Wolfen Den 6120

Biophysical Chemistry 105 (2003) 559572

0301-4622/03/$ - see front matter 2003 Elsevier Science B.V. All rights reserved.doi:10.1016/S0301-462203.00066-8

Thermodynamic and extrathermodynamic requirements of enzymecatalysis

Richard Wolfenden*Department of Biochemistry and Biophysics, University of North Carolina, Chapel Hill, NC 27599-7260, USA

Received 24 October 2002; received in revised form 22 January 2003; accepted 22 January 2003

Abstract

An enzymes affinity for the altered substrate in the transition state (symbolized here as S ) matches the value ofk yK divided by the rate constant for the uncatalyzed reaction in water. The validity of this relationship is notcat maffected by the detailed mechanism by which any particular enzyme may act, or on whether changes in enzymeconformation occur on the path to the transition state. It subsumes potential effects of substrate desolvation, H-bonding and other polar attractions, and the juxtaposition of several substrates in a configuration appropriate forreaction. The startling rate enhancements that some enzymes produce have only recently been recognized. Directmeasurements of the binding affinities of stable transition-state analog inhibitors confirm the remarkable power ofbinding discrimination of enzymes. Several parts of the enzyme and substrate, that contribute to S binding, exhibitextremely large connectivity effects, with effective relative concentrations in excess of 10 M. Exact structures of8enzyme complexes with transition-state analogs also indicate a general tendency of enzyme active sites to closearound S in such a way as to maximize binding contacts. The role of solvent water in these binding equilibria, forwhich Walter Kauzmann provided a primer, is only beginning to be appreciated. 2003 Elsevier Science B.V. All rights reserved.

Keywords: Transition state; Binding; Enzyme catalysis; Inhibition; Thermodynamics

1. Introduction

As he laid the foundations for the presentunderstanding of protein folding, Walter Kauz-mann identified the pervasive influence of solventwater on cellular processes, and the importance ofconsidering solution thermodynamics before seek-ing more exotic explanations of the rates andequilibria on which life depends. As an undergrad-

*Tel.: q1-919-966-1203; fax: q1-919-966-2852.E-mail address: [email protected] (R. Wolfenden).

uate at Princeton, I had the good fortune oflistening to Professor Kauzmanns lectures onphysical chemistry. Those lectures offered a brac-ing antidote to the encyclopedic monotony withwhich organic chemistry was taught in those days.Walter did not gloss over the difficulties. In oneof his more delphic utterances, he once exclaimedAnyone who thinks that he understands entropyis crazy!The visionary biochemist Fritz Lipmann, with

whom I carried out my doctoral work, had alreadybegun to teach biochemists the importance of free

560 R. Wolfenden / Biophysical Chemistry 105 (2003) 559572

energy changes during metabolism. During thatperiod, I also learned from William Jencks andFrank Westheimer that the reactivities of organiccompounds could be described in the language ofphysical chemistry, bringing the genuinely organicchemistry of living systems within the reachifnot necessarily the graspof people with a quan-titative bent. When I returned as an assistantprofessor to Walters department, I benefited fromhis hunch that the future vitality of academicchemistry lies in its application to biological ques-tions. The impact of his teaching, on me as on somany others, has been remarkable.

2. Thermodynamic requirements of an efficientcatalyst

Enzymesubstrate interactions have long beenrecognized as representing an extreme expressionof structural complementarity in biological chem-istry. One of the earliest observations to emergefrom studies of catalysis by enzymes, and fromheat inactivation of enzymes in the presence ofsmall molecules, was that enzymes bind substratesreversibly, forming complexes that appear to dis-sociate at concentrations usually slightly higherthan those that are present physiologically. Unreac-tive structural analogs of the substrate are usuallyfound to be reversible inhibitors. This suggeststhat substrates and substrate analogs vie for a placeon the enzyme, in accord with the possibility thatES complexes are also formed during the catalytictransformation of the substrate (for a review, seew1x). This view led to the well-known proposal byEmil Fischer that substrates fit enzymes as a keyfits a lock. Captivated by that image, medicinalchemists occupied themselves for many decadesin designing substrate-like inhibitors, hoping thatthey would be strong and enzyme-specific.But was Fischers view correct? In considering

that question, it is helpful to focus attention on thevarious stages through which a substrate passes asit undergoes chemical activation. To enhance therate of a reaction, a catalyst must enhance thesubstrate equilibrium constant for attaining thetransition state. As early as 1921, Polanyi recog-nized that a catalyst must bind a reactant withincreasing affinity as the reactant is distorted

toward the structure that it adopts in the transitionstate w2x. In his remarkable textbook, written onlya few years later w3x, Schwab explains:

The energy barrier to be overcome is lowered in theadsorption layer because the activated state is stronglyadsorbed and, therefore, in the adsorption layer, is lessendothermic and therefore more often reached. Hence, it isnot that the adsorbate is activated but that the adsorbate is(more) easily activated and is therefore, at equilibrium,present in the activated state to a greater percentage extentthan in the free gas.

If active site is substituted for adsorptionlayer, this statement contains the essence of ourpresent view of how free energy changes accom-pany enzyme catalysis in aqueous solution.

3. Adsorption of the activated state byenzymes

Many years after Polanyis paper, and with noapparent knowledge of its existence, Linus Paulingw4x and William Jencks w5x speculated that it mightbe possible to develop a powerful enzyme antag-onist in the form of an unreactive compound,analogous in structure to S , the altered substratein the transition state. Then, in 1969, the algebrain Scheme 1 was used to show that an idealtransition-state analog should surpass a conven-tional substrate or product in its affinity for theenzyme, by a factor that matches or surpasses thevery large (see below) rate enhancement that theenzyme produces w6x.Because of its startling implications for catalysis

and inhibitor design, it seems worthwhile to con-sider some qualifications and questions raised bythis scheme.

1. Must an enzyme bind S more tightly than S?If enzymes did not stabilize transition states,no increase in rate would occur. The algebraof Scheme 1 tells us that to lower the freeenergy of activation, an enzyme must bind Smore tightly than S. Accordingly, the distinc-tion that was once made between bindingsites and catalytic sites appears meaningless,since catalysis depends on this transientincrease in binding affinity. When two sub-strates are compared, specificity may appear in

561R. Wolfenden / Biophysical Chemistry 105 (2003) 559572

Scheme 1. If equilibrium is maintained between the groundstate and the transition state in dilute solution, then the formaldissociation constant of the altered substrate in the transitionstate (K ) is expected to be less than that of the substrate intxthe ground state (K ), by a factor matching the factor by whichmthe rate constant of the catalyzed reaction (k ) exceeds thatcatof the uncatalyzed reaction (k ). Effects of desolvation,noncharge separation or proximity in multisubstrate reactions canbe considered to involve subpopulations of ES that depart fromthe mean in the usual statistical description of molecules in theground state. At equilibrium, any of these subpopulations canbe more reactive than ES, but can do so only to the extent thatit is rare. Transition-state affinity may be underestimated if themechanism of reaction in solution differs fundamentally fromthe mechanism of reaction at the enzymes active site, ork K is limited by enzymesubstrate encounter. This relation-cat mship is not applicable to reactions involving quantum mechan-ical tunneling, and requires modification for reactionsproceeding through covalent intermediates.

k or in K , depending on the extent to whichcat mbonding differences in S are already presentin ES w6x.

2. What happens on the path to the transitionstate? Transition state theory is silent aboutintermediates between ES and ES , leaving usfree to speculate about points in between.Those intermediate species resemble a flock of

sheep near a mountain pass. If we couldilluminate the sheep with an instantaneousflash of light, we would observe that theirpopulation dwindled with increasing height.These sheep are not wandering with any pur-pose and have no inherent tendency to congre-gate near the most direct path to the transitionstate. The enzyme is designed in such a waythat the rarer the species of the substrate(between S and S ), the more tightly it isbound, near the path to the transition state w7x.

3. Must the native enzyme be a pre-existingtemplate for the altered substrate in the tran-sition state? No. Scheme 1 rests on no assump-tions about the presence or absence of changesin the conformation of an enzyme duringcatalysis. Scheme 1 implies that an enzyme isa template that is in, or can easily adopt (i.e.without much distortion of the enzyme fromits native structure, as expressed in free energy)a conformation complementary to that of thesubstrate in the transition state. The forces ofattraction in the transition state are so strongthat it would be surprising if some change inenzyme structure did not occur. Moreover,changes in enzyme conformation, as discussedbelow, are probably needed to reconcile maxi-mal forces of attraction in the transition state(tending to involve a closed structure of theactive site), with the conflicting need for rapidsubstrate access to, and product egress from,an open structure w8x. Structural evidence forsuch changes, obtained from the crystal struc-tures of enzyme complexes with transition-state analogs, is now so abundant that itappears to be the rule rather than the exception.

4. What if the mechanisms of the spontaneousand enzyme-catalyzed reactions differ? Is tightbinding of S still required? Of the variouspathways that may be available in water, thenon-enzymatic reaction must follow that path-way that has the lowest free energy of activa-tion. If that pathway differs radically inmechanism from the reaction at the active site,then it must have a lower free energy ofactivation than any reaction in solution thatwould more closely resemble that followed atthe active site. The rate of the observed non-


enzymatic reaction would then be larger thanthe rate of any hypothetical non-enzymaticreaction that would be more appropriate forcomparison. The rate ratio, and hence thebinding affinity in the transition state, wouldhave been underestimated accordingly. Thus,an unsuspected difference in mechanism doesnot weaken, but only tends to reinforce, therequirement that S be very tightly bound w7x.

5. What if the mechanisms of the spontaneousand enzyme-catalyzed reactions are similar, butthe transition state for the enzyme reactionarises from a change in enzyme conformation,or the release of the product from the enzymeproduct complex? If the rate of the enzymereaction is limited by a physical event of thattype, we are led to suppose that chemicalchanges in the substrate occur more rapidly.Thus, the enzymes ability to stabilize thealtered substrate in the transition state for itschemical transformation, and therefore itsbinding affinity for that species, will onceagain have been underestimated.

6. Scheme 1 describes a reaction involving asingle substrate. How large is the transitionstate affinity generated during one of the manyenzyme reactions that involves a second sub-strate or a coenzyme? Scheme 1 is easilyadapted to multisubstrate reactions, incorporat-ing the likelihood that simple juxtaposition oftwo substratesin a configuration appropriatefor reactionmay go far to enhance the rateof such a reaction. Transition-state affinity fora multisubstrate reaction can be estimated bycomparing the third-order rate constant k ycatK K with the second-order rate constantM A m B( ) ( )(k ) for the uncatalyzed reaction betweennontwo substrates, A and B w7x. In such a case, itmay be difficult in practice to determinewhether chemical activation is actually occur-ring, because the upper limit of the advantagethat could in principle be gained by restrictingthe rotational and translational motions of sub-strates in relation to each other is not yet welldefined, but is almost certainly very large w9x.Preliminary experiments in the authors labor-atory on hexokinase, peptide bond formationin the ribosome, alcohol dehydrogenase, and

methyl transfer from SAM to amines, indicatethat positive effects on the entropy of activa-tion play a major role in enzyme catalysis ofsuch reactions. In contrast, enzymes that cata-lyze single-substrate and hydrolytic reactionstend to do so by effects that are mostlyenthalpic (see below). In these latter reactions,catalysis by approximation is not an option.

7. What is the meaning of transition-state affinityin an enzyme reaction during which covalentlybound derivatives of the enzyme are formed,or in which there is quantum mechanical tun-neling of protons? If an enzyme reactioninvolves the formation of a bond between theenzyme and part of the substrate (e.g. reactionof a serine residue at the active site of chy-motrypsin with a peptide substrate, to form aserine ester that is hydrolyzed later), transition-state affinity cannot be estimated in the ordi-nary sense. Nevertheless, an equilibriumconstant for transition-state interchange canbe estimated by comparing the enzyme reac-tion with the rate of reaction of the substratewith a model nucleophile w10x, and numeroustransition-state analog inhibitors have been pre-pared that resemble tetrahedral intermediatesin the formation and breakdown of the acylenzyme. In an enzyme reaction that, unlike itsuncatalyzed counterpart, involves quantummechanical tunneling of hydrogen atoms, therate of reaction is substantially faster than itwould be in the absence of tunneling w11x.Such cases are not amenable to the formalismin Scheme 1, unless the depth of the tunnelbelow the free energy barrier that would applyin the absence of tunneling can be estimated.If, in some particular case, the magnitude ofthe tunneling effect were relatively minor com-pared with other catalytic effects, Scheme 1would tend to apply.

8. Is Scheme 1 adaptable to reactions that aresusceptible to catalysis by desolvation? Allthe species in Scheme 1, as it applies toenzymes that act in watery surroundings, areassumed to be present at equilibrium in diluteaqueous solution. It seems self-evident thatwater must be displaced from the substrate andfrom the enzymes active site when they com-


bine to form an enzymesubstrate complex.Further changes in free energy of solvationoccur during enzyme action, and during thecourse of the benchmark reaction in water.Thus, there can be little doubt that solventwater plays an important role in the catalyticeffect that is observed w12x. In those cases inwhich transition states and their analogs areless polar than the starting materials, thesetransition states and their analogs are expectedto be very tightly bound relative to the sub-strate in the ground state. Enzyme reactionsinvolving thiamine pyrophosphate w13x andSAM w14x offer particularly clear examples ofthis kind of behavior. It should be remembered,however, that desolvation in the ground-stateES complex usually exacts a heavy penalty infree energy w15x. Thus, desolvation may pro-vide a way of increasing k and K , but tendscat mto leave k yK unaffected. The additionalcat mpossibility exists, at least in principle, thatsolvent relaxation effects (as distinct fromequilibria of solvation, which we have justconsidered) might limit the rate of a non-enzymatic reaction w16x. An enzyme mightcatalyze such a reaction by removing the sub-strate from water and reducing solvent fric-tion of this kind. In such a case, the enzymestransition-state binding affinity might be over-estimated, based on simple comparison of rateconstants. However, solvent water is known torelax very rapidly, and solvent relaxationeffects have been reported mainly for fastreactions such as photolysis w17x. In contrast,most biological reactions proceed very slowlyindeed in the absence of enzymes (see below).Although the possibility cannot be ruled out,it would be surprising if solvent relaxationoffered a major impediment to the progress ofbiological reactions in the absence of acatalyst.

9. Might distortion of the substrate, or its con-finement to a high-energy configuration,enhance the reactivity of some fraction ofsubstrate molecules in solution above the ordi-nary level? There are certainly reactions inwhich physical distortion of the substrateseems to play a role. Jencks has identified the

strong inhibition of proline racemase by aplanar proline analog as a possible examplew5x. However, the rigidity of enzyme activesites is probably limited w18x, so that majorphysical distortionin which the substrateresembles a victim of Procrustes w19xnolonger seems likely to provide a very generalmechanism for enzyme catalysis. In Schwabswords, quoted above, it is not that the adsor-bate is activated, but that the adsorbate iseasily activated and is therefore, at equilibrium,present in the activated state to a greaterpercentage extent than in the (unbound state).

10. How is transition-state affinity expressed ther-modynamically? Structural evidence fromcrystal diffraction and NMR spectra of enzymecomplexes with transition state analogs, andthe kinetic effects of mutating enzymes andsubstrates, indicate that enzymesubstratecomplexes usually form new H-bonds or elec-trostatic interactions in the transition state thatwere not present in the ground state. Thattendency appears to be consistent with theobservation that in reactions involving a singlesubstrate, enthalpies of activation are consis-tently more favorable for the enzymatic thanfor the uncatalyzed reaction w20x. With oneexception w21x, entropy changes tend to berelatively small and unpredictable in sign. Thatdoes not mean that they can be neglected. Theentropy loss associated with bringing two mol-ecules together in water can be offset substan-tially or completely by the entropy gainedwhen site-bound water molecules are releasedinto solution w2224x. Thus, entropy is gainedwith the formation of salt bridges betweenoppositely charged groups, or the mating oftwo hydrophobic surfaces w25x.

4. Transition-state analogs vs. substrate analogs

Soon after the derivation of the relationships inScheme 1, this scheme was first tested deliberatelyin the design of the potential transition-state analog2-phosphoglycolate, as an inhibitor of triosephos-phate isomerase, and showed results that seemedpromising w6x. Later C-NMR showed that 2-13phosphoglycolate is bound as a species that is very


rare in solution, and that its dissociation constantfrom this enzyme is approximately five orders ofmagnitude lower than the K value for glyceral-mdehyde 3-phosphate w26x.By 1976, more than 60 transition-state analog

inhibitors had been identified, targeting enzymesof every mechanistic class that was then recog-nized w27x. These inhibitors furnished a test of thegeneral mechanism on which their design had beenpredicated, and a new tool that could be used touncover the structural details of enzymesubstrateinteraction, using exact structural methods. Severaltransition-state analog inhibitors have K values ofiless than 10 M, and in the remarkable case ofy12methionine sulfoximine phosphate (an inhibitor ofglutamine synthetase), exchange experiments seemto place an upper limit of 10 M on they18dissociation constant of the EI complex w28x.Nature has also been found to imitate art, in thatmicroorganisms produce transition-state analogs asantibiotics that include the leupeptins (peptidealdehydes that inhibit proteases by formingenzyme adducts resembling tetrahedral intermedi-ates in peptide hydrolysis) and coformycin (aninhibitor of adenosine deaminase that mimics atetrahedral intermediate in the hydrolytic deami-nation of adenosine). The diurnal rhythm of CO2fixation in plants is now known to be controlledby fluctuations in the concentration of a naturallyoccurring transition-state analog inhibitor of ribu-lose 2,6-bisphosphate carboxylase. The continuingusefulness of this method for generating powerfulinhibitors w7,10,27,2931x has been matched bypractical applications that include the herbicideRoundup (i.e. glyphosate, an inhibitor of aro-matic amino acid biosynthesis), inhibitors of theangiotensin-converting enzyme that are used totreat high blood pressure (Capoten and Vaso-tec) w25x and a group of statine-containing inhib-itors of the HIV protease that are used to controlthe spread of HIV infection w30x. A practicaladvantage of transition-state analog inhibitors, asdrugs, is that they tend not only to be very potent,but also to be specific for the particular enzymewhose activated complexes they resemble, just asthe transition state is unique to that reaction.In contrast, substrate analogs tend to be relative-

ly non-specific and may inhibit any of the several

enzymes for which a particular substrate serves asa substrate or product, sometimes in more thanone pathway. Moreover, the substrate (or product)in the ground state must be relatively weaklybound if catalysis is to ensue, because an enzymecan enhance the rate of reaction only to the extentthat it binds S more tightly than S. Substrateanalogs are therefore expected to be relativelyweak inhibitors, and it is not surprising that fewsubstrate analogs have been reported that are sig-nificantly more tightly bound than the substratesthemselves w32x. That does not mean, however,that the enzymesubstrate complex is uninterest-ing. An important question raised by Scheme 1,for which there does not as yet appear to be ageneral answer, is how an enzyme manages tobind S very tightly in the transition state butavoids binding S almost as tightly, given theirmany similarities in structure. In some cases, suchas triosephosphate isomerase in the ground state,infrared measurements suggest that strain may bepresent in the enzymesubstrate complex w33x. Inother cases, such as adenosine and cytidine deam-inase, NMR experiments suggest that substratesare initially bound by enzymes in forms that areclosely related in structure and energy to forms ofthe substrate that are most abundant in free solutionw34x.

5. Extrathermodynamic requirements of an effi-cient catalyst

5.1. Stereochemical inversion at the scissile bond

In the absence of enzymes, biological reactionstake place very slowly (see below), indicating thattheir transition states differ markedly in energyand structure from substrates in the ground state.The stereochemistry of the transition state mightbe expected to be important in view of the needfor exact structural complementarity to anenzymes active site, which is itself asymmetric.In displacement reactions at sp -hybridized carbon,2transition states with tetrahedral-like carbon atomsare generated, with an inherent chirality that is notpresent in reactants or products. This chirality cansometimes be detected by comparing the effective-ness of two diastereomeric transition-state analog


Fig. 1. Dissociation constants of ligands from calf intestinal adenosine deaminase.

inhibitors. A dramatic example is furnished by 29-deoxycoformycin, whose 8R-form is bound byadenosine deaminase seven orders of magnitudemore tightly than the substrate, whereas the 8S-isomer is less tightly bound than the substrate w35x.Fig. 1 shows these inhibitors, along with the 1,6-hydrate of inosine, which is even more tightlybound w36x, presumably because it has the correctring size. The chirality of the bound hydrate, likethat of the 8R-form of deoxycoformycin, reflectsthe side of the purine ring from which zinc-boundhydroxide ion is believed to mount its attack w37x.At first glance, we might guess that the need

for inversion of configuration in the transition statewould vanish if, as in glycosidase reactions suchas that catalyzed by hen egg white lysozyme w38x,the product retains the same stereochemistry as thereactants. Such behavior usually implies, however,

that a group at the active site forms a covalentintermediate by displacing a part of the substrate,which is then itself displaced by water. In suchdouble displacement w39x reactions, there areactually two transition states, formed on the path-way to and from a metastable covalent intermedi-ate. Both transition states presumably requirestabilization, and could be modeled in the designof an inhibitor.

5.2. Conflicting structural requirement of substrateaccess and product egress vs. the maximization oftransition state affinity

The affinity of an enzyme for the altered sub-strate in the transition state, and its ability todistinguish between S and S , presumably dependon structural complementarity between the host


Fig. 2. A role for conformation changes in enzyme catalysis.An open configuration of the enzyme permits diffusion-con-trolled access of substrate and egress of product. A closed con-figuration of the enzyme allows maximal contact between theenzyme and substrate in the transition state.

and its guest. We might guess that optimal affinitywould be observed if the enzymes active site, inits native or most stable form, were rigidlydesigned to form a perfectly fitting template forS . It was, therefore, a surprise when, in 1970, thecrystal structure of one of the first transition-statecomplexes revealed a tendency of the enzymestructure to change with inhibitor binding. Crystalsof triosephosphate isomerase contracted by 7%along their major axis when 2-phosphoglycolatewas bound, and expanded to their original sizewhen the inhibitor was removed by dialysis w40x.The crystal structures of other enzyme complexeswith transition-state analog inhibitors exhibit asimilar tendency of the enzyme to surround thesubstrate in its activated forms w4143x.Fig. 2 suggests a probable reason for that ten-

dency w8x. Many enzymes are found to act withapparent second-order rate constants (k yK ) thatcat mapproach the limits imposed by the diffusion ofenzyme and substrate in solution. That implies thatmany enzymes tend to be open to substrate accessmost or all of the time, i.e. that an enzymes activesite tends to remain in an open configuration

before it binds the substrate. The movementsmentioned in the previous paragraph would seemunderstandable if the substrate were first boundweakly by this open form of the enzyme, and theactive site were then to change in such a way asto surround the altered substrate in the transitionstate (Fig. 2). That would allow maximization ofthe solid angle of contact, and of attractive forcesof attraction, in the transition state. Thus, alterna-tion of the enzyme between open and closedconfigurations might allow rapid substrate accessto be reconciled with tight binding in the transitionstate. The only formal requirement would seem tobe that this motion of the enzyme not be intrinsi-cally costly from an energetic standpoint, i.e. thatthe enzyme be able to move easily between twostructural extremes, as in the opening and closingof a first basemans glove representing twodomains of the protein. Examples of that kind ofmotion, first noted during substrate binding byhexokinase at low resolution w44x, have nowbecome commonplace. Structural studies, exempli-fied by Charles Carters observations on cytidinedeaminase w45x, show how the potential energy ofthe active sites conformation changes as the reac-tion progresses.To the extent that such behavior is general, it

would probably be a mistake to attempt to designa drug to fit the native (or open) configurationof the enzyme, because much higher affinity isachieved in the transition-state complex, in itsclosed configuration. The latter structure, ratherthan the open structure, would seem to offer abetter template for improvements in drug design.

6. Does transition state affinity depend on a fewor on many interactions?

Differences in structure between S and S areapparently even more obvious to an enzymesactive site than they are to a chemist, viewingtheir structures on paper. The fact remains thatmany of the structural features of S are usuallypresent in S . The differences between them areso few in number that an enzymes ability tomaintain such a sharp, quantitative distinctionbetween these structures, in terms of binding affin-ity, still seems baffling. Confronted by the relative


binding affinities shown in Fig. 1, a reductionistmight guess that any of those several structuralfeatures that distinguish the transition state fromthe ground state might, by itself, tend to confervery high binding affinity on a potential inhibitor.Does the ability of an enzymes active site todistinguish between S and S depend on a fewlocal interactions at the sites of difference, or onan ensemble of interactions that involves everypart of the substrates structure?The answer to that question, insofar as it has

been learned from experiments with transition-state analog inhibitors, seems to be that enzymatictransition states exploit multiple interactions to thefullest extent possible. Experiments involving indi-vidual mutations of either the protein or the ligandshow that elimination of any single binding inter-action in one of these tight complexes can resultin catastrophic losses of binding affinity, even ifthey are distant from the site of chemical transfor-mation of the substrate. Conversely, the gain inbinding strength that individual interactions derivefrom the fact that their binding determinants areproperly connected in adenosine w46x and cytidinew47x deaminases approach the very large incre-ments (;10 M in effective concentration) that8were estimated in theory by Page and Jencks w9x.The fact that catalysis is intensely dependent onthe structural context of the substrate group that isbeing transformed reflects a long-recognized prop-erty of enzymes: their frequent failure to act onsubstrates smaller than their natural substrate,although these truncated versions of the substratesdo not differ from it in inherent reactivity and arepresumably capable of entering the active site.What is surprising is that seemingly irrelevantparts of the substrate (such as a ribose hydroxylgroup in the case of cytidine deaminase w47x orthe phosphoribosyl group in the case of OMPdecarboxylase w48x) sometimes play an over-whelmingly important role in enhancing k rathercatthan K . The behavior of OMP decarboxylase ismshown in Fig. 3.Daniel Koshland, who was the first to recognize

the oddity of this behavior, suggested that it mightserve as a means of organizing the enzymesbinding site into a catalytically active configurationw39x. In relatively rigid substrates such as these,

an unchanging scaffold of non-participating groupsin the substrate appears to provide a setting that isessential for ideal expression of an enzymes cat-alytic action w45x. That behavior seems understand-able by analogy with binding phenomena such asthe chelate effect, in which one binding interac-tion introduces structural constraints that greatlyenhance the probability of a second binding inter-action w9x. Individually, these interactions are soweak as to be unobservable in simple modelsystems in water. Together, they achieve greatstrength. In this way, extremely high affinitiesmight in principle be generated from ordinary H-bonds, electrostatic attraction and non-polarinteractions.

7. How large an affinity is expected of an idealtransition-state analog inhibitor?

Scheme 1 implies that the rate enhancementproduced by an enzyme determines its susceptibil-ity to inhibition by an ideal transition-state analog.Thus, the most reactive of several substrates shouldalso yield the strongest inhibitor, a possibility thathas been confirmed by comparison with the Kivalues for several protease inhibitors w4952x.Similarly, if the structure of the enzyme is alteredby mutagenesis, the enzyme variant with thegreatest catalytic power should be most sensitiveto inhibition by an ideal transition-state analoginhibitor. This latter expectation offers a means ofseparating enzymes, using a transition-state analoginhibitor to elute enzymes in order of decreasingturnover number from a conventional substrateaffinity column w53x.The slow progress of biological reactions in the

absence of catalysts furnishes a standard by whichto judge the catalytic power of existing enzymes,and their consequent susceptibility to inhibition byideal transition-state analog inhibitors. By compar-ing different reactions with respect to the rateenhancements that enzymes produce, it should bepossible to identify those enzymes that offer themost sensitive targets for inhibitor design. How-ever, most biological reactions proceed so slowlyin the absence of enzymes that their uncatalyzedrates in water have never been measured.


Fig. 3. Comparison of the binding affinity of yeast OMP decarboxylase for OMP, in the transition state for its decarboxylation, withorotic acid in the transition state for its decarboxylation, and for ribose 5-phosphate, the missing piece, as a competitive inhibitor.The effective concentration of the substrate in the transition state, )10 M, expresses the advantage the substrate gains by having8its parts properly connected.

Many of these reactions would be impossible toobserve, even at elevated temperatures, if theydoubled in rate for each 10 8C temperature increas-es, as described by an ancient rule of thumbattributable to Harcourt w54x. However, recentexperiments have shown that many biological reac-tions, proceeding spontaneously in solution in theabsence of a catalyst, tend to become more tem-perature-dependent as their rates decrease. Insteadof doubling in rate (DH s12 kcalymol), the veryslow decarboxylation of orotidine 59-phosphateincreases by a factor of 12.5 as the temperatureincreased from 20 to 30 8C (DH s44 kcalymol)w55x. This tendency makes it possible to followeven very slow reactions in neutral solution insealed tubes at high temperature, using Arrheniusplots to extrapolate the rate to room temperature.We have found that the progress of some uncata-

lyzed reactions is slow even on a geological timescale (Fig. 4). At pH 7 and 25 8C, typical half-times are 450 years for the hydrolysis of peptidebonds w56x, 180 000 years for the hydrolysis ofphosphodiesters w57x and 8 000 000 years for thehydrolysis of O-glycosides w58x. For the decarbox-ylation of orotidine 59-phosphate, the last step inpyrimidine biosynthesis, the half-time is78 000 000 years, implying an enzymatic rateenhancement of 10 -fold and a dissociation con-17stant of less than 10 M for the enzymey23substrate complex in the transition state w55x.

8. Analyzing transition-state affinity: the con-founding role of water

How is it possible for an active site to generatesuch extreme affinities in watery surroundings, and


Fig. 4. Rate constants and half-times of biological reactions proceeding spontaneously in water in the absence of enzymes.

to exhibit such acute discrimination between sim-ilar molecules using conventional forces of attrac-tion? That question seems baffling in view of thewell-known weakness of non-covalent interactionsin water, as indicated by the behavior of modelsystems. It can be addressed by measuring thebinding affinities of ground-state and transition-

state analogs and examining their enzyme com-plexes by exact structural methods. The chelateeffect, mentioned in Section 6, appears to becapable of generating extremely high affinitiesfrom ordinary forces of attraction: H-bonds, elec-trostatic interactions and non-polar interactions.Observations on the transition-state binding affin-


Fig. 5. Effects on the transition-state binding affinity of yeast OMP decarboxylase w59x.

ity of OMP decarboxylase w59x, shown in Fig. 5,indicate that any one of the forces involved instabilizing the transition state, if it is eliminatedby chemical alteration or mutagenesis, results indrastic losses in binding affinity. Conversely, theintroduction of a new binding interaction in thetransition state could in principle result in the verylarge increase in binding affinity that is needed toexplain the rate enhancement that an enzymeproduces.To the extent that chemists can satisfy the

delicate conformational requirements of these pow-erful interactions, major improvements in thedesign of stable inhibitors and man-made catalystsshould be possible in future.

Acknowledgments

This work was supported by the National Insti-tutes of Health research grant GM-18325.

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Thermodynamic and extrathermodynamic requirements of enzyme catalysisIntroductionThermodynamic requirements of an efficient catalyst`Adsorption of the activated state;s' by enzymesTransition-state analogs vs. substrate analogsExtrathermodynamic requirements of an efficient catalystStereochemical inversion at the scissile bondConflicting structural requirement of substrate access and product egress vs. the maximization of transition state affinity

Does transition state affinity depend on a few or on many interactions?How large an affinity is expected of an ideal transition-state analog inhibitor?Analyzing transition-state affinity: the confounding role of waterAcknowledgementsReferences

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