Protein Denaturation

PROTEIN DENATURATION PART C.* THEORETICAL MODELS FOR THE MECHANISM OF DENATURATION By CHARLES TANFORD Department of Biochemisfry. Duke University Medical Center. Durham. North Carolina

I. Introduct.ion . . . . . . . . . . . . . . I1. General Equations for Equilibria between Native and Denatured States . . . . . . . A. Localization of Free Energy Contributions B . Effects of Denaturants and Other Substances Expressed in Terms of Binding Equilibria . . . . . . . . . . . . I11. Thermodynamic Data from the Study of Model Compounds . . . A. Basic Concepts . . . . . . . . . . . . B . Experimental Results . . . . . . . . . . .

IV . Principal Denatured States and the Conditions under Which They Are Stable . . . . . . . . . . . . . . . . . . . . . . . A. Description of Principal States . . . . . . . . B . Equilibria in the Native Environment C . Enthalpy Changes and the Product of Heat Denaturation . . . . . . D . Predicted Products from the Addition of Denaturants . . . . . E Stable Intermediates in the Course of Transition . . V. Thermodynamics of Transition from Native to Denatured States . . . . . . . A . Effect of Temperature . The Value of AC, B . Steepness of Transitions with Respect to Denaturant Concentration . . . . . . . . . . VI Binding Sites for Denaturants . A Hydrogen Ion Equilibria . . . . . . . . . . B . Detergents . . . . . . . . . . . . . C . Urea and Guanidine Hydrochloride . . . . . . . . D . Inorganic Salts . . . . . . . . . . . . . . . . . . . . . . VII Kinetics of Denaturation . A . Two-State Transitions to Predominantly Disordered Products . . . . . . . B . Reactions with Detectable Intermediate States VIII Equilibria and Rates under Native Conditions . Relation to Hydrogen . . . . . . . . . . . . . . Exchange . . A . Equilibrium and Rate Constants under Native Conditions . B. Hydrogen Exchange . . . . . . . . . . . . . IX . Relation between Denaturat.ion and t.he “Structure” of Water . X . Older Theoretical Models . . . . . . . . . . . . References . . . . . . . . . . . . . .

.

.

.

. .

2 5 5

12 20 21 26 45 45 47 50 52 55 57 57 60 64 64 67 69 74 74 75 80

82 82 85

90 91 93

* Parts A and B were published in Volume 23 of Advances in Protein Chemistry (1968). starting on p . 121. 1

2

CHARLES TANFORD

I. INTRODUCTION This review of the subject of protein denaturation consists of three parts. Part A, dealing with the characterization of the denatured state, and Part B, dealing with the phenomenological aspects of the transition from the native to the denatured state, were published in the preceding volume of this series (Tanford, 1968): This final portion of the review will consider theoretical models that may be constructed, and equations that may be derived from them, to account for the experimental observations reported in Parts A and B. It should be emphasized that the objective of the theoretical models to be discussed is to understand the process of denaturation per se, and not to use denaturation as a tool for understanding the native state and the forces responsible for maintaining it. With respect to the latter problem, little has occurred in the last ten years to alter earlier conclusions by Kauzmann (1954, 1959) and by the present author (Tanford, 1958, 1962a). 1 A number of interesting papers dealing with the topics of Parts A and B have been published during the last year. Of particular importance is a new calculation of the dimensions of randomly coiled polypeptide chains, which allows for the presence of both glycine and proline (Miller and Goebel, 1968). As predicted, the presence of prolinereduces the random coil dimensions: the new values are in excellent agreement with the values observed in 6 M GuHCl, as given by Eq. (20) of Part A. Miller and Goebel also show, however, that the dimensions are relatively insensitive to the presence of knots of associated residues, and conclude that the agreement between calculated and observed dimensions cannot of itself be used to rule out the presence of such knots. The optical rotation and titration data cited in Part A, for proteins in GuHCl solution, provide additional evidence, of course, and make the presence of sizable regions of associated residues very improbable. It should be noted in this connection that Reisner and Rowe (1969) have isolated from Paramecium what appears to be the longest naturally occurring polypeptide chain reported so far: i t consists of 2930 residues, with a total molecular weight near 300,000. When dissolved in 6 M GuHC1, in the presence of reducing agent, it had a n intrinsic viscosity of 133 cc/gm, in good agreement with a n extension of the data of Fig. 6 of Part A to longer chain lengths. Other Additions and Correctionsfor Part A . An error was made in Part A in the discussion of denaturation of proteins by detergents. This error is corrected in footnote 3 on p. 46. Several substances related to GuHCl have been shown to have greater potency as denaturants: this work is referred to in Section IV,D. Information on the denaturation of proteins by 2-chloroethanol has been considerably augment,ed in a paper by Ikai and Noda (1968), and much new information on the action of alcohols in general and some other organic compounds is provided by Herskovits and Jaillet (1969). Additions to Part B . Steiner and Clark (1968) have shown that proinsulin spontaneously refolds to its native conformation after denaturation and reduction, whereas insulin does not. Unpublished work by R. W. Roxby in the author’s laboratory shows, however, that the denaturation of insulin by GuHCl, without rupture of disulfide bonds, is a reversible process. Polet and Steinhardt (1969) have succeeded in identifying sequential stages in the acid denaturation of ferrihemoglobins. The thermaldenaturation of chymotrypsin has been found to have a A C value ~ much larger than any listed in Table XVI of Part B. Reference to this work is made in Table XV of the present paper.

PROTEIN DENATURATION

3

The problems that come within the scope of this portion of the review may this be summarized as follows: (1) The native and some of the denatured states having been characterized, and the forces responsible for maintaining a given conformation being known in a general way, can we account for the fact that the native state is thermodynamically stable under physiological conditions? (2) Given that the native state is stable under physiological conditions, can we predict the effects of environmental changes (temperature, pH, addition of denaturants) on the equilibrium between native and denatured states so as to account for the loss of stability of the native state and the appearance of different denatured states under specified conditions? If the answer is in the affirmative, can we further account quantitatively for the detailed course of the transition from native to denatured state? (3) Denaturants presumably do not act at long distance from the protein molecule. Can we identify the specific sites a t which they act? The answers to these questions prove to be somewhat disappointing, and it is evident that the overall problem of protein denaturation is not yet solved. The situation is particularly bad with respect to the first question raised above: the models available at this time do not predict that the native state should represent the stable conformation of a protein molecule in dilute aqueous salt solutions at neutral pH. Part of the reason for this is that there are strong forces favoring the native state and other strong forces favoring the denatured state, and that the native state is in fact favored under physiological conditions by only a small difference between these opposing factors. However, it is also evident that there are contradictions between available estimates of the numerical values for some of these factors, such as the free energy of hydrogen bonds within the native protein. These contradictions need to be resolved before a cdculation of the absolute free energy, enthalpy, and entropy of denaturation can be taken very seriously. The problem of assigning sites of action to protein denaturants can also be considered as not completely solved. Predictions can be made on the basis of model compound studies, but the results of protein denaturation studies as such have not so far yielded direct confirmation of such predictions. The sites of action of H+ ions, however, represent an exception, and the effect of pH on denaturation equilibria can be taken as completely understood within the limitations of our knowledge of the precise locations of acidic and basic groups on native proteins, and our ability to calculate pK differences on the basis of interactions between closely spaced groups. The most successful portion of the paper is that dealing with the second question raised above. This question involves not the absolute values for the free energies and other thermodynamic parameters for denaturation processes, but the changes in these parameters with changes in environ-

4

CHARLES TANFORD

mental variables. These changes can be predicted semiyuantitatively. We can account both for the products formed under different conditions and for the character of the transitions from native to denatured state, a t least for the simple proteins that have been studied in detail. Thermal denaturation represents a partial exception: it depends on a knowledge of the absolute values of A H for the various denaturation processes. If empirical values for A H a t one temperature are assumed, however, the variation in A H with temperature is a t least partly understood. Thus one conclusion to be drawn from this paper is that much work remains to be done. However, the areas of uncertainty involve numerical values for factors that are important in denaturation. They do not suggest any error in presently accepted views on the fundamental principles that determine the relative stabilities of native and denatured states of proteins under different conditions.

Symbols to B e Employed The symbols t o be used in Part C differ somewhat from those used in Parts A and B, because the number of thermodynamic and kinetic parameters used in this Part is necessarily larger than those required to describe the experimental results without theoretical interpretation. The following will be used consistently throughout the paper : Conformational States. N represents the native state, D any denatured state, RC the randomly coiled state (usually with disulfide cross-links intact), I D the incompletely disordered state obtained by thermal denaturation. The states RC and ID have been singled out because they are the only states for which we have enough experimental information for comparison with theoretical prediction. Free Energy Changes. The symbol AG without subscript will be used t o designate the free energy change in the transition N -+ D. Subscripts will be used only when AG refers to a reaction or conformational transition other than the process N -+ D, or when two distinct denatured states have to be distinguished in an equation. AGOwill be used to designate the value of AG in an arbitrary reference medium, usually water or a dilute salt solution a t 25OC. The symbol 6G, will represent the free energy of transfer of a protein molecule from one solvent medium to another, without conformational change. The symbol 8AG represents the effect of solvent medium on AG. The symbols Agi and 6gi represent contributions to the corresponding AG or 6G that are assigned to a small portion of a protein molecule, when the method of localization of free energy contributions is used. Other Thermodynamic Variables. Symbols to be used will be consistent

PROTEIN DENATURATION

5

with those given for free energy, e.g., A H , 6Htr,Ah;, 6hi will represent the enthalpy portions of AG, GGtr, Agi, Ggi. Equilibrium Constants. The symbol K without subscript will always refer to the equilibrium constant for a reaction N Z D . Subscripts will be used under the same conditions as apply to AG. The value of K in a reference medium (usually water) will be designated as KO. The symbol K , will be used uniquely for acid dissociation constants.

11. GENERALEQUATIONS FOR EQUILIBRIA BETWEEN NATIVE AND DENATURED STATES Denaturation is a reversible process for many proteins. This means that the native and denatured states represent equilibrium states under the conditions where they exist. The native state must have a lower free energy than all accessible denatured states in the native environment; similarly each particular denatured state must become the state of lowest free energy in the particular environment where it is found experimentally to be the predominant state. A major requirement for any theory of denaturation is that it must be able to account for the free energy differences between the known conformational states, and the effects of environmental conditions upon them. To achieve this goal, it is necessary to consider the various factors that affect the free energy and other thermodynamic parameters and to incorporate them into equations that can form the basis for calculations. The objective of this section is to present such equations in the most basic form, applicable to all equilibria between different conformational states, regardless of the actual characteristics of the states involved.

A . Localization of Free Energy Contributions 1. Isothermal Transitions in Water or Dilute Salt Solutions

It is logical to begin the discussion with the native environment, to consider the native and known denatured states in this environment, and to express the total free energy differences between the states as sums of contributions from all the physical and chemical factors that affect them. There is no unique way in which this must be done: the choice is dictated by convenience and by the ability to evaluate individual contributions either theoretically or from experimental studies of suitable model systems. The procedure used here is essentially that employed in an earlier paper (Tanford, 1962a); a very similar procedure has been used by Brandts (1964b). Both procedures are based to a large extent on two earlier papers by Kauzmann (1954, 1959) in which the various factors that should con-

6

CHARLES TANFORD

tribute to the free energy difference between native and denatured states were enumerated, and their relative importance was evaluated. a. The Order-Disorder Term (AGconr). Most of the atoms of the typical native protein molecule occupy fixed positions. In most denatured states, some or all of the parts of the molecule are randomly disposed. This randomness results from the fact that rotation occurs about single bonds of the polypeptide backbone arid side-chain groups (Raniachandran and Sasiseliharan, 1968). If all allowed orientations about a single bond were to have equal energy, then aGcVnEwould contain only an entropy term. If there are z z , D bonds, each with z alternate orientations (for single bonds involving carbon atoms, usually z = 3), in the denatured state, and X,,N in the native state, the entropy change would be R Z A x , ln z, where Ax, = x,,D - .T,,N, and the sum extends over all values of z. The value of AGconfwould be given by aGconf= - TAS,,,r

=

-1ZTZAx, In x

(1)

I n reality, different rotation angles have unequal energies, even a t the minima that correspond to stable rotational states, and the differences are particularly pronounced for the bonds of the polypeptide backbone (Ramachandran and Sasisekharan, 1988). As a result, one rotational orientation is generally favored over others a t a given bond in a random conformation. The entropy is thus less than that given by Eq. (1). On the other hand, the free energy minima themselves are not particularly sharp, so that an additional contribution to the entropy arises from motility (or “free volume”) in a given rotational state. I n addition, there has to be an energy term, representing the difference between the average energy a t each bond and the fixed energy a t the same bond in the native state. The overall expression for AGconf is thus AGconr

=

AHconi -

TAScvni

(2)

and numerical values cannot be estimated with any confidence a t the present time. The reader is referred to Volkenstein (1963) for further general discussion of this topic, and to Brarit et aZ. (1967) for specific discussion of the random polypeptide chain. b. Short-Range Interactions in Random Regions of a Protein Molecule. Interactions between adjacent peptide groups in random regions of a protein molecule, and interactions with proximal portions of attached side chains, are included in the calculation of the torsional potential function for rotation about single bonds of the polypeptide backbone, and are therefore automatically included in the calculation of AGcvnf. Interactions with solvent will be considered separately below. Ordered c. Short-Range Interactions within Ordered Regions (Agi&.

PROTEIN DENATURATION

7

regions of a protein molecule niay be stabilized by hydrogen bonds and van der Waals forces (nonbonded interactions) between moieties of the molecule that are brought into contact by the three-dimensional order, though they may be far apart in the linear sequence of amino acids. To include the free energy of such interactions in AG for the denaturation process, we arbitrarily divide the protein molecule into convenient portions : each peptide backbone unit, for example, may be considered as a single portion, some side chains may be considered as single portions, others may be considered as consisting of two scparate portions, as, for example, the lysyl side chain, for which the NHSf group niay be taken as a separate entity from the hydrocarbon chain that joins it to the peptide group. The total free energy of all short-range interactions within the ordered regions of a protein molecule is then divided among these separate portions in a logical manner, e.g., the free energy of forming a hydrogen bond between two groups is divided evenly between the two groups. We shall use gi,int to designate the free energy assigned to the ith part of the molecule, and Agi,int the difference between this quantity for denatured and native states. If, in the course of denaturation, a part of the protein molecule is transferred from the inside of the native structure to a position in a random portion, Agi,int will simply be a measure of the loss of interaction free cnergy in the native state, i.e., Agi,int = -gi,int,~. Since only contacts between one part of a protein molecule and other parts of the same molecule are included in the Agi,int terms, these ternis are necessarily independent of the solvent in which a denaturation process may occur. I n general, each Agi,int will include both energy and entropy contributions. If we imagine the reaction N ---f D as occurring in a vacuum, we can write the total free energy change as i

the summation extending over all portions of the protein molecule. d . Short-Range Interactions with the Solvent (AgZJ. When the reaction N D occurs in solution, contacts with the solvent will make important ---f

additional contributions to the free energy. Free energy changes resulting from the hydration of ions, and from hydrophobic interactions between water and nonpolar parts of the protein molecule are included in this category. We shall use g,,, to indicate the free energy associated with the solvent contacts for each portion i of the protein molecule, and Ag,,, for the change in this quantity that accompanies the denaturation process. In a native protein there are many portions that have no contacts with solvent at all. If such portions are exposed to the solvent in a denatured state,

8

CHARLES TAXFORD

Ag1,8will represent the free energy of solvent contacts in the denatured state

only.

If a portion of a protein molecule (e.g., the ionic terminus of a lysine

or arginirie residue) is freely exposed to solvent in both native and denatured states, the Ag,,, term for that portion will be taken to be essentially zero. e. Long-Range Electrostatic Interactions ( A w e , ) , The only long-range

interactions that contribute to the free energy change for protein denaturatiori are Coulombic interactions betn een charged groups. The contribution (We,)of these interactions to a protein molecule in any given conformation can be calculated as described elsewhere (Tanford, 1961). The difference between this calculation for the denatured arid native states is A W e l . There will usually be a pH range near the isoelectric pH of the protein where AHr,, s 0 for any denaturation process. In the subsequent discussion we shall generally assume AWcl to he zero where denaturation processes are considered without reference to a particular pH value. f. The Total Free Energy Change. The total free energy difference between the native state and any denatured state, by summing the contributions discussed above, becomes i

z

It should be rioted that this quantity refers to the difference in free energy between two conformational states of the protein; in the same solvent

medium, without change in protein concentration, temperature, or other external variables. It should be independent of protein concentration over a wide range. It is automatically a “standard” free energy change and related to the equilibrium constant for denaturation, K = (D)/(N)) by the relation AG

-RTlnK

=

(5)

Both AG and K do not in any way depend on the units in which the concentratioris of denatured arid native forms are expressed. 2. Thc Egects of Temperature and Pressure

The ef‘fect of temperature on the equilibrium constant K for any denaturation process is given by the enthalpy change for the reaction,

AH

= -R[d

In K/a(l/T)I

(6)

It is simply the sum of the enthalpy components of the individual terms of Eq. (4), i.e., AH

= ANconf

f

2 i

Ahi,int

+ 1Ahi,s + AHc1 i

(7)

PROTEIN DENATURATION

9

where Ahi is the enthalpy component of each Ag;, and AHel is the enthalpy component of the electrostatic free energy. AH,I is probably negligibly small for all denaturation processes. In our previous paper (Tanford, 1962a), AHconrwas assumed t o be zero. As was pointed out above, this assumption is a n oversimplification. From the difference between AG and A H one obtains the entropy change for the process. In terms of Eq. (4), A S = ASconi

+ 2 ASi,int + 2 Asi,s + As,, i

i

(8)

where As%is the entropy component of each Aga, and ASe*the entropycomponent of Awe]. With AHc! cv 0, AS,1 N - A W e l / T . It is important to note that some of the interactions considered here have large effects on the partial molal heat capacity of the protein molecule. Thus neither A H nor A S can be considered as independent of temperature, i.e., a A-H - T-C3AS = A C P, (9) dT aT

AC, can again be split into components in analogy to Eqs. (7) and (8). The effect of pressure on K can be treated similarly to the effect of temperature, i.e., d In AV -K (10) dP RT and A V is again a sum of contributions from individual interactions as in Eqs. (7) and (8). 3. The Addition of Denaturants and Other Substances

A major simplification is possible in describing the effects of denaturants and other substances on the equilibrium between native and denatured states, a t constant temperature and pH. Those Contributions to AG that d o not represent interactions with the solvent, i.e., those occurring in Eq. (3), are not altered. The major contribution to changes in AG must come from the terms ASi,*, with a possible minor contribution from changes in A w e ] . The change 6 In K or 6AG, that results from any changes in the composition of the solvent, can therefore be expressed as

- R T 6 In K

=

6AG =

2

6Ag;,,

+ 6AW,,

i

The quantity 6AG may also be expressed in terms of the free energy of transfer (6Gtr) of a protein molecule in any given conformation from one solvent to another. From the following diagram,

10

CHARLES TANFORD

Native state solvent I 6Gtr.N

1

(AGbolvent 1

'

Denatured state solvent I 1SGtr.D

Native state Denatured state -(AGholvent 2 solvent 2 solvent 2 ,

it is evident that 6AG =

6Gtr,D

-

6Gtr.N =

A6Gtr

(12)

the symbol 6 referring to the change in going from solvent 1 to solvent 2. 6Gt, may itself be subdivided into contributions from the various parts of the protein molecule, and from the change in Wel,i.e., for any given conformational state,

(The terms 6gi,tr and 6gi,Bare in fact identical.) free energy between denatured and native states,

For the difference in

This equation could have been obtained directly from Eq. ( l l ) , since the order in which addition and subtraction processes are performed does not alter the result. A special situation arises if the substance being added to change the composition of the solvent has a strong affinity for one or more unique binding sites on the protein molecule, and if the binding sites exist only in one of the states involved in a transition, or if the affinity is much stronger in one state than the other. In that event one or a small number of the 6g;,tr terms may dominate the right-hand side of Eq. (14). In this situation, it ceases to be fruitful to express 6AG in terms of the preceding equations. An expression in terms of the number of binding sites arid their binding constants for the added substance would be more meaningful. Appropriate equations are given in Section 11,B. Dependence on Concentration Units. The quantity 6Gtr, unlihe the quantity AG, depends on the choice of concentration units. It is natural to take 6Gtr to be the free energy of transfer of a protein molecule, in a given conformation, from a given concentration in one solvent to the same concentrntion in another solvent. However, the relation bet\\ een concentrations expressed in different units is unique to each solvent system. Thus concentrations that are identical when expressed in one set of units ( e g , moles/liter) will be digerent in another sct of units (e.g., mole fraction). For example, 1 liter of water contains 55.5 moles, whereas 1 liter of ethanol

PROTEIN DENATURATION

11

contains 17.1 moles. A solution containing the same molar concentration of a solute in water and ethanol will differ in mole fraction of the solute by a factor of 3.2. This problem is hardly likely to cause difficulty when Eq. (12) is used, since the same concentration units would be employed for native and denatured states. It does become important when we seek to express 6G,, in terms of contributions from individual parts of the molecule, as in Eq. (13), and the problem will be discussed in that connection in Section II1,A.

4. Effect of p H Equations (11) to (14) apply to changes in pH as well as to other isothermal changes in solvent composition. However, the concentrations of H+ ions that produce effects on denaturation are many orders of magnitude smaller than the concentrations that are required for the observation of effects from most other additives. It is inconceivable that any of theg,,,can be affected by such minute changes in the composition of the environment, except for the terms that apply to acidic and basic groups, i.e., groups that are specific binding sites for H+ ions. The majority of such groups have unimpeded contact with solvent in all conformational states, with the result that their g,,, terms will be the same in all conformations, provided that their states of ionization remain the same, i.e., provided that no direct interaction with H+ ions (e.g., -COOH+ -+ -COOH) accompanies the change in conformation. It has often been tacitly assumed that 26Ag;,, of Eq. (11) is in fact negligibly small for changes in pH, and that effects of p H on denaturation equilibria can be explained entirely in terms of long-range electrostatic interactions, i.e., in terms of the 6AW,1 factor of Eq. (11) or (14). This term is greatly altered by changes in pH, because the distribution of charged sites is altered when the pH is changed. The effect is likely to be especially large a t extreme pH’s, where most of the charged sites on a protein molecule carry charges of the same sign. The mutual repulsion between these charges in a compact conformation will favor transition to a denatured state in which the charges are separated by larger distances, i.e., AWe1 becomes negative for most denaturation processes a t extreme pH values. I n fact it is incorrect to assume that long-range electrostatic forces represent the major part of the effect of pH on AG. While it is undoubtedly true that the 6AWe1 term makes an important contribution a t extreme pH’s, changes in the pK’s of some acidic or basic groups nearly always accompany a denaturation process, and these changes would, in terms of Eqs. (11) to (14), be reflected in changes in g i , s terms a t a given pH. We believe that the effect of pH on AG‘ can therefore be better understood in terms of the analysis of Section II,B, where 6AG is expressed explicitly in terms of binding constants between protein sites and Hf and other substances in the

+

12

CHARLES TANFORD

solvent medium. An explicit calculation of the contribution of 6AW,, to 6 In K will be given on page 18, and it will be seen that it can correctly predict the value of 6 In K only in plateau regions of the titration curve, where the difference in charge between native and denatured protein is independent of pH, and In K itself is independent of pH.

B. Bffects of Denaturants and Other Substances Expressed in Terms of Binding Equilibria I n the preceding section, it was pointed out that some effects of added substances on denaturation equilibria may be the result of strong affinity between the added substance and specific binding sites on the protein, and that in that event changes in K or AG are more realistically expressed in terms of binding equilibria than in terms of nonspecific changes in the free energy of solvent contacts. The objective of this section is to derive suitable equations for this purpose. I t will be shown, in addition, that changes in K or AG can always be formally expressed in terms of binding equilibria even if there is no evidence to suggest that specific sites with strong affinity for a n added substance are present.

1. General Forms of the Equations If the predominant effect of an added substance (X) arises from binding of the added substance to the protein, a t specific binding sites with high affinity for X, then the efTect of the added substance can be desribed in terms of the total concentrations of D arid N in all their forms D, DX, DX2, . . . , N, NX, NX,, . . . , i.e., the observable equilibrium constant is

DK = - total total N

(15)

where n N and n D represent the maximum number of moles of X that may be bound per mole of protein in the two conformations. If L ~ , N is the equilibNXi, and L j , D a similar paramrium constant for the reaction N jX eter for state D, Eq. (15) may be rewritten as

+

~

j=1

13

PROTEIN DENATURATION

where ax is the activity of X and K Ois the equilibrium constant (D)/(N) in the absence of X . Each equilibrium constant L j can be considered a product of the equilibrium constants Z i for the successive addition of single X N X i or ligand molecules, i.e., for the reactions NXi-1 or DXi-l DXi, i.e., Lj = 1112 . . . l j . Unless the number of binding sites is very small, equilibrium constants of the type L j or li are generally not considered to represent a useful description of binding equilibria (Tanford, 1961). Moreover, the effects of X on K can generally be measured only over a very limited range of the activity of X, so that there arc insufficient data to determine the large number of parameters that may be involved if Eq. (16) is employed. The following simplifications of this equation are therefore common : If all binding sites for X are independent of the extent of binding at other sites, each L, or E i can be represented in terms of the intrinsic binding conX S site-X, a t each individual site, and stants lcj for the reaction, site Eq . (16) becomes

+ +

+

n + n + nn

K

(1

=

KO3='

kj,DaX) (17)

nN

(1

kj.NaX)

3=1

If all sites on the native or denatured protein are identical as well as independent, all k j . N and k j v Dmay be replaced by single constants k N and kD, i.e.,

Additional obvious simplifications can be made if k D = k N , the effect of X arising in that case from a difference in the number of binding sites, or if the binding sites exist only in one of the two conformations (nD or nN = 0). Equation (16) and all simplifications thereof can be rigorously related to measures of the extent of binding of X to N and D at any given activity of X. The number of bound X molecules per molecule of native protein ( P X , N ) is given by Zj(NXj)/Z(NXj)

=

Z ~ L ~ , N U X ~ / Z L=~ d, N InU( X Z L~ j , ~ ~ x j )In / dax,

the sums here extending from j = 0 to j = n N , with L0.N = 1. A similar relation applies to the parameter PX,D, giving the amount bound to the denatured form. By differentiation of Eq. (16) we thus obtain

14

CHARLES TANFORD

Although Eq. (19) was derived here on the basis of specific assumptions about the mechanism whereby addition of substance X perturbs the equilibrium, it has been shown (Wyman, 1964; ‘l’anford, 1969) that a slightly modified form of the equation is in fact a completely general equation for the effect of substance X on denaturation equilibria. Equation (19) itself would be generally true if the activity of X and that of the principal solvent (in this case water) were independently variable. I n fact there is an obligatory relationship between the changes in activity of solvent and substance X, which, in a solution containing water, X, and protein a t infinite dilution (other substances, if present, being at constant activity levels), leads to the modified equation

where rnx is the molality of substance X, and A P is~the difference between the number of water molecules “bound” to the denatured and native forms of the protein, respectively. Equation (20) of course reduces to Eq. (19) a t relatively low concentrations of X, i.e., when mx << 55.5. It is important to point out that the complete generality of Eq. (20) is accompanied by complete generality in thc meaning of PX and cW. These parameters include not only molecules of X and of water that tire .tightly bound to the protein, but also weakly bound ones, and niolecules associated with the protein in ways that may not be universally regarded as “binding” a t all : for example, if X is a relatively large niolecule arid thereby excluded from surface regions of the protein molecule into which water molecules can enter, water molecules would become associated with the protein molecule that would have to be considered as “bound” by the definition implicit in the equation. (See also “domain binding,” on p. 16.) An exact definition of APX and APW may be reached if we consider two solutions, one containing water and X, the other containing water, X, and protein (essentially a t infinite dilution), in equilibrium with each other across a membrane impermeable to protein. If one molecule of protein is ~ A P represent ~ the nunibers of molenow converted from N to D, A P and cules of X and water that would have to cross the niembrane to maintain the equilibrium, a positive sign signifying passage to the side containing protein. Prejerentiul Binding. The prefercntial binding of a substance X to a macromolecule is defined as the aniount of X bound to the macromolecule in excess of X and solvent that may bc bound i n the same proportion in which X and solvent are present in the solvent mixture. Thus, if th e solvent mixture contains mx moles of X per kilogram of principal solvent (i.e., per 55.5 moles in the case where water is th e principal solvent), and

15

PROTEIN DENATURATION

if the macromolecule binds PX moles of X and PW moles of water, then (mx/55.5)ijw moles of X represent moles of bound X that are not included in the definition of preferential binding, i.e., fix,pref = PX - (mx/55.5)pW. It is evident that Eq. (20) can be written in the alternative form 8 In K --

a In ax - AijX.pref

Preferential binding can be positive or negative, negative values representing excess hydration. It is directly measurable by a variety of methods. 2. Binding of Ions

If the substance X is an electrolyte, the cation and anion will presumably not be bound to the same degree. If the binding occurs at specific sites, with high affinity, presumably only one ion would ordinarily be responsible. In writing equations of the type of Eqs. (16)-(B), the activity of the ion being bound would have to be used in place of ax.2 It is, however, evident from the definition of ACX given above that it is not possible to distinguish binding by the separate ions if the only experimental data available are for the effect of neutral electrolyte concentration on the equilibrium constant for denaturation, in solutions containing only the electrolyte, water, and protein. Neither ion can cross a membrane without its counterion, and binding of either ion would therefore result in passage of a neutral electrolyte molecule across the membrane. Distinction between the separate ions can be made only if the activities of the ions can be varied independently, and their effects compared. The most obvious example is H+ ion binding. In an experimental study of H+ binding, or of the effect of H+ on denaturation, we cannot of course add H+ ions to a solution without accompanying counterions, e.g., C1- ions if HC1 is used to alter the pH, and if the only measure of binding were the transfer of HCl across the membrane in a dialysis equilibrium experiment, or if one could determine only the effect of HCI concentration on K, no distinction between binding of H+ and C1- could be obtained. In this case, however, the activities of the separate ions can in fact be measured independently, so that it is easy to determine that only H+ activity is significantly affected a t the concentrations of HCI that would commonly be used. Moreover, equations such as Eqs. (16)-(18) can be tested experimentally and can be shown to account for experimental results if aH+is used in place of ax.

+

+

For a 1 : 1 electrolyte, AIX of Eqs. (19) and (20) would be replaced by Jd(l A)&+ 3$(1 - A)As-, where +I and Irefer to the binding of cation and anion, respectively, and A = j d d In ( y + / y - ) / d In mx,with y-pand y- representing activity coefficients of the constituent ions. If the ions are of approximately equal size, A would normally be zero.

16

CHARLES TANFORD

3. Explicit Incorporation

0s IIydration

Sites into the Expression for K

The possible extensions of relatively simple equations, such as Eqs. (17) and (18),to allow for binding of water a t specific sites are virtually infinite in number. For example, retaining the liniitntion to independent sites, we may suppose that some sites can competitively bind water or X in a specific manner. Terms of the type (1 ]<,ax)would then have to be replaced by terms of the type (1 kjax/awz) where x = 1, 2, or more depending 011 whether a molecule of X replaces 1, 2, or niore water molecules. Sites that accommodate only water molecules (page 14) would be permanently hydrated, regardless of the activity of X. If the number of such sites differs in two conformatiorinl states, the difference would enter stoichiometrically into the transition, and would introduce a term into K that would depend solely on the activity of water. If, for example, q tvater molecules of this type are lost in the transition from N to D, a factor I / u ~ Q would be contributed to the equation for K . Thus, allowing for hydration effects, Eq. (17) would have to be replaced by an equation a t least as complex as

+

+

fl (1 + nD

K =

kj,Dax/awZl.D)

j=1

n +

(22)

nN

awq

(1

kj,NaX/aWZJ.N)

j=1

where z, is the value of x appropriate for the jth binding site. Equation (22) would of course reduce to Eq. (17) for solutions of low concentration of denaturant (aw N 1), but denaturation equilibria are in fact frequently studied a t high coricentratioris of denaturant, where aw is significantly less than unity and dependent on the activity of X by virtue of the Gibbs-Duhem equation.

4. Domain Binding It has been shown that even the simplest assumptions concerning binding sites are likely to lead to relatively complicated equations for K if they are to be applied to equilibria a t high concentrations of denaturant, where the reduced activity of water is certain to represent an influential factor. Actually effects observed a t high concentrations of denaturants, corresponding to intririsically weak interaction between the protein and the denaturant, may not be a reflection of binding a t specific sites a t all, but may instead be the result of domain binding, which is an incorporation of substance X or water into the domain of the macroniolecule without the existence of an actual binding site. We may suppose that the influence of

PROTEIN DENATURATION

17

the protein molecule on the surrounding solvent extends over several layers of solvent molecules, so that a single locus of binding may involve many solvent molecules, and that water and X molecules in different proportions may occupy the space assigned to a single locus. The equilibrium would then respond to a function of the activities of both X and water, which would obviously have to be exceedingly complex, i.e., much more complex even than Ey. ( 2 2 ) . 5 . Eflects of p H

Because effects of pH occur a t low activities of H+ ions, Eq. (19) provides a completely general expression for the effect of pH on denaturation, i.e.,

where z H , x is the proton charge of the denatured protein a t any pH, and that of the native protein. The right-hand side of Eq. (23), a t any p H is the difference between the titration curves of denatured and native proteins a t that pH. To express titration curves in terms of the pK’s for H+ dissociation of individual acidic groups is a complex problem (Tanford, 1962b), involving not only the intrinsic dissociation properties of the groups, but also their interaction with each other. In approximate treatments of titration data, this interaction is assumed to be entirely electrostatic, and it enters into the equation for 2 as a derivative of the electrostatic free energy Wel. The term Awe,,which occurs in Eqs. (4), (11), etc., and, as pointed out earlier, would be an important term in the treatment of the effect of p H on denaturation by the method of free energy localization, is thus a n implicit factor in Eq. ( 2 3 ) ,and becomes an explicit factor in approximate developments of the equation. I n more sophisticated treatments of protein titration curves, the overall electrostatic free energy does not enter explicitly. Instead, the electrostatic interactions are estimated separately for each titratable group. The net result of such a treatment, however, is that the titratable groups cannot be treated as independent of each other. The expression for a titration curve in terms of the intrinsic properties of individual groups becomes exceedingly complex. An approximation that frequently provides a usable expression for the difference between the titration curves of the same protein in two states is based on the assumption that the number of groups making a n important contribution to Eq. (23) is small. If these groups in addition titrate independently of each other, an equation analogous to Eq. (17) is obtained. ZH,N

18

CHARLES TANFORD

Since titration results are generally expressed in terms of acid dissociation constants ( K J , the resulting expression would be

n + n + 71

K

=

Koj='

(1

Ka.i.D/aIi+) (24)

n

(1

Ka,j,N/aH+)

j=1

where KO is the value of the equilibrium constant for denaturation, a t uH+= 0 0 , i.e., in the fully protonated state of the protein, and K a , jis the dissociation constant of the jth group, the subscript N or D denoting native or denatured state. The number of groups n is small, and the same riumber is used for both states. If a particular acidic group is not titrated in one conformational state, this can be taken into account by settirig K,,j << uH+ if the group is permanently in its acidic form, or Ka,j>> aII+if it is permanently in its basic form. The corresporidirig expressions for (1 Ka,j/aH+) become unity and K a , j / a ~ + respectively. , Equation (24), using only two acidic groups, provides a fair description of the Bohr effect in hemoglobin, which is the effect of pH on the binding of oxygen to each heme binding site (Wyman, 1964).

+

@Neutral PH >> PKO

PH << PK,

FIG.1. Model structure for calculation of the effect of electrostatic interactioii on In K , as described in the text, The titratable group to which pk', refers is a carboxyl group. Wo represents the pairwise interaction energy between any two charged groups.

Contribution of 6AW,1 to 6 In K . I n many instances the differences between ~ K , , , , Dand p K , , j , ~are entirely due to differences in Coulombic interactions in the native and denatured states, i.e., they are determined by the same factor that determines the electrostatic free energy term in Eqs. (4),(ll),etc. It is worthwhile to show rigorously that it is nevertheless not valid to equate 6AG or 6 In K with changes in Wel, as was pointed out in Section II,A,4. We shall consider a simple example where the effect of pH is due entirely to the presence of a single COOH group located (in the native state) near two fixed positive charges (e.g., arginyl side chains). We assume that the three groups involved are equidistant from each other, as shown in Fig. 1,

19

PROTEIN DENATURATION

so that the values of all three possible pairwise interactions between them are the same. We shall use the symbol W Oto designate the actual value. As the figure shows, the total value of W,I due to these groups will be - Wo when the pH is well above the pK, of the COOH group in the native state and +Wo when this p H is well below that PKa. Assuming that charges are far enough apart in the denatured state t o make We,essentially zero, A W for ~ ~the reaction N -+D becomes + W Oat the higher p H (i.e., electrostatic forces favor the native state), and AWe1 = -Wo a t the lower p H (i.e., the denatured state is favored). TO calculate AWeL as a function of pH ive need only insert the fraction of native molecules ( a ) with ionized carboxyl groups a t any pH, given by a = K a , ~ / ( a ~Ka,N) + where Ka,N is the dissociation constant of the group in the native state. We obtain

+

If we now consider this to be the sole factor influencing In K , we obtain, by Eqs. (4) and (5), with all other contributions to AG considered independent of pH, In K

=

-

AG

-

RT

=

constant

Wo -K a , ~ + iZ!' + K,,N ~ I I +

UH+

If KOis the value of the equilibrium constant for denaturation a t uH+= co , this equation may be written as

On the other hand, the rigorous relation between In K and pH is given implicitly by E q. (24) in terms of the difference between the titration curves of native and denatured forms. Since we have assumed that the single COOH group is the only one affecting K , Ao"+ a t any pH is given by the difference between the values of a for this group, i.e.,

where K , , D is the dissociation constant of the group in the denatured state. With just a single group involved, this expression can be replaced without assumption by Eq. (24), so that, In K

=

In K O

+ In

aII+

+ Ka,D +

~ I I +

&,N

and, since electrostatic effects are assumed to be determinative for the ~ reside entire phenomenon, the difference between K,,D arid K a . must

20

CHARLES TANFORD

entirely in the electrostatic interaction existing in the native state. By the theory of Kirkwood and Westheimer (1938), this gives

Ka,N =

Ka,De2Wo'R'

(30)

and Eq. (29) becomes

This relation is identical to Eq. (27) when U H t >> K a , ~yielding , K = KO. The two equations are also identical when aH+<< K a , ~yielding , In K = In KO - 2Wo/Rl'. But they differ greatly a t intermediate pH values, as can be seen by the sample calculations given in Fig. 2, which is based 011 Wo/RT = 2.303, corresponding to ~ K , , D- ~ K , , N = 2.0.

y"

-c I Y c -

FIG.2. Calculation of In K as a function of pH by Eqs. (27) (curve A) and (311 (curve B).

The reason for the discrepancy is obvious. Equation (4)or ( l l ) , with the entire effect of pH ascribed t o the term AWel, can be correct only if all titratable groups are in the same state in the denatured and native protein, as is true in the example provided by Fig. 2 when (pH - ~ K , , N4 ) - 2 or > 4. This condition can in fact apply in practice only in pH regions where 2 is independent of pH. At all other pH's, by Eq. (23), a change in the state of titration, as well as a change in Weltmust accompany the conversion of N to D. This change in the state of titration would involve a change in one or more of the Agi,Bterms if AG is expressed in terms of Eq. (4). A simpler procedure is to use Eq. (23) or any of the equivalent expressions derived from it.

111. THERMODYNAMIC DATAFROM THE STUDY OF MODELCOMPOUNDS Numerical values for some of the parameters that occur in the equations of Section I1 can be obtained from the thermodyrianiic properties of suit-

21

PROTEIN DENATURATION

able model compounds of low molecular weight. We shall discuss in this section the choice of mode1 systems and summarize the available data based on them.

A . Basic Concepts 1 . Unitary Free Energies f r o m Model Chemical Reactions

Equilibrium constants for chemical reactions in solution are independent of the concentration or activity units employed to designate the amounts of reactants or products present a t equilibriuni if the reaction does not involve a change in the number of molecules. The process N D is a particular example of this situation. On the other hand, if the reaction involves a change in the number of molecules, the equilibrium constant is no longer dimensionless and will assume different values for different concentration units. The same principle applies to standard free energies and entropies for a reaction. Free energy and eritropy changes generally refer to a process in which 1mole of each product is formed a t some standard activity or concentration, a t the expense of 1 mole of each reactant a t the same standard activity or concentration. If the reaction does not involve a change in the number of molecules, AG and A S will be independent of the choice of standard state, except for nonideality corrections. If a change in the number of molecules occurs, AG and A S will depend on the choice of standard concentrations. The value of A H , on the other hand, is always independent of the choice of standard state, apart from nonideality corrections. The physical reason for the dependence of AG and A S on the choice of standard concentrations is that the partial molal entropy of a substance in solution (and, through it, the chemical potential) depends on two factors (Gurney, 1953; Kauzmann, 1959): (1) the inherent properties of an isolated molecule, surrounded by solvent; and (2) the so-called cratic contribution, which is a measure of the randomness of location of the molecule in the solution. The cratic contribution to the partial molal entropy is given in a n ideal solution by - R In z, where z is the mole fraction of the substance in the solution. Therefore, when the partial molal entropy or chemical potential are expressed in ternis of a standard entropy or standard chemical potential plus a term to express the concentration dependence, the standard term will include the cratic contribution in the standard state (e.g., 1 mole/ liter) unless coricentrations are expressed in mole fraction units or as activities based on mole fraction units. In that case the concentration-dependent term will in fact be a measure of the entire cratic contribution, and the standard entropy or chcniical potential nil1 thus be equivalent to the inherent properties of the substance. If Ive wish to use the thermodynamic properties of a reaction between ~

22

CHARLES TANFORD

small molecules as a model for the free energy of interactions that may be involved in protein denaturation, it is the inherent part of the free energy change that is needed: the cratic part in solution corresponds to the orderdisorder part of AG for protein denaturation arid is included in equations such as Eq. (4) as the term AGconr. The entropies and free energies of substances participating in the model reaction should therefore be expressed in terms of mole fraction units. The standard entropy and free energy changes in a reaction, based on these units, are known as the unitary entropy and free energy changes, and designated by the symbols ASu and AG,. The latter is directly related to the equilibrium constant K , for the model reaction, with concentrations or activities in mole fraction units,

AG,,

=

-h?T 111K ,

(32)

2. Thermodynamic Data f r o m Solubilities and Distribution Equilibria

The chemical potential of any solute i in a solution may be expressed in terms of its mole fraction (xi) as pi = pio

+ RT In xi + RT I n

fi

(33)

where f , is the activity coefficient. This equation, with a constant value of pio, is intended here to apply only to a particular solvent system: a new value of p? is used for each different solvent. The activity coefficient term therefore includes only those nonideal contributions to p i that arise from interactions of solute molecules with each other, and the value of f i -+1 as xi -+ 0 in every solvent. Because concentration is expressed in mole fraction units, pLp represents the inherent chemical potential of the solute in dilute solution in the particular solvent being used, without any cratic contribution. When two differentsolvents (A and B) are employed, pi,Boclearly represents the inherent free energy of transfer of 1 mole of i from solvent A to solvent B. We shall designate this quantity as 6Gt,. 6Gt, values can be measured directly froin isopiestic measurements in three-component systems (e.g., Robinson and Stokes, 1961). These measurements yield values for the differewe in chemical potential of a solute as a function of its own concentration and of the concentration of a solvent component. The values for changes in concentration of solvent component, extrapolated to zero concentration of the solute of interest, represent values of 6Gt,, as here defined. An alternative method is to compare solubilities in different solvents (Nozaki and Tanford, 1963). At saturation p l , B must be equal to pi,^, since each one is equal to the chemical potential of the solute in the crystalline state. As the concentration of the solute in the solution is in this case

23

PROTEIN DENATURATION

not controllable, it is necessary to know or to be able to estimate vaIues for the activity coefficient f , as a function of concentration in each solvent, if P L ; , ~ O - pi,Aois to be evaluated rigorously. If this Itnowledge is available, 6Gtr for transfer of one mole of solute i from solvent A to solvent 13 can be determined as

- sG,,

=

RT In

(Z1,H)sitd +

(z I

~

I

1

nr in (f.I , R)sntd

A 8:ltd

(fi,A)satd

(34)

the subscript “satd” referring t o the fact that the parameters in question are measured a t saturation in contact with crystalline phase. The activity coefficient term on the right of Eq. (34) is often not available. Fortunately it is also relatively small, in comparison with the concentration term, a t least when significantly large values of 6G+,are being measured. The concentration term alone is therefore often used as an approximate measure of 6Gt,. I n view of the fact that any attempt to use solvent interactions of parts of model molecules to represent solvent interactions of similar parts of protein molecules is in itself only an approximation, it is not likely that omission of the activity coefficient term of Eq. (34) will introduce serious error. (Where the solubility is very small, RT l n f , will of course tend to be negligible in any case.) Model compounds, like proteins, can be considered as being composed of two or more separate portions, each reacting more or less independently with the solvent, i.e., in analogy with Eq. (13), we can write

each quantity 6gt,,j being a measure of the effect of the change in solvent medium on the interaction of a portion j of the model molecule with the surrounding solvent. Under appropriate conditions these quantities become suitable models for the 6gt,,i terms of Eqs. (13) or (14). a. The Calculation of Group Contributions. One cannot know a priori that it is realistic to consider the interaction of a model compound with the solvent as the sum of more or less independent contributions from different parts of the molecule, as expressed by Eq. (35). To test for the validity of this assumption, it is necessary to use model compounds that have a particular group in common, but are otherwise very different. If similar values for the group contribution are obtained, the validity of the procedure is supported. For example, 6Gt, for the amino acid valine might be considered as made I

up of two contributions, one from the +H,N-CH--COO-

group arid one

24

CHARLES TANFORD

from the isopropyl side chain (iPr). Similarly, 6Gt, for the amino acid glycine can be considered as made up of a Contribution from the +H3N-

I

CH-COO- group plus another, presumably small, contribution from the H atom. Thus

where 6gtr,iPr is the contribution from the isopropyl group. A test for this procedure could be to use the hydrocarbon gases methane and isobutane as model compounds, i.e., 6Gtr,isobutunc

-

6Gtr.rnethone = dgtr,ipr

-

6gtr.H N dgtr,ipr

(37)

This would be a highly sensitive test for the principle of additivity. The hydrocarbons have low solubility in water, in contrast to the high solubility of the amino acids. Their interaction with solvent should be of the same nature over the entire molecular surface, whereas for valine the type of interaction a t the site of the charged amino and carboxyl groups should be entirely different from that which results from contact of the hydrocarbon moiety with the solvent. Tests of this kind generally result in surprisingly good agreement between different estimates for the same 6gt,,,, as some of the actual data, to be presented later, will show. Agreement between different estimates often remains very good even when 6gt,,j values are derived from AGtr values based on Eq. (34) with the activity coefficient term omitted, confirming the assumption made earlicr that this term is often unimportant in comparison with 6G,, itself. The physical size of a part of a molecule chosen for calculation of group contributions is probably a matter of some importance. A methylene group, for example, being smaller than most solvent molecules, is probablx too small to respond uniquely to changes in solvent composition, i.e., too small to be likely to give self-consistent values of 6gtr,l that are independent of the choice of parent compound. If groups of larger size are chosen, only the small part of the group in direct contact with the rest of the molecules is likely to be affected by the exact nature of the rest of the rnoleculc, and more consistent values for the overall group contribution can be expected. 6. Enthalpies, Entropies, and Heat Capacities. Values for AHtr,AS,,, and AC,,,, for transfer of a solute from one solvent to another, and the corresponding group contributions, can be determined from the dependence of AGtr on temperature. It should be noted th a t the precision of the data must be high if ACp valucs are to be obtained, since they involve the second temperature derivative of the measured quantities.

PROTEIN DENATURATION

25

3. Expression of Thermodynamic Data in Terms of Binding Constants

It was suggested in Section I I , B that the interaction of solvent components with constituent parts of protein components could be expressed by considering that the constituent parts contain binding sites that react with solvcnt components in accord with the law of mass action. If this suggestion is valid, the interactions of model compounds should be capable of being represented in the same way. I n applying this idea to protein molecules, different sites are usually assumed to be independent of each other. To preserve correspondence between the thermodynamic treatment of proteiris and model compounds, the same assumption will have t o be used here. This assumption is essentially the same as the assumption of additivity of 6gt,,, contributions that was made in the preceding section [Eq. (3511. The equilibrium constants obtained in this way are the equilibrium constants k j for reaction between group j (considered as a single site) and a substance X, the concentration of which is being varied t o alter the composition of the solvent medium. The relation between 6gt,., and k , is given by 6gt,,, = -RT In (1

+ k,ad

(38)

where ax is the activity of substance X, and 6gt,,j refers to transfer from pure water to a solution containing X at that activity.

4. Thermodynamic Data from Helix-Coil Transitions Two parameters are obtained from equilibrium data for transitions between a polypeptide helix and the corresponding randomly coiled polymer (Zimm, 1962). One measures the free energy for the addition of an amino acid residue to an existing section of helix. Apart from possible contributions from the side chains of the residues, this parameter should be a measure of the inherent free energy of formation of a hydrogen bond between peptide groups. The second parameter measures the free energy of initiating a helical section: this parameter includes the free energy of formation of a hydrogen bond between peptide groups, but also includes the unfavorable entropy of immobilizing peptide groups that lie between the hydrogenbonded groups and become part of the a-helix without stabilization by hydrogen-bond formation. Enthalpies and entropies for these same processes can be obtained from the temperature dependence of the foregoing free energies. 5. Calorimetric Data

Calorimetric data can be used to confirm enthalpy data obtained from the derivatives of the free energy data discussed in the preceding portions of

26

CHARLES TANFORD

this section. I n addition, they may be used to obtain heat capacity data, e.g., 6C, values for transfer of solutes from one solvent to another. Free energy data often cannot be measured over a wide enough temperature range to permit the double differentiation with respect to temperature that would be necessary for the evaluation of heat capacity data for model compound reactions or transfer processes.

B. Experimental Results 1. Association between Peptide Groups I n view of the tendency for peptide groups to associate with each other in native proteins, as, for example, in helical regions, there has been considerable interest in finding model systems that permit evaluation of the inherent association constant for a reaction of the type

I

I

I co

and of the effect of environment upon it. The usual procedure has been to study the self-association of model compounds containing the peptide group on the basis of the concentration dependence of pertinent physical properties at high concentrations. The interpretation of results is usually complicated because many equilibria are involved, including equilibria for solvation of the peptide group (see, e.g., La Planche et al., 1965)) but investigators have taken these into account and have attempted to extract from the data the equilibrium constants for reaction (I), involving formation of a single -C=O . . . H-Nhydrogen bond. I n inert solvents (C6HB,CCl,) the data refer to interaction between unsohated peptide groups. I n solvents that are themselves capable of hydrogen bond formation, the data refer to interaction between solvated peptide groups, with elimination of free solvent. It is generally believed that the equilibrium constant for association between two monomer model molecules to form a dimer is smaller than the equilibrium constant for subsequent reactions, leading to formation of trimers and longer chains (navies and Thomas, 1956). The experimental results indicate that the difference is small for reactions involving solvated peptide groups, which are the most important ones for the present discussion. For the inert solvents, our data will refer to the reaction monomer monomer dimer. The best model substances of low molecular weight for this system have been considered to be the N-alkyl acetamides, in which the amide group is

+

27

PROTEIN DENATURATION

TABLEI

Thermodynamic Data f o r Dimerization of N-Alkyl Acetamides and f o r Some Related Reactions, at 25°C Dimerization of N-Alkyl Acetamides

K,,,”

Solvent

Alkyl group

Me

CeHs CCL CHCla Dioxane DMSO

H20

isoPr Me isoPr Me IsoPr Bu Me isoPr isoPr Me

(mole fraction units) 69 10.5

48 16

13 4.5 3 6.1 3.5 0.65 0.28

AG,

AH

As,

-2500

-3600

-4

-

-2350

a b

-5100

-9

c

(cal/mole) (cal/mole) (cal/deg/mole)

- 1400 - 1650

- 1500 - 900 - 650 -1070 - 750

f250

+750

-

-

-

-

-

b b b 6 d b b

-2

d

-

-

-800 0

Reference

+l

Related Reactions in HzO Reaction

+ + +

urea 2.2 -400 -1400 -3 e Urea Urea peptide group 0.7 200 f Urea two peptide groups 7 . 5 - 1200 9 Davies and Thomas (1956). b La Planche el al. (1965). The values of K and AG, are from I
+

~~~

0

~~

~~

28

CHARLES TANFORD

!ram, as in the polypeptide chain. Results obtained from studies with these substances are shown in Tablc I. The results of Table I indicate that both the free energy and erithalpy for association between peptide units are negative in organic solvents without hydrogen-bonding potential. When solvent molecules can act as hydrogen bond donors (CHCL) or acceptors (dioxane) , the association tendency is weakened. In water, on the basis of the results with N-methyl acetamjde, AG, actually becomes positive and AH becomes zero: the results indicate that the strength of hydrogen bonds between peptide groups and water is greater than the strength of interpeptide hydrogen bonds, and that there should be no irihcrcnt teridcncy for forniation of thc lattcr in a11 aqueous medium. When other model systems are used, the greater tendency for interpcptide association in organic solvents, as compared to water, is confirmed, but the absolute values for AG, and AH in an aqueous medium differ widely. Two results based on the properties of urea are shown in Table I . Thermodynamic data based on the self-association of 6-valerolactam (Susi, 19653 are not included, because the aniide groups in this compound are in the cis configuration, but it is worth noting that the AII for association in water obtained with this lactam is -5500 cal/mole. (The value of AG, is 170 cal/mole, more in accord with other data in Table I.) I n many denaturation processes, hydrogen-bonded structures are disrupted within the interior of an ordered portion of the native structure, but the free peptide units are exposed to the solvent in the dcnatured state. The results of Table I are not really appropriate models for such a process. Klotz and Farnham (1968) and Kresheck arid Klotz (1969) have obtained more relevant data by combining thermodynamic parameters for reaction I

+

TABLE I1 Thermodynamics of Formation of a n Interpeptide B o n d in a n Apolar M e d i u m from Free Peptide Groups in Water, at 25°C

AG,,

AH

(cal/mole) (cal/mole) Reaction I in CCla from Tiihle I Transfer of free groups from H,O to CCl, 'I'otal Reaction I in H,O from Table I

-2350" +3100b $750" +730

-5100 +78UOC $2700

0

AS"

(cal/deg/mole) -9 +I6

+7 -2

Associatioil eqnilibria ohtaiiicd or1 the basis of the calorimetric niensiirrmeiits of lireaheck and Illotz (1969) give AC, = -3300 cnl/mole for re:tctioii (1) iii cc14, arid therefore -200 cal/mole for AG, for the overall process. * Klotz and Farnham (1968). Kreshcck and I
29

PROTEIN DENATURATION

in a n organic medium (CCL was chosen) with thermodynamic parameters for transfer of uncombined N-methyl acetamide molecules from CC14 to water. The result, summarized in Table 11, is not very different from the result obtained simply from study of reaction (I) alone in a n aqueous medium. The free energies are essentially identical. Table I11 shows similar data derived from studies of the helix-coil transiTABLEI11

Thermodynamic Parameters jor Interpeptide Bond Formation Based o n Helix-Coil Transitions of Sgnthetic Polypeptides in AqwoiLs Media, at 25°C Amino acid side chain Glutamyl

LYSYl Leiicyl

AH

(callmole)

(cal/mole)

AS (cal/deg/mole)

- 130 - 105 - 180 - 80 - 840

- 1000 -1120 - 975 -1100 - 885 ( - 500)

-2.8 -3.4 -2.7 -2.7 *O

AG

Miller and P\’yliirid (1965). (1966a). c Olander and Holtzer (1968). d Rialdi and Hermans (1966). This is a calorimetric measurement. AH’S are based on the temperature dependence of AG.

Reference a

b C

d b U

a

* Hermans

All other

tion of synthetic polypeptides in aqueous media, and it is evident that they lead to an opposite conclusion from that reached on the basis of Tables I and 11. The results indicate that inter-peptide hydrogen bonds are more rather than less stable than free peptide groups in contact with water. Attempts to resolve the conflict between these results are necessarily speculative. Side-chain interactions may make significant contributions to the stability of helical polypeptides, e.g., hydrogen bonds between glutamyl side chains may have a relatively favorable free energy of formation in comparison with interpeptide hydrogen bonds; leucyl side chains may gain free energy by being able to order themselves around the helix core so as to avoid contacts with water. However, although hydrophobic groups have a higher free energy in contact with water, they have a lower enthalpy: thus, while AG for leucyl residues (Table 111) could be made more positive by this correction, A H would become more negative. The figures in Table I1 also include contributions from hydrophobic interactions, in that transfer of the solute from HZO to a n organic medium is involved. Since N-methyl acetamide has two CH, groups, whereas only a

I

single -CH-

group is part of the peptide unit, the transfer portion should

30

CHARLES TANFORD

perhaps be corrected for the contribution of a methyl group. This contribution is, however, expected to be negative (see below), i.e., the correction would make AG more positive than the value of +750 cal/nioIe give11 in the table, and would thus magnify the discrepancy from the results of Table 111. Correction of A H for the presence of the extra methyl group would change A H in the desired direction, but not by enough to make it negative. A large discrepancy would thus remain. It must be concluded that the thermodynamics of association betffeen peptide units is not yet fully understood. 2. Free Energies of Transfer for the Backbone Prptide Unit

We shall consider the peptide group plus a11 adjacent CH group as a convenient unit of the protein structure, and designate it as the backborle peptide unit. I n evaluating 6gt, for this unit, we shall actually evaluate 6gt, for the moiety -CHz-CO--NIIor -CO-NH-CI12-. In evaluating 6g, for amino acid side chains, however, we shall actually determine experimentally the 6gt, contribution for substituting the side chain for a hydrogen atom, as shown by Eqs. (36) and (37). The sum of the 6g, terms for the peptide unit and the side chain will thus be truly representative of the contribution of an amino residue in polypeptide linkage to AG,, of a protein molecule. Figure 3 shows values of 6gt, for transfer of a peptide unit from water to solvents containing various concentrations of other components. Most of the figures are based on coinparisoris between solubilities of diglycinc arid glycine in these solvents (Cohn and Edsall, 1943; Nozaki and Tanford, 1963, 1965, 1969). The difference between AG,, for these two solutes is taken as a measure of 6gtr, i.e., the solvent interactions of diglycine are considered as arising from three independent moieties, as indicated by the three blocks in the following formula, +H,N-CH,

CO-NH-CH,

coo-

The contributions from the two terminal blocks in glycine are assumed to be the same as in diglycine. The data for NaCl and C'aC12 shown in the figure are based on solubilities of acetyl tetraglycirie ethyl ester as measured by Robirison arid Jcncks (1965b) and on measurenierits of the distribution of N-methyl acetamidc and N-methyl propionamide between an organic phase arid aqueous solutions containing various concentrations of the salts (Schrier and Schrier, 1967). The analysis in terms of group contributions was carried out by Schrier and Schrier. They chose to carry out the analysis in terms of smaller moieties than we have chosen, i.e., they described all the data in

PROTEIN DENATURATION

31

terms of constant contributions for the peptidc group, the CH2 group, and the CH, group. The 6gt, values shown in the figure, representing a peptide backbone unit, where obtained by combining Schrier and Schrier's values for a peptide group and one CH2group. ? o6

400 al

Concentration of Added Reagent, moles/liter

FIG.3. Contribution of a single backbone peptide unit to the free energy of transfer from water t,o aqueous solutions of various reagents, at 25°C. Resrilts in NaCl and CaC12are based on t,he work of Schrier and Schrier (1967). All ot,her data represent t,he difference between AG,, for diglycirie tirid for glycirie, as given hy Cohri and Edsall (1043) or Nozaki and Tariford (1963, 1965, 1970). Reaiilts in ~ i r c aarid glycol include estimated correct'ions for self-interaction [Eq. (34)]; those i n other solvents (lo not,. See also footnote a of Table IV.

As pointed out on page 24, i t is probably not realistic to consider moieties as small as CH2 or CII, groups as coiitributing independently additive free energies of interaction. I n particular, it seems unlikely that the CH, group in a peptide backbone unit will interact with solvent in the same way as the CH2 group of a hydrocarbon chain. We therefore consider thc data for CaCh and NaCl to be less reliable than the other results in Fig. 3. Schrier arid Schrier (1967) have obtained similar data for salts other than C'aC12and NaC1. Thcy conclude that the value of 6g,, for the pcptide or amide group depends primarily on the charge typc of the salt, not o n the specific ions being used. This conclusion would not apply to the peptide tmkbone unit, which contains a CIT?group in addition to the peptide group. It is evident from the results of Fig. 3 that contacts between the peptide unit arid ethanol are considerably less stnblc than thosc bctween the peptide unit arid ivzter. Glycol s h o ~ the s same effect to a lesser degree. Urea has a very sinall stabilizing effect, arid inorganic. salts have a larger stabilizing

32

CHARLES TANFORD

effect, with relatively little specificity. The divalent Ca2+ion appears to exert a stronger effect than univalent ions, as has already been mentioned. Thc yuuntitative agreenicnt between 6yt, values based on different model systems is not as good for the peptide unit as it will be shown to be for hydrophobic groups. Except for urea arid GuHC1, however, the results are semiquantitatively independent of the chosen model system. Table IV, for example, shows results of Cohn :md Edsall (1943) for transfer of a peptidc unit from water to 100% ethanol, bused on a variety of model systems. The results are reasonably self-consistent. The same is seen to be true for data on the transfer of a peptide unit to ethylene glycol, except for an anomalously large 6gt, obtained from the carbobenzoxy derivatives of diglycine and glycine. A possibly sigriificarit aspect of these results is that, both for ethanol arid glycol, the 6gt, value obtained from comparison between triglycine arid diglycine is somewhat smaller than that obtained from diglycirie and glyTABLE IV Contributions of Backbone Peptide Unat, at 2VC, Based on Dtfferent Model Systems" 6gt, (cal/mole) for transfer from water to 100% EtOHb

Diglycine, glycine Triglycine, diglycine Diglycirie hydantoic acid, glycine liydantoic acid Triglycine hydantoic acid, diglycine hydantoic acid Glycolyl glycine amide, glycol aniide

1330 820 1230 980 980

6gt, (cal/mole) for transfer from water to 60% (10.8 M

) glycolc

Diglycine, glycirie Triglycine, diglycine Benzoyl diglycine, benzoyl glycine Cbz-diglycine, cbz-glycine" Cbz-triglycine, cbz-diglycinee

170 115 260 515 115

6gt, (cal/mole) for transfer from water to 6 M uread

Diglycine, glycine Triglycine, diglycine

- 35 -305

In Fig. 3, in this table, and elsewhere, the "backbone peptide unit" includes a hydrogen atom attached to the a-carbon atom. On the other harid, the side chain contributions to be given Inter actually represent the effect of replacing a hydrogen atom on the a-carbon atom by the side chain. The sum of the two contributioiisis thus truly representative of an amino acid residne in polypeptide linkage. b Cohn and Edsall (1943). Nozaki arid Tanford (1965). Noaaki and Tanford (1963). e cbz Icarbobenzoxy.

33

PROTEIN DENATURATION

cine. This suggests that a single peptide unit is the site of action for the added solvent component, and that steric hindrance may make it somewhat difficult for alcohols t o affect two adjacent sites simultaneously. The results shown in Table I V for the action of urea present a quite different picture. The effect of urea on 6gt, calculated from the difference between triglycine and diglycine is an order of magnitude larger than that calculated on the basis of diglycjne and glycine. A similar discrepancy is found for the action of GuHCl (Nozaki and Tanford, 1970). It is evident that the interaction of urea and GuHCI with two adjacent backbone peptide units is very much stronger than the interaction with a single peptide unit. This result is in accord with the suggestion of Robinson and Jencks (1965a) that urea and GuHCl react with adjacent carbonyl groups to form complexes of the type

H

$

H -Partial

51 -Partial

+ charge - cimrge

It indicates that the data of Fig. 3, for urea and GuHCI, representing their effect on an isolated peptide unit, are not representative of the action of these substances on peptide units in a polypeptide chain. Table V shows 6gt, values for one, two, and four peptide units treated as a single contributing group. It is noted that increase in the number of peptide units from two to four has a realtively small effect on 6gtr. For subsequent calculations we have taken one-fourth the value of 6gt, for four TABLEV Free Energy of Transfer of Adjacent Peptide Backbone Units to Urea and GuHCl Solutions, at 26°C" ~~~~~~

6gt, for chain of peptide

units in cal/mole

Number of peptide units 1 2

4

Model system Diglycine, glycine Triglycine, glycine ATGEE, ethyl acetate

Hz0 to 6 M urea - 35

- 340

-415

HzO to 6 M GuHCl

- 185 -640

- 1000

aBased on data of Nozaki and Tanford (1963, 1970), and Robinson and Jencks (1965,). ATGEE represents N-acetyl tetraglycine ethyl ester. See also footnote a of Table IV.

34

CHARLES TANFORD

adjacent peptide units as representative of the average peptide unit of an exposed polypeptide chain. 3. Free Energies of Transfer for Hydrophobic Groups

The effects of added reagents 011 hydrophobic side chains of proteins are very different from their effects on peptide groups. Quite generally, these groups have a relatively high free energy when in contact with water molecules (as is implied by the term “hydrophobic”), and the free energy of transfer to mixed solvents containing other reagents is generally negative. Inorganic salts represent the sole exception: they tend to “salt out” organic substances, and this is reflected in a positive free energy of transfer from water to concentrated salt solutions. Figure 4 shows typical data, for the leucyl side chain. All the data, except those for NaCl and CaC12, are based on comparisons between the solubilities of leucine and glycine in the solvents of given composition (Cohn and Edsall, 1943; Nozaki and Tanford, 1963, 1965, 1970). The difference between AGt, for these two solutes represents 6gt, for the leucyl side chain less 6gt, for an H atom attached in place of the side chain, as indicated by Eq. (36). As was noted on page 30, this is actually the thermodynamic parameter desired when results for a peptide unit and a side chain are to be combined to represent a portion of a protein molecule. The results for NaCl and CaClz in Fig. 4 are estimated on the basis of the work of Schrier and Schrier (1967). One marked contrast between Fig. 3 and Fig. 4 concerns the position of GuHCl. This salt behaves like other electrolytes toward peptide groups, but clearly acts quite unlike inorganic salts toward hydrophobic groups. The reasons for this difference are not understood a t the present time. Figure 5 shows similar results for an aromatic side chain, that of phenylalanine, based on solubility data of Nozaki and Tanford (1963, 1965, 1970). Except for a somewhat greater magnitude, the 6gt, values are quite similar to those of Fig. 4. Table VI shows results for a variety of hydrophobic or partly hydrophobic side chains a t a single value of the concentration of added reagent. The regularity of the results is self-evident. (1) For the purely hydrocarbon side chains, 6gt, increases in magnitude with the size of the side chain. (2) The OH group of the tyrosyl side chain does not confer a hydrophilic character on it: values of Sg,, for tyrosyl side chains are slightly more negative than those for phenylalanine. The two results given for dihydroxyphenylalanine suggests that even two OH groups on a phenyl ring do not greatly increase the affinity for water. (3) The same remark applies to the nitrogen atom of the indole ring of tryptophan. The tryptophanyl side chain is clearly the most hydrophobic of all protein side chains, gaining the

PROTEIN DENATURATION

35

t 500

0

__ 2 \

0

L

UJ

-500

-1000 0

2 4 6 8 10 Concentration of Added Reagent, rnoles/liter

FIG.4. Contribution of a leucyl side chain to the free energy of transfer from water to aqueous solutions of various reagents, at 23°C. Results in NaCl and CaCl,! are based on the work of Schrier and Schrier (1967). All other data represent the difference between A D , for leucine and A G ~ ,for glycine (see footnote n of Table VI), as given by Cohn and EdsaII (1443) or Nozaki arid Tanford (1963, 1963, 1970), Results in urea and glycol include estimated corrections for self-interaction [Eq. (34)],those in other solvents do not.

greatest free energy by transfer from water to any of the solvent mixtures listed. (4) On the other hand, the nitrogen atoms of histidine do confer some hydrophilic character on it. The total number of N plus C atoms in the side chain is 6, as compared to 10 for tryptophan, but 6g, values are only about one-fourth as large as for tryptophan. ( 5 ) On the basis of

FIG.5. Contribiition of a phenylalanyl side chain to the free energy of transfer from water to aqiieoiis solutions of various reagents, a t 25°C. Details as for Fig. 4.

36

CHARLES TANFORD

TABLEVI Contributions of Hydrophobic or Partly Hydrophobic Side Chains to the F r m Energy of Transfer of A m i n o Acids at 35'C. 8gt, (cal/mole) for transfer from water to 6

aqueous solution of reagent, at 25°C

Side chain Alanine Valine Leiicine Norleucine Phen ylalanine Tyrosine o-Dihydroxyphenylalariine Trypt,ophan Met,hionine Histidine

Glycolb

-

- 140 -250 - 350

-

- 690 - 85 - 120

Urea" EthanoldBe GuHCle

+10 - 225

-

-470 -580 -640 - 730 - 325 - 205

- 190 -310 -410 -470 - 540 -610 - 520 - 820 - 190

-485

-

- 780 -775 - 1245 -540 -425

M

Dioxanee

-770 - 1250 - 1390

-

- 2120 -530

These results (arid those in Figs. 4, 5, and elsewhere) actually represent the effect of substituting each side chain for a hydrogen atom. Since the 6gt,values for the backbone peptide unit given earlier includes an extra hydrogen atom, the sum of the two correctly represents an amino acid residue in polypeptide linkage. * Nozaki and Tanford (1965). An estimated correction far self-interaction [Eq. (34)] has been made. Nozaki and Tailford (1963). An estimated correction for self-interaction has been made. Cohn and Edsall (1943). 0 Nozaki and Tanford (1970).

solubilities in 100% ethanol (Cohn and Edsall, 1943)) the sulfur atom of methionine also confers some hydrophilic character on this side chain, about equivalent to removal of one CH2 group. The relatively large values of -8g,, shown in the table for transfer of methionyl side chains to urea or GuHCl solutions may reflect some specific interaction between these substances and the sulfur atom. (6) Excluding histidine and methionine, which are partly hydrophilic in character, we note that, a t a concentration of B fir, the order of effectiveness of the five substances listed is always the same, dioxane being the most effective. The choice of molarity for the concentration scale in Figs. 4 and 5 is arbitrary. The curves for dioxane and ethanol would have lain much closer t o each other if solvent composition had been expressed in terms of volume or weight percent. The values of hg,, from water to 100% organic solvent are nearly the same for several alcohols and for acetone, as seen in Table VII. The 6g, values for hydrophobic side chains are virtually independent of the modcl compounds on which they are based. The data are more

37

PROTEIN DENATURATION

TABLEVII Contribution of Norleucine Side Chain to Free Energy of Transfer from Water to 100% Organic Solvent, at 25°C" Model compounds Norleucine, glycine Solvent Formamide Methanol E t,hanol Butariol Acetone

Hydantoic acids of norleucine, glycine

6gt, (cal/mole)

- 1180 -2540 -2700 -2860 -2680

- 1320 -2510 - 2710 -2900 - 2670

Based on solubility data cited by Cohn and Edsall (1943). See also footnote a of Table VI. Q

satisfactory from this point of view than the data for the peptide group given in the preceding section. A striking example is provided by Table VII, in which results based on aniino acids and their hydantoic acid derivatives are compared. Another example is provided by Table VIII, where 6g,, values based on the use of amino acids as model compounds are compared with 6g, values based on the use of pure liquid and gaseous hydrocarbons. This is perhaps the most stringent test of the additivity principle TABLEVIII Effect of Choice of Model Compounds on 6gtrfor Hydrophobic Groups' Model compounds

R group

+HsN-CH(CH~R)-COO+HaN-CH (CH3)-COO-

Pure hydrocarbons CHSK, CH,

6gt, (caI/moIe), water to 7

Isopropyl Phenyl Indole

- 270 -540 -830 6gt, (cal/mole), water

Isopropyl Pheriyl Indole

- 380 - 640 - 1070

M urea - 300 - 5.50 - 840

to 4.9 M GLIHCI

- 370 - 670

- 1000

a Data for amino acids from S o z a k i aiid Tanford (1963, 1970). Data for hydrocarbon from Wetlaufer ef 01. (1964). All results are for 25OC.

38

CHARLES TANFORD

that can be devised, and the agreement between the two sets of data is remarkably good. Additional data of this kind are provided by Cohn and Edsall (1943). The identity of 6gt, values based on different model compounds holds true only for hydrophobic groups that are exposed to solvent on all sides except for a single point of attachment to the common moiety of the model compounds that are being compared (e.g., the a-carbon atom of a series of amino acids). Hydrophobic groups that are attached to strongly polar moieties a t two positions appear to interact with the surrounding solvent less strongly than similar groups attached at a single point, presumably indicating that the organization of solvent about a polar group takes precedence over interaction with nonpolar groups when the two possibilities arc in conflict. A striking example is provided by the value of 6gt, for three adjacent CH2 groups, for transfer from watcr to 10.2M ethanol. The value of 6gt, is -740 cal/molc when based on AG, values for a-aminocaproic acid and alanine, but is only -350 cal/mole when based on AG,, values for e-aminocaproic acid and 8-alanine (data of Cohn and Edsall, 1943). This observation may be a partial explanation for the greater diversity of results obtained for 6gtrvalues of the peptide group (Table IV) than the differences for individual hydrophobic groups seen in Table VII and VIII: the definition of 6gt, for a peptide group or peptide unit requires two points of attachment to other parts of the model molecules being used. It also reinforces the remark made on page 24 regarding the desirability of using relatively large groups for subdivision of AGtr into group contributions. Inorganic Salts. It has been well established for a long time that inorganic salts greatly decrease the solubility of hydrocarbons or of molecules or ions that contain dominant hydrocarbon moieties, i.e., 6gt, for transfer of hydrophobic groups from water to concentrated salt solutions is generally positive, as shown in Fig. 4. In contrast to the effect of inorganic salts on peptide groups, their effect on hydrophobic groups is not simply a function of the charge type of the salt, but depends on the actual ions of which the salt is composed. The effects of anions and cations are additive, and quite generally follow a unique order for each kind of ion. For some common anions and cations the order of effectiveness is 504'-

> C1- > BI- > I- > NO,- > ClOa- > CNSCa2+ > Li+ > Nat > K+ > NH4+

Two general reviews of these effects, and their relation to protein denaturation, have recently been presented by von Hippel and Schleich (1969a,b). Quantitative data on free energies of transfer of amino acids or other model compounds containing hydrophobic side chains are unfortunately

39

PROTEIN DENATURATION

not available. Schrier and Schrier (1967) have assigned 6gt, contributions to CH2 and CHa groups on the basis of distribution measurements of N-methyl acetamide arid N-methyl propionamide, and these were used to estimate the effects of NaCl arid CaClz on the Ieucyl side chain, as given in Fig. 4. Because of the undesirability of using elements as small as CH2as the basis for calculations, these results should be rated as only semiquantitatively accurate. Data for aromatic hydrocarbons are given by Long and McDevit (1952), and may be used as the basis for rough estimates of 6gt, for aromatic side chains.

4. Heat Capacities and Enthalpies for Hydrophobic Groups Perhaps the most striking aspect of the ordering of water molecules about hydrophobic groups is its thermal lability, which imparts a huge anomalous heat capacity to aqueous solutions of hydrophobic or partly hydrophobic solutes. This phenomenon was first observed by Edsall (1935), and the now generally accepted explanation in terms of water structure lability was proposed ten years later by Frank and Evans (1945). Edsall's results are summarized in Table IX, together with recent data by Arriett et al. (1969) and calculated results based o n the effect of temperature on the solubilities of amino acids (Dunn ef wl., 1933). The anomalous heat capacTABLE IX Anomalous Heat Capacity Ascribable to the Substitution of Hydrophobic G~oiips jar H Atoms in Aqueous Solution" ~~~

~~

~

Anomalous heat capacity (cal/deg/mole)

R Group

From series R.COOH

From series R.CHiOH*

14 32 48

23 39 56 55 68 62

From series +H,N-CH(R)-COO2.5 60 64c

65c

The data represent the increase in apparent molal heat capacity in excess of that which may he ascribed to the internal motions of the hydrophobic group itself. Except where indicated, the results are cnlcirlatetl on the basis of calorimetric measurements cited by Edsall (1935). b Arnett et al. (1969). Similar results have been obtained by Knight (1962) and Alexander and Hill (1969). The data cited by Edsall (1935) yield values of 14 and 38 cal/deg/mole, respectively, for the methyl and ethyl group. Based on temperature coefficients of solitbilities, as determined by Dunn et al. (1933). Q

40

CHARLES TANFORD

ity is of the same order of magnitude as, or even larger than, the heat capacity from all normal niodcs of absorbing energy. Numerous other examples of this effect have been reported. Figure 6, for example, shows the effect of temperature on the solubilities of several hydrocarbons in water (Rohon and Clausseii, 1951). From these data the anomalous ACp on solution in water is found to be 108 cal/deg/mole for

\

I I % of

Do

3.20 3.30 3.40 3.50 3.60 3.7C I / T x 10.3

FIG.6. Logarithmic plot of solubilities of aromatic hydrocarbons in water (Do)as a function of temperature. From top to bottom: benzene, toluene, p-xylene, m-xylene, ethylbenzene. From Bohon and Claiissen (1951).

benzene, toluene, and xylenes. The molar heat capacity of these substances in the liquid state is only about 40 cal/deg/mole. In similar experiments with methane and ethane (Claussen and Polglase, 1952), AC, for solution in water was found to he 52 and 65 cal/deg/mole, respectively. For solution of these gases in benzene or CC14,ACp is esseritiallyzcro. The effect is observed for hydrophobic groups of ions, as well as those of neutral

PROTEIN DENATURATION

41

molecules. For example, the partial molar heat capacity of tetrabutyl ammonium bromide in water is 260 cal/deg/mole (Frank and Wen, 1957), lvhich exceeds by a factor of two the normally expected value. Similar effects are not observed for solutions of hydrophilic substances in water, e.g., for sugars (Edsall, 1935). Nor are they observed for solutions of hydrophobic substances in organic solvents. Thus the transfer of hydrophobic groups from water to an organic solvent should be accompanied by a large negative 6cp,t,. Actual data for this quantity have not been recorded. From the effect of temperature on the solubilities of amino acids in water and alcohol solutions (Dunn et al., 1933; Dunn and Ross, 1938) approximate estimates can be obtained. For the leucyl side chain, for example, 6cp.tr = -33 cal/deg/mole for transfer from water t o 25% ethanol and -64 cal/deg/mole for transfer t o 50% ethanol. Further increase in the alcohol concentration has little additional effect. By comparison with the actual value for the anomalous heat capacity (Table IX), we see that the total effect has disappeared when the alcohol concentration has reached 50% by volume. It would be of considerable interest to know whether the anomalous heat capacity is also abolished by transfer t o solutions containing polar protein denaturants, e.g., urea and GuHCI. The solubility data for hydrocarbons in 7 ill urea and 4.9 M GuHCI, determined by Wetlaufer et al. (1964) at several temperatures, suggest that 6cp,t, for transfer from water to these solvents is negative, a t least for aromatic groups, but sufficient precision for quantitative estimation was not obtained. One of the consequences of large ACp values is of course to introduce large temperature dependence into AH and A S values. For example, the heat of solution of toluene in water (Bohon and Claussen, 1951; cf. Fig. 6) is -950 cal/mole at 2"C, zero a t 18"C, and +1710 cal/mole a t 42°C. It is generally true, however, that the ordering of water molecules about nonpolar groups involves a small decrease in enthalpy, arid a relatively large negative entropy change at low temperatures (Kauzmann, 1959). The anomalous heat capacity will tend to make both figures more positive as the temperature is increased. For transfer from water to an organic solvent, aht, and astr will accordingly tend to be positive a t low temperature and become more negative a t high temperature. Relatively few quantitative data are available. 5 . Uncharged Hydrophilic Groups

The free energy of interaction of serine and threonine side chains with solvent is relatively unaffected by changes in composition of the solvent medium. The value of 6g,, for transfer from water to 100% ethanol is only -40 cal/mole for serine and -440 cal/mole for threonine (Cohn and Edsall,

42

CHARLES TANFORD

1943). This is t o be compared with a value of -700 cal/mole for the same process for the smallest of the hydrophobic side chains, alanine. (The effect of the OH group of threonine in reducing the influence of solvent interactions on an exposed CH, group should be noted. This effect and the generally hydrophilic nature of sugars indicates that OH groups attached to aliphatic groups have a much stronger influence on solvent interactions than OH groups attached to aromatic rings.) The values of 6gtr for transfer from water to urea or GuHCl solutions are somewhat larger in magnitude, e.g., for threonine 6gtr is - 115 cal/mole for transfer to 8 M urea and - 140 cal/mole for transfer to 4 M GuHCl (Nozaki and Tanford, 1963, 1970). But even these values are much smaller than those for hydrophobic side chains, as given in Table VI and Figs. 4 and 5 . Thermodynamic data for the effects of solvent composition on the amide groups of asparagine and glutamine are given in Table X. They show surTABLE X Contributions of Asparagine and Glutamine Side Chains to Free Energy of Transfer at 2G"Ca 6gt, (cal/mole)

Transfer from water to 10.2 M Elhanol 100% Ethanol 7 M Dioxane 60% Ethylene glycol 8 M Urea 6 M GuHCl

Asparagine - 60

+ 10

- 200 -450 -430 - 645

Glu tamine - 85

+100

-215 40 - 230 -360

+

Peptide unit $495

+1330 +675 +170 - 60 - 220

a Data of Cohn and Edsall (1943) and Nozaki and Tanford (1963, 196.5, 1970). See footnote a of Table VI. Results for the backbone peptide unit are taken from Fig. 3 and similar data.

prising features, for which no explanation can be offered a t this time: (1) The solvent interactions of the asparagine side chain, -CHz--CO--NH2, appear to be entirely unrelated to those of the peptide unit, -CHz-CONH--, which are listed in Table X for sake of comparison. Especially to be noted are the negative values in alcohol and dioxarie solutions, to be contrasted with the large positive values found for the peptide group. (2) The difference between asparagine and glutamine is never the expected difference for introduction of an extra CI-I, group. The value of 6gtr for glutamine is expected on the basis of the results presented earlier to be always more negative than that for asparagine (e.g., -700 cal/mole for transfer to 100% ethanol). The observed differences are either negligibly

PROTEIN DENATURATION

43

small, or, where they are large, have the opposite sign. (On the other hand, the difference between glutamine arid a peptide unit is close to the expected eff'ect of a n added CH, group. The major anomaly evidently resides in the side chain of asparagine.) For uncharged aspartic and glutaniic acid side chains, 6gt, is slightly negative for transfer from water to ethanol solutions. Data for other solvent systems are not available. The results would be of comparatively little interest in any event, since aspartyl and glutamyl residues of proteins are normally ionized except a t low pH. 6. Ionic Groups

Ionic groups of proteins are virtuaIly always a t the moIecuIar surface, in contact with solvent, in all soluble conformations. Their environment therefore does not change when protein conformation changes, i.e., ionic groups tend to make little or no contribution to the Agz terms of Eq. 4. For this reason, quantitative data on transfer of these groups from water to other solvents are not needed. Qualitatively, ionic groups of proteins must behave like charged nioieties of other molecules: they are stabilized by the presence of other ions, at least a t moderate concentrations, i.e., 6gt, for transfer to salt solutioris will be negative; and they are destabilized if the solvent dielectric constant decreases, i.e., 6gt, for transfer to organic solvents will generally be positive. Protein side chains containing ionic groups also have hydrophobic portions, and it may be convenient to think of these as separate entities when free energy contributions are calculated. If this is done, it should be kept in mind that hydrophobic groups adjacent to ionic groups or highly polar groups contribute less to the overall free energy of solvent interactions than o terminal hydrophobic groups; e.g., for transfer from water to 1 0 0 ~ethanol, 6gt, is -2700 callmole for a norleucine side chain, -(CH2)3CH3. On th e basis of results obtained for e-aminocaproic acid, the value of Sg,, for the is estimated as being hydrocarbon moiety of a Iysyl side chain, -(CHZ)4-, only about - 1000 cal/mole. The effectiveness of the smaller hydrocarbon portions of arginine and glutaniic acid side chains as hydrophobic moieties is considered to be negligibly small. 7 . Interpretation of 6gt, in Terms of Binding Constants When a negative value of 6gt,,, is observed, it indicates that g ro u p j has a lower chemical potential in the solvent to which it is transferred, containing some substance X, than it has in water alone. One possible reason is that group j may form a stoichiometric complex with substance X, which may be described in ternis of an equilibrium constant lc, for the reaction, group X group--. The relation betiveen this hypothetical equilibrium con-

+

44

CHARLES TANFORD

stant and Gga,j is given by Eq. (38). There is of course no certainty that such an equilibrium actually ex’ists. It would not do so if the free energy decrease were the result of domain binding. Thermodynamic activities are available for aqueous urea solutions (Scatchard et al., 1938) arid for aqueous GuHCl solutions (E. P. K. IIade, unpublished data), and have been used by N. C. Pace and the author to determine whether the data can in fact be described by Eq. (38), arid what the values of k j would be. The results are considered meaningful only for groups that have relatively large 6gt, values, and they are summarized in Table XI. It is important to note four features of these results. (1) In view of the results obtained earlier for 6gt, of peptide groups to urea arid GuHCl solutions, k j was calculated on the basis that two adjacent peptide units form a single binding site. TABLEXI

Calculation of Binding Constants for Urea and G u H f by Eq. (38)a

Hypothetical reactionb (X = urea or GuH+)

+ 2 adjacent peptide unitas + Leu side chain + Phe side chain + Tyr side chain + T r p chain, considered as having two identical sites X + Asn side chain

X X X X X

Source of 6qLr values

Binding constant, activity referred to molality Urea

GuH+

d

0.125 0.083 0.20 0.28 0.14

1.0 0.56 1.0 1.1 0.8

e

0.13

c

Fig. 4 Fig. 3 d

c

Some of these calculations were carried out by Dr. N. C. Pace. * T h e dependence of 6gt on conceritratiori cannot, be described by Eq. (38) with X = GiiItC1. With X = urea or X = GuH+ (assurriing u& for GuHCl is a good approximation for t,he activity of the ion), 8qtr can be fitted moderately well t,o Eq. (38), wit,h the given value of k j , over the ent,ire concentration range covered by the data. For most of the data a hypothetical reaction of the form X site (HtO) c site-X H,O fit.s the results about as well as the simple binding equilibrium used for the calculatioris of the table. Data similar to those of Table V (2 peptide units) a t vitriolis concentrations of X. The four peptide iinits o f ATGISE can also be treat,ed as single binding sites, with a t least, as good a coiisisteucy with Eq. (38) as for the two peptide unit dat,a. The values of k j woiild be about 50% higher than t,he list,ed values. Data similar to Fig. 3 for tyrosine arid tryptophan. I t is not possible to fit the data for tryptophan with Eq. (38). Results are based on t,hc elation bgtr = -2RT In ( 1 kjox), implying esistence of two ident,ical binding sites. An altewative procedure is to use one site with k j equal t,o that for phenylalatiine, plus a second, weaker site. e Table 1’: results a t varioris concc~itrationsof X. The data in GuHC1 solution could not be fitted t,n Eq. (38).

+

+

+

PROTEIN DENATURATION

45

(2) The &g,, values for tryptophan side chains cannot be fitted to Eq. (38) a t all unless the indole ring is considered to consist of two binding sites for the denaturant. (3) None of the data obtained in GuHCl can be fitted to Eq. (38) if aGuHCl is used for a x . This presumably means that, if stoichjometric binding occurs at all, the ligand must be the GuHf ion alone. If the mean ion activity, a* is used for a x in Eq. (38) reasonable adherence to the equation is obtained, and the results in Table X I were obtained in this way. (4) It was not found possible to discriminate between simple binding, site X = site-X, and competitive binding with water, site (HzO) X $ site-X HZO. In conclusion, it should be noted that adherence to Eq. (38) does not necessarily indicate that site binding is the true mechanism by which urea and GuHCl interact with the groups in question.

+

+

+

IV. PRINCIPAL DENATURED STATES AND THE CONDITIONS UNDER WHICHTHEYARE STABLE

A . Description of Principal States We have seen in Part A of this review (Volume 23) that some denatured

states are common to many proteins. These states are the following. The random coil. All fixed internal noncovalent interactions are disrupted; all parts of the protein molecule are mobile and spend a t least a part of their time in contact with surrounding solvent. This completely disordered state is achieved by all proteins examined so far in concentrated GuHCl solutions, and it is probably the state to which most proteins tend t o go in concentrated urea solutions, though the limited solubility of urea in water is often insufficient for completion of the transition. Incompletely disordered state, with some residual cooperative structure. For a number of small proteins the product of heat denaturation and of denaturation by inorganic salts appears to be a state that is partly randomly coiled. It contains, however, a residual structured portion, involving perhaps about one-fourth of the molecule. It is probable that many hydrophobic groups are shielded from contact with solvent in the residual structured region: the extent to which peptide groups are retained in the interior of this region is not known. State of high helix content. I n organic solvents all proteins examined SO far adopt a state in which the helix content is high. The transition from the native state to this new ordered state appears to involve an intermediate disordered state. I t is reasonable to conclude that the ordered hydrophobic regions of the native state no longer exist in this denatured state, though detailed studies are lacking.

46

CHARLES TANFORD

Complex with detergent micelles. The denatured state attained by proteins in solutions containing detergents appears to be only partly disrupted : the disrupted portions appear able to form cooperative micellar structures containing a high ratio of detergent ions to protein side chains. I-Iydrophobic groups are partially exposed in the formation of this product, and thcre is evidence to suggest that the content of helical scgments of the polypeptide backbone may sometimes be larger than in the native state? In addition to the denatured states just described, there are many special states unique to individual proteins. Thcy may appear as stable products in denaturation by acid or alkali, or as partly stable intermediate states in other denaturation processes. The relative stabilities of these states in an absolute sense are determined by internal interactions within ordered regions of the structure [gl,intterms of Eq. (4)]and by interactions betwecri exposed portions of the protein and the solvent [g2,, terms of Eq. (4)]. The effect of changes in solvent composition is determined solely by the latter [Eqs. (11) or (14)]. I n attempting to account for the stabilities of different states, and how thcy depcnd on solvent composition, it is therefore first necessary to have some idea of which parts of the molecule are involved in internal interactions and which are exposed to solvent. This is done for the native and three principal denatured conformations in Table XII. The detergent complex hGs been omitted because of the present lack of exact information about it, and because of the lack of model compound data in detergent solutions. The information in Table XI1 is in the form of parameters, at,that indicate relative degrees of exposure t o solvent. If (Y% = 1 it indicates that the group in question is as fully exposed to solvent as a similar group on a simple model compound of low molecular weight. If a% = 0 it indicates that the group is completely buried inside an ordered region and has no contact with solvent a t all. The actual values in Table XI1 are intended to represent average values applicable to all backbone peptide units and to all hydrophobic moieties of the protein. We thus do not distinguish groups of a given kind that may be completely buried inside an ordered region of the protein, others that may be only partially buried, and others still that may In Part A of this review it was erronenusly stated that t.here is disagreement between the viscosity measurements of Markus ct al. (1964) and Reynolds et al. (1967) for serum albumin in dodecyl sulfate solntions. The statement resulted from a typographical error in one table in the paper by Markus et al. The results from the two 1aborat.oriesare in fact in agreement,. Subsequent studies by Ur. J. A. Reynolds (personal communication) indicate that most proteins have large intrinsic viscosit,ies, i.e., have greatly expanded conformations, in dodecyl or myrislyl sulfate solutions when the number of bound detergent ions becomes large. On the other hand, as was correctly st.ated in Part A, an expansion of the molecular domain does not occiir, at least for serum albumin, in solw tions of hexyl, octyl, and decyl srilfates, or octyl, decyl, and dodecyl siilfonaten, even though these detergent, ions also become bound in large numbers.

47

PROTEIN DENATURATION

TABLE XI1 Degree of Exposirre to Solrcnt in Principal Conforniational Stales Average degree of exposure (oJa Conformational state

-~

Native (N) Random coil (RC) Incompletely disordered (ID) Helical (H)

Peptide groups

Hydrophobic groups

0 .40b 0 . 75b

0 .40b 0 . 75b 0 . 55c 0.75d

0.6Sc

0 . 40d

~

uai

= 1.0 indicates t.hat each groiip is as fully exposed to the solvent as a similar

group in one of the model compounds used for estimation of free energies of transfer. * Solverit, perturbation of the spectra (Jf native protcins indicates that tyrosyl and tryptophyl side chains are frequently abont, 40% as accessible to reagents such as ethylene glycol as the same side chains on model compounds (Williams et a/., 1965; Laskowski, 1966). Similar data for urea-denatured proteins indicate about 80% exposure. Side chains of a randomly coiled protein should riot be as accessible as side chains on model compounds because of t’hermodyriamic noiiideality (Part A, Vol. 23, p. 130) and becaiise of steric restrictions of the sanie kind as those that restrict the freedom of rotation of the side chains themselves (e.g., NBmethy et al., 1966). Since state ID is the product of denaturac These figures are completely arbitrary. tion by inorganic salts, it is assumed that the degree of exposure of hydrophobic groups is relatively low. Fragmentary data (Part ,4,Volume 23, p. 206) indicate t’hat aromatic side chairis are about as exposed i n this state as in urea-denatured prot,eins. Peptide groups are presumably exposed to t.he same extent as in t.he nat.ive state, or perhaps less so.

be exposed to solvent, but sterically less accessible than a corresponding group on a model compound :all of these effects that reduce ai t o values < 1 are averaged over all groups. No estimates for uncharged hydrophilic side chains have been made: these groups tend t o be exposed to solvent in all conformations, so that changes in C Y ~that accompany changes in conformational state are small. Moreover, their g i , s values tend to be similar in differentsolvents (Section II,B,5), so that they would in any case contribute little to the effect of solvent composition on AG. Ionic groups have also been excluded, as virtually all ionic groups are known to be freely exposed to solvent in each conformation (including the native conformation) so that their A a i values will be essentially zero for all denaturation processes.

R. Equilibria in the Native Environment “Poly-1,-glutamic acid forms a very stable 01 helix; whereas poly-~aspartic acid forms almost no helix, and no one has the vagrrest notion why” (Olanderand Holtzer, 196X).

As the foregoing quotation indicates, it has not been possible so far to account for the fact that the equilibrium in the helix* coil transition of

48

CHARLES TANFORD

poly-a-amino acids in water lies on the sidc of the helix for some polyamino acids, arid on the side of thc randoni coil for others. Thc situation with regard to equilibria between the various conforrr1:ttional states of the typical globular protein, in its native environment, is cxactly the same. I t has not been possible to account for thc stability of the native state over all dcnatured states under native conditions. Were it nccessary to make a prediction in the absence of experimental knowledge, one would probably conclude that the native state should not exist. The difficulty may be illustrated by attempting to calculatc AG for the transition native randoni coil, in aqueous solution a t room temperature, using Eq. (4). We know that AGcunfis likely to be large and negative (i.e., favoring the random coil form). I t is easy to obtain such large numbers for this contribution to AG, that contributions froni other terms in Eq. (4) could not conceivably overcome them to yield a net positive value for AG. For example, Brant ct wl. (1967) have estimated that the conformational entropy of a randomly coiled polypeptide backbone is 10 cal/deg/mole per residue. The rotatioual freedom of the amino acid side chairis must be expected to provide an additional contribution, though steric hindrance exrludes many rotational orientations which would be allowed when the same side chain is not attached to a polypeptide backbone. From the calculations of XCmethy t t nl. (1966) one estimates contributions of 3.7 cal/deg/mole for lysine side chains and lesser amounts for shorter side chains. If all rotational angles are taken as fixed in the native protein, the coriformatiorial entropy in the random state becomes equal to ASconf, arid the resulting values for AGconf become about - 400 lical/mole for ribonuclease, for example, about - 550 kcal/niole for ~ - l a c t o g l o b ~ l i and n , ~ correspondingly larger for larger proteins. The factors that might lead AGconf to be less negative would be the existcrice of some degree of freedom of motion in the native state, and a positive enthalpy change, resulting from the acquisition of rotational frcedom and consequent displacement of rotational positions away from positions of minimum energy. However, the calculations of 13rant et aE. (1967) indicate that the cnergy per residue in randomly coiled poly-L-alanine is only about 0.7 kcal above the absolute minimum potential energy, so that the increasc in energy in going from the native state to a random coil would have to be less than that, i.e., <86 kcal/mole for ribonuclease, and < 112 kcal/mole for 6-lactoglobulin. Moreover, even if this and other factors Ril)oniiclca,se and 6-lacloglohiilili have heen choscii as illiistrative exnmples for numerical ctilculntions becaiise they ropreseiit proteitis with relatively small and relatively large contents of hydrophobic groiips, respectively. Calcrilatioris have been made for other proteins: they t c i i t l to fall between those for ribonuclease a i d for 6-lsctoglobuliri on the basis of free energies per residue.

49

PROTEIN DENATURATION

were to reduce -AGCanf by 200-250 kcal, the result would still favor the random coil state by a prohibitive amount. The major stabilization of the native protein relative to the randomly coiled state (positive contribution to AG) is known to come from the unfavorable interactions between hydrophobic residues and water. These interactions occur to a much greater extent in the random state than in the native state, where most hydrophobic groups are in the interior of the protein molecule, in contact with each other. In terms of the parameters of Eq. 4,each hydrophobic residue contributes a positive gZ,Sterm and a negative gz,intterm. The latter is due to the loss of van der Waals contacts in the native conformation, and is relatively small in magnitude. Tanford (1962a) has assumed that lOOXl ethanol can be taken to represent an adequate facsimile of the interior of a protein molecule, and has used free energies of transfer from this solvent to water as a measure of the contributions of hydrophobic parts of the protein to ZAg.,i,,t ZAgl,, of Eq. (4). If we assume that all hydrophobic moieties are in the interior of the native protein, and all are fully exposed in the random coil form, the contributions of these interactions to AG would amount to about +lo0 kcal/mole for riboriuclease and 190 kcal/mole for P-lactoglobulin. If we allow for the fact that some hydrophobic residues must be exposed to solvent in the native state, and that interactions with the solvent in the random coil state are likely to be less complete than in model compounds, as has been done in the tabulated at values of Table XII, these figures would be reduced. Using the aYzvalues givcn in Table XI1 the contribution of these hydrophobic interactions to AG would become only f35 l
+

+

From solubilities of ethane and methane, 6gtr for transfer from CCll to water is +800 cal/mole for a CI& group. From solubilities of butane and propane, 6gt, from liquid hydrocarbon to water is also +800 cal/molefor a CHI group. Comparing benzene, toluene arid xylenes, we obtain 6gt, from liquid aromatic hydrocarbon to water as ,580 to + l l . i O cal/mole for a CHI group. (These data are taken fro mT a b l e IIIo f I~auzmaiin, 1939.) The value of fig,, for transfer of a CH, group from ethanol to water is +730 cal/niole.

+

50

CHARLES TANPORD

results of Klotz and co-workers, based on the formation of hydrogen bonds between molecules of N-methyl acetamide (Tables I and 11)in fact indicate the opposite, namely that the peptide groups are stabilized by being hydrogen-bonded to water rather than t o each other. If this work is accepted as a suitable model for the Agt,int Agi,Bterms of Eq. (4)for the peptide backbone units, the contribution to AG would be about -700 cal/mole per peptide group, i.e., using the extents of exposure given in Table XII, about -30 kcal/mole for ribonuclease and -40 kcal/mole for P-lactoglobulin. (If there are any non-hydrogen-bonded peptide units in the ordered regions of the protein molecule, this figure would be even more negative. The free energy of transfer of monomeric N-methyl acetamide from CC1, to water is -3100 cal/mole, for example. The figure of about - 1300 cal/mole for transfer of a peptide unit from ethanol to water, in Table 11, may be a low figure, since some hydrogen bonding is likely in ethanol solutions.) If we discard the results obtained with N-methyl acetamide (there are no obvious reasons why they should not be applicable), and use instead the results based on helix-coil transitions of poly-a-amino acids (Table 111)we obtain an estimated contribution to AG which, within experimental error, is equal to zero. Even if the figures of Table 111 (for poly-L-glutamic acid) are used directly, without correction for the contribution of hydrophobic interactions, one would still obtain a stabilizing contribution (positive AG) of only about 100-150 cal/mole per peptide group, i.e., about +12 kcal/ mole for ribonuclease and about 15 kcal/mole for P-lactoglobulin. Conclusion. By combining different alternative possibilities among the estimates made above, we can arrive a t AG values for the native random coil transition that range from -88 to -395 kcal/mole for ribonuclease, and - 70 to - 525 kcal/mole for P-lactoglobulin. The smaller figures are obtained only if we suppose all hydrophobic residues to be 100% “inside” in o to solvent in the random coil, and the native structure and 1 0 0 ~exposed if we divide the original estimate for A G ~ ~in , , ~half. To obtain positive values for AG we must presumably further reduce the contribution from AG,,,r, as it is difficult to see how additional positive contributions of 100 kcal/mole or more could come from any other source. Native ordered protein structures are, of course, marginally stable with respect to the randomly coiled state. As we shall see in Section VIII, typical AG values for the reactions native $ random coil, or native incompletely disordered protein, in the native environment, lie near +lo kcal/ mole. For the present we shall have to accept this as an cxperimental fact, for which no quantitative explanation can be given.

+

+

C . Enthalpy Changes and the Product of Heat Denaturation The estimation of A H for denaturation processes presents as many difficulties as the estmation of the free energies. If we again choose the reac-

51

PROTEIN DENATURATION

tion native -+ random coil, in an aqueous medium, as example, we arrive at the following estimates for contributions from various sources. 1. The transfer of aliphatic hydrocarbon moieties from a nonpolar medium to water is an exothermic process: for valyl, leucyl, or isoleucyl side - 2 kcal/mole a t 25°C. For aromatic side chains aht, may chain, 6ht, be close to zero. If we take these 6ht, values as representative of the contributions of hydrophobic side chains to ZAh,,int %hi,, of Eq. (7), calculate the total contribution expected from valyl, leucyl, and isoleucyl side chains, and then multiply by an arbitrary factor (say 1.5-2) to estimate the total contribution from all hydrophobic moieties, we would get, for the reaction native -+ random coil, in water, a t 25" (with the degrees of exposure given in Table XII), total contributions from this source of about -50 kcal/mole for P-lactoglobulin and -20 kcal/mole for ribonuclease. 2. For the breaking of internal interpeptide hydrogen bonds and formation of hydrogen bonds to water in the random coil state (Tables I-111), we again are confronted with a discrepancy between extimates based on the properties of N-methyl acetamide, and those based on the thermodynamics of helix-coil transitions (Tables 1-111). From the former we get - 1.35 f 1 kcal/mole of peptide groups exposed, and from the latter 1.0 kcal/mole. The total contribution t o AH would be -60 =t40 kcal/mole or +40 kcal/ mole for ribonuclease; -75 f 55 kcal/mole or +55 kcal/mole for 0-lac toglobulin. 3. AHconf is unknown, but assumed to be positive. A maximum of about 85 kcal/mole for ribonuclease, and 110 kcal/mole for p-lactoglobulin was estimated in Section IV,B. The overall AH from all these sources (other sources are not likely t o make important contributions) could be anywhere from -120 to + l o 5 kcal/mole for ribonuclease. For P-lactoglobulin, AH could be anywhere between - 180 and 115 kcal/mole, all figures referring to 25°C. Similar calculations for the reaction, native --$ incompletely disordered protein, in water a t 25OC, give a total AH of -95 to +I10 kcal/mole for ribonuclease, and - 140 to 135 kcal/mole for P-lactoglobulin. Experimental values for AH are about the same for formation of random coils and incompletely disordered conformations, and (at 25") they range from about +50 kcal/mole for ribonuclease to -20 kcal/mole for p-lactoglobulin (see Table XVI in Part B, Volume 23). It is evident that these calculations cannot be used to predict whether the native conformation becomes less stable or more stable as the temperature is increased. Nor could they predict that the actual product of thermal denaturation in aqueous solution is not the randomly coiled protein, but an incompletely disordered product. It may be noted that values of AC, for the reaction N -+ RC can be

-

+

+

+

+

52

CHARLES TANFORD

estimated with somewhat greater assurance than values of A H . This subject will be taken up in Section V,A.

D. Predicted Products from the Addition of Denaturants If the values of AG for transitions in the native environment (which, we have seen, cannot be estimated a priori) are taken as known quantities, the values for AG in other solvent media can be calculated by use of Eq. (14). This calculation depends only on the free energies of interaction between exposed protein moieties and the surrounding solvent, as expressed in terms of the Sgt,,i parameters, and can therefore be made with considerable confidence, in contrast to the calculation for an absolute value of AG itself. The value of AGoonrand the thermodynamic parameters for internal bonding in the native protein, which represent major uncertainties in attempts to calculate AG itself, do not enter into the calculation of SAG. It is convenient to modify Eq. (14) so that the parameters cyi of Table TABLE XI11 Sample Calculations of ~ A G for the Transition N 3 RC for @-Lactoglobulin by Eq. (39)

Type of group" Peptide Trp Phe TYr Leu, Ile

Val

Pro Met

60% EtOH

Number Per molecule (nil

per group (cal/mole)b

161 2 4 4 32 10 8 4

+500 - 1730 - 1235 - 1220 -980 -710 -600 - 580

6gtr.i

6 M urea 6gtr.i

niQtr,i

(kcal/mole)

+80.5 -3.5 -4.9 -4.9 -31.4 -7.1 -4.8 -2.3 +21.6 +7.@

per group (oal/mole)b - 100

-730

-470 -580 -252 - 160 - 125 - 325

ni SDtr, i

(kcal/mole) -16.1 -1.5 -1.9 -2.3 -7.2 -1.6 -1.0 -1.3 -32.9 -113

Hydrophobic amino acid side chains are indicated by the abbreviations for the amino acids. b The values of 6gt,,i are based on the data of Section II1,B. Contributions for alanine side chains, and for the hydrophobic parts of lysine, arginine, histidine, etc., have not been included. These parts of the protein molecule have relatively small 6gtr,, values, and also tend to be exposed on the surface of the native protein to a greater degree than the hydrophobic side chains included in the calculation. Their contribution to ~ A would G be expected not to exceed about 2 kcal/mole for any of the results given in Table XIV. For the transition N + RC, Table XI1 gives Aai = 0.35 for both peptide groups and hydrophobic groups. For other transitions Acu; would differ for the two kinds of groups.

53

PROTEIN DENATURATION

TABLEXIV Changes in Free Energy of Transition (SAG) Relative to AG in Watera

~AG kcal/mole (Eq. 39) Transitionb N-RC N-ID N-+H N-tRC N-tID N-H

60 %

60%

EtOH

6M

Glycol

Urea

6M

GuHCl

-9

Ribonuclease +3 -8 +4 -5 -4 -3

- 15 - 10 -6

4-8 16 -20

8-Lactoglobulin +I -11 +5 -7 -8 -5

-23 - 15 - 12

+12 +14 +

~~

3M

CaClz -3 -8 13

+ +10 -4 +30 ~

~

Calculations are based on Aa, values derived from the assumed degrees of exposure given in Table XII. b Conformational state: N, native; H, helical; RC, random coil; ID, incompletely disordered. 0

XI1 are incorporated specifically. Let gi,. represent the free energy of interaction of a fully exposed group of type i with solvent. Let 6gtr,i be the change in this quantity, again for a fully exposed group, when the solvent medium is changed. Defined in this way, these quantities are constants, independent of the conformational state. The latter enters into the equation through the parameter ai for a group of type i. If a i , N and a i , D represent the values of ai in states N and D, and A a i = a i , ~ ~li,N, the contribution of interactions with solvent to AG becomes z(Aai)gi,s, and since Aa, depends on the conformational states, not on the solvent, the contribution to 6AG becomes Z(Aai)6gi,. = z(AcU;)6gtr,i. Another modification of Eq. (14) that we can make for the purpose of the present discussion is to omit the term 6AWe1. We are not interested in the effect of pH, and can consider the reactions as taking place at a pIZ where AWel is negligibly small. With these modifications, Eq. (14) may be rewritten as -RT6 In K = 6AG

(Aai)6gtr,a

=

(39)

i

The values of 6gtr,i are by definition equal to the values for fully exposed groups of type i, such as are obtained from the model compound studies of Section 111. Two typical calculations of ~ A G for , the reaction native -+ random coil for p-lactoglobulin are shown in Table XIII. The results of several such

54

CHARLES TANFORD

calculations, for ribonuclease and P-lactoglobulin, are summarized in Table XIV. It is evident that Table XIV accounts for the shifts in equilibria that actually occur when different denaturants are used. The value of AG in a given medium is given by AG

=

AGO

+ 6AG

(40)

where AGOis the free energy of transition in aqueous solution, in the absence of denaturant. If, for example, we assign a value of +6 kcnl/niole to AGO for each of the three denaturation processes of ribonuclease,Gwc predict that the native protein will still be stable in 60% glycol, that the random coil lvill be the stable product in concentrated urea and GuHCl solution, that the incompletely disordered conformatiori will be the stable product in 3 Af CaClz and the helical form the stable product in 60% EtOII. The same conclusions apply to P-lactoglobulin, but somewhat higher valucs of AGOare needed (-11 kcal/mole)6 since it is known that a concentration of about 6 M urea is needed to reach the midpoint of the transition to a random coil. Table XIV also shows that GuHCl should be effective a t about half the concentration required if urea is used. The general sirnilarjty between 6gt, values for ethanol and dioxane, a t equal volume fractions (see comments in Section III,B) suggests that ethanol and dioxarie should produce similar products at about equal volume fractions of the reagents. All these results are in agreement with the expcrimental findings as outlined in Part A of this review (Volume 23). I n the absence of precise values for aGoit is not possible to predict quantitatively the concentration of reagent that is required to induce a particular transition. Even if AGO values were known, we would not expect to be able to achieve quantitative predictions because the degrees of exposure of various kinds of groups, as given in Table XII, are rough guesses, and will undoubtedly vary somewhat from protein to protein. In addition, the 6g,, values in Section II1,B vary to some extent, depending on the model compounds used, and it would be unrealistic to expect them to be exactly applicable to exposed portions of a protein molecule. I n a crude way this has been taken into account in assigning thc degrees of exposure given in Table XIV, but again some uncertainty must remain. I n view of all these uncertainties the general agreement between experimental results and the predictions of Table XIV is astonishingly good. Further consideration will be given to the quantitative aspects of these calculations in Section V,B. Actual values of AGo depend strongly on pH, as shown in Table XVIII. Values fur fi-lactoglobulinare significantly higher thari those for ribonuclease.

PROTEIN DENATVRATION

55

a . Denaturants 01Grealer P o l e n q than GuHC1. A paper published too late for mention in Part A of this review (Castcllino and Barker, 1968) showed that several substariccs rclated to GuHCl are able to denature proteins a t concentrations (on the molar scale) lower than those required when GuHCl is used. The substances used were guanylguanidinium salts and carbamoylguanidinium salts, as well as GuHSCN, GuHI, and GuHBr. I n a subsequent paper (Castellino and Barker, 1969), the same substances were reported to produce parallel increases in the solubilities of benzoyl-Ltyrosine ethyl ester arid acetyl tetraglycine ethyl ester. While 6g,, values for individual kinds of groups cannot be estimated from these data without additional information, the results require that these more potent denaturants have more negative 6g,, values for peptide groups, hydrophobic groups, or both, than apply to GuHCl at equal Concentrations. At least semiquantitatively the predictability of the relative effectiveness of urea and GuHCl (Table XIV) can be extended to these compounds. b. Inorganic Salts. Since a review of the denaturing action of inorganic salts (von Rippel and Schleich, 1969a,b) will appear elsewhere, a detailed discussion of results pertaining to the relative effectiveness of different salts in inducing the reactiori N -+ ID would be superfluous. It should be noted, however, that the results are consistent with the model compound studies cited in Section II1,B. The results given there indicate that interactions between peptide groups and salts favor denaturation, whereas interactions between hydrophobic groups and salts contribute positive 6g,, values and thus favor the native state. The interactions with the peptide group are relatively nonspecific, but interactions with hydrophobic groups depend significantly on the nature of the constituent ions of the salt being used. The relative effectiveness of different salts (of the same charge type) is therefore primarily determined by the latter interactions, and, since they favor the native state, the order of effectiveness of individual ions should be the opposite of the order given on page 38 for relative magnitudes of 6g,. This coriclusion agrees completely with experimental observations. It should be noted that riboriuclease is the only globular protein for which detailed studies of the salt-induced N ID transition have been made. Table XIV suggests that this transition n n y not be observable for some proteins a t accessible salt concentrations. For fl-lactoglobulin, for example, the rcsults suggest that it might not be observable if AGO for the values on process is 10 kcal/mole or more, at least for the hypothetical which the calculations of Table XIV are based. E. Stable Intermediates in the Course of Transition Calculations of the ltirid performed in the preceding section also serve to indicate qualitatively why transitions of the type native s random coil

56

CHARLES TANFORD

0 2 4 Denaturont Concentration,

6

moles/liter

Fin. 7. Schematic diagram of free energies of formation (from the native state) as a function of denaturant concentration. RC represents the randomly coiled state, ID the incompletely disordered state, and Y-1 and Y-2 are hypothetical intermediates

often occur as two-state transitions without stable intermediates (Part B, Section I1 in Volume 23), even though there is strong evidence from hydrogen exchange studies (Section VIII), that, in the absence of denaturant, partially unfolded forms of globular proteins arc present a t higher equilibrium concentrations than the raridomly coiled protein. Figure 7 shows AG for formation of three denatured states of a globular protein as a function of denaturant concentration: the three states are the random coil, the incompletely disordered state defined in Table XII, and a hypothetical state, Y, in which both peptide groups and hydrophobic groups are assumed to be 52y0exposed t o solvent. The numerical data for states RC and I D are close to those for the denaturation of lysozyme by GuHCI. AG has been drawn as a linear function of denaturant concentration, which is not correct (see Fig. S), but suffices for the present calculation. It is known that AG,, for the formation of the random coil and the incompletely disordered state are about the same, and a value of +12 kcal/niole is approximately correct for lysozgme. Since ~ A Gfor state ID is smaller in magnitude than for state RC, a t any concentration of GuHCl (Table XIV), AGN-IDwill always be more positive than AGN-rR~.At low concentrations of denaturant the difference is small, but under these conditions both states are unstable with respect t o the native state. When the denaturant concentration becomes high enough for a transition to be observed, i.e., when AGN-RC< about 1 kcal/mole, the curves for ID and RC have diverged considerably, so that AGR~-,IDis large and positive, and state RC will be the exclusive product. Values of 8AG for the only partly unfolded state Y are even smaller than for state ID, and, if AGOfor formation of Y were also to be 12 kcal/mole, there would be no possibility that it could ever make a significant contribution to an equilibrium mixture (curve Y-1). The more important aspect

PROTEIN DENATURATION

57

of Fig, 7, however, is that state Y may also not make a significant contribution t o the equilibrium mixture in the transition from N t o RC even when AGOfor the reaction N -+Y is considerably smaller than AGOfor the reactions N 4 RC or N --+ ID, i.e., when Y would be much more readily accessible under native conditions than KC or I D . Curve Y-2, for example, is drawn with AGO = 6 kcal/mole, so that Y would be present at 3 X lo4 as high a concentration as either RC or I D in the native environment. However, when the denaturant concentration becomes sufficiently high for transition away from the native state to begin to be experimentally observable, the curves Y-2 and RC have crossed, so that the free energy of Y lies above that of RC. For example, a t 4 M denaturant, the free energies of Fig. 7 yield an equilibrium composition of N = %‘yo’,, RC = 41y0, Y = 2%, and so low a concentration of Y would be undetectable within the limits of error when a transition is tested for the presence of stable intermediate states. On the other hand, state Y would of course become a stable intermediate in the transition zone if a lower value of AGO is assigned. For example, with AGO = 4.5 kcal/mole instead of 6 kcal/mole, the equilibrium composition a t 4 M denaturant would be N = 47y0, RC = 33y0, Y = 20%. Whether or not stable intermediates occur during a n experimentally observable transition is thus seen to be highly sensitive to the intrinsic stabilities of potential intermediate states. Intermediates may be expected t o be observable for some proteins, but not for others. V. THERMODYNAMICS OF TRANSITION FROM NATIVETO DENATURED STATES

A . Effect of Temperature. The Value of ACp It was shown in Part B of this review (Volume 23) that the most striking thermodynamic parameter for denaturation processes leading to disordered products is the large positive AC, that invariably accompanies the reaction. Values of AH, a t low temperature, are sometimes positive and sometimes negative, and, because of the large ACp, increase markedly with increasing temperature. As was seen earlier (Section IV,C), we cannot at present predict values of AH on the basis of model compound studies, and therefore have no indication of what feature of the ordered structure might be responsible for the variation in AH from one protein to another. On the other hand, the positive ACp is at least qualitatively predictable, because hydrophobic moieties of the protein become exposed to solvent in the reactions N -+ RC or N -+ ID, and contacts between such moieties end water are in fact characterized by very large anomalous heat capacities, as shown in Table IX. We shall make quantitative estimates of the effect

58

CHARLES TANFORD

predicted from this source here, and will see that the predicted ACpvalues in fact fall short of experimental values. The data given in Table IX are rather sparse and inexact. We have used them to make the following “guesses” as t o reasonable contributions to AC, for fully exposed hydrophobic parts of the protein: Trp side chain, 100 cal/deg/mole; Phe, Tyr, Leu, Ile side chains, 80 cal/deg/mole; Val side chain and hydrophobic part of Lys, 60 cal/deg/mole; Pro and Met side chains and hydrophobic parts of His and Arg, 40 cal/deg/niole; Ala side chain and hydrophobic part of Thr 20 calldeglmolc. The guesses, in anticipation of obtaining a relatively low estimate in comparison with experiment, are on the generous side. We have included hydrophobic moieties that make lesser contributions (e.g., alsnyl side chains and hydrophobic parts of histidine, arginine, etc.), which were excluded from the calculation of 6AG in Section IV,D. To some extent this is justified because contributions to ACp arise from interactions with water molecules, whereas contributions to 6AG arise from interactions with larger solvent molecules that may not be able to sense the influence of hydrophobic moieties that are relatively small. Model compound data indicate that these smaller groups should in fact make greater relative contributions to ACp than to 6AG, e.g., 6g,,,, for transfer of an alanyl side chain from water to urea solutions is actually zero (Nozaki and Tanford, 1963), whereas Table IX shows that the contribution of an alanyl side chain to ACp is as large, per carbon atom, as the contributions from longer aliphatic chains. The contributions for fully exposed groups given above have been combined with the degrees of exposure given in Table XI1 to yield the predicted AC, values shown in Table XV. Experimental values are included for comparison. It is evident that experimental values are generally significantly higher than the predicted values, especially for the reaction N --+ ID. It should be noted however that the better agreement between calculated and observed AC, values for the reaction N + RC may be artifactual. The experimental values for this process are measured in concentrated solutions of urea or GuHCI, whereas the calculated values apply to pure water. There is some evidence that suggests that the anomalous heat capacity associated with solvent interactions of hydrophobic groups should be less in urea or GuHCl solutions than in water (see page 41). The following are possible reasons for the discrepancies between calculated and experimental results. 1. The ( Y ~values given in Table XI1 may be incorrect. Larger values of Act, would lead t o larger predicted AC,’s. As far as the reaction PI: -+ RC is concerned, the values of A o t given in Table XI1 will be seen to besapproximately correct when we attempt to account for the dependencc of In K on denaturant concentration in the following section. However, we are deal-

59

PROTEIN DENATURATION

TABLEXV Predicted AC, Values for Exposure of Hydrophobic Parts to Watera Calculated AC, (cal/deg/mole)

Experimental AC, (eal/deg/mole)

N-+RC

Protein llibonuclease Lysozyme &Lactoglobulin Chymot,rypsinogen Chymo trypsiri

N-RC

N+ID

1200 1400 2100 2700 2700

500 600 900 1200 1200

denat. by urea or GuHCl

N +ID thermal denat.

1800b 1350d 2150’ -

2000c -e

26008 3900h

a Calculated resiilts are based on A a i = 0.35 for the react,iori N -+ R C and Aai = 0.15 for the reaction N ID, in accord with the assumed degrees of exposure of Table XII. * Salahuddin (1968). c Brandts and Hunt (1967), from the temperature dependence of I<, and Da1ifort.h et al. (1967), by direct cslorimetric measiirement, have obtained essentially t,he same result. The mat,hematical analysis of Brandts arid Hunt indicate that AC, is temperature dependent, hut that; conclusion lies within the experimental uncertainty of the data. d Aune and Tanford (1969). e Sophianopouloa and Weiss (1964) have reported a temperature-independent AH for this reaction. All their measurements were made at relatively high temperat.ures, where AH is large, arid a change in AH with temperature could easily have escaped detection. Pace and Tanford (1968). The reaction was treated as a two-state transition, which has subsequently heen showti to he ail erroneous assumption (see Section VII,B). This value is therefore subject to revision. 0 Brandts (1964a). The ACp was reported as being temperature dependent but that conclusion is within the experimental uncertainty of the dab. h This value is calculat,ed from the AH values at, different temperatures, given by Pohl (1968). An even higher value (4000 to 5000 cal/deg/mole) is obtained from the work of Biltonen and Liimry (1969). --f

ing here with degree of exposure to water molecules, and it is possible that groups that permit only poor access to denaturant molecules can be fully accessible to Jvater molecules, i.e., c y i values in the randomly coiled state may be larger from the point of view of ACp evaluation. The relatively small A C Yvalues ~ for hydrophobic groups for the reaction N ---f ID is necessary if we are to account for the stability of state ID in concentrated salt solutions. It is perhaps possible that the ID state obtained by thermal denaturation is riot the same as the state obtained by denaturation in salt solutions, but the evidence given i n Part A of this review (Volume 23) is strongly against this possibility.

60

CHARLES TANFORD

2. The most likely explanation is that there are major contributions to AC, from sources other than the solvent contacts of hydrophobic groups. A large contribution could very easily arise from the order-disorder aspect of the transition, i.e., corresponding to AGco,,f of Eq. (4).

B. Steepness of Transitions with Respect to Denaturant Concentration A thermodynamic parameter that is readily determined experjmeritally for isothermal transitions induced by the addition of denaturants is the variation of the equilibrium constant K with the denaturant concentration C, in the transition zone, where both native and denatured conformations contribute significantly to the equilibrium (0.2 5 K 5 5 , for best accuracy). We and others have in the past frequently used a function of the form K = (constant) C" (41) to describe the transition near its midpoint, and have used the derivative, a In K/d In C = n, as a measure of the steepness of the transition. This procedure is analogous to the procedure used to characterize the degree of cooperativity in reactions such as the binding of oxygen to hemoglobin (Wyman, 1964). This procedure is inappropriate if we wish t o describe the dependence of K on C in terms of the procedure of free energy localization. Hy combining Eqs. (39) and (40) we obtain

-RT In K

=

AG = AGO

+C

(Aai)@tr,i

(42)

z

The results of Section II1,B show that 6gt, often tends to be close to a 1'inear function of denaturant concentration. Therefore In K may be expected to be closer to a linear function of C than of In C. Another advantage in plotting In K versus C is that such a plot can be extrapolated to C = 0, to yield values for the equilibrium constant ( K = KO) in the absence of denaturant. Equation (41) cannot be used in this way. It applies only near the midpoint of a transition, and would always lead to K = 0 (or AG= +w)atC=O. We shall in this section calculate In K as a functioii of C, using Eq. (42), together with 6g, values given in Section III,B, for the reaction native == random coil, in concentrated urea and GuHCl solutions. The degrees of exposure given in Table XI1 will again be used, i.e., we shall take Aa, to be 0.35 for both peptide and hydrophobic groups, and in general nialie the calculation as a function of denaturant concentration in the nianner outlined in Table X III. In most examples, because K itself can be measured only over a very limited range of denaturant concentration, the relation between In K and C is measurable over only a very narrow range of C . In one case, however,

61

PROTEIN DENATURATION

Y

0

I

I

I

1 2 3 Concentration of GuHCl (rnoles/liter)

L

4

FIG.8. Equilibrium constant K for the reaction S RC of lysozyme a t 25" as a function of the concentration of GnHCI (Aul~e,1968). The data were obtained over a wide raiige of pH, arid have been adjusted to pH 6-7 (where K is essentially independent of pH) by Eq. 46. The two curves are theoretical curves according to Eq. (39), curve 1 with ALY%= 0.35,curve 2 with ACU,= 0.275.

the denaturation of lysozyme by GuHC1, data have been obtained over a wide range of C, by making use of the effect of pH on the equilibrium constant for the reaction (Aune, 1968). Because of this effect, the rapges of concentration of denaturant within which K is nieasurable are djff erent at, different pH's. Moreover, the function that describes the effect of pH is itself independent of denaturant concentration, and has been determined quantitatively (see Section VI, Fig. 9), so that all data from different pH values can be corrected to any single arbitrary pH, leading to a plot of In K versus C over a wide range in both K and C. Such a plot is shown in Fig. 8. Figure 8 also shows a theoretical plot of log K versus C , based onEq. (42), with ACY~= 0.35 for all hydrophobic and peptide groups, and with an arbitrary value of the constant (log KO) chosen so that the theoretical curve coincides with the experjmental data near 3 d i GuHCl. It is evident that this curve predicts too steep a dependence of In K on C . I n order to obtain a theoretical curve with the correct slope, it is necessary to use smaller values of Aaz. Curve 2 of Fig. 8, for example, which is drawn according to Eq. (42) with Aa, = 0.275 for both hydrophobic and peptide group, is seen to provide an excellent fit of the experimental data throughout the concentration range covered. It is perhaps not uiireasoiiable that the An2 values which have had to be

62

CHARLES TANFORD

used to fit the experimental data of Fig. 8 are somewhat smallcr than predicted on the basis of Table XII. Lysozyme has an unusually large number of exposed aromatic groups in the native state (Williams et al., 1965), and in its denatured state occupies a remarkably small volume, presumably because of the location of the disulfide bonds, which of course remain intact during denaturation by GuHCl in the absence of reducing agents. As was noted in Part A (Volume 23, p. 165), the volume of the molecular domain in the denatured state in concentrated GuHCl solution is only about twice that of the native protein, and access of solvent to the side chains must be somewhat more restricted than in most other proteins. It is of considerable intercst that the results obtained for the denaturation of lysozyme by GuHCl are entirely consistent with the limited information available on the deriaturatiori of that protein by urea. Lysozyme is known to be resistant to the action of urea to a concentration of nearly 8 Ad, but the measurements of Hamaguchi and Kurono (1963), a t 25°C: and pH 7, indicate that the protein is denatured to the extent of about 25% a t 10 M urea. Assuming that the product is again a cross-linked random coil (as is true for other proteins in urea), arid that the transition is again a twostate process, this would mean that K for the reaction is approximately 0.33 a t 10 M urea, or log K N -0.5. Since the reaction is the same as that occurring in GuHC1, the equilibrium constant in the absence of denaturant must be the same as that which applies to the reaction in GuHC1, which is seen from Fig. 8 to be log KO = -9.26. The equilibrium constant in urea solutions should thus be given by log K

=

-9.26

+ 0.275

Ag,,,;

(43)

i

using the same value for the average degree of exposure as had to be used for the results of Fig. 8. Using 6ge valucs determined between 0 and 8 M urea, and extrapolating to 10 M urea, the calculated results become log K = -2.3 a t 8 M urea, and log K = -0.56 at 10 M urea, in satisfactory agreement with the experimental data. The same method of analysis has been applied to other transitions between native and randomly coiled conformations, and the results are summarized in Table XVI. They may be somewhat less reliable than the results obtained with lysozyine because the concentration ranges covered by measurable eqidibrium data. are more limited. The results show that the steepness of transitioris induced by GuHCl or urea is generally compatible with values of Actt that come close to the figure of 0.35 that is bascd on the degrees of exposure listed in Table XII. A disturbirig feature of the results is that the data obtained for p-lactoglobulin and ribonuclease, unlike those for lysozyme, indicate that the course of denaturation in urea is riot compatible with the same values of

63

PROTEIN DENATURATION

TABLE XVI Course of Denaturation by GuHCl and Urea" Protein ~

Conditions

Affi

GuHCI, pH 6-7b Urea, p H 7c GuHC1, pH 3 . 2d Urea, p H 3.2d GuHCl, p H 6" Ureaf

0.275 (0.275) 0.285 0.32 0.35 -

log K O

~~

Lysosyme @-Lactoglobulin Ribonuclease

-9.26 (-9.26) -11.1 -7.3 -7.7 -

a Parameters of Eq. (42) required to describe the experimental data, a t 25°C. AaI for hydrophobic and peptide groups assumed to be the same. b Data shown in Fig. 8. sparse results of Hamaguchi and Kurono (1963) are compatible with the same parameters as those required for denaturation by GuHCl. dThese calculations are based on the data of Pace and Tanford (1968) and on unpublished results of T. Takagi. The denaturation was treated as a two-state transition, which has subsequently been shown to be incorrect (see Section VI1,B). The listed parameters may therefore be subject to substantial revision. The tentative analysis, on the basis of kinetic studies, given in Section VII,B, would lead to A a , = 0.36 and log KO = - 14.3 for denaturation by GuHCl. e Based on the results of Salahuddin (1968). f The results of Foss and Schellman (1959), Nelson and Hummel (1962), and Barnard (1964) are not self-consistent. The latter indicates that the equilibrium constant for denaturation by urea is unity a t a urea concentration of 6.7 M . This would not be compatible with the parameters for denaturation by GuHC1. If A a z = 0.35, log K Owould have to be -6.5 with log K O= -7.7, A a , would have to be 0.42. The midpoint for urea denaturation would have to be a t 7.8 M for consistency with the parameters given in the table for GuHCl denaturation.

log K Oand Aai as apply to denaturation in GuHC1. It is not clear whether this represents a serious discrepancy because these transitions have not been investigated as carefully as the denaturation of lysozyme, especially with regard to the influence of pH. For p-lactoglobulin there is the additional problem that the denaturation process is not a two-state process over part of the transitibn range, as will be shown in Section VII. It is clear that further investigation of these reactions is needed.7 7 Schechter and Epstein (1968) have studied the denaturation of myoglobin by urea and GuHCl. The midpoints of the transitions for sperm whale metmyglobin, at pH 7.6 and 2 5 T , occur a t 7.2 M urea and 2.5 M GuHCI, respectively. These figures correspond to identical values of log KO if A a , values are the same for both denaturants. There are not enough experimental points in the transition regions to determine average A a Evalues with precision. An approximate value for d In K/d In C has been given by the authors for the urea data, and leads to a rather low value for the average Amt. Litman (1966) gives an approximate value for d In K/d In C for the denaturation of sperm whale metmyoglobin by GL I HCwhich ~ corresponds to a n average Aai of about 0.35, but the midpoint of the transition as reported by him is not consistent with that of Schechter and Epstein.

64

CHARLES TANFORD

VI. BINDINGSITES FOR DENATURANTS When denaturants or other added substances excrt their effects on denaturation equilibria a t very low concentrations, the only conceivable explanation is that the effect is related to binding of the added substance a t specific sites of thc protein nioleculc. Appropriate equations for discussing the effects in these terms were presented in Section II,B, and they will bc applied here to the effects of pH and detergents. We shall also examine (in Sections VI,C and V1,D) the possibility of analyzing denaturation processes at high concentrations of denaturant in similar terms.

A . Hydrogen Ion Equilibria Equation (23) is a rigorous equation for the effect of pH on the equilibrium constant for any reaction of the type N e D, regardless of whether denaturation per se is primarily induced by pH itself, in a medium otherwise benign to the native state, or whether it is primarily induced by some other environmental component, and the effect of pH represents merely a perturbation of the equilibrium. Unequivocal data on the difference between the titration states of native and denatured proteins can thus always be obtained. However, it should be recalled that K values can be measured with accuracy only near the midpoint of a transition. Where pH itself is the primary factor responsible for denaturation, data niay thus be limited to a narrow range of pH. Data over a wider pH range become available if the equilibrium can be simultaneously influenced by pII and some other variable, e.g., if pH is not the primary factor responsible for denaturation. The effect of p H on denaturation equilibria cannot be determined with anything approaching the accuracy with which actual titration curves can be measured. In addition, the maximum values of AaH+ are much smaller than the total number of titratable groups on a protein molecule. It is thus usually possible t o express the effects of pH in terms of a relatively small number of parameters, very much smaller than the number of parameters required to describe the overall titration curve of the protein, either in its native or its denatured state. As an example, we consider the effect of pH on the native S random coil transition of lysozyme, induced by addition of GuHCl. This effect has been studied over a wide pH range, from pH 1 to abovc pH 8. The results from pH 1 to about pH 3.5 (Aune and Tanford, 1969) wcre discussed in Part B of this review (Volume 23). They could be described in terms of only two groups with pK, diff erences between native and denatured forms, the equation uscd being of the form of Eq. 24:

PROTEIN DENATURATION

65

The pk', values in the numerator, applying to the denatured state, should be essentially intrinsic pK's for the groups involved : the values 3.4 and 4.4 are appropriate t o the a-COOH group of the protein, and to a glutamyl side chain. As previously stated, an examination of the model of the structure of lysozyme (Blake et al., 1965) showed that there is good reason to believe that the a-COOH group and glutamyl residue 7 lie close to positive charges in the native protein, and should therefore have abnormally low values of pK,,N. Actually, the position of the a-COOH group is not established with certainty by the crystallographic data, and other data (Dahlquist and Raftery, 1968) indicate that an aspartyl residue should contribute one of the groups with an abnormally low ~ K , , N . If indeed one of the groups with pK,,N = 1.9 is an aspartyl group, rather than the a-COOH group, Eq. (44)must be rewritten to give the appropriate intrinsic pK, of an aspartyl side chain in place of that of an a-COOH group, leading to

Equation (44) fits the data of Aune and Tanford just as well as Eq. (45). Figure 9 shows results at higher p H (and somewhat higher GuHCl concentration) obtained by Ogasahara and Hamaguchi (1967). Curve 1 represents Eq. (44), and is seen to describe the results from pH 3.3 to pH 4.5 quite adequately. Curve 2 represents Eq. (451, and provides a somewhat better fit to the experimental results between pH 3.3 arid p H 4. However, it is evident that neither equation can fit the results above p H 4.5. These can be fitted, however, if a third group with ~ K , , N# PK,,D is introduced. > ~ K , , Din, contrast to the two groups inThis group must have ~ K , , N volved in Eqs. (44) and (45), which have ~ K , , N < pK,,D. Curve 3 of Fig. 9 is drawn according to the equation

and evidently gives an adequate fit, though the two points a t highest p H suggest that another group with p k ' , , ~> PK,,D is required if the equation is to apply above pH 8. About 13 or 14 acidic groups contribute to the actual titration curve of Iysozyme between pH 1 and pH 8. Although it is not particularly surprising that only three of these groups undergo significant alterations in pK, upon denaturation, it must be emphasized that Eq. (46) represents the simplest possible equation that is compatible with the results. More complex equations, involving more than three groups, may fit the data as well

66

CHARLES TANFORD

1.01

I ’

I

I

I

4

PH

6

1

I

8

FIG.9. The effect of pH on the equilibrium constant K for the N

RC reaction of lysozyme. The data are from Ogasnhara and Hamagrlchi (1967), a t 3.84 A4 GuH(’1, 25°C. Curves 1, 2, and 3 represent Eqs. (44),(45), arid (46), iespectively.

or even better. Even if we retain the simple format of Eq. (24), the number of groups with altered pK, can easily appear to be smaller than the true number of such groups if one of the groups whose pK, is affected by denaturation has ~ K , , Napproximately equal t o pK,,D of another such group. This situation, as a matter of fact, very likely applies to lysozyme. There are several lines of evidence (Rupley el aE., 1967; Dahlquist and Raftery, 1968) that indicate that glutamyl residue 35 of lysozyme has ~ K , , N somewhat above 6. Since pK,,D should be 4.4, this group should contribute a 3, to Eq. (46). This is not in accord 10-4.4)/(aH+ quotient ( u H + with the experimental results. A likely explanation lies in the fact that pK,,n for the histidyl side chain is also somewhat above 6, arid if this group has an anomalously low pK,,N of 5.1, another quotient (uH+ (UH+ would be introduced into the equation. The factor (uN+ 10--6J) would appear in both denominator and numerator, and would thus cancel. In other words, the third term in Eq. (46), suggesting that there is a single glutamyl residue with pK,,N = 5.1 and ~ K , , D= 4.4, is actually likely to represent an artifact. This term very likely represents the combined effects of the glutamyl and histidyl residues just discussed.

+

+ +

+

+

PROTEIN DENATURATION

67

Histidine 15 is in fact quite close to lysine 13 in the native structure, and a pK,,N value of about 5.1 is not at all improbable.8 It is interesting to compare the results of Fig. 9, and their description b y Eq. (46), or by any equation of the form of Eq. (24), with the approximate treatment of titration curves of proteins in terms of the Linderstrgm-Lang equation, which has been the foundation of the analysis of titration curves for forty years (see, e.g., Tanford, 196213). According to this admittedly oversimplified method of analysis, nearly all titratable groups are assumed to have an essentially normal intrinsic pK, in the native state, on which is superimposed a generalized electrostatic effect, which is a function of the total molecular charge only and affects all titratable groups equally. If this treatment were applicable to lysozyme, every titratable group would be affected equally by the transition from the native to the random coil state, with ~ K , , N always less than ~ K , , D a t pH's below the isoelectric point (which lies well above pH 8), the difference increasing as the pH is reduced, in proportion to the charge on the native protein. The value of log K would have to increase monotonically with decreasing pH. It is evident from the results here presented that the Linderstrgm-Lang model is not valid, although it must be pointed out that we are dealing with experiments a t very high ionic strength, where all but short-range electrostatic effects are eliminated, and that the Linderstrgm-Lang treatment may be more acceptable when applied to titration data at lower ionic strength, especially if provision is made to allow for special treatment of a few acidic groups that may be located very close to other charged groups.

B. Detergents It was pointed out in Part A, Section K (Volume 23) that the changes in protein conformation that are induced by detergents occur a t very low detergent concentrations. Their interactions with the protein molecule must therefore be very strong, i.e., they must be interactions that involve binding of the detergent to specific sites of the protein. An important aspect of the problem is that extremely low concentrations of detergent stabilize native proteins against all denaturing agents, and that the denaturation induced by detergents (the product of which has not been well characterized) is a cooperative process, occurring only after the detergent concentration has reached some critical value. It follows from Eq. (19) (with X representing detergent) that V X , N > GX,Dwhen CX is very Meadows et al. (1967) have in fact shown that the single h i d d i n e of lysosyme has a lower-than-normal pk',, although their value is not as low as the one given here. We have not attempted to make adjustments to the four-group equivalent of Eq. (46) to determine the possible ranges of pKo,N values for glutamyl residue 35 and the histidyl residue that are compatible with the experimental data.

68

CHARLES TANFORD

small, and P X , D > CX,N when CX exceeds the critical concentration for the transition N -+ D. The exact nature of the statc D need riot be known to write equations in terms of binding constants for which these inequalities hold true. The equations must satisfy the following two conditions: (a) that the binding constants of sites on the native protein are larger than those on the denatured protein, so that they will bind detergent to a greater extent a t very small concentrations of detergent; and (b) that the total number of detergent molecules or ions that can be bound to the denatured protein is greater than the maximum number that can be bound to thc native protein, so that CX,D will overtake VX,N a t concentrations where the sites on the native protein approach saturation. I t is likely that binding to the denatured protein is micellar, i.e., in terms of Eq. (15), relatively few species of form DXj contribute to the equilibrium, all with large values of j . On the other hand, a t least for serum albumin, binding to the native proteins involves a Iiumbcr of more-or-less independent binding sites for individual detergent molecules or ions. T o illustrate the effect of detergent concentration on the equilibrium constant K , for the process N $ D, we may imagine a simple situation in which there is just a single form of the complex between denatured protein arid detergent with j = nD, and formation constant LD (no other subscript needed, since only one such constant is required). For the binding a t discrete sites of the native protein, we assume all sites to be identical. We shall use detergent concentration in place of activity, us the concentrations arc small. By appropriate extension of Eqs. (16)-(18), we get

This equation will automatically satisfy the conditions imposed above if nD

> nN.

As has been pointed out, however, both by Decker and Foster (1966) and Reynolds et al. (1967), micellar binding to the denatured protein is not necessary to achieve a cooperative transition. If binding to the denatured protein also occurs a t discrete sites, assumed to be identical to each other, we may use Eq. (18), with CX in place of a x , instead of Eq. (47). The conditions imposed for the system will apply if 7111 > TLN and li,y >> IiD, such that k N n N > kDnD. Both the steepness of the transition, and the precipitous increase in binding that accompanies it can be accounted for by this relation if KO is made sufficiently small. I n fact, Eq. (18) cannot bc distinguished from Eq. (47) if knCx >> 1 in the transition region, which is the situation in the binding of alkylbenzene sulfonates to serum albuniin (Decker and Foster, 1966). For the binding of dodecyl sulfate to seruin x 1 in the transition region, so that, albumin (Reynolds et al., 1967), k ~ C ‘v

PROTEIN DENATURATION

69

in principle, a distinction between Eqs. (18) and (47) could be made. The latter would predict a steeper transition curve arid a concomitantly steeper curve for binding of the detergent. However, the steepness predicted by Eq. (18) is already so great that the difference may not be experimentally detectable. I n any event, serum albumin is a poor protein for a study of this kind, since it is probably not a homogeneous protein. Both transition and binding curves thus reflect microheterogeneity of the protein, as well as the characteristics of detergent binding. The suggestion that detergent binding to denatured proteins is micellar in nature must thus be considered at present as intuitive. The experimental data do not permit distinction between models based on micellar binding and on discrete binding sites for individual detergent ions. It may be noted that a good picture of a binding site of a native protein for a detergent ion or molecule can be obtained from the work of Wishnia and Pinder (1966) with p-lactoglobulin.

C . Urea and Cuanidine Hydrochloride We have seen that the effects of GuHCl and urea can be explained satisfactorily on the basis of localized free energy effects at hydrophobic side chains and peptide groups of the protein molecule, similar to free energy changes that affect model compounds bearing the same kinds of groups. To a chemist such an explanation is less satisfying than the model used to account for the effects of pH and detergents, as the latter provides a physical picture of the manner of interaction between the added substance of the protein, such as the free energy parameters do not. We have shown that Eq. (20) must be rigorously applicable to the interaction of GuHCl or urea with proteins. Changes in the “binding” of denaturant or water to the protein molecule are thus a necessary manifestation of the effects described in Section V in terms of localized free energy contributions. Can we analyze the data in terms of “binding” equilibria, and thereby obtain better insight into the mechanism of action of GuHCl and urea? This is the question we shall briefly consider here. We shall see that no definite conclusion can be reached, for the simple reason that the truly characteristic feature of site binding, which is that it obeys a simple mass action law, can be demonstrated only if we are able to make measurenierits a t concentrations of ligand that extend at least an order of magnitude on either side of the point of half-saturation. This is easily accomplished when we deal with strong binding, but it becomes inipossible when we deal with a phenomenon in which the point of half-saturation (if there is one) occurs a t a ligand concentration of several molar. We shall discuss this problem in terms of the dependence of the equilibrium constmt for the N + RC of lysozyme on GuHCI, using the data

70

CHARLES TANFORD

already presented in Fig. 8. The calculations to be reported u-ere carried out by K. C. Aune and R. W. Roxby. It should be noted that thefactthat GuHCl is an electrolyte introduces an ambiguity into the discussion, because either of the ions or both can be involved in binding equilibria. This ambiguity could have been avoided if a urea-induced deriat,uration had been used as the basis for discussion. However, experimental results of the quality of those of Fig. 8 are not available for any transition induced by urea. 1. Binding

05 Neutral GuHCl Molecules

We assume first that the first term on the right-hand side of Eq. (20) is the predominant one, and that water binding can be neglected. We first consider the ligand to be a neutral GuHCl molecule, implying concerted binding by GuHf and C1- ions, which is not very realistic. It is, however, the easiest situation to treat mathematically. Activities of GuHCl have been determined by the isopiestic iiiethod (E. P. K. Hade, unpublished data), and Fig. I0 shows the results of Fig. 8 replotted as a function of uG,,HcI. We desire to fit these results to an equation of the type of Eq. (17). Clearly, the number of parameters that can be determined from the closeto-linear plot of the data is very small and simplifying assumptions- have to be made. The assumption we have considered most reasonable is that

FIG.10. The results of Fig. 8, replott,ed as a fuiiction of the activity of GuHC1. The curve represents either Eq. (49), with logKO = -7.80, An = 7.84, and k = 3.00, or Eq. ( 5 2 ) , with log KO = - 10.44, An = 31.5, arid k = 1.30. The two theoretical curves agree to within 0.01 iii log K through the entire range covered by the figure.

71

PROTEIN DENATURATION

the difference between native and denatured states lies in the number of binding sites rather than in the binding co1istants, i.e., we suppose th a t protein molecules niay have binding sites for GuHCl molecules with binding constants kl, k,, etc., that are the same in the two states, but that the num, in the denatured state exceeds the number ber of such sites (nl,D,n z , ~etc.) (nl,N,n2,N, etc.) in the native state, as a result of the unfolding that has occurred. Thus

K

=

Ko(1

+

h

~

~

~

~

+

~

. . .

ih ) a ~ ~ ~ ~ 1 ~ ( ~l l

)

~

~

p (48)

where An1 = nl,D - nl,N, etc. Even this equation has more parameters than can be determined from the data. We have further simplified it by considering all sites that contribute significantly to the variation of K with GuHCl concentration to have the same binding constant k , i.e.,

K = Ka(1

+

(49)

Best values of KO,An, and k were determined by a least-squares procedure. They were An = 7.84, k = 3.00, and log KO = -7.80. The curve in Fig. 10 is drawn according to Eq. (49) with these parameters. The nonintegral number of An is permissible in view of the approximation made in going from Eq. (48) to Eq. (49). The result niay be thought of as implying that perhaps 5 , 6, or 7 sites with approximately the given value of k are actually newly exposed in the denaturation process, and that the rest of the expression represents a larger number of weaker binding sites, forced into the format of Eq. (49). The surprising aspect of the result is the small value for An. It is obviously incompatible, for example, with the idea that peptide groups represent the major binding sites for GuHC1, or even that a set of two or three adjacent peptide groups forms a binding site. The value of An would be expected to be larger since all of the 128 peptide groups of the protein are available for binding in the denatured state. A possible interpretation is that the sites represent aromatic side chains. They are the protein moieties with the largest 6gt,,i values for stabilization by GuHCl (Table VI), and it is thus appropriate that they may be the principal binding sites for GuHCl when a binding model is used. Moreover, though there are 12 aromatic residues in lysozyme, about half of them are exposed a t the surface in the native protein, so that only about 6 would be newly exposed on denaturation. However, 6gt,,, values in GuHCl have not been interpretable in terms of Eq. (38), with ax = U G ~ H C I ,and with a constant value of k, independent of concentration. Average binding constants fall well below the value of 3.0 required to fit Eq. (49). Similar results are obtained if the binding is thought of as competitive between GuHCl and water, which is one way of assigning some role to the AOw term of Eq. (20). We have replaced Eq. (49) by

72

CHARLES TANFORD

K

=

Ko(1

+ kaGuHCl/aW2)An

(50)

which assumes that two water niolecules occupy a site for a single GuHCl molecule. The best fit to the data is obtairied with An = 6.28, k = 5.15, log Ko = -8.35. 2. Binding of GuH+ Ions

Both GuH+ and its accompanying anions must play a role in denaturation by guanidirlium salts (Part A, Volunic 23, p. 187) so that, if ion binding is invoked, the simplest possible equation for K , analogous to Eq. (49), would be of the form

K

=

Ko(1

+ klaGuH+)Anl(l + 1c2aA-)Anz

(51)

where A- represents the anion. However, GuIICl is a less effective denaturing agent than salts of GuH+ with most other anions, and the anion term is therefore presumably relatively unimportant. Unfortunately activities for the separate ions of GuHCl have not been estimated (nonthermodynainic assumptions are needed to do so), and the only recourse if we wish to use an equation involving aGuH+ is to hope that the mean ion activity of the salt, a* = u G ~ H c ~ ”is~ a reasonable measure of it. We have accordingly fitted the results of Fig. 10 to the relation

K = Ko(1

+ ka*)An

(52)

and obtained best fit with An = 21.5, k = 1.20, log K O= -10.45. It is interesting that the value of An is significantly larger than thc value required for Eqs. (49) and (50), and that the value of k is of the same order of magnitude as k values that are obtained when Sg,, values for backbone peptide units (two peptide groups per binding site) and aromatic groups of model compounds, for transfer from water to GuHC1, are treated by Eq. (38), with ax = a, (see Table X I ) . The total number of backbone binding sites and aromatic groups exposed in the reaction N 3 RC should probably be somewhat larger than 21.5, but not sufficiently so to cause us to reject this result as inadmissible. 3. Hydration Sites on thx Native Protein

It is possible that part of the denaturing action of GuHC1 may arise from a negative value of APWin Eq. (20) rather than a positive value of A ~ H c ~ . In fact this would be the situation if Eq. (50) is used to describe the varjation of K with GuHCl activity. Theoretically, it is even possible that all of the denaturing action arises in this way. If, for example, there are q sites on the native protein that can accommodate watcr molecules, but not GuHCI, and 110 such sites in the randomly coiled form, and if this nere

PROTEIN DENATURATION

73

the only factor responsible for the denaturing action of GuHCl, the equation for K would be [from Eq. (22)]

K = Ko/awg (53) This suggestion is, of course, absurd. If Eq. (53) were true, then K would be a unique function of UW, regardless of the denaturant being added. This is not the case. GuHCl has no special effect on water activity. The activity of water in a 6 M solution is 0.78, and can be made to fall to this level by the addition of many other substances without causing denaturation.

FIG.11. The results of Fig. 8, replotted as a function of the activity of water. straight line represents Eq. (53), with q = 107 and log KO= -6.4.

The

It is therefore instructive to note that the experimental data of Fig. 8 can in fact be described in terms of Eq. (53) with a not unreasonable value of q. A plot of In K versus In a, is shown in Fig. 11. Allowing oneself a little license, one can describe the data by means of a linear plot, as required by Eq. (53). The slope gives q = 107, and the intercept at uw = 1 gives logKO= -6.4. The value of q corresponds to a preferential hydration of the native protein of about 0.14 gm per gram of protein. This is not an unreasonable figure a t all. Native serum albumin in concentrated CsCI, for example, has a preferential hydration of 0.18 gm per gram of p r ~ t e i n . ~ 9 Unpublished measurements of E. P. K. Hade indicate that native serum albumin and other proteins are not preferentially hydrated in moderately concentrated GuHCl solutions. Evidently GuH+ ions can enter the domain of the protein molecule a t places from which Cs+ ionx are excluded.

74

CHARLES TANFORD

The value of log KO is considerably larger than values obtained by use of the equations applied earlier, but by no means incompatible with the experimental results, as is evident from Fig. 8. The importance of this result is that it permits us to evaluate with better perspective the ability to fit the data with the more reasonable binding mechanisms proposed earlier in this section. The fact that a mechanism yields an equation compatible with experimental plots of In K versus u G u H C l is evidently not sufficient evidence on which to base a judgment of the correctness of the mechanism. I t is in fact likely that thermodynamic data alone cannot provide this kind of information. What seems to be needed are direct measures of the sites of interaction, such as might be provided by nuclear magnetic resonance spectroscopy, for example. I n view of the good correlation between 6g,, values derived from model compounds and 6AG values for protein denaturation, it might be easier to seek the evidence for the locus of action of GuHCl and other denaturants by examining suitable model compounds in solutions containing denaturants than by studying protein solutions directly.

D. Inorganic Salts As has been mentioned before, denaturation by inorganic salts is being reviewed elsewhere by von Rippel and Schleich (1969n,b) and is thus riot treated in detail here. Therniodynamic data for salt-induced transitions are very sparse, and data that could be subjected to an arialysis such as we have applied to denaturation by GuRCI are not available. However, independent binding data are available for inorganic salts, based on retardation of salts on polyacrylamide columns. These results show that both cations and anions are bound to peptide groups and are compatible with the explanation that the relatively large negative 6g,, values for transfer of peptide groups to salt solutions (Fig. 3) are in fact a manifestation of site binding. Furthermore, X-ray studies of crystalline complexes of LiCl with N-methyl acetamide and other arnide systems show that Li+ ions tend to associate with the oxygen atom of the peptide group, and C1- ions with the nitrogen atom (Bello at al., 1966). The reader is referred t o the articles by von Hippel and Schleich for further details.

VII. KINETICS OF DENATURATION We shall first consider two-state processes hi

N--’D kr

for which the rate of reaction can be described in terms of ti single rate constant Icr for thc forwird reaction and a single rate constarit li, for the

PROTEIN DENATURATION

75

reverse reaction. The rate of interconversion of N and D is determined by the characteristics of a single activated complex (Y*), in addition to the properties of the native and denatured states. Extension to more complex reaction mechanisms that involve stable intermediates (Yl, Yz, . . .) requires no new principles. The only difference is that more conformational states are involved, i.e., the rates are determined by the properties of each equilibrium state, and by a distinct activated complex (Ylt, Y2*, . . .) for every allowed conversion between equilibrium states.

A . Two-State Transitions lo Predominantly Disordered Products The transition from the ordered native state to a disordered denatured state must occur progressively. The precisely folded polypeptide chain must unravel piece by piece, passing through states with increased disorder, and increased exposure of hydrophobic groups and peptide groups to the solvent. The free energy accompanying each step of the process will sometimes be positive and sometimes negative, depending on the exact balance between the contributions made by the various terms of Eq. (4) to each stage. €Ionever, if a transition is a two-state transition, in which none of the intermediate states make a significant contribution to the equilibrium mixture of conformations a t any stage of the transition, all intermediate states must have a free energy that is higher than the free energy of either the native or the denatured state. A schematic representation of this situation is shown in Fig. 12, where we have characterized successive stages of unfolding in terms of the degree of esposure of hydrophobic and peptide groups to the solvent. In this purely schematic diagram, we have absigried just a single value of the relative h, to each stage of the transition, applicable toall kinds of groups. In practice, of course, a given stage of the process would expose only a sniall part of the molecule, :tnd a different relative Aa, would apply to each kind of group a t each step. In an actual unfolding process there are also likely to be alternate pathways, and side reactions that lead to partially folded states. Provided that all such states have higher free energy than the initial and final stiltcs, the grmter complesity of the true pathway of unfolding, as compared to that of Fig. 12, will not alter the conclusions to be drawn here. The rate constants 7ir and k , for a reversible two-state process depend only on the maiimzim free energy that has to be traversed on the pnthn a y from N to D. The conformational state corresponding to this niasiinum is known as the critical activated state (see Part 13, Section VI in Volume 23), and is designated by Y’. Thc free energy of formation from the native that from the deriaturated state is AC,*, and they are related state is Mf*,

76

CHARLES TANFORD

NATIVE

CRITICALLY AC TIVAT ED STATE DENATURED

+

0

Relative Lldi

1

FIG. 12. Schematic diagram of free energy versus degree of urifolditlg for a two-state transition: (A) At a denaturant coilcentration below the midpoint of the transition; (B) a t the midpoint; (C) at a dena(uraut concentration above the midpoint of the transition. Further decrease of deuatnraiit concenhtiotl (below that in sketch A) can cause the free energy of the denatured state to rise above some of the minima iriterveriing between native arid denatured states, ah has also been indicated in Fig. 7.

by the fact that the difference between them must be equal to AG for the overall reaction,

AG; - AG,' = AG

(54)

The rate constants niay be written in the form [see Eqs. (69) and (70) of Part U] In kr = constant - AG;/IZT In k , = constant - AG,'/IZT

As vas true for AG itself (Section IV,B), we are unable to predict absolute valucs for aGr*or AG,'. We can, however, predict the change in AG' with solvent composition in the same way as was used for AG itself, by the: procedure employed in Section V,B; i.c., in analogy with Eq. (30), -1ZTS 111 kr

where AaZ

=

(Y:

- aL,x.

=

6 ~ G r *= ZAai*Gg,,,,

(57)

A similar relation m:~ybe written for 6AG,*, mid,

77

PROTEIN DENATURATION

as indicated in Fig. 12, for the value of 6AG at any stage of the unfolding process. A more convenient way to write Eq. (57) is in terms of the relative degree of exposure of groups in the activated state, (Aai)rel* = (a? -

-

ai,~)/(ai.~ ai

,~)

(58)

This is the parameter used as the abscissa for Fig. 12. With the simplifying assumption that ( A ( ~ i ) at ~ ~ all l stages of the transition is the same for all kinds of constituent groups of the protein molecule, 6 In kt/6 In K = GAG;/SAG 61nkr/6ln K = 6AG,'/6AG

=

(Acx,)~~?

=

1 - (A(~i),~l*

(59)

(60)

and can thus be determined, for example, by comparing d In k/dC with d In K/dC in experiments in which the concentration of denaturant is varied. An example is provided by Fig. 13, which shows kf and k, for the denaturation of lysozyme by GuHCI. The data represent unpublished results of K. C. Aune, determined in this laboratory. Measurementswere madeat various pH values and corrected to pH N 7 by the use of appropriate analytical expressions for the pH dependence, of the same kind as given by Eq. (46) for the pH dependence of the equilibrium constant for this reaction.

-2

-5

I-\

2

8

,Renaturation (k,)

I

3

Concentration of GuHCI,

I

4

moles/liter

FIG.13. Logarithmic plots of kf and k,, for the N RC reaction of lysozyme at 25", as a function of GuHCl concentration. Measurements were made at various pH values and adjusted to pH 6-7 (Aune and Tanford, 1969).

78

CHARLES TANFORD

The curves drawn through the data are theoretical, according to the relations

+

log kr = -6.40 0.075Z6gtr,; log k , = f2.73 - 0*1926gtr,i

(61) (62)

N The coefficients of the last term in each equation represent a: - O L ~ , and The difference between them is 0.265, consistent with the value of 0.275 (Table XVI) obtained from the variation of the equilibrium constant with CuHCl concentration. The value of the equilibrium constant in the absence of denaturant is log kr.0 - log I C , , ~ = -6.40 - 2.73 = -9.13, and this is also consistent with the value -9.26 obtained from equilibrium measurements directly (Fig. 8). The value of (Aa;*)wl for this denaturation is (0.075)/(0.075 0.19) = 0.28. The activated state is evidently considerably closer to the native state than to the denatured state. In analogy with the treatment of equilibrium constants, &AG*can be expressed in terms of binding equilibria as an alternative to Eq. (67). Thus, for either rate constant,

at - LY(,D, respectively.

+

the right-hand side of Eq. (63) representing the difference in preferential binding between the critical activated state and the native or denatured state, depending on whether the equation refers to kr or k,. The value of A v ~ . , , ~ ~relative f*, t o the Aik,pref that accompaniest the process N + 11, can again be considered as a measure of ( A a ~ ) r c lwhich , would in that case measure the degree to which binding sites for X are exposed. A list of values of (ACX;)~~Iobtained for various reactions is shown in Table XVII. It is seen that the critical activated state lies close to the native state for some reactions, and close t o the denatured state for others. The effect of temperature on the rate of denaturation represents a more complex phenomenon than the effect of denaturant concentration. Values of AH for denaturation are a t present uninterpretable (Section IV,C), and the same must be true for activation energies for kinetic processes. There is no reason to believe that A H is in any way related to the degree of unfolding. An early step of the reaction may involve the rupture of many hydrogen bonds without an accompanying exposure of many groups t o the solvent. The activation energy would be high, and the effect of temperature on such a step might in fact represent the major part of AH'. (One incidental result of this is that the position of the activated state, as represented in a diagram such as Fig. 12, may alter with temperature.) On the other hand, the second derivative of the reaction rate with respect

79

PROTEIN DENATURATION

TABLE XVII Relative Degree of Unfolding of the Activated State for Transitions to Predomiriantly Disordered Prod~tcts Protein and denaturant,

(Aw*)roi

Method Eq. (58)

Lysozyme, GiiHCl, 25" Lysozyme, GitHC1, 25" Lysozyme, GuHCI, 30" Ribonuclease, GuHC1, 25" Itibonuclease, urea, 30" p-Lactoglolnilin, CuHC1, 25' Chymotrypsin, thermal denat.

U

b C

C C

d

e

0.28 0.31 0.31 0.83 0.88 0.54 (0.25)

a By fitting kinetic data over a wide range of denaturant concentration by Eq. (57), and applying Eq. (58) directly. Data are shown i n Fig. 13. From the same data, by ube of Eq. (63). From comparison of d ln k/dC with d ln K/dC near the midpoint of the denatnration eqiiilibriiim curve. The data used are those of Tanford et al. (1966) a t pH 5.5 for lysozyme, Salahuddin (1968) at pH 3.7 for ribonriclease GuHC1, Nelson and Hummel (1962) a t pH 7.3 for riboriuclease urea. d From the tentative assignrnent~made on page 82. The values of d ln lc/d In C given in Part B (Volume 23, p. 270), for the urea denaturation of p-lactoglobulin, are based 011 an assumed two-state transition arid therefore are invalid. Based on comparison between AC,* for the refolding reaction and AC, for the overall process. Data of Pohl (1968) were used.

+

+

to temperature, ahich of course is difficult to determine with precision, yields the heat capacity change that accompanies formation of the activated state (AC,*), and, to the extent that this quantity is a measure of the exposure of hydrophobic groups (see page 59), it will serve as a measure of (Aff%*),l.

Pohl (1968) has studied the effect of temperature on the rates of the reversible thermal denaturation of chymotrypsin. The enthalpy change for the overall process varies from AH N 50 kcal/mole a t 25°C to AH _N 150 ltcal/ mole a t 50°C (AC, is exceptionally large, cf. Table XV). The activation energy is much larger for the rate of denaturation than for the reverse reaction. At 33"C, AH: 'v 82 kcal/mole and AH,* N 0. On the other hand, AC,* is larger for the reverse reaction. According to Pohl, AHf* is independent of temperature within experimental error, but the error is actually very large: because AH{* is so high, the temperature range over which kf could be determined is very narrow, arid the data in fact are conipatible with very large values of AC,,?. For the reverse reaction, AC,,,* is determinable from Pohl's data with better precision. It appears to have a value of ca. -3000 calldeglmole, uhich, coupled with the AC, for the overall reaction (Table XV) leads to AC,,? +lo00 cal/deg/mole, or ( A ( Y % *N ) ~ ~0.25. ~

-

80

CHARLES TANFORD

1 100

al

0

-

7

1

I

1

1

I

I

I

I

80

C

0

LI V

- 60 0

c

P Lt

c

40

C

m

2

d

20

0

I 0

2

4

I 6

GuHCl Conc moles/liter

FIG. 14. Eqiiilibrium and kinrtir data for the denaturation of p-lactoglobulin by GuHC1, a t 25"C, pH 3.2 (unpublished results of T. Takagi). The heavy h i e shows the equilibrium curve, as measured by optical rotation or difference spectroscopy. The arrows indicate typical initial and filial measurements obtained from hilietic experiments in both directions. Initial mensuiements from all kinetic renaturation experimcnts are sliowri as circles. They represent early kiiietic data, extrapolated to zero time.

B. Reactions with Deteclable Intermediate States

No detailed analysis has yet been made of the kinetics of a denaturation process involving stable intermediates. I present hcre a tentative interpretation of an incomplete study of the denaturation of p-lactoglobulin by GuHCl a t 25°C (Takagi and Tanford, 1968, also unpublished results), which indicates that the study of reactions with stable intermediates can yield valuable information about the unfolding and refolding of protein polypeptide chains. Figure 14 shows a sketch of the state of equilibrium in this reaction, as measured by optical rotation or difference spectroscopy, and, by means of arrows, shows the range of GuHCl concentrations within which kinetic experiments were carried out in the forward and reverse directions. Measurements made in the forward direction followed first-order kinetics, and extrapolation to zero time indicated that the first-order process always started from the native conformation. Measurements of the refolding reaction also followed first-order ltirietics a t GuHCl concentrations above about 2.8 M , but extrapolation to zero time did not indicate that the firstorder process began with the randomly coiled product of the reaction.

PROTEIN DENATURATION

81

The circles in the figure show the initial points of the kinetic experiments: transition from the denatured state to the average conformational states represented by these points occurred much more rapidly than the subsequent first-order transition to the final equilibrium mixture. (There are additional complications in the kinetics of refolding at GuHCl concentrations below 2.8 M. We shall not discuss them here.) A possible interpretation of the experimental points of Fig. 14 is that they represent a rapidly established two-state equilibrium between the denatured state (D) and an intermediate (Y) that has optical properties about half-way between the native and denatured states. The curve drawn through the points can then yield values of the equilibrium constant K y D for the process Y D. The apparent equilibrium constant obtained from the final equilibrium curve is given by Eq. (32) of Part B (with aY = 0.5),10 i.e., ~

where K is the true equilibrium constant for the process N D and KNY = K / K Y Dis the equilibrium constant for the process N Y. The data permit evaluation of each of the equilibrium constants as a function of the concentration of GuHCl, and, hence, determination of the average degree of exposure in each state of groups that are stabilized by GuHCl. It was first assumed that Y is an intermediate on the pathway between N and D. The kinetics may then be described in terms of the following scheme : ki

rapid equil.

NeY+D ki

and k, and k2, and their dependence on GuHCl can be evaluated from the first-order kinetic plots. The following results were obtained near the midpoint of the overall transition (near 3.3 M GuHCl).

d In K N Y = 3.43 dC - In -

- 8.67 dC d In k~ -- 4.72 dC

10 I t should be noted that the CXYused here, and defined by Eq. (27) of Part B, is a quite different parameter from the C X ~used elsewhere in this part of the review.

82

CHARLES TANFORD

CRITICAL ACTIVATED STATES

Free

Energy

N

I

Y

D 1

I

0 0.5 1 Relative Degree of Exposure

FIG.15. Hypothetical free energy diagram for the denaturation of ,9-lactoglobulin by GuHCl. The barrier between Y and D is low, so that interconversion of these forms occurs rapidly. The barrier between N and Y is high, so that interconversion of N and D occurs along a different pathway, not involving state Y.

I n terms of relative degrees of exposure of hydrophobic and peptide groups (atfor state D = l.O), we get A C(& = 0.40 for state Y and ( A ( ~ i * ) ~=~ 0.54 l for the activated state of the process governed by k,. These results are clearly incompatible with the proposed reaction scheme, which requires that the activated state for the process governed by 1cl have ( A ( Y Z * ) ~<~ I0.40. The results are compatible with an alternative reaction scheme, in which Y represents a partially folded state that is not on the pathway from N to D, i.e., kr

rapid equil.

N s D e Y kn

No changes in the numerical values of the derivatives given above occur when the results are analyzed in terms of this scheme. (Only the k z values derived from the kinetic data depend on the chosen mechanism.) A possible free energy profile for the reaction, showing only the three states N, D, Y, and the intervening activated states, is shown in Fig. 15. VIII. EQUILIBRIA AND RATESUNDER NATIVECONDITIONS. RELATION TO HYDROGEN EXCHANGE A . Equilibrium and Rate Constants under Native Conditions An important consequence of the development of equations that describe the effects of pH, temperature, and denaturant concentration on equilibrium and rate constants for denaturation is that they enable us to determine numerical values for these parameters under native conditions, i.c., a t ambient temperature, neutral pH, and in the absence of denaturants. The determination cannot be carried out with high precision, partly because the

83

PROTEIN DENATURATION

TABLE XVIII Equilibrium Constants in Aqueous Media in the Absence of Denaturants Protein, reaction

Method of extrapolation

log KO

aGo

(kcal/mole)

-

Lysoayme, N g RC, 25", pH 6-7 (from data in GuHCl solns.) Same reaction, p H 3 Same reaction, p H 1 Ribonuclease, N g RC, 25", pH 6 (from data in GuHCl solns.) Ribonuclease, N C ID, 30", pH 3 . 2 pH 1 1 Chyrnotrypsinogen, N S ID, 2j0, pH 3 Chymotrypsin, N G ID, 25", p H 2 . 5 Myoglobin, N G ID, 25", pH 9 RC, 25", p H 3 . 2 p-lactoglobulin, N (from data in GuHCl solns.) (from data in urea solns.) a

Eq. Eq. Eq. Eq. Eq. Eq. Eq. Eq. Eq.

(.52)" (42)b (50) (49)" (52)d (42)d (52)d (42)d (42)'

Thermal' Thermal/ Thermal' Thermal' Thermal' Eq. (42)g Eq. (42). Eq. (42).

-10.4 -9.3 -8.4 -7.8 -8.7 -7.6 -6.6 -5.5 -7.7

14.2 12.6 11.4 10.6 11.8 10.4 9.0 7.5 10.5

-2.2 +0.8 -5.4 -4.0 -10.0 (- 14.3) (-11.1) (-7.3)

3.1 -1.1 7.4 5.5 13.6 (19.5) (15.1) (10.0)

Data of Fig. 10.

* Data of Fig. 8.

Results for thesame reaction in urea are compatible with the same value of KO. This is considered to be the least realistic of the four methods of c Data of Fig. 10. extrapolation which have been used for these data. Figure 11 represents an obviously false method of extrapolation and leads to log ZG = -6.4, A G ~= 8.7 kcal/mole. d Results a t p H 6-7, adjusted by Eq. (46). e Data of Salahiiddin (1968). A G ~decreases with decreasing pH, but exact data are not available. Thermal denaturation data, extrapolated (where necessary) from knowledge of AG, A H , and ACp as a function of temperature. Data of Brandts (1964a), Brandtsand Hunt (1967), Hermans and Acampora (1967), and Pohl (1968). RC reaction for this 0 Results for p-lactoglobulin are uncertain because the AT protein is not a two-stateprocess. The first figure given i n theTable (log KO = - 14.3, AGO = 19.5 kcaljmole) incorporates a tentative correction for this, as indicated in Table XVI. Preliminary results show t$hat,the etrect of pH on p-lactoglobulin is in the opposite direction from that observed for lysozyme and ribonuclease. AG, values a t p H 6-7 would be srtbstantially smaller.

equations we have used are mostly approximate, and partly because they contain parameters (heats of reaction, degrees of esposure of various kinds of groups) that must be obtairied from the experimental data themselves, and cannot usually be evaluated ivith high precision. Since it is usually necessary to carry out quite a long extrapolation from experimental condi-

84

CHARLES TANFORD

tions under which actual data are obtained to the conditions of the native state, the accuracy of the extrapolated result necessarily suffers. Figure 8, which represents one of the more favorable cases, provides a good example. Some of thc results obtained for equilibrium constants (KO)for transitions to predominantly disordered states are summarized in Table XVIII. For the N RC reaction of lysozyme several values are given, corresponding to the different methods of interpreting the dependence of K on GuHCl concentration which were used in Sections V arid VI. The agreement between them is quite satisfactory: it is evident that all reasonable models for accounting for the concentration dependence of K lead to a value of K O that is self-consistent to within an order of magnitude. The most significarit aspect of Table XVIII is that it shows the native conformation of all the proteins investigated to be only marginally stable with respect to predominantly disordered states of the protein. Considering that a single buried aromatic side chain contributes about 3 kcal/mole to the stability of a native protein, an overall stabilization of about 10 kcall niole for the entire riative protein is a remarkably small figure. A possible implication is that the familiar compact ordered structure of globular proteins may not be a “natural” kind of structure for polypeptide chains in general, but a rather rare event, made possible only by very special amino acid sequences. The fact that virtually all known soluble proteins have a globular structure might then be the result of evolutionary pressure: disordered proteins would be uriablc to survivc in a milieu containing proteolytic enzymcs. A similar proposal has been made by Edsall (1968). Rate constants under native conditions can be evaluated by the same procedure used for the evaluation of K O (Table XIX). For example, the constant portions of Eqs. A 1 and 62 can be regarded as the values of log kf,o and log IC,,~ for the reversible first order N RC transition of lysozyme. It is possible, however, that such rate constants will riot be meaningful, for it is likely that processes observed to be reversible first-order processes, i.e., processes without stable intermediates, in the transition zone will not remain so in the native environment. This reservation applies especially to k,, the value of which increases as the conceritratiori of denaturant is decreased (Fig. 13). It is clear that the rate of renaturatiori cannot increase without limit: new rate-limiting steps in the refolding process are likely to become manifest. Alternatively, an intermediate such as the state 1 ‘ envisaged in Fig. 7 may become important in the absence of denaturant, and the rates of interconversion of Y and RC ni:Ly become rapid relative to the rates of interconversion of N and Y or PI: and RC. The parameter kt,o may be niorc meaningful. This rate corist:mt becomes very small as native conditions are approached (Fig. 13). Since the overall rate of conversion from N to RC is determined by the highest free energy barrier ~

a5

PROTEIN DENATURATION

TABLEXIX Rate Constants an the Absence of Denaturants" kr.o

Protein, reaction

(sec-1)

Lysozyme, N RC, 25", pH 6-7 pLactoglobulin, N RC, 25", pH 3.2 Chymotrypsin, N ID, 25", pH 2.5

4

3 1.1

x 10-7 x 10-11

x

10-8

kr,o

(sec-1) (540)

1 . 1 x 10-2

Notes

b b C

For reversible first-order denaturation processes. reactions are measured in GuHCl solutions and extrapolated to zero concentration of denaturant. As pointed out in the text, denaturation processes found to he reversible first-order processes in the presence of denaturants are likely to cease to be so in the absence of denaturants. The rate constants given in the table thus represent maximum rates. The value of kr.0 for 8-lactoglobulin does not depend on the choice between mechanisms h and B (Section VI1,B). The renaturation process becomes kinetically complex a t GuHCl concentrations below 2.8 M , and no value for k,,o is therefore given. I t is likely that a similar sititation will apply to lysozyme a t very low GuHCl concentrations, and the value of k,,o has therefore been placed in parentheses. (Current work in this laboratory by A. Ikai has confirmed this prediction and indicates that the value of kr,o for lysosyme is about 1 sec-I.) c The thermal denattiration of chymotrypsin (Pohl, 1968) remains first order in both directions down to 2.5". a

* Values for N S RC

encountered along the reaction path, the rate cannot exceed the rate of the first-order process determined by kr.0 even though the reaction itself may cease t o be first order; e.g., if higher barriers appear on the reaction path between the original critical activated state and the state RC, they can only further decrease the reaction rate. Thus kf,,,would represent a maximal rate for the conversion N -+RC under native conditions unless an entirely different pathway with lower free energy barriers can be found.

B. Hydrogen Exchange 1. The Mechanism of Hydrogen Exchange

Many of the labile hydrogen atoms of a protein molecule are buried in the interior of the native structure, and are not in contact with the surrounding solvent. When the surrounding solvent, which in these experiments is water or a dilute salt solution, contains water niolecules with a n isotopic species of hydrogen atom different from the isotopic species of the protein's hydrogen atoms, exposed labile hydrogen atonis of the proteiu are rapidly exchanged for atoms of the new isotopic species. Those that are buried in the interior clearly cannot be exchanged. It is found, nevertheless, that most of the buried hydrogen atonis do undergo exchange if sufficient time is allowed : they can be divided into more or less arbitrary sets, depending on the time required for escharige t o take place.

86

CHARLES TANFORD

The generally accepted mechanisni for exchange of buried hydrogen atoms (Hvidt and Nielsen, 1966) assumes that altered states in which these atoms are exposed to the solvent are accessible to the protein molecule even under native conditions, so that every molecule in fact spends part of its time in a variety of unfolded or partly unfolded conformations. This assumption is clearly confirmed by the results presented in Section VIII,A, which have shown that even the most drastically unfolded state of many proteins (i.e., the random coil) is present in significant amount a t equilibrium under nativelike conditions. A number of partially disordered states are likely to be present in even larger amounts, as indicated, for example, by Fig. 7. If Dj represents a given denatured state, a labile hydrogen atom exposed in that state, but buried in the native state, will be exchanged a t a rate determined by the rate constslnts of the reaction scheme (IIvidt and Nielsen, 1966) k>,t

N ;--.=' D,

ka

+ exchange

kz,r

provided that the denatured state D, is formed from N in a reversible firstorder step. The rate constant k , for the rate of exchange of an exposed hydrogen atom is generally assumed to be the same in all states in which the hydrogen atom is exposed, and values for it are obtained from studies of the rate of exchange in suitable model compounds. The observable rate constant ( k x ) for exchange of any particular hydrogen atom will be the sum of the rates of exchange in all dcnatured states in which it is exposed, i.e.,

with the assumption that all states Dj are present a t negligible equilibrium concentrations with respect to N, i.e., K j = (D,)/(N) = k,,f/lc,,, << 1. For most hydrogen atoms one term in the sum of Eq. (65) is likely to be larger than the rest; i.c., exchange is likely to occur predominantly via a particular denatured state for each hydrogen atom. The various sets of hydrogen atoms with given values of li, will thus correspond to the sets of atoms most readily exchanged via different states D,. From the results analyzed in this paper thermodynamic and kinetic data are available only for the most drastically altered states, i.e., those that may be expected to be the most diEcult to attain from the native state. It may be surmised that there are partly unfolded states that are more readily accessible in the native environment, as was indicated in Fig. 7, but no experimental information on these states is available. Indeed, hydrogen exchange studies probably provide the best source of information on such

PROTEIN DENATURATION

87

states a t the present time. We can therefore attempt a calculation of I;, only for the slowest exchanging hydrogen atoms, i.e., those that become exposed in the state EC, but remain buried in all the partly unfolded states that have a lower frcc energy than RC in the native environment. The value of k , for these particular hydrogen atoms, assuming reversible first order interconversion, is given by

where kf.0 arid k,,, are the values for the forward and reverse rate constants for the reaction N RC in the native environment, as given in Table XIX. Hvidt and Nielsen (1966) have pointed out that there are two liniiting forms of Eq. (66) [or any of the terms of the sum of Eq. (65)], depending on the relative magnitudes of k3 and k , , ~ . If k 3 >> k,,o arid if k ,

k,

=

kf,O

(67)

k,

=

k3Ko

(6s)

<< k , , ~

where K O is the equilibrium constant for the reaction N RC, K O= kf,o/kr,o, under native conditions, corresponding to the values given in Table XVIII. Hvidt and Nielsen have introduced the terms “EXI mechanism” and “EX, mechanism” to apply to rates of exchange governed by Eqs. (67) and (G8), respectively. Equations (66) and (67) of course become invalid if the process N + RC ceases to be a first-order process in the native environment, but the principle that k , is determined by the kinetics of unfolding if ks is relatively fast, and by Eq. (68) if k 3 is relatively slow, must be generally valid. 2 . Mechanism and Rate of fixchange for the Slowest

Exchanging Hydrogen Atoms

Values of the intrinsic rate coristant k g for exchange of a n exposed hydrogen atom are obtained from suitable model systems. Most labile hydrogen atoms on amino acid side chains exchange comparatively rapidly, amide side chains being the only cxception (Englander, 1967). Even amide side chains exchange more rapidly than protons on peptide groups (Englander and Stalcy, 1969). The slowest exchanging hydrogen atoms therefore presumably originate from the peptide groups that are exposed in the randomly coiled protein, but not in lesser denatured forms. The value of k 3 for peptide groups is given approximately by the relation (Englander arid Poulson, 7 969) 1.L3 - 3.5

x

+

10-3(10+~..0jr)(10~rr-~ 103-PH)

(69)

88

CHARLES TANFORD

where k 3 is in min-' and T is in "C. This relation does not differ significantly from an earlier relation given by Hvidt arid Nielsen (1966). The relation is only approximate because li, is afl'ected to some extent by electrostatic forces from side-chain charges and possibly by other factors. An important feature of the equation is that k 3 has a minimum value a t pH 3 and increases by a factor of 10 for each pII unit above about pH 4. Comparison of this rate constant with the expected rates of reriaturation of randomly coiled proteins indicates that k3 1) ill often be slow compared to the rate of renaturation a t low ~ € 1 but , that it may become faster than the rate of renaturatiori a t high pH. Thus the EX2 mechanism should prevail a t low pH, but the EX1 mechanism may become applicable a t high pH. For lysozyme, for example, Table XIX gives a value of 540 sec-' for I Z , , ~ a t 25°C. It is likely to he essentially independent of pH between pH 5 and pH 8. This rate constant represents the maximal value for kr.o, as was noted above. The minimum value can certainly not be less than the fastest experimentally measured rate of renaturation, which (at 2 N GuHCI) is sec-' a t pH 3, 0.1 scc-1 a t 25°C. The value of ka, at 25"C, is 2 x 0.1 sec-1 a t pH 5, 10 sec-' at pII 7, 1 0 sec-' a t pH 9. Thus transition from an EX2 mechanism to an EX1 mechanism should occur somewhere between p€I 5 arid pH 9. The limited information available on the effect of temperature on the kinetics of lysozyme renaturation (Tanford et al., 1966), indicates that the activation energies of k,,,, and k3 are of similar magnitude, and these conclusions regarding the transition from EX2 to EX1 mechanism should therefore apply at 0°C also. Another protein for which we have experimental data is 0-lactoglobulin. The kinetics of renaturation arc complex, as shown in Fig. 14, but the rate of disappearance of RC, to form the intermediate Y, is very fast. At 25"C, p1-I 3, 2 21.1 GuHCl, the rate constant has so far been too fast to measure: the minimal vsllue is about 10 sec-'. Preliminary estimates indicate that the rate constant for conversion of RC to Y ( k , in scheme 13 on page 82), which cannot be measured directly, is about 1 sec-1 under the same conditions. Both these rates are very much faster than k 3 a t pH 3 and 25", SO that the EX, mechanism can be expected to prevail not only a t pH 3, but for a t lcast 2-3 pH units above that. The predicted rate constants for exchange are readily evaluated from Eq. (67) or Eq. (68). Unfortunately, the slowest exchanging hydrogen atoms for most proteins do not exchange a t all a t 0°C in the time iiormally allotted to a11 exchange experiment (Hvidt and Nielsen, 1966). Thus we can only confirm that an extremely slow rate is expected, and cannot make exact quantitative comparisons. RC is about lo-' a t For lysozyme, the value of K Ofor the reaction N 25°C (Table XVIII). It is essentially independent of pII between pH 5

PROTEIN DENATURATION

89

and pH 8 (Fig. 9). The tempcrature dependence has been measured by K. C. Aune (unpublished data). There is a minimum in KO near 10" (cf. Part B, Table XVI, in Volunie 23, for similar data for other proteins), and the values a t 0" and 25°C are nearly the same. The rate constant calculated for O"C, for the EX2 mechanism, is thus only 6 x sec-l a t p H 5, and 6 x sec-I a t pH 8, corresponding to half-times for exchange of about 107 and lo4 hours, respectively, a t the two pH's. If the EX1mechanism applies to lysozyme Ic, for the slowest exchanging hydrogen atonis would be equal to kf,o, and would depend relatively little sec-l, on pI-1. The maximum value for k f . 0 a t 25°C (Table XIX) is 10-6.40 corresponding to a half-time of about 1000 hours. At 0°C the rate can be expected to be at least an order of magnitude slower. Experimental exchange studies (Hvidt and Kanarek, 1963) show that more than 30 hydrogen atoms remain unexchanged after 20 hours a t pH 5.5, and essentially the same number remain unexchanged a t pH 8.7. An increase in the number of unexchangeable hydrogen atoms occurs only below pH 5.5, where k 3 becomes very small. It is reasonable to believe that the 30 or more "slowest" hydrogen atoms come from a very stable region of the lysozynie structure that remains intact in all denatured states except in the randomly coiled state. The results of calculations for ribonuclease and /3-lactoglobulin are similar to those for lysozyme. Although, as we noted in connection with Table XVIII, A G O for the reaction N + RC is surprisingly small, it is big enough to prevent any observable exchange for those hydrogen atoms that require transition to the random coil form before they can be exchanged. 3 . General Statement Regarding the p H Dependence of Hydrogen Exchange

Experimental results from hydrogen exchange studies have generally been rather vague concerning the altered states of the protein that make hydrogen atoms accessible for exchange. In particular, in considering the dependence of k , on pH, they have generally not allowed for the possibility that KO [EX2 mechanism, Eq. (68)] or kf,o [EX1 mechanism, Eq. (67)] can contribute significantly to the pH dependence. When the pH dependence of k , has not agreed with the p H dependence of I c g it has often been surmised to reflect a pHdependent conformational change of the native protein. It is clear from the results presented here that all intermediate states in hydrogen exchange are likely to be denatured states. It is also clear from Section VI,A and from Part B of this review (Volume 23) that both the equilibrium and rate constants for transition to these denatured states must normally be pH dependent, sometimes quite strongly so. (It is likely that the relatively sniall effect of pH on the N $ RC reaction of lysozynie

90

CHARLES TANFORD

in the neutral pH region is exceptional.) This pH dependence does not imply an effect of pH on the conformations of the states themselves, but simply an effect on the equilibrium as described by Eq. (23) or by the corresponding equation (in terms of A h + * ) for the rate of denaturation. AND IX. RELATIONBETWEEN DENATURATION “STRUCTURE” OF WATER

THE

It is now firmly established that the compact ordered structures of typical native proteins owe their existence to the fact that the hydrophobic side chains of proteins have an unfavorable free energy of interaction with water. This unfavorable free energy can be traced to the properties of the solvent itself. Water molecules tend to adopt a local ordered arrangement, which is isotropic in space. This is often referred to as the ‘(structure” of water, although this term, implying fixed bond distances and angles, may be a misnomer (Lennard-Jones and Pople, 1951). Hydrophobic moieties of organic molecules necessarily interfere with the ability of water molecules in their vicinity to adopt this preferred arrangement, and they do so without compensating effects, such as formation of hydrogen bonds with water molecules. Hence the free energy goes up. These facts have sometimes been used (e.g., by von Hippel and Wong, 1965) as a basis for the hypothesis that some denaturants operate on the protein indirectly, through their effects on the ordering of water molecules. Many substances that are protein denaturants (especially electrolytes) interact strongly with water. At high concentrations they will tend to organize most of the solvent molecules into “structures” quite different from that of unperturbed water. Therefore, according to the hypothesis of indirect action, the constraint upon the presence of hydrophobic moieties in the water is removed, and the initial reason for the existence of the native protein structure disappears. This argument is fallacious (and has in fact been repudiated by von Hippel and Schleich, 1969a,b). The native conformation of a protein is not the result of the arrangement of water molecules per se, but arises from the inability of that arrangement to accommodate itself to hydrophobic moieties. Thus changes in the arrangement of water molecules per se do not lead to denaturation. What can cause denaturation is a n augmented ability to accommodate hydrophobic moieties (i.e., negative 6g, for hydrophobic groups), and there is no necessary relation between this property and the effect on water “structure.” Additives that have relatively little tendency to alter the organization of the solvent may well facilitate accommodation of hydrophobic residues; additives that have a strong influence on water “structure” may not. Electrolytes in fact are an excellent example of the latter. Despite their ability to reorganize the ordering of water

PROTEIN DENATURATION

91

molecules, their presence increases the solvent’s inability to accommodate hydrophobic groups. Their denaturing action is due to an altogether different mechanism, namely an affinity for exposed peptide groups. There is of course no intention here to belittle the importance of solvent “structure” in relation to protein denaturation. I n fact, the thermodynamic explanations given for protein denaturation in this paper solve only half the problem. They have shown that protein denaturation can be accounted for on the basis of interactions between protein moieties and the water-denaturant medium that are just like similar interactions that one observes with simple model compounds. No definite interpretation of these interactions in ternis of molecular organization could be given, however. It is indeed an important problem to find out, for example, why hydrophobic groups have a lower free energy in an aqueous GuHCl solution than in water alone. The point that is being made in this section is that the answer to this problem cannot come from studies of the effect of GuHCl on the properties of water. It requires an investigation of the molecular organization in a three-component system: hydrocarbon, GuHCI, and water. It may be noted that current concepts of water “structure” have been criticized in recent papers by Holtzer and Emerson (1969) and Narten and Levy (1969).

X. OLDER THEORETICAL MODELS We have previously considered two theoretical concepts that have frequently been invoked as explanations for protein denaturation, and have shown the limitations or fallacies inherent in them. One of these is the concept that electrostatic repulsion between like charges is primarily responsible for denaturation a t extreme pH’s (Section 11,B15),and the other is the concept that denaturation may be the indirect result of changes in the arrangement of water molecules in the bulk solvent (Section IX) . It remains t o record one other model that has frequently been employed in the analysis of the effects of denaturants and other substances on the kinetics of denaturation. This is the (‘trigger group” model, probably first used by Steinhardt (1937) t o account for the denaturation of pepsin by OHions. It was used subsequently by several workers for other denaturation processes, including urea denaturation (Simpson and Kauzmann, 1953). The objective of this model was to account for the steepness of the denaturation curve with respect to the concentration of denaturant. The basic idea was that the combination of the added substance X with particular sites of the native protein alters the properties of the native protein in such a way that the transition to the activated state for denaturation (Y*) is facilitated. Where N represents the native protein uncombined with X, NXi represents a native molecule with i of the critical

92

CHARLES TANFORD

sites filled, ko represents the rate constant for denaturation of N (assumed to be very small), and k, the rate constant for denaturation of NX,, this idea may be expressed by the inequality

ko

< kl < . . .k,-l < ka . . . < k,

(70) In the simplest version of this model, only k , was assumed t o be large enough to allow denaturation a t a significant rate, so that the overall rate constant for denaturation (kobs) could be written as

knLnCxn (71) where L , is the equilibrium constant for the reaction N nX NX,. In other versions contributions to the observed rate from less than saturated protein molecules (NX,-I, etc.) were allowed for. An implicit feature of Eq. (70) is that the equilibrium constants (I,,*) for the combination of Y’ with X must be larger than the equilibrium constants (I,%)for combination of N with X, i.e., by the principle of linked functions (Wyman, 1964), applied to the formation of YX,’, koha

=

L,*ILa = kJko

+

(72)

(This implication may not have been realized by all proponents of the model.) It follows therefore that the “trigger group” model is a special case of the general binding model we have used throughout this paper. Equation (63) is obeyed, with A B X , ~ assumed ~ ~ ~ * to be equivalent to Aiix’, and the binding of X to the protein is implicitly incorporated in the form of the analog of Eq. (16) for the activation process. The model is a special case in that it is assumed that the number of binding sites for X in Eq. (16) is the same for the native protein and the activated state, an assumption that is not necessary to account for the experimental data, and not generally warranted by our present knowledge of the conformations of native and denatured proteins. In describing denaturation processes in terms of binding equilibria we have in fact assumed that it is more realistic to consider that most of the binding sites for denaturants such as urea, GuHC1, inorganic salts, etc., do not exist on the native protein a t all, but that they appear only after unfolding of the native structure has led to the exposure of previously buried parts of the molecule.

ACKNOWLEDGMENTS The preparation of this review, and the work in the author’s laboratory that forms the basis for much of it, have been supported by a Research Career Award from the National Institutes of Health, United States Public Health Service, and by research grants from the same source and from the National Science Foundation. I should like to acknowledge, in addition, my debt to the postdoctoral research associates and graduate students who have been associated with me in this work. Not only

PROTEIN DENATURATION

93

have they been responsible for most of the experimental data, but they have also participated actively in the development and testing of the theoretical models that have been used to interpret their results. Special mention should be made of Dr. Y. Nozaki, whose painstaking solubility measurements constitute the backbone of this third part of the paper. Without these measurements interpretive models would have been largely speculative, and a discussion of them would hardly have been worth the time of the author or the reader.

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