J. Phys. Chem. B 2001, 105, 7087-7095
7087
An MD/QM Study of the Chorismate Mutase-Catalyzed Claisen Rearrangement Reaction Sharon E. Worthington,*,† Adrian E. Roitberg,‡ and Morris Krauss† Center for AdVanced Research in Biotechnology, 9600 Gudelsky DriVe, RockVille, Maryland 20850, and “Quantum Theory Project” UniVersity of Florida, P.O. Box 118435, GainesVille, Florida 32611-8435 ReceiVed: January 22, 2001
The reaction path for the rearrangement of chorismate to prephenate, catalyzed by chorismate mutase, has been calculated with ab initio quantum chemistry. The calculation of the reaction path is initiated from two catalytically competent conformations of the enzyme that are selected from an X-ray structure and from a snapshot of a molecular dynamics simulation leveraged from the X-ray structure. The quantum calculations employ effective fragment potentials (EFPs) to model the interaction of the protein active site with the substrate in the quantum Hamiltonian. The ability to leverage the X-ray structure into a range of protein conformations abstracted from molecular dynamics simulations to be further analyzed using ab initio methods is demonstrated. Ab initio optimized enzyme-substrate complexes for the oxabicyclic transition state analogue (TSA) and the product, prephenate, compare well with the X-ray structures. We predict the geometry of the active site complex with the reactant, chorismate, and the transition state for the pericyclic reaction. We identify two residues as critical to catalysis, glu78 and tyr108. Binding of the cyclohexadienyl ring’s C4-OH substituent of chorismate to the carboxylate of glu78 activates the breaking ether bond. The tyr108 residue is essential in providing the appropriate orientation of the transition-state fragments within the active site to ensure that prephenate is formed. The calculated electronic activation energies for both enzyme conformations studied are lower than the reaction barrier obtained experimentally. The large kinetic isotope effect (KIE) for O18 in the ether bond agrees qualitatively with the experimental value that suggests a very polarized transition state.
1. Introduction The conversion of chorismate to prephenate is catalyzed by chorismate mutase, an essential enzyme in the Shikimate pathway. The pathway is responsible for the biosynthesis of aromatic amino acids in bacteria, fungi, and plants.12,24,25 The absence of this pathway in mammals has made it a desirable target for designing novel antibiotics, fungicides, and herbicides. Thus, the ability to rationally engineer this pathway is of great importance. Chorismate mutase is inherently interesting since it is a rare example of an enzyme that catalyzes a pericyclic reaction, formally a Claisen rearrangement. This rearrangement also proceeds independent of the enzyme, providing a unique opportunity to directly compare the catalyzed and uncatalyzed reactions. For these reasons, chorismate mutase has been the focus of numerous studies spanning two decades.10,15-19,21-23,29,30,32-34,36,38,42,45 X-ray structures of chorismate mutase are reported for three organisms, but we shall focus on B. subtilis.7 Despite extensive experimental and theoretical work, the enzymatic reaction mechanism and the molecular basis of the catalytic behavior of chorismate mutase remains elusive. Electrostatic stabilization of the transition state by the enzyme and restriction of chorismate to the reactive but higher-energy pseudodiaxial conformer by the enzyme17 have each been proposed as contributing factors for the enzymatic rate enhancement. Both of these possibilities have found experimental support.8,21,20,31,39 X-ray structures7 of the active site support the binding of the pseudodiaxial conformer and also show that ionic hydrogen bonding is likely to the ether oxygen. The * Corresponding author. † Center for Advanced Research in Biotechnology. ‡ “Quantum Theory Project” University of Florida.
enzyme may also distort this pseudodiaxial conformer from its solution geometry by forcing the bonding carbon atoms closer to one another.14,23 An arginine residue binding to the ring carboxylate of chorismate is thought to be an important interaction in this distortion.14 Even though distortion of the reactant by binding in the active site29 has been dismissed, we will show direct theoretical evidence for such distortion. Additionally, mutagenesis studies have identified two residues, arg90 and glu78, to have a substantial effect on the activity of Bacillus subtilis chorismate mutase.21 Mutating either of these residues results in at least a 1000-fold decrease in the enzymatic activity. However, the role that each of these residues plays in the activity of this enzyme at the molecular level is still unclear. The mutagenesis data does not extend to the effect on kcat or Km individually, so the mutation may not directly affect the activation energy. Furthermore, substantial experimental evidence suggests that the rate-limiting step is either reactantbinding1,33 or product release, depending on substrate concentration.15 Hence, the experimental data regarding the activation energy may not be informative for the chemical behavior.22 A more detailed understanding of the molecular basis of catalytic action of chorismate mutase requires knowledge of the interactions of the reactant and transition state with the enzyme active site, which are not available experimentally. The in vacuo transition states for model pericyclic reactions and the chorismate to prephenate rearrangement have been calculated.42 Supporting evidence for this general transition state structure was offered by kinetic isotope effect (KIE) data.39 However, the structural and electronic properties of the transition state are influenced by its surrounding environment. Hence, it is essential to accurately determine the conformational and electronic properties of the protein-substrate complex. Obtaining
10.1021/jp010227w CCC: $20.00 © 2001 American Chemical Society Published on Web 06/19/2001
7088 J. Phys. Chem. B, Vol. 105, No. 29, 2001 this information experimentally for the native reaction path is nearly impossible. However, ab initio quantum methods have enjoyed great success in characterizing transition states and determining reaction paths.43 Application of ab initio methods is essential for accurate prediction of the properties of enzyme active sites, since these sites usually possess many ionic residues that form strong ionic hydrogen bonds with the substrate. Even the first shell of an enzyme active site will possess several hundred atoms, making current all-electron methods intractable. The effective fragment potential (EFP) method11 which models solvation effects may be appropriately extended to describe protein active site effects and has recently been applied to biomolecules.26,27,44,47 Thus, calculating binding and reaction paths at enzyme active sites is now feasible with ab initio methods. Quantum dynamics is not tractable for this system. However, a combined molecular dynamics (MD) simulation and quantum chemical (QM) analysis of enzyme active sites has been developed in order to obtain insight into the electronic basis of catalysis and estimate the energetics along the reaction path. With this methodology (MD/QM), available experimental structures can be leveraged to characterize the catalytically competent active site binding of substrate and transition state complexes of the enzyme. Applying this method, we shall determine substrate binding and the enzymatic reaction path for B. subtilis chorismate mutase. 2. Theoretical Methods Calculating the binding and reaction paths at enzyme active sites has recently been made tractable by the use of the effective fragment potential (EFP) method. In this method, the enzyme active site is divided into two regions, the chemically active region and the protein spectator region. The chemically active region, which is composed of the substrate and the protein residues directly involved in the chemistry, is treated by ab initio all-electron quantum chemistry. The protein environment or spectator region is described by effective fragments potentials (EFP) that represent the electrostatic, polarization, charge transfer, and repulsive interactions for the complex in the Hamiltonian. Movement in the spectator region is not possible for the amino acid residues in the current implementation of the EFP method. Thus, the initial structure of this region must be carefully chosen. We choose the initial protein active site conformation from either an appropriate X-ray structure or a snapshot from a MD simulation initiated from an experimental structure. A catalytically competent conformation (the initial protein active site conformation) is defined here as the protein environment suitable for reaction along a given reaction path from the stationary point of reactant/protein complex to the transition-state/protein complex. We suggest that substrate binding and rearrangement of the protein/substrate complex into a catalytically competent conformation occurs on a much longer time scale than that of the chemical reaction, which is on the order of picoseconds. Thus, for the reaction path calculations, it is reasonable to assume a fixed “protein” structure. This fixed protein is assumed to provide the average field within which the reaction proceeds. Dynamical motions of the protein during the reaction are assumed not to affect this field substantially. By solvating ionic residues or altering the ionicity of binding residues, we can obtain different catalytically competent conformations of hydrogen-bonded active sites from both the X-ray data and the MD simulations. A range of catalytically competent conformations is assumed to contribute to the overall catalytic reaction. We have no means of appropriately weighting the catalytic properties of these conformations, but analysis of these
Worthington et al. properties and electronic behavior along the reaction path provides insight into the molecular basis for the enzymatic catalysis. The starting structures for these quantum optimizations were obtained from the experimentally determined crystal structure and molecular dynamics simulations, hence our designation for the method as MD/QM. The assumption that a classical determination of a reactive protein environment is obtained prior to the quantum calculation of the reaction path is analogous to other recent approaches.4,46 However, it differs from these in the assumption that a single protein environment is suitable for the reaction path involving heavy-atom motions. We believe that an enzyme can adopt several different catalytically competent conformations that will contribute to the overall effectiveness and energetics of the enzyme. In this present work, we establish the methodology and provide new insight into the enzyme catalysis using two different conformations. 3. Computational Details The molecular dynamics runs were performed using the program Amber, version 5.0.6 The parameters were taken from the standard amber database, with special parameters generated for the chorismate molecule. For this, a 6-31G** Hartree-Fock in vacuo calculation was done, with the point charges assigned to the classical atoms based on a global fit to the electrostatic potential.2 The overall charge of the molecule was -2. The parameters are available from the authors upon request. Chorismate mutase was built using a mixed template from the original Chook structure7 (ABC trimer), with the last 10 residues in the C-terminal taken from a recent, complete structure for B. subtilis chorismate mutase (1DBF).28 The simulated complex has chorismate inside the active site, modeled after the original TSA molecule. The enzyme-substrate trimer was immersed in a box of TIP3P waters. The wetting was set up such that at least 10 Å was available between the surface of the molecule and the box sides. At least 2 Å was left between the surface of the molecule and the closest oxygen atom of any water molecule to prevent unfavorable overlaps. A total of 12432 water molecules are added this way. The overall CM + chorismate charge is -15 (-5 for each monomer), so 15 sodium counterions were added to the system to ensure charge neutrality. The system was heated from 0 to 300 K over 100 ps, using periodic boundary conditions, a constant pressure algorithm (with a pressure relaxation time of 0.2 ps), and a particle mesh Ewald (PME) implementation of the Ewald sum for long-range electrostatics. A dielectric constant of one was used throughout. A spherical cutoff of 8 Å was used for the Lennard Jones nonbonded potentials and the direct part of the Ewald sum calculation. The time step was 2 fs. The nonbonded list was updated every 20 fs. The bonds that involved a hydrogen atom were constrained to their equilibrium lengths by using the SHAKE method. After the heating period was completed, another 100 ps of equilibration was performed with the same set of parameters. During the equilibration period, the pressure stabilized around 1 atm and the temperature around 300 K. The final simulation box stabilized around 69.2 × 74.5 × 85.6 Å3, with a density close to 0.98 g/cm3. Simulations of various lengths were run this way, totaling over 3 ns. The simulations with solvated chorismate were done under essentially the same conditions, with a total of 2004 atoms, consisting of a single chorismate molecule and 660 TIP3P waters. The periodic box was 27.7 × 28.6 × 26.3 Å3. The effective fragment potential (EFP) method is implemented in the GAMESS program suite and is described in detail
Chorismate Mutase-Catalyzed Claisen Rearrangement elsewhere.11 Briefly, EFPs represent the exchange repulsion, electrostatic potential, polarization, and constrained charge transfer from the spectator region in the quantum Hamiltonian of the total complex. An accurate EFP for water is included in the GAMESS code, but all the components of the EFPs for protein residues are not readily available. The parameters for the electrostatic and polarization EFP are generated using GAMESS for the residues in the protein environment. We have determined the parameters for the repulsive EFPs to describe the amino acid residues in the active site of chorismate mutase. A detailed account of these EFPs is found elsewhere.47 Using these EFPs, we have obtained optimized structures of enzyme-substrate complexes at the Hartree-Fock (HF) level of theory. All restricted Hartree-Fock (RHF) calculations are done with effective core potentials and their concomitant basis sets. In this study, all calculations were done with the 4-31G SBK basis set.40,41 The structures for the reactant, transition state analogue, and product embedded in the “protein” or EFP environment are optimized at the HF/SBK level, followed by second-order Moller-Plesset(MP2) corrections to the energies. Transition states were located both in vacuo and in the protein environment at the HF level of theory, and their energies were further characterized at the MP2 level in the EFP field for the HF structure. An intrinsic reaction coordinate (IRC) calculation was followed for the catalyzed and uncatalyzed rearrangements at the HF/SBK level of theory. Kinetic isotope effects are also reported here at the HF/SBK level for the substrate embedded in the EFP active site. The calculated KIE reported in this work have been accomplished by numerical methods for determining the vibrational frequencies. 4. Active Site Model Chorismate mutase of B. subtilis crystallizes as a tetramer of trimers and thus yields 12 independent active sites, which are located at the interfaces of adjacent monomers and all are different in the X-ray structure. The X-ray structure for the oxabicyclic transition-state analogue (TSA) bound complex shows the inhibitor bound in all the 12 active sites, while the prephenate bound structure has nine active sites occupied.7 The experimental binding of the endo-oxabicyclic transition-state analogue (TSA) is found in the protein data bank (PDB) as 2CHT.7 To our surprise, we discovered that the first active site we examined from the PDB3 coordinates for 2CHT did not agree qualitatively with the site depicted in the Chook et al. report.7 The site described for CM from B. subtilis was shown to lack the arginine residues (arg63 and arg116) that hydrogen bond to the carboxylate on the cyclohexadienyl ring. The apparent lack of this binding has often been noted.33 30 It has been suggested that CM from B. subtilis differed essentially from the other chorismate mutases, whose structures have been determined from Escherichia coli and yeast, which possess arginine residues for binding the cyclohexadienyl carboxylate group. It should also be noted that a recent B. subtilis chorismate mutase structure, which crystallizes as a homotrimer, shows arg63 binding to the carboxylate in all sites.28 One or both of the arginines, arg63 and arg116, are included in the reactive models of the active site conformation chosen for this work. All calculations of substrate binding and reactive behavior are initiated from the crystal structure of the active site situated at the A/B interface with bound TSA. The model active site is comprised of the ionic and polar amino acid residues: lys60, arg63, and cys75 from monomer A and arg7, glu78, met79, arg90, and tyr108 from monomer B. The active site model also included the nonpolar residue, phe57.
J. Phys. Chem. B, Vol. 105, No. 29, 2001 7089 The choice of these residues for the active site is based on the examination of the active sites of several different chorismate mutases, the depicted active site of Chook et al.7 for B. subtilis, and the 2CHT X-ray structure at the A/B interface. These residues comprise most of the first protein shell around the substrate. For the ab initio calculations, the active (all-electron) region is the substrate and glu78 constrained at the R carbon, while the remaining residues are modeled with EFPs. The molecular dynamics simulations with chorismate in the active site were initiated using 2CHT A/B/C trimer unit. The reactive conformer (quantum motif) from the MD simulation, which is further processed by ab initio methods, was selected by analyzing hydrogen bond arrangements at the A/B site. Two additional residues from monomer B, arg116, and asp118 are included in the quantum active site for the MD active site motif. Although no waters are found in the active site from the X-ray structure, the MD motif has nine water molecules. The MD catalytic conformation was chosen to examine the effect of the waters found in the active site on the energetics of the reaction path. Analysis of the MD results shows the active site of CM exhibiting large fluctuations in a subnanosecond time scale around an average structure. Hydrogen bonding patterns can change during the dynamics. Among the hydrogen bonds that do not change significantly (populations higher than 0.95), we find arg90-O7, arg7-O13(14), tyr108-O13(14), and glu78H(C4-OH). Arginine 116 corresponds to a special case, where two of the three active sites had a stable hydrogen bond between it and O13 in chorismate, while for the third active site, this hydrogen bond is completely absent. Arginine 63 made an H-bond with the free C10 carboxylate for the complete simulation time in one active site, only half the time in the second site, and never with chorismate in the third site. Cysteine 75 made a backbone hydrogen bond to the C4-OH oxygen of chorismate most of the time, while its S-H group made H-bonds to this oxygen with a 50% population. This shows that the structure of the active site should be considered as a dynamically changing entity, with no possibility of a complete description based on a single, rigid snapshot. In this article, we show that different numerical answers can be obtained if one chooses widely different “protein” structures to initiate the quantum reaction path calculations. The first conformation was derived from the X-ray structure as discussed above. For the second motif, we chose to use a conformation of the active site that differed substantially in its hydrogen bond pattern from the first motif used. For this purpose, we monitored the water around three chorismate molecules, keeping track of the first and second shells (as extracted from the radial distribution functions). In this manner, we found a water molecule diffusing deep into the active site and stationing itself close to the carboxylate group of glu78, where it stood for almost half a nanosecond. It is worth commenting that the number of waters (and standard deviation) in the first shell around a single chorismate molecule in the enzyme was found to be 7.6 (1.2) and 15.3 (2.1) in the second shell. This represents a large number of waters that are not seen in the X-ray structure because their residence time and position is not long enough to be seen in the seconds time scale. Nevertheless these waters can alter structure, chemistry, and dynamics in shorter (and relevant for the reaction) time scales. There are a number of different arrangements in the hydrogenbond patterns around the active site in a time scale over 100 ps. These different motifs provide different templates from which the quantum reaction can occur. However, one can look
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TABLE 1: Comparison of X-Ray and Optimized TSA Complex Structure distance (Å)
A/B X-ray
X-ray (Chook et al.)
EFP-X-ray CM
EFP-MD CM
Y108-O14 R7-O13 R90-O7 E78-O12 C75(N)-O12 C75(S)-O12
2.73 2.97 3.68 3.80 3.39 3.26
2.90 2.95 2.92 2.91 2.92 3.07
2.79 2.91 3.24 2.73 3.64 3.53
3.09 2.95 3.10 2.77 2.97 3.88
TABLE 2: Comparison of X-Ray and Optimized Prephenate Complex Structure distance (Å)
A/B X-ray
X-ray (Chook et al.)
EFP-X-ray CM
EFP-MD CM
Y108-O14 R7-O13 R90-O7 E78-O12 C75(N)-O12 C75(S)-O12
2.86 2.82 3.08 2.89 2.87 3.51
3.04 2.89 3.11 2.90 2.89 3.63
2.77 2.93 3.79 2.73 3.38 3.49
2.89 2.87 4.32 2.87 3.01 3.82
SCHEME 1: Chorismate with Relevant Numbering.
at the shorter time fluctuations that will happen within a single basin of attraction. For instance, the H-bond distance between glu78 and the H(C4-OH) of chorismate has an average of 1.91 Å, with a standard deviation of 0.31 Å. This is a very large fluctuation in the picosecond time scale. We start the quantum calculations by locating a stationary point corresponding to the bound substrate in the active site. In this way, all structures within the aforementioned fluctuation range will most likely optimize to the same stationary structure upon local minimization of the dynamic frame using quantum mechanics. We observe differences in the fine structure of the two motifs chosen for further analysis by quantum methods. These differences result from the addition of the water molecules in the MD motif. Most of the water molecules insert and replace the hydrogen bonding between the carboxylate oxygens of the cyclohexandienyl ring and arg63. The waters are able to insert into these hydrogen bonds and effectively replace them without changing the overall stability of the complex. A water molecule in the MD motif is hydrogen bonding with the glu78 residue. This hydrogen bond screens and reduces the strength of the hydrogen bond between glu78 and the substrate. Determination of the catalytic role of glu78 should be possible by examining the differences in these motifs. 5. Results and Discussion a. Substrate BindingsPrephenate and TSA. The binding of the TSA and the product, prephenate, in the active site are considered first, since X-ray structures are available for comparison. Selected structural parameters of these complexes bound in the X-ray active site are presented in Tables 1 and 2 respectively, using the chorismate numbering in Scheme 1. The optimized structures of TSA complex agree well with the X-ray structure of the A/B interface and with the average X-ray structure reported by Chook et al.7 Most distances listed in Table 1 for the optimized structures are within the reported ‘upper limit’ error of 0.25 Å for the atomic positions in the X-ray structure, which was refined to 2.2 Å. It should be noted that
for the A/B site, the experimental arg90-oxygen ether distance of 3.68 Å is substantially larger than the value of 2.92 Å given in the paper describing this enzyme. The observed short distance is the basis for the many observations that arg90 serves to stabilize the developing charge on oxygen in the separating moieties in the transition state. However, our quantum EFP optimized structures for the TSA in both the X-ray and MD active site are closer to 2.92 Å. The optimized structures that result from using the MD reactive conformer are in good agreement with the others although the fine structure of hydrogen bonding and residue side-chain positions may be different. Overall, the TSA binding complex shows excellent agreement between the computationally optimized and experimental structures, given the error reported for the experimental structure of 0.25 Å in atomic positions. Using the two protein active site motifs (X-ray and MD) initiated from 2CHT, we optimize the product in these two sites. The X-ray structure of prephenate bound in the active site of B. subtilis chorismate mutase is reported in the PDB as 1COM.7 As seen in Table 2, the similarities between the optimized and X-ray structures of the prephenate binding complex are reasonable, and structural agreement can be considered very good for all interactions but the arg90-ether oxygen interaction when we consider the accuracy reported for the experimental atomic position. The reported “upper limit” error in atomic position for the 2.2 Å structure of the prephenate complex is 0.23 Å. With the exception of the arg90-ether oxygen distance, the calculated structures are within the error of the experimental structure. For the calculated structures, the arg90-ether oxygen distance is quite large, reflecting the rotation of arg90 toward the glutamate (glu78) and/or the relative binding of prephenate to arg63 and arg116. The molecular dynamics motif has a different spatial orientation for arg90 but still possesses similar hydrogen bonding. The reaction path with the TSA protein environment is used here to determine the product binding. The protein backbones are similar in the crystal structures for the TSA and prephenate X-ray structures. In Figure 2, the A/B interfacial active site of 2CHT is compared with the A/B interfacial active site of 1COM. Slight variation in the position of the arg63 side chain is observed, but the other residues align quite well. The changes are considered minor since the reported temperature factors suggest that this region is quite flexible. The RMSD value for these two structures of 0.23 Å further indicates only slight differences in the spatial conformation of these two active sites. The RMSD value was obtained by aligning 71 heavy atoms in the active site with B factors less than 25.00 Å2. Minor changes in the side chain position of the arg90 residue for the two active sites is in accord with the differences observed for the arg90-ether oxygen interaction between the calculated and observed structures. In addition, it is possible that relaxation of the protein/prephenate complex may occur prior to product release since this is a rate-limiting step for high substrate concentration. This relaxation may account for the structural discrepancies found for this interaction. Hydrogen bond distances and presumably their apparent strengths could be probed by spectroscopic means. The calculated distance from arg90 to the ether oxygen is not in very good agreement with the crystal structure. However, there is evidence that the binding of prephenate in the active site does not perturb the carbonyl bond,16 suggesting that a strong hydrogen bond to the carbonyl oxygen is not dominant. It should be noted that both the infrared (IR) spectrum16 and the calculated structures of prephenate were initiated from the reaction path conformation of the enzyme. The IR spectrum of prephenate is
Chorismate Mutase-Catalyzed Claisen Rearrangement
J. Phys. Chem. B, Vol. 105, No. 29, 2001 7091
Figure 2. Superposition of the two active sites at the A/B interface from the experimental X-ray data for the TSA bound complex (red) and the prephenate bound complex (blue).
TABLE 3: Distances (Å) for the Chorismate Complex bond C3-O7 C1-C9 C4-O12 O12-H R90-O7 E78-H(O12) Y108-O14
Figure 1. (a) Diagram of the active site of chorismate mutase with the transition-state analogue bound. This is the model active site used to define the protein environment or catalytically competent conformation for the X-ray motif. (b) Diagram of the active site of chorismate mutase with chorismate bound. This model active site is used to define the protein environment or catalytically competent conformation for the MD motif.
obtained after chorismate reacts in the enzyme. However, for the X-ray structure, prephenate is directly bound into the active site not made in the enzyme. Thus, the relaxation of the protein/ prephenate complex prior to product release may account for the differences found in the arg90-ether oxygen distance. Again, the optimized structures were initiated from the X-ray structure of the TSA complex, and thus, the agreement of these structures with the X-ray structures for the prephenate complex shows the versatility of the EFP methodology. b. Substrate BindingsChorismate and Transition State. Direct examination of the chorismate-binding complex is the first step in understanding the enzyme’s role in catalysis. Sincethe ability to observe the binding of the native substrate in the native enzyme active site is experimentally highly improbable to impossible, chorismate bound in the active site has not been experimentally determined. Computational methods are the only avenue for studying such a native protein/substrate complex. Several Monte Carlo and QM/MM studies5,9,32 have examined the chorismate mutase-catalyzed rearrangement with
in vacuo in vacuo w/acetate EFP-X-ray CM EFP-MD CM 1.453 3.836 1.474 0.965
1.483 3.672 1.452 0.980 2.028
1.505 3.644 1.437 0.983 2.601 1.864 1.956
1.491 3.588 1.441 0.980 2.040 2.181 1.929
reasonable success. However, determination of accurate electronic properties of the bound complex can only be accomplished with ab initio quantum chemical methods. The previous studies5,9,32 have embedded substrate structures that were optimized in vacuo and do not allow further optimization to account for the electronic effects of the protein environment. With the EFP method, we have fully optimized chorismate influenced by the surrounding protein environment. One notes several differences between the in vacuo optimized structure and the optimized protein-substrate complex. The first is the change in the bond distance of the ether bond that is ultimately cleaved in the reaction. Upon binding of chorismate in the enzyme active site, the ether bond distance is lengthened by 0.05 Å, corresponding to a 20% decrease in bond order (Table 3). The change in the ether bond distance is a result of the inductive effect of the hydrogen-bonding interaction between chorismate and the glu78 residue. The in vacuo optimization of the acetate-chorismate complex finds that the C-O bond is lengthened to 1.48 Å, illustrating the importance of this hydrogen-bonding interaction but also showing that the ionic interaction from the overall active site also has a role in activating the substrate. These changes in heavy atom distances indicate that the enzyme affects the electronic structure of chorismate upon binding. This is a new and significant result since previously it was thought that the enzyme merely engaged in selective binding of the reactive pseudodiaxial conformation of chorismate. Besides breaking the ether bond, the Claisen rearrangement requires the making of a C1-C9 bond to form prephenate. An earlier suggestion by Gorisch14 that the C-C distance is reduced in the active site by the concurrent binding of both carboxylates is borne out by this calculation. This suggestion was initially dismissed since the B. subtilis chorismate mutase was believed to lack this concurrent binding; however, as previously discussed, the B. subtilis enzyme does possess this important binding. This decrease in the distance between the two carbons that ultimately form a bond in the product is seen in the binding
7092 J. Phys. Chem. B, Vol. 105, No. 29, 2001
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Figure 3. Graph of the C1-C9 bond distance throughout the solution and enzyme molecular dynamics simulations.
TABLE 4: Distances (Å) for Transition State Complex bond
in vacuo
EFP-X-ray CM
EFP-MD CM
C3-O7 C1-C9 C4-O12 O(C4)-H R90-O7 E78-H(O12) Y108-O14
2.099 2.451 1.481 0.965
2.351 2.552 1.430 0.993 2.526 1.696 1.950
2.499 2.629 1.436 0.973 2.074 2.290 2.069
of chorismate for both optimized conformations (Table 3). In the MD simulations, we monitored the C1-C9 distance versus time for chorismate free in solution (constrained to the pseudodiaxial conformation) and for chorismate in the active site of CM. Figure 3 presents histograms for this distance in the solution and in the active site expressed as the percentage of time the systems sampled that particular distance. The solution range of attack distance is very large, with an average (standard deviation) value of 3.75 (0.23) Å. In turn, the distance in the active site has a value of 3.23 (0.15) Å. The range of C-C distances in the active site found in the MD simulation is more restricted and shorter than the value found in solution, as seen in Figure 3. These changes in the electronic structure of chorismate when it complexes with the enzyme indicate that the enzyme is preactivating the reactant upon binding. This preactivation by the enzyme is a new catalytic role assigned to the enzyme on the basis of this work. For the first time, the optimized structure of the transition state (TS) embedded in the protein is reported in Table 4 and Figure 4. This is significantly different from previous computational studies5,9,32 in which the in vacuo transition state structure is embedded in the protein environment without further optimization to account for the environmental effects of the protein. We determine that the transition state, which is a true first-order saddle point embedded in the protein active site, is an asymmetric chairlike structure in agreement with previous work.39 The transition state for the native enzyme shows that the ionic active site has a substantial influence. The two fragments of the transition state are more separated in the enzyme than in vacuo, reflecting the ability of the ionic field of the enzyme active site to support a very polarized TS. This conclusion is in accord with the experimental observation that a more dissociative transition state exists in the enzyme than in solution.18 Even though, most of these enzymatic interactions are stabilizing for the dianionic reactant, chorismate, the additional separated charges residing on the two separated
Figure 4. (a) Optimized structure of the transition state for the Claisen rearrangement in the X-ray motif. (b) Optimized structure of the transition state for the Claisen rearrangement in the MD motif.
fragments of the transition state are preferentially stabilized by the ionic nature of the active site. The optimized chorismate and transition state structures demonstrate that this new method is a powerful tool that can leverage one crystal structure with an appropriate bound substrate into another substrate bound complex that may be of interest for protein engineering applications. c. Enzyme Mechanism. We have identified three residues, glu78, tyr108, and arg90, as important for the activity of this enzyme. The interactions of these three residues are necessary for the reaction to initiate and proceed to prephenate. The importance of glu78 and arg90 has been substantiated by mutagenesis studies.8 However, we present for the first time the role each of these residues plays in the enzyme activity. This is the first report to identify tyr108 as an essential residue for the activity of chorismate mutase.
Chorismate Mutase-Catalyzed Claisen Rearrangement The residue, glu78, is very critical to the enzyme catalysis. The important role of glu78 is supported by mutagenesis studies that find mutating glu78 to gln78 decreases the activity by at least a 1000-fold.8 Furthermore, the deoxy chorismate substrate shows decreased activity by several orders of magnitude.17,35 Even a slight change in the strength of the glu78-H(C4OH) hydrogen bonding interactions has a large effect on the calculated electronic activation energy. The hydrogen bond between glu78 and the substrate is approximately 0.3 and 0.6 Å longer in the MD motif than in the X-ray motif for optimized structures of chorismate and the transition state, respectively. This change in hydrogen bonding has a significant effect on the activation energies calculated for these two motifs, 3.9 (16.5) and 11.3 (47.3) kcal/mol (kJ/mol) for the X-ray and MD motifs, respectively. The snapshot from the molecular dynamics represents an extreme case in the variation of the hydrogen bonding interaction between glu78 and H (C4OH). As mentioned earlier, the average distance in the simulations for this interaction is 1.91 ( 0.31 Å. The MD motif is representative of a protein environment in which this interaction is 1 standard deviation from the average. In the ionic active site, the breaking C-O bond is elongated upon binding due to the inductive effect of the strong hydrogen bond formed between the C4-OH and glu78. The increased distance corresponds to a 20% decrease in bond order and therefore the C-O bond can be considered preactivated upon binding to the enzyme. This preactivation of the C-O bond or de-stabilization of the reactant is negligible in solution since the polar hydrogen bond is not strong enough to produce the lengthening of this bond. We have performed several calculations to further substantiate this preactivation is a result of the hydrogen bond formed between chorismate and glu78 upon binding. For the first calculation, we lengthened the O-H bond distance from the optimized in vacuo value to determine the effect on the ether bond. We observed no significant change in the ether bond distance with only a change in the hydroxyl distance from the in vacuo chorismate electronic structure. In the second calculation, we optimized chorismate with an acetate anion to determine the effect of the strong ionic hydrogen bond on preactivation of the ether bond in chorismate. The ether bond distance is elongated by 0.03 Å, corresponding to greater than 50% of the difference in the ether bond distance for the solution reactant and the embedded reactant (Table 3). Therefore, the hydrogen bond formed between the glu78 and chorismate upon binding is an essential catalytic interaction in the enzyme. This preactivation of the breaking bond by ionic residue is a key difference in the mechanism between the solution and enzyme reaction. This preactivation is a significantly different catalytic behavior assigned to the enzyme and should not be viewed as a different way of expressing electrostatic stabilization. This change in electronic structure has not been observed by other methods and demonstrates the effectiveness of the MD/QM-EFP methodology in elucidating how the enzyme catalyzes this reaction. The second interaction that we observe to play a subtle but significant role is the tyr108-carboxylate oxygen interaction. We suggest that this interaction is essential for the formation of the prephenate product, as it helps to orient the separated cyclohexadienyl and pyruval moieties along the reaction path. This residue’s hydrogen bonding interaction with the pyruval fragment of the transition state helps position the fragment in the appropriate orientation in the very ionic active site to produce the C-C bond formation of prephenate. Slight changes in the orientation of this fragment in the active site may lead to other possible products since several other carbons may be activated
J. Phys. Chem. B, Vol. 105, No. 29, 2001 7093 TABLE 5: IRC Distances (Å) point
O-H embedded
C-O embedded
O-H in vacuo
C-O in vacuo
chorismate 5 10 15 20 25 30 35 transition state 45 50 55 60 65 70 75 80
0.983 0.991 0.991 0.995 0.996 0.995 0.994 0.993 0.993 0.993 0.993 0.993 0.990 0.989 0.988 0.988 0.988
1.505 1.531 1.641 1.881 2.111 2.256 2.309 2.326 2.351 2.375 2.389 2.431 2.540 2.626 2.719 2.857 3.000
0.965 0.964 0.964 0.964 0.964 0.964 0.964 0.964 0.965 0.965 0.965 0.965 0.964 0.964 0.964 0.964 0.964
1.453 1.474 1.477 1.480 1.485 1.495 1.568 1.808 2.099 2.285 2.423 2.557 2.762 2.990 3.211 3.395 3.523
TABLE 6: Mulliken Charges in vacuo in vacuo X-ray X-ray MD atom chorismate TS chorismate TS chorismate C1 C2 C3 C4 C5 C6 O7 C8 C9 O12 O12H
-0.27 -0.11 0.28 0.01 -0.22 -0.05 -0.43 0.09 -0.24 -0.55 0.27
-0.25 0.00 0.17 0.00 -0.13 -0.02 -0.40 -0.04 -0.17 -0.54 0.28
-0.26 -0.01 0.18 0.14 -0.28 0.24 -0.48 0.09 -0.17 -0.54 0.38
-0.38 0.14 -0.02 0.12 -0.25 0.23 -0.46 0.07 -0.22 -0.53 0.38
-0.27 -0.09 0.11 0.23 -0.31 0.29 -0.50 0.05 -0.13 -0.59 0.40
MD TS -0.45 0.14 -0.27 0.16 -0.30 0.22 -0.52 0.09 -0.37 -0.52 0.37
and susceptible to attack to form other carbon-carbon bonds. For example, it is possible with a slight change in geometric parameters induced by a mutation of tyr108 to produce a bonding interaction that leads to a prephenate tautomer. This will be shown in a future report. This is the first report to indicate that the tyr108 residue is important for the production of prephenate. A previous mutagenesis study does not identify tyr108 as important to the activity of chorismate mutase.8 It should be noted that this study follows the disappearance of the reactant, chorismate, but does not determine that prephenate is the product formed. Therefore, our findings are not in disagreement with the mutagenesis study. d. Electrostatic stabilization and Arg90. The interaction between arg90 residue and the ether oxygen of the substrate has been identified as an important catalytic interaction by a number of studies.8,21 It has been proposed that the arg90 stabilizes the large negative charge on the oxygen atom in the transition state. This role of arg90 is based on the observed short distance for the arg90-ether oxygen interaction. However, it is observed in this work that the charge previously associated with the separating oxygen atom is delocalized throughout the pyruval fragment as seen in Table 6, and the difference in the partial charge of this oxygen atom in the reactant and transition state is not large (0.02). The stabilization of this increasing negative charge of the oxygen in the transition state by an interaction with arg90 may play a small role but is not enough for significant rate acceleration. Comparison of the relative binding behavior to arginine 90 along the reaction path must be done to determine whether there is a differential improvement in binding of the ether oxygen with the development of the transition state. We have examined the possible differential preference of this interaction for the reactant, chorismate, and the transition state, which are not observed experimentally. As
7094 J. Phys. Chem. B, Vol. 105, No. 29, 2001 demonstrated by the partial charge on the ether oxygen, -0.48, -0.50, -0.46, and -0.52, for the X-ray and MD chorismates and the X-ray and MD transition states, respectively, the binding to the TS is not significantly stronger than the binding to the reactant. Further, it should be noted that these results are not affected by including the arg90 residue in the all-electron complex. For this calculation, the CR of the backbone is frozen, and only a slight change in the arg90-ether oxygen hydrogen bond distance (0.06 Å) is observed compared to the fixed fragment calculation. The experimental studies on mutating arg90 observe only the effect on the activity and do not determine the effect on kcat so that there is no contradiction between experiment and theory. e. Activation Energy and Intrinsic Reaction Coordinate. The correlation-corrected activation energies (MP2) support the concept that the chemical step is not the rate-limiting step of the enzyme, since the calculated activation energies for the reaction of 3.9 (16.5) and 11.3 (47.3) kcal/mol (kJ/mol) for the X-ray and MD motifs, respectively, are less than the experimentally observed barrier of 12 kcal/mol. For the MP2 energy surface, the low activation energy suggests that the free energy of activation can include substantial vibrational entropy. This is observed experimentally in a catalytic antibody for a comparable rearrangement where there is evidence the chemical step is rate limiting.13 The results of the MD motif coupled with the other optimized structures indicate flexibility in the reactive conformation in enzymes, which may assist in the effectiveness of the enzyme to catalyze the reaction. Examination of the difference in the fine structures of hydrogen bonding and residue positions for the X-ray motif and the MD motif demonstrates that slight changes in the reactive conformation of the protein does not change the chemistry. We suggest that the enzyme may not be limited to one effective reactive conformation and that slight differences in hydrogen bonding or the geometry of a residue do not significantly alter the enzyme’s chemical effectiveness as long as key interactions are conserved. We followed the intrinsic reaction coordinate (IRC) pathway from the transition state to the reactant and product to verify that the identified transition state was indeed the appropriate one. The IRC proceeds smoothly for the in vacuo reaction, indicating no additional reactive intermediates or transition state occur for this reaction. The embedded IRC also proceeds smoothly and confirms the presumption that the catalyzed reaction is concerted and asymmetric with bond cleavage proceeding bond formation. Figure 5 graphs the C-O and O-H distances along the reaction paths for the in vacuo and embedded reactions. The O-H distances for the in vacuo calculation do not change along the IRC. However, the same bond distances change significantly along the embedded IRC. For the embedded reaction, the breaking of the ether bond correlates well with the lengthening of the O-H bond, as seen in Figure 5 and Table 5. The C-O bond begins to lengthen further from the reactant binding geometry at the same point along the reaction coordinate as the O-H distance for the embedded reaction. This effect is not observed for the in vacuo reaction. This difference in the two reaction paths supports the important catalytic role of glu78 in the enzymatic reaction. It is also interesting to note that the breaking of the ether bond is earlier for the embedded reaction than that for the in vacuo reaction. These differences in the reaction paths, as illustrated by monitoring the bond distances along the pathway, suggest that the mechanisms for the solution and enzyme reactions are subtly yet significantly different. This finding differs from previous studies, which propose that the solution and enzyme mechanisms are essentially the same.
Worthington et al.
Figure 5. Graphs of the C-O and O-H bond distances along the reaction pathway of the embedded and in vacuo reaction paths.
f. Kinetic Isotope Effects and Absorption Spectrum. The kinetic isotope effect for the O16/O18 replacement of the ether oxygen from this work (1.071) is in qualitative agreement with the experimental value. This KIE supports the evidence that the transition state of the enzyme reaction is more polar than the in vacuo or solution reaction. The qualitative agreement between the predicted KIE for the ether oxygen in this work with the experimental KIE reported by Gustin et al.18 supports the MD/QM-EFP methodology as an effective and accurate method for studying enzyme systems. The absorption spectrum of prephenate in solution and in the enzyme active site has been calculated. The results of the solution spectrum are reported elsewhere in much greater detail.37 For this work, it is sufficient to say that the solution absorption spectrum calculated using a combined MD/QM approach agrees quite nicely with the measured spectrum. Thus, we believe the calculated prephenate spectrum embedded in the active site is a reasonable estimate of the absorption spectrum for this species. The enzyme-embedded prephenate spectrum is calculated to have peaks at 346, 160, and 159 nm, with relative intensities of 1.00, 0.17, and 0.05, respectively. The absorption spectrum for the embedded prephenate has not been measured experimentally, and therefore, the validation of the EFP method for accurately predicting spectra of biomolecular complexes must await the appropriate measured absorption spectrum. 6. Conclusions The ability to leverage the X-ray structure into a range of protein conformations abstracted from MD simulations to further analyze using ab initio methods has been demonstrated. The
Chorismate Mutase-Catalyzed Claisen Rearrangement success of this method to predict the binding of substrates is proven by comparison to direct experimental data (prephenate and TSA). The use of this methodology to leverage one crystal structure into insightful computational information about native substrate binding has been validated. The power of this new molecular dynamics/quantum mechanical-effective fragment potential (MD/QM-EFP) methodology lies in the ability to leverage an available structure into the relevant structure of the reactant/active site complex. Even though considerable strides have been made in experimental methods for determining protein structures, producing protein structures with bound substrates that are relevant to activity is still difficult and slows down the determination of structure/function relationships in proteins. The MD/QM-EFP method can use a single structure to produce essential information about native and mutant proteins and binding of native and other substrates and therefore may be used to help illuminate structure/function relationships pertaining to the chemistry. This information can then be utilized to design substrates that may inhibit the enzyme or may allow the production of novel and useful products through mutagenesis of an active site residue. Additionally, unusual substrates may be successfully introduced into the enzyme to produce novel binding complexes or new products. We are presently using the MD/QM-EFP method to study the effects of mutating glu78 and tyr108 on the catalysis of the reaction. We are also exploring the substitution of chorismate by unusual substrates in the enzyme active site. Optimized structures of the chorismate and the transition state embedded in the enzymatic environment are readily obtained with the EFP methodology. Examination of these structures allows us to provide a different and significant explanation of the catalytic role of chorismate mutase in the Claisen rearrangement of chorismate to prephenate. The preactivation of chorismate through hydrogen bonding to glu78 has presented a new catalytic feature of the enzyme and its observation is only possible using quantum chemical methods. The binding of the higher energy pseudodiaxial conformer of chorismate in the active site is substantiated. Evidence that the enzyme further distorts this conformer from its solution geometry by concurrent binding of the carboxylate groups by arginine residues is presented. This concurrent binding is also determined to be an important catalytic interaction of the enzyme by restricting the movement of the two carbon atoms that form a bond in prephenate. The tyr108 residue is identified as essential, and its catalytic role is determined. Finally, it is concluded that the electrostatic stabilization of arg90 is needed along the entire reaction path but is not found to be stronger for the transition state than the reactant.4,8 References and Notes (1) Addadi, L.; Jaffe, E. K.; Knowles, J. R. Biochemistry 1983, 22, 4494-501. (2) Bayley, C. I.; Cieplak, P.; Cornell, W. D.; Kollman, P. A. J. Phys. Chem. 1993, 97, 10269-10280. (3) Berman, H. M.; Westbrook, J.; Feng, Z.; Gilliland, G.; Bhat, T. N.; Weissig, H.; Shindyalov, I.N.; Bourne, P.E. Nucleic Acids Res. 2000, 28, 235-42. (4) Bruice, T. C.; Lightstone, F. C. Acc. Chem. Res. 1999, 32, 127136. (5) Carlson, H. A.; Jorgensen, W. L. J. Am. Chem. Soc. 1996, 118, 8475-8484. (6) Case, D. A.; Pearlman, D. A.; Caldwell, J. W.; Cheatam, T. E., III; Ross, W. S.; Simmerling, C. L.; Darden, T. A.; Merz, K. M.; Stanton, R. V.; Cheng, A. L.; Vincent, J. J.; Crowley, M.; Ferguson, D. M.; Radner, R. J.; Seibel, G. L.; Singh, U. C.; Weiner, P. K.; Kollman, P. A. Amber, 5.0 ed.; University of California: San Francisco, 1997.
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