Disulfide bond formation in proteins

[19]

DISULFIDE BOND FORMATION

305

[19] D i s u l f i d e B o n d F o r m a t i o n in P r o t e i n s

By THOMAS E. CRE1GHTON Disulfide bond formation between cysteine (Cys) residues is one of the posttranslational modifications most dependent on the conformation of the protein. For a disulfide bond to be formed between them, two Cys residues must have their alpha carbon atoms within 4-9 .~ of each other, and the adjoining peptide backbones must also be in the proper orientation so that all five bond rotations between the side-chain atoms can adopt favorable conformations, as is found in proteins of known crystal structure. ~,2 Which Cys residues of a protein are joined in a disulfide does not depend simply upon the number of amino acid residues between them in the polypeptide chain. The known disulfides have no characteristics to indicate that they are greatly different from the other types of interactions between amino acid side chains in proteins, in that they are determined largely by the protein conformation, while, together with all the other interactions, contributing to its stability. The covalent nature of disulfides gives them some unique and useful properties, although it has also served to inspire some unfortunate myths about their roles in proteins. A common one is that they are irreversible covalent cross-links that determine the folded structure by limiting the conformations that are possible. This obviously cannot be true at the time and under the conditions when the protein disulfides are formed; otherwise, other or no disulfides would be formed. Disulfides are also often considered to be part of the protein primary structure, probably because they are often determined in the course of a primary structure determination, but they should not be so considered. 3 Little is known about the in vivo mechanism of protein disulfide bond formation. The few studies with biosynthesis of secreted proteins have indicated that disulfides are incorporated during or shortly after secretion of the nascent chain into the endoplasmic reticulum, ~6 but not how or why.

i j. S. Richardson, Adv. Protein Chem. 34, 167 (1981). 2 j. M. Thornton, J. Mol. Biol. 151, 261 (1981). 3 I U P A C - - I U B Commission on Biochemical Nomenclature, J. Mol. Biol. 52, l (1970). 4 L. W. Bergmann and W. M. Kuehl, J. Biol. Chem. 254, 5690 (1979). G. Scheele and R. Jacoby, J. Biol. Chem. 257, 12277 (1982). 6 T. Peters and L. K. Davidson, J. Biol. Chem. 257, 8847 (1982).

METHODS IN ENZYMOLOGY,VOL. 107

Copyright © 1984by Academic Press, Inc. All rights of reproduction in any formreserved. ISBN 0-12-182007-6

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OXIDATIONS, HYDROXYLATIONS, AND HALOGENATIONS

[19]

In vitro studies of disulfide bond reduction and re-formation in intact proteins have elucidated many of the details of disulfide formation, but only in a few proteins. Nevertheless, they demonstrate that whether, and which, Cys residues are linked in disulfides depends upon both the conformation of the protein and the redox potential of the environment. 7,8 A disulfide bond has no inherent stability, relative to the thiol moiety, but is dependent upon the relative concentrations of appropriate electron donors and acceptors. With a given redox potential, the stabilities of the different disulfides possible between different Cys residues depend upon the degree to which the protein conformation keeps each pair of Cys residues in proximity when no disulfide is present. This can be expressed and measured as the effective concentration of the two thiol groups, which is given by the stability of the protein disulfide relative to that of a comparable intermolecular disulfide. 9 Those with very high effective concentrations, due to the protein structure keeping the thiol groups in favorable proximity for forming a disulfide, may form a stable disulfide, even in a relatively reducing redox environment. Cys residues that might only rarely be in suitable proximity, either owing to flexibility of the protein or the need to strain it to form a disulfide, will form less stable disulfides that would be present only in more oxidizing environments. Cys residues that are kept apart by a folded protein conformation should not form a disulfide bond. Other considerations, such as the accessibilities and electrostatic environments of the Cys residues, can also affect somewhat their tendency to form disulfides. Once formed, disulfides stabilize the conformation that brought them together, so protein conformation and disulfide bond stability are linked functions and dependent upon each other. Protein disulfide formation in vivo as a posttranslational modification would then be expected to depend upon both the conformation and the environment of the polypeptide chain during and after biosynthesis; very little is known about either. Extrapolations from the in vitro results may be informative, 7,s but the in vivo process should be amenable directly to study with the appropriate protein biosynthesis system, using the techniques that have been developed in vitro. Those techniques and the major observations will be presented here.

7 T. E. Creighton, Prog. Biophys. Mol. Biol. 33, 231 (1978). 8 T. E. Creighton, Adv. Biophys. (in press). 9 T. E. Creighton, in "Functions of Glutathione: Biochemical, Physiological, Toxicological, and Clinical Aspects" (A. Larsson, S. Orrenius, A. Holmgren, and B. Mannervik, eds.), p. 203. Raven, New York, 1983.

[19]

DISULFIDE BOND FORMATION

307

Chemistry of Disulfide Formation Disulfides do not form spontaneously between thiols, even when in close proximity, unless there is an appropriate electron acceptor (A) present. 2--SH + A ~--S--S--

+ AH2

(l)

Numerous acceptors are possible and have been used, depending upon the purpose of the study. The classic oxidant has been 02, but the chemical reaction is not understood; consequently, interpretation of different rates of disulfide formation is not possible. The reaction is apparently dependent upon metal ions, such as Cu 2+, which transiently bind to the thiol group. They act catalytically in low concentrations, so the rate is difficult to control, unless large concentrations are added, when they become part of the system. The greatest practical difficulty with the oxidation reaction is that hydrogen peroxide and radicals such as superoxide anion are produced/TM which can then react with other parts of the protein. Such side reactions should be minimized in all studies of disulfide bond formation and breakage by excluding air and other oxidants. Apparent covalent modifications of unknown nature have always occurred in both the oxidized and reduced forms of ribonuclease A and have seriously hindered my studies with this protein 12; they may have arisen from only small extents of oxidation of protein and reagent thiols produced by residual oxygen. The most pertinent electron donor and acceptor to use would be the one that is involved in vivo, but its identity is unknown. Glutathione (GSH) in its oxidized form, GSSG, is the most likely candidate owing to its ubiquity and relatively high concentrations in most organisms.13 Glutathione interacts chemically with all thiols and disulfides in the thioldisulfide exchange reaction GSH + RSSR ~ GSSR + RSH GSH + GSSR ~,~ GSSG + RSH

(2)

(3)

This reaction has the advantage of being rapid at alkaline pH (since the thiolate anion is the actual reactive species), simple, extremely specific,

l0 H. P. Misra, J. Biol. Chem. 249, 2151 (1974). N M. Costa, L. Pecci, B. Pensa, and C. Cannella, Biochem. Biophys. Res. Commun. 78,596 (1977). ~2T. E. Creighton, J. Mol. Biol. 129, 411 (1979). ~3A. Larsson, S. Orrenius, A. Holmgren, and B. Mannervik, eds., "Functions of Glutathione: Biochemical, Physiological, Toxicological, and Clinical Aspects." Raven, New York, 1983.

308

OXIDATIONS, HYDROXYLATIONS, AND HALOGENATIONS

[19]

and easy to control (see Wetlaufer, this volume [18]). The rate of the reaction depends primarily on the concentrations of the reactants, but also somewhat on the nature of the groups attached to the sulfur atoms, the ionic strength, temperature, pH, etc. Unless the thiol group is situated within a folded protein, where its environment may be drastically perturbed, these other factors affect the thiol-disulfide exchange reaction in generally straightforward ways, and different rates of forming and breaking disulfides usually may be interpreted with some degree of confidence. For example, the rate at which a thiol group reacts is predictable from its pKa v a l u e . 14 The reactivity of a model disulfide also depends somewhat upon its electrostatic environment, but in a way that is predictable from the pKa value of the thiol produced, and this effect is minimized at high ionic strengths (Fig. 1). Energetically strained disulfides react more rapidly, as in lipoic acid, which reacts 160-fold more rapidly than otherwise expected, presumably because the five-membered ring prevents normal disulfide geometry.~5 More stable, intramolecular disulfides react more slowly, if at all; for example, GSH is unable to reduce to any significant extent the disulfide of oxidized dithiothreitol (DTT s) or that between Cys-14 and -38 in bovine pancreatic trypsin inhibitor (BPTI). In both of these molecules, the reverse reaction is extremely fast, with a half-time of about 10 -6 sec, since the two free thiol groups generated are kept in reasonable proximity. The effective concentrations of the two thiol groups in these reduced molecules are both about 104 M, 9'15-17 so that the intramolecular disulfides are highly favored.

HO,[7"--s" K" IO*M osso

+

"----"

"°T-"'~ s 2 os.

+

(4) SH DTTsH

DTT~

The rates of model thiol-disulfide interchange reactions may be readily measured under a variety of conditions using DTTSnn and a variety of model disulfides, since DTT s absorbs substantially at 260-310 nm ~6,~8and because the above two-step reaction is rate-limited by only the first step, giving simple kinetics.

14 Z. Shaked, R. P. Szajewski, and G. M. Whitesides, Biochemistry 19, 4156 (1980). 15 T. E. Creighton, J. Mol. Biol. 96, 767 (1975). 16 W. W. Cleland, Biochemistry 3, 480 (1964). 17 R. P. Szajewski and G. M. Whitesides, J. Am. Chem. Soc. 102, 2011 (1980). t8 K. S. Iyer and W. A. Klee, J. Biol. Chem. 248, 707 (1973).

[19]

DISULFIDE BOND FORMATION

~

©

309

• 6M OuHCI

"'ll ...........~ ............. ~X~

..............

1

0

8

i

i

9

10 PKRsH

FIG. 1. Reactivities of different disulfides in the thiol-disulfide exchange reaction in three different aqueous solutions at 25°. The logarithm of the second-order rate constant for reduction by dithiothreitol, k (in units of sec -~ M-l), is plotted versus the pKa value in water of the thiol group produced. In order of increasing pK a value, the disulfides were cystamine, glutathione disulfide, hydroxyethyl disulfide, and dithiodiglycolic acid. The rates were measured from the increase in absorbance at 283 nm resulting from the disulfide form of dithiothreitol. In each case, the buffer was 0.10 M Tris-HC1 (pH 8.7), 0.20 M KC1, 1 mM EDTA, with the indicated additions. The electrostatic properties of the disulfide reagents in aqueous solution affect equally their reactivity in thiol-disulfide exchange and the ionization in water of the thiol group product of the reaction, since the solid line has a slope of unity. This electrostatic effect is apparently suppressed by the high ionic strength of 6 M guanidinium chloride, and the disulfides are more equally reactive. Taken from Creighton. 2~

Upon adding a disulfide reagent to a reduced protein, two sequential thiol-disulfide exchange reactions are required to form one protein disulfide. The first is the simple chemical reaction between the disulfide reagent and one Cys thiol group, to generate the mixed disulfide. SH

+ RSH

+ RSSR k.-~ HS

(5)

310

OXIDATIONS, HYDROXYLATIONS, AND HALOGENATIONS

[19]

This reaction is bimolecular in both directions, so the rates should be dependent upon the concentrations of the disulfide and thiol forms of the reagent. The second step is the one in which a second Cys thiol group reacts with the mixed disulfide to form the protein disulfide.

4- RSH

(6)

This step is intramolecular in the forward direction, and its rate depends primarily upon the tendencies of the thiols of different Cys residues to come into proximity of the mixed disulfide, which is determined primarily by the protein conformation. Adding excess disulfide reagent to a reduced protein will result in all accessible Cys residues becoming involved in either intramolecular or mixed disulfides, unless sufficient concentrations of thiol reagent are also present to make the reverse steps significant. Otherwise, the mixed-disulfide form of a Cys residue will accumulate to significant levels only if no other Cys residue reacts with it in the second step [reaction (6)] as rapidly as it was formed in the first step [reaction (5)]. On the other hand, the intramolecular step in protein disulfide formation can occur on the 10 - 6 sec time scale, so the mixed disulfide does not then accumulate. The rate of forming such a protein disulfide is then determined by the rate of the first step. Since accessible Cys thiols tend to have similar reactivities, 19 they tend to form disulfides at similar rates with such disulfide reagents, even though the second steps differ in rate. This can be an advantage, in that it ensures that intermediates in disulfide formation accumulate to significant levels, since all the disulfides tend to be formed at comparable rates. Other possible intramolecular steps are rearrangements of protein and mixed disulfides [reactions (7) and (8)].

~

k#$SR

~9 T. E. Creighton, J. Mol. Biol. 96, 777 (1975).

~

SH

(7)

[191

DISULFIDE BONDFORMATION

311

.

(8)

Other studies of protein disulfide formation have utilized as starting material the protein in which all Cys groups are present initially as mixed disulfides with a reagent, z° Intramolecular protein disulfide formation is then initiated by adding catalytic amounts of the thiol form of the reagent [reaction (9)]. SH

" ~ RSS " ~

;

_

_

U

+ RSH

(9)

This procedure may have the practical benefit of using a more soluble starting form of the protein; reduced proteins are often notoriously insoluble, and this can be a severe technical problem. An appropriate mixed disulfide on each Cys residue can improve the solubility in some cases. However, this procedure appears to have the complication that the nature of the starting protein has been altered, in that the reagent is part of the initial protein, and that the concentrations of the thiol and disulfide forms of the reagent will fluctuate greatly during the reaction. It can also be difficult to ensure that the starting protein has all Cys residues in mixed disulfides. It is generally prepared by adding a large excess of a linear disulfide reagent to the reduced protein in an unfolding solvent; formation of mixed disulfide must then compete with intramolecular disulfide formation [reactions (6) and (9)]. However, the rate of forming intramolecular disulfides within even an unfolded protein in 8 M urea can be very rapid, 21 and it has been found to be impossible to generate only mixed disulfides with BPTI. Otherwise, the procedure using the mixed disulfide is exactly analogous to that described here using the reduced protein, except that the roles of the Cys thiol and mixed disulfides are reversed.

20 R. A. Bradshaw, L. Kanarek, and R. L. Hill, J. Biol. Chem. 242, 3789 (1967). 21 T. E. Creighton, J. Mol. Biol. 113, 313 (1977).

312

OXIDATIONS, HYDROXYLATIONS, AND HALOGENATIONS

[19]

Choosing a Disulfide Reagent Metabolites other than glutathione have been proposed as in vivo participants in disulfide bond formation in proteins, 22,23 often in conjunction with an appropriate enzyme. The impetus for these suggestions has usually been the mistaken belief that the GSH and GSSG levels in cells are too reducing to allow protein disulfide bond formation, since most of the glutathione is present as GSH.13,24 However, because they are intramolecular, protein disulfides may be much more stable than those between unlinked groups, as in GSSG, when two molecules result from reduction of the disulfide. Where the folded protein conformation keeps two Cys thiol groups in appropriate proximity, they may have effective concentrations of up to 10 7 M , 9 possibly higher, 25,26 and thus a disulfide bond between them is much more stable than one between two different molecules (e.g., GSH) present at practical or physiological concentrations of about 10-2 M. Proposals of other means of forming protein disulfides have unnecessarily attempted to insulate the protein disulfide redox potential from that controlling the other thiol-disulfide status of the cell, 22 but the two are certain to be linked, since all thiols and disulfides would participate in the chemical thiol-disulfide exchange reaction, even in the absence of the many known enzymes or other catalysts. Consequently, thiol-disulfide exchange involving the ubiquitous, abundant GSSG, or any other disulfide reagent, is the most favorable procedure for generating disulfides in proteins in vitro. Which particular reagent is used depends upon what techniques are to be used to trap, analyze, and identify the species generated (i.e., the charge and other chemical properties it will give the protein if attached via a mixed disulfide). It must be remembered also that the reagent will be part of the protein in the course of disulfide formation and thus has the potential for affecting the protein conformation and disulfide bond formation. Use of different reagents should uncover such phenomena. GSSG has been observed to have no such effects with at least some proteins and is comparable to other disulfides. It has the added advantage of possessing one net negative charge on each half, which is useful when analyzing for protein mixed disulfides.

22 D. M. Ziegler and L. L. Poulsen, Trends Biochem. Sci. 2, 79 (1977). 23 V. G. Janolino, M. X. Sliwkowski, H. E. Swaisgood, and H. R. Horton, Arch. Biochem. Biophys. 19L 269 (1978). 24 G. Harisch, J. Eikemeyer and J. Schole, Experientia 35, 719 (1979). 25 M. I. Page and W. P. Jencks, Proc. Natl. Acad. Sci. U.S.A. 68, 1678 (1971). 26 A. J. Kirby, Adv. Phys. Org. Chem. 17, 183 (1980).

[19]

DISULFIDE BOND FORMATION

313

Disulfide formation using a stable cyclic reagent, such as oxidized dithiothreitol (DTTS), ~6 is much more discriminating than with a linear reagent. The mixed disulfide is energetically unfavorable and rapidly dissociates intramolecularly, so it should not accumulate significantly. Only very favorable protein disulfides are formed with this reagent, at a rate that should be proportional to the rate of the intramolecular step of reaction (10).

k

+DTT KDTT .

*ntra m

~

+DTTS~

(10)

L SH k obs= k

.....

KDTT

Purification of DTT s These measurements require that the DTT s be very pure, as c o m m o n impurities have less stable disulfides that react much more rapidly; consequently, even relatively minor impurities can dominate the observed kinetics. Fortunately, they can be preferentially reduced by DTTsSH H and removed on the basis of their thiol groups, as in the following purification p r o c e d u r e . 27

Commercially purchased DTT s (2 g) is dissolved in 100 ml of 0.1 M NH3 at room temperature, under an atmosphere of N2, and approximately 200 mg of DTTSH H is added. Thiol-disulfide exchange to reduce preferentially less stable disulfides is permitted for about 3 hr. Any insoluble material is then removed with a paper filter. All thiol-containing compounds are removed by passing the solution through a 1.5 cm diameter × 17 cm length column of Amberlite IRA-410 in the H O - form. The column is washed extensively with water to recover most of the DTT s, which tends to adhere to the column; DTTss is monitored by its absorbance at 283 nm (molar extinction coefficient = 273 c m - l ) . J6 The efficiency of the column is confirmed by the absence of thiol groups. 28 The DTT s is recovered by lyophilization and stored at 4 °. It has a melting point of between 130 and 131 ° and is significantly more soluble in water than the original material. This purification procedure would not be expected to remove any impurities with more stable disulfides, but in small quantities they should 27 T. E. Creighton, J. Mol. Biol. 113, 295 (1977). 28 G. L. Ellman, Arch. Biochem. Biophys. 82, 70 (1959).

314

OXIDATIONS, HYDROXYLATIONS, AND HALOGENATIONS

[19]

not affect significantly the kinetics of disulfide bond formation. All other disulfide and thiol reagents have been obtained commercially and used without further purification.

Choosing the Conditions A wide variety of conditions may be used, dependent upon the individual protein and questions to be studied. The one essential requirement is that the pH be neutral or alkaline, since the rate of the thiol-disulfide interchange reaction is dependent upon ionized thiols, the pKa values for which are generally in the region of 8 to 10. Covalent modifications of proteins become significant at very alkaline pH values, so most studies have been done at between pH 7 and 9; the values of rate and equilibrium constants given here were obtained at pH 8.7 and 25°. Ionization of protein thiol groups might also affect protein conformation; in particular, it may destabilize any folded conformation in which the thiol groups would be buried in a nonpolar environment, as they often are if involved in disulfide bonds. It is probably one factor that contributes to the tendency of reduced proteins to be unfolded. Other than pH, the thiol-disulfide exchange reaction appears to be little affected by other variables, such as buffers and temperature, z9 High ionic strength diminishes the electrostatic difference between different thiols and disulfides (Fig. 1), in the same way that it diminishes electrostatic interactions in proteins. Different salts may be added to diminish or increase hydrophobic interactions, according to the Hofmeister series. Denaturants such as urea and guanidinium chloride have little effect on thiol-disulfide exchange (Fig. 1), but large effects on protein conformation. 2~ Enzymes that catalyze thiol-disulfide exchange may also be included 3° (see Hillson et al., this volume [16]). On the other hand, some unidentified factors can interfere with proper folding and disulfide formation. Initial experiments carried out in plastic containers gave poor yields of correctly refolded BPTI and numerous atypical intermediate species, so all folding procedures are routinely performed in glass vessels. Even so, BPTI refolding reactions have suddenly become aberrant on a few occasions; filtration through activated charcoal of all solutions involved in the refolding mixture has always alleviated this problem. The basis for these phenomena has not been investigated.

29 T. E. Creighton, J. Mol. Biol. 144, 521 (1980). 3o T. E. Creighton, D. A. Hillson, and R. B. F r e e d m a n , J. Mol. Biol. 142, 43 (1980).

[19]

DISULFIDE BOND FORMATION

315

Trapping Species The order of disulfide bond formation in a protein can be determined only from the intermediate states that comprise the kinetic pathway. These intermediates are transient and will persist only if they are trapped in some way. All protein species with free thiol groups are inherently unstable, with respect to both oxidation and participation in thiol-disulfide exchange; those encountered as transient intermediates in a multistep process are likely to be least stable. However, disulfide bond formation, breakage, and interchange can be quenched to trap such intermediates in a stable form. The trapped intermediates are sufficiently stable to be characterized in virtually any manner at one's leisure; it is necessary only to avoid conditions that might permit disulfide rearrangements. With any trapping procedure, there is always the possibility that the quenching reaction could alter the spectrum of species present originally at the time of quenching. For example, some of the species present in a rapid equilibrium might react more rapidly than the others and thereby be trapped in elevated quantities, or the quenching reaction at one site could cause changes, such as disulfide rearrangements, at other parts of the protein. Such conceivable complications can be minimized by using a quenching reaction that is much more rapid than any other steps in the reaction being studied and has no substantial effects on the protein conformation. Protonation of thiol groups by acidification quenches thiol-disulfide exchange, is extremely rapid, and produces a negligible change in the thiol groups, although it can affect protein conformation. The main drawback is that quenching is not complete or irreversible, since the thioldisulfide exchange reaction is not abolished, merely slowed, decreasing by a factor of 10 for each pH unit decrease below the pKa value. Intramolecular thiol-disulfide interchanges can occur on the 10 6-sec time scale at pH 8, so they would be expected to occur on the second time scale at pH 2. Such a phenomenon has been observed with the initial two-disulfide intermediates of BPTI trapped by acid; they rearrange intramolecularly to the native-like species with the 30-51, 5-55 disulfide bonds during electrophoresis at acid pH and are not detectable in this way. Similar phenomena are almost certain to have occurred with other studies that have utilized only acid-trapping, 31-36 but would not have been detected; they

31 L. G. C h a v e z and H. A. Scheraga, 32 L. G. C h a v e z and H. A. Scheraga,

Biochemistry 16, Biochemistry 19,

1849 (1977). 996 (1980).

316

OXIDATIONS, HYDROXYLATIONS, AND HALOGENATIONS

[19]

probably account for the contradictory results obtained. 32,37 Any lengthy studies of acid-trapped species must be suspect, particularly if they are incubated with thiol- or disulfide-containing materials, such as antibodies.31, 32 Reaction of thiols with reagents such as iodoacetic acid and iodoacetamide is irreversible under essentially all conditions and has been used extensively. Normal, accessible protein thiol groups react with these reagents with rate constants of between 2 and 16 sec -1 M -j (Fig. 2), so the half-time for reaction with reagent added to a final concentration of 0.1 M should be 0.4-3 secs. Consequently the reaction is not instantaneous, even with such high concentrations of reagents, and the possibility that it has perturbed the spectrum of species originally present should be checked by comparing different reagents. In the case of disulfide bond formation in BPTI, it was shown that 0.1 M iodoacetamide and iodoacetare trapped the same species, in the same proportions, including the same intrinsically unstable one- and two-disulfide intermediates. 37,38 The one-disulfide intermediates were the same as those trapped with acid, which acts much more rapidly. Also, extensive variation of the conditions of refolding has demonstrated that the species trapped with iodoacetate reflect the conditions of refolding, not the trapping conditions. 21,29 The difficulty with these reagents is that inaccessible thiol groups do not react, 39 and one two-disulfide species of BPTI was missed in the early studies because it folded into a native-like conformation with the Cys 30 and 51 thiols buried. It could be trapped only by adding denaturants after the iodoacetic acid, to make accessible the two thiol g r o u p s , a° However, substantial rearrangements of the two disulfides occurred in this process, presumably upon unfolding and before reaction of the thiols. This is an intrinsic problem of all such studies when the protein folds up, and it also illustrates the necessity of blocking irreversibly all thiol groups to prevent intramolecular thiol-disulfide exchange. However, if a denaturant is to be added to unmask inaccessible thiol groups, it should be added after the reagent has trapped most species; if both are added at the same time, 41~3 33 y . Konishi and H. A. Scheraga, Biochemistry 19, 1308 (1980). 34 y . Konishi and H. A. Scheraga, Biochemistry 19, 1316 (1980). 35 y . Konishi, T. Ooi, and H. A. Scheraga, Biochemistry 20, 3945 (1981). 36 y . Konishi, T. Ooi, and H. A. Scheraga, Biochemistry 21, 4734 (1982). 37 T. E. Creighton, J. Mol. Biol. 87, 579 (1974). 38 T. E. Creighton, J. Mol. Biol. 87, 603 (1974). ~9 y . Goto and K. Hamaguchi, J. Mol. Biol. 146, 321 (1981). 40 D. J. States, C. M. Dobson, M. Karplus, and T. E. Creighton, J. Mol. Biol., in press. 41 A. S. Acharya and H. Taniuchi, J. Biol. Chem. 251, 6934 (1976). 42 W. L. Anderson and D. B. Wetlaufer, J. Biol. Chem. 251, 3147 (1976). 43 T. Dubois, R. Guillard, J.-P. Prieels, and J. P. Perraudin, Biochemistry 21, 6516 (1982).

[19]

DISULFIDE BOND FORMATION

4

01234

5

317

61AT

6

Migration

FIG. 2. Electrophoretic analysis of the kinetics of reaction of the Cys thiol groups of reduced BPTI with iodoacetate. Fully reduced BPTI (30/zM) was incubated at 25° in 0.10 M Tris-HCl (pH 8.7), 0.20 M KC1, 1 mM EDTA, and 2.5 mM iodoacetic acid. At the indicated times, the reaction was stopped by addition of iodoacetamide to 0.1 M. The protein molecules with the indicated number of acidic carboxymethyl groups were resolved by 15% polyacrylamide gel electrophoresis, using the discontinuous buffer system of R. A. Reisfield, U. J. Lewis, and D. E. Williams [Nature (London) 195, 281 (1962)]. Densitometer traces of Coomassie Blue-stained gels are shown. Computer simulations of these kinetics indicate that the first to last thiol groups to react with iodoacetate do so with second-order rate constants varying from 5.2 to 2.2 sec ~M t. The protein molecules with one carboxymethyl group were isolated by cation exchange and shown to have the carboxymethyl groups nearly uniformly distributed on the six Cys residues, indicating that their thiol groups have essentially the same reactivity in the reduced protein. The data on which this figure is based were presented by Creighton. 19

disulfide r e a r r a n g e m e n t s p r o d u c e d b y the d e n a t u r a n t ar e a l m o s t c e r t a i n to t a k e p l a c e b e f o r e t r a p p i n g is c o m p l e t e . High concentrations of iodoacetate or iodoacetamide can produce m o d i f i c a t i o n s o f o t h e r p r o t e i n g r o u p s , so it is o f t e n n e c e s s a r y a l s o to a d j u s t t h e p H to m i n i m i z e s u c h side r e a c t i o n s an d to r e m o v e the r e a g e n t b y gel filtration a f t e r r e a c t i o n w i t h thiols is c o m p l e t e . N e v e r t h e l e s s , high c o n c e n t r a t i o n s o f r e a g e n t s a r e r e q u i r e d f o r a c c u r a t e t r a p p i n g an d a d d i n g a

318

OXIDATIONS, HYDROXYLATIONS, AND HALOGENATIONS

[19]

slight excess of reagent 41'42'44 in the usually acceptable manner is unlikely to be satisfactory, as the rate of trapping will be too slow. Many other thiol-blocking reagents are available and may be suitable, but the completeness and irreversibility of their reaction should be demonstrated, for even trace quantities of thiol groups can produce complete disulfide arrangements under some conditions. The other commonly used reagent, N-ethylmaleimide, does not produce stable adducts and can reregenerate thiol g r o u p s Y Analyzing Trapped Species The possible pathways of disulfide bond formation become very complex with more than just two or three Cys residues in a protein. Even formation of a single disulfide bond between two Cys residues is a multistep process with up to five different species involved, those with the two Cys residues reduced, disulfide, doubly mixed disulfide, and two single mixed disulfides (Fig. 3). Most multistep reactions produce at intermediate times complex mixtures of the original, intermediate, and final forms of the reactant (Figs. 2-5), so it is necessary to resolve the various species by fractionating the trapped mixtures. It is impractical to attempt to elucidate the pathway by following as a function of time just the average properties of the mixture, such as the average thiol, disulfide, and mixeddisulfide content or other physical or enzymatic measures. Attempts to do so have not been satisfactory, 36'42 especially if assumptions are required about the natures of the various species. 36 Also, such unsatisfactory procedures are not necessary, because the trapped species may be purified and their individual properties determined directly and unambiguously. The various species trapped in the above ways will differ in the states of their Cys residues (whether in intramolecular disulfides, mixed disulfides with reagent, or originally free thiols that reacted with the trapping reagent) and can often be separated on this basis. For example, the disulfide reagent and the trapping reagent can be charged (e.g., negatively charged glutathione and iodoacetate), so that the net charge of the protein will depend on the number of such groups attached. Electrophoretic, ionexchange, isoelectric focusing, etc., procedures may then be used to separate the species (Figs. 3-5). Not only the net charge, but also the clustering of charges on the molecule and its conformation, determine the ion-exchange chromatographic properties of the species, so virtually all

R. R. Hantgan, G. G. Hammes, and H. A. Scheraga, Biochemistry 13, 3421 (1974). 45 E. Beutler, S. Srivastava, and C. West, Biochem. Biophys. Res. Commun. 38, 341 (1970).

0 ~,.~

.,~

,-~ i~1 ,.~

t~

,~, ~

~ o~?

0

¢~ ~

~

¢~

=

c"

E E t--

o "4

q q

CXl U~ ,r.,-

q .,..,

o

~

r~

..

~

t Z tt

,~

~

-~

....

~...~

~ .-, ~

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OXIDATIONS,

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AND HALOGENATIONS

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FIG. 4. Chromatographic analysis of the kinetics of disulfide bond formation in reduced BPTI using 0.15 mM GSSG as disulfide reagent. Reduced BPTI was incubated at 25° in 0.10 M Tris-HCl (pH 8.7), 0.2 M KC1, 1 mM EDTA, and 0.15 mM GSSG. At the indicated times, 0.5 M iodoacetate was added to a final concentration of 0.1 M. After 2 min, the protein was separated from reagents by gel filtration on Sephadex G-25 equilibrated with 0.02 M imidazole-HCl (pH 6.2), 1 mM EDTA. Each protein mixture was placed on a column of CMcellulose (1.5 cm diameter by 80 cm length) equilibrated with the same buffer; elution was with a concave gradient of NaCI concentrations, from 0 to 0.6 M NaC1 (1.5 liters total). The protein was monitored by its absorbance at 280 nm. Fully reduced BPTI, R, elutes first, owing to the six negatively charged carboxymethyl groups. It is followed by the one-disulfide intermediates, then the two-disulfide intermediates, and finally the refolded BPTI, N. Peak N contains native-like BPTI, with the three disulfides linking Cys 30 to 51, 5 to 55, and 14 to 38, plus native-like molecules lacking the 30 to 51 disulfide and with the 2 thiol groups buried and unreactive. The other intermediates are identified by the residue numbers of the Cys residues paired in disulfides. Only minor quantities of mixed-disulfide protein species accumulate under these conditions. The data on which this figure is based were published in Creighton. 52

[19]

DISULFIDE BOND FORMATION

321

)

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FIG. 5. Electrophoretic analysis of disulfide bond formation in reduced BPT1 using 5 mM DTT s as disulfide reagent. Reduced BPTI (30/xM) was incubated at 25 ° in 0. l0 M Tris-HCI (pH 8.7), 0.2 M KCI, 1 mM EDTA, and 5 mM DTT s. At the indicated times, the reaction was quenched by the addition of either iodoacetamide (left) or iodoacetate (right) to 0.1 M. Portions of the trapped mixtures were analyzed by electrophoresis as in Fig. 2. The iodoacetamide-trapped species (left) should all have essentially the same net charge, and their different mobilities reflect primarily their different conformations, i.e., hydrodynamic volumes. The fully reduced protein, R, is very unfolded and migrates most slowly; the refolded protein, N, most rapidly. The intermediates A, B, and C are different one-disulfide intermediates. The iodoacetate-trapped species (right) differ also in the number of negatively charged carboxymethyl groups they contain, and the mobilities of all the species, except N, are reduced accordingly. The decreased mobility of R indicates the effect of six carboxymethyl groups. The positions indicated for At, Bt, Ct, and N3 are those predicted from their mobilities when trapped with iodoacetamide, assuming that their mobility is decreased in proportion to the number of carboxymethyl groups they contain and that they have the number of disulfides indicated by the subscript. The original data on which this figure is based were published in Creighton. 37

the major intermediates trapped by iodoacetate during refolding of reduced BPTI were isolated in essentially pure form by one column chromatography separation (Fig. 4). Using cation exchange of mixtures trapped with iodoacetate, the various species elute essentially in decreasing number of carboxymethyl (CM) groups on originally free Cys residues, i.e., increasing order of the number of disulfide bonds they contain. If one or more of these Cys residues is in a mixed disulfide with glutathione, the elution volume is

322

OXIDATIONS, HYDROXYLATIONS, AND HALOGENATIONS

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only slightly altered, generally being decreased46; an acidic glutathione moiety is therefore nearly comparable in this case to a CM group. Neutral or basic disulfide reagents produce the expected change in elution profile, but this has been found to complicate the purification of the trapped species. It is preferable to isolate together all molecules with the same protein disulfides, irrespective of whether the other Cys residues are blocked with CM groups or mixed disulfides with the reagent. The states of these Cys residues can be determined by diagonal maps (see below) or the disulfide or trapping reagent can be radioactive, permitting their presence to be readily detected, lz,46 The number of Cys residues involved in disulfides, either intramolecular or mixed, can be determined readily in pure species by reducing the proteins, then allowing these to react with mixtures of iodoacetate and iodoacetamide, and counting the number of electrophoretic bands generated 47 (Fig. 6). Other properties of the protein species can also depend upon the state of the Cys residues, especially their conformations, and can be used to analyze the trapped species. Electrophoretic mobility through polyacrylamide gels depends upon both the net charge and the hydrodynamic volume of the protein (Fig. 5). For example, reduced BPTI trapped by acid or iodoacetamide has essentially the same net charge as native BPTI, but only two-thirds of the electrophoretic mobility, owing to being unfolded and having a substantially greater hydrodynamic volume. 7,37 Consequently, the relative mobilities of the iodoacetamide- or acid-trapped intermediates give information about their relative compactness. Trapping the intermediates with iodoacetate introduces an acidic CM group at each free Cys residue, with consequent effects on the net charge. The charge effect of six such groups is given by the decreased mobility of reduced BPTI trapped with iodoacetate rather than iodoacetamide. There is no effect on the native protein, which has no free thiol groups. The relative mobilities of all the intermediates when trapped with iodoacetamide or iodoacetate show excellent agreement with those expected if each CM group is equivalent in charge to one of the six on RCM-BPTI and if the hydrodynamic property of the protein is the same irrespective of which trapping reagent was used. Consequently, it is possible to correlate the two electrophoretic profiles to determine the number of disulfide bonds_present in each species. Gel filtration is also sensitive to the hydrodynamic volume and has been used extensively to separate folded from unfolded species of lyso-

46 T. E. Creighton, J. Mol. Biol. 113, 275 (1977). 47 T. E. Creighton, Nature (London) 284, 487 (1980).

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DISULFIDE BOND FORMATION

323

zyme generated during disulfide bond formation and breakage. 48 Unfortunately, the disulfides of the folded species were assumed to be native-like, rather than identified. Using gel filtration, a native-like three-disulfide intermediate of RNase was isolated in pure form and extensively characterized. 12,49,50 Identifying and Characterizing the Trapped Species Many chemical procedures are available for determining which Cys residues in a protein are paired in disulfides, which involved in mixed disulfides with the disulfide reagent, and which reacted with the trapping reagent. Nevertheless, the diagonal electrophoresis method of Brown and Hartley 5~ has been found to be most useful, especially if performed at pH 3.5 with iodoacetate-trapped species. The reason for this is apparent from the diagonal maps of trapped reduced BPTI and the major one-disulfide intermediate in Fig. 7. The fully reduced form of BPTI has no disulfides, but its diagonal map has a second diagonal of six peptides that were slightly more acidic in the second dimension and contain the six CM Cys residues of the protein. These peptides do not separate from the other peptides if the electrophoresis is performed at pH 2.1 or pH 6.5 or if the Cys residues were blocked with iodoacetamide. Therefore, this "CM Cys diagonal" probably arises because the oxidation with performic acid that occurs between the two electrophoretic separations oxidizes the CM Cys residues to the sulfone (CM CysO2), which lowers their pKa values slightly, making them somewhat more acidic. Consequently, all peptides containing Cys residues lie off the diagonal of other peptides and can be identified. Disulfide bonds between Cys residues cause their peptides to have the same mobility in the first dimension, but the performic oxidation cleaves this disulfide and converts the two Cys residues to CysO3H. The two peptides are then usually more acidic than in the first dimension and lie off the major diagonal (Fig. 7, right). Which pairs of peptides were so linked originally is usually obvious from their common mobility in the first dimension. Ambiguities may often be resolved if the first-dimension mobilities of the various possible pairs are known. In Fig. 7 (right), the absence of these two peptides from the "CM Cys diagonal" indicates that the

48 A. S. Acharya and H. Taniuchi, Mol. Cell. Biochem. 44, 129 (1982). 49 T. E. Creighton, FEBS Lett. 118, 283 (1980). 5o A. Galat, T. E. Creighton, R. C. Lord, and E. R. Blout, Biochemistry 20, 594 (1981). 51 j. R. Brown and B. S. Hartley, Biochem. J. 101, 214 (1966).

324

OXIDATIONS, HYDROXYLATIONS, AND HALOGENATIONS

[19]

FIG. 6. Counting the integral number of Cys residues in reduced BPTI (top) and that with two Cys residues irreversibly blocked (bottom). Molecules with 0 to n acidic groups on the n Cys thiols are generated by reacting them with varying mixtures of neutral iodoacetamide and acidic iodoacetate. The proteins were reduced and unfolded by incubation at 37° for 30 min in 1.0 ml of 8 M urea, 10 mM dithiothreitol, 10 mM Tris-HC1, 1 mM EDTA, at pH 8.0. They were then alkylated by adding 200 pA of this solution to 50 pA of 0.25 M iodoacetamide, iodoacetic acid adjusted to pH 8.0 with KOH, or mixtures of the two. After 15 min at room

[19]

DISULFIDE BOND FORMATION

325

FI6.7. Diagonal maps of (left) carboxymethylated reduced BPTI and (right) the singledisulfide intermediate with the 30-51 disulfide trapped with iodoacetate. The proteins were digested with trypsin followed by chymotrypsin. The peptides were separated by electrophoresis at pH 3.5 in the horizontal direction (anode at the right). After exposure to performic acid, the electrophoresis was repeated in the vertical direction (anode at the top). The peptides were detected by dipping through 0.4% ninhydrin, 0.1% cadmium acetate, 5% acetic acid, and 10% water in acetone. The numbered peptides lie below the diagonal of peptides with the same mobility in both dimensions. They were identified from their amino acid compositions to contain the 6 Cys residues of BPTI: peptide 1, residues 36 to 39; peptide 2, 1 to 15; peptide 3, 47 to 53; peptide 4, 5 to 15; peptide 5, 27 to 33; peptide 6, 54 to 58. The positions of peptides 3 and 5 (right) indicate that a disulfide bond was originally present between Cys 30 and 51. The absence of these peptides on the "CM Cys" diagonal, as in left, indicate that essentially all the molecules had the intramolecular 30-51 disulfide bond. Taken from Creighton. 38

temperature, 50-p,l portions were subjected to electrophoresis in 15% polyacrylamide gels containing 8 M urea and the buffer system of R. A. Reisfield, U. J. Lewis, and D. E. Williams [Nature (London) 195, 281 (1962)]. The iodoacetamide-treated proteins (left) have the greatest electrophoretic mobility due to the greatest net positive charge. Molecules of BPTI (top) with 1 to 6 acidic carboxymethyl groups are generated, from left to right, by reacting with 1 : 1, 1 : 3, 1 : 9, and 0 : 1 mixtures of iodoacetamide and iodoacetate. The sample on the far right is a mixture of the five other samples. BPTI in which Cys 14 and 38 had been irreversibly blocked by reaction with iodoacetamide (bottom) gave the expected four additional bands. Taken from Creighton. 47

326

OXIDATIONS, HYDROXYLATIONS, AND HALOGENATIONS

[19]

protein analyzed was homogeneous and that the disulfide bond was intramolecular. The other four Cys residues were blocked with CM groups. Mixed disulfides between protein and reagent behave analogously, depending on the nature of the reagent. Peptides that were involved in mixed disulfides with glutathione generally appear in very similar positions as those that had reacted with iodoacetate, but they may be readily distinguished by their amino acid compositions, since the former have CysO3H residues, the latter CM CysO2. The states of all the Cys residues of a homogeneous species may be determined from a single diagonal map. Mixtures of one-disulfide species may often be analyzed in the same way, even giving semiquantitative estimates of the relative proportions of the various species. However, species with two or more protein disulfides must be nearly homogeneous in order to give interpretable diagonal maps, unless they are closely related, as in differing in only one disulfide.52 No problems are generally encountered with disulfide interchange, even though proteolytic digestions are often carried out at pH 7.5 and 65 ° for 2 or 3 hr. This contrasts with earlier reports of extensive, seemingly spontaneous, interchangC 3 for reasons that are unknown, but may be due to the present greater purity of reagents, irreversible blocking of all thiol groups, and care not to introduce nucleophiles that can catalyze disulfide interchange. Besides the states of their Cys residues, the trapped intermediates can be characterized in the same way as any other protein, 5°,54-56 since they are stable under all conditions except those that would permit disulfide interchange.

Preparation of Diagonal Maps The protein to be analyzed is digested proteolytically under conditions where disulfides are stable. No thiols or other nucleophiles likely to catalyze disulfide interchange should be present, which precludes the use of thiol-containing proteases or very high pH. The ideal protease is one that produces quantitative cleavage between all the Cys residues of the protein. We routinely use thermolysin at 1 mg/ml in 0.2 M ammonium acetate

52 T. E. Creighton, J. Mol. Biol. 95, 167 (1975). 53 D. H. Spackman, W. H, Stein, and S. Moore, J. Biol. Chem. 235, 648 (1960). 54 T. E. Creighton, E. Kalef, and R. Arnon, J. Mol. Biol. 123, 129 (1978). ~5 p. A. Kosen, T. E. Creighton, and E. R. Blout, Biochemistry 19, 4936 (1980). 56 p. A. Kosen, T. E. Creighton, and E. R. Blout, Biochemistry 20, 5744 (1981).

[19]

DISULFIDE BOND FORMATION

327

buffer containing 1 mM CaC12 at pH 7.0-7.5, digesting the protein at a concentration of 0.2-0.5 mM for 2-3 hr at 65°; disulfide interchange is negligible. Even very stable proteins, such as BPTI, are digested with this procedure. High concentrations of thermolysin do not interfere with diagonal maps because it contains no Cys residues and any peptides that arise from it lie on the normal diagonal. After digestion, the mixture is lyophilized. An aliquot of the digestion mixture containing about 0.1-0.3/xmol of the original protein is applied as a 1 x 3 cm band to Whatman 3 MM paper and subjected to electrophoresis in one dimension. A mixture of the dyes xylene cyanole, acid fuchsin, and methyl orange is used to monitor the electrophoretic migration. After thorough drying of the paper at room temperature, it is placed in a closed container containing in a shallow dish a freshly prepared mixture of 19 ml of formic acid and 1 ml of 30% H202. Chloride ions should be avoided, as they are converted to chlorine by performic acid. The extent of the oxidation can be followed by the conversion of the blue tracking dye to a green color. After the 2-3 hr of exposure required for this change, the paper is removed and dried thoroughly at room temperature. The thin strip of paper containing the peptides is then stitched across a second sheet of chromatography paper, and as much as possible of the overlapping new sheet is removed. Whatman 1 paper for the second dimension gives somewhat greater sensitivity than 3 MM paper. The paper is wetted with electrophoresis buffer on both sides of the first strip, and the merging fronts are used to concentrate the peptides into a thin, straight line down the center of its length. Electrophoresis in the second dimension is repeated in exactly the same way as in the first, but at right angles to it. The sheet of paper is then dried thoroughly at room temperature. The peptides may be visualized by any of the available methods, but staining with fluorescamine permits recovery of the peptides for amino acid analysis. The paper is dipped once or twice through 1% triethylamine in acetone if the electrophoresis buffer was acidic. It is then dipped through a solution of 1 mg of fluorescamine per 100 ml of acetone. After drying sufficiently, the peptides are visualized by their fluorescence under an ultraviolet lamp. All fluorescent spots off the diagonal are eluted with 0.1 M NH3 and subjected to amino acid analysis, for the intensity of fluorescence can be a grossly misleading guide to the amount of peptide present. The recovery of peptides is low but remarkably constant, so that the quantity of each peptide recovered can assist with interpretation of the diagonal map if the protein was not homogeneous or if the proteolytic

328

OXIDATIONS, HYDROXYLATIONS, AND HALOGENATIONS

[19]

cleavages were not complete. It should be noted that CM Cys and Met residues are converted to the sulfone by the performic acid treatment, and CM Cys sulfone is usually destroyed completely by acid hydrolysisJ7 Reconstructing the Pathway of Disulfide Formation Having trapped, isolated, and characterized all the intermediates that accumulate during disulfide bond formation or breakage, one must determine their kinetic roles experimentally. The identities of the species will give many clues to the pathway, but it is not sufficient to assume that the native disulfides are formed sequentially, or even that all one-disulfide species are formed directly from the reduced protein and then give rise to all the two-disulfide species, etc. The known pathways have been found to be unexpectedly complex. 7'8 The kinetic roles of all the intermediates must be elucidated by determining experimentally their levels of accumulation as a function of time, using various concentrations of disulfide and thiol reagents; all other conditions are kept constant. The kinetics of both disulfide bond formation and breakage need to be examined. It is then possible to determine whether the rates of appearance and disappearance of an intermediate depend upon the concentration of (1) disulfide reagent, (2) thiol reagent, or (3) neither, indicating, respectively, that the rate-limiting step involves (1) protein disulfide formation, (2) disulfide breakage, or (3) intramolecular transitions, such as conformational changes or disulfide rearrangements. With sufficient kinetic data, it should be possible to elucidate a pathway with a single set of rate constants, containing where appropriate the dependence upon the concentration of thiol or disulfide reagent, which will fit all the kinetic observations. This can be demonstrated by using numerical integration to determine the time-dependence of all the relevant species present and showing that this simulates satisfactorily all the kinetic observations, z7'39'46 Still, it must be kept in mind that kinetic analysis can only exclude possible pathways, not prove any to be correct. Also remember that essential intermediates need not accumulate to detectable levels. The pathway should be reasonable in terms of the identities of the species and should also be thermodynamically sound; in particular, free energy changes around all cyclic paths should be zero, so one rate or equilibrium constant of each such cycle is determined by the values of all the others. Complex pathways can be dissected by modifying some of the Cys thiol groups irreversibly, so that they cannot participate in disulfide bond 57 C. Zervos and E. A d a m s , Int. J. Peptide Protein Res. 10, ! (1977).

[19]

DISULFIDE BOND FORMATION

329

formation. 46 Disulfide bond formation in such modified species should reflect the absence of paths involving the altered Cys residues. The trapped intermediates provide some such species, as whatever disulfides they have can be reduced, leaving the irreversible blocking groups introduced by trapping; the kinetics of disulfide bond formation in the reduced species can be determined under the normal conditions. Disulfide bond formation may be nearly normal in all such species in which the disulfides are formed directly, but will be blocked if the original disulfides arose only by rearrangements involving the other Cys residues. The kinetic analysis should not depend upon the assumption that each kinetic species is homogeneous, for different protein molecules with the same disulfide bonds can differ in their conformation, the topology of the disulfide loops, cis-trans isomers of peptide bonds adjacent to Pro residues, 58 etc., that could affect the rates and paths with which they form disulfides. Early studies of the kinetics of protein folding59erred in making this assumption about the unfolded states of proteins. 6° More recently, Konishi et al. 36 concluded that there must be multiple rate-limiting steps in refolding of reduced RNase because they were unable to simulate the kinetics of appearance of native-like RNase with a single step. They assumed each of their kinetic intermediates to be homogeneous, even though multiple species were grouped together solely on the basis of the n u m b e r of intramolecular and mixed disulfides they contained, irrespective of their identities. The rates at which the various one-, two-, and three-disulfide species form disulfide bonds are known to vary enormously. 8,12 Also, the types of experimental procedures they used are known to introduce presumably covalent modifications of the structure.12 Not surprisingly, their conclusions differ from those reached by a more direct analysis of the pathway, 8,12'61 using the procedures described here. A further check on the validity of a kinetic pathway is whether the equilibrium constants for the individual steps, and for the overall pathway, calculated from the forward and reverse rate constants agree with the experimental values at true equilibrium. 27 Equilibria can be attained by leaving reaction mixtures for suitable lengths of time in the appropriate mixtures of thiol and disulfide reagents. The approach to equilibrium can be monitored and should ideally be attained from both directions.

~8 j. F. Brandts, H. R. Halvorson, and M. Brennan, Biochemistry 14, 4953 (1975). 59 A. Ikai and C. Tanford, J. Mol. Biol. 73, 145 (1973). 60 R. L. Baldwin, Annu. Rev. Biochem. 44, 453 (1975). 61 T. E. Creighton, J. Mol. Biol. 113, 329 (1977).