the precipitate is gelatinous, so that water and hydrogen and hydroxyl ions appear able to react with the acidic and basic groups rapidly and reversibly. The only abnormality is that the observed values of w, in the region of precipitation, become more than three times larger than at pH’s where the protein is soluble. The presence of large aggregates in the precipitate is the most likely explanation.

110

CHARLES TANFORD

6. Erroneous Calculation o j the Electrostatic Interaction

The titration of the carboxyl groups of lysozyme (Fig. 16) is an instance of the occurrence of unexpectedly large values of w. I n this example aggregation does not provide a possible explanation, for molecular weights of lysozyme have been determined at different pH’s without indicating any tendency for aggregation. An alternative explanation must be sought, and the simplest place to seek it is in the basic assumptions which underlie the Linderstrom-Lang treatment. A more sophisticated method for calculation of the electrostatic interaction between charged groups will be considered in Section VII. It will be seen that sizable deviations from the Linderstrom-Lang theory will occur whenever a titratable group is located in close proximity to another charged group. If the vicinal charged group is charged throughout the range of titration of the group being analyzed (e.g., an amino group near a carboxyl group), then the anomalously high interaction between the groups will affect the pKint term of Eq. (14) (see Section VI, 0).If the groups in close proximity are titrated within the same range of pH, on the other hand, the result will be an interaction between them which is stronger than the Linderstrom-Lang treatment would predict. The result will be an anomalously large value for w, and it is possible that the anomalously high w values found for lysozyme are ascribable to this cause.

7. Identical Groups Do Not Have the Same Intrinsic p K In the Linderstrflm-Lang treatment, groups which are chemically identical are assumed to have the same pKint. The fact that the dissociation constant of Eq. (2) (for titration of several chemically identical groups) depends on the extent of titration is ascribed entirely to electrostatic interaction between the groups. It is true of course that a spread in apparent pK over the titration region could be obtained without electrostatic interaction if the various groups of a given chemical kind have different intrinsic pK values (e.g., Karush and Sonenberg, 1949). This effect is not used as a hypothetical explanation for the normal variation of pK with extent of titration for two reasons: ( a ) because this effect would be independent of ionic strength, whereas the normal result is that w depends on ionic strength in the way expected for electrostatic interactions; and ( b ) because the very nature of a protein molecule requires that electrostatic interaction between charged groups exist, and no mechanism is conceivable whereby it could be eliminated. On the other hand, large differences between pKint values for chemically identical groups do exist. The four phenolic groups of chymotrypsinogen (Fig. 4) for example clearly fall into three distinctly different classes with very different dissociation constants. If smaller differences between pKint

HYDROGEN ION TITRATION CURVES OF PROTEIN

111

values of chemically similar groups were to exist, then the groups would be titrated in the same range of pH, but the curve would be more spread out than if the spread were due to electrostatic interaction alone. I n terms of the Linderstrgm-Lang treatment, this would reflect itself in abnormally large values of w. The abnormally large w values for lysozyme could be due to such an effect, then, as well as to abnormally strong vicinal electrostatic interactions. (As was pointed out earlier, however, changes in pKi,t can within the present treatment be themselves the result of strong vicinal electrostatic interactions.)

D. Intrinsic pK’s and Their Interpretation 1. Experimental Values

The preceding section has considered the electrostatic interaction factor w of the Linderstrgm-Lang equation. We consider now the value of the intrinsic pK, which is obtained formally as the value of pH - log[x/. (1 - z)], for any given kind of titratable group, a t the point 2 = 0. The value of pKint can be determined directly from a logarithmic plot of the data if, as in the example of Figs. 13 and 14, the point 2 = 0 falls within the range of titration of the type of group under consideration, If, on the other hand, the titration range is removed from the point 2 = 0, then an extrapolation is required to determine pKi,t. If the logarithmic plot has roughly the theoretical slope, and if similar plots, for other groups which do titrate in the region near 2 = 0, also show normal values of w, then such an extrapolation can be performed with some confidence that the result will be meaningful. Another criterion for validity of a pKint value determined by extrapolation is the dependence on ionic strength. Theoretically the effect of ionic strength should be small (see Section VI, D, 4). These criteria indicate that in a situation of the kind shown in Fig. 16, where the slope is abnormally large, and where a different intercept at 2 = 0 is obtained a t each ionic strength, the value of this intercept would have no meaning. It cannot be considered to represent the intrinsic pK of the groups being titrated. We have compiled in Table V the reliable values of pKi,t which have been reported in the literature. The values are to be regarded as having a significance of &O.l to 0.2, except that the values for imidazole groups are subject to somewhat greater error. These groups are usually present in smaller numbers than carboxyl and amino groups, so that the overlap between the different titration regions makes proportionately a larger contribution. The values of pKint for a-carboxyl and a-amino groups cannot usually be derived from experiment a t all because they represent such a small portion of the groups titrated.

112

CHARLES TANFORD

TABLEV Intrinsic p K Values at M°Ca Type of group

a-Carboxyl Expected value (Table I) Insulin Side-chain carboxyl Expected value (Table I) Lysozyme (3 of ca. 16 groups) Serum albumin Ovalbuinin Conalbumin Corticotropin Insulin @-Lactoglobulin(49 of 51 groups) p-Lactoglobulin (2 of 51 groups) Imidazole Expected value (Table I) Myoglobin (6 of 12 groups) Hemoglobin (ca. 22 of ca. 38 groups) Insulin R i bonuclease Myoglobin (6 of 12 groups) Chymotrypsinogen Ovalbumin Conalbumin Lysoz yme Serum albumin ,%Lactoglobulin a-tlmino Expected value (Table I) None of the experimental values can be considered reliable Phenolic Expected value (Tahle I) Conalbumin (11 of 18 groups) Insu 1in Chymotrypsinogen (1 of 4 groups) Corticotropin Papain (11 of 17 groups) Ribonuclease (3 of 6 groups) Serum albumin Chymotrypsinogen (1 of 4 groups) Lysoz yme Chymotrypsinogen (2 of 4 groups) Conalbumin (7 of 18 groups) Ovalbumin Papaiii (6 of 17 groups)

PK 3.8 3.6 4.6 - w

4.0 4.3 4.4 4.6 4.7 4.8 7.3 6.3b --m --m

6.4 6.5 6.6 6.7 6.7 6.8 6.8 6.9 7.4 7.5

9.6 9.4 9.6 9.7 9.8 9.8 9.9 10.4 10.6 10.8

113

HYDROGEN ION TITRATION CURVES OF PROTEIN

TABLE V-Continued Type of group

Ribonuclease (3 of 6 groups) Side chain amino Expected value (Table 1) Conalbumin Serum albumin &Lactoglobulin a-Corticotropin Ovalbumin Ribonuclease Lysoa yme Chyniotrypsinogen (3 of 13 groups) Guanidyl Expected value (Table I ) Insulin a-Corticotropin Ferriheme waterC Myoglobin Hemoglobin

PK 00

10.4 9.6 9.8 9.9 10.0 10.1 10.2 10.4 W

> 12

11.9 -12 8.9 8.W

a Only pK values observed for the native conformation of proteins are listed. A value of m is used to indicate that a group appears incapable of dissociation in the native molecule, a value of - co that i t appears incapable of binding a proton. References t o all data are given in Section X. * See text. There is considerable question as to the pKi,t value expected for an unperturbed imidazole group. c No suitable model compounds are available on which an expected value could be based. d Estimated from the data of George and Hanania (1953).

Table V shows that the vast majority of the titratable groups of the smaller protein molecules have pKint values which are quite close to the values predicted from the pK’s of model compounds. This feature of protein titration curves has been well known for a long time, and is accepted as normal. It is however really an astonishing result, for it implies that most of the titratable groups of the smaller protein molecules are in as intimate contact with the solvent as similar groups on smaller molecules, and that they are able to accept or release hydrogen ions in this location without requiring any modification of the protein conformation in the vicinity of the titratable group. Since most of the proteins examined have been globular proteins, tightly folded so as to exclude solvent from most of the interior portions, the titratable groups must be nearly always at the surface. When the molecular weight of a globular protein exceeds 100,000, the surface per unit mass begins to be too small to accommodate all the titrat-

114

CHARLES TANFORD

able groups. Titration anomalies should therefore become more frequent as the molecular weight is increased. No complete titration curves of globular proteins with molecular weights above 100,000 have been reported so far. 2. Major Anomalies

The most striking anomaly observed among the pK values of Table V is the existence of groups which cannot be titrated at all as long as the native conformation of a protein is retained. This observation is made most frequently for phenolic groups. All of the phenolic groups in ovalbumin, half of those in ribonuelease and ehymotrypsinogen, seven out of eighteen in conalbumin, and about one-third of those in myosin are not titrated even partly at a pH where normal phenolic groups have been converted almost 100% to their anionic form. The simplest explanation is that these phenolic groups are buried in the hydrophobic interior of the protein molecule and thus are inaccessible to the solvent. Only a major change in conformation will then permit the transfer of the dissociable hydrogen ion to a water molecule or OH- ion, and as long as it does not occur the phenolic group will remain intact. This explanation is especially attractive because phenolic groups are more frequently involved than other groups. The uncharged tyrosine side chain happens to be among the most hydrophobic of all the parts of a protein molecule, and, since the phenolic group is uncharged at neutral pH, where the choice of protein conformation is made in the native environment, it is in fact expected to be an “inside” group much of the time. It should be observed that uncharged lysine and histidine side chains are also quite strongly hydrophobic. When these side chains are charged, however, they require the normal hydration for the charged nitrogen group, and that group of the side chain becomes strongly hydrophilic. Since amino groups are charged at neutral pH, we do not expect them to enter the hydrophobic interior of the native protein, and indeed no titration anomaly suggesting buried uncharged amino groups has been reported. Lysine side chains can of course be partly buried, in such a way as to leave the charged group exposed at the protein/solvent interface, and this is undoubtedly the way they often exist. They could also be buried totally even a t neutral pH if they were first converted to their basic form. However, the free energy it would cost, to become dissociated at neutral pH, would be large [it would be equal to 2.303RT (pK - pH)], and would thus vitiate the free energy gained by elimination of the hydrophobic interaction with the solvent. Buried imidazole groups should be more frequent than buried side-chain amino groups, because they are at neutral pH close to their expected pK. Indeed, six imidazole groups in myoglobin and about twenty-two in hemo-

HYDROGEN ION TITRATION CURVES OF PROTEIN

115

globin are not titratable in the native state, and this presumably means that they are buried in the interior in the same way as nontitratable phenolic groups. Another way in which a normally titratable group can be made nontitratable is by formation of a very strong complex. I n the complex of conalbumin with iron, each of the two bound iron atoms is attached to three phenolate groups with an association constant of about lo3"(Warner and Weber, 1953). The six phenolic groups involved in this interaction are not titratable, being held in their anionic form as long as the iron complex retains its stability (Wishnia et al., 1961). These six groups are among the eleven which in conalbumin show normal behavior, and that they are still at the protein/solvent interface in the iron complex is shown by the fact that the iron atoms can be reversibly dissociated from the complex by reagents such as citrate which themselves form strong iron complexes. It is worth noting that the seven phenolic groups which are buried in the interior as uncharged groups in conalbumin remain in the same state in the iron complex. One of the abnormal imidazole groups in myoglobin, and four of those in hemoglobin (one for each iron atom) are also nontitratable by virtue of a covalent bond to an iron atom, these being the imidazole groups by which the hemes are attached to the protein portions of the two molecules. In addition, these groups are buried and inaccessible to the solvent. Two instances have been reported of nontitratable groups which are present on the native molecule in charged form, these being three carboxyl groups in lysozyme and three side-chain amino groups in chymotrypsinogen. No logical explanation exists. The removal of a single charged group from contact with solvent is accompanied by an unfavorable free energy of 10,000 to 100,OOO cal/mole (see footnote 14 in Tanford and Kirkwood, 1957). This unfavorable free energy would be greatly reduced if two oppositely charged groups were removed from contact with solvent as an ion pair, but in the two instances cited here there is no evidence which suggests that there are anomalous groups opposite in charge to the nontitratable groups. It is possible that titratable groups in their uncharged states can be buried in the hydrophobic interior of a protein molecule, but that a reversible change in conformation can bring them to the exterior where they are accessible to the solvent. If the change in conformation is such as to alter the titration characteristics of just a single group, and if no unfolding occurs (an example might be a refolding of a single loop of a polypeptide chain), then the only titration anomaly will be a shift in the pK of the group which is involved: the equation for titration of the group will still be Eq. (14), with the same value of w as applies to other groups. If the buried group is an uncharged acidic group, the anomalous pK (des-

116

CHARLES TANFORD

ignated by an asterisk) is given by (Tanford, 1961c)

*

pKint = PKint

+ log (1 + k)

(18)

where pKint is the normal pK of the group and k is the equilibrium constant which favors the native form a t a pH where the group would normally be uncharged. If the buried group is an uncharged basic group, the corresponding equation is PKrnt = pKint

- log (1 + k)

(19)

It is clear that large changes in pKint can arise in this way.

The intrinsic pK of 7.3 found for two anomalous carboxyl groups of p-lactoglobulin (Tanford and Taggart, 1961) has been ascribed to this mechanism. A conformational change is observed to accompany the titration of the groups by optical rotation and other measurements. Although there are two anomalous groups, they are in separate polypeptide chains, and the titration and conformational change occur independently in each chain, so that the equations for a single group apply. If two or more groups are buried in the same hydrophobic region, and they can be brought to the surface only by a conformational change which involves all of the groups together, then a steepening of the titration curve is expected, as well as an anomalous pK. A steepening of the curve is also observed if a change in w accompanies the conformational change which brings buried groups to the surface. These situations were discussed in Section VI, C . 3. Minor Anomalies

Apart from the major anomalies which have already been discussed, all pKintvalues in Table V lie within about 1.0 pK unit of their expected value. Most of them are even closer. There is however a consistency in the direction of deviations from expectation which merits discussion. As the table shows, phenolic and imidazole groups tend to have pKint values larger than expected, and side-chain amino groups tend to have pKint values smaller than expected. In other words, the native structure tends to favor the uncharged form of the phenolic and amino groups; the special problem of the imidazole groups is discussed below. At least as far as the lysine amino groups and tyrosine phenolic groups are concerned, this cannot be considered an artifact of the way the data have been obtained, for the relative ease of dissociation of these groups can be determined unequivocally by comparing the course of titration of the phenolic groups (determined spectroscopically) with the course of titration of side-chain amino plus phenolic groups (determined electrometrically) . Even after discounting the phenolic groups which do not titrate at all, we find that amino groups dissociate at lower pH than phenolic groups in @-lac-

HYDROGEN ION TITRATION CURVES OF PROTEIN

117

toglobulin, serum albumin, and lysozyme. The data of Table I, however, predict that lysine amino groups should have a pK which is 0.8 higher than that of phenolic groups. Since the major part of tyrosine and lysine side chains is strongly hydrophobic, as was discussed above, in connection with the occurrence of nontitratability of phenolic groups, a simple explanation of these minor anomalies is to suppose that the hydrophobic parts of tyrosine and lysine side chains tend to be buried in the interior of the native structure. Although the titratable parts must project outward into the solvent to be titratable, it is possible that they may vary in the precise extent to which they can free themselves from the influence of the hydrophobic region. If they do not project sufficiently far, the uncharged form of the group will become stabilized relative to the charged form, and the pK will be altered accordingly. This same explanation clearly cannot be invoked to account for the observed pK values of imidazole groups, since these pK’s differ from expectation in the wrong direction. This result should perhaps not he taken too seriously since the intrinsic pK’s of protein imidazole groups are relatively imprecise. Moreover, there is some question about the expected pK of an imidazole group (Table I, h ) . On the other hand, the volume changes which accompany dissociation of imidazole groups, to be discussed in Section VIII, are also anomalous, and the over-all conclusion must be that some effect of protein structure on the titration of imidazole groups has so far been overlooked in theoretical treatments of the problem. Some other explanations which have been or could be offered for the smaller deviations of observed pKint values from expected values are the following. ( 1 ) Inadequacy of the Linderstr@-Lang treatment. The approximate way in which electrostatic interactions are treated in this section would have no effect on the estimation of pKint if the point 2 = 0 in fact represents a point where electrostatic interactions vanish. The value of pKint which one obtains by this treatment for a polymer containing only one kind of dissociable group (polyglutamic acid or polytyrosine, for example) must be the correct pKint reflecting only the chemical environment of the dissociable groups, with no contribution from long-range electrostatic interactions. In a protein, however, the distribution of charges may be quite irregular and, when 2 = 0, some groups may well be in an environment rich in positive charges and others may be in an environment rich in negative charges. For these groups the observed pK at 2 = 0 will not be the true intrinsic pK, a positive environment leading to a reduced value for pKint as defined by Eq. (14), and a negative environment to an increased value (Tanford, 1957b). A possible example of this kind of effect occurs in the three basic proteins

118

CHARLES TANFORD

which have been examined in detail. Figure 16 shows the anomalous titration behavior of the carboxyl groups of lysozyme, and, as was pointed out earlier, a possible explanation is the existence of apparently different pKintvalues among the side-chain carboxyl groups. Application of Eq. (14) to the carboxyl groups of chymotrypsinogen (Wilcox, 1961) and ribonuclease (Tanford and Hauenstein, 1956b) leads to a similar result, though the anomaly is not as pronounced as in lysozyme. The fact that all three of these proteins possess a large number of positively charged basic groups in the pH region where carboxyl groups are titrated makes an explanation based on irregular distribution of charged groups an attractive one. It is quite likely that some carboxyl groups of each of these proteins may lie on a region of the surface which is rich in basic groups, and these carboxyl groups would appear to have a lower pKin++than carboxyl groups elsewhere on the molecules. (2) Binding of salt ions. Ions of the neutral salt which is used to adjust the ionic strength of protein solutions may be bound to the protein. If the binding has been measured and corrected for, then no anomaly will result unless the binding sites are the groups whose pK values are being determined (see Section IX, A ) . But if the binding of salt ions occurs without the knowledge of the investigator, and if it is incorrectly assumed that 2, = 2, then an erroneous pKint value is obtained. The error is equal to ~i0.868qniziwhere pi is the number of ions of charge zi bound a t the point 2, = 0. (3) Conformational changes between conformations which d i f e r little in free energy. Equations (18) and (19) have been cited as providing a possible explanation for large anomalies in PKint . With small values of k they could clearly also account for small deviations from the expected pKint values. ( 4 ) Side-chain hydrogen bonds. It has often been suggested that sidechain hydrogen bonds may be responsible for small anomalies in pKint. The suggestion is supported by a calculation made by Laskowski and Scheraga (1954), but their calculation is based on an erroneous value for the heat of formation of a hydrogen bond in an aqueous medium. It is improbable that such hydrogen bonds can in fact have any stability unless the side chains which are involved are removed, at least to some extent, from contact with water. ( 5 ) Salt bridges. It has sometimes been suggested that attraction between positive and negative charges may lead to “salt bridges” (intramolecular ion pairs) which would favor the charged forms of titratable groups, and would account for anomalously low PKint values for carboxyl groups and for high values for amino or imidazole groups. That such attractions should exist in an aqueous environment is improbable. I n any

HYDROGEN ION TITRATION CURVES O F PROTEIN

119

event, anomalously high pK values for amino or imidazole groups have not been observed. All attempts to explain minor variations in pKint by any of the foregoing possibilities must be regarded as purely speculative. Of considerable interest in connection with speculations of this kind is an experiment by Klote and Ayers ( 1957). An S-(p-dimethylaminobenzeneazophenylmercuric) derivative of serum albumin was prepared. Only a single group of this kind can be attached to a serum albumin molecule because the protein contains only a single sulfhydryl group. The titration of the dimethylamino moiety of the group can be followed spectroscopically, because the attached group is a dye which has a different color in its acidic and basic forms. It was found that the group had a pK of about 1.8 in aqueous solution, whereas the same dye attached t o cysteine had a pK of about 3.3. In 8 M urea, on the other hand, the protein-bound dye had a pK of 3.3, and the cysteine-bound dye a pK of 3.4. This result, and the corresponding heats and entropies (KlOt5 and Mittleman, 1962) can be interpreted by several mechanisms, discussion of which is out of place here. (The interpretation of the data is hampered by the fact that native albumin, under the conditions of the experiment, is wholly or partly unfolded.) The really important conclusion to be drawn is that the work points out the possibility of new and imaginative experiments which may prove more instructive at the present time than further speculation concerning the data already in existence. 4. E$ect of Ionic Strength on Intrinsic pK’s The value of pKint in Eq. (14) should depend on ionic strength. The electrostatic term in this equation includes the effect of ionic strength on the interaction between charges, but not the effect on the chemical potential of the isolated dissociating group in its acidic and basic forms, and this effect therefore remains a factor in pKint. The effect of ionic strength is to stabilize charged groups, and pKint should therefore decrease with increasing ionic strength for dissociation of an uncharged acidic group, whereas it should increase for dissociation of positively charged groups. The magnitude of the effect at low ionic strength should be roughly the same as 6iT In y for a univalent ion (y being the activity coefficient), so that, a t 25°C in water, there should be a difference of about 0.05 between pKint values a t ionic strengths 0.01 and 0.15, and a difference of about 0.08 between values a t ionic strengths 0.15 and 1.00. The experimental error in determining pKjnt usually exceeds these differences. E. Heats and Entropies of Dissociation If values of pKint for a dissociable group are measured at several temperatures, heats and entropies of dissociation can be determined from the

120

CHARLES TANFORD

temperature-dependence. An alternative procedure is to obtain apparent heats of dissociation by Eq. ( I ) from regions of the electrometric titration can curve where a single kind of group predominates. The value of then be determined from a value of pKint at a single temperature. The latter procedure introduces an uncertainty because apparent heats of disTABLE VI Heats and Entropies of Dissociation i n Natiee Proteins AH

Type of group Carboxyl Normal valuese Conalbuminb Serum albumin" Phenolic Normal values" Conalbuminb Lysozymed Ribonucleasee Serum albuminc Imidazole Normal values" Conalbumin6 Amino Normal values' Conalbumin* Iodinated insulin, Ferriheme water M yoglobing Hemoglobin9 ~

ASiO,t

(kcal/mole)

(cal/deg/mole)

0 to 1 2 -2

-18 t o -21 - 13 - 12

6 8 6 to 7

-24 - 15

7

11.5 7 8 13 t o 14 I1 13.4 6 4

-26 t o -29 -22 -9 -8

-3

-3 to -8 -6

-s

-22

-27

~~~~~~

Edsall and Wyman (1958), Edsall (1943). Wishnia et aE. (1961). Tanford et al. (1955b). Donovan et al. (1961). * Tanford et al. (1955a). Gruen et al. (1959a). 0 George and Hanania (1952, 1953, 1957). No model compounds are available on which 60 base normal values. a

6

sociation may differ by 1 or 2 kcal from true AHint values obtained from the temperature coefficient of pKint . However, pKint values themselves are not very precise, as we have pointed out, so that a AH value obtained from their temperature-dependence is also quite imprecise. Some heats and entropies obtained in this way are listed in Table VI, and comparative values for model compounds are included. The uncertainties in the experimental determination of these values, coupled with

HYDROGEN ION TITRATION CURVES O F PROTEIN

121

the uncertain meaning of pKint when obtained by the empirical procedures of this section, suggest that no interpretation of the data is warranted. It should be noted in particular that the strikingly anomalous figures for ionization of the phenolic groups of serum albumin, which have been the subject of considerable speculation in the past, are now known to be without significance. They are based on an apparent AH, obtained in a pH range where serum albumin is now known to undergo unfolding, and must reflect in part the thermodynamic parameters for the unfolding process.

VII. MOREEXACT THERMODYNAMIC ANALYSIS The major deficiency of the Linderstrprm-Lang theory of titration curves lies in the calculation of the electrostatic interaction between charged groups. It is an oversimplificationto regard all charges as smeared evenly over the surface of the molecule. In reality these charges are discrete, and a given charged group is influenced much more by other charged groups which lie close to it than by more distant groups. The exact location of neighboring charged groups will thus necessarily have an important effect on the titration curve, as we have already noted qualitatively in Sections VI, C and D. An attempt has been made (Tanford and Kirkwood, 1957) to include this effect in the equation for the titration curve. We assume as before that many groups will have the same intrinsic pK, but no longer assume that all groups with the same intrinsic pK will be titrated simultaneously, allowing for variations which depend on the specific electrostatic interactions to which each group is subject. Since the theory has been described in three separate places (Linderstrgm-Lang and Nielsen, 1959; Rice and Nagasawa, 1961; Tanford, 1961a), in addition to the original publication, we shall not describe it here. It suffices to say that the theory involves calculation of the concentrations of individual species P, PH, . . -,PH, , . PHn-I , 1’15, , where v is the number of dissociable protons per molecule in a given species and n the maximum number of such protons which the molecule van contain. Each species is further subdivided into subspecies PHI”, PHf”’, PHI”, the superscripts indicating different arrangements of protons among groups which differ in intrinsic dissociation constants. There may he v1 protons bound to sites of class 1, vz to sites of class 2, and in general v I to sites of v j = v. Each different set of values for classj, with the proviso that Vl , VZ 1 . . , v j leads to a subspecies identified by a different superscript (i). It should be noted that each subspecies still has many possible distinguishable configurations, for the v j protons on sites of class j can be distributed in general in different ways over the total number ( n j ) of groups which belong to classj. We now let k:’) represent the equilibrium constant for the reaction

122

CHARLES TANFORD

P

+ vH+

PHP'

The value of this constant will be the product of an intrinsic term independent of configuration, and an electrostatic term which will depend on configuration, and is averaged by an appropriate statistical procedure over all configurations. The basis for the calculation of the electrostatic term in a given configuration is the generalized multicharge model of Kirkwood (1934). It depends on knowing the precise positions of all charges on the protein molecule, and also on knowing an effective distance ( d ) of closest approach of solvent to each charge. Since it seems improbable that two similar groups can have the same intrinsic pK without also being equally accessible to the solvent, it is likely that the parameter d has the same value for all groups of a given class. Moreover, if the intrinsic properties of titratable groups on protein molecules are the same as the properties of such groups on simpler molecules, then the parameter d should be the same on protein molecules as on simple molecules. Consideration of appropriate simple molecules (Tanford, 1957b) suggests that at 25°C in water d = 1.0 A for all pertinent groups. With this value of d one gets over-all electrostatic effects of about the same magnitude as would be calculated by the Linderstrplm-Lang treatment (Tanford, 1957b), but one also predicts variations whenever the distribution of charged groups over the protein molecule is an uneven one. The ways in which such variations might account for deviations from the Linderstrplm-Lang theory have ,already been brought out. There is a typographical error in three of the equations of one of the references cited above (Tanford, 1961a, Eqs. 30-10 to 30-12). The correct form of these equations should be obtained as follows. The concentration of species PH;" at any pH is

[PHI"']= ~L"[P]u;I+

(20)

where square brackets represent concentrations. The concentration of all species PH, is

cy

The total protein concentration is simply (PH,), the sum extending from v = 0 to v = n so that the average number of bound protons per molecule ( J ) is

Y

U.i

One can also calculate the average number (rj) of protons bound at any pH

HYDROGEN ION TITRATION CURVES OF PROTEIN

123

specifically to groups of class j,

where

vj

is the number of protons bound to groups of class j in the species

PHS". One can also compute the average of any desired function of For example,

v.

The preceding equations have not yet been used as basis for the analysis of any actual titration curve of a protein. It should be feasible soon to apply the theory to the titration curve of myoglobin, the complete threedimensional structure of which should be available soon (Kendrew et al., 1961). This will permit exact localization of all titratable groups on the protein molecule and, hence, the theoretical evaluation of the kJi' from assumed intrinsic pK's. It is not to be expected that these kii' values will accurately reproduce the titration curve, but it is to be expected that the cause of observed deviations will be relatively easy to determine. Essentially three possibilities would be looked for in such a first application of the theory. (1) That the theory itself is incorrect. (The model on which it is based is still very crude even though exact locations of discrete charges are specified.) It is likely that an error in the theory can be corrected by a small change in the parameter d, from the value of 1.0 A which has been used for computations so far (Tanford, 1957b). (2) That some groups do not have expected pKint values. If the exact structure is known, it should be possible to identify such groups. (As was previously mentioned, six imidazole groups of myoglobin are already known to be highly anomalous. They will presumably be identifiable on immediate inspection of the final structure since they should be in positions that are inaccessible to solvent.) (3) That the structure determined by X-ray diffraction of protein crystals is not exactly the same as the structure in solution. To test this possibility one would have to make a guess as to the probable location of possible structural changes (e.g., at points of contact between neighboring molecules in the crystal), and would then determine whether they improve the agreement between calculated and experimental titration curves. It is likely that a computer program will have to be devised to perform actual calculations for a molecule as complicated as myoglobin.

124

CHARLES TANFORD

VIlI. VOLUMECHANGES ACCOMPANYING TITRATION The change in volume which accompanies the titration of acidic and basic groups of proteins was measured by Weber and Nachmansohn (1929; also Weber, 1930) more than 30 years ago. The results were approximately in accord with the volume changes measured on suitable model compounds, and they are of historical importance because they helped demonstrate that proteins are amphoteric ions, containing a t neutral pH charged carboxyl and amino groups which do not differ greatly from similar groups on small molecules. New and more precise measurements of volume changes have been made recently by Kauzmann and co-workers (Kauzmann, 1958; Rasper and Kauzmann, 1962; Kauzmann et al., 1962). These measurements show TABLEVII Volume Change for the Binding of Hydrogen Ions by Cmboxylate Groups at 30°C and Ionic Strength 0 . 1 ~ 5 ~

a

Protein

A V (ml/H+ ion bound)

Lysozyme Ovalbumin Ribonuclease Serum albumin (above pH 4) Serum albumin (below pH 4)

10

12 11 11 -5

Data from Kauzmann (1958), Rasper and Kauzmann (1962).

that there are in fact significant differences between the behavior of proteins and model compounds. Kauzmann and co-workers measured AV for the addition of Hf ions to proteins below pH 5 . Normally only carboxyl groups are titrated in this range of pH, so that the results represent AV values for the reaction -COO-

+ H+ + -COOH

In simple molecules, the AV for this reaction is sensitive to the environment of the carboxyl group. Normal values lie between 10 and 14 ml per mole of hydrogen ions bound. If there is a positively charged group near the carboxyl group, AV is decreased to 6 or 7 ml, and near a negatively charged group AV rises to 15-20 ml and even larger values. If anomalous values were obtained for proteins they could thus be readily rationalized. In fact, as the results of Table VII show, anomalous results are not obtained, except for serum albumin, below pH 4.3. As serum albumin undergoes configurational changes below pH 4.3, the A V value must reflect the volume change which accompanies the conformational change, in addition to that which

HYDROGEN ION TITRATION CURVES OF PROTEIN

125

accompanies hydrogen ion binding. An anomalous value is therefore not unexpected. Kauzmann and co-workers also measured AV for the addition of OH- ions to proteins from pH 5 to pH 10 or above. These values mostly represent AV for the reactions -COOH

+ OH+ OH-

--t

-COO-

+ HzO

+ H20 -+ -NH2 + HzO -NH: + OH-CJIaOH + OH- -+ --Ce,H50- + HzO -1mHf

+ -1m

where I m represents the imidazole group. The carboxyl groups make a significant contribution only at the lowest part of the pH range studied. The phenolic groups make a contribution only at the highest pH values, and so do lysine amino groups. Terminal a-amino groups and imidazole groups are titrated entirely within the region of pH which was studied. The number of a-amino groups, however, is always small, so that the measured AV values represent primarily the volume change accompanying titration of imidazole groups. In small molecules containing basic nitrogen atoms, the value of AV for the reaction -NH+

+ OH- -+ -N + H20

is 23 to 25 ml per mole of OH- ions added. In contrast to what one finds in the case of carboxyl groups, this value is insensitive to the nature of other groups which may be present on the small molecule. Even closely located charges have little effect, and there is no significant difference between imidazole groups, primary amines, secondary amines, and tertiary amines. Therefore it is of considerable significance that the A V values found in proteins are always substantially below the expected value of 23 to 25 ml, as the results in Table VIII show. No explanation for this phenomenon exists as yet. The more nearly normal value of AV found for pepsin, which is denatured in the pH range of the measurements, suggests that the anomaly is associated only with the native state of the protein. It is possible then that the anomaly is caused by the large hydrophobic groups to which the basic nitrogen atoms, both of imidazole groups and of lysine amino groups, are attached. These hydrophobic groups might tend to pull the entire group towards the hydrophobic interior of t,he protein molecule, diminishing the amount of tightly bound water about the group in its acidic form, and thereby decreasing the value of AV, which must

126

CHARLES TANFORD

reflect in part the bound water which is released when the group is converted to its uncharged basic form. If this were the correct explanation, we should also expect a decrease in pKint , since the acidic form of imidazole and amino groups would become less stable if it could not be hydrated to its normal extent. As Table V shows, there is in fact a tendency for the pKintof amino groups to be below expected values. The pKlntvalues for imidazole groups however are above rather than below expected values. Moreover, the amino groups of lysozyme do not have an anomalous pKint , so that AV for lysozyme should approach a normal value at higher pH, where these groups begin to make an important contribution to the titration curve. In fact the opposite result TABLEVIII Volume Change for the Binding of Hydroxyl Ions by Proteins (Primarily by Imidazole GTOOUPS) at 30°C and Ionic Strength 0.16"

a

b

Protein

Range of pH

Chymotrypsin Hemoglobin Lysosyme Lysoz yme Ovalbumin Oval bumin Pepsin Ribonuclease Serum albumin

7.5-11 5.5-7.5 7.5-10.5 5.2-6.8 6.8-10 7-10 5.5-10 6-10

8-8

AV (ml/OH- ion

bound)

17 18.6 17 15 6.7 16 20b 16 17

Data from Rasper and Kauamann (1962). Pepsin is denatured in the pH range covered.

is obtained, and AV falls to even lower values than are observed for other proteins. Table VIII shows that the volume changes for ovalbumin between pH 5.2 and 6.8 are especially low. This cannot be explained in a simple way, e.g., by the fact that there are phosphate groups in ovalbumin which titrate in this range of pH (because only four of the twenty groups which are titrated are phosphate groups). There is also no evidence that ovalbumin undergoes a significant conformational change between pH 5 and pH 7. It is clear from this discussion that the measurement of volume changes which accompany titration of proteins and of model compounds represents a potentially fruitful area of research. It would be of special interest to have available AV values for synthetic polypeptides (or for naturally occurring substances such as a-corticotropin) , which exist in aqueous solutions in a randomly coiled conformation.

HYDROGEN ION TITRATION CURVES OF PROTEIN

127

IX. MISCELLANEOUS TOPICS

A . Binding of Ions Other Than Hydrogen Ions If a titratable group on a protein molecule can combine with substances, other than hydrogen ions, which may be present in a protein solution, then its titration properties will be altered. If the combining substance is present a t a thermodynamic activity a M, and if it combines with the basic

form of the titratable group only, the equilibrium constant for association being k M , then the apparent hydrogen ion dissociation constant Kappof the group becomes

Kapp= K(1

+ kaM)

(25)

where K is the true dissociation constant. If, on the other hand, the combining substance reacts only with the acidic group, Kapp

= K/(1

+

~ U M )

(26)

In these equations both K and k will depend on pH through interactions with other charges, the effect on K being given in the LinderstrGm-Lang approximation by Eq. (3). The effect on k depends on the charge of the combining substance. If combination requires two titratable sites on the protein molecule, more complex equations are of course obtained, as discussed elsewhere (Tanford, 1961a). Most easily recognized are those examples in which kax is very large. In that case, the group in question will be combined with the combining substances throughout the normal range of titration, and the group will be titrated with a highly anomalous pK, i.e., Kapp = KkaM or K a p p = K / k a M , the titration being in fact a substitution of H+ or OH- for the combining substance, It is an association of this type which is responsible for the large displacements observed, for example, when zinc combines with carboxypeptidase (Fig. 7 ) . Weak binding (small haM)could produce smaller effects, leading to small changes in observed pK values. However, no example ascribable to this cause has been found, and none of the variations in pKint shown in Table V can be reasonably ascribed to such ion binding. If ions are bound to any part of a protein molecule other than the groups which are being titrated in a particular pH range, they will not directly influence the dissociation of hydrogen ions. They will influence it indirectly however by contributing to the electrostatic interactions. In terms of the treatment of Section VI this influence enters solely into the value of the net molecular charge If binding occurs, but is not recognized, the values used in the analysis of the titration curve will be false, leading to false values of w and pKi,t, as discussed in Sections VI, C and D.

z

z.

128

CHARLES TANFORD

B. The Isoionic Point An isoionic solution is defined as a solution which contains only protein ions of average charge H+ ions, and OH- ions. No other ions may be present. An isoionic solution can be prepared by means of a mixed-bed ion-exchange column (Dintzis, 1952), or by electrodialysis, and only for proteins which are soluble in salt-free water. (Refer to Section 111, B ) . The condition that any solution must be electrically neutral requires that in an isoionic protein solution, containing protein a t a concentration Cp moles/liter,

z,

CpZ

+

CH+

=

(27)

COH-

where C,+ and CoH- also represent molar concentrations. be noted that Z = ZH, and that

C,+Co,-

It should also

KL (28) where KL is the apparent ionization constant of water, which will be equal t o the thermodynamic ionization constant K,, under most, condit,ions, since activity coefficients are essentially unity unless the total ion concentration becomes large. A third equation applicable to the isoionic solution is the titration curve of the protein, which may be written for the present purpose as

Z,

=

= unique function of

C,+

=

cp(C,+)

(29)

This equation will usually be independent of Cp as long as Cp is reasonably small. Only if a protein is subject to aggregation will there be a dependence of Eq. (29) on Cp . Equations (27-29) can be solved to yield values for CH+and for 2, (or 2 ) a t the isoionic point. We get

c@(c,+)= K ~ / c ~-+c,+

zH

(30)

from which it is clear that CH+and hence do not have unique values, but depend on protein concentration. It is for this reason that we earlier (Section 111, B ) chose the point a t which 2, = 0 as a reference point for titration curves, rather than the isoionic point. It may be noted that the value of 2, a t the isoionic point can be cslculated by Eq. (27) if the pH of the isoionic solution is measured, even if t,he equation for the titration curve is not known. Setting pH = -log C,+ we obtain the close approximation

2,

(KL/c,+

- cH+>/c~

(31 1 It is evident from this equation that ZH will not bt: significantly different from zero if the measured p H lies between pH 5 and p H 9, and if the protein

Z

=

=

HYDROGEN ION TITRATION CURVES OF PROTEIN

129

concentration is of the order 1 gm/100 ml, corresponding to C, of order For salt-free isoionic p-lactoglobulin, for example, the pH at 25°C is 5.39. At a concentration of 1 gm/lOO ml, Cp is 2.8 X lo-*, so that 2, = 0.015. We consider now the addition of a neutral salt to an isoionic protein solution. Equation (27) still applies if 2 is replaced by 2, , since the charges provided by the neutral salt balance each other, regardless of whether salt ions are bound to the protein. Thus 2, can still be calculated by Eq. (31). It is generally found that the pH of an isoionic solution is changed when a neutral salt is added. The theory of this effect has been discussed by Scatchard and Black (1949), with the assumption that 2, is negligibly different from zero. The analysis is within the framework of the Linderstrcim-Lang treatment, and thus only approximate. Scatchard and Black give the following equation for the effect of ionic strength on the isoionic pH if no binding of ions occurs:

In this equation, I is the ionic strength, and w is given by ICq. (4). The derivatives of 2, are obtained directly from the titration curve, and must be evaluated at 2, = 0. The effect of ionic strength on the isoionic pH, which is predicted by Eq. (32), is usually extremely small, and, in particular, is often much smaller than the experimentally observed variation. Large effects of ionic strength on the pH have been generally considered as evidence for binding of the ions of the added salt. If the salt is composed of cations of charge x+ and anions of charge x- , respectively, and if a+ and T- are the average numbers of each kind bound at a given concentration of the salt,

-

z

= B+Z+

+

(33)

a-2-

(where x- is of course a negative number). Since 2, = 0 at each ionic strength, the degree of dissociation of all groups remains unchanged, so that Eq. (14) gives for the pH, at any ionic strength, pH

=

- 0 . 8 6 8 ~ (a+z+

+ a d - ) + constant

(34)

At zero ionic strength, a+ and F- must both be equal to zero, so that pH

-

(pH)I=o = - 0 . 8 6 8 ~ (a++

+ PA-)

(35)

where w is the value appropriate to the ionic strength at which the pH is measured. Equation (35) shows that the pH will fall with increasing I if cations are bound, but will rise if anions are bound.

130

CHARLES TANFORD

Some experimental data on the effect of KC1 on the pH of isoionic protein solutions are shown in Fig. 19. (All the isoionic pH values lie close enough to pH 7 so that 2, = 0 is within experimental error.) The data indicate that C1- ions are bound to serum albumin, that K+ ions are bound to p-lactoglobulin, and that little or no binding to hemoglobin occurs, the small changes in pH observed for this protein being of the order of magnitude predicted by Eq. (32). These results agree with results obtained by direct binding studies in the case of serum albumin (Scatchard et al., 1950, 1957) and of hemoglobin (Nozaki, 1959; Scatchard et al., 1962).

I

-0.b

I

0.2 (Concentration) "e

I

0.4

I

FIG.19. The effect of KC1 on the isoionic pH of three proteins. The serum albumin data are from Scatchard and Black (1949), the hemoglobin data from Noeaki (1959), the &lactoglobulin data from Noeaki et al. (1959).

Direct binding studies for p-lactoglobulin, however, show a contrary result. Saroff (1961) found that K+ is bound a t p H 7, but not at the isoionic pH. The discrepancy is unresolved at present.

C. Charge Fluctuations Throughout this paper we have so far discussed only the average number of hydrogen ions bound to or dissociated from a protein molecule a t any pH. It should be pointed out that individual protein molecules may a t any given instant have ZH values which can be larger or smaller than the average value 2,. Edsall (1943) has shown for example that in hemoglobin at pH 6.4, where 'v 0, 4 % of all molecules have Z , = +3, 9 % have 2, = +2,17% have ZH = $1, 22% have ZH = 0, 21 % have

zH

131

HYDROGEN ION TITRATION CURVES O F PROTEIN

-

1, 14 % have 2, = -2, 7 % have 2, = -3, with smaller fractions having 2, > +3 or < -3. A given molecule will have a fluctuating charge, varying about the mean charge ZH = gH. Titration curves cannot measure these variations in charge. Only is determinable. However, theoretical equations relate charge fluctuations to the titration curve, so that they can be calculated. One obvious result , and this is in of charge fluctuations is that (ZH)2is not the same as fact the parameter by which the spread of molecules among different values of 2, is usually characterized. The difference between and (ZH)2is identical with the difference between 3 and (5)' given by Eqs. (22) and (24). Differentiating Eq. (22), we get 2, =

z,

As is shown elsewhere (Tanford, 1961a), the left-hand side of Eq. (36) may be evaluated by use of the LinderstrGm-Lang equation, giving

-

(ZH)2

- .j>

= Cnj~j(1 i

(37)

where nj is the number of groups of class j, and xj the degree of dissociation of groups of that class, as given by Eq. (6). It should be noted that Eq. (36) is given incorrectly in the reference just cited (Tanford, l96la).

X. RESULTSFOR INDIVIDUAL PROTEINS A . Chymolrypsinogen Titration curves for bovine a-chymotrypsinogen have been determined under a variety of conditions by Wilcox (1961). The results are summarized in Table IX. The spectrophotometric titration of the phenolic groups is shown in Fig. 4. It is seen that all four phenolic groups are titrated together in 6.4 M urea, whereas only two are titrated in the native protein. Even these two have sufficiently different pK's so that the titration of one is essentially complete before that of the second has begun. The count of side-chain amino groups corresponds to the analytical figure for lysine side chains in a denaturing solvent (8 M urea). I n the native protein, however, three of the thirteen lysine groups cannot be observed to titrate. The maximum positive proton charge ( ZN') is however the same in the native and denatured states, within the uncertainty of about

132

CHARLES TANFORD

f l in the determination of the quantity in the native state. This means presumably that the native structure stabilizes the charged form of three lysine side chains, preventing their dissociation to an uncharged state. The count of “carboxyl” groups is larger than expected from analysis. No explanation has been offered. The usual explanation for this observation is that the analytical figure for free carboxyl groups is too small because of too high an estimate for amide nitrogen. This explanation is unlikely here because asparagine and glutamine were determined by direct analysis. TABLEIX Titration Data for a-Chymotrypsinogenil

Type of group

a-Carboxyl Side-chain carboxyl Imidaeole a-Amino Phenolic Side-chain amino Guanidyl ZNi ~

-

Titration Analysis

Native protein

2 1

4 13 4 20

(native protein)

14

-

3

3

G.7c

2d

4 -13 10.5

9 . 7 , 10.6” -

-14

l j

Denatured proteinb

[>Kin&, 25°C

10d -20

_.

-

~~~

a Molecular weight is 25,000. Titration data are from Wilcox (1961), analytical d a t a from Wilcox et al. (1957). * Data were obtained in 4 M guanidine hydrochloride and in 6.4 M or 8 M urea. c The same P K , , ~was assigned to all three groups which titrate in the neutral region. d More phenolic and amino groups are titrated slowly above pH 12 as the protein becomes denatured. See Fig. 4. 6 Each phenolic group has a different pK.

Wilcox (1961) has also obtained a partial titration curve for a guanidinated derivative of chymotrypsinogcn (lysine side chains converted to homoarginine). The only major difference was the disappearance of the ten side-chain amino groups. No spectrophotometric titration was carried out, but the electrometric titration curve in the alkaline region suggests that the two phenolic groups which are inaccessible to titration in the native protein are still inaccessible in the guanidinated derivative. The titration curve of native chymotrypsinogen is reversible between pH 2.5 and pH 11. Analysis hy the methods of Section VI shows that the neutral pH region can be described by a single intrinsic dissociation constant for all three groups which titrate in the region, together with a w

HYDROGEN ION TITRATION CURVES O F PROTEIX

133

value of 0.065 (at ionic strength 0.1). As Table 111shows, this is a reasonable value for a compact globular protein of the size of chymotrypsinogen. The carboxyl region of the titration curve cannot be described by a single pK and a reasonable value of w. It is likely that the explanation lies in the fact that chymotrypsinogen is rich in basic nitrogen groups (isoionic point is at pH 9.4),so that the carboxyl groups are titrated in an environment rich in positive charges. If these charges are unevenly distributed with respect to the carboxyl groups, then the latter will appear not to have identical pKint values, as was discussed in Section VI, D. The major problems which this titration curve poses are identification of the two unexplained groups in the carboxyl region, and an explanation for the failure to titrate three of the thirteen side-chain amino groups in the native protein.

B. Chymotrypsin Havsteen and Hess ( 1 9 6 2 ) have studied the titration of the phenolic groups of a-chymotrypsin and of its diisopropylphosphoryl (DIP) derivative. The result is similar to that observed with chymotrypsinogen (Fig. 4) in that oiily two of the four groups are available for titration in the native protein, as well as in the DIP derivative. The data do not have sufficient precision to determine whether the two titratable groups have different pK’s, as they do in chymotrypsinogen, but the wide spread of the titration curve suggests that they do. All four tyrosyl groups are titrated normally in solvents which denature chymotrypsin. C. Collagen Fibrils Martin et al. (1961) have shown that the titration curve of suspensions of freshly precipitated collagen fibrils depends markedly on the pH at which aggregation to fibrils takes place. As this pH increases the count of “imidazole” groups decreases, and there is a corresponding increase in the number of groups titrated in the carboxyl region (in which the fibrils go into solution). There is a correlation between the titration characteristics and the occurrence of periodic banding in the fibrils, the incidence of thc latter increasing with pH. It is suggested therefore that the banded regions contain uncharged imidazole groups which cannot be titrated as long as the fibrils remain intact.

D. Conalbumin The titration curve of conalbumin (Wishnia et al., 1 9 6 1 ) is complicated by time-dependent reactions in the acid range. These reactions, however, appear to influence only the shape of the titration curve, and the count of

134

CHARLES TANFORD

various kinds of groups presented in Table X is taken to apply to the native and modified protein alike. The agreement between the titration count and the result expected from analysis is remarkably good, the only discrepancy being in the figure for the maximum proton charge ( E N + ) , where the titration value is seven less than the analytical value for the total of all basic nitrogen groups. No explanation for the discrepancy exists. The small difference between the number of observed “carboxyl” groups and the analytical value is well within the experimental error of the latter. A spectrophotometric titration of phenolic groups was carried out. The TABLEX Titration Data for Cona16umina ~

Type of group

a-Carboxyl Side-chain carboxyl Imidazole a-Amino Phenolic Side-chain amino Guanidyl ZN+

Number of groups

8t

Analysis

Titration 86

131

14

19 52 33 99

11

52

-

92

PKnt

25°C

:1

-

9.41

9.64

-

5°C

4.54 7.20

-

9.85 10.20 -

-

aMolecular weight is 76,600. Titration data are from Wishnia et al. (1961). Analytical data are as given by Wishnia et al. (196l), derived from studies by Lewis et al. (1960). b Eleven groups are titrated in the native protein, the remaining seven are titrated upon denaturation.

results are qualitatively similar to those for ribonuclease shown in Fig. 11, except that the total number of groups per molecule is larger. Eleven of the eighteen phenolic groups are titrated reversibly in the native protein, another seven appear with accompanying denaturation, and their appearance can be delayed by reducing the temperature. An interesting example of difference counting is provided in the conalbumin study. Conalbumin can bind two iron atoms very tightly and it had been concluded earlier (Warner and Weber, 1953) that each iron atom might be bound to three phenolic groups, which would remain ionized at all pH’s where the iron complex is stable. This earlier conclusion was firmly established by spectrophotometric titration of the iron complex. Only five phenolic groups were titrated between pH 8 and 12, compared to eleven in native iron-free conalbumin. The result shows, incidentally,

HYDROGEN ION TITRATION CURVES O F PROTEIN

135

that the seven phenolic groups inaccessible to titration in the native protein (presumably buried as un-ionized groups) are still inaccessible in the iron complex. At 25°C the titration curve was reversible and independent of time between pH 4.2 and pH 11.2. By use of a flow method the reversible portion could be extended to somewhat lower pH. At 5°C it was possible to extend it on the alkaline side to pH 12. The treatment of Section VI was applied to the reversible region of the curve. It was possible to account for the major part of this region by using a single value of w, which was somewhat below that calculated by Eq. (4)) but the difference is only of the order of 25% and does not suggest that conalbumin is not a globular protein in its native state. Below pH 4 and above pH 11.2 (at 25OC) there is a marked decrease in electrostatic interaction (resembling that shown for serum albumin in Fig. 17)) indicative of a reversible transition, presumably to an expanded conformation. It is interesting that the over-all change in conformation which takes place in acid solution is by these measurements found to occur in two parts: a rapid and reversible part when 2, N 20 and then a slower irreversible reaction when 2, ‘v 32. The intrinsic pK values deduced from the part of the curve which could be fitted with a constant w are shown in Table X. The values are comparable to those found for other proteins (Table V) . The heats and entropies for dissociation are given in Table VI and are also found to be unremarkable. The over-all conclusion is that the titratable groups of conalbumin are largely accessible to the solvent, except for the phenolic groups discussed earlier.

E. a-corticotropin a-Corticotropin ( ACTH) has a molecular weight of only 4541 and should contain less than twenty titratable groups. The titration curve (of sheep corticotropin) has been studied by LBonis and Li ( 1959), the results being shown in Table XI. The corticotropin is usually isolated as thc trichloroacetate, and the titration was first carried out on this salt. The count of groups was in accord with expectation, except for the presence of one anomalous group in the neutral region. The corticotropin was then deionized by ion exchange, but the anomalous group remained. Moreover, two additional anomalous groups appeared as a result of deionization, one being a “carboxyl,” the other a “side-chain amino” group. LBonis and Li present evidence that the neutral anomalous group is due to an impurity. An unusual feature of the titration curve of corticotropin is the relatively low pH for titration of the guanidine groups. The titration of these groups

136

CHARLES TANFORD

is not visually distinct from the titration of the side-chain amino groups, though the distinction becomes apparent on mathematical analysis of the alkaline region of the curve. The titration curve of beef corticotropin (LBonis and Li, 1959) and a partial curve for pork corticotropin (Danckwerts, 1952) are essentially identical to the curve for the sheep product. The titration curve is reversible and has been analyzed by the methods of Section VI. The values of w which are obtained from titration of the phenolic and amino groups at ionic strength 0.1 are near 0.03. A somewhat TABLEXI Titration Data f o r a-Corticotropin" Number of groups

Titration

Type of group

pKint

Trichloro- Deionized acetate salt sample a-Carboxyl Side-chain carboxyl Imidaaole a-Amino Phenolic Side-chain amino Guanidyl ZNi

7

8

1 1 l i 2

2

2

3 4 9 }

7"

8"

-

5 or 6*

3

10

a These dat>aare for sheep corticotropin, with molecular weight 4541. Titration data from LBonis and Li (1959);analytical d a t a from Li et al. (1955). * There are 5 residues of glutamic acid and 2 of aspartic acid. Either one or two of them may be present as arnides. c The titration of guanidyl groups overlaps t h a t of amino groups, so t h a t they cannot be differerhiated on inspection.

higher value (0.0'3) is obtained from the titration of carboxyl groups, but it is probable that this is in part due to the fact that some of the carboxyl groups are bunched together on the corticotropin chain: the sequence -Gln.Asp.hsp.Clu.occurs at one point and accounts for more than half the carboxyl groups. As explained in Section VI, C , such close juxtaposition of titratable groups is expected to lead to a high value of w. In any event, the value of 0.03 is far below the value of w expected on the basis of the compact sphere model (Table III), and thus the titration curve clearly indicates that a-corticotropin does not have a globular structure. This conclusion agrees with the results of other measurements which all indicate that this molecule has a flexibly coiled conformation.

HYDROGEN ION TITRATION CURVES O F PROTEIN

137

As might be expected of a molecule with an essentially random structure, the pKint values which are given in Table X I are essentially normal. I t is especially noteworthy that the phenolic groups have a lower pKint than the side-chain amino groups, as is expected from the data of Table I. In most proteins with a typical globular structure this order is reversed (see Table V). The pKint values given in Table X I for the imidazole and aamino groups must be regarded as quite uncertain, because of the anomalous group which is titrated in the same range of pH.

F. Cytochrome c Titration curves of oxidized and reduced cytochrome c (from beef heart or horse heart) have been determined by Theorell and ikeson (1941) and by PalBus (1954). A major problem concerns the titration of the imidazole groups, of which there are three in the protein (Margoliash et al., 1962). According to Theorell and Akeson, there are two groups titrated with a pK approximately that of imidazole groups. Since cytochrome c has no free a-amino group, a reasonable interpretation is that both of these are in fact imidazole groups, and that the one imidazole group which is not titrated is linked to the heme iron atom of the protein. This result is compatible with the proposal of Margoliash et al. (1959)) that the two basic groups coordinated to the heme iron atom are one imidazole group and one lysine amino group. Theorell and ikeson, on rather weak evidence, suggested that one of the groups titrated in the neutral region is actually not an imidazole group, and PalBus, with more accurate data, comes to the same conclusion, demonstrating quite convincingly that just a single group with pK near 7 (actually pK = 6.8) is being titrated. This would seem to favor the hypothesis that two imidazole groups are coordinated to the heme iron atom. An undecapeptide which can be obtained from peptic hydrolysis has also been subjected to titration (PalBus et al., 1955). This peptide contains the heme group, attached to the polypeptide chain through two half-cystine residues, and possesses one histidine residue, which is thought to be covalently linked to the iron atom. There is not a unique way of interpreting the titration curve. It is possible to arrive at an interpretation which assigns a pK of 3.5 to the imidazole group, but it must be regarded as specultLtive. Seventeen groups arc titrated in the carboxyl region on the basis of a molecular weight of 12,500. This figure agrees with expectation. There are twelve side-chain carboxyl groups and one terminal a-carboxyl group (Margoliash, 1962). The other four titratable groups represent the two free propionic acid groups of the heme, and the two iron-linked basic groups, which should be freed from their bonds to iron, and titrated, when

138

CHARLES TANFORD

the pH becomes sufficiently low. (This process does not lead to separation of the heme from the protein in the case of cytochrome c, because the heme is linked to the protein through its side chains, which form thio-ether bonds to the two half-cystine residues mentioned earlier.) The absorption spectrum of ferricytochrome c changes with pH, and indicates that several hydrogen ions are dissociated with accompanyin effect on the electronic structure of the heme iron atom (Theorell and keson, 1941;Boeri et al., 1953). The results are complicated by an influence of chloride ion, and a simple interpretation of all the changes is not possible. However, a change involving two H+ ions, titrated simultaneously at pH 2.1, appears to reflect the dissociation of the basic nitrogen groups from the heme iron atom. In the undecapeptide studied by Paleus et al. (1955), the corresponding change occurs when Hf ions are added or removed at pH 3.4 and 5.8.

f

G . Fetuin Fetuin is a glycoprotein which has titratable groups associated with its carbohydrate moiety (sialic acid) in addition to those present on the protein. Spiro (1960) has determined the titration curve of the native protein, as well as that of a preparation from which sialic acid had been removed. The group count differed only in the number of groups assignable to sialic acid. In particular, the value of 2 N + was the same for both proteins. It is clear from these results that the combination of sialic acid with the protein does not involve any of the basic groups of the protein.

H . F i b h o g e n and Fibrin The difference between the titration curves of fibrinogen and fibrin, in 3.3 M urea solution, has been determined by Mihalyi (1954a). It was found that the reaction fibrinogen -+ fibrin leads to the production of 3.5 new groups per molecule, with a pK near 8.0. These groups are presumably a-amino groups which arise from the proteolytic nature of the activation process. It is known that two peptide bonds per molecule of fibrinogen are broken in this process, two peptides being split off. At pH 5.5 (the reference point of Mihalyi's data) no net difference in dissociated hydrogen ions is involved, since one end of each split bond will be in the form -COOand the other end in the form -NHt. The resulting amino groups will however be titratable, losing their hydrogen ions near pH 8. The fact that 3.5 new groups, rather than two were observed, is perhaps the result of some nonspecific splitting of peptide bonds by thrombin. Mihalyi (1954b) studied in a similar way the difference in the titration curves of fibrinogen and of polymerized (clotted) fibrin. By subtracting from this difference the difference described above between fibrinogen and

HYDROGEN ION TITRATION CURVES O F PROTEIN

139

fibrin, he was able to compute the difference due to the polymerization of fibrin alone. (The clotting experiments were carried out in 0.3 M KCI, whereas the fibrinogen -+ fibrin experiment was carried out in the presence of urea. Urea was found to have only a small effect on the titration curve of fibrinogen in the pH range of interest. It was assumed that the effect on unpolymerized fibrin would be the same, and the small correction required for the change in solvent was applied on this basis.) The observed change on clotting consisted of the appearance of three or four new titratable groups with a pK of 7.0 and the disappearance of three or four groups which originally had a pK of 8.2. Several different explanations have been proposed by Mihalyi and others, none of which carries conviction. Scheraga and Laskowski (1957) consider that the altered titration curve arises not from the disappearance of groups with pK of 8.2 and the appearance of new groups with pK of 7.0, but from a small pK shift of a larger number of groups. This may well be correct, as the original interpretation of Mihalyi depends on ignoring some of the experimental points. However, the elaborate mechanism used by Scheraga and Laskowski to account for such a shift in pK is an improbable one. It may be that nothing more complicated is involved than the necessity to maintain charge neutrality of areas of contact between fibrin molecules in the polymer.

I . Gelatin Kenchington and Ward (1954) have used titration studies to resolve the molecular difference between gelatin extracted by processes employing acid and alkaline media. Acid-processed gelatin was found to have an isoionic point a t pH 9.1 and to possess 85 titratable carboxyl groups per 100,000 grams. The alkali-processed material was isoionic at pH 4.92 and contained 123 titratable carboxyl groups, essentially equivalent to the total amount of glutamic acid and aspartic acid plus the corresponding amides, which gelatin is known to contain. It is clear that processing in alkaline solution hydrolyzes side-chain amide groups to the corresponding carboxyl groups.

J . Hemoglobin Titration studies of hemoglobin have made important contributions to our knowledge of this protein. The three outstanding features are : (1) Four groups are titrated (pK near 8.0) in ferrihemoglobin,which are not titrated in hemoglobin itself, nor in the complexes of hemoglobin with 0 2 or CO (German and Wyman, 1937; Wyman and Ingalls, 1941). The same groups, with similar pK, are observed by spectrophotometric titration (Austin and Drakbin, 1935; George and Hananis, 1953), and by observation of the effect of pH on magnetic properties (Coryell et al., 1937).

140

CHARLES TANFORD

+

These groups represent the dissociation Fe(HzO)+s Fe(0H) H’, from the heme iron atom. (2) Four groups, which have a pK near 7.9 in hemoglobin, are titrated at much lower pH (pK near 6.7) in the hemoglobin-oxygen complex. These are the four “heme-linked” imidazole groups, which are responsible for the effect of pH and of COzon the hemoglobin-oxygenequilibrium (BohrHasselbach-Krogh effect). Pour other groups have an altered pK when oxygen is combined with hemoglobin, the pK being near 5.25 in hemoglobin and near 5.75 in the oxygen complex. These are also believed to be imidazole groups, though the identification is less secure. It is of interest that all eight of these groups have the same pK in ferrihemoglobin as in the hemoglobin-oxygen complex (Wyman and Ingalls, 1941), so that the pK differences observed are presumably associated with a conformational difference in the region of the molecule which contains the heme, rather than with a specific effect of oxygen (Wyman and Allen, 1951). The subject of the heme-linked groups has been previously reviewed (Wyman, 1948), and the reader is referred to that review for a detailed discussion of the subject. (3) The titration curve in the acid region is time-dependent and irreversible, as was first clearly demonstrated by Steinhardt and Zaiser (1951). This aspect of the titration of hemoglobin has also been reviewed previously (Steinhardt and Zaiser, 1955), but there was some ambiguity about the meaning of this phenomenon at the time of the review, which has been removed by more recent work, as will be briefly described here. The original observation (Fig. 9) was that a difference of up to thirtyeight groups could be obtained in the number of groups required to titrate an initially neutral protein to pH 3.5, depending on whether data were obtained by a rapid-flow method or by slower procedures. A parallel study of spectral changes indicated that protein examined immediately on attainment of pH 3.5 would be largely in its native state, but that conversion to a denatured state takes place rapidly. It was not possible however to determine whether the extra thirty-eight groups which were titrated represent an effect of conformation on the number of groups titrated in the acid range, or whether they reflect a change only in the shape of the acid part of the titration curve, brought about by unfolding and hence decreased electrostatic interaction. It appeared that at least a part of the effect, must be due to the latter phenomenon (Tanford, 1957). The question has been essentially decided by more recent experiments (Beychok and Steinhardt, 1959; Steinhardt et al., 19G2). One procedure was to reduce the temperature and increase the ionic strength, the increase in ionic strength being for the purpose of diminishing the importance of electrostatic interactions. A second procedure was to use hemoglobin derivatives which are especially stable in the native state, these being the

HYDROQEN ION TITRATION CURVES OF PROTEIN

141

CO-hemoglobin complex and the cyanide complex of ferrihemoglobin. Both procedures resolved the ambiguity in the interpretation of the earlier results. Figure 10 shows the titration curves of the stable complexes and the rapid back titration of the corresponding denatured proteins over a wide range of pH. What these curves show is that the number of groups in the carboxyl region is essentially the same in the native and denatured states, but that the number of groups titrated in the neutral (imidazole) region is about twenty-two greater for the denatured protein. These twenty-two groups (all assumed to be imidazole groups) are in their uncharged form in the native state and cannot be titrated with acid. Upon denaturation they become free from the restraint to which they were subject, so that, in going from a neutral reference point towards lower pH, under conditions where denaturation occurs, these groups are titrated as an accompaniment of denaturation. Reverse titration of the denatured protein then shows these groups as titrating in the normal region for imidazole groups. (The maximum difference of thirty-eight hydrogen ions per mole observed in Fig. 9 must represent these twenty-two imidazole groups plus an additional difference of sixteen hydrogen ions per mole which reflects the difference in electrostatic interactions between native and denatured protein.) It should be noted that four of the anomalous imidazole groups are the four groups by which the heme iron atoms are attached to the protein. These cannot be titrated as long as the hemes remain attached. The other groups must be simply “buried” in the interior. Such groups occur in myoglobin (see below), as well as in hemoglobin. Nozaki (1959) has carried out careful titration curves of bovine ferrihemoglobin over the entire accessible pH range. A preliminary group count was made. Starting with native isoionic protein, titration to the acid end point (where the protein is of course denatured) required 102 hydrogen ions/mole, so that the maximum positive charge is 102. The expected figure (based on 14 arginine, 48 lysine, 36 histidine, and 4 iron atoms, each contributing one charge) is 106. Starting with native protein and titrating towards the alkaline side gave a count of 28 groups in the neutral pH region. The expected figure is 44 [36 histidine, 4 N-terminal amino groups, and 4 Fe(Hz0)+ groups], so that there is a discrepancy of 16. This discrepancy confirms the conclusion of Steinhardt et al., given above, that many of the imidazole groups of the native protein are inaccessible to titration, the difference between the actual group numbers (22 versus 161 being probably within the experimental error of both determinations. Nozaki’s figure for the alkaline range is 60 groups per mole, in agreement with expectation (48 lysine, 12 tyrosine). The total number of groups titrated in the carboxyl region, including those released on denaturation, was 88,

142

CHARLES TANFORD

which is approximately the expected figure when the eight carhoxyl groups on the side chains of the four heme groups are included. Another titration curve, this time for human CO-hemoglobin, has been determined by Vodrazka and Cejka (1961). Unfortunately, their group counting procedure is not valid: all groups titrating below pH 4.7 were arbitrarily assigned to the “carboxyl” region and those titrating between pH 4.7 and pH 8.5 were assigned to the “imidazole plus a-amino” region. This procedure assigns too large a number of groups to the latter region and led the authors to the conclusion that the anomalous groups which titrate in the acid pH range are basic groups other than imidazole groups. The data in fact do not support this conclusion. Vodrazka and Cejka (1961) titrated the phenolic groups spectrophotometrically, and found no evidence for buried groups. Hermans ( 1962), has reported from a similar study that four groups per molecule (one per polypeptide chain) are not titratable in the native protein. Hermans’ study employed absorption at 245 mp instead of the customary wavelength of 295 mp.

K . Insulin Titration curves of insulin have been determined by Tanford and Epstein (1954) and by Fredericq (1954, 1956). As Table XI1 shows, the count of groups obtained for zinc-free insulin is in agreement with analytical data. This is true in spite of the fact that insulin is insoluble between pH and pH 7. The precipitate is evidently highly hydrated, so that titration of the acidic groups occurs as if they were in solution. Tanford and Epstein also determined the titration curve of crystalline zinc insulin, containing one atom of Zn++ per two insulin molecules. The titration curve of this material differs from that of zinc-free insulin in two ways. (1) Two new groups are titrated for each zinc ion, one near pH 8, the other near pH 12. These presumably represent acidic water molecules attached to Zn“, Zn(H20)2++ -+ ZnOH(H20)+

-+

Zn(OH)z

(2) The count of imidazole groups is reduced from four (per two insulin molecules) to two, and, at the same time, two new “carboxyl” groups appear. The titration of these new groups (in the direction of hydrogen ion addition) parallels the dissociation of Zn++ from the zinc insulin. Each Zn++ ion is evidently associated with two imidazole groups in their basic uncharged form. The value of the binding constant for zinc confirms this conclusion. Gurd and Wilcox (1956) have pointed out that the binding groups could

143

HYDROGEN ION TITRATION CURVES OF PROTEIN

be terminal amino groups rather than imidazole groups, since these groups have essentially identical pK's in the free state. Marcker (1960) has presented evidence that the amino groups are in fact the more likely binding sites. The curve for zinc-free insulin was analyzed by the method of Section TABLExrr Titration Data for Insulin at $ 6 ' 0 Number of groups Type of group

a-Carboxyl Side-chain carboxyl Imidazole a-Amino Side-chain amino Phenolic Guanidyl Zn(H,O)++

Analysis

8.5* 4 4 2

-

Titration Zinc-free insulin

Zinc insulin

12.5

14.56

pKint

4 4

2 4

6.4 7.4

10

10

9.6'

2

2 2

11.9

-

-

a Data of Tanford and Epstein (1954; see also Fredericq 1954, 1956), calculated for an insulin dimer of molecular weight 11,466. The zinc insulin preparation contained one zinc atom per dimer molecule. The pKint values are for the zinc-free protein. * The fractional number arises from the probable presence of two forms of insulin which differ in the number of free carboxyl groups. c Two of the groups titrating as carboxyl groups are the imidazole groups t o which the Znf+ ion is bound. I, This pK was determinable because the titration curve of the carboxyl groups was clearly not compatible with the presence of 12.5 identical groups. Assuming 4 groups with a lower pK, this was the value required. 6 No attempt was made t o distinguish between amino and phenolic groups in the analysis.

VI. The pKint values are shown in Table XI1 and reveal no important anomalies. The apparent value of w rises to very high values in the region where the protein is precipitated. (See Section VI, C . ) The dissociation of the single lysine amino group of iodinated insulin has been studied by Gruen et al. (1959a). (The iodination separated the titration region of phenolic residues from the titration region of the amine group. ) No abnormalities were observed. The over-all difference between the titration curves of iodinated and nor-

144

CHARLES TANFORD

ma1 insulin corresponded to that which is expected as due to the lowered pK characteristic of iodjnated phenolic groups (Gruen et al., 1959b).

L. @-Lactoglobulin Complete titration curves of 0-lactoglobulin have been determined by Cannan et al. (1942) and by Nozaki et al. (1959). Between the acid end point and the onset of alkaline denaturation near pH 9.7, the data of the two studies are indistinguishable. Above pH 9.7, Nozaki et al., by use of the pH-stat were able to obtain two curves, one representing an extrapolation to zero time (corresponding to the titration of the native protein), the other representing infinite time (corresponding to titration of denatured protein). Both curves are shown in Fig. 2. The curve for the native protein could be obtained over a limited range of pH only, so that it is not possible to decide whether the difference between the two curves represents a difference in the number of groups accessible to titration, or whether it lies in the shape of the curve alone. It was possible to fit the data for the native protein by assuming that all amino and phenolic groups are accessible, and that the value of 20 is the same as that which is applicable to the reversible part of the titration curve. The side-chain amino and phenolic groups were assumed to have the same pKintand a reasonable value of 9.95 was obtained from this analysis. This suggests that the difference between the curves lies primarily in the steepness, and not in the count of groups. It was assumed, however, that the four thiol groups of the protein are not titrated in the native state because they are found to be quite unreactive by other methods. Since thiol groups are expected to have a somewhat lower pK than amino or phenolic groups (Table I ) , it would probably have been difficult in any case to fit the native curve with reasonable pKint values if the thiol groups had been included. The titration curve of 0-lactoglobulin denatured a t pH 12.5 has also been determined (Tanford el al., 1959). It was found that the curve is reversible. The denatured protein is insoluble near its isoelectric point and this region was not studied in detail. The group counting results obtained from these studies are reported in the last two columns of Table XITI. ( I n comparing these results with the analytical data of the first two columns of this table it should be noted that the p-lactoglobulin studied was a mixture of the two genetic isomers, 0-lactoglobulins A and B.) The most significant feature of the analysis is that the native protein appears to contain six imidazole groups, compared to the analytical figure of four. At the same time, the number of carboxyl groups titrated is less than the analytical figure by two groups. After denaturation, however, the group count agrees with the amino acid analysis. It is evident that two carboxyl groups of the native protein are titrated with

HYDROGEN ION TITRATION CURVES OF PROTEIN

145

a pK which is characteristic of imidazole groups. The probable reason has been discussed in Section VI, D. Titration curves of pure /3-lactoglobulins A and B have also been determined (Tanford and Nozaki, 1959). The two genetic variants differ in isoionic point, but they possess the same maximum positive charge (Fig. TABLE XI11 Group Counting for @-Lactoglobulin

Native B-Lact A

1

Native @-IdactB

1

52

I

50

I

Amino acid analysisType of group

a-COOH Side-chain COOH Imidazole a-NHz Thiol Phenolic Side-chain NH2 Guanidyl

ZN+

@-LactA

8-Lact R

2 52 4 2 2 8 28 6 40

4 2 2 8 28 6 40

Titration curveb Native lenatured mixturec mixtureC 51

a Gordon et al. (1961), Pie2 et al. (1961). The figures have been adjusted t o the nearest even integer for a two-chain molecule of molecular weight 35,500. * Titration data of Nozaki et al. (1959), Tanford et al. (1959), Tanford and Noeaki (1959). The mixture contained essentially equimolar amounts of the two genetic isomers, &lactoglobulins A and B. d Figures in parentheses are subject t o considerable uncertainty. The number of phenolic groups was determined from the total change i n extinction a t 295 mfi in going from native protein with undissociated phenolic groups t o denatured protein with all phenolic groups dissociated. No correction was made for the change i n extinction a t this wavelength which results from unfolding of the protein as a result of the emergence of the tryptophan residues from the inside of the native structure. There are four tryptophan residues per molecule, so that this change can be expected t o be quite large, certainly large enough t o account for an error of two groups in the count of phenolic groups.

20) and the same two anomalous carboxyl groups with pKintof 7.5. Thus the difference between them lies in the number of normally exposed carboxyI groups, two more of these being in form A than in form B. This result has since been confirmed by amino acid analysis (Gordon et al., 1961; I’iez et al., 1961). Another interesting feature of the titration studies (Nozaki et al., 1959) is the fact that addition of KC1 and CaClz depresses the pH of isoionic protein solutions. This means that I(+ and Ca++ ions are bound by the iso-

140

CHARLES TANFORD

ionic protein, a result which is apparently in agreement with published studies of ion binding by direct means (Carr, 1953, 1956). These studies show that K+ and Ca++ ions are bound at pH 7.4, and the quantitative difference between the number found bound at that pH, and the number calculated as bound from the pH change at the isoionic point (Section IX, B ) , is of the order of magnitude expected on the basis of the difference in protein charge a t the two pH's. More recently, however, Saroff (1961) has measured ion binding as a function of pH and has observed that there is

I

2.0

PH

2.5

I 3.0

FIG.20. Approach t o the acid end point of the titration curves of p-lactoglobulins A and B, and for the normal equimolar mixture of the two, a t 25°C and ionic strength 0.15. The value of 2 , is calculated relative t o the point of zero net proton charge, which occurs a t a different pH for each of the three samples (Tanford and Nozaki, 1959).

essentially no binding of K+ at the isoionic pH. He observes binding a t higher pH, the appearance of binding sites occurring in parallel with the conformational change during which the two anomalous carboxyl groups are titrated. The discrepancy between his results and those derived from the titration studies is at present unresolved. The values of w which one obtains from the carboxyl region of the titration curve by application of Eq. (4), assuming 2, = 2, are 0.072 and 0.039, respectively, at ionic strength 0.01 and 0.15, i.e., they are somewhat below the calculated values of Table 111. (As was mentioned earlier, the same values are compatible with the entire titration curve of the native protein.) If one attempts to evaluate the difference between 2 and 2, at all pH's

147

HYDROGEN ION TITRATION CIJRVES OF PROTEIN

from the few values of ion binding at different pH's which are available, larger values are observed (w = 0.090 and 0.058 at ionic strengths 0.01 and 0.15). Both sets of values are within the range expected for a compact globular protein. The slopes of logarithmic plots for the alkaline titration curve at t = (Fig. 2) are however very much less, showing that the alkali-denatured protein is randomly coiled. The intrinsic pK values obtained from these studies at 25OC and ionic strength 0.15, without correcting for K+ ion binding, are 4.7 for the sidechain carboxyl groups, 7.3 for the imidazole groups, and 9.9 for phenolic Q,

TABLEXIV Carboxyl Groups of LysozymeR Carboxyl groups titrated Lot number

in 0.15 M KCl

in 8 M GHCl or 5 M GHCl 1.2 M urea*

+

003L1 381-187 D638040 381-187Methylated

10.5 9 14 1 (or 2)

13.5 12

381-187Acetylated

12

12

9

12

381-187Guanidinated

-

1 (or 2)

Remarks

-

12.2Methoxyl groupsper

molecule Acetylation occurs principally at amino groups Guanidination converts amino groups to hornoarginine groups

= Data from Tanford and Wagner (1954);Donovan et al. (1960,1961). b GHCl = guanidine hydrochloride.

and lysine amino groups. Correction for K+ ion binding increases the pKint values by 0.15.

M . Lysozyme Titration studies of lysozyme have revealed two unique features, both occurring in the carboxyl region of the titration curve. The pertinent data are shown in Table XIV. It is seen ( a ) that the count of carboxyl groups varies widely from one preparation of lysoByme to another, and ( b ) that three extra carboxyl groups appear in denaturing solvents such as 8 M guanidine hydrochloride. The three extra carboxyl groups which appear in denaturing solvents were apparently in their carboxylate ion form in the native protein. Since these groups are not detectable at all in the titration of the native protein

148

CHARLES TANFORD

down to pH 2, a true plateau being approached at pH 2, they must in effect be inaccessible to the solvent. It is possible for a charged group to be so located only if it is in close contact with a similarly inaccessible group of opposite charge. There is no evidence that any of the titratable cationic groups of lysozyme are so located. However, the twelve guanidyl groups are never titrated, so that three of these could be located away from the protein/solvent interface. A number of chemical derivatives of lysozyme were studied by Donovan et al. (1960), with the results shown in Table XIV. The guanidinated derivative, in which charged lysine groups are simply replaced by similarly charged homoarginine groups, showed behavior similar to that of the native protein. The acetylated derivative, in which lysine side chains are rcplaced by uncharged acetyllysine groups, titrated like denatured untreated lysozyme. The most interesting result was that obtained with the methylated derivative, in which most of the carboxyl groups are esterified and only a single titratable group in the carboxyl region is observed. The number of methoxyl groups introduced was found by analysis to be equal to the number of carboxyl groups titrated in the denatured protein, essentially confirming that the three extra groups titrated upon denaturation are in fact carboxyl groups. The only aspect of the titration data which raises a question about the existence of buried carboxylate ions in the native protein is the maximum positive charge estimated by Tanford and Wagner (1954). The figure is based on an assumed location of the point of zero net proton charge at pH 11.1. (Lysozyme precipitates on deionization, so that the normal procedure for determining this reference point is not possible.) This assumed pH, however, is supported by the fact that titration curves at three different ionic strengths, which should intersect a t Z = 0, do intersect at pH 11.1, and by the fact that the isoelectric point has been determined electrophoretically to be at pH 11.1. With this assumed pH of zero net proton charge, the maximum positive charge ( Z N + , Section IV, A ) becomes 19, which is just the analytical figure for the total number of cationic groups. If three carboxyl groups are still in their anionic form a t the acid end point of the titration curve, the experimental maximum positive charge should have been 3 less than the anlaytical figure. It would appear that the problem of the carboxyl groups of lysozyme merits further investigation. The count of other titratable groups of lysozyme agrees with analytical data. Moreover, no variation between different preparations has been reported. The titration curve of the native protein is reversible and has been analyzed by the methods of Section VI. As we have already noted (Fig. 16),

HYDROGEN ION TITRATION CURVES OF PROTEIN

149

the carboxyl region does not obey Eq. (14) if all carboxyl groups are assumed to have the same pKint. This is not an anomaly unique to lysozyme, but is shared by other proteins (chymotrypsinogen, ribonuclease) which are rich in basic nitrogen groups. The anomaly presumably reflects uneven spatial distribution of these groups, relative to the carboxyl groups. The neutral and alkaline region of the titration curve is compatible with values of w of magnitude similar to those calculated by Eq. (4). The intrinsic pK values are not remarkable (see Table V ) , except that pKint for the phenolic groups is 1.2 higher than the expected value. The likely reason has already been discussed in Section VI, D . It may be noted that Tanford and Wagner (1954) found the spectral change corresponding to dissociation of the phenolic groups to be quite abnormal, though an approximate pK for the dissociation could be determined. Their difficulties have been elegantly explained by Donovan el al. (1961) as arising from changes in the spectrum of tryptophan side chains, which occur in the same region of pH as the ionization of phenolic groups. When these changes are corrected for, the residual spectral change becomes that which is normally expected for phenolic ionization.

N . Myoglobin Special interest attaches to the titration of sperm whale myoglobin because the three-dimensional structure of this protein is well on the way to being completely elucidated (Kendrew el al., 1961). The speculative structural features, which have been invoked to explain titration data that do not conform to expectation, will in this protein soon be subject to actual test. A titration curve for sperm whale myoglobin has been reported by Breslow and Curd (1962). The most striking feature is that it exhibits a timedependent acid denaturation, which resembles that observed for the similar protein hemoglobin. To elucidate the physical nature of this reaction, emphasis was placed on the back titration to neutral pH of denatured protein. As in the case of hemoglobin (mentioned earlier) ,there are two major differences between the titration curves of native and denatured myoglobin, as shown by the data of Table XV. The first difference is in the count of imidazole groups. Only six of the twelve groups known to be present are titrated in the normal pH range in the native protein. When the native protein is titrated towards acid pH, these six groups are titrated in the carboxyl region as the protein becomes denatured. In the back titration of the denatured protein, all twelve of the groups are titrated with approximately the expected pK. To confirm the identification of the groups concerned, the kinetics of hydrolysis of p-nitrophenylacetate (Section 111, D) was studied. This method gives

150

CHARLES TANFORD

direct information as to the number of accessible uncharged imidazole groups, and in the present study confirmed exactly the conculsions reached from the titration curve as a whole. It is concluded therefore that six of the twelve imidazole groups of native myoglobin are buried in the interior in their uncharged form. One of these is of course the imidazole group by which the heme iron atom is attached to the protein. The other five have not been identified. The expectation from the present study is that the complete three-dimensional structure of the protein, when available, will show these groups in positions where they are not in contact with the solvent. The second difference between native and denatured myoglobin lies in TABLEXV Titration of Myoglobin in the Neutral pH Region" ~

Native protein Number of imidaaole groups: By analysis By titration By reaction with NPAh pKi.t for imidazole groups w At ionic strength 0.16 w At ionic strength 0.06

6 6 6.62 0.050

0.085

After acid denaturation 12

12 12 6.48 0.034" 0.044O

a Titration data of Breslow and Gurd (1962). Analytical data by Edmundsori and Hirs (1961). The protein studied was ferrimyoglobin from the sperm whale. Its molecular weight is 17,816. NPA p-nitrophenyIacetate. See Section 111, D. Determined from the carboxyl region rather than the imidazole region, assuming that all 23 carboxyl groups found by analysis are titratable with the same pKint. =i

0

the value of the electrostatic interaction factor w. In the native molecule this factor is somewhat, but not much smaller than calculated by Eq. (4). Using a radius derived from the volume of the molecule as it appears in myoglobin crystals, Breslow and Gurd (1962) calculated w = 0.106 and 0.065, respectively, at ionic strengths 0.06 and 0.16. The experimental values at the same ionic strengths are 0.085 and 0.050. (It was assumed that = ? .& , which is likely to be essentially correct for myoglobin.) The values of w for the denatured protein are considerably smaller, indicating that unfolding of the protein occurs. The values given in Table XV are obtained by assuming that all of the carboxyl groups of myoglobin have identical pKint values. If this assumption is in error, the actual values would be smaller than those given in the table. (The intrinsic pK of the carboxyl groups, obtained by a rather long extrapolation to = 0, is 4.4.) Apart from the imidazole groups of myoglobin, only one other group has

z

z

HYDROGEN ION TITRATION CURVES O F PROTEIN

151

been studied in any detail, this being the 17e(HzO)+group, which dissociates to Fc(OH) near pK 9. The pK value for this group has been determined by Theorell and Ehrenberg (1951), George and Hanania (1952), and Rreslow and Gurd (1962) from the spectral change which accompanies the dissociation. The values are given in Table V, together with comparable data from other proteins. In a recent study, Hermans (1962) has indicated that only two of the three tyrosyl phenolic groups of myoglobin titrate below pH 13, this result being obtained for both whale and horse myoglobins.

0. Myosin The titration of myosin has been studied by Mihalyi ( 1950). The count of groups in the various regions of the curve agrees with analysis to better than lo%, except for the carboxyl region, where titration indicates 165 groups per 100,OOO gm, as compared with the analytical figure of 132. It is likely that the analytical assay for amide groups is the source of the error. Mihalyi’s titration curves were obtained a t a series of ionic strengths, ranging from quite a low value to I = 1.2 M . The curves were reversible over a wide range of pH, and were considered to represent equilibrium. They were not analyzed by the methods of Section VI, but even a cursory examination shows that the carboxyl region at least would not obey the behavior predicted by the Linderstrfim-Lang equations. The carboxyl regions of the titration curves are quite flat, indicating fairly strong interaction between the groups, but if the data were plotted according to Eq. (14), with 2, as abscissa, the w values would be essentially independent of ionic strength. On the other hand, the pKint values would depend strongly on the ionic strength. Mihalyi suggests that strong anion binding in the acid region would be responsible for this kind of behavior. A spectrophotometric titration of the phenolic groups of myosin and its subunits has been reported by Stracher ( 1960). The data resemble those shown for ribonuclease in Fig. 11. About two-thirds of the tyrosine residues are titrated normally, and about one-third appear inaccessible in native myosin. An interesting feature is that 6 M urea has no effect a t all on the titration curve. Similar studies were performed on the subunits L-meromyosin and Hmeromyosin. In the former 90 % of the phenolic groups appear abnormal, but they are titrated normally in 5 M urea. In H-meromyosin all of the groups are normal, even in aqueous solution.

P. Ovalbumin The very first electrometric titration curve of a protein to be reported in the literature is a study of ovalbumin (Bugarszky and Liebermann, 1898).

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CHARLES TANFORD

The first detailed analysis of a protein titration curve, according to the semiempirical treatment used for most of the titration curves reviewed in this paper, also involves ovalbumin (Cannan el al., 1941). The first discovery of phenolic groups inaccessible to titration was again made with this protein (Crammer and Neuberger, 1943). Within the limits of error of amino acid analyses available a t the time, the count of groups obtained by Cannan et al. agreed with expectation, except in so far as the alkaline part of the curve was concerned. The number of groups titrated here is essentially the same as the number of amino groups, rather than the sum of amino and phenolic groups. This result is in accord with the later spectrophotometric titration of phenolic groups: essentially all of these groups are inaccessible to titration in the native protein. Cannan et al. (1941) were able to describe the entire titration curve, at eight different ionic strengths, by Linderstrgim-Lang’s equation, using a single value of w a t each ionic strength. The variation of w with ionic strength was essentially that of Eq. (4),experimental values being about 0.8 of those calculated by that equation. [Itwas found that the isoionic pH depends on the concentration of KCl which was used to vary the ionic strength, the direction of the effect indicating that chloride ion is bound. Correction for the effect was made by an adjustment factor introduced into Eq. (14), this factor being a measure of the number of chloride ions bound by the protein at its isoionic point. The possibility of variation in chloride ion binding with pH was not allowed for, and this is one reason why experimental values of w fall below calculated ones. The intrinsic pK values required to fit the data were not far from expected values: 4.3 for the carboxyl groups, 6.7 for imidazole groups, and 10.0 for lysine amino groups.] Harrington (1955) has used the pH-stat method to show that there is a large difference between the titration curves of native ovalbumin in 2.6 M guanidine hydrochloride, and the denatured protein which is formed by a measurably slow reaction in this solvent. The result has been interpreted as indicating the release of eight carboxyl and eight phenolic groups which are not accessible to titration in the native protein. Since the two branches of the difference titration curve reach plateaus a t extreme acid and alkaline pH (i.e., they resemble the curve shown in the lower part of Fig. 5 ) , the interpretation of the difference as newly liberated groups appears indisputable. That the phenolic groups should be so liberated on denaturation is not surprising, since these groups are known to be buried in the interior in the native protein. The liberation of carboxyl groups is surprising, however, since the expected number is titrated in the native protein. Furthermore, the carboxyl groups which are unavailable in the native protein appear to be in their anionic form. In this form they would reduce the maximum possible positive charge of the native protein by eight groups, whereas

HYDROGEN ION TITRATION CURVES OF PROTEIN

153

Cannan et al. (1941) find complete agreement between the experimental maximum positive charge and the analytical figure for Z N'.

Q . Papain Glazer and Smith (1961) have carried out a spectrophotometric titration of the phenolic groups of papain. Of the seventeen phenolic groups known to be present, eleven to twelve ionize normally (pKint = 9.8). The remainder ionize only upon denaturation, which takes place only slowly in the range of pH 12 to 13.

R. Paramyosin A detailed study of the hydrogen ion titration of clam paramyosin has recently been reported by Riddiford and Scheraga ( 1962). Essentially all the groups expected to be titratable from analytical data were found to be titrated reversibly both in 0.3 M KC1 and in a guanidine-urea mixture in which extensive denaturation had occurred. In the native state the protein is precipitated between pH 3.5 and 6.5, but this apparently did not interfere with titration, indicating that the precipitated protein is gellike in nature, permitting free passage of water and of ions to the individual molecules. Earlier Johnson and Kahn (1959) had reported that the titration curve of paramyosin has a plateau between pH 3 and pH 5. They concluded that the carboxyl groups were titrated in two distinct steps, one near pH 6 and one below pH 3. This finding would have suggested highly unusual interactions within the molecule. Riddiford and Scheraga (1962) did not find such a plateau in their studies. However, the fact that the protein is in an insoluble state between pH 3.5 and 6.5 suggests that the differences between the two sets of results may depend upon the particular conditions of preparation and handling of the protein, in a manner not yet adequately defined. The electrostatic interaction factor w for the native protein was found by Riddiford and Scheraga to be much smaller than would be expected for a compact spherical particle by Eq. ( 4 ) . In order of magnitude, the w value agreed with the value predicted for long cylindrical rods by Hill (1955). This is in agreement with the known dimensions of the paramyosin molecule. However, a considerably larger value of w was required to fit the alkaline part of the titration curve than was required for the acid branch. In the denaturing solvent, w values even smaller than those for the native state were observed. On the alkaline side, electrostatic interaction disappeared almost entirely, presumably because extensive unfolding with penetration of salt ions into the domain of the protein had occurred. The intrinsic pK values in the guanidine-urea mixture were found to be close to the normally expected values. The pK values for the native pro-

154

CHARLES TANFORD

tein were also remarkably close to expected values. Only the pK for the lysine amino groups deviated significantly from expectation, a low value of 9.65 being obtained. Spectrophotometric titration of the phenolic groups led to the conclusion that all of the fifty-eight phenolic groups present on each paramyosin molecule were titrated in the guanidine-urea mixture, but that only forty-nine were titrated in the native state in 0.3 M KC1. (All of these had an essentially normal pKint of 9.6.) This conclusion however was based entirely on the fact that the total change in absorbance at 295 mp, between neutral pH and pH 14, is about 15 % less in the native protein than in the denatured state. If the change in absorbance per group titrated were to differ in the two solvents, then the conclusion reached would have to be revised.

S. Pep& It is not possible to determine the titration curve of pepsin over a wide range of pH because autolysis, with liberation of free carboxyl and amino groups, occurs at acid pH. Titration studies have been performed (Edelhoch, 1958) in the range of pH 5 to 8, however. This is the pH range within which pepsin undergoes denaturation, and the data clearly show that more hydrogen ions are dissociated in this pH range from the denatured protein than from the native protein. The difference is greater at low ionic strength than at high ionic strength, but a difference of six H+ ions per molecule persists at ionic strengths from 0.4 to 1.0. These six H+ ions are thought to represent a difference in the number of titratable groups, the additional difference at lower ionic strength being a measure of the greater steepness of the titration curve of the denatured protein which is the result of diminished electrostatic interaction after unfolding has taken place. The simplest explanation of the difference in group count would be that native pepsin has six uncharged carboxyl groups inaccessible to titration, and that these are exposed during denaturation.

T . Peroxidase A titration study of a peroxidase from Japanese radish has been rcported by Morita and Kameda (1958). The titration curves of native protein, acid-denatured protein, and alkali-denatured protein are dramatically different. Unfortunately only continuous titration curves were obtained, so that an interpretation of the data is not possible at this time,

U. Ribonuclease The best-known feature of the titration of ribonuclease is the fact that only three of the six phenolic groups of this protein can be titrated while the protein is in its native state, as was first reported by Shugar (1952).

HYDROGEN ION TITRATION CURVES OF PROTEIN

155

These three groups have an essentially normal intrinsic pK and their titration curve yields essentially normal values for the interaction parameter w (Tanford et al., 1955a). The three phenolic groups which are not available for titration in the native protein are titrated a t 25°C near pH 13, where the protein becomes denatured. At 6"C, where the rate of denaturation is slower, a pH of 14 can be reached with only partial titration of these groups. The titration curve of ribonuclease (Tanford and Hauenstein, 1956b) is reversible between its acid end point and the onset of alkaline denaturation. All titratable groups, which are expected to be present on the basis of amino acid analysis, are found to be titrated in the expected parts of the titration curve, with the exception of the abnormal phenolic groups mentioned above. The amino and imidasole groups appear to have normal pK's, and the neutral and alkaline regions in which they occur are compatible with the same values of w as are required to fit the titration curves of the three normal phenolic groups. A second (minor) anomaly is found in the acid part of the titration curve. Although the expected number of groups is titrated, the observed values of w are anomalously large. It is possible that this is simply a manifestation of the inadequacy of the Linderstrgm-Lang treatment, as was pointed out in Section VI, C . Two alternate explanations have been proposed, neither of which deserves to be taken very seriously. (1) Tanford and Hauenstein showed that the acid part of the titration curve could be compatible with the same values of w as were used to fit the rest of the titration curve, if one were to assume that five of the ten sidechain carboxyl groups have pKi,t = 4.0, while five others have pKint = 4.7. (2) Hermans and Scheraga (1961b) showed that a fair fit of the titration data could be obtained with these same values of w, if one assumed that one of the side-chain carboxyl groups has pKint = 2.5, another has pKint = 3.65, and the remaining eight have pKint = 4.6. The existence of groups with pKint 2.5 and 3.65 was inferred from low pH conformational changes (Hermans and Scheraga, 1961a). It is to be expected that these special features of the titration curve of ribonuclease will disappear when the protein is unfolded. In agreement with this expectation, it has been found that all six phenolic groups are titrated together in ethylene glycol (Sage and Singer, 1958, 1962), in 8 M aqueous urea (Blumenfeld and Levy, 1958), and in aqueous solutions containing 5 M guanidine hydrochloride and 1.2 M urea (Cha and Scheraga, 1960). I n the guanidine-urea medium the electrometric titration curve has also been determined (Cha and Scheraga, 1960), and it was found possible to fit the entire curve with a single value of w,including all carboxyl groups as a single set with pKint = 4.6.

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CHARLES TANFORD

The only unexplained feature in these experiments concerns the value of w. In the guanidine-urea medium the ionic strength is exceedingly large, so that a very small value of w would be expected even if the protein were not unfolded. For an unfolded protein, w should become essentially zero. The value observed by Cha and Scheraga, both for the titration curve as a whole and for the spectrophotometric titration of the phenolic groups alone, is 0.056, which is almost as large as the value found for the native protein at an ionic strength of 0.15. In 8 M urea, by contrast, the expected result is obtained. Blumenfeld and Levy (1958) obtained w = 0.018 at an ionic strength of 0.1, which is far below the value expected for the native protein a t this ionic strength, as predicted for an unfolded protein molecule. Bigelow (1960) has found that all six of the phenolic groups of performic acid-oxidized ribonuclease behave normally, which is to be expected since the oxidized protein is believed to be highly unfolded. More interesting is his finding that a pepsin-inactivated preparation of ribonuclease can be prepared which contains five normal phenolic groups and one buried one. Tanford and Hauenstein ( 1956a) observed that the chromatographic minor component of one commercial preparation of ribonuclease has an isoionic point of 9.23, whereas the major component (ribonuclease A) has an isoionic point of 9.65. This difference corresponds to a difference of one tit,ratable group, so that the minor component either has one fewer amino or guanidyl group than ribonuclease A, or else it has an extra carboxyl group. Titration curves of the two components indicated that the latter explanation is correct, for the two components gave the same maximum positive charge, but a difference of one in the number of carboxyl groups. T t appears now that these experimental data were incorrect, as Eaker (1961) has found by amino acid analysis that this minor component in fact consists of two sub-components, both of which lack the N-terminal lysine residue of ribonuclease A, so that the glutamic acid residue normally in the second position becomes the terminal residue. In one of the sub-components this glutamic acid residue has itself been converted to a pyroglutamyl residue. These findings are incompatible with the unaltered maximum positive charge found by titration. (The titration curve error presumably resulted from the fact that only a small amount of the second component was available for study, so that all the data depend on a single determination.)

V . Serum Albumin The titration curve of serum albumin (Tanford et aE., 1955b) is independent of time and essentially completely reversible. However, the protein undergoes at least three changes in conformation during the course of titration. These changes are themselves rapid and reversible, so that sepa-

157

HYDROGEN ION TITRATION CURVES OF PROTEIN

rate titration curves for individual conformations cannot be obtained. The interpretation of the titration curve is thus dependent on an interpretation of conformational changes which are observed by other means. The over-all count of titratable groups is shown in Table XVI. The agreement with analytical data is excellent, except that about nine more carboxyl groups are titrated than the analysis predicts. This discrepancy has been ascribed to an erroneously high analytical estimate of amide groups, and no recent data have appeared to support or gainsay this. When the data are analyzed according to the methods of Section VI, one obtains essentially normal values of w between pH 4.3 and 10.5. The TABLEXVI Titration Data for Serum Albumin" Number of groups Type of group

a-Carboxyl Side-chain carboxyl Imidazole a-Amino Thiol Side-chain amino Phenolic Guanidino EN+

Analysis

'i

90ll

<57 18 I 22 97

Titration curve 100

18

57 19 96

pK

int,

1;:

25°C

-

4.0

10.35 -

a The data are for bovine albumin, with an assumed molecular weight of 65,OOO. Analytical data from Stein and Moore (1949); titration data from Tanford et al. (1955b). Titration data for human serum albumin (Tanford, 1950) are not significantly different.

actual values reported by Tanford et al. are somewhat below those calculated in Table 111, but Scatchard et al. (1957) have suggested that the calculated values themselves would fit the data about as well. Below pH 4.3 and above pH 10.5 there is a sharp decrease in the slopes of plots according to Eq. (14), as shown by Figs. 17 and 21. As we have pointed out in Section VI, C , such a break is an indication that a drastic conformational change occurs. The simplest possibility is that the protein becomes unfolded at these pH's. That such unfolding actually occurs is confirmed by numerous other studies by a variety of methods, including viscosity, optical rotation, etc. The experimental values of the degree of dissociation of carboxyl, amino, and phenolic groups, which were used to obtain the data of Figs. 17 and 21 were of course based on the notion that all titratable groups are accessible

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CHARLES TANFORD

to titration throughout the entire pH range of the titration curve, because the group counting procedure had produced no evidence for inaccessible groups. Furthermore, it is an inherent part of the treatment of Section VI that any given group has the same pKint value throughout the course of titration. As was noted in Section VI, 6 ,however, these assumptions need no longer hold true if conformational changes occur which indicate (as they do here) that most of the groups are in fact titrated with the protein no longer in the native state. It now becomes possible that the count of

11.5 h

w

I

rl \

v

w

2? 11.0 I %i 10.6

-60

~-

-40

2

-80

-100

FIG.21. Titration data for the phenolic groups (upper curve) and the side-chain amino groups (lower curve) of bovine serum albumin, a t 25°C and ionic strength 0.15, plotted according t o Eq. (14) (Tanford rt al., 1955b).

titratable groups in Table XVI does not apply to the native protein or that, pKintvaluesin the native protein differ from those which apply to the conditions under which most of the groups are actually titrated. This possibility was not considered by Tanford et al. It was assumed t h a t the conformational change involved only unfolding, without ot,her change. The p I L values which then result from the customary analysis are shown in Table XVI. It is seen that they are all somewhat abnormal. The value for the phenolic groups is a little higher than expected, and the pK's for imidazole and side-chain amino groups are somewhat lower. As was pointed out in Section VI, D, deviations in the same directions occur for these groups in many proteins, and they may have their origin in the

159

HYDROGEN ION TITRATION CURVES OF PROTEIN

hydrophobic nature of the side chains of which these dissociable acidic groups are a part. A more unusual anomaly is the pKint of 4.0 for sidechain carboxyl groups. The anomaly is within the limits of variation allowed by the explanations for small differences in pKint which were given in Section VI, D, 3. It is however unexpected that any of the possible causes listed there should apply equally to almost one hundred side-chain carboxyl groups. (The data of Figs. 17 and 21 are based on true values of so that the anomaly cannot be due to a mistaken location of the point = 0.) The anomalous pKint for the carboxyl groups just cited is one reason which suggests the desirability of a deeper probe into the titration curve of serum albumin and its relation to the conformational changes which this protein undergoes. An even more compelling reason lies in the detailed study of the conformational changes themselves. (Only those on the acid side have been studied in detail.) Much of the work in this area has been done by Foster and co-workers (the earliest paper being by Yang and Foster, 1954), and it has been recently reviewed by Foster (1960). These studies show that the conformational change near pH 4 occurs in at least two stages, each of which may itself consist of several successive steps. The first stage is the so-called N + F transition, which does not involve an appreciable expansion of the molecule, but which may involve an uptake a t constant pH of about twelve hydrogen ions per molecule. In other words, in the region near pH 4 there appear to be present two kinds of serum albumin molecules, which do not differ in size but do differ in charge by 12, the form F having the greater number of bound hydrogen ions. The second stage of the reaction is the expansion of the F form, brought about by electrostatic repulsion between positive charges as the pH is reduced from pH 4 to 2. From the point of view of the analysis of the titration curve, these oonformational studies create a problem because the major part of the apparent decrease in w (Fig. 17) , at least at the higher ionic strengths, occurs during the first stage of the reaction, where little expansion occurs. I t is evident then that a large part of the anomalous behavior seen in Fig. 17 cannot in fact represent an actual decrease in w,due to expansion, without other change. It becomes necessary to explain the conformational change either by supposing that the number of titratable carboxyl groups is not the same in the two conformations, or that the number is the same, but pKint is different. The first alternative leads t o the conclusion that the native eonformation contains about thirty-six buried carboxyl groups, in the carboxylate ion form. It is not possible to bury charged groups in the interior of a protein molecule unless they are associated with an equal number of positively charged groups. There is however no evidence that thirty-six positively charged buried groups (i.e., groups with abnormally high pK)

z

z,

160

CHARLES TANFORD

exist. On the contrary, the side-chain amino groups, which do have an abnormal pK, deviate from expectation in the opposite direction. The second alternative is that the N and F forms contain the same number of groups, but with different pKint. Aoki and Foster (1957) have found that this possibility is indeed compatible with all known facts, the pKint values which are required being 3.7 for the native conformation, and an essentially normal value of 4.4 for the F conformation. The Aoki-Foster hypothesis, while satisfactorily correlating the data of Fig. 17 with data on the conformational change at low pH, thus increases the anomaly in the intrinsic pK of the carboxyl groups of the native protein. We now have pKint = 3.7 instead of the former value of 4.0. It should be noted in fact that the problem of the value of pKint is really independent of the mechanism proposed to account for the shape of the titration curve. The pH at which 2, of serum albumin is zero falls about 0.5 pH units lower than one would estimate on the basis of the expected pK’s of the groups known to be present, and to account for this is difficult regardless of the conformational changes which serum albumin undergoes. Of the explanations which were offered in Section VI, D for small pK anomalies, one (mistaken identification of 2, with 2 ) is not applicable here, and one (hydrophobic interactions) would lead to an anomalously high pKint. The other explanations can lead to a low pKint, but only if all one hundred carboxylate anions are involved in some stabilizing interaction which becomes weakened when the groups are converted to their acidic form. Only positively charged cationic groups would seem capable of interacting with carboxylate ions in this way, but if they did they would themselves acquire anomalously high pK values. Experimentally, it is found that the pKint of the fifty-seven side-chain amino groups is itself very low, and that of the seventeen imidazole groups is certainly not higher than is normal. These groups together comprise three-quarters of the available positively charged groups. The final solution to this problem must await future research.

W . Thyroglobulin Preliminary titration data have been reported (Edelhoch, 1960; Edelhoch and Metzger, 1961). They show that denaturation by various means facilitates titration of both phenolic and carboxyl groups. The data are not sufficiently detailed to permit a decision as to whether a difference in the count of titratable groups is involved.

X . Trypsinogen The titration of the phenolic groups of trypsinogen has been studied by Smillie and Kay ( 1961). Four groups are titrated reversibly with a normal

HYDROGEN ION TITRATION CURVES OF PROTEIN

161

pK. Four more are titrated at much higher pH, with a steep titration curve suggesting that their titration is accompanied by unfolding. That such unfolding occurs is confirmed by studies of sedimentation and viscosity. Both the titration and the conformational change are reversible at 10°C, but not at higher temperatures.

Y . Trypsin Titration curves of trypsin were obtained under a variety of conditions by Duke et al. (1952). The most noteworthy feature is a specific effect of calcium, which displaces the acid part of the titration curve to lower pH, and decreases the total number of groups which are titrated between pH 6 to 9. It is likely that the groups titrated between pH 6 and 9 in the absence of Ca++ are a-amino groups, produced by self-digestion of the enzyme. The effect of Ca” thus appears to result from a complex with the carboxyl groups of the protein, which stabilizes the anionic form of these groups so as to produce the displacement of the acid part of the titration curve. This complex is more resistant to self-digestion than the enzyme alone. ACKNOWLEDGMENTS The preparation of this review was supported by research grants from the National Science Foundation and from the National Institute of Arthritis and Metabolic Diseases, United States Public Health Services. The author wishes to express his indebtedness to Drs. F. R. N. Gurd, G. P. Hess, W. Kauzmann, H. A. Saroff, J. Steinhardt, B. L. Vallee, and P. E. Wilcox, for providing him with results of investigations in advance of publication.

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Cannan, R. K., PaImer, A. H., and Kibrick, A. C. (1942). J . Biol. Chem. 142,803. Carr, C. W. (1953). Arch. Biochem. Biophys. 46, 424. Carr, C. W. (1955). In “Electrochemistry in Biology and Medicine” (T. Shedlovsky, ed.), Chapter 14. Wiley, New York. Carr, C. W. (1956). Arhc. Biochem. Riophys. 62, 476. Cha, C.-Y., and Scheraga, H. A. (1960). J . Am. Chem. SOC.82, 54.

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Charlwood, P. A., and Ens, A. (1957). Can. J . Chem. 36, 99. Coleman, J. E., and Vallee, B. L. (1961). J . B i d . Chem. 236,2244. Coryell, C. D., Stitt, F., and Pauling, L. (1937). J . A m . Chem. SOC.69. 633. Crammer, J. L., and Neuberger, A. (1943). Biochem. J . 37,302. Danckwerts, P. V. (1952). Research (London) 6, 363. Dintzis, H. (1952). Ph.D. Thesis, Harvard University, Cambridge, Massachusetts. Donovan, J. W., Laskowski, M., Jr., and Scheraga, H. A. (1959). J . Mol. Biol. 1, 293 Donovan, J. W., Laskowski, M., Jr., and Scheraga, H. A. (1960). J . A m . Chem. Sac. 82, 2154. Donovan, J. W . ,Laskowski, M., Jr., and Scheraga, H. A. (1961). J . A m . Chem. Sac. as, 2686. Duke, J. A., Bier, M., and Nord, F. F. (1952). Arch. Biochem. Biophys. 40, 424. Eaker, D. (1961). J . Polymer Sci. 49, 45. Edelhoch, H. (1958). J. A m . Chem. SOC.80, 6640. Edelhoch, H. (1960). J. Phys. Chem. 64, 1771. Edelhoch, H., and Metzger, H. (1961). J . A m . Chem. SOC.85, 1428. Edmundson, A. B., and Hirs, C. H. W. (1961). Nature 190, 663. Edsall, J. T. (1943). I n “Proteins, Amino Acids and Peptides” (E. J. Cohn and J. T. Edsall, eds.), Chapter 4, 5, 20. Reinhold, New York. Edsall, J. T., and Wyman, J. (1958). “Biophysical Chemistry.” Vol. I, Chapter 8, 9. Academic Press, New York. Ehrlich, G., and Sutherland, G. B. B. M. (1954). J . A m . Chem. Sac. 76, 5268. Folsch, G., and osterberg, R . (1959). J . B i d . Chem. 234, 2298. Foster, J. F. (1960). I n “ThePlasmaProteins” (F. W. Putnam, ed.), Vol. I, Chapter 6. Academic Press, New York. Fredericq, E. (1954). J . Polymer Sci. 12, 287. Fredericq, E. (1956). Ph.D. Thesis, Universite de Liege. George, P., and Hanania, G. (1952). Biochem. J . 62, 517. George, P., and Hanania, G. (1953). Riochem. J . 66, 236. George, P., and Hanania, G. (1957). Biochem. J . 66, 756. German, B., and Wyman, J., Jr. (1937). J . B i d . Chem. 117,533. Glazer, A. N., and Smith, E. L. (1961). J . B i d . Chem. 236. 2948. Gordon, W. G., Basch, J. J., and Kalan, E. (1961). J . B i d . Chem. 236, 2908. Gruen, L., Laskowski, M., Jr., and Scheraga, H. A. (1959a). J . A m . Chem. Sac. 81, 3891. Gruen, L., Laskowski, M.. Jr., and Scheraga, H. A. (1959b). J . 12iol. Chem. 234, 2050. Gurd, F. R. N., and Wilcox, P. E. (1956). Advances in Protein Chem. 11, 311. Harrington, W. F. (1955). Biochim. et Biophys. Acta 18, 450. Havsteen, B. H., and Hess, G. P. (1962). In press. Hermans, J., Jr. (1962). Biochemistry 1, 193. Hermans, J., Jr., and Scheraga, H. A. (1961a). J . A m . Chem. Sac. 83, 3283. Hermans, J., J r . , itrid Scheraga, H. A. (1961b). .F. Am. Chehem. Sac. 83, 3293. Hill, T. I,. (1955). Arch. Biochem. Biophys. 67, 229. Jacobsen, C. F., LBonis, J., Linderstr0m-Lang, K., and Ottesen, M. (1957). In “Methods of Biochemical Analysis” (D. Glick, ed.), Vol. IV. Interscience, New York. Johnson, W. H., and Kahn, J. S. (1959). Science 130, 1190. Karush, F., and Sonenberg, J. (1949). J . A m . Chem. SOC.71, 1369.

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