Analysis of Catalytic Mechanism of Serine Proteases. Viability of the

J. Phys. Chem. B 2008, 112, 6837–6846

6837

Analysis of Catalytic Mechanism of Serine Proteases. Viability of the Ring-Flip Hypothesis Steve Scheiner* Department of Chemistry & Biochemistry, Utah State UniVersity, Logan, Utah 84322-0300 ReceiVed: NoVember 5, 2007; ReVised Manuscript ReceiVed: March 19, 2008

Quantum calculations are applied to the active site of serine proteases, including four specific residues and a water molecule, as well as a substrate and proton donors in the oxyanion hole. Residues are tethered to the protein backbone of an X-ray structure but otherwise allowed to move freely to their lowest energy positions. The viability of the ring-flip hypothesis, which proposes that a 180° rotation of the His-57 imidazole ring facilitates the catalysis, is assessed by comparison of energies of configurations both before and after such a flip. Specifically considered is the contribution to catalysis of the Ser-214 residue and a water molecule that is observed in the active site. The calculations provide detailed information concerning the nature, geometry, and strength of hydrogen bonds that are formed within the active site at each stage of the enzymatic mechanism. The serine proteases comprise a large family1 of enzymes, including chymotrypsin, elastase, and subtilisin among others. The enzymes share a number of features, but perhaps the most important is the presence of a so-called charge relay system, which includes a Asp-His-Ser triad of residues. The presence of the anionic aspartate acts through the intermediacy of the His imidazole ring to facilitate the ability of the Ser Oγ nucleophile to attack a C atom of the substrate. The His residue is thought to act in part by picking up a proton in one stage of the catalytic cycle and delivering it to another site later. The orientation of this His ring is thus very important for this process, leading to the concept2 of a “directed proton transfer”. This family of enzymes has been the subject of a number of theoretical and computational studies over the years, in order to better understand the catalytic mechanism. The earliest calculations were approximate in nature, making use of the semiempirical procedures that were permitted by technical limitations of that period.3,4 This work monitored the breaking of the scissile peptide bond in chymotrypsin and the ensuing reaction to products, including an emphasis on the detailed mechanism of the charge relay system. A later work5 dealing with the related papain enzyme indicated that the electric field generated by a neighboring R-helix might enable the full charge relay by pushing a proton up to the Asp-102 residue. On the other hand, some of the earliest ab initio calculations6 questioned whether the proton would indeed be fully transferred. The retention of the proton on the His residue was supported by later calculations7 that included specific interactions with the surrounding protein. Semiempirical and molecular mechanics calculations confirmed8 that it is the formation of the tetrahedral intermediate that is rate-determining not only for amides but for esters as well. The data were encouraging for theoretical investigations in that the essence of the reaction was able to be extracted from a reduced model that excluded most of the protein residing outside of the active site. Other calculations expanded the size of the system under study, considering larger segments of the protein via a different approximate method.9 It was found, as an example, that the replacement of aqueous solvent by a more complete treatment of the protein environment10 reduces the activation energy by * E-mail: [email protected].

7 kcal/mol. Another conclusion emanating from this work11,12 was the importance of an oxyanion hole that accommodates the O atom of the tetrahedral intermediate, which bears a partial negative charge. Another question addressed once again concerned whether the charge relay system in fact moves a proton up to the Asp-102 residue or if it remains on His-57. In contrast to some of the earlier work, Warshel et al. concluded there was no catalytic advantage to this particular transfer,11,13 which appeared to be energetically uphill. Other computations14,15 reinforce this idea, going further and explaining the prior NMR chemical shifts16,17 without recourse to such a proton transfer. Other work has attempted to understand why certain substrates react much more readily with the enzymes than others, focusing in one example18 on a trypsin inhibitor. Another area that has been pursued is the effect of point mutations on the catalytic mechanism and rate.7,19 The more recent idea that a low barrier hydrogen bond (LBHB) between the Asp and His residues may speed up the catalysis has been discussed in recent years. Some consensus has emerged for the idea that such a notion is not necessary to explain experimental data;13,20,21 moreover, the distance separating the Asp and His residues may in fact be too long22 for such a bond in any case. Calculated and experimentally determined NMR parameters15,20,23 have also been used as a window into this question of proton position. An interesting possibility that has emerged of late24 concerns the participation of the Cε1H of His-57 in a H-bond to Ser-214 that was proposed in 1994,25 along with some ideas as to how this interaction might facilitate the catalysis. There are indications26 of such an interaction, but the energetic contribution to catalysis has not been assessed to date. NMR measurements by Bachovchin et al.27,28 supported this H-bond and reaffirmed that the interaction could be an important functional component of R-lytic protease, subtilisin, and other related enzymes. Indeed, their assessment led them to the innovative suggestion that a 180° rotation of the His-57 ring might be an integral part of the catalytic process, proposing a so-called “ring-flip” mechanism. The basic structural elements of the ring-flip mechanism are illustrated in Figure 1, which depicts the residues that lie in the active site. Configuration A in the upper left panel refers to the initial geometry, prior to the binding of the substrate in the active site. The charge relay system of Asp102 anion, His-57, and Ser-195 is supplemented by the Ser-

10.1021/jp710617w CCC: $40.75  2008 American Chemical Society Published on Web 05/08/2008

6838 J. Phys. Chem. B, Vol. 112, No. 22, 2008

Figure 1. A-D configuration labels involved in the ring-flip hypothesis. B and D refer to configurations that follow the formation of a tetrahedral intermediate, adapted from ref 27.

214 residue and a water molecule that lies in the active site. Upon binding of the substrate, proton transfer from Ser-195 to His-57, and the attack of the serine oxygen atom on the scissile peptide, one arrives at the tetrahedral intermediate (TI) of configuration B. At either stage, a “flip” of the imidazole ring of His-57, i.e. an approximate 180° rotation around the Cβ-Cγ bond indicated, can occur, leading to configurations C and D, respectively. As proposed, all four potentially H-bonding sites of the Im ring do in fact engage in H-bonding in configurations A, B, and D. However, the unprotonated Nε2 of configuration C is unable to form such a bond with the Ser-214 carbonyl, thereby destabilizing C relative to A. As a result, the ring flip in the initial stage, AfC, is supposed to require more energy than does the same flip in the TI (BfD) stage. It is important to stress that this mechanism is based on the premise that CH groups can participate in H-bonds, even if perhaps weaker than NH donors. The better ability of the Im ring to lie in its rotated position in the TI is claimed to be important, as the His is then well-suited to push the reaction onward toward the next step of the catalytic cycle. These ideas have witnessed a certain amount of support in the observation29 of a rotated Im ring in subtilisin, combined with 50% DMF at low pH. A more recent study30 found the flipped arrangement of His-57 to be more stable than the unflipped conformation, albeit in a Asp102fAsn mutated form of the enzyme. On the other hand, there is some dispute as to whether the NMR evidence originally presented for a ring flip was interpreted correctly21 With specific regard to the ideas contained in the ring-flip hypothesis, calculations have not addressed this issue in a definitive fashion. Some have argued it is not a necessary component of the catalytic mechanism22,24,26,31,32 but have not attempted to directly assess its actual viability with any confidence. As an example, the time scale relevant to a recent dynamics calculation24 was not long enough to have allowed for a ring flip, even should it be a valid component of the mechanism. On the whole, then, researchers have not been able to provide an unambiguous answer to the question of His-57 motions and their contribution to catalysis.1,2 This ring-flip hypothesis contains a number of implicit assumptions that warrant detailed scrutiny. In the first place, what are the relevant energetics? For example, how much energy

Scheiner does it take to flip the His ring, and does this quantity in fact become smaller after the TI has been formed? Are there energy barriers to ring-flipping of the right magnitude: the absence of a barrier would lead to the immediate decay of a ring-flipped conformer before it can act in a catalytic fashion; too large a barrier would prevent the ring from flipping at all. Are the H-bonds presumed to form in Figure 1 actually present? For example, can the TI in configurations B and D truly reach around so as to form H-bonds with both the CH and NH donors of the His-57 ring? And, if present, are these H-bonds strong enough to play a catalytic role? How important is the presence of the water molecule? Similarly, would the catalysis occur as efficiently were there not a connection between the Cε1H of His57 and Ser-214? Derewenda et al.25 had pointed out the difficulty of examining this question by experimental means, as the latter is part of the protein backbone and is thus not amenable to point mutation. As a point that augurs well for a detailed study, computations of the serine proteases R-chymotrypsin and R-lytic protease23 indicate that some of the most important geometric parameters of these enzymes are nicely reproduced by theoretical calculations. The present work considers these questions directly, thereby assessing the viability of the ring-flip mechanism. At the same time, the calculations described below offer some insights into the mechanistic contributions of certain groups, such as Ser-214 and the water molecule. The work also provides detail about the particular arrangements of the various residues at each step during the catalytic cycle and locates any H-bonds that are present, including potential CH · · · X interactions that have been suggested to constitute an important ingredient25,27,28 in enzyme activity. And in the latter context, it is important to stress that the calculations are carried out here at the full ab initio level, with a polarized basis set, which has proven far superior to molecular mechanics and force field approaches in terms of accurately and reliably treating hydrogen bonds, which are such an essential ingredient of this enzyme’s activity. This greater reliability of ab initio techniques is amplified in dealing with the unconventional CH · · · O interactions that have been hypothesized to be important for the serine proteases, but which are typically completely ignored by force field models. Methods and Models The first issue to be addressed concerns a selection of model groups that can adequately represent the functional components of the various residues in the enzyme’s active site. The functional part of the Asp-102 residue consists of its carboxylate group, so this residue was represented by a CH3COO- anion. The His-57 residue was approximated by a methylimidazole molecule, again containing the entire functional unit of this catalytic residue. Similarly, the hydroxyl group of Ser-195, was modeled by a CH3OH molecule. The peptide oxygen atom of Ser-214 ought to be well approximated by a molecule of formamide, which contains a full peptide functionality, and likewise for the peptide substrate. A second crucial question concerns where to situate these various groups so as to best model the structure of the enzyme, while the groups are permitted to move as they might during the catalytic cycle. On one hand, full geometry optimization of the assembly of all these groups would not be appropriate, as it would take the various groups far afield from their positions within the enzyme, where they are held in place to some degree by the scaffold of the protein. At the opposite extreme, freezing the positions of all the non-H atoms in their X-ray coordinates would not permit the side chain motions at each stage of the catalytic cycle. Moreover, this prescription would also lead to

Catalytic Mechanism of Serine Proteases poor internal bond lengths and angles due to the inaccuracies inherent in the X-ray structure determination. The procedure chosen attempts to use the X-ray geometry as a general scaffold that holds the various residues in place to some degree, preventing them from migrating too far afield from their positions in the protein. The protein backbone was considered here to be rigid, but the side chains were permitted full flexibility as they might achieve within the context of the enzyme. To that end, the 1.7 Å-resolution crystal structure of R-lytic protease33 was taken as a starting point, as a representative structure of the protein. The CR atom of each residue, part of the protein backbone, was used to anchor each residue in place, by fixing this atom to its X-ray coordinates and holding it there. For the three catalytic residues, whose side chains participate in the reaction mechanism, the second anchor atom chosen was Cβ. Together, the CR and Cβ atoms comprise an axis about which the catalytic side chain groups can rotate freely. In the case of His-57, for example, the CR and Cβ atoms were superimposed precisely on their X-ray coordinates. All other aspects of the methylimidazole model were optimized, allowing the imidazole ring the same free movement, i.e. displacement and rotation of its γ, δ, and ε atoms, it would acquire within the enzyme itself. Similarly for Asp-102, this prescription permitted free motion and/or rotation of the entire CγO2segment around its pivoting CR-Cβ axis, as was also the case for the catalytic -OH group of Ser-195. In the case of Ser214, since it is the peptide group itself that interacts with the His-57, the O and N atoms of the peptide group, together with CR, were used as anchors. This general procedure of fixing certain atoms of residues within an active site, within the framework of an experimental structure, finds a number of precedents in the literature. It was used recently, for example, to help elucidate34 the mechanism of human butyrylcholinesterase, an enzyme that bears certain similarities to the serine proteases. This same group of workers simulated the interior of the protein via a dielectric continuum model, as is carried out here as well. These sorts of molecular models and geometrical restraints are also consistent with many of the schemes used by other researchers working with these enzymes15,20,35 and others.36 There were a number of refinements that were added to this basic model as follows. Since the model of His-57 is methylimidazole, the C atom of the methyl group corresponds to the Cβ atom of His. While the latter atom can be left intact as carbon, CR has been replaced by a H atom of the methyl group. This “HR” atom was of course permitted to move closer to Cβ during the optimization, but it was restricted to the original CRCβ axis. All other aspects of the methylimidazole were optimized, allowing the imidazole species the same free movement, and internal adjustments, it would acquire within the enzyme itself. Likewise for Asp-102, the CR atom of the actual residue is replaced by one of the methyl H atoms of the acetate model. Again, the C-H bond length is optimized, but the H atom is restricted to the original CR-Cβ axis. The same prescription is used for the methyl group of the methanol model of Ser-195, containing Cβ and a H replacing CR. Finally, in order to avoid the use of distorted bond lengths resulting from inaccuracies in the X-ray data, the C-O and C-N distances of the formamide model of Ser-214 were allowed to vary during the optimizations, holding the CR-O and CR-N axes intact in their X-ray directions. Unless specified otherwise, all other geometrical parameters of the systems were fully optimized. It is anticipated that this procedure allows the quantum calculations to achieve the lowest-

J. Phys. Chem. B, Vol. 112, No. 22, 2008 6839

Figure 2. Geometries optimized for the model active site of R-lytic protease. H-bond distances reported in Å. Asterisks indicate those atoms held in place during the optimization, in X-ray positions (see the text for more details). TI refers to the tetrahedral intermediate in configurations B and D.

energy structures, while remaining faithful to the geometrical restrictions that result from the overall protein structure itself. Since X-ray diffraction experiments cannot unambiguously determine proton position, the position of the His-57 Hδ1 proton is an important and potentially thorny issue. In order to account for a possible double-well potential for the transfer of this proton to Asp-102, optimizations were carried out using two separate starting points, one with this proton on His-57 and another with it located on Asp-102. With regard to the quantum calculations themselves, it was necessary to identify a procedure that permits the very time consuming geometry optimizations of the large systems while providing a sufficiently flexible basis set to accurately reproduce the energetics. The polarized 6-31G* basis set was applied to this purpose. Geometry optimizations were carried out at the Hartree-Fock level. In order to assess the reliability of this level of theory, additional calculations were carried out at the correlated MP2 level, with the somewhat larger and more flexible 6-31+G** basis set. The effects of displacing these systems from an in vacuo situation to a polarizable environment more akin to the interior of a protein were assessed via the PCM37–39 approach, which places the system within a realistically shaped cavity, hollowed out of a dielectric medium characterized by dielectric constant ε. Calculations were executed via the Gaussian 0340 set of codes. Results Geometry optimizations under the conditions described above were carried out first for the initial configuration A of the system, and the structure obtained is exhibited in the upper left portion of Figure 2. Due to the importance of H-bonds to the mechanism of this class of enzymes, the relevant H-bond lengths are included in this figure and those that follow. Asterisks are affixed to those atoms that were held fixed in place during these optimizations (see above). One of the most important H-bonds present in configuration A connects the Asp-102 anion to Nδ1H of His-57 with a rather short R(O · · · H) distance of 1.76 Å. The shortness of this bond

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Scheiner

TABLE 1: Energy (kcal/mol) Required To Flip His-57 Ring AfC HF/6-31G* HF/6-31+G** MP2/6-31+G** ε)4 ε ) 47

(a) Four Protein Residues 17.7 23.4 15.5 20.6 19.7 22.4 7.9 18.8 7.0 20.4

HF/6-31G* HF/6-31+G** MP2/6-31+G** ε ) 47

(b) Water 21.6 19.2 24.4 8.8

HF/6-31G* HF/6-31+G** MP2/6-31+G** ε ) 47

(c) Ser-214 21.4 19.9 25.0 8.9

HF/6-31G* HF/6-31+G** MP2/6-31+G** ε)4

BfD

(BfD) - (AfC) 5.7 5.1 2.7 10.8 13.4

Added 16.0 14.5 13.4 15.9

-5.6 -4.7 -11.0 +6.4

Deleted 24.7 23.6 23.3 20.2

+3.3 +3.7 -1.7 +11.3

(d) Idealized Constraints 31.5 15.7 28.4 15.0 39.5 17.5 8.9 5.8

-15.8 -13.4 -22.0 -3.1

can likely be attributed to the anionic nature of Asp-102, which would tend to strengthen and shorten any such interaction. Displacement of the Nδ1 hydrogen to the Asp-102 residue, followed by reoptimization, results in a local minimum, but one that is higher in energy than configuration A by 11 kcal/mol. The other H-bonds are more typical of neutral systems: The unprotonated Nε2 atom accepts a proton from the hydroxyl of Ser-195, of length 2.09 Å, and the peptide O atom of Ser-214 forms the anticipated H-bond with the Cε1H. This bond is fairly short at 2.30 Å, but on the other hand, it is quite nonlinear with a θ(CH · · · O) angle of 132°. Another probably weak H-bond occurs between the other O atom of Asp-102 and one of the methylene H atoms of the His-57 residue. The H · · · O separation is 2.47 Å, and the θ(CH · · · O) angle is 151°. (It is worth stressing that this particular CH proton is present not only in the methylimidazole model, but also in the full His residue, so the H-bond is not an artifact of the modeling.) Configuration C arises by rotating the imidazole ring of His57 180° about the Cβ-Cγ axis to create a starting point, and then reoptimizing the geometry of the entire system under the same constraints as in A. As is evident in the upper right portion of Figure 2, the Asp-102 is no longer able to interact with the Nδ1H; its substitute H-bond with Cδ2H is nearly a full angstrom longer, and presumably much weaker. The Ser-195 residue is able to maintain its OH · · · Nε2 contact, as this is the strongest H-bond in this configuration, and the His-57 adjusts itself so as to maintain it. Having lost contact with the Cε1H of configuration A, Ser-214 instead forms a weak interaction with the Cδ2H. But the latter H-bond is quite long, with R(H · · · O) more than 3 Å, so any stabilizing effect is questionable. Configuration C is 17.7 kcal/mol higher in energy than A, so this quantity represents the energetic cost of the ring flip, as reported in the first row of Table 1. Enlarging the basis set to 6-31+G** lowers this value by 2 kcal/mol, but including correlation has the opposite result of raising it. Consequently, the MP2/6-31+G** AfC ring flip energy is 19.7 kcal/mol. Overall, this quantity is fairly insensitive to details of basis set or inclusion of electron correlation. A large fraction of the destabilization of C vs A can be attributed to the replacement of the very strong Asp-102 anion · · · Nδ1H interaction by a much weaker H-bond with a CH group of the His-57. Configuration

C leaves the Nδ1H group without a proton acceptor, an energetically costly situation. It may be noted, however, that surrounding the system with a polarizable medium, whether ε ) 4 or 47, preferentially stabilizes configuration C, lowering the ring-flip energy below 8 kcal/mol. As the catalytic mechanism proceeds, the Ser-195 donates a proton to His-57, while attacking the C atom of the peptide substrate, forming a tetrahedral intermediate (TI). Taking HCONH2 as a model substrate, the latter intermediate is modeled in the calculations by a CH3O-CHONH2- anionic species. The entire system at this point of the catalytic cycle thus contains this tetrahedral intermediate, a protonated His-57, and the Asp-102 anion, plus the Ser-214 whose peptide group is in position to interact with the His residue. Alternately, a transfer of the proton from the Nδ1 atom of His-57 to Asp-102 would neutralize both of these residues. The same atoms of each residue were tethered to their polypeptide backbone as above and are illustrated in configuration B of Figure 2 by the asterisks. The enzyme contains an “oxyanion hole”, which stabilizes the developing negative charge on the O atom of the scissile peptide as it forms the tetrahedral intermediate. In order to remain faithful to the enzyme structural restraints, this O atom was fixed at the coordinates it attains within the crystal structure that corresponds to the tetrahedral intermediate. It should be reiterated that there were no constraints placed upon the Nδ1H proton, which was free to transfer across to the Asp-102 anion. Indeed, an optimization of the B configuration in which the His proton has been transferred to Asp-102 results in a slightly lower energy, so it is this structure that is illustrated in the lower left segment of Figure 2 as configuration B. It may be of interest that the neutral Asp-His pair depicted as B in Figure 2, is only marginally more stable than the anion-cation pair, by between 1 and 3 kcal/mol, depending upon the level of theory, so the proton transfer between these two residues is almost thermoneutral. The OH · · · N H-bond connecting Asp-102 with His-57 in B contains a R(H · · · N) distance of 1.86 Å; the Ser-214 moves in to within 2.21 Å of Cε1H. The latter bond is distorted from linearity by 40°, limiting any potential stabilizing influence. The Nε2H finds two proton acceptors on the tetrahedral intermediate anion, most notably the N atom, which lies within 1.85 Å and a θ(NH · · · N) angle of 168°. Rotation of the His-57 Im ring by 180°, followed by geometry optimization, leads to structure D in Figure 2. (This structure would be highly destabilized were the Hδ1 to remain on the Asp-102, so the system is most stable as the Asp- · · · His+ · · · TItriad.) The His rotation leaves the Asp-102 anion able to interact only with the pair of CH donors, just as in configuration C. One of these bonds is particularly strong, with R(H · · · O) ) 1.92 Å and θ(CH · · · O) ) 171°. The Nε2H is displaced from the tetrahedral intermediate anion, which is replaced by the Ser214 carbonyl O. The latter TI forms a pair of H-bonds to the Cε1H. These H-bonds are significantly shorter than typical CH · · · X bonds, due presumably to the cation · · · anion interaction here. In energetic terms, the cost of the ring flip in the tetrahedral intermediate stage, i.e. BfD, is computed to be 23.4 kcal/mol at the HF/6-31G* level, about 6 kcal/mol higher than the corresponding AfC ring flip. Further perusal of the energetics in the uppermost section of Table 1 illustrates that this 6 kcal/ mol difference is fairly constant in the face of a larger basis set and is lowered by 3 kcal/mol after inclusion of electron correlation. In short, the calculations suggest that the cost of a ring flip is roughly 15-23 kcal/mol, at any level, and is somewhat higher after the TI is formed than before. The next

Catalytic Mechanism of Serine Proteases

Figure 3. Geometries optimized with water added to the enzymatic system.

two rows of Table 1 indicate that immersion of the system in a dielectric continuum, better approximating the interior of the protein, lowers this AfC ring-flip energy to less than 8 kcal/ mol, while having a much smaller effect on the BfD flip. The value of ε ) 4 was chosen as one commonly accepted approximation to the interior of a protein.41–45 The higher value of 47 was employed as well so as to be sure that a more polarizable model of the enzyme would not affect the results by much. In fact, the precise value of the dielectric constant, whether 4 or 47, is largely irrelevant. What does hold constant is the larger ring-flip energy after formation of the TI, by an amount of about 11-13 kcal/mol within a dielectric medium. Water Molecule. One of the factors that mitigates against the flipping of the His-57 ring would appear to be the “unsatisfied” Nδ1H proton donor after the flip has occurred in configurations C and D. The crystal structure does contain a water molecule that could act as an acceptor for this group, so an additional set of parallel computations was carried out in the presence of this water molecule. In particular, the initial coordinates for this water were taken from the X-ray structure of R-lytic protease (specifically water number 53 from that structure). Importantly, there were no constraints placed upon the position or orientation of this water molecule, so it was completely free to move about. The resulting configurations, including salient H-bond lengths, are displayed in Figure 3. Note that in configuration A the water is not satisfied to accept a proton from the weak donor Cδ2H group but instead moves down toward the Ser-195 methanol model. In that location, the water can donate protons to both the Ser-195 O and the His-57 Nε2 acceptors simultaneously, both with R ) 2.3 Å. In contrast, there is a much weaker Cδ2H · · · Ow contact in configuration B. This bond is rather long, at 2.62 Å, and the water forms a stronger H-bond with the N atom of the TI, with R ) 2.21 Å. As anticipated, the water plays perhaps a more direct role in configurations C and D, where it can accept a proton from the Nδ1H, with H-bond lengths of 2.24 Å (C) and 1.94 Å (D). The shorter bond in the latter case is likely due to the positive charge on the Im ring. The water in D acts as a charge bridge from the cationic His-57 to the negatively charged TI. In terms of the geometry perturbations of the four-residue system caused by the presence of the water, comparison of Figures 2 and 3 indicates relatively minor changes. In configuration A, for example, H-bond lengths are altered by less than 0.02 Å; configuration C is also affected only to a minor degree.

J. Phys. Chem. B, Vol. 112, No. 22, 2008 6841 The water in configuration B donates a proton to the anionic TI, thereby ameliorating its negative charge. As a result, the NH · · · N bond between the His and TI is lengthened significantly, from 1.85 to 1.98 Å. In D, the water also accepts a proton from the Nδ1H, simultaneously reducing the positive charge on the His-57 while lowering the negative charge on the TI. This combined effect lengthens the Cε1H · · · N H-bond length by 0.3 Å. The effects of the water molecule upon the ring-flip energetics may be deduced by comparison of sections a and b of Table 1. The AfC flip requires about 4 kcal/mol more energy after the water has been added. This increase may be attributed to a competition between opposing effects. The water’s presence undoubtedly stabilizes configuration C by providing a proton acceptor for the Nδ1H of His-57. On the other hand, this same water stabilizes configuration A by even more, via the H-bonds it is able to form, not only with Nε2 of His-57 but also with the Ser-195 O atom. A calculation confirms this idea, as the interaction energy of the water molecule with the remainder of the system is 8 kcal/mol in A but only 4 kcal/mol in C. In contrast, the water molecule lowers the BfD ring flip energy by some 6-9 kcal/mol. This result makes sense in that the water is able to accept a proton from either the Cδ2H (in B) or the Nδ1H (D), and the latter is clearly more important, especially given the positive charge of the Im ring. Energetics again confirm this supposition, as the interaction energy of the water with the rest of the system jumps from 8.0 kcal/mol in B to 13.7 kcal/mol in D. The last column of Table 1 illustrates the comparison of the ring flip energetics in the initial (AfC) stage of the catalytic cycle, as compared to the later (BfD) stage. Without the water, the ring flip is more costly in the second stage (hence the positive entries in the last column) by some 2-6 kcal/mol, more if in polarizable medium. However, after the water has been included, the ring flip is considerably more facile in the second stage, by as much as 11 kcal/mol. The sign of this last quantity is positive when the system is immersed in a dielectric continuum, modeling the protein interior. Nonetheless, even this positive value of 6.4 kcal/mol is significantly smaller than the 13.4 kcal/ mol when the water is absent. In other words, considering the situation wherein all relevant groups are placed within the active site of the enzyme, the ring flip is always energetically uphill. However, the energy required for this flip is very significantly lower in the tetrahedral intermediate stage of the catalytic cycle than in the prior stage, before the attack of the Ser-195 upon the substrate. The exception to this observation pertains to immersion in a polarizable environment, wherein the BfD ring flip requires more energy than does AfC. Contribution of Ser-214. There has been a good deal of discussion concerning the import of the Ser-214 residue and how it might influence the catalysis. This issue was addressed by carrying out the calculations of the active site in the absence of this residue. The associated geometry optimizations, carried out under the same restrictions upon the backbone atoms of the various residues, led to structures that are generally similar to those depicted in Figure 3, but there were a number of differences. For example, in configuration A, the water molecule swings down away from the His-57 Nε2 atom, forming a tighter OH · · · O bond with the Ser-195, which in turn strengthens and shortens the Ser-195 · · · His-57 H-bond. This change sacrifices little as the Nε2 was serving as double acceptor in A, a generally unfavorable situation. There is very little adjustment in the C configuration connected with the deletion of Ser-214. It is consequently not surprising to note that the energetics of the

6842 J. Phys. Chem. B, Vol. 112, No. 22, 2008 AfC flip are little affected by the absence of this residue at any level of theory. The B and D TI configurations undergo fairly minor geometry changes when Ser-214 is removed. D is scarcely affected at all, whereas removal of this Ser residue causes some readjustment of the TI relative to the His-57. The O atom moves in a little closer to the Nε2H donor, but the TI N atom moves further away by some 0.4 Å. Section c of Table 1 lists the energetics of the process after the Ser-214 has been deleted. The values for the AfC process are essentially unchanged from the quantities reported above, so the Ser-214 has little effect upon this ring flip. This similarity belies any importance of this residue at this stage of the catalysis, before the TI has been formed. On one hand, there does appear to be a H-bond between Ser-214 and Cε1H in the A configuration, with R(H · · · O) ) 2.30 Å, and the serine has no notable interactions at all in configuration C. The favorable interaction in A would lead one to anticipate that its removal, via deletion of Ser-214, ought to lower the AfC energy difference. However, the elimination of this bond, via removal of Ser-214, has little effect upon the AfC energetics, suggesting no energetic consequence. Indeed, the interaction energy between this residue and the remainder of the system indicates no H-bonding energy, in either the A or C configurations. The situation is different after TI formation, where the loss of the Ser-214 residue raises the BfD ring flip energy by some 8-10 kcal/mol. The obvious reason for this rise has to do with the group with which Ser-214 is interacting in the two configurations. Of course, the loss of the Cε1H · · · O H-bond in configuration B is unfavorable, but this effect is overshadowed by the even greater instability that occurs when the Nε2H+ · · · OdC H-bond in configuration D is removed. A computation suggests that this particular interaction requires some 4-5 kcal/mol in order to break. The net result is that the Ser-214 residue plays an important role in facilitating any ring flip after, but not before, TI formation. In sum, the entries in the last column of section c of Table 1 tend to be positive, especially within a dielectric medium. Other Factors. There were other lessons learned via these calculations concerning the enzyme mechanism. For example, the oxyanion hole plays an important role, not only in terms of energetics and charge stabilization but structurally as well. When the O atom of the substrate was not held fixed in the oxyanion hole, it tended to move toward the Nε2H of the protonated His57 and then remove this proton from the latter residue, thereby short-circuiting the entire mechanism. Even if the proton in question is forced to remain on the His residue, keeping the latter positively charged, the mobile O atom of the TI becomes a better proton acceptor for the Nε2H than either the Ser-195 O or the N atom of the scissile peptide. A second issue that was examined has to do with the overall charge state of the entire catalytic system. If one more proton is added to the system, the A state consists of the original Asp102 carboxylate anion, neutral methanol, and formamide, but now a protonated ImH+ cation replaces the original neutral Im species. In the A configuration (prior to ring flip), the Nδ1H proton migrates across to the Asp-102, neutralizing both this residue and the His. However, after the ring flip, the His-57 remains protonated in configuration C, leaving the Nε2H to form a H-bond with the O atom of the Ser-195 residue. The preferential stabilization of configuration A leads to a very high energetic cost, 30 kcal/mol, for ring flipping. This value remains high, around 20 kcal/mol, even when the system is placed within a dielectric medium.

Scheiner

Figure 4. Geometries optimized with greater flexibility and idealized restraints as described in text.

Likewise, one might wonder how the process might be affected by a change in protonation state at the TI stage. Removing a proton from the His-57 leaves a neutral Im separating carboxylate and TI anions. This change grossly stretches the Nδ1H · · · O H-bond between these two residues, by 0.7 Å, in configuration B, as well as a like elongation of the Cε1H · · · O bond to the Ser-214. The N lone pair of the now deprotonated Nε2 atom is occupied by one of the NH atoms of the TI. The D configuration is destabilized by the absence of a H-bonding partner for either His N atom, leaving the two anions to form bonds with CH groups only. Since both B and D are destabilized by similar amounts, the overall BfD ring flip energy is affected by only a small amount by the deprotonation, rising by some 1-3 kcal/mol. Another issue that was considered here had to do with the specific locations of the various residues. As discussed above, each of the catalytic residues had been anchored to the backbone as determined from an X-ray structure. It was considered of some interest to examine the catalytic effect exerted by the protein backbone purely through its securing the groups in these particular positions. One means of addressing the question might be to remove all structural restraints and fully optimize all parameters of each configuration. However, such a prescription would lead to nonrelevant motions and interactions. For example, with no restraints at all, the Ser-214 model translates and reorients itself so as to form a CH · · · O H-bond with the Asp-102 anion in configuration A. It would appear, therefore, that a certain number of judiciously chosen restrictions are necessary in order to correctly simulate the enzyme situation. In order to probe the question further, a flexible model was adopted, but one in which restrictions are applied only to prevent motions that would obviously be prohibited within the enzyme. In general, H-bonds were held to be linear so as to prevent largescale motions of the residues. The aforementioned problem with Ser-214 migration was prevented by placing the carbonyl O of Ser-214 so that its CdO axis was collinear with the Cε1H axis of His-57 in configuration A. After the ring flip, repulsion with the unprotonated Nε2 of His-57 in configuration C pushes the serine away. Likewise in configuration C, one O of Asp-102 was held along the Cδ2H axis and the Ser-195 O along the Cε1H axis. Similar linearities were imposed after formation of the TI state, as indicated in Figure 4. (The freedom to deviate from the X-ray backbone also permitted some slight adjustments of models of the various residues as follows. Since the C atom is

Catalytic Mechanism of Serine Proteases no longer needed to hold Ser-214 in place, the carbonyl O was represented by H2CO rather than H2CNHO; methylimidazole was replaced by imidazole for a similar reason.) The energetics obtained with these idealized constraints are displayed in the bottom section of Table 1. The AfC flip is obviously highly disfavored by some 28-40 kcal/mol, but this quantity is lowered to 8.9 kcal/mol in dielectric medium. The BfD transition is also disfavored but less so, by a factor of about half. Consequently, the negative entries in the last column of Table 1 illustrate that the flip is considerably facilitated after the TI has been formed, with or without a dielectric medium. One may wonder how the ring flip might accelerate or inhibit the enzymatic reaction itself. In other words, how does the flipping of the ring affect the energetics of the formation of the tetrahedral intermediate, after the substrate has been bound? This TI formation, according to Figure 1, represents the AfB transition if the His-57 has not flipped and the CfD transition if the flip has occurred. The relevant [E(D)-E(C)] - [E(B)-E(A)] quantity can be rearranged to [E(D)-E(B)] - [E(C)-E(A)], which is reported explicitly in the last column of Table 1. As discussed above, one can conclude from the signs of the quantities in the table that the ring flip acts to catalyze the TI formation only when the water molecule is present (section b of Table 1). The opposite effect, that the ring flip makes the TI formation more difficult, is associated with removal of the water (section a) or Ser-214 (section c). By adding a formamide molecule model substrate to configurations A and C, one can directly compare their energies to B and D, respectively. In keeping with the geometric prescription used for B and D, the O atom of this formamide substrate was fixed in the oxyanion hole and held there; the rest of the molecule was free to move as needed. It was found that the energy required to take the initial structure A to the TI B was essentially identical to this same quantity following a His-57 ring flip (CfD). Hence, the ring flip does not enhance the accessibility of the tetrahedral intermediate from the original configuration, and in that sense the ring-flip hypothesis is not an effective means of speeding up the catalysis. The peptide groups of Ser-195 and Gly-193 serve as proton donors to the carbonyl O atom of the tetrahedral intermediate, acting to partially neutralize its negative charge in the so-called oxyanion hole. To this point, the effect of this oxyanion hole has been taken into account only in a geometric sense. That is, the oxyanionic O atom was tethered to the location it occupies in the X-ray structure, but the proton donors that interact with this O atom in the enzyme were absent. In order to simulate the energetic effects of these proton donors, and following the example of Kollman et al.,8 water molecules were added to the model as proton donors. The O atoms of the two waters were placed precisely in the positions where these two peptide group proton donors occur in the X-ray structure, but the positions of the two H atoms on each water were allowed full geometric freedom, so as to maximize their stabilizing interactions with the oxyanionic O of the tetrahedral intermediate. The B and D configurations were of course stabilized by the H-bonds to these proton donors. On the other hand, this stabilization is very nearly equal for the two structures, so that the BfD ring-flip energy is essentially unchanged (varying by only 1 kcal/mol) by adding this more complete treatment of the oxyanion hole. One may thus conclude that the more thorough treatment of the oxyanion hole does not alter any of the conclusions above. Discussion One of the prime issues concerns how the data computed here conform with the notion of a His-57 ring flip. It is first

J. Phys. Chem. B, Vol. 112, No. 22, 2008 6843 clear that for all situations examined the flipping of this ring is energetically uphill. However, the central thesis of the proposal was not that the flip would make the system more stable, simply that the flip was not overly endothermic. The results are inconclusive in this regard. The flip energies are rather high in the isolated systems, in some cases more than 20 kcal/mol. They tend toward lower values when immersed in a polarizable environment, but even here, some of the flip energies may exceed 15 kcal/mol. It is worth stressing that the ring finds a local minimum after it has flipped, which would tend to stabilize it in this position for a certain length of time. In order to examine whether the flipped conformation has a finite lifetime and will not instantly rotate back to its normal position, at lower energy, calculations were performed in order to assess the height of the energy barrier for this His-57 rotation. It was determined that the energy barrier that the system must overcome in order to convert from conformation C to A is 5 kcal/mol; i.e., this quantity separates the flipped from the unflipped structure. This quantity is consistent with a barrier of 2.2 kcal/mol computed by a QM/ MM technique, which explicitly includes the effects of residues surrounding the active site.30 After the tetrahedral intermediate has been formed, this same quantity for the DfB conversion rises a bit to 10 kcal/mol. It seems clear that the barriers are large enough so as to hold both the flipped C and D conformers for a reasonable duration. Bachovchin et al.27,28 had emphasized the idea of a “reactiondriven” ring flip by which it was meant that this flip is more favorable energetically after the TI has been formed than before. And indeed, in the full configuration, which includes all four residues plus the water molecule, the TI BfD flip is less energetically costly than is AfC. The last column of Table 1 places this favoring of the TI ring flip in the 5-11 kcal/mol range. As an important contrast, however, when the system is placed within the context of a polarizable medium, the BfD conversion is more endothermic than is AfC, in contrast to the basic premise of the ring-flip hypothesis. The upper portion of Table 1 suggests that any reduction in ring-flip energy following TI formation relies on the presence of the water molecule; in its absence, the cost of rotating the ring is uniformly higher after the TI has been formed. The presence of the Ser-214 residue had been conceived to be an integral component of the ring-flip hypothesis. While comparison of sections b and c of Table 1 indicates that this residue has little effect upon the energetics of the AfC ring flip, it clearly lowers the endothermicity of the post-TI BfD flip, so in this sense it may be important to the ring-flip hypothesis. On the other hand, the Ser-214 does not appear to act in the manner originally envisioned. The only H-bond in which this residue engages, of any energetic consequence, occurs in the D conformation. One last point concerns the water molecule. Bachovchin et al. had presented a picture wherein the water is present prior to TI formation but is absent thereafter. If this were indeed the case, then one would compare the AfC column of the “water added” segment b of Table 1 with the “four protein residues” BfD section a above it. In this comparison, the ring flip is indeed less costly after the TI has been formed, but by a narrower margin than if the water is present throughout. For example, the MP2/6-31+G** [(BfD) - (AfC)] energy difference is -2.0 kcal/mol when water is removed in the TI stage, as compared to -11.0 when water is present throughout. Bachovchin et al. had proposed that an important parameter for their ring-flip hypothesis would be the relative proportions

6844 J. Phys. Chem. B, Vol. 112, No. 22, 2008 TABLE 2: Dihedral Angles (deg) HRCβCγNδ1-57

HRCβCγO-102

HRCβOγH(C)-195

A C B D

-98.7 68.3 -110.2 70.3

(a) Four Protein Residues -129.2 -133.0 -157.9 -178.8

-169.1 -149.6 104.4 103.3

A C B D

-99.0 66.6 -108.2 71.4

(b) Water Added -130.4 -134.9 -167.5 -177.4

-159.2 -151.8 100.9 100.7

A C B D

-79.7 68.5 -92.3 73.9

(c) Ser-214 Deleted -88.8 -92.9 -100.9 -178.7

-159.7 -154.3 98.9 100.0

of the ring-flipped configurations after vs before the formation of the TI. Taking the highest level MP2/6-31+G** values from Table 1, the ring flip would provide a C/A ratio of 6 × 10-18 at 310 K. This ratio would increase to 4 × 10-10 after the TI has been formed, a magnification by a factor of 6 × 107. However, the populations of the ring-flipped states are obviously quite small, placing the viability of the entire process in question. Immersion of the system in a proteinaceous environment leads to a much larger C/A ratio of 6 × 10-7. On the other hand, this same environment drastically lowers the D/B ratio to 6 × 10-12, considerably lower than the C/A ratio. As a result, the consideration of populations of the relevant species argues against the viability of the ring-flip hypothesis. The calculations dealing with the catalytic system following the addition of a proton had led to the result that the AfC flip is very much disfavored, by at least 20 kcal/mol. On the other hand, protonation state had much less effect upon the TI BfD flip, so the protonation in question would enhance the “reactiondriven” ring flip, although the populations of these flipped states might be quite small. Regarding the details of the position of the His-57 ring, perusal of Table 2 reports certain important dihedral angles. The uppermost set of data refer to the system containing all residues but not the water molecule, i.e. Figure 2. The AfC ring flip takes the φ(HRCβCγNδ1) dihedral angle from -99° to +68°, a change of 167°, close to the idealized 180° flip. The angles for the BfD flip are fairly similar, within about 10°. Scanning down the other entries in the first column of Table 2, the addition of water has little effect upon these dihedral angles, which are all within 2° or less. Removal of the Ser-214, on the other hand, causes an approximate 20° reorientation of the His ring in configurations A and B, i.e. prior to the flip. That is, the absence of this residue makes the angle in A 20° less negative, with a similar increment for B. Hence, the Ser-214 residue does appear to exert some geometric effect upon the His ring, via the Cε1H · · · O H-bond that has been discussed in the literature. On the other hand, this same residue perturbs the His ring position much less in the C and D configurations, after the ring flip has occurred. Apparently, Ser-214 is already in good position to interact with the Nε2H in D, so no further adjustments of the ring are needed; Ser-214 is essentially a nonfactor in C. The next dihedral angle reported in Table 2 refers to the Asp102 residue. The φ(HRCβCγO) angle appears to hover in the range between -129 and -135° for A and C and is more negative for B. This angle approaches 180° in D, where this orientation appears better able to interact simultaneously with both CH donors of the His-57 residue. The exception occurs when Ser-

Scheiner 214 is removed, wherein the Asp-102 dihedral angle in the preTI configurations A and C is roughly -90°, with only a slightly more negative value in B. The orientation of the Ser-195 residue was monitored via its φ(HRCβOγH) dihedral angle prior to formation of the TI and the analogous angle within the TI itself. First considering configurations A and C, this angle remains in the -(150-170°) range. There is a tendency for the angle to become less negative as a result of the AfC ring flip, especially when the water is absent. This change is apparently a means for the Ser-OH group to maintain contact with the Nε2 proton acceptor atom of His-57 as the latter flips. The HRCβOγC angle within the TI stays right around 100° both before and after the ring flip and is little affected by the absence of either the water or Ser-214. The optimized geometries reported here can be used to assess the realism of some of the idealized general notions about group interactions in the enzyme. The H-bond between the Asp-102 anion and the Nδ1H of His-57 in the initial state is clearly borne out, but the calculations suggest that the other O atom of this anion also engages in an auxiliary H-bond with a CβH of the His that is not part of the Im ring. And, indeed, this secondary interaction persists throughout the full catalytic cycle, both before and after any ring flip that may occur. There does appear to be a His Cε1H · · · O(Ser-214) interaction that is fairly short (2.2-2.3 Å) prior to ring flipping, which helps orient the His57 ring. On the other hand, the interactions with the Ser-214 are quite weak and have little energetic significance. After flipping, however, the Ser-214 forms an important H-bond with the Nε2H of the His. Unless restricted from doing so by other structural restraints, the water molecule would likely forego an interaction with Cδ2H of His-57 in the initial state in favor of stronger H-bonds with both Nε2 and the Ser-195 hydroxyl group. Moreover, this water molecule forms H-bonds after TI formation not only with the His ring as normally envisioned but also with the TI N atom, acting as a charge bridge between the two groups. It is commonly thought that the TI interacts in two places with the protonated His-57 ring: its ester O atom H-bonds with the Nε2H, and the N atom with Cδ2H. While the former interaction is supported by the calculations, the latter is not. That is, fixing the TI O atom in its oxyanion hole prevents the N atom from extending itself up to the Cδ2H. Instead this N atom of the TI accepts a proton from both the His-57 Nε2H and the water molecule, if present. But even if the latter is absent, this N atom still cannot reach up to the Cδ2H. Of course, the TI N atom could reach up to Cδ2H under certain circumstances, but would do so at the cost of pulling the TI O atom from the oxyanion hole. Some of the same findings extend to the situation following a His-57 ring flip. In the case of the TI, maintaining the O atom in the oxyanion hole prevents the N atom from reaching the Nδ1H and can only do so through the intermediacy of a water molecule if one is present in the TI state. The expected Nε2H · · · O(Ser-214) H-bond is present in the TI and there is geometric and energetic evidence that this bond contributes to the stability of this structure. One perhaps unexpected finding was the ability, if not the preference, of the Ser-195 hydroxyl group to follow the Nε2 atom after the ring flip as opposed to accepting the Cε1H proton. As another important point, the calculations belie the overly simplistic notion that there is a one-to-one correspondence between each H-bonding group on the central His-57 residue and a single partner. In configuration A, for example, the water molecule forgoes the Cδ2H group entirely and instead forms a H-bond with the Nε2 acceptor, which is itself simultaneously

Catalytic Mechanism of Serine Proteases engaged in a H-bond with the Ser-195 residue. Likewise in configurations B and D, the His Nε2H is donated to both the O and N atoms of the TI. It is also apparent that the water molecule seldom limits itself to a single H-bond, which is consistent with its two protons and a proton-accepting O atom. In configuration A, the water donates two protons, one to the His Nε2 and the other to the Ser O atom. The water acts as both donor and acceptor in configurations B and D. It is also worth stressing that both carboxylate O atoms of the Asp-102 engage in H-bonding, not a surprise in view of the full negative charge on this species. While one O atom accepts a proton from the His Im ring, the other does the same for one of the CβH atoms of the same residue, with R(H · · · O) distances of some 2.4-2.5 Å. Derewenda et al.25 had compiled a list of Cε1H · · · O separations in 22 native related enzymes and noted a range of 2.04-2.59 Å, with an average of 2.3 Å. The distance computed here in configuration A is 2.30 Å, with or without the water, nicely coinciding with the experimental observation. Also consistent is the occupation of the lone pair of the Ser-214 O atom that is anti to its peptide bond that engages in this H-bond. As indicated above, there have been a number of other theoretical attempts to understand the reaction of this family of enzymes. Some of these works have applied a QM/MM methodology21,24,26,30,31 wherein the surrounding residues are modeled by a molecular mechanical procedure, which differs from the polarizability approach applied here. These QM/MM calculations have not tethered the residues to the enzyme skeleton but have permitted freer motions within the confines of the enzyme. These QM/MM studies have not focused upon the contributions of specific groups such as Ser-214 or the water molecule, by comparing results with and without them. Nonetheless, some comparison of results might be worthwhile. For reasons indicated above, energetics are not directly comparable between the two sorts of calculations. There is some possibility for comparison of geometries, however. Optimized geometries were supplied in a work by Ishida and Kato.26 The structures correspond loosely to the A and B geometries studied here, i.e. the enzyme-substrate complex before and after formation of the tetrahedral intermediate. Of course, comparison is clouded by the fact that the QM/MM work was referenced to a trypsin-inhibitor complex and the calculations described here to R-lytic protease. In any case, the pattern of H-bonds is the same in the two cases. Some of the interatomic distances are quite similar as well. For example, the Asp102-His57 H-bond distance in configuration A is almost identical in the two cases. The His57-Ser195 H-bonds are within about 0.2 Å of one another. These same similarities are noted in the B (tetrahedral intermediate) structures as well. There are a number of points that might merit more detailed study in the future. The skeletal geometry chosen was derived from one particular serine protease, R-lytic protease. It might be worthwhile to use the structures of other enzymes in this class as starting points. The water molecule was given complete freedom of motion here; there may be certain restrictions on its position that might be set in place. For example, the water molecule might not be entirely free to move as far away from the Cδ2H group in configuration A as the calculations suggested. Finally, the work here has been designed to determine the single most stable structure of each configuration, within the bounds of the geometric restraints imposed. It would be interesting to perform a dynamics type calculation that would explore the potential energy surface in the vicinity of each such minimum

J. Phys. Chem. B, Vol. 112, No. 22, 2008 6845 and thereby develop a manifold of related geometries, rather than a single one. In summary, the calculations are consistent with some of the critical aspects of the ring-flip hypothesis, but there are a number of important discrepancies and uncertainties as well. The amount of energy required for rotation of the His-57 residue is perhaps excessive, possibly more than 20 kcal/mol. This flip requires less energy after the tetrahedral intermediate has been formed than before, buttressing the possibility of a “reaction-driven” process. Energy barriers separate the unflipped and flipped conformers, and these barriers are not so high as to preclude the flipping process. The viability of the hypothesis requires a polarizable medium, as would be found in the interior of a protein, in order to make the flipped configurations energetically accessible. On the other hand, this same sort of environment disfavors the ring flip after the formation of the TI, in contrast to one of the central tenets of the hypothesis. The water molecule in the active site would also seem to be an important element, as it provides a crucial acceptor for the Nδ1H proton of the protonated His-57 residue in the TI. This water molecule was provided full geometric flexibility in the model calculations. However, if restraints were to be placed upon the mobility of this water, its ability to facilitate the ring flip might be compromised. The Ser-214 residue does form the presumed H-bonds, and the residue appears to contribute to the viability of the ring-flip idea. On the other hand, in contrast to the general hypothesis, the Cε1H · · · O-Ser214 bond energy is vanishingly small in the initial configuration and plays no energetic role in the ring flip prior to formation of the TI. Some of the idealized predictions of specific H-bonds are altered by the calculations, which indicate, for example, that the water molecule prefers interaction with Nε2 and Ser-195 versus Cδ2H in the initial configuration. Acknowledgment. The author is indebted to Drs. Jim Sudmeier and William Bachovchin for motivating this study and providing valuable advice concerning experimental matters. References and Notes (1) Kraut, J. Annu. ReV. Biochem. 1977, 46, 331–358. (2) Wang, J. H. Proc. Natl. Acad. Sci., U.S.A. 1970, 66, 874–881. (3) Scheiner, S.; Kleier, D. A.; Lipscomb, W. N. Proc. Natl. Acad. Sci., U.S.A. 1975, 72, 2606–2610. (4) Scheiner, S.; Lipscomb, W. N. Proc. Natl. Acad. Sci., U.S.A. 1976, 73, 432–436. (5) Duijnen, P. T.v.; Thole, B. T.; Hol, W. G. J. Biophys. Chem. 1979, 9, 273–280. (6) Kollman, P. A.; Hayes, D. M. J. Am. Chem. Soc. 1981, 103, 2955– 2961. (7) Warshel, A.; Naray-Szabo, G.; Sussman, F.; Hwang, J. K. Biochemistry 1989, 28, 3629–3637. (8) Daggett, V.; Schro¨der, S.; Kollman, P. J. Am. Chem. Soc. 1991, 113, 8926–8935. (9) Russell, S. T.; Warshel, A. J. Mol. Biol. 1985, 185, 389–404. (10) Bentzien, J.; Muller, R. P.; Floria´n, J.; Warshel, A. J. Phys. Chem. B 1998, 102, 2293–2301. (11) Warshel, A.; Russell, S. J. Am. Chem. Soc. 1986, 108, 6569–6579. (12) Aaqvist, J.; Warshel, A. Chem. Soc. ReV. 1993, 93, 2523–44. (13) Schutz, C. N.; Warshel, A. Proteins 2004, 55, 711–723. (14) Monard, G.; Loos, M.; The´ry, V.; Baka, K.; Rivail, J.-L. Int. J. Quantum Chem. 1996, 58, 153–159. (15) Molina, P. A.; Sikorski, R. S.; Jensen, J. H. Theor. Chem. Acc. 2003, 109, 100–107. (16) Robillard, G.; Shulman, R. G. J. Mol. Biol. 1972, 71, 507–511. (17) Robillard, G.; Shulman, R. G. J. Mol. Biol. 1978, 86, 519–540. (18) Pera¨kyla¨, M.; Kollman, P. A. J. Am. Chem. Soc. 2000, 122, 3436– 3444. (19) Warshel, A.; Sussman, F.; Hwang, J.-K. J. Mol. Biol. 1988, 201, 139–159. (20) Westler, W. M.; Weinhold, F.; Markley, J. L. J. Am. Chem. Soc. 2002, 124, 14373–14381.

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