Enthalpy-entropy compensation phenomena in water ...

VOL. 9, PI’. 1125-1227 (1970)

BIOI’OLY MEltS

Enthalpy-Entropy Compensation Phenomena in Water Solutions of Proteins and Small Molecules: A Ubiquitous Property of Water RUFUS LUMRY arid SHYAMALA RAJENDER, Laboratory for Biophysical Chemistry, Ijepartnzent of Cheniislry , University of Minnesota, Minneapolis, Minnesota 55455

Synopsis This article presents evidence for the existence of a specific h e a r relationship between the entropy change and the enthalpy change in a variety of processes of small solutes in water solution. The processes include solvation of ions and nonelectrolytes, hydrolysis, oxidation-reduction, ionization of weak electrolytes, and quenching of indole fluorescence among others. The values of the proportionality constant, called the compensation temperature, lie in a relatively narrow range, from about 250 to 315”K, for all these processes. Such behavior can be a consequence of experimental errors but for a number of the processes the precision of the data is sufficient,to show that the enthalpy-entropy compensation pattern is real. It is tentatively concluded that the pat-ternis real, very cornmon and a consequence of the properties of liquid water as a solvent regardless of the solutes and the solute processes studied. As such the phenomenon requires that theoretical treatments of solute processes in water be expanded by inclusion of a specific treatment of the characteristic of water responsible for compensation behavior. The possible bases of the effect are proposed to be temperatureindependent heat-capacity changes and/or shifts in concentrations of the two phenomenologically significant species of water. The relationship of these alternatives to the two-state process of water suggested by spectroscopic and relaxation studies is examined. The existence of a similar and probably identical relationship between enthalpy and entropy change in a variety of protein reactions suggests that liquid water plays a direct role in many protein processes and may be a common participant in the physiological function of prot.eins. It is proposed that the linear enthalpy-entropy relationship be used as a diagnostic test for the participation of water in protein processes. On t,his basis the catalytic processes of chyniotrypsin and acetylcholinesterase are dominated by the properties of bulk wat,er. The binding of oxygen by hemoglobin may fall in the same category. Similarities and difyerences in the behavior of small-solute and protein processes are examined to show how they may be related. No positive conclusions are established, but it is possible that protein processes are coupled to water via expansions and contractions of the protein and that in general the special pattern of enthalpy-entropy compensation is a consequence of the properties of water which require that expansions and contractions of solut,es efiect. changes in the free volume of t.he nearby liquid water. It is shown that proteins can be expect,edt,o respond lo changes in nearby water and interfacial free energy by expailsions arid cont.ract.ions. Such responses may explain a variety of currently unexplained cliitracteristics of protein solutions. More generally, t,he enthalpy-entropy conipeiisation pattern appears to be the thermodynamic manifestation of “st,ructrira making” and “structure breaking,” operationally defined t,erms much used in discussions of water solutions. If so, the compensation pattern is ubiquitous and requires re1125 @ 1970 by John Wiley & Sons, Inc.

1120

LUMRY AND RAJENDER

examination of a large body of molecular interpretations derived from quantitative studies of processes in water. Theories of processes in water may have to be expanded to accommodate this aspect of water behavior.

INTRODUCTION Data from a variety of experiments suggest the existence of a single very common and phenomenologically simple response of water to changes in solutes, regardless of the way these changes are produced. Phenomenologically, this response appears to be revealed by simple patterns of enthalpy and entropy changes having such similar quantitative characteristics as to suggest that they are all manifestations of the same property of liquid water. These patterns consist of parallel enthalpy and entropy changes which compensate each other to produce minor changes in the free energy of the process under investigation. Such compensation is often remarkably precise. The major experimental finding which suggests that these patterns have a single source is the similarity of the ratio of enthalpy change to entropy change found among the many examples. In this article we confine our attention to these patterns of enthalpy-entropy compensation chosen not only on the basis of the quality of the data but also t o show the relationship between compensation behavior in small-solute and protein solutions. Although this article is intended to stress the probable existence and importance of compensation phenomena in problems of protein stability and physiological function, the general implications of the data for water solutions of all types may prove to be even more important. We have formed the impression that protein behavior provides a promisingly fresh viewpoint and a powerful experimental basis for the examination of the properties of water solutions. Thus, although this article is directed primarily to protein chemists, its contents may prove uPeful to those with different and less restricted interests in liquid water. Chemical mechanisms of protein function are uniquely dependent 011 the conformational behavior of proteins but there is not much information from any source about the kinds of conformational rearrangements which proteins can undergo. Only reversible unfolding processes have some quantitative description,I-7 though even in these the conformational details of both “folded” and the “unfolded” statess-10 are still a t a primitive level of knowledge. Recent x-ray diffraction results with carboxypeptidaseA reveal coordinated atom readjustments involving as many as five residues but more extensive adjustments, if any, are below the precision l e ~ e l . ~ * - ’ ~ Small displacements in large protein regions without change in folding have been inferred in interpreting rate data for protein unfolding6 These processes, called “subtle” changes, have not been established in function and are likely to be undetectable by x-ray methods. Current. descriptions of catalysis by Iy so ~ y me’~ -’~ include as the major fetLt,iire a dist,ortioii of the substrate toward the configuration of the activated complex for primary-bond rearrangements. The positive free-energy cost of this distortion is thought to be supplied from the favorable free-energy changes

ENTHALPY-ENTROPY COMPENSATION

1127

in forming the secondary bonds between substrate and protein. This mechanism is the simplest form and the first form of (‘rack” mechanisms proposed by Eyring et al.,l’ who discussed both the distortion18 and the use of bonding free energy to pay for distortion.lg It is of present interest in that it seems to minimize the importance of the passive bonding required by Koshland’s “induced-fit” mechanism. 2o However, the lysozyme mechanism as it now stands is undoubtedly crude, since it ignores the necessity for the protein conformation to change as the enzymesubstrate complexes move into actual activated complex configurations and it contains no detail on the local electric field and other characteristics of the protein which are probably of considerable importance. Since this enzymic mechanism appears to be the best advanced a t the present time, we must conclude that the conformational basis of protein function is not yet understood a t the “ball and stick” level and certainly not in the quantitative terms necessary to provide actual rather than pictorial understanding. Pictorial descriptions are attractive, but may be very deceptive even when based on x-ray diffraction results. The information from x-ray diffraction is essential to progress but is likely to be quantitatively and even qualitatively insufficient to describe the mechanism. An important example of the kind of subtle phenomena which are difficult to detect and quantify with x-ray diffraction methods and yet may be of considerable significance in some protein mechanisms appears to be that responsible for the comperisation pattern. Compensation of an enthalpy change, produced by change of a11indept.11dent variable, by entropy change is a common occurrence in small-molecule reactions.z1-30 The frequency with which compensation phenomena appears in protein chemistry is less well known, but is sufficiently great to suggest that, there has been an important omission in our qualitative understanding of protein behavior. We shall thus devote this article to a description of compensation, a review of the evidence for enthalpy-entropy compensation in several types of small-solute and protein processes, a presentation of arguments which suggests that the compensation characteristic of proteins is the result of one or a very few fundamental mechanisms, and a discussion of the possible relationship of these mechanisms to the interaction between the protein and its water solvent. Compensation phenomena may provide a particularly easy pathway toward an understanding of the role of solvent and surface water in protein reactions. That there is such a role and that it is important has long been ~ - e c o g n i z e d . ’ ~ . ~There ~ - ~ ~has been no shortage of imaginative proposals, but the complexity of water and water-protein interactions a t both experimental and theoretical levels have limited progress in this direction. Likhten~htein~jproposed several years ago that enthalpy-entropy compensation plays an essential role in enzymic mechanism and he associated i t with both the protein conformation and a solvent shell, invoking an energy-chain mechanism whereby energy released in one

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LUMltY AND RGTENDER

complete enzymic process is stored in the water shell and then released to be used for activation in the subsequent catalytic cycle. His proposal is difficult to rationalize with the existing evidence which provides little if any support for chain mechanisms of either chemical or energy types but the large amount of evidence for compensation which he presented does suggest the general participation of one or a few compensation processes in enzymic reactions. We had earlier supposed6 that this might be the case, but analyses of compensation behavior as they began to appear? did not provide unequivocal evidence that enzymic catalysis or other protein functions derive their unique characteristics from the mechunisms which support compensation behavior. We will show that although compensation processes probably make large contributions to the enthulpy and entropy changes in some and perhaps very many protein processes, their effect on the free-energy changes in the element.ary steps of enzymic catalysis is small, as judged by those few cases which have been examined in quantitative detail. As we shall see, for coldblooded organisms in which enthalpy changes rival free-energy changes in importance, compensation processes may be of relatively great importance but for thermostatted organisms, although they are an important guide to understanding mechanism, their quantitative significance may be minor. However, we shall see that there is evidence for suspecting that the specificity in substrate selection which enzymes manifest as well as the mechanism whereby free-energy is transferred from one oxygen-binding process to another in hemoglobin to effect the important linkage relationship called heme-heme interaction are closely related to the source of the compensation behavior and may be at least partially identical. The particular variety of compensation of enthalpy by entropy which is our major subject is that in which the enthalpy change in an isothermal process is linearly related t o the entropy change. This relationship is not in any way a consequence of thermodynamic laws and as an extrathermodynamic relation has been extensively discussed by Leffler and G r u n ~ a l d , ~ l - ~Ritchie 3 and Sager,36 and Shorter,37 who emphasize linear free-energy relationships, and by several other authors. 38-41* This type of compensation is well known among physical organic chemists in particular and has been generally and probably cor.-ectly attributed by them t o solvation. Rate processes as well as equilibria fit the compensation pattern. Compensation plots of standard enthalpy change versus standard entropy change or (standard) activation enthalpy versus activation entropy change :we straight lines and can be characterized by the values of the slopes which, becwse they have the dimensions of absolute temperature arc often c:dled “isoecluilibrium” or “isokirietic” We will usc, instead, thc general term “compensation temperature” with tlie symbol Ye. This purameter is the only basis for classifying and c:)mparing different examples of 1ine:i.r compensation

* T. Berizinger has recently shown that this statement is not strictly correct. See note added in proof.

ENTHALPY-RNTR,OPY COMPENSATION

1129

behavior. It is not unreasonable to propose that two examples of linear compensation phenomcn:t in water which have the same value of Toare manifestations of the s:tme property of the solvent. In small-solute systems there :ire two general methods for gcwcrating the pairs of AS-AH qi1:antitic.s which provide the points of a compensation plot. The first w:iy is to wiry thc chemical structure of it parent compound to produce a homologous series of reactants for a particular process. The second way is to vary the solvent composition. In water systems, the latter is often effected by adding increasing amounts of a monohydroxy alcohol. For protein systems, both of these alternatives have been found to be effective ways to obtain the AH-AS pairs but in addition, i t has also been found possible to vary the AH-AS values by changing the hydrogen-ion activity of the solution. The sources of compensation in protein systems may be quite different from those a t work in systems of smaller molecules, in which case, compensation may be a special property of proteins rather than a general characteristic of water. However, the data now available tend to suggest that most examples of compensation behavior for processes in water solution are due to a single unique characteristic of water. It would not be remarkable to find such a basis for compensation in protein reactions since the evolution of proteins has had to adapt them to the characteristics of water. It should be relatively easy to establish the existence of a relationship between protein folding and solvation as a source of compensation if in fact such a relationship does exist. A full explanation of compensation phenomena will be much harder to provide if it requires a detailed understanding of water behavior. Not only are there several schools of thought in considerable disagreement about the molecular description of water b e h a v i ~ r ,but ~ ~ recently .~~ there have appeared rather startling experimental observations on water which, if not experimental artifacts, add further complexity since they do not appear to be explicable on the basis of any of the more popular models for water. One such example is the slope discontinuities observed in studies of v i s ~ o s i t y , ~ ~ - ~ ~ nuclear spin relaxation, and a number of other physical properties in pure water as a function of t e m p e r a t ~ r e . ~ ’ - ~ This ~ type of behavior has come to be known as the “Drost-Hansen kinks” or “breaks” since DrostHan~en50.5~ has played a major role in championing their study. Since in systems a t constant pressure the occurrence of a sharp change in the slope of a parameter plotted as a function of temperature can occur only if there is a large entropy change, the kinks have been attributed to the cooperative behavior of a number of water molecules. However, such behavior must reveal itself by heat-capacity spikes which have thus far defied detection. There has been considerable skepticism as to the reality of the kinks, although they seem to be experimentally reproducible often, even in the laboratories of the most ~ k e p t i c a l . ~ * - ~If~ the * kinks are real,

* Ihost-Hansen has shown that some of the examples, e.g ,viscosity,46~46are artifacts and hah recently provided evidence that some may be surface pheiioniena rather than hlk-phase phenomena.

1120

TATJ M It Y AN I > 1t A.J ICN I ) li:R.

they may prove important to biology. Drost-Hansen e t al.45,46,413 have made a number of interesting suggestions in this connection. Another remarkable development is the discovery of a new “form” of water by Deryagin and his co-worker~.~’-~~ Apparently this new species is formed catalytically a t the inner surface of freshly drawn, thin, quartz or glass capillaries. O r t h ~ w a t e r ~or~ “po1ywater,’’60 -~~ as it is called, has bulk properties quite different from those of ordinary liquid water. These properties are now interpreted m indicating the generation of a new molecular species larger than HzO, rather than a consequence of any long range molecular organization of ordinary HzO molecules. Orthowater or polywater has already been reproduced in other laboratorie~@J-~3 and has become a matter of considerable scientific interest. Whether or not this singular phenomenon, if a physical reality, has any biological significance, remains to be seen but the amount of high-quality confirming evidence already available that water can form other chemical species under the influence of a variety of solid surfaces is impressive. The phenomenon will have to be taken very seriously by biological scientists until such time as its physiological significance is proved to be negligible. At the present time there is no reason to exclude it as the basis for the compensation process under consideration in this review.

Brief Review of the Analysis of Enthalpy-Entropy Compensation From the thermodynamic point of view, any process, even if it consists of a single elementary step, can be considered to be a sum of part processes. Such divisions are never unique but one choice for such dissection may be more useful than others. Por purposes of illustration, the dissociation of a weak uni-uni acid, HA,; as shown in eq. (l), can be described as consisting of two part processes,24~64-67 a “chemical” part process (la) and a “solvation” part process (lb). The chemical part process includes all inductive and resonance rearrangements of electrons to produce an electrostatic ion pair and might be termed the Hammett part process, since the partial-free-energy changes, corresponding to various substitutions in the acid anion would be expected to change in accord with values of u, U* or other appropriate parameters. Part process (lb) includes separation of the ions and all associated solvation effects. I n a more complex reaction, however, we should find it more convenient to replace the enthalpy change AH”,!, and the entropy change ASoa,i by a sum over the enthalpy arid entropy contributions from all part processes other than (lb). (HA?).,,,

+ water

4 (H+),,,, Total process

(HAi)soi { H+Ai-J “chemical” p:irt process +

+ (Af).,,i

(1)

ENTIIAT,PY-ENTItOPY COMPENSATION

water

+

{H+Ai-) (H+)sol (At-)so~ "solvation" (compensation) part process

1131

(1b)

I n the study of organic-acid dissociation reactions, enthalpy-entropy compensation has usually been brought to light by measuring the pairs of (AH",, AS",) values for homologous series of acids. Although AS", and AH",may change rapidly with temperature, they must be related by the grneral thermodynamic expressions

ant1 AS", = ASorri, 4-

which give a strictly linear relationship between precisely measured AS", and AH"%only in the trivial case that AC",, is zero for all i. (We shall discuss a more interesting case a t another point.) Extrathermodynamic compensation behavior is indicated if when the temperature is held fixed and the acid species is varied, a simple monotonic relationship exists between the AH", and ASo*, even though the ACp, are not zero. The detection of this behavior may be difficult, since in the total thermodynamic expressions A G O z = A G O , , , AGob,z, AHot = AH",,, AHOb,, and ASo< = AS",,, ASOb.,, the quantities and AS,., also may depend on the nature of i so that considerable interpretation is required to abstract AH'b,, and AS"b,t. The methods of I v e ~ , Hepler,29r64-67 ~* and other^^^-^' for this undertaking confirm the existence of a linear relationship,AH"b,, = a TcASob,l. The intercept, a,is usually taken to be zero. The slope T, is not detectably dependent on temperature, and the general significance of the phenomenon is established by the close similarity of the T, values obtained with different homologous series of acids. The significance of T, and its near constancy have not been explained. The relationship

+

+

+

+

AHOh,,

= CI

+ T,AS"h,,

found for the homologous series of acids defines linear enthalpy-entropy compensation. We will be interested primarily in linear compensation behavior and so we shall henceforth use the term compensation to mean linear compensation except in cases in which further distinction is necessary. Most examples of compensation we need to discuss are of a simpler type for which the following relationships apply: AH"b,,(T) = a T,a"b,,(T) for the series i but AHoS,,(T) and ASo,,,(T) are essentially independent of i. In this situation, on eliminating AHob,, and AS",,.,: wr obtain eq. (8), which can be written in more detail as eq. ( 5 )

+

AHot(T) = a'( T )

+ T',AL~",(T)

(3

LUMltY AND RAJENDER

1132

AG'", =

+ AH",(T) - T,AS",(T) - ( T - T c ) ~ S o , , . i ( T ) + AIIo,(T) - T,.AS",(T)+ TcASo,(T) = + AFI",(T) - T,AS",(T)

AII",(T) = a

(4)

(5) (6)

The total enthalpy arid ontropy ch:tngcas :trc 1itw:dy related in such cases but there is no a priori way to determine how As", and AH", are to be divided with respect to processes (la) and (1b). Additional information is required. Some information about process (la) can be obtained from the intercept of the compensation plot (AH", versus Ah'",) if (Y can be assumed to be small, since at AS" = 0, AH" = AH",(T) - T,ASoa( T ) = AGO, (T,). Thus in favorable cases, the slope of the compensation line T , characterizes the compensation part process and the intercept gives information about the "chemical" part process, step (la). Unfortunately even in this simple example in which only two part processes need be recognized there are five independent quantities: AH",, AS",, a plus any single set of Afi?"b,iand AS'b,, values, and only two fitting parameters] af and T,, so that a variety of supporting information must be introduced t o obtain values for all the independent quantities. Compensation is characteristic of a number of reactions of small molecules in various solvents though most marked when there is a change in the charge. Simpler compensation behavior is found when the reaction of a single chemical species is studied in binary (water) solvents of different relative composition. If, however, more than one part-process depends on the solvent composition, plots of the points (AH",, AS",), i now being the index of solvent composition, may not show linear compensation at all. It is quite possible that linear compensation is much more common than generally recognized but is made difficult to detect for this reason. As already mentioned, in the cases of the ionization of homologous series of organic acids, the linear nature of compensation between mob,{ and &Sob,l is not usually detectable in a plot of AHoi versus AS",.

Compensation Behavior in Processes Involving Small Molecules in Water Solution It would be out of place here to attempt a comprehensive review of this complicated subject. Instead, a few examples particularly appropriate for the discussion of compensation in protein systems, have been singled out for a brief description. Many examples of compensation in both rate and equilibrium processes are listed by Leffler and GrunwaldZ3 and others. 24 25,29 36 The ionization of weak organic acids in water solvents has provided an abundant source of compensation example^.^-^' Granting the validity of the decomposition of AH", into AH",,, and AH"b,, by the procedures of H e ~ l e r , 2 9 , 6 ~Ives124 - ~ ~ Laidler25 and others26,70,71 compensation between AHob,i and Ah'"b,* is very common. Furthermore, the T, values found usually lie in a fairly narrow range from 2,50 to 320°K Since there is 8

e

ENTHALPY-ENTROPY COMPENSATION

1133

some skepticism about the validity of the methods of interpretation, a recent study by Ojelund and W a d ~ 8is ~worth citing. These authors report the enthalpy and entropy values fsr proton loss from simple primary alkyl ammonium compounds. These (AHo$, AS",) points when plotted, are reasonably well fitted by a straight line with a slope of about 300°K as shown in Figure la. For this to be the case, either AHoS.,and ASoa,, must be only weakly dependent on the change in the aliphatic group or these values must also manifest compensation with a T, value near 300"IC. Since the Taft u* values are very similar for the unsubstituted alkyl groups, the former alternative is favored. Then M o b . $ and ASob,$ are responsible for most of the appearance of compensation behavior but neither the linear fit nor the T , value is quite valid because of the small contributions from AHo,,( and AS".,,. This interpretation is consistent with those given for more obviously complicated ionization processes.6447 The monotonic movement along the compensation plot with increasing size of the hydrophobic group found by Ojelund and W a d ~ shows o ~ ~ a n ordering which is characteristic of this type of example and which is clearly due to the interaction of the hydrophobic groups and the water solvent. Detailed hypotheses of solvent water adjustment to such groups have been proposed to explain the effect. Relevant features of these proposals will be cliscussed in a subsequent section. A diff ererit kind of compensation example for a small-solute process is the intrinsic quenching of indole fluorescence in alcohol-water mixt ~ r e d 3 - ~which 5 exhibits compensation between the values of the activation enthalpy AH' and activation entropy AS' obtained at different methanol-water ratios or different tert-butanol-water ratios as shown in Figure l b . Different indole compounds can be used, but T, is always about 285°K for both alcohols. This is an important example in two respects. The first has to do with dependence on alcohol concentration. For any given indole compound in which the indole nucleus is freely exposed t o the solvent, as the concentration of alcohol is increased, both AH' and AS* increase until maximum values are reached a t a mole fraction of about 0.025 for tert-butanol and 0.07 for methanol. The (AH', ASs) points then move back down the compensation line as alcohol concentrations are further increased. T , is constant a t 285°K within an error of about *5OT\. I n a later section we shall report several examples of this kind of behavior on adding alcohol to water solutions of proteins. For the present, however, this behavior is important insofar as it suggests that n number of processes showing a qualitatively similar pattern of enthalpy and entropy change on increasing alcohol concentration may be closely related t o the linear compensation phenomena we have already discussed even though many of these examples do not show linear compensation. There is a large group of such reactions including, for example, the solvolysis of tert-butyl chl~ride,'~-~~ benzyl ~ h l o r i d e , ~ -the ~ * solubility of quarternary ammonium ions with large hydrocarbon N-substituents8s-88 and the shift in maximum of the charge-transfer spectrum of iodide ion.89.90

WJMILY A N D €3AJEN DEl:

1134

i

-14.5

A

Hf

( k a ~ ~ ~ s - 1-4 . 0

- 13.5I

0

-I

-2

-3

-4

-5

AS? (pibbs/rnol$

I

0

0.02

0.04 006 0.08 0.10 0.12 ALCOHOL MOLE F R A C T I O N

0.14

0.16

.I8

Fig. 1. Enthalpy-entropy plots: (a)standard enthalpy and shndard ent,ropyof ionization of some primary alkyl ammonium compounds (dab from Ojelund and WadsW); ( b ) enthalpies and entropies of activation for the quenching of indole fliioreseenee vs. alcohol mole fractions for t-BuOH and MeOH at 2 5 ' 1 3 . 7 3 - ~ ~

TABLE I Some Processes Showing 1)ependence on Akohol Concentration at. the Magic Mole Fraction Mole fract,ion Process Solvolysis of t-BuC1 (Activation parameters) IXssolution of sodium-tetraphenyl boron: M

S

Alcohol

S,of property

(XZ1

ext,rema

EtOH EtOH t-BuOH EtOH

Racemization of a biphenyl (Activation entholpy) 1)issolution of various electrolytes and EtOH non-electrolytes in binaries t-BIiOH Transition energy-composition profile for 1-BuOH the dissolution of a merocyanine dye 1)issolution of argon (thermodynamic EtOH parameters) MeOH Walden products and viscosities for waterEtOH alcohol solutions MeOH Changes in the Soret band of cytochrome c MeOH-t-BuOH Sound absorption in water-alcohol mixtures MeOH EtOH i-PrOH n-PrOH t-BuOH Partial mold voliime rhnnges MeOH Et,OH n-PiOII i-PIOH l-B1iOlT Elevation of temperature of maximiini n-PrOH density EtOH 1-BitOH MeOH Heats of mixing for water-alcohol sohit,ions MeOH (minimum in a H M ) EtOH n-PrOH t-BuOH Quenching of indole fluorescence (sct>ivation EtOH parameters) t-BuOH MeOH Proton chemical shifts in water t-BtiOH Relative intensities of x-ray diffract,ionbands EtOH Volume of activation for the solvolysis of t-BiiOH bennyl chloride i-PrOH EtOH MeOH Minimum in water activity coefTic-ieiiL t-B1iOH Viscosity maxima MeOIT EtOH Critical micelle concentration of sodinm t-B\iOH dodecyl sulfate Solubilit,y of merciiric chloride EtOH n-PrOH i-PrOH t-BuOH Heat capacity changes for ihe solvolysis of EtOH t-BuC1 i-PrOH t-R1tOH

0.1.5 0.15 0.05 0.15 0.1s-0.20 0.05 0.04 0.1.5-0.20 0.20-0.2.5 0.25 0.30 0.3-0.05 0.25 0.20-0.275 0.15 0.10 0.70 0.15 0.08 0.117 o.oc,5 0.04 0.01.5 0.03

Iteference 80 94

94, 96 97,98 99, 100 101, 102 103, 104 105 106, 107 391

108, lo!)

110

0.02

>0.05 0.20 0.175 0.08 0.04 0.05 0.025 0.09 0.04 0.1 0.07 0.10

91-93

74, 75

111-113 114 8%-84

0.3

0.37 0.03 0.30 0.25 0.04 0.08 0.06 0.07 0.05 0.17 0.10 0.05

115, 116 103 I 04 117 118

94, 119, 193

11%

LUM1I.Y AN11 R A J EN11ER,

This motley collection arid other procmes with a similar qualitative dependence of eiithdpy and mtropy ch:tnge on alcohol concentration arch well known. A number of cw~rnplrhhas bwn discussed by Franks and. Ives91 -93 and by Arri~t~t.!’~+’~ Table I lists somr of thc procrssw rshibitirig this typr of drj)endcriccbo t i :ilcohol cotirc~iitr:itioii. 1 ti m:ttiy itistarlces the changes in A S tirid AH, arid thus it1 A(/ can be explained entirely in terms of solvation changes induced by alcohol. Although enthalpyentropy compensation is prominent in these examples where studied, the members of the group (for convenience hereafter called the “alcoholperturbed” processes) do not in general demonstrate linear compensation or if they do over some interval of alcohol concentration, the apparent T, value is much larger or much smaller than values in our range of 270-300°K. This type of complication is to be expected when there is more than one part-process which manifests compensation. It is also to be expected when the quantitative break-down into part-processes has not been properly carried out or in a rate process in which both normal reactants and activated complexes are sensitive to changes in solvent?? The complexity of the analysis is demonstrated in treatment of the data for solvolysis of benzyl and tert-butyl chloride^.^^-^^ The intrinsic quenching of indole f l u ~ r e s c e n c e ~is~ -thus ~ ~ of some importance for a second reason since in addition to showing the alcohol dependence of the “alcohol-perturbed” group of processes, the Tovalues are those observed with other classes of compensation reactions in water. The characteristics suggest the possibility that all the reactions are manifestations of the same property of liquid water. Recently, Hepler et a1.I2O have shown that the alcohol-perturbation effect, can also be demonstrated in the ionization processes of weak acids. This finding adds further support for the hypothesis that the alcohol-perturbation group and the group of weak-acid dissociation processes already discussed are members of a common family of water-dependent processes. Hopkins and Lumry121have recently shown that, although the fluorescence-quenching process of indole produces hydrated e l e c t r o r ~ s , ~ ~ ~ ~ ~ ~ ~ the step in the overall process demonstrating compensation is the production of an intermediate state from the first excited singlet state of a complex formed between indole and water. The intermediate state is probably a solvent-caged ion-pair of electron and cationic indole radical of the type discussed by Jortner, Ottolenghi, and Stein12P127and by Grossweiner and ,Joschek.122 These “caged pairs” have been studied by Weller and cow o r k e r ~ ~ ~and ~ - found ’ ~ ~ to be marked by a large separation of charge. Arnett e t a1.94-96 offer a similar explanation for the effect of alcohol on the solvolysis of tert-butyl chloride which is believed to go through a salt like or ion-pair transition ~ t a t e . ~ ~As J *the effective solvation shell changes by progressive additions of alcohol, the nature of the activated complex and the reactant must vary accordingly. The wide variation in enthalpy changes compensated to a varying degree by entropy changes is therefore attributed t o differences in the solvation between the ground state and the

ENTHALPY-ENTROPY COMPENSATION

1137

transition state. Since it is the solvation changes due to charge rearrangements which are isolated in the latter type of Compensation process by the and Ives2*there appears to be a distinct similarity method of Hepler29*64-67 between the quenching processes of indole in water, the ionization of weak acids, and hydrolysis of benzyl and tert-butyl chlorides.* It is most important to note that Arnett and c o - w o r k e r ~in~their ~ ~ ~analysis ~ of alcohol effects on hydrolysis rates of tert-butyl chloride find that these effects influence the equilibrium solvated state of teyt-butyl chloride somewhat more than the activated complex despite the fact that the condition of separated charge which might have been expected to be highly sensitive to changes in solvent occurs in the activated complex. Hyne and c o - w o r k e r ~have ~~~~ found the same important result in benzyl chloride hydrolysis. The latter investigators also found that volume changes with alcohol mole fraction for the two states correspond closely to the enthalpy effects. The solubility of argon in methanol-water mixtures studied by BenNaim'O' reveals yet another class of small-solute compensation phenomena. As shown by the compensation lines in Figure 2a calculated from his data, AHosol and ASosol increase monotonically with increasing methanol concentration until the lines level off at alcohol mole fractions of about 0.5 (not shown in this figure). The (AH",,, ASosol) points do not move back down the compensation lines. I n methanol-water solutions the compensation temperature is about 277°K at 5 and 15°C but drops abruptly at 25°C. In the ethanol-water results in Figure 2b obtained by Ben-Naim and Baer,lo2a deviation is found at low alcohol mole fractions and low temperature. We cannot explain this deviation but we will advance a phenomenologically simple explanation for linear compensation in this type of process at a later point. The thermodynamic parameters describing the helix-random coil transition in synthetic polypeptides also appear to respond to mixed solvent composition. The parameter describing the extension of a helical sequence is a monotonic function of the alcohol composition in both polylysine and poly(g1utamic acid).131,132 The parameter, u, describing the cooperativity of the transition depends in a more complex manner on the nature and amount of alcohol present. The most noteworthy feature of these studies from the point of view of this review are first that the cooperativity parameier is sensitive to small mole fractions of alcohols-more so in fact than the s parameter; and secondly, that it goes through an extremum-a maximum in this case-at alcohol mole fractions characteristic of extrema in the "alcohol-perturbation" cases already discussed.131v132This correspondence holds for all of the lower alcohols up through teit-butanol. Studies on mixed solvents may prove to be an important tool in providing insight into the origin of cooperative polymer transitions.131.134

* The eflect of alcohol on the rate of hydroly& of beiizyl chloride 112~5beeti htdied extensively by Hyne and co-workers. At low alrohol inole fractions, linear compensation between AH$and A S # appears, and the 7,values are in the range of present interebt.80.81

LUlLlltY AN11 ItAJENDEIt

1138

SOLUBILITY of ARGON in H20 - CH30H MIXTURES

-3001

j0.l

/

EXPERIMENTAL TEMPERATURES -5.C 0

-15.c -25.C

(0.1)

Tc =277.K

-200(

/

(0.2)

AH’

cal mole

-loo(

C -6

-8

-10

-12

- I4

-16

A So (edrnole) Fig. 2 (continues)

Arnett and c o - w o r k e r ~ ~showed ~ ~ ~ ~that - ~ ~although small additions of lertbutanol to water solutions of such compounds as p-nitroaniline produced easily detectable extinction coefficient and positional changes in electronic absorption bands, they further demonstrated with the one compound they examined in detail, a merocyanine dye due to Brooker,lm a quantitative shift and reversal pattern with maximum effect at a mole fraction 0.04 of the alcohol. The spectral changes reflected only a small percentage of the actual energy changes in ground and excited states produced by solvation changes. Recently Iiaminsky and Davison1n6reported large extinction-coefficient exaltation of the Soret band in the spectrum of oxidized cytochrome c with several alcohols. The monohydroxy alcohols produced exaltation maxima at very nearly the “magic mole fractions” for extrema found in many other types of alcohol-perturbed processes thus demonstrating the similarity of this phenomenon to other alcohol-perturba-

1139

I~NTIiALl'Y-l~NTILOPY COMPUNSA'I'ION SOLUBILITY of ARGON in $0- EtOH SYSTEM

(0.01

1-9

\;'

EXPERIMENTAL o 6°C x 14OC

TEMPERATURES

26%

-6

-8

-10 -12 ASo (e.u./mole)

-14

-16

-11

Fig. 2. Compensation plots for the solubility of argon in water containing various concentrations of (a)methanol or ( b ) ethanol. Calculated from the data of Ben-Naim1O1 slid Ben-Naim and Baer.102 The alcohol mole fraction at which the data for the points were obtained are given in parentheses.

tion phenomena. Somewhat similar spectral changes were found in the Soret band of the heme group attached to an unfolded undecapeptide obtained from the protein. Comparisons with the solvatochromic model studies of Arnett et a1.79~94.95 mentioned above, and the ribonuclease unfolding model of Brandts and Hunt4 indicate that, the response of cytochrome c and the unstructured heme pept,ide to solvent changes as measured by the exaltation patterns can be attributed to changes in water behavior rather than to any direct alcohol-protein interactions except perhaps a t the highest, alcohol concentrations employed.

1140

LUMltY AND RAJENDElt

In some examples of apparent compensation found in the literature of small-solute processes in water, the T, values lie well outside the 250-320°K range,23but for most of the cases studied T, values cluster in the range from 270 to 290°K and it seems remarkable that this fact has not attracted more attention. Despite the experimental errors in estimating T, values and the fact that even the significance of this quantity is not known, the relative constancy of T, in widely different systems the only common feature of which is the water solvent, suggests that many of these reactions reflect in their compensation behavior a single property of liquid water. Although there appears to be an abundance of supporting data, proof of this hypothesis is complicated by the special nature of the possible errors. Appropriate skepticism about the reality of compensation phenomena is engendered hy the criticisms of Exner which we shall now discuss. The existence and significance of enthalpy-entropy compensation in equilibria and rate processes have been the subjects of considerable debate since the early 1930’s. E ~ n e r l 3 ~ *lists * ~ 5most of the major references on the subject in his own important papers. The basic text reference since 1963 has been Leffler and G r ~ n w a l d . ~ Exner, ~ with considerable justification, criticized the somewhat casual acceptance of compensation which had marked much of the literature before 1964. His criticism was directed toward the usual procedure for determining AS from AG and AH or AH from AG and AS which, in effect, tends to force an approximate functional relationship between AH and AS such that data of low precision will often demonstrate compensation as an error profile whether or not true compensation behavior is present. Exner advocates a different procedure which uses the original independent experimental observations, (either rate or equilibrium constants) directly. For situations in which heat-capacity changes are small, the van’t Hoff equation and the expression for the free-energy change in a process at constant temperature and pressure can be readily recast into eqs. (7) and (8), where K1 and K 2 are equilibrium constants at T I and Tz for otherwise identical experiments. In the cases he specifically considers pairs of ( K I , Kz) values are assumed to have been obtained by varying the chemical nature of the reactants but the argument hat3 general validity. For one set, (TI, Tz), K1,( and Kz,IE are obtained for each member i of a homologous series in the reaction under consideration, for example, the ionization equilibrium of halogen-substituted benzoic acids. AHt = R[TITz/(Tz - TI)] (In K z , ~ hi K1,J ASa = [RTd(T, - TI)] [In

K2,i

-

(TdT,) In K I , , ]

(7) (8)

Then AHo,arid ASo,are computed from appropriate plots of In K2,tversus In K I , ~and , the procedure is repeated for the remaining independent pairs of temperatures, ( T j ,TJ. The resulting ( A H j h ,Ah‘,,) points are compared to see if compensation occurs in the process. However, Exner pointed out that as the interval TZ- T1 decreases so that T1/T2 approaches unity,

ENTHALPY-ENTROPY COMPENSATION

1141

the calculated value of AH" approaches that of TIAS". Spurious compensation thus can be indicated when T2 - T , is small and data of higher and higher precision are required t o distinguish between real and apparent compensation as the difference decreases. If Tz - T I is small, say 20°, which is not unusual in biochemical studies, by approximating the logarithmic values in eqs. (7) and (8) we obtain eq. (9) as the approximate and AHoi, expression between the apparent values of ASoi; ASoapp,i, AHoaP,,+ T , is the midpoint of the experimental temperature range,AT. AH"app.i

=

(Tm - AT)ASouDI,,i -R -R

111

Ki

($8

If the R I11 K , and thus the AGoi(Tn,)/Tm are small with respect to AS",,, spurious compensation behavior with a T , value ( T , - AT) lying well below the experimental temperature range will be demonstrated, unless the precision is sufficient to detect the small variations in In K i . On the other hand, if ln K , is nearly constant, the compensation behavior is real rather than spurious, provided that the experiments have been properly designed t o avoid trivial errors, the most common of which is the selection of systems i which will give rates or equilibrium constants in a limited experimental range. Exner proposed the use of eq. (10) derived from eqs. (7) and (8) on the assumption that AH", = a TAS",.

+

If In K z , ,plotted versus In Kl,, yields a straight line, compensation behavior is present, and T,can be computed from the slope. Exner's objective is to test for compensation using the truly independent observables Kl,$and K2,irather than the often strongly correlated quantities AHoi, AS",. This is a laudable goal but one which is in general so strict that, by using eq. (lo), true compensation cases are thrown out with the false cases. Extremely high precision is required if this test is to be used, and the experimental AT should be as large as possible and as far away as possible from T,. If K I , , ,KZ,*have been studied a t more than two temperatures, the data must be fitted for each independent pair of T i , Th and then averaged after application of a correctly weighted least-squares procedure. The scattering of points in our experience is so large that linear regression procedures are necessary. A much more useful testing procedure is based on eq. ( lla ) or ( l l b ) derived as before for the condition AH",= a TCASot:

+

In K i ( T ) = - (a/RT,)

+ (AHoi/R)[(l/T,)

AG"i(T) = a(T/Tc)

- (l/T)I

+ AH"i(2') [l - ( T / T c ) ]

( lla ) (1lb)

It is customary and desirable to use a number of values of T spaced over the largest possible experimental range when the van't Hoff or Arrhenius method for determining AHo,or M I i is employed. Hence K ior AGO,

LUMRY A N 0 RAJENDEI:

1142

2x1

1.5

@N-I4-7 N

Y

-

0 0

N-A-L-1.

1.0

0.5

/

N-A-D-T

ENTHALPY-ENTROPY COMl'ENSA'l'ION

1143

"I

I 0

d2

E

.-

0 In

-

IS%

323.0-

28 26

-

5

I

I5 20 STANDARD ENTHALPY CHANGE

)'(

30

Fig. 3. Three dill'ereiit. types of compensation p1ot.s for the binding of N-acelyl-1t8rypt,ophan,N-acetyl-u-t,ryptophari, hydrocinnamat.e, and indole t.o a-Chymot,rypsin : I % ( u ) the more familiar A H " vs. AS" plot (Tovalues are 283°K for indole and 270°K for t.he charged species, lllexpt = l3'C; line 2 shown in the figure represents indole points plotted witb the ordinate shift,ed upscale by 10 kcal); (b) In K I vs. 111 K2 plot (Cotnpensat,ioii is not. obvious here and no preferable linear fit is seen); (c) AGO vs. A H o plot, by the relntioiiship, AG" = (aT/TC) AHo [ 1 - ( 2 ' / T C ) ] .Hydrocinriamate and iV-acet,yl-r,tryptophan lie 011one straight, line wit.h a 1', = 267°K. N-Acetyl-D-tryptophan lies 0 1 1 R ditrerent straight line with T o = 269"K, and indole falls on yet a different line with TC= 283OK. Note that in all these cases TeXPt< I:, and therefore the slope is positive as predicted by the equation. When Texpt> T,, t8heslope is negative, illustrated by the second indole line, the dat,a p0int.s for which %'ere obtained at 3°C at (0)pH 7.0, (x ) pH 7.5; ( 0 )pH 8.0.

+

and AH", are reasonably considered to be the independent experimental quantities. This reliance on AH"( does not require any assumptions about the temperature dependence of AH"*,since the slope of the tangent to the van't Hoff plot at T is always the correct value of - AH",/R a t T . The use of eq. (lla) or ( l l b ) is a valid compromise and is certainly preferable to the use of either the A H o t versus AS", relationship or the In K I . ~ versus In K z , , relationship. Unless the experimental precision is high, AC",(T) versus AEIoi(T) plots show a wide scatter of data points a t temperatures near T,. Generally speaking, if the data tested for linear compensation are of such low precision that they do not give a linear fit with eq. (11s) or ( l l b ) , then such data cannot be tested for compensation using any other relationship. This does not necessarily mean that such cases are spurious but simply that such data are not good enough for statistically

LUMR.Y AND RAJENDEI:

1144

significant testing of the occurrence of linear compensation.* The AG",(T) versus A H o f ( T )plot, therefore, may serve as a diagnostic test. Equation (lla) or (llb) is also particularly appropriate when the AH", values are obtained calorimetrically. The three methods of testing for compensation behavior are illustrated in Figure 3 by application to Yapel's very precise data for the binding of inhibitors to a - c h y m o t r y p ~ i n . ~In ~ , Figure ~ ~ ~ 3a, which is the usual A H o versus AS" plot, the inhibitors N-acetyl-L-tryptophan, N-acetyl-D-tryptophan, and hydrocinnamate all fall on one line and indole on another. Figure 3c is a plot of aGoi versus AHoafrom Franks and Johnson.'"g

to establish similarity appears to be sound. It is in this sense that linear compensation behavior becomes especially important to the protein chemist and the biological scientist, since this compensation behavior may be the only indication he has that water plays a direct role in the processes of interest to him. A number of processes of biological interest involving macromolecules will be examined in this connection in a subsequent section. The group of processes in which, we believe, a direct participation of water is revealed by linear compensation behavior, have T , values in the range from about 260 to 315°K. However, the so-called Barclay-Butler type of reactions which includes some of the best-known examples of linear compensation2w-202 are not included in our subclass of compensation processes on the basis of the following arguments. Barclay-Butler behavior is said to occur with homologous series of compounds such as the small monohydroxy alcohols and the small alkanes if the standard heats of solution plotted against the standard entropies of solution form a linear plot when a

1162

LUMRY AND RAJENDElt

gas-phase standard state is chosen. In Figure G two characteristic examples of Barclay-Butler behavior in water solution are shown. I’or reasons that are by no means clear, in these cases the T,. values lie in the middle of the range of our interest but the solubility processes are nevertheless not examples of the class of processes under discussion although the linearity and T , value may be due in part to small temperature dependencies of the heat capacities of the water solutions. When the data are adjusted to liquid standard states rather than gas-phase standard states, the simple linear behavior disappears. Hence, the observed linear compensation must be due primarily to the van der Waal’s interactions between alcohol or alkane and water which, of course, increase the enthalpy of solution with the size of the solute and an entropy decrease due primarily to the unusual interaction of nonpolar groups with water. 28 Despite apparent similarities between these solubility processes and the phenomena we emphasize the two kinds of processes are not usefully grouped together for purposes of this review. The compensation behavior manifested by the solution of argon in water-alcohol solutions, which we have included in our class of compensation processes, does not suffer from the choice of a gas-phase standard state since only one solute is involved. The use of a gas-phase standard state, in this case influences only the intercept value and not the linearity or the slope. Obviously considerable judgement may be required in comparing and classifying compensation processes. While it is true that highly aqueous alcohol solutions behave in qualitatively similar ways in compensation behavior so that it is probably safe to assume that this behavior is a result of the perturbation of liquid water by the alcohols, there is a variety of quantitative patterns which vary from alcohol to alcohol and may have considerable complexity for any single alcohol. Near room temperature the effect of tert-butanol on many compensation processes usually produces an extremum in free energy, enthalpy , entropy, or volume change near an alcohol mole fraction of 0.05 a t 25”C, so that i t is not too misleading to speak of a “magic” mole fraction. But other quantitative patterns also appear. For example, the effects of this alcohol on the intrinsic fluorescence quenching of indole compounds produce extrema in enthalpy and entropy change a t X , of about 0.024 a t 25°C. Ethanol effects appear to be still more complicated, as might be suggested by the data of Franks and Johnson1ogon partial molal volume shown in Figure 7. A t 30” for example, although the minimum on the left-hand side of the figure may prove to be a point of inflection, there are a t least three and perhaps four separate effects of ethanol on water a t mole fractions below 0.1 as indicated by the number of extrema and points of inflection. Recently i t has been reported that small monohydroxy alcohols at concentrations above 10 percent (Xz = 0.04 for ethanol) associate to form micellelike aggregates.205, 206 The similarity between the effects of ethanol and methanol on the solubility of argon in water and the effects of ethanol on the unfolding of ribonuclense appear to be consistent with Rrandts’ analysis of the thermo-

ENTHALPY-ENTROPY COMPENSATION

I

Ion

dynamic changes in protein unfolding reactions. These processes are dominated by a large heat-capacity change attributed by Brandts to the int,eractions of non-polar side chains and bulk water which develop when the polypeptide unfolds. Brandts and Hunt4 extended this picture to explain the effects of ethanol addition in terms of these important interactions and the explanation we have given is built on this extension. However, water is a poor solvent for unfolded polypeptides and there is a strong belief based primarily on the low viscosities of unfolded proteins and information about synthetic-polypeptide behavior in water solutions that the “unfolded” parts of proteins still have extensively cross linked though mobile portions and are not free On the other hand the use of heat capacities for the transfer of the nonpolar side chains of amino acids from a polar hydrocarbon solvent to water as quantitative models for estimating the heat capacity changes on unfolding have been surprisingly successful thus far.5~731~~ In these models, the side chains, although somewhat shielded by the water around the carboxylate and ammonium groups, are otherwise freely exposed to water. However, in protein unfolding, if the unfolded polypeptide is held in a mesh or net state, solvation by water must be far from free. Either there is an accidental cancellation of errors in the comparisons or the interesting idea arises that the important interactions between nonpolar side chains of the unfolded polypeptide and water do not require a large volume of normal liquid water. An understanding of this apparent or real paradox is essential to a better understanding of the socalled hydrophobic bond,207and it may prove that the relatively simple picture based on the similarity between argon, an honorary hydrocarbon, and the unfolded protein is incorrect. In this connection, we might also point out that, not the least important observation in Pohl’s rate studies of transition I for t r y p ~ i n is ’ ~the ~ lack of sensitivity of the unfolding rate process to the presence of alcohol. The possible significance of this finding for protein processes will become evident as we move on to less easily interpretable examples of compensation in protein systems, which are also more closely related to physiologicd fiinction.

The Case of a-Chymotrypsin Vaslow and D ~ h e r t y l measured ~ ~ J ~ ~ the standard enthalpy and entropy of binding of “virtual substrates” and their enantiomorphs to a-chymotrypsin. N-Acetyl-L-tryptophan is a typical virtual substrate for chymotrypsin by definition, since the enzyme catalyzes the exchange of carboxylate oxygen with the oxygen of 180-enrichedwater. No such exchange occurs with the D-enantiomorphs of virtual substrates though they are usually effective inhibitors. Virtual substrates and inhibitors like indole, and hydrocinnamate ion not surprisingly belong in the Vaslow-Doherty group as is demonstrated by comparisons of these compounds among themselves or by studying the pH-dependent variation in AH” and AS”, both quantities becoming increasingly negative with increasing pH (see Fig. 3).

1164

LUMRY AND RAJENUER

AH” and AS” for the D-enantiomorphs of virtual substrates, on the other hand, in this work were only weakly dependent on pH from 7 to 8. Yapel, employing the rate of proton exchange between two acid groups of chymot r y p ~ i n , ’presumably ~ ~ * ~ ~ ~ the imidazolium groups of HIS 57 and HIS 40, and freely dissolved pH-indicator molecules, studied the inhibitor-binding process by measuring the disappearance of one of these groups which occurs when inhibitors are bound. Like Vaslow and Doherty before him, he found precise linear compensation.* Insofar as it is reasonable to assume that the indole- and hydrocinnamate-binding processes are nearly identical, an assumption bolstered by Kim’s findingls7that the charge difference between hydrocinnamate ion and hydrocinnamoyl alcohol is of minor importance for enthalpy-entropy compensation in these binding processes, we might elect to limit the classification of the Vaslow-Doherty processes to a range of T , values from 265 to 285°K. However, it has already been shown that some compensation processes of small solutes in water have T,values lying well out of this range, and it will be shown in the discussion of ligand binding by methemoglobin that these narrow limits are too restrictive. By such exclusions as the Barclay-Butler examples in water, exclusions which can be misleading only insofar as we exclude legitimate cases, and by the limitation of the T , range to the interval to 250-320°K we hope to isolate a set of closely related processes which we have called the “VaslowDoherty compensation processes.” The thesis of this review is that there is a significantnumber of examples of compensationbehavior from both smallsolute and protein processes which do belong to the Vaslow-Doherty group, and that these processes are manifestations of the same properties of water. With this thesis in mind we can now return to a consideration of Yapel’s findings and other examples which appear to relate physiological function of protein systems to Vaslow-Doherty compensationbehavior. Yape1138s210 finds a compensation pattern for N-acetyl-D-tryptophan binding by a-chymotrypsin which is quantitatively similar to those of hydrocinnamate and N-acetyl-L-tryptophan binding, insofar as the T, value lies near 270°K (see Fig. 3) but the AHo and AS” values are much smaller at a given pH. I n addition the binding process in this case can be broken down into two steps, E I -+ EI and EI + EI’, both of which are several orders of magnitude faster than the binding process for the other compounds. I n this sense, the binding of N-acetyl-D-tryptophan mimics more closely the binding of normal “good” substrates in that the steps of interaction are fast and the attendant thermodynamic changes, considerably smaller than those found with the L compound. Thus the studies of Vaslow and Doherty, 164,165 Yapel, 138 and Kimxs7might be called studies in

+

* Yapel’s results were obtained in buffer-free solutions. Shiao and Sturtevantms and Shiao’s obtain slightly lower heats of binding for the same compounds with the except ion of N-acetyl-D-trypt80phan, for which their value is higher. The reason for these discrepancies has not yet been established. Nevertheless, the data of these authors verifies the existence of compensation behavior with Yapel’s compounds and demonstrates a T. of about 275’K.

ENTHALPY-ENTROPY COMPENSATION

AF

AH

-TA S

1165

T

T

I E*S + H20

+

ES

+ HZ0

’

EA* +H20 + EtOH

7

EP2H +

EtOH

7

E+P2H *EtOH

Fig. 8. (Standard) free-energy, enthalpy, and entropy changes along the formal reaction coordinate for the chymotryptic hydrolysis of N-acetyl-ctryptophan ethyl ester determined by Rajender, Han, and Lumry.210 The points marked with double daggers are the activated complexes. The metastable states (not actually metastable in this example) are ES, first major Michaelis-Menten complex between enzyme and substrate; EA, “acyl enzyme” state; and EPZH, major Michaelis-Menten complex between protonated acid product and the protein.

enzyme pathology, especially since the most dramatic AH” and AS” values occur at pH values well above the physiological p H of chymotryptic action (pH 6-6.5) and at temperature well below body temperature. However, their quantitative significance for catalytic function is far from trivial, as can be shown by the results of Rajender, Han, and Lumry (vide injru). Rajender, Han, and Lumry2*1*212 have established by steady-state methods an extensive grid of the pH, temperature, and ethanol-concentration dependencies for the empirical rate parameters obtainable in the chymotryptic hydrolysis of N-acetyl-L-tryptophan ethyl ester. Since Bender and c o - w o r k e r ~ ~have ~ ~ -confirmed ~~~ the existence in this process of an acyl intermediate formed between the N-acetyl-L-tryptophanyl moiety and the hydroxyl group of SER 195, the analysis of the kinetics data to provide equilibrium constants proves to be quite simple a t p H 8. As seen in Figure 8, the free-energy profile plotted along the reaction path shows that the reaction is symmetrical about the acyl-enzyme intermediate, EA. At a standard state of 1M ethanol and at 35”C, there is no single rate-limiting step. The enthalpy and the entropy of formation from separated reactants for the “metastable” intermediates ES (the major Michaelis-Menten

I IGG

LUMRY ANI) IIAJENIIRR

-7 I-

1

-

I

-I 2

-I

I

-I4

7

I

-18

- I 2 -14 -16 -18-20 -22 -24 -26 -28 A So (gibbr/molr)

4

Fig. 9. Compensation p1ot.s for t.he estimat.ed st,andard ent,halpies and entropies of formation of the three met.ast,ableint,ermediat,es,ES,EA, and EPZH wit,h increasing pH, in the chymotxyptic hydrolysis of Ar-acetyl-Ltryptophan ethyl estrer. The indole compensation line of Yape113*is shown for comparison. The points are cornpiitledfrom rat,e dat,a on the assumption t,hat the pH dependencies of t.he pairs of rat,e const,ants ki and k-i for each st,ep cancel. This rtssumpt,ion is relatively poor. at' extreme pH values.

ENTHALPY-ENTROPY COMPENSATION

1 I67

complex) , EA, and EPzH (the major Michaelis-Menten complex formed between the protonated form of N-acetyl-ctryptophan and the protein) are plotted for a number of pH valnes in Figure 9 arid can be seen there to lie close to Yapel’s compensation line for indole binding. The EPZH species is which participates in the normal chymotryptic hydrolysis quantitatively different from the enzyme-inhibitor species studied by Yapel. Its formation and decomposition are much faster and its position on the compensation line is much closer to the origin. The enthalpy and entropy changes in forming ES, EA, and EPZH at pH values from 6.0 to 9.5 are scattered along the same compensation line (Fig. 9), and there is evidence that the “on-acylation” and “off-acylation” activated complexes are formed by additional motion up this compensation line.6 It would be unwise to put much faith in any ideas about mechanism which can be drawn from these data for chymotryptic catalysis and inhibitor binding. The reaction is very complicated, not only because there is a variety of substates of state A163*157 but it is also probable that there exist alternative binding sites for substrates and inhibitors, some of which may be strongly linked, e.g., proflavine. However, the pattern of VaslowDoherty compensation is clearly demonstrated in Y apel’s phenomenological analysis which is based on the mass-action law with no assumptions about mechanism. The binding reaction is firsborder in protein concentration and in the concentration of inhibitor and the experimental precision was unusually high (standard errors lower than 1%) in both Yapel’s studies and in the steady-state velocity determinations.211 The linear compensation behavior obtained by Yapel appears to be better explained by the two-state application than by some other special case of the temperature-independent heat-capacity explanation, but the movement of ( A H ” , AS”) points up the Compensationline toward more negative values with increasing pH does not follow a simple mass-action dependence on the concentrations of one or two acid groups and thus may require a more elaborate mechanism based on many charges. A mechanism of the latter type has been suggested by Orttung et al.2179218 to explain the pH dependence of oxygen binding to hemoglobin (the Bohr effect). Orttung has initiated a major attempt to achieve a quantitative understanding of the ionization behavior of proteins and particularly hemoglobin through careful application of the Iiirltwood-Tanford21s~zzo method using the x-ray positional parameters (see also Brausse et a1.221). In the following section it will be shown that ligand-binding reactions of methemog’obin may also require consideration of many charges on the protein rather than a few. We conclude this section by emphasizing the probability that some part process of normal chymotrypsin catalysis manifests the same compensation pattern found in inhibitor binding, in which case the experimental enthalpy and entropy changes along the reaction coordinate must contain contributions from the compensation process. As can be seen in Figure 8, the enthalpy and entropy values along the reaction coordinate are quite remarkable. I n particular, note that the activation enthalpies for both 211,2159216

1168

LUMRY AND RAJENDER

“on-acylation” and “off-acylation” steps are essentially eero with respect to the separated reactants. In contrast to the explanation we have given for Vaslow-Doherty compensation in the unfolding reactions of ribonuclease and trypsin, there is no evidence that large changes in folding occur when inhibitors are bound by a-chymotrypsin. Nevertheless, specificity is obviously closely connected to motion along the compensation line.6’188 Furthermore, Rajender, Han, and Lumry find that the estimated activation enthalpies and entropies for “on-acylation” and “off-acylation” obtained at the several pH values also form compensation lines with T,values in the Vaslow-Doherty range. However, the latter observations are subject to uncertainty due to the fact that the pH dependencies of the chemical part process and the compensation part, process cannot be uniquely determined from the rate data. Note added in proof: Additional evidence for compensation in chymotryptic hydrolysis has been provided by Cohen e t al.4lO These authors measured the formal enthalpy and entropy changes associated with the Michaelis constants for hydrolysis of the following compounds: methyl-N-acetyl-fl-phenylalanine, D-1-keto-3-carbomethoxytetrahydroisoquinoline and methyl 3,4-dihydroisocoumarin-3-carboxylateand the activation enthalpies and entropies associated with the maximum-velocity (kcat)parameters. For K , the T. values is about 295°K and for koatabout 285°K. The Michaelis constant is not a n equilibrium constant but is accidentally very similar t o a true equilibrium constant for ester hydrolysis by chymotrypsin. The parameter k,,t is very nearly the true rate constant for deacylation. It is of considerable importance that the compensation line for kcat, within a n error of 0.5 kcal in AH and 1e.u. in AS is identical to that obtained by Rajender, Lumry, and Han21*for the deacylation rate constant in the chymotryptic hydrolysis of N-acetyl-ctryptophan ethyl ester on varying pH up t o about pH 8.5. Furthermore, the (AH:, ASS) points for kmt with N-acetyl-ctyrosine ethyl ester, benzoylcphenylalanine ethyl ester and benzoyl-ctyrosine ethyl ester also lie very close to this compensation line.411 The compensation behavior of the koet parameter implies that all these esters substrates are chemically identical with respect to the formation of the activated complex for deacylation from the acyl-enzyme species. Differences in activation enthalpy and entropy among them then must be due entirely to differences in position along the compensation line. This behavior is similar to that obtained by Yapel and LumryZ10 for the equilibrium binding of substrate-similar inhibitors but appears to be much more remarkable since in the deacylation process the chemical part process makes large contributions to enthalpies and entropies of activation. The finding of a single k,t compensation line for all these esters suggests that some protein process, independent of the nature of the acylating group, dominates kcat. However, studies of the behavior of the imidazole group of HIS 57 show that kost for N-acetyl-ctryptophan ethyl ester does apply to the deacylation step as expected on the basis of studies by Bender and coworkers.Zl3-216 The thermodynamic changes obtained by Cohen e t al. may not be accurate, as these authors point out, but the combination of observations nevertheless suggests the possibility that the side-chains play a major role in determining the activation enthalpies and entropies for deacylation and that they do so by fixing the position of the acyl-enzyme and activated complex along the compensation lines and not through any important influence on the electronic aspects of bond rearrangements. These observations expand on the discussion of the controlling effect of side-chain binding sites on bond-rearrangement steps given in the text. They fit in nicely with the compensation behavior demonstrated by the activation enthalpies and entropies for deacylation of the acyl enzymes in the series from acetyl through caproyl but they may be more important than the results with this series. This follows from the finding by Rajender and Lumry412that the cornpensation behavior associated with the deacylation

ENTHALPY-ENTltOPY C0,IIIPENYATION

116'3

as well as the acylation rat,e constants in the chymot,ryptic hydrolysis of N-acetyl-Ltryptophan ethyl ester apparently must be attributed almost entirely to the activated complexes in these steps rather than to the metastable intermediate stat,es. If t.his analysis proves correct, we shall have to conclude that despite the fact that the enthalpy and entropy contributions from the compensation part process nearly cancel in free energy, the bond-rearrangement steps are just as much dependent on compensation as are the equilibrium binding processes for chymotrypsin. This is contrary to what. we have stated in the body of this article, but see Ref. 6. It is interesting to note that those deacylation processes for ester substrates for which data now exist will all have the same free energy of activation when the experimental temperature is about 285'K a t least a t the pH values of the reported experiments. If, as the data for N-acetyl-Ltryptophan ethyl ester suggest and in keeping with Likhtenshtein's proposa1,as the kOst parameters for the other substrates are found to produce the same compensat.ion line on pH variation, the statement will have wider and even more remarkable validity. Bolen and Bilt0nen~~3 in calorimetric studies of t,he binding of 3'-cytidine monophosphate to ribonuclease A find on pH variat,ion a comperisation pattern similar to that, for the methemoglobins (Fig. 10) including a turn-around point just, below the isoelectric point. The compensation temperat,uieis about 260'K but the chemical part process has a weak dependence on pH which makes this value uncertain.

Compensation Phenomena in AcetylcholinesteraseSystems Note added in proof: Since this article was written we have become aware of earlier publications of which show that he was the first to propose the direct participation of liquid water in protein reactions 011 the basis of the liiiear-compensatiori pattern he found in acetylcholinesterase systems. Likhtenshtein's proposal that linear compensation is a general characteristic of biological macromolecules appeared about the same time.

Belleau and LavoieZz2 have recently reported the thermodynamic changes in the binding of 30 inhibitors of the N-alkyl-N,N,N, trimethylammonium series t o bovine erythrocyte acetylcholinesterase. The work, of necessity, had somewhat lower precision than that of Yapel and does not yield a good AGO versus AH" plot so that, for the reasons already discussed, i t is possible that some of the compensation behavior demonstrated by this large group of inhibitors is spurious. As a result, the good linear correlation obtained by Belleau and Lavoie may not be reliable, although there is a good rationalization for compensation in chemical reasonableness based on the volumes of tlic inhibitors as is discussed by the authors. The slope of the compeiis:btion plot is about 288°K and the compensation line is indistinguis1i;iblc n-ithin error from that obtained by Yapel with indole binding by chymotrypain. The similarity of the intercepts would appear to be accidental. The range of AHo in the ncet?-lcholiiiesterasr work is -7 to +S kcal/niole and the range of AS'" is -10 to +20 eu/mole. Both ranges are smaller than the corresponding ranges observed by Yapel and as a consequence do not so clearly suggest a process involving many water molecules. Thus although Belleau and Lavoie, on the basis of the analogy with the findings of Ives2*and Hepler29~30 and their co-workers, implicate water, they discuss the compensation process as being localized to a few water molecules in the region of inhibitor and substrate binding sites. If, for example, the process w r e the melting of ice, 30 eu would imply that only six water molcculcs are

1170

LUMItY AND RAJENDER

involved. The point of view of Belleau and Lavoie is very similar to that of Beetlestone and his c o - w ~ r k e r s to ~ ~be~discussed - ~ ~ ~ in the following section and to the point of view of Bernhard and R o s ~ i ~in~their ' . ~consideration ~ of the catalytic mechanism of chymotrypsin, (vide infra). Belleau and D i T ~ l l i ohave ~~~ very recently determined the influence of these inhibitors, which bind a t the substrate side-chain site, on the irreversible reaction of methanesulfonyl chloride with the serine hydroxyl group at the "chemical" site. They isolate different patterns for the cyclic inhibitors, the branched-chain inhibitors, and the straight-chain inhibitors, respectively, but Vaslow-Doherty compensation is suggested in each pattern and the correlation between the quantitative enhancement of the rate of the methanesulfonyl chloride reaction and the enthalpies or entropies of binding determined by Belleau and Lavoie222 is quite good. Again, experimental problems with acetyl cholinesterase make the data somewhat less precise than is required for absolute proof of this relationship. The correlation of inhibitor volume with rate enhancement is also fair and appears to provide a promising method of attack on the problem of the compensation-specificity relationship.

Compensation Reactions of Methemoglobin Interesting examples of compensation phenomena which lend themselves to a more critical examination are presented in a remarkable set of studies carried out by Beetlestone and Irvine and their c o - w ~ r k e r s ~ during ~~-~ the ~~ last few years. The original aim of the work was to show that conventiorial coilsiderations of electrostatic effects, primarily by using thc dielectricc:tvity model of I'

/

METHEMOGLOBIN A c SCN-

,

-2 0

T = 2OoC I = 0.05M

0

I

i

+I

0

I

-I -2 T A So ( kcol /mole)

I

-3

-4

-5

Fig. 10. Staiidard enthalpy changes vs. standard entropy changes for the bindiiig of SCN- to humaii hemoglobins A and C at 20°C with increasing P H . ~ "Arrows point in the directiori of increasing pH. pH values in parentheses indicate turn-around points.

relative sterility of studies of protein systems at one temperature and, as Beetlestone and Irvine228.229 point out, show that deductions about the chemical nature of ionizing groups based on comparisons of heats of ionization of acidic or basic groups of proteins with heats of ionization of the same groups in small molecules can be quite misleading. For the organisms in the series which are all, but one, warmblooded, it is the free-energy change rather than the enthalpy or entropy change which is important for eficient functioning. Hence if compensation does occur in alkalirie methemoglobin production, the variations in ASo arid AHo are

LUMRY AND RAJENDER

1172

1-

- 4.0 n

I

w w

L

-I STANDARD E N T H A L P Y CHANGE

-51 -5

- 1I0

I

STANDARD ENTHALPY - A S A W E

({

(s)-

I

Fig. 11 (continues)

related in the same way as these quantities are related in the production of error leading to a false identification of compensation. That is, mutations which produce a change in AHo are not acceptable unless they also produce a change in ASo which leaves the value of AGO unchanged or alters it to n different value suitable for a different body temperature or a different

ENTHALPY-ENTltOPY COMPENSATION

1173

n

$ -

v

-1

W (3

z 4

I

u

> 0 a w

z W

-€

W W

a lL

a

a 4

a

z

3 v)

-5

I

'

-10 STANDARD ENTHALPY CHANGE

(m)

I

-15

Fig. 11. AGO vs. AH" plots for the binding of ligands to various hemoglobin species to illustrate the reasonably good fit obtained with this type of plot:227-aai( a ) binding of SCN- to human hemoglobins A and C; ( b ) binding of Na- to guinea pig, human A and C hemoglobins; (c) binding of Na- to ( 0 )pigeon and (€3) dog hemoglobins.

metabolism. Of course, the protolysis of the water molecule in methemoglobin is not known to have direct physiological significance but it is undoubtedly closely controlled by some of those aspects of structure responsible for the established physiological processes of hemoglobin. The net charges on the proteins, estimated from the ionic-strength dependence of the equilibrium constant, are found to have no simple relationship either to the free-energy changes or to the enthalpy changes, and the pairs of points (AH", AS") for the different species do not retain the same sequential pattern along the compensation line a t high ionic strength as at low ionic strength. Furthermore, the AGO versus AH" plot shows a poor tit. It is riot clear whether these characteristics are due to experimental error, are :~nindication of a more complex compensation pattern, or imply that compensation behavior is accidental. I n the formation of alkaline methemoglobin, Beetlestone and Irvine explain the variations of the thermodynamic quantities with species, isoelectric point and charge, on the basis of a strictly electrostatic model. Species variations are attributed to differences in charge distribution. The quantities AHo and AS" are assumed to be pH-independent in the experimental range of p H 8-9 in which presumably only COz-free ammonium groups change charge state. This invariance of AHa and AS" with p H is supported by their data (see IGg. 10) but is nevertheless surprising, as will become evident in thc discussion of the second part of their studics.

LUMRY AND RAJENDEIt

1174

-2

c4

3

v

4

W a

f 5 5 0

-I

4

W

a n

d t 4c "

.

1

&

-; -k

-k STANDARD

-k

-iO

ENTHALPY

-2'4 6 ;CHANGE

-&

-?,6

-& -&

Fig. 12. Composite coinpetisat ion plolssfor I.he tiiidiiig of various ligaiids 1.0 differelit, methemoglobins and myoglobiii t o demoiist.ra1e (.he hehavior of the st,andardeiithalpy and ent,ropy of binding with increasiiig pI~I.22'-2:14No1.e (,heex(-eediiiglygood h e a r fit a.ndnear coiistancy of YC.

In the second major set of studies, Beetlestone and his co-workers determined the equilibrium constants for the binding of azide,228cyanide,23othiocya1iate,~30and fluoride ions230s232 t o human methemoglobins A and C , as a function of temperature arid pH. Not the least important consequence of this precise work is the demonstration of a complete absence of any hemeheme interaction in the binding of any of these ions. Representative AG" versus AH" plots are given as Figure 11. The fit to two linear segments in each case is very good considering the small changes in both quantities over the experimental p H range, and similar plots of the other ligands are equally linear despite a n estimated maximum standard error of 500 cal/mole in AH". The p H values of the experiment a t which each (AGO, AH") point was obtained are marked in this figure. With the arbitrary choice of temperature for AGO made in preparing the figures, the plots break up into an upper segment obtained with rising p H followed by a lower segment obtained after the p H values pass some critical value near neutrality. Two cornpensation patterns seem to be clearly delineated each having its own compensation temperature. The sharpness of the change

ICNTIIALPY-ENTROPY COMPENSATION

1175

from the upper to the lower segment with p H is noteworthy, since i t suggests a high-order dependence on hydrogen-ion activity. We have seen turn-around behavior which seems similar in some of the "alcohol-perturbed" processes. Though this similarity may be misleading, the very abrupt turn-around behavior in those plots indicates that the controlling process also has a high-order dependence, in this case a high-order dependence on alcohol concentration. Figure 12 gives a composite picture of the compensation process as manifested in ligand binding reactions of methemoglobin and metmyoglobin, plotted as AH" versus AS" with the corresponding T , values to illustrate the improved linear fit given by this less sensitive plot. I n calculating AGO, AH", arid AS", Beetlestone e t al. corrected their data for the protolysis process m hich, as has been mentioned, appears to have pH-independent values of AH" and AS". However, the protolysis process may be converted to an equivalent ligand-binding process by writing i t as ey. (27), which gives a t zero ionic strength (on the assumption of pHHbH20

+ OH-

+ HbOH

+ H2O

(27)

independent AH" and AS" values for the protolysis process) A(;" = -7.3 kcal/mole, AH" = - 10.2 lical/mole, and AS" = -9.9 eu/moJe for metHb A and AG" = -7.5 kcal/mole, AHo = -8.7 lical/mole, and AS" = -4.2 eu/mole for metHb C. These values are riot much different from those observed with SCN - binding, which demonstrates the characteristic rising and falling compensation pattern as pH is increased. It is thus puzzling that AH" and AS" for the protolysis process of metHb H,O are found to hc indepetiderit of pH.228v23",24U.241 George a.nd H a ; 1 i a n i a ~ ~ noted ~ ~ ~ ~the 4 ~pcculiarity of the abserice of a dependence of AH" and AS" for the protolgsis process of metmyoglobin on chdnges in number iind distribution of charges. However, metHb .H 2 0 arid metHb .OH- are high-spin ferric-ion complexes in contrast to metHb. CN- and metHb .azide, which are low-spin complexes (see Kotani et a1.242.243) and may require different consideration as a result.* Recently Bailey, Beetlestone and I r ~ i n e have * ~ ~ reported the enthalpy and entropy changes in the formation of alkaline metmyoglobin from metmyoglobin. These quantities are pH-dependent and show Vaslow-Doherty compensation behavior. The azide binding characteristics of both methemoglobin and metmyoglobin are quite similar (in terms of linear compensation lines, T 3 values, and turn-around points) but the alkaline metmyoglobiri exhibits a different pattern. The qualitative differences suggest that t.he protolysis processes of both metmyoglobin and methemoglobins are more complex than the ligand-binding processes involving F-,SCN-, N3-, and CN-. Beetlestone and I r ~ i n were e ~ able ~ ~to ~provide ~ ~ a~ quantitative reconciliation of their protolysis data with differences in charge arrangements

* Fabry and co-workerslSQin studies of the efficiency o f RbFe"1 in relaxing water protons have observed a compensationpatl.em when pH is used as the ii~dependentvariable.

1176

LUMItY AND RAJENDISI1

using a dielectric-cavity model, but it became apparent to them early in their studies of ligand binding that the same type of purely electrostatic explanation, although satisfactory in the analysis of the free-energy changes, was not adequate to explain the compensating changes of AS" and AH". They first proposed as the source of compensation a n "orientation" process in the protein conformation, perhaps one involving changes in some charged groups and their methylene tethering chains near the heme group. The separation of the two part-processes, both pH-dependent, so that one dominates AGO and the other is detectable only in AS", and AH" variation is, of course, quite reasonable since their experimental temperatures were never very far away from the T,values. Although T,did not generally equal the mean temperature of their experiments, the contributions to AH" and TAS" from the compensation part process nearly cancel out a t all their experimental temperatures. It may be noticed that on the assumption that compensation is due to interactions with solvent and protein conformation the chemical changes in the ligand-binding reactions are measured by AH" a t AS" equal to zero (Fig. 12). The intercept values of AH" probably are equal or close to the free energies of the chemical part processes a t T = T, with this assumed division into part processes. If the maxima in (negative) enthalpy change near p H 7 and p H 7.5 in Figures l l a and l l b (human Hb) are not due to the protolysis of HbH20. they are true maxima for the compensation part process (the "orientation" effect) and must be explained on the basis of some pH-dependent characteristic of the protein. Three obvious alternatives are the small net charges a t these p H values, the nearly maximal values of total charge, or some peculiarity controlled by imidazole deprotonation of this hist idinerich protein. We shall ignore a fourth alternative that changes in hydrogen-ion or hydroxyl-ion activity alter the properties of liquid water. Such effects may be anticipated a t the extreme ends of the p H scale, but can hardly be important when hydrogen-ion concentrations are of the order of 10-8M. Detailed proposals are given by Anusiem, Beetlestone, and Irvine2" for the control of the compensation part process by charge tautomerism on the distal imidazole group or by counterion binding near the heme group. In connection with thest. proposals they broaden their earlier descriptiori of the orienttition cffcct to incorporate chatigcs iii thc structure of hydration water iiriir thtk distd imidazole. This cbxtwsioii is based on the similarity of the comprnsatioii pattern iii ligand binding to the protolysis of weak acids, and their description of the process follows from the description given by Ives and M a r ~ d e nfor ~ ~compensation behavior in the latter processes. This is a very attractive hypothesis on which t o base new studies of both ferric and ferrous forms of hemoglobin and myoglobin, but we suspect that although hydration changes in a general sense will be found to be the source of compensation behavior, these changes will not be found to be entirely confined to the region near the distal imidaaole group. One reason for this suspicion is derived from the quantitative differences in compcrisntioii bctwcwi mcthcmoglobins A aiicl C which

ENTHALPY-ENTROPY COMPENSATION

1177

differ chemically by the replacement of glutamic acid by lysirie at position 3 of a-helix A of the /3 chains.223'244As shown by x-ray diffraction studies, this position is at about the maximum possible distance from the hemtl group (about 30 &,227,244 and the charged groups at this position should be as fully solvated as is possible for a surface residue since it is neither in nor near the surfaces of interaction of the subunits. It remains to be seen whether or not the hydration hypothesis can explain the quantitative variations of compensation with ligand, pH, and hemoglobin species. Regardless of pH, the differences in the enthalpy and entropy of h y d r tion of 14'- and CN- must appear in the thermodynamic changes for the binding of these two ligands but the differences must be confined to the contributions from the part-processes not responsible for compensation. Obviously, these ion-hydration differences cannot be responsible for compensation contributions to the entropy and enthalpy nor can the protolysis processes of HCN and H F since the A H and AS values plotted have been corrected for their acid equilibrium. The compensation part process, even if due primarily to water, must be triggered by some change in the protein. There is as yet little evidence for correlation between compensation and conformation changes but a significant correlation may exist between the magnetic susceptibilities of the methemoglobin derivatives and the relative changes in compensating AH" and AS" values. Hb111CN4 at 20°C has a susceptibility characteristic of low-spin ferric complex ions.z4z~z43 Hbrrr(N3)4and Hbr11(SCN)4have susceptibilities intermediate between those of the high-spin and low-spin limits, though Hbr11(N3)4 is close t o the low-spin l e ~ e 1 . ~ ~(Hb4II1)F4 5 has high-spin characteristics. Anusiem, Beetlestone, and Irvine227,230 have shown that there is a linear correlation between the magnetic susceptibilities and the total changes which take place in AH" or AS" when the p H is varied from 6.0 to 7.0 for HbA or from 6.0 to 7.5 for H b C. They did not consider Hb11r(OH)4. There is also a close correlation between AGO for the several derivatives a t any fixed p H and the measured susceptibilities as can be seen in the relative positions of the compensation lines on the AH" axis a t Ah'" = 0 in Figure 11. This second correlation may be explicable on the basis of the nephelauxetic parameters246of the ligands and their known electrostatic field strength as ligands, but Blanck and S ~ h e l e r , like ~ ~ ' Iijuka and K ~ t a n i attribute , ~ ~ ~ the existence of compensation to involvement of the protein conformation. Blanck and Scheler determined the activation enthalpy and activation entropy for the formation rate of binding of the ligands F-, HCOO-, SCN-, OCN-, SeCN-, N02-, N3-, CN-, and imidazole to horse metmyoglobin and to human and tubifex methemoglobin at constant p H 7.0. It is somewhat startling to find that the plot of AHS versus ASs is roughly linear with an apparent T, value of about 300°K. The AGx versus A H xplot is not entirely convincing. The order of decreasing activation enthalpies and thus activation entropies for metmyoglobin is CN- > F- > N3- > imidazole > SeCN- > NO2- > OCN- > SCN- > HCOO-. Only F- is inconsistent with the ordering found by Reetle-

1178

LUMRY AND RAJENDER.

stone e t al. for methemoglobin.2" Blanck and Scheler relate this order to the static magnetic susceptibilities and show a good correlation as to order between the susceptibilities and the activation enthalpies. Similar correlations have been obtained by others as we shall now discuss. George, et al. ,245 Ehrenberg,248and more recently Iijuka and K 0 t a n i ~ 4 ~ and Brill and Sandberg249*250 have shown that the magnetic susceptibilities of a number of metmyoglobin derivatives produced by substitution a t the sixth position of heme iron are average values determined by the distribution of the molecules of a derivative between high-spin and lowspin states. This fact is apparently extendable to the methemoglobin but although it is quite reasonable to find a correlation between average susceptibility and the A G O values, the susceptibilitycompensation relationship is by no means to be expected. It is of considerable interest that Iijuka and Kotani studying the high-spin to lowspin equilibrium for the aquo form, and for the imidazole, OCN-, and N3derivatives of metmyoglobin in water solution and ice find an enthalpyentropy compensation pattern for this equilibrium which is linear and has a T,value of about 310°K. The aquo complex was completely converted t o the high-spin state in ice. The van't Hoff plots for the imidazole and NS- derivatives are linear; only the OCN- derivative shows some curvature at the melting point, but the latter may be attributable to a change in chemical state or state of aggregation of this derivative. These observations on spin-state equilibria of metmyoglobin are not obviously consistent with a participation of water in the compensation part process studied by Anusiem et al. The detection of compensation in the change of spin-state and the relatively large standard entropy changes, as large as -33 eu/mole for the imidazole derivative, suggest that the susceptibility change is coupled to changes in the protein since transitions between electronic states of complex ions not accompanied by changes in coordination number can produce only small entropy changes especially if there are geometric restrictions on solvent change at the heme as is the case in the heme-proteins. Iijuka and Kotani favor the conformationchange explanation but also discuss alternative possibilities. The relevant AS" and AH" data for ligand binding in model heme systems required to assess this proposal are not yet available.* As a result of the x-ray diffraction information due to Rendrew and Watson, and their c ~ - w o r k e r s ~ ~and ' - ~the ~ ~work of G e ~ r g e , Beetle~ ~ , ~ ~ ~ stone,223-236Kotani242v243 and their respective associates as well as that of a number of other workers, the metmyoglobin and methemoglobin systems form a particularly attractive area for concentrated quantitative investigation using a number of methods. There are important problems of contamination and homogeneity with these proteins which deserve attention in future work, but these have been solved for myoglobin and may be solved for hemoglobin in the not-too-distant f ~ t u r e . ~ ~An ~,~" * For amplifirrttion and new development.; in the qtiidies of the Beetlestone groiip see Note added in proof.

ISNTHAIJPY-ENTROPY COMPENSATION

1 179

example of the application of new methods to proteins is the work of McConnell and colleague^^^^-^^^ on spin-labeled protein derivatives by EPR spectrometry. However, in view of the possible importance of changes in protein hydration water with the chemical state of the protein as proposed by Anusiem et al.,230it becomes necessary to question how much of the changes in local environment, indirectly relayed through the EPR signals or any other “reporter group” signal, is due to conformation changes in the protein fabric and how much to conformation changes in the hydration water. I n conclusion we note the developing lines of similarity connecting the inhibitor (and substrate) binding processes studied by Y a ~ e 1 ’and ~ ~ by Relleau and Lavoie,222the compensation process in ligand binding by methemoglobin, the oxidation Bohr effects in hemoglobin and myoglobin217s218and the Bohr effect in (ferrous) hemoglobin.260 Despite numerous efforts it does not appear that the Bohr effect in hemoglobin has been satisfactorily explained on the basis of a small collection of ionizable groups of the protein. Perutz has recently made some interesting pictorial proposals for Bohr-effect groups using the x-ray diffraction model, and it may prove that a few charged groups are responsible, although the chemical evidence is not encouraging.z61*2fi2 The pH dependence of both Yapel’s chymotrypsin compensation processes and the compensation processes of ligand-binding studied by Beetlestone et al. also appear to be inconsistent with the simple mass-action behavior of a few ionizable protein groups. ~ ~Brausse , ~ ~ * et already mentioned, The approach of O r t t ~ n g ~and is a step toward a more flexible explanation insofar as all or a large number of ionizable groups of the protein are involved, so that, simple mass-act,ion behavior may be badly obscured. The direct participation of water in the Bohr effect of hemoglobin seems entirely reasonable. The sequestered water held in the interstices of the tetrameric hemoglobin molecule while presenting some problems in its own right also serves as an answer to other perplexing questions of function which are characteristic of multiple-subunit protein aggregates of all types. The maximum thermodynamic stability of globular proteins where known is relatively small, egrationconst,ant,for the first integral is zero and for tshesecond AEo PAVOleading t.o eq. (b).

+

AQT = - AGT -- -

T

(b)

So long as AEo and AVOare constant, A&/T is determined by the behavior of A+T, whirh Benzinger calls the "Planck free entropy" change. The latter quantity ran be related to ranoniral partition fonrtions, Q, and the complexion numbers, n, as shown in eqs. (r).

+

As a source of chemical insight the formulation AGT = AEo PAVo - TAQT has considerable to recommend it. since AEo, is t,he elect,ronicpotent(ia1energy plus the zero-point energies, and A+ alone changes wit,h temperature and t.he other variables of the system. So long as the chemical description of the reactants and produrt,s, does not change, AEo aild PAVo are constant, and A@'T will behave like AGOTIT and will be constant to the extent that AG'T/T is constant. The constancy of A@'T is achieved in general only by enthalpy-entropy compensation a s is clear from eqs. ( c ) in which A(EOT - E'o) is the temperatmure dependent, part, of AE'T. In a single component syst,eni or in solvent domains of n dilute solution only weakly int.eractitig wit,h solutes, AE"o and AVO0 me zero

1212

LUMRY AND RAJENDER

and approximate compensation behavior must occur whenever (a) AG"T/T is nearly constant and ( b ) the component exists in two or more macroscopic states, i.e., in two or more reasonably well separated regions of phase space. Linear compensation behavior can occur as a special case when there are more than two such states but in general its appearance can be correctly taken t o indicate t h a t there are two and only two such states. We suspect that mixed solvents, particularly combinations of non-polar and polar solvents but also combinations of strongly interacting solvents, may frequently exist in more than one macroscopic state. The two-state behavior of water is not unique but neither is it a basis for believing that multistate behavior in a single component-in a single phase-is a common characteristic of other liquids. The formulation Benzinger champions albeit impractical as a bookkeeping device because of the requirement for low-temperature data, has some conceptual utility as we have just shown and considerable chemical utility. The conventionalexpression, A& = AHT - TAST, has its own advantages which may be more useful in some applications. For example, although Benzinger's formulation more clearly reveals the t,hermodynamic basis for compensation behavior in processes of single component,s or mixed solvents, the more useful thermodynamic quantities are AHOT and AS'T and not AE"0 and A@'T. Similarly in some protein systems AEOo and PAVOOmay be constant in which case the formulation used by Benzinger shows that compensation behavior is certain to be found particularly near aGoo = 0, but again the thermodynamic information of most use is AHOT and ASOT. The observations do not, of course, provide any basis for assuming that such processes of proteins as unfolding will have a common T,value and the understanding of protein unfolding has progressed to a point such that we know no common T, value exists. On chemical grounds the same conclusion is possible in other protein processes but we cannot exclude the possibility that some physiologically important processes of proteins are quantitatively similar from protein to protein of a given class as a result of natural selection. (We are indebted to Drs. T. Benxinger and H. Frank for bringing the utility of Planck's formulation of AGT to our attention.)

We can make no generalizations about the behavior of aqueous solutions containing considerable concentrations of the non-aqueous solvent component. As soon as the concentrations of the cosolvent influence the specific solvation, the simple linear pattern must be expected to break down. Sometimes the concentrations at which the linear pattern first, disappears are rather high, e.g., 30y0by weight for ethanol or methanol in Ben-Naim's studies of argon solubility, but there is a clear indication in the experiments thus far that the simple linear compensation pattern with T , value in our provisional range depends on the maintenance of the qualitative properties of pure water. Studies such as those of the hydrolysis of terkbutyl chloride show that although compensation of enthalpy by entropy change in the activation quantities occurs at all X , values when the cosolvent is a small alcohol, linear Vaslow-Doherty behavior occurs only over a small range of X , values near zero. The persistence of the Vaslow-Doherty pattern in the absence of cosolvents is dependent on the concentrations of the solutes. Ionic processes studied a t low concentration will give different results at least for enthalpy and entropy changes than when studied at high concentrations and, of course, attempts to explain the changes in behavior on the basis of activity coefficient may look reasonably adequate until the temperature dependence of the effects is examined.

ENTHALPY-ENTROPY COMPENSATION

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From the point of view of those specifically interested in the behavior of water the good linearity obtained in many examples of Vaslow-Doherty compensation is the most interesting feature of the compensation process. We have discussed two bases for this characteristic: a weakly temperaturedependent heat-capacity change in a process demonstrating this pattern ; and a two-state process in water. When the heat-capacity change is large and strongly dependent on such coso1vent.s as the simple alcohols, the first explanation may be appropriate. It appears less satisfactory when the enthalpy and entropy changes are not dependent on cosolvent or the heat-capacity change is not dependent on solute in homologous series of solute processes. On the other hand, the two-state explanation may be satisfactory for all cases since the large heat-capacity effects observed with solutes having large nonpolar parts can be attributed to n in the enthalpy and entropy expressions corresponding to eq. (20a) :

Thus if the number of the water species W1 converted into species W, depends on cosolvent concentration and temperature, AHawl-twz and ASawl+wz, need not depend on X2 and T. Similarly, in the protein examples, if n depends on pH, A H 0 ~ , + w 1and ASow1.+w2need not. Consequently, although two-state behavior can be quite complex, there is no reason a t present to conclude that it indicates anything other than that water exists in two and only two macroscopic states. This idea has, of course, a wide popularity among some specialists in water research despite the low a priori probability that such a complex substance should demonstrate such simple phenomenological behavior. Our evidence tends t o support the two-state interpretation rather strongly and thus suggests that we ought t o consider very seriously such essentially two-state theories as those of Ben-Naim294+295 and Eyring274-277 and their co-workers. From the point of view of the protein chemist and enzymologist there can be little hope for a suitable molecular theory of Vaslow-Doherty compensation in the immediate future and one must be satisfied for the present with the phenomenological approach in this aspect of protein reactions as also in all other aspects. If Vaslow-Doherty behavior in proteins and small solutes rests on the same properties of water, the phenomenological question which appears to be of most immediate importance for such investigators is that relating to the direction of change along the compensation line: what specific influences of a solute cause change toward larger enthalpy and entropy values and what cause change toward negative enthalpy and entropy values. I n other words, we must find out why the simple freevolume approach of Eley has had to be replaced by the approach of Ben-

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LUMRY AND RAJENDEH.

Naim. Perhaps this fundamental question can be answered by experiments with proteins more retidily than by experiments with small solutes.

SUMMARY I n summary, our assessment of the situation a t present is as follows. 1 . If volume changes link enzyme reaction to the Vaslow-Doherty compensation process, even in Yapel's studies of the binding of N-acetyl-Ltryptophan to chymotrypsin, the maximum measured compensated change in AHois about -27 kcal/mole and in ASoabout -100 eu/mole, and the total maximum volume change estimated by using the AV value for structural relaxation in water would be about -83 ml/mole or 0.45% of the volume of the protein. Unless contractions of this magnitude occur in a very anisotropic way, they cannot be detected with the best x-ray diffraction precision now available and considering the poor lattice energy of protein crystals they may not be sufficient to disrupt the crystalline state. 2. I n the case of chymotrypsin, although the catalytic process is somewhat reduced a t temperatures near 270-285"IL210.401 this process still retains the high rate characteristic of enzymic catalysis. A t this temperature, the compensating contributions to AH and A S from the VaslowDoherty process, whatever its nature, make a very minor contribution to the free energy of any catalytic step in which it participates. Hence, for this single-subunit protein, compensation cannot in itself play a n important role in the rate of catalysis. If compensation does indeed rest on volume changes, its most important apparent implication is that the volume of the protein changes during catalysis and that specificity is associated with the amount of change in protein volume. 3. At 37°C in the chymotryptic catalysis of N-acetyl-L-tryptophan ethyl ester, the compensation process provides a reservoir of free energy in the form of a negative enthalpy change in water which is used to offset the positive activation enthalpy contribution from the chemical steps of catalysis and t o enhance the rate of catalytic steps by a small factor. The manner in which this might come about, using the protein as a machine to apply P , t o force changes in protein conformation and substrate which carry substrates into difficultly formed activated complexes has been described e l s e ~ h e r e . ~ ?The ' net amount of negative free energy contributed in this way to reduce the chemical free energy of activation is about 2 kcal/ mole. 4. HammesBs and Lumrylg have discussed the possible importance of compensation in achieving biologically useful adjustments of the enthalpy and entropy along the reaction coordinate, but in a warm-blooded organism it is only the free-energy changes which are important so that compensation may have less utility for such organisms. The situation is quite different for cold-blooded organisms, since the coupling of the compensation part process to the chemical part process in these limiting steps has the effect of replacing an unfavorable enthalpy of activation by an

ENTHALPY-ENTROPY COMPENSATION

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unfavorable entropy of activation. From the point of view of those organisms which are not thermostatted this is a highly desirable achievement, since i t greatly reduces the temperature sensitivity of the rate-limiting steps. The on-acylation and off-acylation processes have essentially no temperature dependence in the chymotryptic example we have used for exposition. Thus, the Vaslow-Doherty process may have played a major role in evolution and may still serve the functional needs of cold-blooded organisms to maintain metabolic ,respiratory, and regulatory balance under wide variations of environmental temperature. An example which appears appropriate is the remarkably small temperature dependence for the oxygenation of tuna hemoglobinJM2AHo = -2 kcal/mole, in contrast to much larger values found in mammalian hemoglobins. This fish divides its time between warm surface waters and the cold ocean depths and may profit considerably from the temperature insensitivity of its respiratory pigment. It has already been shown that Vaslow-Doherty compensation is involved in some reactions of respiratory pigments and it may be responsible for the fortunate adaptation of tunafish hemoglobin. 5. If the Vaslow-Doherty phenomenon does prove to rest on volume changes in the protein or protein-controlled changes in hydration shells, its implications for linkage between distant sites in single subunit proteins, in multiple subunit proteins such as hemoglobin, and in particulate systems like the mitochondrion are of major importance. An important and perhaps the major important characteristic of such linkage systems is their ability t o transmit free energy from one point to another through the protein and associated water, presumably in the form of mechanical free energy. Allosteric behavior in information transfer from point to point is only one manifestation of the fundamental free-energy transfer mechanisms. Linkage mechanisms now appear to be due to conformational rearrangements (distortion mechanisms), a water readjustment mechanism or both. It remains to be determined whether or not the mechanism or mechanisms of Vaslow-Doherty compensation are parts of the mechanism of freeenergy transfer though this situation now seems quite probable. 6. At the present time the only estimate of the magnitude of large conformation changes in proteins is the change in enthalpy and entropy. Rearrangements in the positions of atoms and the distances involved in these rearrangements may be of major importance in some protein functions but their ultimate importance, as in all chemical processes, must be judged in terms of conventional thermodynamic quantities. However, the indication of participation of water at the surface, in the bulk phase or as sequestered water in the protein, raises doubts as to the interpretation of the thermodynamic quantities in terms of changes in the conformation of the polypeptide chains of the protein. A possible case in point is the Ab-At transition of a-chymotrypsin which has been detected in catalytic s t ~ d i e s " ~and , ~ in ~ studies of the transient and equilibrium fluorescence behavior. 15' If these observations have been correctly interpreted, the protein is present in equal amoiints of the two substates a t about 25°C at

1216

LUMRY AND RAJENDER

pH 8, and the enthalpy change can be estimaked as between 48 and 100 kcal/mole. Kim has shown that it is a two-state process not accompanied by a significant change in the heat capacity.157 Rajender et aL2I0have found that both forms are catalytically active though with slightly different rate parameters. It has been suggested that the process is an expansion or less likely, a compression of the protein. However, the entropy change just balances the enthalpy change at 298°K and may indicate that the process is a compensation process involving water alone. It seems improbable that this type of process is limited to chymotrypsin. 7. If the chemical part process and the compensation part process in any total protein process are both pH-dependent, linear compensation behavior will not be found when pH is the independent variable used to produce compensation. This is probably very often the case in enzyme reactions, Note added in proof: This is true if the dependence is large. However, when the dependence is small, linearity or near linearity will still be observed but the apparent To value will deviate from the true value. This sitnation can be visualized in terms of a compensation diagram with a line of correct slope, probably 285OK, drawn through each experimental point. The curve formed by connecting the experimental points approximates a line with greater or smaller slope than that of the family of true compensation lines. Many of the deviations of experimental To values from the T. value for pure water may be due to this type of weak dependence of the chemical part-process and the specific solvation,which usually is included as part of the chemical part-process.

so that more complex compensation patterns are to be expected at least in some enzyme systems. However, in both the binding of inhibitors to achymotrypsin and the binding of anion ligands to methemoglobin the (AH",AAS")points produced by varying pH fall on a straight line (we restrict ourselves to the points obtained below the isoelectric point by Beetlestone et al.).223-2a6Hence AH" at AS" = 0 must be independent of pH, which implies that the chemical part process is independent of pH. In the enzymic processes of chymotrypsin this behavior is no longer found since the chemical part process contains a strong pH dependence presumably due in major part to the imidazole group or groups acting as base catalysts. However, even when this complication does not occur, in these examples a t least, the pH dependence of the compensation part processes cannot be described by simple mass-action expressions involving one or two ionizable groups. As described earlier, the general approach in unraveling these problems is to examine the enthalpy and entropy profiles of the total process evaluated or computed for the prevailing Tovalue. With luck, the pH dependence of the free-energy profile of the chemical part process can be extracted by trial and error in the usual way as outlined by Laidler, for e ~ a m p l e . ~ ' - "The ~ pH dependence of the compensation part process is more difficult to extract and probably cannot be obtained from conventional rate data alone in most instances. The degree of complexity can thus be considerable and compensation may be completely hidden. Until it can be established that there is no compensation part process in the overall mechanism, simple analyses of the pH dependencies

ENTHALPY-ENTROPY COMPENSATION

1217

of enzymic processes which have beer1 conventional in the past must be viewed with caution. 8. Vaslow-Doherty compensation in small-solute solutions is characteristic of water, perhaps in ways we have suggested, i.e., all solute systems which change volume in water introduce contributions to enthalpy and entropy changes due to the response of water as a volume buffer. But, although dissolved proteins manifest the same behavior as other solutes, evolutionary changes may not have occurred in such a way as to utilize this property of water for important functional purposes. Thus we have seen that the rate of enzymic catalysis as judged from the limited number of systems forwhich data exist is not remarkablyenhanced by the participation of Vaslow-Doherty compensation regardless of its cause. On the other hand, Yapel found that both inhibitors N-acetyl-L- and D-tryptophan are bound by chymotrypsin with very nearly the same free-energy change, but the enthalpy and entropy changes are very different. N-Acetyl-Ltryptophan moves easily along the Vaslow-Doherty coordinate, i.e., the coordinate measuring the degree of advancement of the compensation process, but N-acetyl-D-tryptophan is restricted to minor motion along the coordinate. The ratio of the rates of hydrolysis of the corresponding substrates, N-acetyl-L-tryptophan ethyl ester and N-acetyl-D-tryptophan It seems not only probable but very imethyl ester, is about 1010.406,407 portant that the specificity difference is directly due to the difficulty with which these substrates move along the compensation coordinate to the activated complexes. We can reasonably suspect that this difficulty is associated with distortions of the protein conformation resulting from the geometry of the D-substrate. If so, these distortions seem to be closely related t o the source of compensation so that specificity must be determined by dynamic rather than static aspects of protein-water conformation. It is thus obvious that the Vaslow-Doherty compensation phenomenon must be understood if enzyme specificity is to be understood.* It is quite possible that these observations on the Vaslow-Doherty phenomenon are simply the opening wedge in the discovery of a water-based phenomenon of widespread biological importance, not only in specific physiological processes but also in chemical e v o l ~ t i o n . ~ ~ ~ ~ * We are iudebted t,o I h s . A. Alfseu, E. Arttet,t, B. Bellenu, 1:. Biltoiien, J . I3ra11d(s, W. I)rost-I-Ianse~i,11. Ilorne, AI. h-ohii, W. Ort,twg, 1). P’. Shiao, 1’. von Hippel, I. Wadsii and G . Walrafeti, for kiiidly niakiiig manuscripts available to IIR plior to piib1i1::~tion. We are also itidebt.ed to T. Fabrp, H. Fisher, H. Frank, H. Golinkin. J. Lefflcr, W. Lipscomb, W. hIiller :tiid T. Steits for personal roninirinicat.ionsof informst,ionand suggestions. We are indebted to F. Franks for particularly important critical suggestions. The preparation of this review was supported by the U.S. Public Health Service through N.I.H. grant AM-05853-07; by the National Science Foundation grant, GB7896, by the Air Force, AFOSR-1222-67 and by the U.S.Atomic Energy Commission under contract AT(l1-1)-894. This is publication number 38 from the Laboratory for Biophysical Chemistry.

* These statements have been found to require modification.

See Note added in pmof.

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LUMltY AND ItAJENDEIt

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