All Electron Quantum Chemical Calculation of the Entire Enzyme

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J. Phys. Chem. B 2006, 110, 1457-1463

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All Electron Quantum Chemical Calculation of the Entire Enzyme System Confirms a Collective Catalytic Device in the Chorismate Mutase Reaction Toyokazu Ishida,* Dmitri G. Fedorov, and Kazuo Kitaura Research Institute for Computational Science (RICS), National Institute of AdVanced Industrial Science and Technology (AIST), Tsukuba Central 2, 1-1-1 Umezono, Tsukuba, 305-8568, Japan ReceiVed: October 7, 2005; In Final Form: October 20, 2005

To elucidate the catalytic power of enzymes, we analyzed the reaction profile of Claisen rearrangement of Bacillus subtilis chorismate mutase (BsCM) by all electron quantum chemical calculations using the fragment molecular orbital (FMO) method. To the best of our knowledge, this is the first report of ab initio-based quantum chemical calculations of the entire enzyme system, where we provide a detailed analysis of the catalytic factors that accomplish transition-state stabilization (TSS). FMO calculations deliver an ab initiolevel estimate of the intermolecular interaction between the substrate and the amino acid residues of the enzyme. To clarify the catalytic role of Arg90, we calculated the reaction profile of the wild-type BsCM as well as Lys90 and Cit90 mutant BsCMs. Structural refinement and the reaction path determination were performed at the ab initio QM/MM level, and FMO calculations were applied to the QM/MM refined structures. Comparison between three types of reactions established two collective catalytic factors in the BsCM reaction: (1) the hydrogen bonds connecting the Glu78-Arg90-substrate cooperatively control the stability of TS relative to the ES complex and (2) the positive charge on Arg90 polarizes the substrate in the TS region to gain more electrostatic stabilization.

1. Introduction The elucidation of the catalytic power of enzymes is one of the major challenges in modern theoretical chemistry. Although the general concept of transition-state stabilization (TSS) is well recognized; the factors that accomplish TSS on the atomic level still remain elusive. To address this question, we analyze the reaction profile of Claisen rearrangement of Bacillus subtilis chorismate mutase (BsCM) by all electron quantum chemical calculations using the fragment molecular orbital (FMO) method.1,2 On the basis of the state-of-the-art all electron MO method for an entire enzyme (the first report to the best of our knowledge), we establish the cooperative catalytic device through the hydrogen-bonding network of the Glu78-Arg90substrate and the importance of the electrostatic field exerted by protein. Chorismate mutases are the enzymes that catalyze the conversion of chorismate to prephenate in the shikimate pathway, known as the biosynthetic route of aromatic amino acids in plants and microorganisms.3-5 The enzymatic reaction is considered to proceed via a chairlike pericyclic transition state.6 Structural/biochemical investigations suggested that polarized TS may be stabilized by the electrostatic interaction of the positively charged residue (Arg or Lys) adjacent to the ether oxygen of the substrate,3,4,6-8 The most essential residue in BsCM is considered to be Arg90. Experimental studies revealed that the lack of Arg90 leads to a large loss of catalytic activity. However, whether the critical catalytic element of Arg is the positive charge or the molecular shape is not understood clearly. Mutagenesis studies showed that even in a chargeconserved substitution of Arg with Lys, substantial catalytic reduction is observed.7,8 To overcome the steric effect of the * Corresponding author. E-mail: [email protected].

side chain in the active site, Hilvert and co-workers prepared a BsCM variant containing citrulline (isosteric/neutral arginine analogue) in the Arg90 position and measured kinetic parameters. On the basis of the series of experiments, they concluded that the electrostatic stabilization of the polarized TS is the paramount factor.9 Today, BsCM becomes an ideal candidate for the theoretical approach of analyzing the TSS factor by protein environment.10-19 Despite much theoretical work in the past few decades, the catalytic power of the enzyme still remains controversial. Although some calculations support the electrostatic stabilization hypothesis,10-13,17 others argued the importance of the conformational restriction of the substrate.18,19 At present, many QM/ MM applications are still limited to semiempirical MO methods.10,11 In ab initio MO models, the catalytic interaction is usually estimated by the small cluster model extracted from the QM/MM modeling structure.12,13,15 We focus on the all electron MO analysis of the protein-substrate interaction during the catalytic process. To clarify the effect of both molecular shape and charge on Arg90 that was not addressed in other theoretical studies, we calculated the reaction profile of the wild-type BsCM as well as Lys90 and Cit90 mutant BsCMs. The FMO method is an ab initio-based approach for calculating the electronic structure (the total electron density and energy) of large molecules by dividing the system into fragments and performing ab initio calculations of fragments and their dimers in the electrostatic field of environment.1,2 Quantitative fragmentfragment interaction comes out as a byproduct, whereas such information is usually hidden in the conventional ab initio MO calculations. The whole enzyme system is treated quantum mechanically in the FMO method. In contrast to QM/MM, no fitted parameters, such as MM potentials, are used, and second,

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Figure 1. (left) Quantum chemical model for Cit90 fragments. N-terminus and C-terminus are capped by CO-Me and NH-Me, respectively. (right) Calculated RESP charges at the RHF/6-31G* level. The calculated dipole moments in each theoretical method (QM and model MM) are shown in the left part.

polarization and charge transfer for all residues in the enzyme and substrate are accounted for properly. For practical reasons, we employed the following procedure. (1) An ES complex of wild-type BsCM was modeled based on the X-ray structure of BsCM bound to an endo-oxabicyclic transition-state analogue. (2) The TS structure and minimum energy reaction path (MEP) were determined by the ab initio QM/MM method. (3) The ES, TS, and product structures of Lys90 and Cit90 mutants were determined based on the wildtype structure. (4) Finally, to take into account the collective polarization effect and charge transfer between the substrate and protein, which is very difficult with the standard QM/MM treatment,10-14,17,19,20 we performed FMO calculations for these QM/MM refined structures. 2. Method and Computational Details 2.1. QM/MM Structural Determination. The structural refinement and reaction path search were performed by the ab initio QM/MM calculations, and the details are described in earlier publications.20 We chose the AMBER standard parameter set (parm.96) for the MM force-field calculations.21 The initial set of coordinates for the enzyme-substrate (ES) complex was taken from the X-ray crystal structure of Bacillus subtilis chorismate mutase (BsCM) bound to the endo-oxabicyclic transition state analogue (PDB code 2CHT). The substrate (chorismate) structure was modeled and placed at the original X-ray coordinate of TSA. Among three identical catalytic sites at the interface of the three protein units (domains), we considered only the single binding site (between domains 1 and 2). All polar residues (Asp, Glu, Lys, and Arg) were assumed to be in the ionized state, and all His residues were in the protonated form. Hydrogen atoms were added to the ES complex in the standard fashion. In the initial model, no crystal waters and counterions were considered. Unfavorable steric contact was removed by first rough MM energy minimization (steepest

decent method) while fixing the chorismate in the gas-phase QM geometry and charge distribution. Then, the structure of the ES complex was refined by ab initio QM/MM optimizations. Because the main purpose of QM/MM geometry optimizations is the preparation of reasonable structures for FMO calculations, the QM region was limited to the substrate molecule. In all QM/ MM calculations, we used the Hartree-Fock (HF) method with the 6-31(+)G** basis set (diffuse functions were added to the two carboxylic groups). The convergence criteria used in ab initio QM/MM optimizations were the following: the maximum gradient less than 5 × 10-4 au/bohr in the QM region and the RMS gradient less than 1 × 10-2 kcal/mol‚Å-1 in the MM region. As for the reaction path search, we defined the reaction coordinate as a linear combination of two bond distances: the breaking C-O and forming C-C bonds. On the basis of the gas-phase IRC (intrinsic reaction coordinate) profile of chorismate isomerization, we first calculated the linear reaction path in the two-dimensional coordinate space, while gradually changing the two bond lengths. Then we refined the TS structure starting from the highest energy geometry found along the initial path. In this TS search, we considered only the Hessian matrix corresponding to the QM region. To avoid some low-frequency collective modes of protein, we followed only the imaginary mode of the QM Hessian matrix and the MM region was fully relaxed as in the standard QM/MM geometry optimizations.22 In this case, we employed tight convergence criteria (the maximum gradient less than 1 × 10-4 au/bohr in the QM region and the RMS gradient less than 5 × 10-3 kcal/mol‚Å-1 in the MM region). Note that in the QM Hessian matrix, MM contributions (electrostatic and van der Waals interactions, in this case) are included in the standard QM/MM manner.23 After determining the TS geometry, we calculated the minimum energy path (MEP) that connects the TS to the reactant or

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Figure 2. Schematic figure of the active site of BsCM. Important hydrogen-bond lengths for three types of enzymes (wild-type in black, lys90 mutant in green, cit90 mutant in magenta) are also given in pairs for ES/TS (in Å). “- - -” indicates no hydrogen bond. For convenience, the side chain atoms of residue90 are represented by X and Y.

product. The restrained geometry optimizations were performed in the internal coordinate space with two selected bond distances fixed. The ES, TS, and product structures of Lys90/Cit90 mutant reactions were determined based on those of a wild-type reaction, assuming that in the two mutants chemical reaction progresses in a similar way. The original Arg90 position was replaced by Lys90 or Cit90, with the maximum overlap of the heavy atom coordinates. In each mutant, all structures were optimized by ab initio QM/MM-level calculations. For Cit90, the missing charge parameters were determined by the RHF/ 6-31G* RESP fit procedure, in a manner similar to the AMBER force field determination.24 On this stage, we considered only the extended conformation observed in the X-ray structure of the original wild-type Arg90 geometry. Figure 1 (left) shows the quantum chemical model of the Cit90 fragment. On the basis of this structure, we determined the RESP charges for the Cit90 residue. The results are also included in Figure 1 (right). All of the stationary structures were confirmed by vibrational frequency calculations. 2.2. Fragment Molecular Orbital Calculations. All of the FMO2,28 calculations were performed using the GAMESS quantum chemical program package25 and parallelized by the generalized distributed data interface (GDDI).26 Input data for FMO calculations were prepared using the FMOutil modeling utility,27 which converts PDB data into GAMESS format automatically and sets up the FMO calculation. We employed two amino acid residues per fragment partition (larger fragments in general have smaller error compared to ab initio MO methods) and compared energetics with the QM/MM results for all three types of the reaction (see below). For the energy decomposition analysis of TSS factors including the dispersion interaction, we used one amino acid residue per fragment partition to look at contribution from each residue. In FMO calculations, the protein is divided into fragments at the CR position, keeping peptide bonds intact. The hybrid sp3 orbitals of carbon atoms were used to divide molecular orbital space properly at the bond fraction points. In GAMESS calculations, both the atomic and molecular orbital accuracy were raised to 10-12 using ICUT ) 12, ITOL ) 24, and CUTOFF ) 10-12 and SCF convergence was tightened to 10-7. The same values were used during the monomer SCF cycle where monomer densities converge.

We employed the multilayer FMO (MFMO) framework,28 where all fragments are assigned to layers and each layer can be described with a different basis set/wave functions. Higher layers correspond to higher-level wave functions, possibly with a larger basis set. Note that in contrast to the similar approach,29 in MFMO all of the fragments in the higher layer are not calculated in vacuum but in the surrounding electrostatic potential (ESP) generated by the fragments assigned to lower layers. The electron correlation should be taken into account in order to describe the molecular interaction between the substrate and the enzyme accurately. All of the interfragment (intermolecular) interactions between the substrate and the surrounding amino acid residues were evaluated by the FMO2-MP2 method,2 where FMO2 indicates that two-body FMO expansion was used. On the basis of the structural analyses of the wild-type BsCM reaction along the MEP, we assigned the important residues around the substrate to the higher layer (MP2 layer): Leu47, Phe57 - Glu64, Val73 - Glu77 (in domain1), Arg7 - Thr10, Ser48, Glu78, Met79, Val81, Cys88, Arg90 (or Lys90, Cit90 for Lys90/Cit90 mutants, respectively), Val91, Tyr108, Ala112, Val113, Leu115 - Asp118 (in domain2), and the substrate. We employed the 6-31(+)G* basis set, where diffuse functions were added to all carboxyl groups (Asp, Glu, C-Term) in the enzyme and the substrate. The option to remove s contaminants from d functions was used. In all FMO2-RHF/ 6-31(+)G* calculations, we used the following approximations: RESPAP ) 0 (the atomic population approximation to compute ESP), RESPPC ) 2.0 (the point charge approximation to compute ESP), and RESDIM ) 2.5 (dimer energies approximation based on quantum mechanical electrostatic interaction). Also, we used the approximation of RCORSD ) 2.0 (neglect electron correlation for far separated dimers) in the FMO2-RHF/6-31(+)G*:MP2/6-31(+)G* calculations, which is a multilayer FMO method with RHF and MP2 wave function in the lower and higher layers, respectively. All approximations were applied when the distance between two fragments is larger than a threshold (distances are measured relative to the sum of van der Waals radii of closest contact atoms). In the MP2 calculation, core orbitals were not correlated (1s orbitals for carbon, nitrogen, and oxygen atoms). Most of the FMO calculations reported in this paper were performed on the P32 subsystem of the AIST Super Cluster.

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Each node is a dual Opteron (2.0 GHz) system operated by SuSE Linux 8.1 with 6 GB of memory and is interconnected by both Gigabit Ethernet and Myrinet. Among 1024 calculation nodes in the P32 cluster, we used 64 nodes for every single structure energy calculation. The wild-type BsCM system contains 5687 atoms and 48 488 basis functions. It took ∼51 h to calculate single point energy by FMO2-RHF/6-31(+)G* (2residues/ 1fragment), and ∼28 h by FMO2-RHF/6-31(+)G*:MP2/6-31(+)G* (1residue/1fragment). 3. Results and Discussion 3.1. Active Site Geometry in Each Enzyme System. In the ES complex of wild-type BsCM, typical hydrogen bonds are formed between the chorismate and the polar amino acid residues at the active site: Arg7 and Tyr108 (both in domain2) form strong hydrogen bonds to the carboxyl group in the enolpyruvyl side chain, Arg63 (in domain1) and Arg116 (in domain2) also form strong ones with the other carboxyl group, Cys75 (in domain1) and Glu78 (in domain2) are hydrogen bonded to the hydroxyl group of the substrate, and Arg90 (in domain2) makes hydrogen bonds with the ether oxygen, buried enol-pyruvyl carboxyl part of the substrate. We did not find large geometrical changes in and around the active site along the reaction path: only a small rearrangement of the hydrogenbonding network is observed in the particular hydrogen-bond sites. Figure 2 summarizes the important hydrogen-bond parameters in ES and TS at the active site of the wild-type BsCM. Only the important residues mentioned above are included in this schematic picture. Also, the optimized TS structure is shown in Figure 3. In the case of the wild-type reaction, Arg63, Arg116, Arg7, and Tyr108 work to fix the relative orientation of the substrate at the active site, and the structural rearrangement in the Glu78Arg90-substrate controls the strength of the hydrogen bonds. As for Lys90/Cit90 mutant reactions, no large conformational change is observed in the overall protein structure except for the geometries around the mutation point. Because of loss of the steric hindrance by the guanidium side chain of Arg90, most of the hydrogen bonds shown in Figure 2 are slightly weaker in the ES complex. As a result, the substrate forms a strong hydrogen bond with Glu78, and ES is more stabilized than the wild-type reaction in the mutants. A slight modification of the geometrical parameters largely influences the relative stability of the substrate along the reaction path. For all mutants, the hydrogen-bond lengths and optimized TS geometries are also included in Figures 2 and 3, respectively. In the present theoretical models, the geometrical factor of Arg90 that bridges Glu78 to the substrate by hydrogen bonds seems to be the key element in achieving an efficient TSS. 3.2. Reaction Energetics. Table 1 shows the reaction energetics of FMO calculations. The calculated activation energies (FMO2-RHF/6-31(+)G*, two residues per fragment) for each system are 22.4 kcal/mol (wild-type), 27.4 kcal/mol (Lys90 mutant), and 27.7 kcal/mol (Cit90 mutant). For comparison, ab initio QM/MM results are also summarized in Table 1. These results are potential energy, not free energy. Our theoretical prediction of a wild-type/Cit90 mutant activation energy difference of 5.3 kcal/mol agrees well with the experimental observations. (As for the Cit90 mutant reaction, a 104fold decrease in the catalytic activity of kcat is observed. This corresponds to ∼6 kcal/mol energy difference based on the estimation of the transition state theory.9 In the case of the Lys90 mutant, a 104-fold decrease in the catalytic activity of kcat/KM is obtained.7,8) Comparing the QM/MM results, the FMO

Figure 3. Optimized active site TS geometries in each enzyme reaction: wild-type (top), lys90 mutant (middle), cit90 mutant (bottom). Only the important residues are shown in this picture: Arg63, Cys75 (in domain1), Arg7, Glu78, Arg90 (or Lys90/Cit90 shown in green), Tyr108 and Arg116 (in domain2), and the substrate (in red).

TABLE 1: Activation Energies in the Three Enzyme Reactions by Ab Initio QM/MM RHF/6-31(+)G**/AMBER and FMO2-RHF/6-31(+)G* Calculationsa (in kcal/mol)

wid-type (Arg90) Lys90 mutant Cit90 mutant

RHF/6-31(+)G**/ AMBERb

FMO2-RHF/ 6-31(+)G*

26.3 31.5 36.3

22.4 27.4 27.7

a Note that in all FMO2 calculations the geometries of the enzyme systems were determined by the ab initio QM/MM level. Therefore, the protein structures in both theoretical calculations were exactly the same. b In all QM/MM optimizations, the QM region was limited to the substrate only. In QM/MM calculations, the total energy is composed of three terms: QM part (substrate), MM part (enzyme), and QM/MM interaction energy (including electrostatic, vdW term).

calculations reproduce lower activation energies. This is reasonable because the MM environment is not polarized in the present QM/MM model, whereas in the FMO case both the substrate and environment are treated quantum mechanically, including

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Figure 4. Decomposition of the substrate-enzyme interaction energy difference between TS and ES at the FMO2-RHF:MP2/6-31(+)G* level: wild-type (top), lys90 mutant (middle), cit90 mutant (bottom). The x axis is the amino residue serial number, and the y axis shows the interaction energy difference, ∆EIJ, between TS and ES (in kcal/mol).

charge-transfer consideration. The present FMO analyses show the importance of protein polarization for the BsCM reactions. Comparing the experimental activation free energy5,7,8 of ∼15 kcal/mol with the present results, our estimations (ab initio QM/ MM and FMO2) give slightly overestimated activation barriers. This type of reaction is known to be difficult for describing the accurate electronic structure correctly. To improve the results, better levels of electron correlation treatment can be tried; however, for the main purpose of this work (comparative study of mutants and analysis of TSS factors) the agreement is reasonable. 3.3. All Electron Interaction Residue Analysis. Next, we discuss the detailed molecular interaction between the substrate and the enzyme based on the energetically reasonable chemical structures. In FMO2, the total energy of the molecule is calculated by the following equation,1,2

Etotal )

(EIJ - EI - EJ) ∑I EI + ∑ I>J

(1)

where EI and EIJ are the monomer and dimer energies, respectively. Both the monomer and the dimer total energies include the electrostatic interaction energy with surrounding monomers. Introducing internal monomer E′I and dimer energies E′IJ by subtracting the environmental electrostatic interaction energy from EI and EIJ, eq 1 is rewritten as a sum of the modified monomer and the interfragment interaction energies, ∆EIJ:

Etotal )

∆EIJ ∑I E′I +∑ I>J

(2)

The second term of eq 2, ∆EIJ, is the effectiVe pair interaction energy that includes many-body effects through the many-body Coulomb potential. Note that internal monomer energies, E′I, in eq 2 are usually destabilized by the polarization effect of the surrounding ESP, whereas the effective pair interaction energy term contains both repulsive and attractive interactions. All of the intermolecular interactions between the substrate and surrounding residues in the complex are evaluated by correlated calculations at the FMO2-RHF:MP2/6-31(+)G* level. The effective pair interaction energy in eq 2 thus includes contribu-

1462 J. Phys. Chem. B, Vol. 110, No. 3, 2006 tions at the MP2 level. By analyzing the difference of the interaction energy, ∆EIJ, for the substrate and each amino acid residue of the enzyme, we obtained detailed information about the TSS factor. Figure 4 shows the interaction energy decomposition into each residue contribution. It is apparent from these results that only a limited number of residues are responsible for TSS. Among them, Arg90 has the most crucial contribution in the wild-type reaction. Also, Glu78 and Arg7 show large attractive interactions. Interestingly, all polar residues that have strong interactions are located inside the binding pocket: Arg90 interacts with the ether oxygen and the carboxylate group of the enol-pyruvyl side chain of the substrate, Glu78 is bound to the substrate hydroxyl group, and Arg7 forms hydrogen bonds with the buried carboxylate part. A slight movement of the C-terminal helix (Glu110-Arg116) is observed along the MEP. In accordance with the structural change of the enol-pyruvyl group, the C-term helix closely approaches the substrate during the TS formation process. The large catalytic contribution of nonpolar Leu115, which is just located on the lid position of the catalytic pocket, originates from this structural movement. In the Lys90 mutant, although the charge effect that polarizes the substrate is similar to that of Arg90, a large catalytic loss is observed because of Lys90. The main reason is that ES is more stabilized by loss of the steric factor that prevents Glu78 from forming the strong hydrogen bond with the substrate. In addition to the structural changes that destroy the fine balance of the hydrogen bonds in the Glu78-Arg90-substrate, in the Cit90 mutant, the charge distribution of the substrate is different from the other two cases and a rather large dipole is observed in the ES complex. As a result, the buried carboxylate part of the substrate forms strong hydrogen bonds with Arg7 even in ES. The catalytic contribution of Cit90 comes mainly from the strong attraction with the buried carboxylate of the substrate, not the induced charge on the ether oxygen at TS region. Thus, Cit90 stabilizes TS in a different way from Arg90 in the wild-type reaction. 4. Concluding Remarks In this article, we analyzed the reaction mechanism of BsCM by calculating the electronic structure of the entire enzyme systems based on the all electron FMO method. For practical reasons, we employed the ab initio QM/MM modeling technique and calculated the reaction path by relaxing the degrees of freedom in the protein systems. On the basis of the ab initio QM/MM optimized geometries, we investigated the details of molecular interaction energy between the enzyme and the substrate from ab initio viewpoint. The main focus on this article is to clarify the effect of both molecular shape and charge on the catalytically important residues, which no earlier theoretical works mentioned before. For this purpose, we surveyed the reaction profile of wild-type BsCM as well as Lys90/Cit90 mutants. Careful analyses in each enzyme system clarify the details of the reaction mechanism. Although the catalytic activity of Lys90 is inferior to that of Arg90, the enzymatic mechanism of the Lys90 mutant is similar to that of the wild-type BsCM. The main anticatalytic factor of Cit90 mutant is the ES stabilization as a result of destabilizing the substrate by the surrounding electrostatic field because of the mutated enzyme. Therefore, the TS stabilization mechanism of the Cit90 mutant is quite different from that of the wild-type BsCM as seen from Figure 4. The present all electron FMO calculations of the entire enzymatic system clearly demonstrate the importance of the cooperative catalytic device through the hydrogen-bonding

Ishida et al. network, where Arg90 plays a central role. The wild-type active site is designed to highly polarize and stabilize the substrate at TS region. Comparison among three types of the reactions clarifies the two important catalytic roles of Arg90: one is to control the relative stability of the substrate through the collective hydrogen-bonding network in the Glu78-Arg90substrate, and the other is to polarize the substrate at the appropriate location on the reaction path to gain the maximum electrostatic stabilization factor for TSS. Acknowledgment. This work was partially supported by the NAREGI Nanoscience Project from the Ministry of Education, Culture, Sports, Science and Technology, Japan and the CRESTJST. Part of the numerical calculations were carried out on the Computer Center of the Institute for Molecular Science (IMS). References and Notes (1) (a) Kitaura, K.; Ikeo, E.; Asada, T.; Nakano, T.; Uebayasi, U. Chem. Phys. Lett. 1999, 313, 701-706. (b) Kitaura, K.; Sugiki, S.; Nakano, T.; Komeiji, U.; Uebayasi, U. Chem. Phys. Lett. 2001, 336, 163-170. (c) Nakano, T.; Kaminuma, T.; Sato, T.; Fukuzawa, K.; Akiyama, U.; Uebayasi, U.; Kitaura, K. Chem. Phys. Lett. 2002, 351, 475-480. (2) (a) Fedorov, D. G.; Kitaura, K. J. Chem. Phys. 2004, 120, 68326840. (b) Fedorov, D. G.; Kitaura, K. J. Chem. Phys. 2004, 121, 24832490. (3) Chook, Y. M.; Ke, H.; Lipscomb, W. N. Proc. Natl. Acad. Sci. U.S.A. 1993, 90, 8600-8603. (4) Kast, P.; Asif-Ullah, M.; Jiang, N.; Hilvert, D. Proc. Natl. Acad. Sci. U.S.A. 1996, 93, 5043-5048. (5) Kast, P.; Asif-Ullah, M.; Hilvert, D. Tetrahedron Lett. 1996, 37, 2691-2694. (6) Gustin, D. J.; Mattei, P.; Kast, P.; Wiest, O.; Lee, L.; Cleland, W. W.; Hilvert, D. J. Am. Chem. Soc. 1999, 121, 1756-1757. (7) Cload, S. T.; Liu, D. R.; Pastor, R. M.; Schults, P. G. J. Am. Chem. Soc. 1996, 118, 1787-1788. (8) Kast, P.; Grisostomi, C.; Chen, I. A.; Li, S.; Krengel, U.; Xue, Y.; Hilvert, D. J. Biol. Chem. 2000, 275, 36832-36838. (9) Kienho¨fer, A.; Kast, P.; Hilvert, D. J. Am. Chem. Soc. 2003, 125, 3206-3207. (10) Lyne, P. D.; Mulholland, A. J.; Richards, W. G. J. Am. Chem. Soc. 1995, 117, 11345-11350. (11) (a) Martı´, S.; Andre´s, J.; Moliner, V.; Silla, E.; Tun˜o´n, I.; Bertra´n. J. Theor. Chem. Acc. 2001, 105, 207-212. (b) Martı´, S.; Andre´s, J.; Moliner, V.; Silla, E.; Tun˜o´n, I.; Bertra´n. J.; Field, M. J. J. Am. Chem. Soc. 2001, 123, 1709-1712. (c) Martı´, S.; Andre´s, J.; Moliner, V.; Silla, E.; Tun˜o´n, I.; Bertra´n. J. J. Am. Chem. Soc. 2004, 126, 311-319. (12) Lee, Y. S.; Worthington, S. E.; Krauss, M.; Brooks, B. R. J. Phys. Chem. B 2001, 105, 7087-7095. (13) (a) Ranaghan, K. E.; Ridder, L.; Szefczyk, B.; Sokalski, W. A.; Hermann, J. C.; Mulholland, A. J. Org. Biomol. Chem. 2004, 2, 968-980. (b) Szefczyk, B.; Mulholland, A. J.; Ranaghan, K. E.; Sokalski, W. A. J. Am. Chem. Soc. 2004, 126, 16148-16159. (14) Crespo, A.; Scherlis, D. A.; Martı´, M. A.; Ordejo´n, P.; Roitberg, A. E.; Estrin, D. A. J. Phys. Chem. B 2003, 107, 13728-13736. (15) Worthington, S. E.; Roitberg, A. E.; Krauss, M. J. Phys. Chem. B 2001, 105, 7087-7095. (16) Kangas, E.; Tidor, B. J. Phys. Chem. B 2001, 105, 880-888. (17) Sˇ trajbl, M.; Shurki, A.; Kato, M.; Warshel, A. J. Am. Chem. Soc. 2003, 125, 10228-10237. (18) (a) Hur, S.; Bruice, T. C. J. Am. Chem. Soc. 2003, 125, 59645972. (b) Hur, S.; Bruice, T. C. Proc. Natl. Acad. Sci. U.S.A. 2003, 100, 12015-12020. (19) (a) Guimara˜es, C. R. W.; Repasky, M. P.; Chandrasekhar, J.; TiradoRieves, J.; Jorgensen, W. L. J. Am. Chem. Soc. 2003, 125, 6892-6899. (b) Guimara˜es, C. R. W.; Udier-Blagovic´, M.; Tubert-Brohman, I.; Jorgensen, W. L. J. Chem. Theory Comput. 2005, 1, 617-625. (20) (a) Ishida, T.; Kato, S. J. Am. Chem. Soc. 2003, 125, 12035-12048. (b) Ishida, T.; Kato, S. J. Am. Chem. Soc. 2004, 126, 7111-7118. (21) (a) Cornell, W. D.; Cieplak, P.; Bayly, C. I.; Gould, I. R.; Merz, K. M., Jr.; Ferguson, D. M.; Spellmeyer, D. C.; Fox, T.; Caldwell, J. W.; Kollman, P. A. J. Am. Chem. Soc. 1995, 117, 5179-5197. (b) Kollman, P.; Dixon, R.; Cornell, W.; Fox, T.; Chipot, C.; Pohorille, A. In Computer Simulation of Biomolecular Systems; van Gunsteren, W. F., Weiner, P. K.,

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