Computational enzymology

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Computational enzymology Thomas C Bruice* and Kalju Kahn† Recent advances in computational methods and the availability of fast, affordable computers have made the modeling of enzymatic reactions practical. The remaining challenges include achieving the accuracy level at which thermodynamic parameters and kinetic constants for different substrates, mutant enzymes, or in the presence of allosteric effectors can be predicted quantitatively. Addresses Department of Chemistry and Biochemistry, University of California Santa Barbara, Santa Barbara, CA 93106, USA *e-mail: [email protected] † e-mail: [email protected] Current Opinion in Chemical Biology 2000, 4:540–544 1367-5931/00/$ — see front matter © 2000 Elsevier Science Ltd. All rights reserved. Abbreviations BSSE basis set superposition error DFT density functional theory ES enzyme−substrate FE free energy MD molecular dynamics MM molecular mechanical NAC near attack conformer QM quantum mechanical TS transition state

Introduction The mathematical formalism needed for the accurate description of all chemical reactions is, in principle, available by solving the Schrödinger equation. It is well known that exact solutions are possible for only the simplest systems, and practical calculations must rely on approximate methods. In recent years, methods have been developed that allow approximate computational treatment of whole proteins and permit study of reactions as they occur in the enzyme active site. One of the most important developments has been in the area of hybrid methods where the active site is described by quantum mechanics while the surrounding protein and solvent are treated classically. This is a brief review of selected recent developments in computational enzymology. Particular emphasis is placed on methodological aspects in order to draw attention to the inherent capabilities and limitations of available methods. Recent reviews in this field have discussed applications prior to 1998 [1], and summarized work with hybrid quantum mechanical (QM)/molecular mechanical (MM) methods [2•,3•]. We will start by outlining the application of classical simulations to enzymes, followed by quantum treatment of reactions, and conclude with an overview of QM/MM methods.

Classical, force-field-based simulations of enzymes MM force fields allow one to study the dynamics of molecules, but not bond breaking and making processes.

Computational study of the conformations of enzyme and substrate is based preferably on high-resolution X-ray structures of enzyme−substrate (ES) complexes, but enzyme–inhibitor complexes may be used to generate the ES structure. The motions in time are obtained by molecular dynamics (MD) simulations of ES complexes submerged in a water pool. This allows sampling of conformers of the active-site sidechains and substrates that is free from crystal lattice effects. However, because of limited time scales (on the order of 10 ns, currently), only local conformational changes are sampled, whereas large-scale conversions (for example, interconversion between open and closed forms) cannot be modeled. The high-resolution of the structures employed and the quality of modern force fields, such as CHARMM [4] and AMBER [5], however, appear to be sufficient for stable MD sampling of proteins. The dynamics of ES complexes of catechol O-methyltransferase [6], HhaI methyltransferase [7], haloalkane dehalogenase [8], formate dehydrogenase [9] and a hammerhead ribozyme [10•] have been studied. The corollary of these studies is that the bound reactants retain significant freedom of motion in the active site. Those conformers through which the substrate must pass to enter the transition state (TS) are called near attack conformers (NACs) [11,12•]. In cases where the structure of the TS can be estimated, MD simulations can be performed on the enzyme–TS complex. This has been done with formate dehydrogenase [9], and haloalkane dehalogenase [8]. Results suggest that only small changes in the enzyme structure occur upon going from enzyme–NAC to enzyme–TS.

Uncatalyzed reactions studied by quantummechanical calculations Studies of the uncatalyzed equivalent of the enzymatic reaction by QM calculations establish the intrinsic energetics of the reaction and provide a reference for estimating the rate acceleration brought about by the enzyme. Combinations of high-level ab initio calculations with continuum solvation models permit the estimation of reaction profiles and pKa values in aqueous solution [13]. Gas-phase optimizations yield information about TS structures, but these structures are not always relevant because they often are not accommodated by the enzyme active site. For some reactions, such as identity SN2 displacement reactions, the TS structures are implastic and rather insensitive to the environment [14]. For the reactions where charge annihilation or creation occurs, the environment is expected to change both the structure and relative energy of the TS. A good example is the study of a noncatalyzed transmethylation reaction between S-adenosylmethionine and catecholate where an unconstrained gas-phase calculation yielded a strongly interacting reactant complex as the ground state and activation energy of about 20 kcal/mol [15]. Subsequent constrained optimizations, where the

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reactants were fixed in the NAC orientation found in the enzyme, yielded significantly lower activation barriers, indicating that the rate enhancement in this enzyme is largely due to preorganizing the reactants [16–18].

Quantum-mechanical studies using active-site models The role an enzyme plays in catalysis can be approximated by positioning active-site residues about the substrate, using crystallographic or MD-derived coordinates, and subjecting this structure to the quantum chemical calculation. The practical implementation of this approach, however, is complicated for two reasons: the number of residues that are needed for faithful reproduction of the active site milieu is large; and computational cost of accurate QM methods rises steeply with the size of the system. The accurate description of intermolecular (e.g. van der Waals) interactions between nonbonded groups becomes crucial in calculations involving active-site residues, and it has been found that calculations employing electron correlation with large basis sets must be used [19]. Another, largely unresolved, problem is the presence of intermolecular basis set superposition error (BSSE) [20]. The BSSE arises because the basis functions from one molecule contribute to the energy of the other molecule, and vice versa, when the two molecules are close (as in a complex) but not when they are apart. The presence of BSSE leads to an apparent increase in interaction strength between fragments and results in the reduction in intermolecular equilibrium distances [21]. Modeling of enzyme active sites containing metal ions has become possible because of advances in density functional theory (DFT), and many biological applications have been discussed in a recent review [22]. One of the largest systems studied by DFT methods is methane monooxygenase, a diiron enzyme responsible for the conversion of methane to methanol. This conversion involves several spectroscopically observable intermediates, the structures of which had not been well understood. The DFT optimization of the active site models in various redox states provided valuable new information about the possible mechanism of this reaction [23••].

QM/MM optimization of transition states and reaction paths The practical limit for pure QM DFT calculations is currently about 100 atoms, and Møller–Plesset perturbation theory second order (MP2) calculations using localized orbitals methods can handle systems that are almost as large [24•]. In contrast, linear-scaling semiempirical QM methods can handle thousands of atoms [25,26•]. Still, QM calculations are significantly more expensive than classical molecular mechanics calculations, and to combine the speed of the latter with the functionality of the former, several hybrid methods have been developed [2•,27]. In these QM/MM methods, the system is divided into a quantum region and a classical region, separated by a boundary. Semiempirical Hamiltonians have usually been utilized for describing the

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quantum region because of efficiency considerations. In a most common type of application, the reaction paths are minimized in the presence of the enzyme, and activation energies are obtained as energy differences between the ground state and the TS. Frequently, only residues near the active site are optimized while positions of remote atoms are kept fixed. Such studies have been recently performed on a number of enzymes including p-hydroxybenzoate hydroxylase [28•], dihydrofolate reductase [26•,29•], Rubisco [30], lactate dehydrogenase [31,32] and aldose reductase [33]. The major limitation of modern QM/MM calculations is the low reliability of semiempirical methods. The AM1 and PM3 semiempirical methods have been parametrized to reproduce gas-phase ground-state geometries, heats of formation, heats of reactions, dipole moments, and ionization potentials [34,35], and their performance for ground-state properties is satisfactory. For example, the mean absolute deviation of PM3-calculated heats of formation from the experimental values is 7.8 kcal/mol [36], and the reaction energies can be predicted with similar accuracy [37]. However, larger errors occur when proton transfer between carboxylate groups and water is described at the AM1 level [26•]. Semiempirical methods are less reliable in calculating TS structures and energies. Proton transfer activation energies are particularly important in enzyme catalysis, and PM3 overestimates these by as much as 20 kcal/mol when proton donor and acceptor are hydrogen bonded [38]. Basicities are always overestimated and nucleophilicities underestimated, so this may lead to anomalous ion-molecule and transition structures [39]. Also, semiempirical methods systematically overestimate the charge transfer, a process important in biological interactions [40•]. A recommended procedure for performing semiempirical QM/MM calculations includes the comparison of semiempirical results with experimental or high level ab initio data for a nonenzymatic model of the enzymatic reaction. In the case of significant disagreement, reparameterization of the semiempirical model for the specific reaction in question can be performed [41]. There are some methodological problems with the definition of the QM/MM boundary. The original implementation [42] of link-atoms neglected the electrostatic interactions between the link atom and the rest of the protein atoms in the quantum calculation. This neglect leads to unrealistically large partial charges on link atoms and adjacent atoms and introduces significant errors when quantum link atoms are too close to the reactive centers [29•]. Recent comparison of different link-atom treatments has confirmed that using a link atom that does not interact with the MM charges (e.g. as implemented in AM1/CHARMM) can lead to large errors in energy computations [43 ••]. Two alternative schemes, local self-consistent field (LSCF) [44], and generalized hybrid orbital (GHO) [45], have been developed to circumvent this problem (see also Update). During the past few years, ab initio and density functional methods have been implemented in QM/MM schemes [46],

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and first calculations on the enzymes (nickel-iron hydrogenase [47••], citrate synthase [48], and triosephosphate isomerase [49]) have been published (see also Update). Use of QM/MM calculations provides important insights on the role of protein environment on the activation energies and structures of the TS. For example, it was found that dihydrofolate reductase molds the substrate and the cofactor in a conformation that resembles an exo-TS, and not an endo conformation that was energetically favored in the gas phase [29•]. Similarly, the study on the mechanism of Rubisco concluded that the substrate molding into geometries compatible with the TS structures is essential to allow catalytic activity [30]. Another conceptual advance has been the realization that the enzyme active site accommodates many nearly degenerate transition structures, and the experimental TS for the enzymatic reaction represents an average of the properties of these structures [29•].

QM/MM statistical mechanics simulations In contrast to previously considered QM/MM optimization methods, the statistical mechanics simulations, employing either molecular dynamics or Monte Carlo sampling, can provide free energies of reaction and activation. From these quantities, equilibrium and rate constants can be calculated. Such free energy simulations have proven valuable and reliable for modeling chemical reactions in solution. Different approaches have been used to calculate free energies along the reaction path for the enzymatic reaction. Kollman and co-workers have extended the QM–free energy (FE) approach, which was pioneered for organic reactions in solution by Jorgensen et al. [50,51] to enzymatic systems [18]. Recent examples are the studies of amide hydrolysis in trypsin [52] and the SN2 methyl transfer step in catechol O-methyltransferase where the reaction path was first determined in vacuo, and then a series of classical MD simulations was performed along this reaction coordinate [17]. Interestingly, in the QM–FE study of the trypsin reaction [52], the TS stabilization by the enzyme versus water was found to be too small to explain the enzymatic rate enhancement. Instead, catalysis in trypsin appears to have a large contribution from preorganization of the reacting groups. An alternative, more closely coupled scheme has been proposed and illustrated on the study of the initial proton transfer step in triosephosphate isomerase. In this QM/MM method, the minimum energy reaction path in the active site was first determined by QM/MM iterative optimization, followed by five separate molecular dynamics simulations around the frozen QM sub-system ([53]; see also Update). In both approaches, the free energy difference is obtained by adding the difference in quantum mechanical energies along the reaction path to the difference of the free energy of interaction between the QM and MM system. The QM–FE method is potentially more accurate because very high levels of ab initio calculations can be employed to determine the gas-phase reaction profile but the iterative optimization has the advantage of calculating the reaction path in the enzyme environment.

Free energies along the reaction path can also be obtained by calculating the potential of the mean force using the method of umbrella sampling. This approach has been taken with neuraminidase [54••], tyrosine phosphatase [55], and orotidine monophosphate decarboxylase [56•]. Because a very large number of QM/MM energy evaluations is required to obtain converged free energies, such calculations tend to be expensive even with semiempirical Hamiltonians. This bottleneck is eliminated in the empirical valence bond method [57], which uses reaction-specific parametrization to provide smooth interpolation of the potential energy surface for the reaction region. This approach has been recently used to study the reaction mechanisms of subtilisin [58], acetylcholinesterase [59], glyoxalase I [60••], and the GTPase reaction of Ras [61].

Conclusions The combination of powerful new algorithms, especially in the field of hybrid QM/MM methods, and sustained increases in the computer power have made the application of computational methods to enzymes both feasible and useful. The future development will focus on improving the accuracy of hybrid QM/MM methods by solving the issues with QM/MM boundary and replacing the semiempirical model with a more accurate DFT description. In the next decade, the computational methods will be widely used for solving both the fundamental questions in enzymology as well as designing new pharmaceuticals based on the human genome data.

Update Important developments of new methods and algorithms as well as interesting applications of QM/MM methods to new problems have occurred while this review was in preparation. A new approach to deal with boundaries between the QM and MM regions has been proposed based on frozen localized molecular orbitals [62]. A freely available Fortran 90 module library (Dynamo) has been developed for the simulation of molecular systems using hybrid QM/MM potentials [63]. The mechanisms of protein kinase and thymidine phosphorylase have been investigated using semiempirical and ab initio QM/MM optimization techniques [64]. The iterative QM–FE approach developed by Zhang, Liu and Wang [53] has been applied to the enolase reaction [65•].

Acknowledgement This work is funded by a grant from the National Science Foundation (MCB–9727937).

References and recommended reading Papers of particular interest, published within the annual period of review, have been highlighted as:

• of special interest •• of outstanding interest 1.

Friesner RA, Beachy MD: Quantum mechanical calculations on biological systems. Curr Opin Struct Biol 1998, 8:257-262.

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2. •

Amara P, Field MJ: Hybrid potentials for large molecular systems. In Computational Molecular Biology. Edited by Leszczynski J. Amsterdam: Elsevier Science; 1999:1-33. This recent review presents the theory behind the QM/MM approach and briefly discusses the studies of lactate and malate dehydrogenase, acetylcholinesterase, chorismate mutase, carbonic anhydrase, Ni–Fe hydrogenase, tyrosine phosphatase, HIV protease, aspartylglucosaminidase, and triosephosphate isomerase. 3. •

Monard G, Merz KM: Combined quantum mechanical/molecular mechanical methodologies applied to biomolecular systems. Acc Chem Res 1999, 32:904-911. This review provides a nonmathematical approach to the QM/MM methodology and discusses recent work with human carbonic anhydrase and thermolysin. 4.

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Lau EY, Bruice TC: Importance of correlated motions in forming highly reactive near attack conformations in catechol O-methyltransferase. J Am Chem Soc 1998, 120:12387-12394.

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Lau EY, Bruice TC: Active site dynamics of the Hhal methyltransferase: insights from computer simulation. J Mol Biol 1999, 293:9-18.

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Lightstone FC, Zheng YJ, Bruice TC: Molecular dynamics simulations of ground and transition states for the SN2 displacement of Cl– from 1,2-dichloroethane at the active site of Xanthobacter autotrophicus haloalkane dehalogenase. J Am Chem Soc 1998, 120:5611-5621.

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Torres RA, Schiøtt B, Bruice TC: Molecular dynamics simulations of ground and transition states for the hydride transfer from formate to NAD+ in the active site of formate dehydrogenase. J Am Chem Soc 1999, 121:8164-8173.

10. Torres RA, Bruice TC: The mechanism of phosphodiester • hydrolysis: near in-line attack conformations in the hammerhead ribozyme. J Am Chem Soc 2000, 122:781-791. Molecular dynamics simulations yielded conformations of a ribozyme that allow in-line attack of ribose 2′ oxygen on the adjoining phosphodiester linkage. This advances the understanding of the ribozyme mechanism as previously known X-ray structures required an unfeasible adjacent attack. 11. Bruice TC, Lightstone FC: Ground state and transition state contributions to the rates of intramolecular and enzymatic reactions. Acc Chem Res 1999, 32:127-136. 12. Bruice TC, Benkovic SJ: Chemical basis for enzyme catalysis. • Biochemistry 2000, 39:6267-6274. This paper explores the concepts in enzyme catalysis and reviews recent molecular dynamics simulations of enzymatic ground states and transition states. Interestingly, for enzymes where E•TS simulations were performed, no evidence for the TS stabilization was found. 13. Peräkylä M: A model study of the enzyme-catalyzed cytosine methylation using ab initio quantum mechanical and density functional theory calculations: pKa of the cytosine N3 in the intermediates and transition states of the reaction. J Am Chem Soc 1998, 120:12895-12902. 14. Shaik SS, Schlegel HB, Wolfe S: Theoretical Aspects of Physical Organic Chemistry. The SN2 Mechanism. New York: John Wiley & Sons; 1992. 15. Zheng YJ, Bruice TC: A theoretical examination of the factors controlling the catalytic efficiency of a transmethylation enzyme: catechol O-methyltransferase. J Am Chem Soc 1997, 119:8137-8145. 16. Kahn K, Bruice TC: Transition-state and ground-state structures and their interaction with the active-site residues in catechol O-methyltransferase. J Am Chem Soc 2000, 122:46-51. 17.

Kuhn B, Kollman PA: QM–FE and molecular dynamics calculations on catechol O-methyltransferase: free energy of activation in the enzyme and in aqueous solution and regioselectivity of the enzyme-catalyzed reaction. J Am Chem Soc 2000, 122:2586-2596.

18. Lee TS, Massova I, Kuhn B, Kollman PA: QM and QM–FE simulations on reactions of relevance to enzyme catalysis: trypsin, catechol O-methyltransferase, beta-lactamase and pseudouridine synthase. J Chem Soc Perkin Trans 2000:409-415.

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28. Ridder L, Mulholland AJ, Rietjens IMCM, Vervoort J: Combined • quantum mechanical and molecular mechanical reaction pathway calculation for aromatic hydroxylation by p-hydroxybenzoate-3hydroxylase. J Mol Graph Model 1999, 17:163-175. This work reports the reaction coordinate optimization for the hydroxylation step in this enzyme. Reactions with neutral and anionic substrate were considered, and the lowering of the activation barrier upon ionization was observed. Stabilization of the TS was found to be small and the main role of this enzyme appears to be providing the environment where the deprotonated substrate and protonated C4a-hydroperoxyflavin coexist in the right orientation. 29. Castillo R, Andrés J, Moliner V: Catalytic mechanism of dihydrofolate • reductase enzyme. A combined quantum-mechanical/molecularmechanical characterization of transition state structure for the hydride transfer step. J Am Chem Soc 1999, 121:12140-12147. This paper explores the mechanism of hydride transfer reaction in dihydrofolate reductase. The TS was located by grid scanning followed by refinement using auxiliary GRACE software. It was concluded that the enzyme compresses the substrate and cofactor into a conformation close to the TS structure, thus facilitating the hydride transfer. 30. Moliner V, Andrés J, Oliva M, Safont VS, Tapia O: Transition state structure invariance to model system size and calculation levels: a QM/MM study of the carboxylation step catalyzed by Rubisco. Theor Chem Acc 1999, 101:228-233. 31. Moliner V, Turner AJ, Williams IH: Transition-state structural refinement with GRACE and CHARMM: realistic modelling of lactate dehydrogenase using a combined quantum/classical method. Chem Comm 1997:1271-1272. 32. Turner AJ, Moliner V, Williams IH: Transition-state structural refinement with GRACE and CHARMM: flexible QM/MM modelling for lactate dehydrogenase. Phys Chem Chem Phys 1999, 1:1323-1331. 33. Varnai P, Richards WG, Lyne PD: Modelling the catalytic reaction in human aldose reductase. Proteins 1999, 37:218-227.

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58. Bentzien J, Muller RP, Florián J, Warshel A: Hybrid ab initio quantum mechanics molecular mechanics calculations of free energy surfaces for enzymatic reactions: the nucleophilic attack in subtilisin. J Phys Chem B 1998, 102:2293-2301. 59. Fuxreiter M, Warshel A: Origin of the catalytic power of acetylcholinesterase: computer simulation studies. J Am Chem Soc 1998, 120:183-194. 60. Feierberg I, Luzhkov V, Åqvist J: Computer simulation of primary •• kinetic isotope effects in the proposed rate-limiting step of glyoxalase I catalyzed reaction. J Biol Chem 2000, 275:22657-22662. This study employs path integral simulation technique together with the empirical valence bond method, molecular dynamics and free energy perturbation simulations to investigate H/D/T kinetic isotope effects for the proton abstraction step of glyoxalase I. The isotope effects in enzyme, water solution, and gas phase were similar, suggesting that the initial proton transfer is the rate-limiting step. 61. Glennon TM, Villà J, Warshel A: How does GAP catalyze the GTPase reaction of Ras?: a computer simulation study. Biochemistry 2000, 39:9641-9651. 62. Kairys V, Jensen JH: QM/MM boundaries across covalent bonds: a frozen localized molecular orbital-based approach for the effective fragment potential method. J Phys Chem A 2000, 104:6656-6665. 63. Field MJ, Albe M, Bret C, Proust-De Martin F, Thomas A: The Dynamo library for molecular simulations using hybrid quantum mechanical and molecular mechanical potentials. J Comput Chem 2000, 21:1088-1100. 64. Sheppard DW, Burton NA, Hillier IH: Ab initio hybrid quantum mechanical/molecular mechanical studies of the mechanisms of the enzymes protein kinase and thymidine phosphorylase. J Mol Struct (THEOCHEM) 2000, 506:35-44. 65. Liu H, Zhang Y, Yang W: How is the active site of enolase • organized to catalyze two different reaction steps? J Am Chem Soc 2000, 122:6560-6570. In this ab initio QM/MM study, the free energies for the α-proton abstraction step and for the β-hydroxyl group leaving step were determined by combining the QM part of the potential energy and the free energy perturbation calculations. The role of two metal ions and the rest of the enzyme in catalyzing these two steps is discussed.