computer simulations of enzyme catalysis

10 Apr 2003 17:21 AR AR185-BB32-18.tex AR185-BB32-18.sgm LaTeX2e(2002/01/18)P1: IKH10.1146/annurev.biophys.32.110601.141807

Annu. Rev. Biophys. Biomol. Struct. 2003. 32:425–43doi: 10.1146/annurev.biophys.32.110601.141807

Copyright c© 2003 by Annual Reviews. All rights reservedFirst published online as a Review in Advance on February 5, 2003

COMPUTER SIMULATIONS OF ENZYME CATALYSIS:Methods, Progress, and Insights

Arieh WarshelDepartment of Chemistry, University of Southern California, Los Angeles, California90089; email: [email protected]

Key Words QM/MM, EVB, transition state stabilization, catalysis

■ Abstract Understanding the action of enzymes on an atomistic level is one ofthe important aims of modern biophysics. This review describes the state of the artin addressing this challenge by simulating enzymatic reactions. It considers differentmodeling methods including the empirical valence bond (EVB) and more standardmolecular orbital quantum mechanics/molecular mechanics (QM/MM) methods. Theimportance of proper configurational averaging of QM/MM energies is emphasized,pointing out that at present such averages are performed most effectively by the EVBmethod. It is clarified that all properly conducted simulation studies have identifiedelectrostatic preorganization effects as the source of enzyme catalysis. It is arguedthat the ability to simulate enzymatic reactions also provides the chance to examinethe importance of nonelectrostatic contributions and the validity of the correspondingproposals. In fact, simulation studies have indicated that prominent proposals suchas desolvation, steric strain, near attack conformation, entropy traps, and coherentdynamics do not account for a major part of the catalytic power of enzymes. Finally, itis pointed out that although some of the issues are likely to remain controversial for sometime, computer modeling approaches can provide a powerful tool for understandingenzyme catalysis.

CONTENTS

INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 426WHAT IS THE PROBLEM? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 426SIMULATION METHODS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 427

Incomplete Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 427QM/MM Molecular Orbital Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 428The EVB as a Reliable QM/MM Method. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 430QM Treatments of the Entire Protein. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 431

REPRODUCING THE OVERALL CATALYTIC EFFECT. . . . . . . . . . . . . . . . . . . . . 432Beware of Improper Models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 432Systems Studied by Justified Approaches. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433

EXAMINING CATALYTIC PROPOSALS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 434Electrostatic Preorganization is the Key Catalytic Factor. . . . . . . . . . . . . . . . . . . . . 434Steric Effects and the NAC Proposal. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 435

1056-8700/03/0609-0425$14.00 425

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426 WARSHEL

Defining and Assessing the Entropic Proposal. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 436Dynamical Proposals. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 437Reactant State Destabilization by Electrostatic Effects: A Lesson fromODCase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 437

Polar-Preoriented Hydrogen Bonds Versus Low-Barrier HydrogenBonds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 438

CONCLUDING REMARKS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 439

INTRODUCTION

Enzymes are involved in the catalysis and the control of most life processes. Thusthere is a major fundamental and practical interest in finding out what makesenzymes so efficient. Although many crucial pieces of this puzzle were elucidatedby biochemical and structural studies, the source of the catalytic power of enzymesis not widely understood. This catalytic power cannot be explained by stating that“the enzyme binds the transition state stronger than the ground state” because thereal question is how this differential binding is accomplished.

In order to define our problem, it is convenient to start by describing a typicalenzymatic reaction using the generic equation:

E + S↔ ESK←→ES‡ kcat−→EP→ E + P, 1.

whereE, S, andP are the enzyme, substrate, and product, respectively, whileES,EP, andES‡ are the enzyme-substrate complex, enzyme-product complex, andtransition state, respectively. Many enzymes were evolved by optimizing kcat/KM,(59, 69), where K= k1/k−1, KM= (k−1+ kcat)/k1 and can be approximated as KM

' k−1/k1.It is well known (69) that many enzymes evolved by optimizing kcat/KM. How-

ever, this and related findings did not identify the factors responsible to the catalyticeffect. As is shown in the next section, the key question is related to the reduc-tion of the activation barrier in the chemical step. Unfortunately, even mutationexperiments, which were extremely useful in identifying catalytic factors (35),cannot tell us in a unique way what is the origin of the catalytic effect (60). Whatis needed is a quantitative tool for structure-function correlation and the abilityto decompose the catalytic effect to different energy contributions. It is becomingmore and more clear that this requirement can best be accomplished by computersimulation approaches, and this review describes my own insight into the currentstate of these approaches.

WHAT IS THE PROBLEM?

The discussion of enzyme catalysis is almost pointless without a proper definitionof the relevant questions. When talking about catalysis it is essential to clarifywhat is meant by the term catalysis. Here we must define a reference reaction,

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MODELING ENZYMATIC REACTIONS 427

and the most obvious reference is the uncatalyzed reaction in water. Because themechanism in water can be different from that in the enzyme, we should considerthe effect of having different mechanisms and having different environments sep-arately. Fortunately, the difference in mechanism can be classified as a “chemicaleffect” (e.g., the effect of having a general base instead of a water as a base), andsuch effects are well understood. Therefore, we can focus on the difference in theeffect of the environment. In this way we can focus on comparing the rate constantof a reaction that involves the same mechanism and the same chemical groups butis conducted in water. Thus [see also (60)], our question boils down to the differ-ence between the activation barrier in water (1g‡

w) and the activation barrier inthe protein (1g‡

p). However, the enzyme can reduce1g‡p by binding the substrate

equally in the reactant state (RS) and the transition state (TS) (this corresponds to1Gbind) and by reducing the activation barrier1g‡

cat for the chemical step. Becausethe factors that control binding are well understood, the real puzzle is related to thereduction of the activation barrier of the chemical step (1g‡

cat). Polanyi (48) andPauling (47) long ago stated that catalysts and enzymes reduce activation barriers,but this statement does not tell us how the reduction is accomplished.

Even the question of whether the enzyme works by stabilizing the RS or TS isnot easily resolved experimentally, although mutational analysis can help in thisrespect (60). Thus, we should focus on two main questions: (a) What contributionsare responsible for the difference between (1g‡

cat) and (1g‡w), and (b) how do these

contributions operate (i.e., do they destabilize the RS or stabilize the TS).Possible answers to these two questions have been offered by many proposals

[see (56) for a partial list]. However, most of the proposals have not been properlydefined or properly examined by their proponents. Moreover, many proposals havenot considered a proper thermodynamic cycle. At any rate, as will be shown below,with a clear definition of the problem and with a combination of experimental andcomputational studies, it is possible to elucidate the source of the catalytic powerof enzymes.

In my discussion and analyses of the reference reaction, I refer to1g‡cage, which

corresponds to the activation barrier in a water cage, where the reactants are alreadyat an interaction distance [see (56) for a rigorous definition].

SIMULATION METHODS

As is clear from the above discussion, we are interested in accurate evaluations ofthe activation free energies of reactions in enzymes and in solutions. I consider themain options for accomplishing this task and evaluate their effectiveness.

Incomplete Models

One seemingly obvious option is to study the energetics of the reactants in thegas phase. With such a model one can use a relatively high level and rigorousquantum mechanical approaches. Although such studies have been instrumental

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428 WARSHEL

in providing insight about the reacting system, they are problematic. That is, theentire issue of catalysis is related to the effect of the environment. Thus, omittingthe environment from the calculations prevents one from exploring key catalyticeffects. Furthermore, the effect of the environment is not a small perturbation butfrequently involves enormous energy contributions.

Another option is to consider the reacting system plus a few protein residues.Although this can help in providing some insight, it cannot be considered as areasonable model of the enzyme-active site. In particular such approaches fre-quently assume that some residues are ionized (which is true in the completesystem), but in the model used the ionized form of these residues can be extremelyunstable and would not be ionized. Some specific examples of the problem asso-ciated with gas phase models are given below (see Beware of Improper Models,below).

Despite our warning about the risk of using gas phase models, there are clearexceptions. Most notable are the cases of large metal clusters, where the effectof the environment might be relatively unimportant. In such cases one can obtaininstructive mechanistic information from ab initio studies that do not include theeffect of the environment around the reacting cluster (7).

A seemingly reasonable way to treat a reaction in an enzyme is to use gasphase ab initio calculations to obtain the charges and force field of the substrate(solute). These charges and force field can then be used in free energy calculationsin solution and in the enzyme-active site (51). Unfortunately, the solute chargesin the enzyme-active site may be different from those in the gas phase. This canlead to major problems in case of charge separation reactions, where the differencebetween the solvation energies of the correct charges (those obtained in solution)and the solvation of the gas phase charges can be enormous (30). Other problemsare considered elsewhere (56).

QM/MM Molecular Orbital Methods

The realization that the effect of the environment of the reacting fragments mustbe included in studies of enzymatic reactions led to the development of the hy-brid quantum mechanics/molecular mechanics (QM/MM) approach (62). Thisapproach divides the simulation system (e.g., the enzyme-substrate complex) intotwo regions. The inner region (region I) contains the reacting fragments repre-sented quantum mechanically. The surrounding protein (region II) is representedby a molecular mechanics force field. QM calculations require the solution of theSchorodinger equation for a Hamiltonian that represents the sum of the potentialenergy and kinetic energy of the electrons and nuclei of the system as a mathe-matical operator (58). In the present case the Hamiltonian of the complete systemis given by:

H = HQM + HQM/MM + HMM , 2.

where the HQM is the QM Hamiltonian, HQM/MM is the Hamiltonian that couples

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region I and II, and HMM is the Hamiltonian of region II. HQM is evaluated by astandard QM approach:

Vtotal =⟨9∣∣HQM + HQM/MM + HMM

∣∣9⟩ = EQM +⟨9∣∣HQM/MM

∣∣9⟩+ EMM . 3.

The QM/MM approach was introduced in the mid-1970s (62). However, the ac-ceptance of this approach took a long time (perhaps because of the difficulty in real-izing that medium-range electrostatic effects can be incorporated in quantum treat-ments using classical concepts). At any rate, the QM/MM method is now widelyused and we only mention several applications of it (1, 4, 6, 18, 19, 23, 25, 26, 44,53, 74).

The connection between the QM and MM regions can be accomplished throughthe so-called linked-atom treatment (19, 53, 62, 74). Fortunately, as far as enzymecatalysis is concerned, the linked-atom problem is much less serious than com-monly assumed. That is, in such studies we compare enzyme and solution reactionsand the effect of the linked atoms cancels itself out to a significant extent.

QM/MM approaches that involve several regions of quantum mechanical treat-ments have also been developed. Typically region I is treated at the most rigorouslevel, region II is treated by an approximated QM method, and the outside regionis represented by a MM force field (an approximated implementation of this ideais presented in Reference 57). It is also possible to represent region II by fixed(frozen) electronic density, while retaining a regular density functional theory(DFT) formulation for region I (see QM Treatment of the Entire Protein, below).

The reliability of QM/MM approaches is far from obvious. In particular it isessential to use accurate QM methods and to perform an extensive configurationalsampling of the reacting systems (this is essential for reliable free energy cal-culations). Unfortunately, regular semiempirical approaches are not sufficientlyaccurate, although the accuracy of such approaches can be increased by forcingthem to reproduce the energetics of the reference solution reaction (14, 56, 71).

The most reliable potential surfaces are obtained by ab initio (ai) QM/MMapproaches [referred to here as QM(ai)/MM approaches]. At present, however, theenormous computer time needed for obtaining proper sampling by QM(ai)/MMapproaches makes such studies close to impossible. A novel way to reduce thisproblem is provided by using the empirical valence bond (EVB) potential as areference for the QM(ai)/MM calculations (6). In this way one evaluates the freeenergy profile of the EVB surface by free energy perturbation (FEP) calculationsand then calculates the free energy1G (EVB→ ai) of moving from the EVBto the ab initio surface. These calculations are usually done by a single-step FEPcalculation that involves molecular dynamics (MD) runs on the EVB surface. Whenthe EVB surface is not sufficiently similar to the ab initio surface, it is possibleto improve the convergence by using the linear response approximation approach(36). In this way one uses

1G(EVB→ ai) = 0.5[〈Eai − EVB〉EVB+ 〈Eai − EEVB〉ai

], 4.

where〈〉 designates an MD average of the designated potential (51a).

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430 WARSHEL

Zhang et al. (74) used an interesting approach that took into account the effectof the solvent environment in ab initio free energy calculations. This approach,however, constrains the reacting fragments to move along a predefined reactioncoordinate obtained from QM(ai)/MM calculations and thus neglects the effect ofthe solute fluctuations.

In summary, a significant advantage of QM(molecular orbital)/MM [QM(MO)/MM] approaches is that they can be easily integrated with standard QM programpackages. However, the problems mentioned above still slow down the progress inrealistic studies of enzymatic reactions by such approaches. Nevertheless, advanceshave been made in studies of different enzymatic reactions (1, 6, 18, 26, 44, 62, 74).

The EVB as a Reliable QM/MM Method

Reliable studies of enzyme catalysis require accurate results for the differencebetween the activation barriers in enzyme and solution. The early realization ofthis point led to a search for a method that could be calibrated using experimentaland theoretical information about reactions in solution. It also became apparent thatin studies of chemical reactions it is more physical to calibrate surfaces that reflectbond properties (i.e., valence-bond-based surfaces) than to calibrate surfaces thatreflect atomic properties (e.g., MO-based surfaces). The resulting EVB method(3, 59) is outlined briefly below.

The EVB is a QM/MM method that describes reactions by mixing resonancestructures that correspond to classical valence-bond structures. The correspondingHamiltonian is represented as a matrix of semiempirical integrals (59). The diago-nal elements of the EVB Hamiltonian are represented by classical MM force fieldsthat include the interaction between the charges of each state of the reaction region(region I) and the surrounding system (region II). The off-diagonal elements ofthe Hamiltonian are represented by simple analytical functions that are indepen-dent of region II. The ground state energy is obtained by diagonalzing the EVBHamiltonian.

The EVB treatment provides a natural picture of intersecting electronic statesthat is useful for exploring environmental effects on chemical reactions in con-densed phases (3, 59). The ground state charge distribution of the reacting species(solute) polarizes the surroundings (solvent), and the charges of each resonancestructure of the solute then interact with the polarized solvent (59). This cou-pling enables the EVB model to capture the effect of the solvent on the quantummechanical mixing of ionic and covalent states of the solute (59).

The EVB provides an extremely convenient and reliable way of obtaining ac-tivation free energies. This is done by using a mapping procedure that graduallymoves between the different EVB states (3), forcing the system to move graduallyfrom the reactant to the product state. The mapping is performed while takinginto account the change in the solute charge distribution and not only changes inthe solute structure. In this way the EVB umbrella sampling procedure finds thecorrect TS in the combined solute-solvent reaction coordinate. This includes the

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important ability to evaluate nonequilibrium solvation effects. Other advantagesof the EVB are discussed elsewhere (56).

The seemingly simple appearance of the EVB method may have led to the initialimpression that this is an oversimplified qualitative model rather than a powerfulquantitative approach. However, the model has been widely adopted as a generalmodel for studies of reactions within large molecules and in condensed phases[see references in (56)]. Several closely related versions have been put forwardwith basically the same ingredients as in the EVB method [see discussion in (20)].Nevertheless, it has been argued (54) that various adaptations of the EVB methodare useful because they involve calibration using ab initio surfaces rather thanexperimental information. However, EVB potential surfaces have been calibratedby ab initio surfaces [e.g., (30)]. The EVB approach has been used extensivelyin studies of different enzymatic reactions, and some studies are considered insubsequent sections.

QM Treatments of the Entire Protein

A QM treatment of the entire protein/substrate/solvent system is possible, at leastin principle. Promising progress in this direction has been offered by the so-calleddivide and conquer approach (73). This approach, which was originally developedfor ab initio DFT studies (73), divides a large system into many subsystems, wherethe electron density of each subsystem reflects the effect of its surroundings. Un-fortunately, the treatment of the entire protein by an ab initio approach is extremelyexpensive and cannot be used in free energy calculations of enzymatic reactions.Thus, most current efforts in treating the entire protein by QM approaches havebeen invested in semiempirical treatments with different tricks for accelerating thesolution of the large self-consistent field (SCF) problem (16, 38). This approachcannot be used in ab initio studies of enzymes owing to the computational cost ofevaluating the relevant integrals.

One of the most promising options for treating larger systems by ab initioapproaches is provided by the frozen DFT (FDFT) and constraint DFT (CDFT)approaches (29, 51a, 68). The basic idea behind these approaches is to treat theentire protein solvent system quantum mechanically while freezing (or constrain-ing) the electron density of the groups in region II. In this way the entire system istreated by an ab initio DFT approach, and a formally rigorous nonadditive kineticenergy functional evaluates the coupling between regions II and I.

The FDFT approach presents a general way of coupling two subsystems bymeans of an orbital-free and first-principle effective potential. This makes it pos-sible to cast the concept of “embedding potential” in DFT terms. The FDFT ap-proach is related in a formal way to the work of Cortona (13), who did not deal,however, with the issue of embedding a subsystem in a larger system, which isdescribed by a more approximate method. Wesolowski & Warshel (68) realizedthat the coupling term in any hybrid method could be obtained by a partial min-imization of the total energy functionals. The CDFT embedding idea has been

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432 WARSHEL

adopted in related fields such as studies of molecules on metal surfaces [(33); seediscussion in (67)].

In concluding this section, it is important to comment on the Car-Parrinellomolecular dynamics (CPMD) approach (10), which emerged in recent years as aneffective way for studying complex molecular systems. The CPMD approach wasapplied, for example, in studies of proton transfer in solution (55). However, the useof periodic boundary conditions makes it hard to apply this method to enzymaticreactions. The use of the method in gas phase calculations of the reacting fragmentsand a few protein residues has led to only confusing results (see Beware of ImproperModels, below). Nevertheless, the option of embedding the CP method in an MMsurrounding and considering it as a QM/MM method should provide a promisingoption (15, 70).

REPRODUCING THE OVERALL CATALYTIC EFFECT

A prerequisite for any reliable analysis of enzyme catalysis is the ability to re-produce the observed reduction of the corresponding activation free energies. Theprogress in addressing these problems is reviewed below.

Beware of Improper Models

The use of standard ab initio computer packages without the protein environmentcan result in incorrect models. This neglect of solvation effects leads, for example,to incorrect pKas of key catalytic residues (e.g., lysine residues would tend to beneutral in this model) and completely incorrect energies for proton transfer pro-cesses. A glaring example is provided by the study of Futatsugi et al. (24), whostudied the mechanism of p21ras. The problem with this work [see discussion in(27)] includes the use of a protonated Lys16 in the RS (without realizing that thisresidue will not be protonated in the gas phase environment used in the calcula-tions). The unstable lysine thus serves as an artificial proton relay [see discussionin (27)]. More reasonable gas phase treatments have paid more attention to elec-troneutrality and to the system chosen. However, when such treatments are appliedto mechanistic questions they may favor an incorrect mechanism because they ig-nore the effect of the protein environment [see discussion in (21)]. Other types ofproblems occur when one studies enzyme catalysis by modeling the reacting sys-tem in water. Such approaches preclude any chance to study catalysis because theenzyme and solution reactions are modeled in the same way (see Polar-PreorientedHydrogen Bonds Versus Low-Barrier Hydrogen Bonds, below).

Finally, an uncritical use of the powerful CPMD model may lead to major prob-lems. An example is given by the work of Cavalli & Carloni (11) who concludedthat Gln61 is the general base in the catalytic reaction of the ras/GAP complex [see(27) for a discussion of this reaction]. To determine whether a residue may serve asa base in a nucleophilic reaction, it is essential to evaluate the free energy of protontransfer (PT) between the nucleophile and this residue. It is also useful to examine

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the pKa of the proposed base (in its protein site). Such studies that used the EVBapproach [for review see (27)] have shown that Gln61 cannot be the general basein ras and that theγ -phosphate is more suitable for this role. Nevertheless, Cavalli& Carloni studied this system by the CPMD approach without being aware of theprevious theoretical study and the need to validate their results by pKa calculations.They started with a subsystem that included the substrate Gln61 and a few otherresidues and the attacking water molecule (whose orientation was selected basedon problematic force field calculations). Next they performed a short MD runwhile constraining the distance between the oxygen of the attacking water and theγ -phosphate to 1.8A. The water proton collapsed to Gln61 during this relaxation,and this led Cavalli & Carloni to conclude that Gln61 must be the general base.Of course, pushing the attacking oxygen to a bonding distance from the phosphatewould force the proton to migrate to the closest base. However, this is not an ad-equate way to examine reaction mechanism or to identify a general base. A morevalid study would require (in addition to having a complete system) starting from arelaxed RS and then calculating the free energy profile for different feasible mech-anisms. This requires proper equilibration and long simulations in a FEP study.

Systems Studied by Justified Approaches

The ability to obtain reliable free energy (or even energy) profiles for enzymaticreactions was restricted almost exclusively to the EVB method until about 1996.The difficulty of using other approaches can be realized by comparing the reliableEVB profile for the reaction of triose phosphate isomerase (TIM) obtained byAqvist & Fothergill (2) to the corresponding QM/MM results of Bash et al. (5). Thelatter results reflected apparently unstable calculations and probably incompletetreatment of long-range electrostatic effects. QM/MM studies with semiempericalQM Hamiltonians started to give stable results following the work of Bash andcoworkers (14), who adopted the EVB idea of calibration based on the energeticsof solution reactions. The past few years have witnessed a significant progressin the reliability of semiempirical QM/MM calculations with reasonable resultsand proper sampling, although EVB studies are probably still more reliable. Thesystems studied by reasonably reliable QM/MM approaches now include a widerange of reactions. Representative studies are reported in References 2, 3, 5, 14, 17,18, 28, 39, 41, 59, 63, 66, 71, 72. Most of the reported studies involved EVB andQM/MM semiempirical MO approaches, although some studies with QM(ai)/MMmethods [e.g., (74)] also gave promising results. It is important to clarify, however,that even reasonable QM(MO)/MM studies of catalysis still treat the reaction inthe enzyme and in the solution by different models (e.g., QM/MM model for theenzyme and continuum model for the solution reaction). This makes it hard toassess the validity of the corresponding conclusions.

In all cases that were analyzed correctly, it was found that the catalytic effectwas due to electrostatic contributions. The nature of these effects are consideredbelow.

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EXAMINING CATALYTIC PROPOSALS

As stated in the introduction, the main open questions regarding the energeticsof enzyme catalysis are related to the origin of the difference between1g‡

cat and1g‡

w. Many proposals have been put forward to explain the difference between kcat

and kw [a partial list is given in (56, 60)]. Unfortunately, some of these proposalsare so poorly defined that it is essential to reformulate them before examining theirvalidity. It also appears that some proposals violate the law of thermodynamicsand thus cannot be examined by using thermodynamic cycles. I contend that theprerequisite to any analysis of a catalytic proposal is the existence of a well-definedlogical argument that can actually be tested. With the above comments in mind, Itry to provide a critical evaluation of the relative merit of key catalytic proposals.

Electrostatic Preorganization is the Key Catalytic Factor

Simulation studies that consistently compared1g‡cat and1g‡

cage have found that1g‡

cat is smaller because of electrostatic effects (17, 35, 47, 56, 59). It was alsofound that enzymes “solvate” their TS more than the corresponding TS in thereference solution reactions (58). However, the origin of this electrostatic stabi-lization appeared to be quite elusive. That is, the calculated interaction energybetween the TS charges of the reacting atoms and the enzyme appeared to besimilar to the corresponding interaction energies in solution. This puzzling obser-vation was resolved by the realization that what counts is the entire electrostaticfree energy associated with the formation of the TS (58) and not just the elec-trostatic interaction at the TS. This includes, of course, the penalty for the struc-tural changes (reorganization) upon “charging” the TS. To quantify this point it isuseful to express the electrostatic free energy of the TS charges using the linearresponse approximation with the expression introduced by Warshel and coworkers(36):

1G(Q‡) = 0.5(〈U (Q = Q‡)−U (Q = 0)〉Q=Q‡

+〈U (Q = Q‡)−U (Q = 0)〉Q=0) = 0.5(〈1U 〉Q‡ + 〈1U 〉0), 5.

where U is the solute-solvent interaction potential,Q designates the residualcharges of the solute atoms at the TS, and〈1U〉Q designates an MD averageover configurations generated with the given solute charge distribution. The firstterm in Equation 5 is the abovementioned interaction energy at the TS, whereQ=Q‡. The second term expresses the effect of the preorganization of the envi-ronment. If the environment is randomly oriented toward the TS (as is the case inwater) then the second term is zero and we obtain the well-known expression:

1G(Q‡)w = 1

2〈1U 〉Q‡ . 6.

However, in the preorganized environment the enzyme provides a significantcontribution from the second term, and the overall1G(Q‡) is more negative than

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in water. Another way to see this effect is to realize that in water, where the solventdipoles are randomly oriented around the uncharged form of the TS, it is essentialto invest free energy to reorganize these dipoles toward the changed TS. The reac-tion in the protein costs less reorganization energy because the active-site dipoles(associated with polar groups, charged groups, and water molecules) are alreadypartially preorganized toward the TS charges (59). The above TS stabilization ef-fect is related to the well-known Marcus’ reorganization energy (40) for the givenstep of the reaction, but it is not equal to it. More specifically, the activation energyfor the i→ j step of a reaction can be related by a modified Marcus equation (59) tothe reorganization energyλij and the free energy1Gij. For example, in the analysisof Reference 17, the enzymes studied catalyze their reactions by reducing bothλij and1Gij. However, both contributions reflect the same preorganization effect.That is,1Gij is reduced by the preorganization term of Equation 5 because theenzyme dipoles are already pointing toward the charges of the ith intermediate,while λij is reduced because the enzyme dipole tries to minimize the reorientationof its dipoles in the i→ j step [e.g., see (72)]. More discussion of the evidencefor the preorganization idea is given elsewhere (17, 56, 59). Finally, the reductionof the reorganization energy in an enzyme-active site is not due to a nonpolarenvironment as was proposed by some (34), but to a polar preoriented active site.

Steric Effects and the NAC Proposal

Several proposals for the origin of enzyme catalysis involve some form of groundstate steric strain (22, 52). The original strain hypothesis (22) and related subse-quent works (52) invoked the idea of “molding” the substrate toward the TS bystrong steric forces. This idea is inconsistent with simulation studies that demon-strated that enzymes are too flexible to apply strong steric forces (59, 62). A relatedbut more reasonable proposal has been put forward by Bruice and coworkers [e.g.,(9)], who suggested that the steric confinement of enzyme-active sites brings thesubstrates to a so-called near attack conformation (NAC), which is closer to thecorresponding TS than to the reference reaction in water. Unfortunately, this pro-posal was not defined in clear terms that would allow its verification. That is, theNAC configuration was taken as a rather arbitrary point along the reaction coor-dinate, and the location of such a point cannot be related directly to the differencebetween1g‡

w and1g‡cat. Furthermore, the NAC idea does not tell us what is the

reason for catalysis. The absence of a clear definition motivated Shurki et al. (50)to reformulate the NAC idea by relating the enzyme confinement effect to thecorresponding reduction in activation free energy. This was done by adding anexternal restraint potential, V′ to the potential surfaces of the substrate in water,Vw, and forcing the RS probability distribution to satisfy the relationship:

ρ(r )RSVw+V ′

∼= ρ(r )RSVp, 7.

whereVp is the potential surface of the substrate in the protein. The reduction of1g‡

w upon addition of the restraint potential is the most logical definition of the

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436 WARSHEL

NAC effect. The actual effect of V′ can be examined by FEP approaches withseveral alternative thermodynamic cycles (50).

An actual examination of the effect of the protein restraint was performed inthe specific case of haloalkane dehalogenase. The probability distribution in theprotein is different from the corresponding distribution in water. However, thefree energy needed for changing Vw to Vp by the constraint V′ was found tobe rather small. More specifically, V′ reduces to1g‡

w by less than 3 kcal/mol,whereas the total catalytic effect is∼7 kcal/mol. More importantly, it appearedthat the pure steric component of the NAC contribution is less than 1 kcal/mol. Theremaining contribution reflected electrostatic effects, which have little to do withthe original idea of steric contributions to enzyme catalysis. The finding of non-negligible electrostatic contributions from the NAC effect might simply reflect theelectrostatic stabilization effect of the previous section. That is, when the enzymestabilizes the TS it pushes down the potential surface along the reaction coordinate.Obviously the average RS configuration,〈r 〉RS, is shifted toward〈r 〉T S. Now withthis effect 〈r 〉RS

w is displaced farther to the left than〈r 〉RSp . Thus, if we examine

the extreme case where the barrier in the protein is reduced to zero we wouldconclude that the NAC effect contributes to the entire catalytic effect. This is,however, an artificial consequence of having an ill-defined concept of NAC, sincewe just considered a model where the catalysis and the reduction of1g‡ are dueto electrostatic effects.

In summary, it is important to point out that the NAC proposal does not reallyexplain the origin of enzyme catalysis. That is, this proposal tells us that the enzymereduces〈r 〉RS relative to water. It does not tell us, however, how this reductionis being accomplished (steric or electrostatic effect) or whether we have an RSdestabilization or a TS stabilization effect. If the NAC proposal implies that wehave a pure steric effect (i.e., the catalysis is due to van der Waals forces), then itleads to a small contribution to catalysis (50). The only way for the NAC effect tobe significant is for it to reflect a part of the overall TS stabilization by electrostaticeffects. In this case the apparent steric effect reflects the response of the solventto the solute charges. Here, the change in the solute charges is coupled to thechanges of both the solvent and the solute components of the reaction coordinate.As demonstrated repeatedly [e.g., (50)], the change in the solvent coordinates leadsto the largest contribution to catalysis, and this change is not an NAC effect (itdoes not depend on the solute coordinate).

Defining and Assessing the Entropic Proposal

Many proposals [e.g., (8, 31, 51)] and many textbooks [see a partial list in (56)]invoke entropic effects as major sources of enzyme catalysis. These proposalsassume (correctly) that the large configurational space of the reacting fragmentsis drastically reduced by the enzyme, but then conclude that this leads to a largeincrease in kcat. The entropic proposal is frequently presented using appealing butnot quantitative terms (e.g., “the entropy trap effect”), and is rarely formulated in

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a valid way. Recent analysis (55a) demonstrates that the customary formulationleads to a major overestimate because it ignores the entropy of the TS in water(65, 56). A proper computational analysis (55a) demonstrates that the entropiccontributions to catalysis are much smaller than previously thought.

Dynamical Proposals

The idea that special “dynamical” effects play a major role in enzyme catalysis hasgained significant popularity in recent years [see references in (56)]. Here again,the issue of definition appears to be a major problem. Many proposals overlook thedifference between the well-known fact that all reactions involve atomic motionsand a requirement from true dynamical contributions to catalysis. This issue andother problems with the dynamical proposal has been analyzed in great length inseveral recent reviews (56, 65), where it is shown that dynamical effects do notcontribute significantly to catalysis. Due to space limitations we refer the readersto the above reviews.

Reactant State Destabilization by ElectrostaticEffects: A Lesson from ODCase

The general idea of reactant state destabilization (RSD) has played a major rolein various catalytic proposals, including the abovementioned strain and entropyproposals. One of the most popular versions of the RSD concept is the idea thatenzymes work by providing a nonpolar environment that destabilizes a highlycharged ground state [see references in (66)]. As shown in Reference 59, theseproposals involve improper thermodynamic cycles and do not use a proper refer-ence state. This amounts to ignoring the desolvation energy associated with takingthe RS from water into a hypothetical nonpolar enzyme site. With a proper ref-erence state, one finds (59) that a polar TS is less stable in nonpolar sites than inwater and that the RSD does not help in increasing kcat/kM. In fact, many desol-vation models [e.g., (37)] involve ionized residues in nonpolar environment, butsuch residues would be un-ionized in nonpolar sites.

The difficulties with the RSD proposal can be illustrated by the case of ODCase[see (42) for a review]. This enzyme has the largest rate acceleration (kcat/kw∼ 1017),and the understanding of this effect is thus a challenging task. Before the evalu-ation of the structure of ODCase it was proposed (37) that the enzyme providesa nonpolar low-dielectric environment and works by a desolvation mechanism.Warshel & Florian (61) demonstrated that this proposal is based on an incorrectthermodynamic cycle, and proposed that the enzyme must provide a polar environ-ment. The recent elucidation of the structure of the enzyme [see (42) for a review]revealed that the active site contains two aspartic residues whose carbonyl groupsare located near the carboxyl group of the substrate (Figure 1). Presumably, ifboth carbonyl groups were negatively charged, their interactions with the orotatecarboxyl would be strongly destabilizing. Wu et al. (71) performed QM/MM PMF(potential of mean force) calculations, which reproduce the catalytic effect. They

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438 WARSHEL

then performed FEP calculations of the binding free energy of the TS and the RSand concluded that the enzyme works by an RSD mechanism. Many workers havealmost instantly embraced this idea (49). However, Warshel et al. (66) pointed outthat the proposed electrostatic destabilization is questionable because the strongelectrostatic interaction of the carboxyl groups would result in protonation of oneor the other of these groups. They also pointed out that the binding calculations ofWu et al. (71) did not reproduce the catalytic effect and that the binding calculationsthat were used to support the RSD proposal are challenging. The FEP calculationsof Reference 66, which involved a careful assignment of special boundary con-dition and a proper treatment of long-range effects, did not reproduce significantRSD for the same reacting system considered by Wu et al. Furthermore, it waspointed out that the reacting system includes the entire pyrimidine ring of the sub-strate along with a protonated lysine amino group that most probably donates aproton to the ring during the reaction. Stabilizing interactions with the lysine andother residues largely cancels the repulsive interactions with the two asparates.When this larger region is considered as the reacting system, one finds that thedipole moment of the system increases in the TS. The preoriented Asp residuesof the enzyme favor this change in dipole moment. These calculations support theview that the catalytic effect of ODCase results mainly from TS stabilization, andadditional evidences against the RSD mechanism are available (66).

The RSD proposal was probably put to rest by the recent studies of Miller &Wolfenden (42), who demonstrated that mutations of Asp96 and other residues thatwere supposed to destabilize the orotate led to weaker rather than stronger binding.As predicted (66), this result is inconsistent with the RSD because destabilizationof the RS should result in a reduction of the binding energy.

Polar-Preoriented Hydrogen Bonds VersusLow-Barrier Hydrogen Bonds

It was recognized long ago (35, 58) that hydrogen bonds (HBs) contribute signifi-cantly to catalysis. In fact, the preorganization idea includes a major emphasis onTS stabilization by the electrostatic contributions of HBs (58). The experimentalfindings about TS stabilization by HBs led several research groups [see review in(12)] to come up with an idea that recognized the importance of HBs but tried toattribute the HB contribution to its covalent rather than electrostatic character. Aspointed out elsewhere (60), the only new element in the low-barrier (LBHB) idea isthe proposal that HBs between the enzyme and charged TS of substrates involve amuch larger covalent character (X−δ · · ·H+δ · · ·Y−δ) than the corresponding HBsin solution; otherwise we have a regular (X− H-Y) electrostatic HB. The LBHBproposal is inconsistent with energy considerations (64) and is based on somewhatarbitrary interpretations of experiments rather than on direct experimental results(60). Due to space limitations, I comment only on theoretical basis of this pro-posal. The confusion in the field has been compounded by a series of improper

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calculations (46) of irrelevant systems (i.e., no protein was studied) that confusedionic HBs with LBHBs. The problems associated with these studies are consideredelsewhere (60).

It is also instructive to consider the calculations by Kim et al. (32), which maybe taken as a partial support for the LBHB proposal. These calculations consideredthe reacting fragments in water rather than in the protein. Furthermore, the fewprotein residues that were immersed in the water model were subjected to anartificial constraint, which led to an artificial preorganization effect. One cannotassess the LBHB contribution without comparing calculations of this effect inwater with those in a protein environment.

The LBHB proposal is not supported by calculations that properly consideredthe effect of the protein environment. These include EVB (17, 63, 64) and QM/MM(26, 43, 45) studies. Although the conclusions are similar, I argue that most ofthem are tentative. That is, a reliable analysis of the LBHB proposal must involvecalculations of the free energy (rather than energy) profile for the transfer of therelevant proton between the donor and acceptor that are postulated to form thegiven LBHB. It is also essential to compare this profile for the reaction in proteinto the corresponding profile in water. This helps to determine whether there isany catalytic advantage to the LBHB charge transfer effect (64) and to validatethe reliability of the calculated pKas. At present only EVB studies (17, 64) haveexplored this issue in a more or less complete way. Nevertheless, in some cases[e.g., (45)] the QM/MM energy differences for the two extreme points on the LBHBproton transfer profile are sufficiently large as to be considered fairly conclusiveresults. Thus, the LBHB proposal is not supported at present by any consistentsimulation study.

CONCLUDING REMARKS

Recent years witnessed accelerated progress in modeling of enzymatic reactions.At present the EVB method still provides the most reliable results and the mostcareful analyses of enzyme catalysis. However, QM(MO)/MM methods are start-ing to provide reliable results as well, although these QM/MM approaches do notyet involve calculations of the free energy of the combined solute-solvent systemswith ab initio QM surfaces. Unfortunately, there are still many attempts that do notinclude the enzyme in studies of enzyme catalysis. The fact that such studies arestill presented illustrates that the field has not yet matured. Nevertheless, the gen-eral direction of the field is promising. There is no doubt that the next few yearspromise great progress in the use of reliable QM/MM and related approaches.This will involve a wider realization of the importance of proper configurationalaveraging (51a) in QM(ai)/MM calculations and a better understanding of the im-portance of clearly defined catalytic proposals. It is also certain that there will bea growing realization that consistent simulation studies provide the ultimate toolfor structure-function correlation of enzymes.

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ACKNOWLEDGMENTS

This work was supported by NIH grant GM 24492 and NSF grant MCB-0003872.

The Annual Review of Biophysics and Biomolecular Structureis online athttp://biophys.annualreviews.org

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51. Stanton RV, Per¨akyla M, Bakowies D,Kollman PA. 1998. Combined ab initioand free energy calculations to study reac-tions in enzymes and solution: amide hy-drolysis in trypsin and aqueous solution.J. Am. Chem. Soc.120:3448–57

51a. Strajbl M, Hong G, Warshel A. 2002. Ab-inition QM/MM simulation with propersampling: “first principle” calculations ofthe free energy of the auto-dissociation ofwater in aqueous solution.J. Phys. Chem.B. 106:13333–43

52. Tapia OA, Andrˆes J, Safront VS. 1994.Enzyme catalysis and transition structuresin vacuo. Transition structures for theenolization, carboxylation and oxygena-tion reactions in ribulose-1,5-bisphos-phate carboxylase/oxygenase enzyme(rubisco).J. Chem. Soc. Faraday Trans.90:2365–74

53. Thery V, Rinaldi D, Rivail J-L, Maigret B,Ferenczy GG. 1994. Quantum mechani-cal computations on very large molecu-lar systems: the local self-consistent fieldmethod.J. Comp. Chem.15:269–82

54. Truhlar DG. 2003. Reply to comment onmolecular mechanics for chemical reac-tions.J. Phys. Chem. A106(19):5048–50

55. Tuckerman M, Marx D, Klein ML, Par-rinello M. 1997. On the quantum natureof the shared proton in hydrogen bonds.Science275:817–20

55a. Villa J, Strajbl M, Glennon TM, ShamYY, Chu T, Warshel A. 2000. How im-portant are entropic contributions to en-zyme catalysis?Proc. Natl. Acad. Sci.USA97:11899–904

56. Vill a J, Warshel A. 2001. Energetics anddynamics of enzymatic reactions.J. Phys.Chem. B33:7887–907

57. Vreven T, Morokuma K. 2000. The oniom(our own n-layered integrated molecularorbital + molecular mechanics) methodfor the first singlet excited (s1) state pho-toisomerization path of a retinal proto-nated Schiff base.J. Chem. Phys.113:2969–75

58. Warshel A. 1978. Energetics of enzymecatalysis.Proc. Natl. Acad. Sci. USA75:5250–54

59. Warshel A. 1991.Computer Modeling ofChemical Reactions in Enzymes and So-lutions. New York: Wiley

60. Warshel A. 1998. Electrostatic origin of

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the catalytic power of enzymes and therole of preorganized active sites.J. Biol.Chem.273:27035–38

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64. Warshel A, Papazyan A. 1996. Energyconsiderations show that low-barrier hy-drogen bonds do not offer a catalytic ad-vantage over ordinary hydrogen bonds.Proc. Natl. Acad. Sci. USA93:13665–70

65. Warshel A, Parson WW. 2001. Dynam-ics of biochemical and biophysical reac-tions: insight from computer simluations.Q. Rev. Biophys.34:563–679

66. Warshel A, Villa J,Strajbl M, Florian J.2000. Remarkable rate enhancement oforotidine 5′-monophosphate decarboxy-lase is due to transition state stabilizationrather than ground state destabilization.Biochemistry39:14728–38

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72. Yadav A, Jackson RM, Holbrook JJ,Warshel A. 1991. Role of solvent reorga-nization energies in the catalytic activityof enzymes.J. Am. Chem. Soc.113:4800–5

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25 Apr 2003 17:23 AR AR185-18-COLOR.tex AR185-18-COLOR.SGM LaTeX2e(2002/01/18)P1: GDL

Figure 1 The active-site region of ODCase. The presented structure is based on thecrystal structure of ODCase with a TS analog (PDB entry 1DV7) in which the TSanalog was converted into orotidine 5′-monophosphate (OMP), and the ODCase-OMPcomplex was relaxed by a molecular dynamics calculation.

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P1: FDS

April 10, 2003 17:24 Annual Reviews AR185-FM

Annual Review of Biophysics and Biomolecular StructureVolume 32, 2003

CONTENTS

PROTEIN ANALYSIS BY HYDROGEN EXCHANGE MASS SPECTROMETRY,Andrew N. Hoofnagle, Katheryn A. Resing, and Natalie G. Ahn 1

CATIONS AS HYDROGEN BOND DONORS: A VIEW OF ELECTROSTATICINTERACTIONS IN DNA, Juan A. Subirana and Montserrat Soler-Lopez 27

OPTICAL SINGLE TRANSPORTER RECORDING: TRANSPORT KINETICS INMICROARRAYS OF MEMBRANE PATCHES, Reiner Peters 47

THE ROLE OF DYNAMICS IN ENZYME ACTIVITY, R.M. Daniel, R.V. Dunn,J.L. Finney, and J.C. Smith 69

STRUCTURE AND FUNCTION OF NATURAL KILLER CELL SURFACERECEPTORS, Sergei Radaev and Peter D. Sun 93

NUCLEIC ACID RECOGNITION BY OB-FOLD PROTEINS,Douglas L. Theobald, Rachel M. Mitton-Fry, and Deborah S. Wuttke 115

NEW INSIGHT INTO SITE-SPECIFIC RECOMBINATION FROM FLPRECOMBINASE-DNA STRUCTURES, Yu Chen and Phoebe A. Rice 135

THE POWER AND PROSPECTS OF FLUORESCENCE MICROSCOPIES ANDSPECTROSCOPIES, Xavier Michalet, Achillefs N. Kapanidis, Ted Laurence,Fabien Pinaud, Soeren Doose, Malte Pflughoefft, and Shimon Weiss 161

THE STRUCTURE OF MAMMALIAN CYCLOOXYGENASES,R. Michael Garavito and Anne M. Mulichak 183

VOLUMETRIC PROPERTIES OF PROTEINS, Tigran V. Chalikian 207

THE BINDING OF COFACTORS TO PHOTOSYSTEM I ANALYZED BYSPECTROSCOPIC AND MUTAGENIC METHODS, John H. Golbeck 237

THE STATE OF LIPID RAFTS: FROM MODEL MEMBRANES TO CELLS,Michael Edidin 257

X-RAY CRYSTALLOGRAPHIC ANALYSIS OF LIPID-PROTEININTERACTIONS IN THE BACTERIORHODOPSIN PURPLE MEMBRANE,Jean-Philippe Cartailler and Hartmut Luecke 285

ACETYLCHOLINE BINDING PROTEIN (ACHBP): A SECRETED GLIALPROTEIN THAT PROVIDES A HIGH-RESOLUTION MODEL FOR THEEXTRACELLULAR DOMAIN OF PENTAMERIC LIGAND-GATED IONCHANNELS, Titia K. Sixma and August B. Smit 311

ix

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April 10, 2003 17:24 Annual Reviews AR185-FM

x CONTENTS

MOLECULAR RECOGNITION AND DOCKING ALGORITHMS,Natasja Brooijmans and Irwin D. Kuntz 335

THE CRYSTALLOGRAPHIC MODEL OF RHODOPSIN AND ITS USE INSTUDIES OF OTHER G PROTEIN–COUPLED RECEPTORS,Slawomir Filipek, David C. Teller, Krzysztof Palczewski,and Ronald Stenkamp 375

PROTEOME ANALYSIS BY MASS SPECTROMETRY, P. Lee Fergusonand Richard D. Smith 399

COMPUTER SIMULATIONS OF ENZYME CATALYSIS: METHODS,PROGRESS, AND INSIGHTS, Arieh Warshel 425

STRUCTURE AND FUNCTION OF THE CALCIUM PUMP, David L. Stokesand N. Michael Green 445

LIQUID-LIQUID IMMISCIBILITY IN MEMBRANES, Harden M. McConnelland Marija Vrljic 469

INDEXESSubject Index 493Cumulative Index of Contributing Authors, Volumes 28–32 511Cumulative Index of Chapter Titles, Volumes 28–32 514

ERRATAAn online log of corrections to Annual Review of Biophysicsand Biomolecular Structure chapters may be found athttp://biophys.annualreviews.org/errata.shtml

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computer simulations of enzyme catalysis

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