J. Phys. Chem. B 2004, 108, 15347-15354
15347
Catalytic Mechanism of Pyruvate-Formate Lyase Revisited Jing-Dong Guo and Fahmi Himo* Theoretical Chemistry, Department of Biotechnology, Royal Institute of Technology, ALBANOVA, SE-106 91 Stockholm, Sweden ReceiVed: May 21, 2004; In Final Form: July 15, 2004
The catalytic mechanism of the glycyl-radical-containing enzyme pyruvate-formate lyase (PFL) is investigated using high-level quantum chemical methods. PFL catalyzes the reversible conversion of pyruvate and coenzyme A (CoA) into formate and acetylated CoA. Large models are employed, based on a recent X-ray crystal structure of PFL in complex with the pyruvate substrate. The rate-limiting step is shown to be the homolytic C1-C2 bond cleavage of pyruvate, which occurs after the attack of the Cys418 radical on the carbonyl carbon of pyruvate. For the acetylation of CoA, we propose a new mechanism, in which the released formyl radical anion abstracts a hydrogen atom directly from CoA. This way, the acetyl group transfer from Cys418 becomes facile. The full potential energy curve for the PFL reactions is presented.
I. Introduction Pyruvate-formate lyase (PFL) was the first enzyme discovered to harbor a stable glycyl radical.1,2 It catalyzes the reversible conversion of pyruvate and coenzyme A (CoA) into acetylated CoA and formate (Scheme 1), a reaction that is a key component of the anaerobic carbon metabolism in Escherichia coli and other prokaryotes. SCHEME 1: Reaction Catalyzed by Pyruvate-Formate Lyase
From early mutagenesis experiments, it is known that, in addition to the glycyl radical at Gly734, two other residues are essential for catalysis, namely Cys418 and Cys419.3 The X-ray crystal structure of PFL was solved recently4-6 (active site shown in Figure 1). The structure shows that the Gly734 residue is in close proximity to Cys419. The position of the substrate implies that Cys418 is the residue performing the attack on pyruvate. Based on the crystal structure and numerous earlier biochemical, spectroscopic, and theoretical studies (as will be discussed below), the following mechanism is the currently accepted one for PFL (see Scheme 2). The first two steps involve hydrogen atom transfer, first from the Cys419 to the glycyl radical (Step 1), and then from Cys418 at the substrate-binding site to Cys419 (Step 2). This kind of hydrogen transfer is now believed to be a paradigm in glycyl radical enzymes, that is, the glycine residue serves as a site for radical storage, and starts catalysis by abstracting a hydrogen atom from a neighboring cysteine, which then activates the substrate.7,8 Next, the Cys418 radical adds to the keto group of pyruvate, forming a tetrahedral oxy-radical intermediate (Step 3), which subsequently collapses into an acetylated cysteine and a formyl radical anion (Step 4). This homolytic mechanism was originally modeled after the Minisci reaction for the cleavage of R-ketoesters by Fenton’s reagent,9 although there were problems in assigning which of the cysteines was the one involved in the reaction.10,11 Later, this chemistry was substantiated by theoretical calculations by Himo and
Figure 1. X-ray structure of the active site of pyruvate-formate lyase in complex with the substrate [6].
Eriksson12 where the reaction step was shown to have a feasible energy barrier. In the next step (Step 5) the formyl radical anion is suggested to be quenched by Cys419, creating a thiyl radical at that position, which then abstracts the thiol hydrogen of CoA-SH (Step 6). This step was proposed by the theoretical study12 to make the acetyl group transfer between Cys418 and CoA in the next step (Step 7) facile. At this point the reaction is completed, and the enzyme can either take a new substrate or regenerate the stable glycyl radical by a hydrogen atom transfer chain backward (Scheme 2). The mechanism of PFL was studied with density functional theory (DFT) methods twice earlier. The first study is the one mentioned above by Himo and Eriksson in 1998,12 that is, before the crystal structure was solved. This study used quite small models of the residues involved. In addition, the study assumed a charge-neutral substrate, that is, the pyruvate was in the calculations protonated to become pyruvic acid. The rationale
10.1021/jp0478054 CCC: $27.50 © 2004 American Chemical Society Published on Web 08/27/2004
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SCHEME 2: Currently Accepted Reaction Mechanism for Pyruvate-Formate Lyase
behind this is that these kinds of carboxylate moieties in enzymes are often found to form quite strong hydrogen bonds to positively charged groups, such as arginines and lysines. It was believed to be better to model the situation using a fully protonated substrate rather than the anionic species. In the case of PFL, the X-ray structure showed later that the carboxylate of pyruvate is hydrogen bonded to two positively charged groups, Arg176 and Arg435. Based on these small models and crude assumptions, this theoretical study provided strong substantiation of the homolytic mechanism and also suggested the intriguing radical step for the acetyl transfer to CoA. Recently, Lucas et al.13 performed new DFT calculations on the mechanism, based on the crystal structure. Comparing the models, the largest differences compared to the earlier study is the use of an anionic pyruvate substrate and that the peptide backbone link between the two cysteines (Cys418 and Cys419) was also included in the calculations. Another difference is that they used polarizable continuum calculations to model the protein surrounding. Although there were some differences in the energetics compared to the other theoretical study, the general picture of the catalytic mechanism was the same. The main mechanistic difference is that steps 3 and 4 were found to be concerted. That is, the attack of the cysteinyl radical and the release of the formyl radical anion occur in one step. In the neutral model12 there was a shallow minimum of ca. 3 kcal/mol between the two steps. In the present paper, we revisit the mechanism of PFL, employing a quite large model that consists of up to 75 atoms, based on the crystal structure of Becker et al.6 We included two positively charged arginine side chains that are involved in binding the negatively charged pyruvate substrate. This model resembles the active site in a better way than both the negatively charged substrate used by Lucas et al.,13 and the protonated substrate used by Himo and Eriksson.12 II. Computational Details All geometries and energies presented in the present study were computed using the B3LYP14-17 density functional theory method as implemented in the Gaussian98 program package.18 Geometry optimizations were performed using the double-ζ plus
polarization basis set 6-31G(d,p). Based on these geometries, single point calculations with the larger basis set 6-311+G(2d,2p) were done to obtain more accurate energies. Spin densities reported are calculated using Mulliken population analysis. Hessians for evaluation of zero-point vibrational effects were calculated at the B3LYP/3-21G level of theory. Solvation energies were added as single point calculations using the conductorlike solvation model COSMO19 at the B3LYP/lacvp level, as implemented in the Jaguar program package.20 In this model, a cavity around the system is surrounded by a polarizable dielectric continuum. The dielectric constant was chosen to be the standard value used for protein surrounding, ) 4. To determine which minima were connected by the different transition states, the structures of these were slightly perturbed manually and reoptimized. Finally, spin contamination, as measured by the expectation value of the S2 operator, was found to be very low in all the calculations ( lower than 0.760. III. Chemical Models III.a. General. As always in quantum chemical studies, one has to make tradeoffs. On one hand, it is essential to choose the models to accurately represent the chemical situation. On the other hand, the models cannot be of the size that makes the calculations impossible to realize. To test one or several reaction pathways and to find the transition states connecting the intermediates, a large number of calculations are usually required, and one has to keep the models at a moderate size. In the present study, we have modeled the active site of PFL in the following manner (see Figure 2). A model of the Gly734 radical, to be discussed below, was included. The two cysteines (Cys418 and Cys419) and the backbone link between them were included. The pyruvate substrate was modeled as an anion, and parts of the side chains of two arginine residues, Arg435 and Arg176, were included. These positively charged groups help binding and stabilizing the substrate, and as such, it is thus enough to include the charged part of their side chains. A negatively charged acetate group was included to model the Asp661 residue that is forming a salt bridge to the Arg176 residue. With all these groups, the net charge of the whole system becomes zero.
Catalytic Mechanism of Pyruvate-Formate Lyase
Figure 2. Model of the PFL active site used in the present calculations. Arrows indicate centers frozen to their X-ray coordinates.
To keep the different parts of the model close to the X-ray structure, we employed a so-called frame model. In this model, we keep certain atoms frozen to their X-ray positions. Typically, these centers are chosen to be the atoms at which one makes the truncation. These positions are indicated by arrows in Figure 2. III.b. Glycine Model. Considering the lack of structural information, the glycine residue was previously modeled using a CHO-NH-CH2-CO-NH2 moiety, that is, including the peptide bonds of the neighboring residues.12 Electronically, this model was found to be adequate, reproducing the π-electron delocalization and the capto-dative effect known to be present in the radical. The CR-H bond dissociation energy (BDE) of this model was calculated to be ca. 3.4 kcal/mol lower than that of the cysteine residue, This fits well with the experimental finding that the glycyl radical is more stable than the cysteinyl radical, since it is the one seen by EPR spectroscopy on the activated enzyme. The glycyl radical is perfectly planar in its ideal conformation. From the crystal structure it is seen, however, that the glycine residue is located at the tip of a loop. This fact sets some geometrical constraints on the glycine residue both in its parent and radical forms. This will modify its BDE, since the radical form cannot be perfectly planar now. In the present study, we have investigated this issue further. We modeled the glycine residue by including increasing parts of the loop around Gly734, as shown in Figure 3. To keep the optimized structures close to the X-ray structure, we kept some of the outermost atoms in the models frozen, as indicated by arrows in the figure. As can immediately be seen from X-ray structure (Figure 3A), the two nitrogens of the amide bonds around the glycine unit are very close to each other. In fact, when we add hydrogen atoms to the crystal structures, the protons of these amide bonds are only 1.5 Å away from each other. This is clearly an artifact of the crystal structure, and any geometry optimization of this structure would make the groups rotate away from each other,
J. Phys. Chem. B, Vol. 108, No. 39, 2004 15349 decreasing the planarity of the radical species and hence increasing the BDE. The previously used model, CHO-NH-CH2-CO-NH2, which has a CR-H BDE of 78.8 kcal/mol without constraints, has a BDE of 86.9 kcal/mol when the end points are kept fixed from the crystal structure. This increase of as much as 8.1 kcal/ mol is due to unfavorable radical geometry. Increasing the size of the model to include more of the neighboring residues in the loop and fixing the outermost atoms does not result in any significant change of the BDE. The largest model, for instance, which consists of 67 atoms, has a CR-H BDE of 87.3 kcal/mol, only 0.4 kcal/mol higher than the model of 19 atoms. Thus, the CHO-NH-CH2-CO-NH2 unit can still serve as a good model of the glycine residue, but now with the end atoms kept fixed. This model is accordingly used in the calculations presented below. As can be seen in Figure 3, the calculated spin for glycyl is quite delocalized. The spin density on the CR center varies between 0.70 and 0.85 depending on the degree of planarity. The two carbonyl-oxygens, furthermore, have a relatively high concentration of spin (up to 0.13). III.c. Cysteine Model. Previously, the cysteine residue was modeled using methylthiol, CH3SH. It was shown that the S-H BDE is quite insensitive to the size of the model, since the radical character is entirely localized to the sulfur center. In the present study, we use the full residues of both Cys418 and Cys419, including the backbone atoms between them. This way, the sterics of the system are better accounted for. IV. Reaction Mechanism IV.a. Hydrogen Atom Transfer from Cys419 to Gly734 Radical. The first step in the catalytic reaction of PFL is the hydrogen atom transfer from Cys419 to Gly734. The calculated barrier for this step, using the cysteine and glycine models discussed above, is 9.3 kcal/mol, very close to the previously obtained barrier of 9.9 kcal/mol for the small models.12 The optimized geometry of the transition state (TS1) structure is displayed in Figure 4A. This step with the large models is now exothermic by 4.6 kcal/mol (3.4 kcal/mol endothermic using the small models). That is, the Cys419 radical is 4.6 kcal/mol more stable than the Gly734 radical, which contradicts the EPR experiments. In the activated enzyme, the glycyl radical is the one observed, not the cysteinyl radical. This energy difference between the models originates almost entirely from the breaking of the planarity of the glycyl radical, as discussed above. The PFL crystal structure, from which the coordinates were taken, is in the inactive nonradical form. One can envisage that upon activation (that is, hydrogen atom abstraction from the glycine residue), the loop with the glycyl radical opens up to accommodate a more planar glycyl radical at the tip, making the radical more stable. IV.b. Hydrogen Atom Transfer from Cys418 to Cys419 Radical. The next step (step 2) in the proposed mechanism is hydrogen atom transfer from Cys418 to Cys419. This will create the thiyl radical, which will then attack the substrate. The barrier, using the current models, is calculated to be 5.7 kcal/mol and the step is exothermic by 1.3 kcal/mol. The transition state structure (TS2) is shown in Figure 4B. Lucas et al.12 also used a large model with backbone connection between the cysteines. They obtained a quite similar barrier (4.9 kcal/mol). However, the reaction was found to be quite asymmetric, with a reaction energy of -4.9 kcal/mol. Using two methylthiol groups to model this hydrogen atom
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Figure 3. (A) X-ray structure of the Gly734 and neighboring residues. Hydrogen atoms added manually. (B) to (F): optimized structures of glycyl radical models of different sizes. In parentheses, CR-H bond dissociation energies are given in kcal/mol for the different models. Arrows indicate frozen centers in the optimization. Distances are given in Å.
Figure 4. Optimized transition-state structures for hydrogen atom transfer between (A) Cys419 and Gly734 (TS1) and (B) between Cys418 and Cys419 (TS2).
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Figure 5. Optimized structures of (A) the transition state for the thiyl attack on pyruvate (TS3), (B) the resulting intermediate (Intermediate I), and (C) a second intermediate (Intermediate II) in which the formyl radical anion is not completely dissociated.
transfer, the reaction is, of course, completely symmetric (reaction energy equals zero) and a barrier of 2.4 kcal/mol, as reported previously.12 IV.c. Formation and Collapse of Tetrahedral Radical Intermediate. In the following steps, the Cys418 radical is proposed to attack the substrate to form a tetrahedral oxy-radical intermediate, which then collapses into acetylated cysteine (Cys418-acetyl) and a formyl radical anion. Previous calculations12 with small models and a neutral substrate gave a barrier of 12.3 kcal/mol for the S-C bond formation step, and the intermediate was found to be in a shallow potential well, only 2.4 kcal/mol lower than the transition state. The barrier for the subsequent C-C bond cleavage, to yield acetylated cysteine and formyl radical anion, was calculated to be only 2.8 kcal/ mol with an exothermicity of 3.9 kcal/mol, resulting in an overall endothermicity of 6.0 kcal/mol for the two steps together. In contrast, the calculations of Lucas et al.,13 using a negatively charged substrate, gave a concerted mechanism for the two reaction steps. The barrier was calculated to 11.8 kcal/ mol and the reaction was found to be endothermic by 7.8 kcal/ mol. In the product species, however, the formyl radical anion is not completely dissociated from the pyruvate; the C-C distance was found to be only 2.02 Å. The spin-density distribution for this species also shows that the dissociation is not complete, since as much as half of the unpaired spin is still located at the acetyl-cysteine moiety. This suggests that the optimized product complex is not the final product for this step, and that complete release of the formyl radical anion will be associated with further lowering of the energy. In the present calculations, the barrier for the first thiyl attack (step 3 in Scheme 2) is found to be 12.9 kcal/mol (the transition state structure, TS3, is shown in Figure 5A). The TS is characterized by an imaginary frequency of 242 cm-1. The critical S-C and C1-C2 are 2.11 and 1.57 Å, respectively. The barrier agrees well with the previously calculated barriers, both the neutral and the anionic barriers. The spin is shared between the sulfur center (0.57) and the oxygen of the pyruvate carbonyl (0.45). The optimized structure of the resulting tetrahedral radical intermediate (Intermediate I) is shown in Figure 5B. It is interesting to note that this optimized well-defined minimum has almost the same energy as the transition state. In the gas
Figure 6. Optimized transition state structure for hydrogen atom transfer between Cys419 and the formyl radical anion.
phase, the intermediate is 0.4 kcal/mol higher than TS3, and in the solvent phase the value is 0.7 kcal/mol. The S-C distance is 1.97 Å and the C-C distance is 1.57 Å. The spin-density distribution shows that some spin has moved over from the sulfur to the oxygen. The fact that the intermediate, although distinct and well-defined, has a very similar energy as the transition state, means that it is kinetically quite insignificant. That is probably the reason why the reaction was seen to be concerted in previous calculations.13 In trying to find the transition state for the dissociation of the formyl radical anion, we found another well-defined minimum, shown in Figure 5C. This intermediate is characterized by an elongated C1-C2 distance of 1.89 Å and an S-C bond distance of 1.91 Å. About half of the unpaired spin has now moved to the formyl moiety. This second intermediate
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Figure 7. Optimized structures of (A) CoA-SH active thiol group bound to the active site of PFL. (B) Transition state for hydrogen atom transfer from CoA-SH to the formyl radical anion. (C) The resulting CoA radical. (D) Transition state for acetyl group transfer between Cys418 and CoA radical.
(Intermediate II) is 5.3 kcal/mol lower than the first one (Intermediate I). By linear transit stepping calculations, the barrier between the two intermediates (TS4) could be estimated to ca. 3 kcal/mol. Intermediate II is reminiscent of the product compound found by Lucas et al.;13 its energy, structure, and spin characteristics are very similar. However, for the formyl radical anion to abstract a hydrogen atom in the following step, it has to dissociate completely from the acetyl species. The barrier for this dissociation (TS5) is estimated to ca. 2 kcal/mol, again from a stepping procedure. The energy after the complete dissociation goes down by 11.3 kcal/mol compared to Intermediate II. This quite large exothermicity originates to some extent from the fact that the models used, although representing the largest calculations so far, are still relatively small. We believe that the system is allowed to over-relax. Thus, if a much larger part of the protein surrounding is included, the energy will be higher, because the various groups will not move as much as in the current models. Another solution could be to freeze more centers to their X-ray positions, making the models more rigid. IV.d. Quenching of Formyl Radical Anion. On the basis of the previous DFT calculations,12 it was proposed that the was quenched by a cysteine residue (Cys419), with a calculated barrier and exothermicity of 1.1 and 14.1 kcal/mol, respectively,
for this hydrogen atom transfer step. In the next step, the Cys419 radical was suggested to abstract a hydrogen atom from CoASH (barrier 2.4 kcal/mol). This way, it was argued, the acetyl group transfer between Cys418 and the created CoA radical becomes energetically plausible, with a a quite reasonable barrier of 11.6 kcal/mol.12 In the present study, we have used the large models to examine these steps. Having released the formyl radical anion completely from the Cys418-acetyl moiety in the previous step, the hydrogen atom transfer from Cys419 to the formyl radical anion has an extremely low barrier here as well, only 0.3 kcal/ mol, and the reaction step is exothermic by 3.4 kcal/mol. The transition state (TS6) structure is displayed in Figure 6. IV.e. Acetyl Transfer to CoA. In the crystal structure of Becker et al.,6 PFL is crystallized in complex with both the substrate and CoA. However, the functional thiol group of CoA was found to point away from the active site. In the present study, we have tried to model the reactions leading to the acetylation of CoA. We have assumed that CoA is bound in such a way that its thiol group is in the proximity of the formyl radical. Accordingly, we placed a model of the active thiol group of CoA (CH3SH, also used in the previous theoretical study12) close to the newly formed formyl radical anion and we optimized the geometry. In these calculations,
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SCHEME 3: Modified Reaction Mechanism for Pyruvate-Formate Lyase Suggested in the Present Study
the glycine was removed from the model, since it is not directly involved in the reaction. The optimized geometry of this structure is shown in Figure 7A. We can immediately see that it is going to be quite difficult for the Cys419 radical to abstract a hydrogen from CoA, because they are quite far away from each other. We propose the following mechanism for the acetylation of CoA instead. Once the formyl radical anion is dissociated from the Cys418-acetyl moiety, it abstracts a hydrogen atom directly from CoA, instead of Cys419, as previously suggested and calculated. The calculated barrier for this is also extremely low, 0.2 kcal/mol, and reaction step is exothermic by 4.1 kcal/mol. The transition state structure and the resulting CoA radical intermediate are displayed in Figures 7B and 7C, respectively. Having created the thiyl radical at the CoA, the acetyl transfer from Cys418 is now quite facile. The calculated barrier for this step is 13.5 kcal/mol and the reaction is exothermic by 1.8 kcal/ mol. The optimized transition state structure (TS7) is shown in Figure 7D. IV.f. Regeneration of Glycyl Radical. At this point, CoA is acetylated, the formate product is formed, and the Cys418 radical is regenerated. The final steps of the catalytic reactions are to regenerate the glycyl radical by hydrogen atom transfers, first between Cys419 and Cys418, and then between glycine and Cys419. These steps are the reverse of the second and first steps, respectively. The barriers in the reverse direction are now 7.0 and 13.9 kcal/ mol, respectively. V. Conclusions We have, in the present paper, revisited the mechanism of pyruvate-formate lyase using much larger quantum models than in previous calculations. The models were based on the X-ray structure of Becker et al. and consist of up to 75 atoms. Based on the new calculations, we propose the slightly modified reaction mechanism shown in Scheme 3. This mechanism differs from the previously suggested mechanism in the following point. We propose that the formyl radical anion is quenched by hydrogen atom transfer directly from coenzyme A. This way, the acetyl transfer from the enzyme to CoA becomes energetically feasible.
The steps leading to the formation of the formyl radical anion are as before. The reactions start by two hydrogen atom transfer steps, first from Cys419 to the Gly734 radical and then from Cys418 to the Cys419 radical. The attack of the Cys418 radical on the pyruvate and the release of the formyl radical anion were found to occur in a stepwise fashion. Here, we find an interesting intermediate (called Intermediate II in the text above) in which the C-C bond of pyruvate is quite elongated (1.89 Å) but not completely broken. The calculated potential energy surface (PES) for the full reaction is presented in Figure 8.
Figure 8. Calculated potential energy surface for the reactions of pyruvate-formate lyase as suggested in Scheme 3. Steps 1R and 2R are the reverse of Steps 1 and 2, respectively.
Although the current calculations are the largest ones done for PFL so far, there are some aspects that still need to be addressed in future studies. The most important one has to do with the reversibility of the reaction. PFL catalyzes the reversible conversion of CoA and pyruvate into acetyl-CoA and formate. As seen from the PES (Figure 8), the rate-limiting step is to break the C1-C2 bond of the pyruvate substrate (TS4) and it is ca. 16 kcal/mol higher than the Cys418 radical intermediate. In the backward direction, however, the highest barrier is ca. 24 kcal/mol (the difference between the lowest point, Cys418 radical, and the highest point, TS4), which makes the reaction in the backward direction much slower than in the forward direction.
15354 J. Phys. Chem. B, Vol. 108, No. 39, 2004 This could originate from the fact that our models, because of their size and flexibility, overestimate the exothermic energy of some of the reaction steps. For example, the step where the formyl radical anion is released. We believe that with larger models, which include more of the surrounding protein matrix (using QM/MM methods for instance), this problem can be greatly diminished. Another unresolved issue is the stability of the Gly734 radical. We find the Cys419 radical to be more stable than the glycyl radical, mainly due to loss of planarity in the glycyl moiety. We speculated that PFL, upon activation (i.e., creation of the glycyl radical) allows some flexibility to accommodate a more planar glycyl radical at the tip of the loop were it is located. Finally, in the present study we have completely neglected the entropic effects. The frame-freezing scheme employed here introduces uncertainty in the calculated low vibrational frequencies, which are important in the evaluation of entropy. This prevents the calculation of accurate entropic effects. Acknowledgment. The Wenner-Gren Foundations is acknowledged for financial support. We also thank the NSC for computer time. References and Notes (1) Knappe, J.; Neugebauer, F. A.; Blaschkowski, H. P.; Ga¨nzler, M., Proc. Natl. Acad. Sci. U.S.A. 1984, 81, 1332. (2) Wagner, A. F. V.; Frey, M.; Neugebauer, F. A.; Schafer, W.; Knappe, J. Proc. Natl. Acad. Sci. U.S.A. 1992, 89, 996. (3) Knappe, J.; Albert, S.; Frey, M.; Wagner, A. F. V., Biochem. Soc. Trans. 1993, 21, 731.
Guo and Himo (4) Leppa¨nen, V.-M.; Merckel, M. C.; Ollis, D. L.; Wong, K. K.; Kozarich, J. W.; Goldman, A. Structure 1999, 7, 733. (5) Becker, A.; Fritz-Wolf, K.; Kabsch, W.; Knappe, J.; Schultz, S.; Wagner, A. F. V., Nature Struct. Biol. 1999, 6, 969. (6) Becker, A.; Kabsch, W., J. Biol. Chem. 2002, 277, 40036. (7) Eklund, H.; Fontecave, M., Structure 1999, 7, R257. (8) Himo, F., Biochim. Biophys. Acta. 2004, in press. (9) Bernardi, R.; Caronna, T.; Galli, R., Minisci, F.; Perchinunn, M., Tetrahedron Lett. 1973, 9, 645. (10) Brush, E. J.; Lipsett, K. A.; Kozarich, J. W., Biochemistry 1988, 27, 2217. (11) Plaga, W.; Frank, R.; Knappe, J., Eur. J. Biochem. 1988, 178, 445. (12) Himo, F. and Eriksson, L. A. J. Am. Chem. Soc. 1998, 120, 11449. (13) Lucas, M. F.; Fernandes, P. A.; Eriksson, L. A.; Ramos, M. J., J. Phys. Chem. B 2003, 107, 5751. (14) Becke, A. D., Phys. ReV. 1988, A38, 3098. (15) Becke, A. D., J. Chem. Phys. 1992, 96, 2155. (16) Becke, A. D., J. Chem. Phys. 1992, 97, 9173. (17) Becke A. D., J. Chem. Phys. 1993, 98, 5648. (18) Gaussian 98, Revision A.9; Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Zakrzewski, V. G.; Montgomery, Jr., J. A.; Stratmann, R. E.; Burant, J. C.; Dapprich, S.; Millam, J. M.; Daniels, A. D.; Kudin, K. N.; Strain, M. C.; Farkas, O.; Tomasi, J.; Barone, V.; Cossi, M.; Cammi, R.; Mennucci, B.; Pomelli, C.; Adamo, C.; Clifford, S.; Ochterski, J.; Petersson, G. A.; Ayala, P. Y.; Cui, Q.; Morokuma, K.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Cioslowski, J.; Ortiz, J. V.; Baboul, A. G.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Gomperts, R.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Andres, J. L.; Gonzalez, C.; Head-Gordon, M.; Replogle, E. S.; Pople, J.A. Gaussian, Inc., Pittsburgh PA, 1998. (19) (a) Barone, V.; Cossi, M., J. Phys. Chem. 1998, 102, 1995. (b) Barone, B.; Cossi, M.; Tomasi, J., J. Comput. Chem. 1998, 19, 404. (20) Jaguar 4.2; Schrodinger, Inc.: Portland, Oregon, 2000.
