Biochemistry Table 4. Summary of the Agreement between Experiment and QM/MM Calculations for the t-DPPO(1) Modela Article ΔG⧧[C(1)] ΔΔG⧧[C(2)−C(1)] selectivity [C(1):C(2)] experiment 13−16b 2.1c 32:1c AM1 19.0 6.0 23755:1 B3LYP 9.7 1.3 9:1 SCS-MP2//B3LYP 12.8 3.0 154:1 aΔG⧧[C(1)] and ΔΔG⧧[C(2)−C(1)] are the activation free energy for nucleophilic attack at C(1) and the difference between the C(1) and C(2) barriers (in kilocalories per mole), respectively. Selectivity [C(1):C(2)] refers to the ratio of products, predicted by the ratio of the calculated rate constants from ΔΔG⧧[C(2)−C(1)]. bEstimated from rate constants obtained for similar epoxide hydrolases and substrates.27,44,51,79 cFrom the 97:3 ratio observed by Borhan et al. for the reaction of t-DPPO in murine sEH.22 orientations of t-DPPO (1 and 2); i.e., there is a lower barrier to attack, regardless of which carbon atom is closer to the nucleophilic Asp333 oxygen atom in the reactant complex. The barrier to nucleophilic attack is lower for C(1) attack than for C(2) attack, because the transition state to attack at both C(1) and C(2) requires partial sp2 hybridization of the carbon atom undergoing attack. When nucleophilic attack occurs at C(1), the proximal phenyl ring stabilizes this sp2 hybrid carbon to a larger extent than in the case of C(2) attack. This is an intrinsic electronic effect present in the substrate and is not due to the enzyme. The binding mode of t-DPPO in the t-DPPO(1) model is likely to be more catalytically relevant in the enzyme than the binding mode in the t-DPPO(2) model, because lower free energy barriers are observed for the former than for the latter. Additionally, similar distances are observed between the Asp333 Oδ2 atom and C(1) and C(2) in the unrestrained MD simulations of t-DPPO(1), whereas C(1) is significantly closer to the Asp333 Oδ2 atom in the t-DPPO(2) simulations (Table 1). For t-SO, the calculated free energy barriers suggest a large preference for nucleophilic attack at C(1) over C(2). Such a large effect is surprising, given that the two carbon atoms are chemically equivalent. However, C(1) is much closer to the Oδ2 atom of Asp333 than C(2) in the unrestrained MD simulations and hence is in a more favorable position for nucleophilic attack at C(1) than at C(2) (see Table 1). The quantitative agreement between the experimental and theoretical values for the relative barriers to C(1) and C(2) nucleophilic attack in t-DPPO (ΔΔG⧧) is summarized in Table 4. It is clear that although AM1 shows the correct selectivity preference, this is significantly overestimated. A difference in the barrier of 6 kcal/mol would result in exclusive attack at C(1), whereas the experimental observation is a 97:3 preference.22 A much better agreement is found in the B3LYP and SCS-MP2 values (1.7 and 3.0 kcal/mol, respectively). As discussed below, this is because the agreement between theory and experiment for the absolute values of the barriers calculated with B3LYP and SCS-MP2 is greatly superior to that in AM1. Reaction Rate. The potential energy barriers calculated at the AM1/CHARMM22, B3LYP/CHARMM22, and SCS-MP2// B3LYP/CHARMM22 levels of theory are given in the Supporting Information. The average activation entropy correction (at 300 K)65 is 1.8 kcal/mol. This value is small and is comparable to the calculated65 and experimental78 values of entropic contribu- tion (TΔS⧧) for the conversion of chorismate to prephenate in chorismate mutase at 300 K (2.5 and 2.7 kcal/mol, respectively). As mentioned above, the B3LYP/CHARMM22 potential energy barriers are significantly lower than the corresponding AM1/CHARMM22 potential energy barriers, but the opti- mized geometries and hydrogen bonding environments are very similar (bond lengths and bond angles are provided in the Supporting Information). As found for the AM1/CHARMM22 free energy and potential energy barriers, the B3LYP potential energy barriers span a wide range of values [e.g., 4.7−11.2 kcal/mol for attack at C(1) of t-SO (see the Supporting Information)] over the 10 profiles obtained for each of the three model systems. This variation is due to differences in the conformation of the enzyme, and the orientation of the substrate, in the initial structures. The effect of basis set size was explored by calculat- ing B3LYP/6-311+G(d,p) single-point energies for the B3LYP/ 6-31G(d) geometries and yielded energy barriers within 0.1 kcal mol−1 of the B3LYP/6-31G(d) energy barriers. The average B3LYP/CHARMM22 potential energy barrier for nucleophilic attack at C(1) of t-SO (7.9 kcal/mol) is in good agreement with the barrier of 7.8 kcal/mol reported for the nucleophilic ring opening of t-MSO by human sEH in a DFT study on an active site model by Hopmann et al.50 We are not aware of any published experimental rate constant values for the nucleophilic ring opening in murine sEH with the substrates used in this study. However, for S. tuberosum epoxide hydrolase 1 (StEH1) reacting with t-SO, rate constants correspond- ing to formation of the covalent ester intermediate of 18 and 100 s−1 have been measured.27,44 The formation of an ester intermediate between EH isolated from A. radiobacter and (R)- styrene oxide was found to have a rate constant of 1100 s−1.79 Additionally, a rate constant of 330 s−1 has been measured for microsomal EH with the substrate glycidyl-4-nitrobenzoate.51 These rate constants correspond to a range of activation free energies of 13−16 kcal/mol. Hence, the B3LYP/CHARMM22 calculated free energy barrier of 7.3 kcal/mol for nucleophilic attack at C(1) of t-SO is rather low compared to the value calculated from experiment. Likewise, the free energy barrier of 6.8 kcal/mol for attack at C(1) in the t-DPPO(2) model is lower than expected. It is a common tendency for B3LYP to under- or overestimate reaction barriers for some systems.80 The neglect of dispersion in B3LYP is one cause of inaccuracies in the calculation of barriers. For example, a significant improvement in the relative barriers calculated for epoxidation and hydroxylation reactions catalyzed by cytochrome P450 is observed when an empirical dispersion correction is applied to the B3LYP functional.81 The missing dispersion interaction in B3LYP is unlikely to be important here, as including an empirical dispersion correction would be expected to lower the barriers even further. Testing different density functionals is generally a good idea, as different potential energy barriers are often observed when calculated for the same reaction with different functionals.58 As mentioned in Computational Methods, several adiabatic mapping energy profiles were calculated using the BP86 and BHandHLYP functionals. The potential energy barriers obtained with these functionals are detailed in the Supporting Information. It should be noted that both of these functionals share the same lack of dispersion as B3LYP. The BP86 barriers were found to be typically 2−3 kcal/mol lower than the same barriers calculated with B3LYP. In contrast, the BHandHLYP barriers were found to be 5−7 kcal/mol higher 1780 dx.doi.org/10.1021/bi201722j | Biochemistry 2012, 51, 1774−1786