Unravelling the Molecular Origin of the Regiospecificity in Extradiol

Article pubs.acs.org/IC

Unravelling the Molecular Origin of the Regiospecificity in Extradiol Catechol Dioxygenases Gemma J. Christian,†,‡ Frank Neese,† and Shengfa Ye*,† †

Max-Planck Institute for Chemical Energy Conversion, Stiftstrasse 34−36, D-45470 Mülheim an der Ruhr, Germany Avondale College of Higher Education, Cooranbong, New South Wales 2265, Australia

‡

S Supporting Information *

ABSTRACT: Many factors have been suggested to control the selectivity for extradiol or intradiol cleavage in catechol dioxygenases. The varied selectivity of model complexes and the ability to force an extradiol enzyme to do intradiol cleavage indicate that the problem may be complex. In this paper we focus on the regiospecificity of the proximal extradiol dioxygenase, homoprotocatechuate 2,3-dioxygenase (HPCD), for which considerable advances have been made in our understanding of the mechanism from an experimental and computational standpoint. Two key steps in the reaction mechanism were investigated: (1) attack of the substrate by the superoxide moiety and (2) attack of the substrate by the oxyl radical generated by O−O bond cleavage. The selectivity at both steps was investigated through a systematic study of the role of the substrate and the first and second coordination spheres. For the isolated native substrate, intradiol cleavage is calculated to be both kinetically and thermodynamically favored, therefore nature must use the enzyme environment to reverse this preference. Two second sphere residues were found to play key roles in controlling the regiospecificity of the reaction: Tyr257 and His200. Tyr257 controls the selectivity by modulating the electronic structure of the substrate, while His200 controls selectivity through steric effects and by preventing alternative pathways to intradiol cleavage.

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INTRODUCTION

the enzymes control the selectivity for intradiol or extradiol behavior is one of the most intriguing puzzles in the study of dioxygenase reactivity.1a,2 Both extradiol and intradiol dioxygenases are non-heme iron enzymes, in which the substrate binds directly to the active site via the hydroxyl groups of the catechol. Despite the similarity of the substrates and binding modes, intradiol and extradiol enzymes have no structural or sequence similarities and show high regiospecificity for intradiol or extradiol behavior.1a,b The active site of extradiol enzymes consists of an iron or manganese center in the MII oxidation state coordinated by two histidine ligands and a carboxylate group, a common motif in the non-heme enzyme superfamily. The enzyme−substrate complex of intradiol dioxygenases, in contrast, contains an active site FeIII, which is ligated by two histidine and one tyrosine residues. Although it would be tempting to ascribe the enzyme selectivity to the differences in the active site and the metal oxidation state, a mutant of homoprotocatechuate 2,3dioxygenase (HPCD), His200Phe, was found to perform intradiol ring opening of a substrate analogue, 2,3-dihydroxybenzoate (2,3-DHB).3 This was the first time that an extradiol enzyme had been induced to show intradiol behavior. The

Catechol dioxygenases catalyze C−C bond cleavage and ring opening of catecholates, assisting in the degradation of aromatic compounds in soils.1 The aromatic ring of the substrate can be opened either between the two hydroxyl groups, as shown in Figure 1, which is known as intradiol cleavage, or to one side, which is referred to as extradiol cleavage. The question of how

Received: December 27, 2015

Figure 1. Intradiol and extradiol cleavage of substituted catechols. © XXXX American Chemical Society

A

DOI: 10.1021/acs.inorgchem.5b02978 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry

Figure 2. Proposed mechanism for extradiol dioxygenases: homoprotocatechuate 2,3-dioxygenase [M = Fe].8a

3,4-dioxygenase, a related intradiol dioxgenase, with a slow substrate 4-fluorocatechol (4FC).12 Comparison of the crystal structures of the alkylperoxo intermediates found for extra- and intradiol dioxyganses suggests that the alignment of the bridging peroxo relative to the C−C bonds being cleaved may play a role in dictating the final reaction outcome.7b,12 HPCD carries out exclusively proximal ring opening in nature (see Figure 1). Our proposed mechanism8a shown in Figure 2 is supported by the isolation and spectroscopic characterization of many of the key intermediates7,13 as well as other computational work.8d The first step of the reaction is binding of the substrate to the FeII center, displacing the solvent molecules. Spectroscopic and crystallographic studies show that as the substrate binds to the metal it is singly deprotonated and the deprotonated hydroxyl function forms a hydrogen bond with second sphere residue Tyr257 (vide infra).14 The displacement of the solvent opens a coordination site where oxygen binds and is reduced to a superoxo species. During the reaction His200 is shown to function as an acid/ base catalyst to relay protons from the substrate to the oxygen species yielding the dianionic form of the substrate,15 a facile process involving negligible barriers.8a As a consequence, a hydrogen bond between the proton and the proximal O atom in O2 is formed as found in the crystal structure of the O2 adduct of HPCD with a slow substrate, 4-nitrocatechol (4NC) (HPCD-4NCInt1 in Table 1),7b primed for the further reaction. The superoxo species then attacks the substrate to generate a hydroperoxo complex bridging the metal center and the substrate. This FeII-alkylperoxo complex undergoes homolytic O−O bond cleavage to give a FeIII-hydroxo unit bound to an epoxide, which then rearranges to a FeII-lactone intermediate. Hydrolysis of the lactone leads to the final product. Experimentally, a detailed mechanistic study on HPCA and its variants has been undertaken. For HPCD with the native substrate HPCA, only the FeII-alkylperoxo intermediate (Table

subtleties of this question are highlighted by the fact that His200Phe with the native substrate, homoprotocatechuate (HPCA), still selectively yields the proximal extradiol product, and the wild-type enzyme HPCD with both substrates only gives extradiol products. Also, as early as 1975 an intradiol enzyme was found to carry out small amounts of extradiol cleavage for modified substrates.4 This, along with other model studies,5 demonstrates that the FeIII oxidation state is not a prerequisite for intradiol activity. The complexity of the problem is further manifested by the reactivity of FeIII model complexes. While a large range of model complexes exhibit intradiol cleavage,1a,2 a far smaller number are found to perform extradiol cleavage.2,5,6 Furthermore, the regiospecificity for extradiol cleavage can in some cases be reversed by changes in the solvent.6e Thus, despite recent exciting advances7,8 in our understanding of these enzymes, one of the most basic problems is yet to be solved. Among the factors which have been suggested to influence selectivity3 are the metal oxidation state, coordination number and geometry of the metal center,6e and Lewis basicity of residues or ligands close to the site of oxygen binding.5,6f The importance of some of these factors can be explained by differences in the proposed mechanisms for extradiol and intradiol cleavage. Intradiol cleavage is suggested to proceed via substrate activation where oxygen directly attacks the substrate.1b,c,9 In contrast, extradiol cleavage is proposed to occur via oxygen activation wherein oxygen binds to the metal center to form a superoxide, which then attacks the substrate.10 Thus, tuning the Lewis acidity or electron withdrawing properties of the substrate via different substituents is suggested to favor one mechanism over the other.6e,11 However, none of these explains the reversal of the selectivity of HPCD upon the mutation of His200 and the change of substrates. Recently, two key intermediates, namely, FeIII-alkylperoxo and anhydride, have been trapped by the crystallo-reaction of protocatechuate B


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recombination mechanism. In our earlier work, we have carefully evaluated the electronic structures of the O2-bound species in HPCD and His200Asn with the two substrates (HPCA and 4NC) using a combined experimental and theoretical approach.8a By enlarging the model to include the second coordination sphere, our theoretical results revealed that the reactive quintet O2 adducts are best formulated as a HS-FeIII-O2−•-HPCA/4NC species. This superoxo intermediate can readily convert to a HS-FeIII-hydroperoxo-SQHPCA complex, a dead end of the actual reaction,8a which may correspond to the (hydro)peroxo species detected experimentally in His200Asn and His200Cys.7f,h Remarkably, the computed electronic structures are able to successfully reproduce the experimental Mössbauer parameters measured for His200Asn-4NCInt1 and His200Asn-HPCAInt1, hence lending credence to our proposed electronic structure for the corresponding intermediate in the wild-type enzyme with the native substrate. However, quantum mechanical/molecular mechanical (QM/MM) calculations recently reported by Dong et al. showed that the O2 adduct in HPCD with HPCA is best formulated as a hybrid electronic structure of HSFeII-O2−•-SQHPCA ↔ HS-FeIII-O2−•-HPCA (vide infra),8d and that the O2 adduct trapped in the crystal might be a FeIIIhydroperoxo-SQ4NC species.8e Despite this delicate difference, the formation of the hydroperoxo bridge has been predicted to proceed via proton coupled electron transfer in a concerted manner.8a,d,e Although substantial efforts have been invested to elucidate the reaction mechanism, there are some key differences between experimental and computational findings. First, the crystal structure of HPCD-4NCInt1 reveals that the O2 adduct contains a side-on bound O2 moiety and a nonplanar sixmember ring of the catecholate, the latter indicating some radical character in the substrate, congruous with its proposed electronic structure of FeII-O2−•-SQ4NC.7b Both geometric features have also been observed in the crystal structure of the oxy intermediate in related homogentisate 1,2-dioxygenase.16 However, computational studies with the reasonable models including key second sphere residues favored an end-on bonding mode for O2, and a planar conformation for the ring, consistent with the different electronic structure (FeIII-O2−•HPCA) predicted by the calculations.8a,d The electronic structure of FeII-O2−•-SQHPCA has only been found in the previous studies with the small model (vide supra).8b,c Second, theoretical results suggest that during the reaction the iron

Table 1. Detected Intermediates in Extradiol Dioxygenase HPCD and Its Variants intermediate HPCD-HPCAInt1 His200Asn-HPCAInt1 His200Asn-HPCAInt2 His200Asn-4NCInt1 His200Asn-4NCInt2 Tyr257Phe-HPCAInt1 Tyr257Phe-HPCAInt2 H200Cys-HPCA HPCD-4NCInt1 HPCD-4NCInt2 HPCD-4NCInt2

assignment In Solution HS-FeII-alkylperoxo HS-FeIII-(hydro)peroxo-SQHPCA HS-FeII-alkylperoxo HS-FeIII-O2−•-4NC HS-FeIII-(hydro)peroxo-SQ4NC HS-FeII-O20-HPCA HS-FeII-(hydro)peroxo-QHPCA HS-FeIII-hydroperoxo-SQHPCA In Crystal FeII-O2−•-SQ4NC FeII-alkylperoxo FeII-semialdehyde

ref 7f 7f 7f 7e 7e 7g 7g 7h 7b 7b 7b

1) has been detected, whereas the O2-bound intermediate has not been accumulated in high enough concentrations to allow thorough spectroscopic characterizations.7f The O2 adduct generated by the crystallo-reaction of HPCD with 4NC is shown likely to be a FeII-O2−• species ligated by a semiquione (SQ) radical.7b In the case of His200Asn and His200Cys,7f,h Mössbauer and EPR studies unequivocally demonstrated that the O2 adduct with HPCA is best described as a HS-FeIII(hydro)peroxo-SQHPCA species, which eventually transforms into the correct extradiol product. The corresponding intermediate of His200Asn with 4NC contains a HS-FeIII center that is antiferromagnetically coupled to an O2−• with no detectable radical character on the substrate, viz., HS-FeIIIO2−•-4NC.7e This species decays to release quinone (Q) and H2O2 instead of undergoing extradiol cleavage. For Tyr257Phe,7h two intermediates assigned as HS-FeII-O20-HPCA and HS-FeII-(hydro)peroxo-QHPCA have been trapped and characterized. It has been shown that the peroxo intermediate can go forward to attack QHPCA, generating the proximal extradiol product, although the reaction rate is slowed by 100-fold due to the mutation. Computationally, earlier investigations using a small model containing only the first coordination sphere suggested that the quintet O2 adduct consists of a high-spin (HS) FeII center bound to a superoxo and a SQ radical with the latter two fragments antiferromagnetically coupled, viz., HS-FeII-O2−•SQHPCA.8b,c Thus, C−O bond formation follows a radical

Figure 3. Divergence of the extradiol and intradiol pathways. C


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Inorganic Chemistry oxidation state cycles between FeII and FeIII.8a,d,e Interestingly, the enzyme kinetics are similar for the Fe, Mn, and Co enzymes despite the considerable difference in their one-electron oxidation potentials,7a,10 thereby implying that there is no change in the metal oxidation state during the reaction. More critically, the reaction of HPCD with HPCA is so fast that the theoretically proposed FeIII intermediate except FeII-(hydro)peroxo has not been detected thus far,7f indicating that the O2 adduct in the actual reaction has an exceedingly short lifetime. Third, for the ring cleavage, experimentally a concerted twoelectron Criegee rearrangement process has been proposed to convert the FeII-alkylperoxo complex directly into the lactone intermediate.2,9c,d,17 Experimental studies show that for a related enzyme, 2,3-dihydroxylphenylpropionate 1,2-dioxygenase, His115 and His179, corresponding to His200 and Tyr257 in HPCD, function as acid−base catalysts5 and play a role in the conversion from alkylperoxo bridge to lactone and the subsequent lactone hydrolysis,18 while computations favor a stepwise transformation to form the lactone via the epoxide intermediate (vide infra).8a,d,f Our earlier computational study shows that the epoxide-to-lactone conversion encounters a large driving force, hence the epoxide likely eludes experimental detection due its transient nature. Experimental and theoretical findings unanimously show that the FeII-alkylperoxo species is a common intermediate for both intradiol and extradiol pathways.2,9c,d,17 From the alkylperoxo intermediate, computational studies show that breaking the O− O bond may result in formation of a quasi-intermediate with radical oxyl character,8 as shown in Figure 3. The radical can then attack either at the carbon atom adjacent to the hydroxyl groups to form an epoxide (extradiol pathway) or at the carbon atom bound to the second hydroxyl group to give an anhydride (intradiol pathway). The epoxide undergoes ring opening leading to the extradiol product, while the anhydride eventually evolves to the intradiol product. The reaction preferentially proceeds on the quintet spin surface, and the two state reactivity was not predicted to play an important role in this reaction for M = Fe.8a Computational studies of the intradiol and extradiol mechanisms for the iron enzyme found that the intradiol pathway is kinetically disfavored, while the extradiol pathway was predicted to be essentially barrierless after O−O bond breaking.8c,d,17b In these studies, the influence of second sphere residues His248 and Asn157 was examined. When both were removed from the modeling, the barrier to intradiol cleavage was reduced to zero, which was attributed to changes in the anionic character of the substrate. This study did not test the importance of His200 and hence does not explain why in experiment the mutation of His200 influences the selectivity of the enzyme. In this study, we use computational methods to undertake a detailed study of the electronic and environmental factors that control the regiospecificity of the proximal extradiol enzyme HPCD, through a careful exploration of the effects of the enzyme environment on the reactivity of the substrate. This approach makes it possible to uncover the electronic basis for the reactivity of the enzyme and the importance of the second sphere residues in dictating the selectivity of the reaction at key steps in the reaction mechanism.

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corrections were treated using the zeroth-order regular approximation (ZORA).21 The ZORA-TZVP basis set22 was used for Fe, N, and C and the ZORA-SVP basis set22 for H. Calculations were accelerated with the resolution of identity and chain of sphere (RIJCOSX) approximations23 in conjunction with the TZVP/J auxiliary basis set.24 The effect of the protein environment on the active site was modeled using the COSMO continuum solvation model25 with the value of epsilon set at 4.0. Dispersion effects were accounted for by using the semiempirical van der Waals corrections by Grimme26 implemented in ORCA. To calibrate our computational setup, we compared the electronic structure of the quintet O2 adduct computed by using the nonrelativistic Hamiltonian. The calculations deliver a spin population on the substrate of ∼0.68 (Table S1) with 40% delocalized on the sixmember ring. Therefore, the bonding of this so-calculated O2 adduct is best interpreted as a resonance structure between HS-Fe(II)-O2−•SQHPCA and HS-Fe(III)-O2−•-HPCA (Figure S1), in agreement with that reported in ref 8d. In contrast, the corresponding relativistic computations predict a different electronic structure of a HS ferric center antiferromagnetically coupled to a superoxo ligand. This difference can be traced back to the distinct coordination geometry. Our earlier benchmark calculations showed that nonrelativistic allelectron DFT calculations often slightly overestimate metal−ligand bond lengths in comparison with precise experimental structural data.27 In the present case, the relativistic corrections shrink the Fe− OHPCA bond distances by ∼0.05 Å (Table S1). As expected, the shorter Fe−OHPCA distances lead to the higher degree of ligand-to-metal charge donation, which increases the energies of the metal d-orbitals and simultaneously decreases the energies of the ligand orbitals. As a consequence, both factors suppress the electron transfer from the HPCA π-orbital to the metal center. The different electronic structure for the O2 adduct deduced from the QM/MM computations is thus likely due to lack of the proper treatment of relativistic effects. Construction of a Cluster Model. In the cluster model protein residues were truncated to their functional groups, i.e., histidine to imidazole, glutamate acid to acetate, arginine to guanidinium, tryptophan to indole, and tyrosine to phenol, etc. The constraints of the protein were modeled by fixing the atoms marked with asterisks in Figure 4, which prevents geometry rearrangements in the calculations that are unfeasible in the protein environment. The cluster model was constructed from the available crystal structure data (protein database number 1Q0C for the native enzyme) and is shown in Figure 4.14b The model includes the first coordination sphere residues: two histidine residues and one glutamic acid, the so-

COMPUTATIONAL DETAILS

The calculations were carried out with the ORCA program package.19 Geometries were optimized with the B3LYP functional.20 Relativistic

Figure 4. Cluster model of Fe-HPCD with the native substrate. Constrained atoms are marked with asterisks. D


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Inorganic Chemistry called 2-His 1-carboxylate motif. The second coordination sphere residues His200, Asn157, Tyr257, His248, and Arg243 were included as they involve strong interactions with the substrate and/or the bound oxygen species (vide infra). This model has been used previously for the study of the superoxo species and the oxygen activation mechanism of the extradiol enzymes.8a A larger model including the second sphere residue Trp192 was also tested, however no significant differences were observed. The recent QM/MM study showed that there are no noticeable effects of the protein environment on the reaction mechanism.8d Furthermore, in comparison with the QM/MM results, our calculations predicted similar barriers for key steps within the uncertainty of DFT approaches, thereby indicating that our results based on the cluster model with the constraints are reliable.

confirmed that the superoxide attacks the ring at C2, as shown in Figure 2.7b Note that at this point the second proton of the substrate has been transferred to His200, which then forms a hydrogen bond with the superoxo moiety. This hydrogen bond, along with a second hydrogen bond formed between the superoxide and Asn157, position the superoxide over C2. Rotation of the superoxide slightly to the right, however, could allow attack at C1, and this alternative channel is rarely considered.17b In this study, both attack at C1 and C2 are explored. Attack of the superoxide species on the substrate is here referred to as step 1. Step 2 is then the attack of the oxyl radical on the substrate. The combination of steps 1 and 2 gives rise to four possible reaction pathways, illustrated in a flowchart (Figure 5), where the subscripts C1 and C2 are used to indicate that step 1 proceeds via attack at C1 or C2. The present study aims to rationalize the extradiol regiospecificity observed for HPCD, focusing on the electronic driving force and the influence of the enzyme active site on the reaction mechanism.8a,b,17b Selectivity of Step 1. The first step that could influence the selectivity of the enzyme is the attack of the superoxo species on the substrate to give the hydroperoxo bridge (Br). Earlier computational studies8a,d showed that this step is best described as a proton coupled two-electron transfer, viz., the reductions of the superoxide to a hydroperoxide and of FeIII to FeII are concurrent with the protonation of the O2 moiety by neighboring His200. In the transition state, the substrate first undergoes two-electron oxidation to form a quinone, which is then attacked by the hydroperoxo to yield the alkylperoxo intermediate. Remarkably, the computed transition state features the same electronic structure as that found for Tyr257Phe-HPCAInt2.7g The electron transfer is complete very shortly after the transition state where the C2−O2 bond distance is ∼2.0 Å. The calculated transition state geometry shows a contraction of the C1−OC1 and C2−OC2 bond lengths in the substrate, consistent with the formation of CO double bonds (see the Supporting Information for further details). After the transition state, C−O bond formation occurs through nucleophilic attack of the nascent hydroperoxo on the CO groups to generate the hydroperoxo bridge. Although step 1 is concerted, it can be divided into two substeps: (1a) two electron oxidation of the substrate to give FeII and hydroperoxo and (1b) nucleophilic attack of the hydroperoxo on the CO groups of QHPCA to form the C−O bond. Attack of the substrate may occur at either C1 or C2 to give two distinct hydroperoxo bridges labeled here BrC1 and BrC2. Experimentally, there is no evidence for formation of any reactive FeIIIO2−• species in any forms of HPCD in which His200 is present. This is consistent with our observation that in step 1a His200 serves as an acid/base catalyst15 to induce the proposed proton coupled two-electron transfer. The full reaction profile for the C2 pathway has been calculated previously.8a To complement this work the C1 pathway was also explored. The calculated reaction profile is shown in Figure 6, and the calculated structures of TS1C1 and BrC1 are shown in Figure 7 and Figure 8. The electronic structure of TS1C1 is included in the Supporting Information along with the electronic structure of TS1C2 calculated previously, for reference.8a As described in the previous study,8a attack at C2 via TS1C2 to form BrC2 encounters a barrier of 28.8 kJ mol−1. In the present study, the barrier to formation of the hydroperoxo

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RESULTS AND DISCUSSION The reaction mechanism for HPCD has been studied both experimentally and computationally and is reasonably well understood. In the proposed mechanism shown in Figure 2, there are two steps that have the potential to control the selectivity of the reaction for proximal extradiol or intradiol behavior. Perhaps the most evident step, as highlighted in the Introduction, occurs directly after O−O bond cleavage. Breaking the O−O bond leads to formation of a quasi intermediate with oxyl radical character which may attack the carbon centers of the substrate on either side, eventually culminating in either the extradiol or intradiol products, as shown in Figure 3. Another step that controls the proximal selectivity occurs earlier in the reaction mechanism: the initial attack of the superoxide species on the substrate ring. Early studies suggested two sites at which the superoxide may attack the aromatic ring of the substrate: C1 or C2 using the numbering scheme depicted in Figure 5.28 Subsequent X-ray crystallography studies indicated that the attack at C3 is unlikely14b and

Figure 5. Steps that control selectivity in the reaction mechanism. E


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Figure 6. Calculated reaction profile in kJ mol−1 for extradiol and intradiol cleavage by HPCD. Free energies are included in parentheses.

Figure 7. Calculated geometry and electronic structure of TS1C1.

bridge at C1 (BrC1) was calculated to be 31.3 kJ mol−1, only 3 kJ mol−1 higher in energy than TS1C2. However, formation of BrC1 is endothermic by 25.5 kJ mol−1, whereas formation of BrC2 is almost thermoneutral (Figure 6). As a consequence, BrC1 is 28.4 kJ mol−1 higher in energy than BrC2. In analogy to TS1C2, proton transfer from His200 to O2 is complete by formation of TS1C1. Molecular orbital (MO) analysis found a FeII center for TS1C1 (Figure 7), thereby suggesting that the reduction of the metal center is complete. In comparison, the electron transfer to the metal center is completed shortly after TS1C2. Along with a difference of only 3 kJ mol−1 in the barriers for the two pathways, the similarity of the electronic structure indicates that step 1a, or the oxidation of the substrate, does not significantly

influence the selectivity. Although the two transition states are nearly isoenergetic, the energy difference between the two peroxo-bridged species, BrC1 and BrC2, is much more pronounced. Therefore, it is the relative stability of BrC1 and BrC2 that controls the selectivity of step 1. A number of factors could control the nucleophilic attacks at C1 or C2 of the substrate. These include steric or geometric factors, or electronic effects. For the convenience of the study the different contributing factors are divided into three groups: (1) the intrinsic selectivity of the isolated substrate, (2) the influence of the first coordination sphere on the selectivity, and (3) the influence of second sphere residues. F


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Figure 8. Optimized structures of the hydroperoxo bridges.

presence of the substituent R group at C4, which is closer to C2 than C1 on the aromatic ring. Similar calculations on the alternative substrate 2,3-DHB show that the attack at C1 is only 4 kJ mol−1 more favorable than that at C2. In comparison, for the full model the formation of BrC2 is calculated to dominate over that of BrC1 by 28.4 kJ mol−1. These results suggest that there is no intrinsic thermodynamic driving force from the substrate itself, and that it is instead the enzyme environment that controls the selectivity of this step. To test the importance of the first coordination sphere on the selectivity of step 1, we calculated the relative energies of the two hydroperoxo bridge species for a model including only the first coordination sphere. Constraints on the atoms at the truncation points were maintained, as has been described for the larger models. For this model, the formation of the hydroperoxo bridge at C1 is calculated to be 1.4 kJ mol−1 more favorable than the formation of the bridge at C2. However, this energy separation is certainly not enough to explain the selectivity of the full enzyme system. Therefore, we can exclude the first coordination sphere as having a significant influence on the regiospecificity of step 1. Influence of the Enzyme Active Site (Second Sphere Residues). Having ruled out the substrate and the first coordination sphere as the major drivers of the selectivity of step 1, the influence of the second sphere residues in the active site was investigated. Of these, there are four residues which interact strongly with the substrate or the superoxo moiety (see Figure 9): Tyr257, His200, Asn157, and Arg243. Tyr257 forms a hydrogen bond with OC2 of the substrate, while His200 and Asn157 are both involved in hydrogen bonding to the superoxide, positioned at either side and stabilizing its binding to the metal center. Arg243, in contrast, is not situated near the oxygen or hydroxyl groups, but forms a salt bridge with the carboxylate tail of the substrate. Hence, Arg243 is not expected to have a significant influence on the selectivity. Trp192 is also close to the superoxide moiety. To test the influence of each of these residues, the relative energies of the hydroperoxo bridges formed at C1 and C2, BrC1 and BrC2, were calculated for models with each residue and/or combinations thereof removed from the computational model. The results are presented in Table 2. These results are not

To test which factors are most significant, calculations were carried out on the hydroperoxo bridge intermediates, BrC1 and BrC2, for a range of models including a model of the isolated substrate. To examine the influence of the coordination sphere, models of the active site were used with selected neighboring residues removed. This approach does not probe the effect of the corresponding mutations, as the mutations may result in significant changes to the active site. Instead, it focuses on the effect of these residues in the native enzyme by systematically evaluating their influence on the energy and electronic structure of intermediates. The calculated relative energies for the attacks at C1 or C2 for these models are summarized in Table 2. Table 2. Relative Energies in kJ mol−1 of Hydroperoxo Bridge, BrC1 and BrC2, for the Isolated Substrates, the Wild Type Enzyme, and Mutants with Tyr257, Asn157, and/or His200 Removed from the Model native substrate HPCA alternate substrate 2,3-DHB WT enzyme with HPCA (without Asn157) (without His200) (without Tyr257) (without both Tyr257 and His200) (only first coordination sphere) WT enzyme with 2,3-DHB

BrC2 (kJ mol−1)

BrC1 (kJ mol−1)

0.0 3.6 0.0 0.0 0.0 0.0 0.0 1.4 11.4

1.8 0.0 28.4 28.1 22.2 7.1 2.2 0.0 0.0

Influence of the Substrate and First Coordination Sphere. To test the importance of the substrate itself, calculations were carried out for the isolated substrate HPCA with a hydroperoxo bound to either C1 or C2, referred to as SubsC1 and SubsC2, respectively. Both of the hydroxyl groups of the substrate were deprotonated, since by this stage of the enzymatic reaction the second proton from the substrate has been transferred to His200. The carboxylate tail of the substrate was protonated to mimic the effect of Arg243. For the substrate in the absence of the metal and the enzyme environment, SubsC2 is calculated to be 1.8 kJ mol−1 lower in energy than SubsC1. This marginal difference is likely due to the G


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activation catalyzed by α-ketoglutarate dependent dioxygenases.32 In comparison to Tyr257, His200 has a much less significant effect, reducing the preference for the attack at C2 by approximately 6 kJ mol−1. This may explain why the selectivity is unaffected by the mutation of His200 for the native substrate. Unlike Tyr257, His200 cannot modulate the electronic properties of the EAOs and there is a negligible change in electronic structure of the metal or substrate when His200 is removed from the model. In the absence of an electronic effect on the substrate, the effect of the hydrogen bonding between His200 and the hydroperoxo bridge was examined. As shown in Figure 8, apart from the obvious differences in the position of the attack on the substrate, the structure for BrC1 shows some distortion from linearity in the hydrogen bond with His200 (see Supporting Information), suggesting that the active site may impose geometric constraints. A systematic release of the constraints on the first and second sphere residues showed that the combination of the constraints on His200 and His155 is the most significant. When these constraints are removed, BrC1 is stabilized in energy by 24 kJ/mol compared to the model with the constraints, while BrC2 is stabilized to a smaller extent. Therefore, for step 1, it appears that there is a trade-off between maximizing the hydrogen bond with the hydroperoxo bridge and the steric interactions between residues in the active site. Thus, the hydrogen bond with His200 influences the selectivity through geometric rather than electronic effects. Further details are given in the Supporting Information. Thus, in addition to its importance in proton transfer,15 His200 plays a role in dictating the regiospecificity of the enzyme. Although these results give us insight into how the active site influences the selectivity of the enzyme, experimental evidence suggests that there must be still more factors at play, since both the mutation of His200 and the change in substrate are required to achieve intradiol behavior in HPCD. Replacement of the native substrate with 2,3-DHB in the enzyme active site leads to a reversal in the selectivity with formation of BrC1 preferred by 11.4 kJ mol−1. This value, however, falls within the uncertainty range of our calculations (∼12 kJ mol−1).1d More importantly, this result presupposes that 2,3-DHB has a similar binding mode to that found for the native substrate. In fact, 2,3DHB has three neighboring groups containing O atoms which could act as ligand donors and can bind to the metal in several different manners. Therefore, it is difficult to evaluate the influence of the substrate on the selectivity of the reaction with high certainty. Note that the reaction of HPCD with 2,3-DHB was found to yield the same product as that with HPCA.3 Our results nevertheless demonstrate that the identity of the substrate may have a directing effect. In summary, for step 1 the selectivity of the attack on the substrate is influenced primarily by the presence of Tyr257, which modulates the relative energies of the EAOs for nucleophilic attack and direct C−O bond formation. Thus, the enhanced the driving force of step 1 due to Tyr257 may speed up the reaction and prevent other transformations from occurring (vide infra). There is a secondary effect due to the hydrogen bonding network between second sphere residues and the oxygen species, positioning the latter to promote attack at C2. Because the electronic structure changes from the O2 adduct to TS1C1 or TS1C2 are nearly identical, it is the different thermodynamic driving force that leads to the formation of the hydroperoxo bridge at C2. Thus, our theoretical results

Figure 9. Hydrogen bonding network within the active site of HPCD.

designed to test the influence of the corresponding mutations since in the full enzyme the active site is flexible. Instead this method probes the contribution of each residue in the active site of the native enzyme. The general trends and changes in the electronic structure should be well replicated. For the enzymatic reaction with the native substrate, BrC1 is 28.4 kJ mol−1 higher in energy than BrC2, as discussed earlier. Removal of His200 from the model has only a marginal effect, slightly lowering the preference of the nucleophilic attack at C2 by 6.1 kJ mol−1. Asn157 has a negligible effect on the selectivity as well, either on its own or in combination with other residues. In contrast, removal of Tyr257 from the modeling results in a significant loss of the selectivity with the energy difference between BrC1 and BrC2 reduced to 7.1 kJ mol−1, a change of over 21 kJ mol−1 from that calculated for the entire model. Deleting both His200 and Tyr257 leads to an almost complete loss of the selectivity with the attack at C2 only favored by 2.2 kJ mol−1. Since the preference for BrC2 is initially 28.4 kJ mol−1, their influence appears to be roughly additive, rather than concerted. To understand the role of Tyr257 in dictating the selectivity, attention is turned to the energetics of the nucleophilic attack of the hydroperoxide on QHPCA. In the absence of other geometric influences, the preference of the nucleophilic attack is governed by the relative energy of the electron accepting orbitals (EAOs).29 In this case the EAOs are the two QHPCA CO π* orbitals, which in the isolated substrate are almost energetically degenerate. In the enzyme active site, however, the hydrogen bond between OC2 and Tyr257 stabilizes the C2−OC2 π* orbital, making it a better EAO and hence favoring the attack of the hydroperoxo at C2. More importantly, the hydrogen interaction with OC2 increases the contribution of the O-p orbital in the C2OC2 π bonding MO and the weight of the C-p orbital in the corresponding antibonding MO (electrophilic assistance),30 thereby resulting in more efficient overlap between the EAO and the electron donating orbital (EDO). In addition to the electronic effects, Tyr257 was found to induce a nonplanar distortion at C2 of the aromatic ring and to further strengthen this geometric feature by forming a hydrogen bond with O C2 .31 Therefore, the electronic importance of Tyr257 lies in its ability to lower the energy of the C2OC2 π* orbitals and promote C2−O2 bond formation. The importance of EAO/EDO energies and their overlap in determining reaction outcomes has also been observed for O2 H


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Inorganic Chemistry

Figure 10. Spin-down orbitals from the spin-coupled pairs for the quasi-intermediate (oxyl radical), epoxide, and anhydride. The HOMO and HOMO−1 for QHPCA are included for comparison.

The radical character of the epoxide is centered on C4, C5, and C6 of the substrate ring and bears resemblance to the HOMO−1 (HOMO = highest-occupied molecular orbital) of the isolated substrate. This indicates that the formation of the epoxide involves the electrophilic attack of the oxyl radical on the π-system of the ligand, thereby leaving radical character on the substrate. The epoxide intermediate hence features an antiferromagnetic coupling between the metal and the substrate π-radical. Therefore, for the extradiol channel the EDO is the πorbital of the substrate centered around C3 to C6. Also starting from the quasi-intermediate, the intradiol pathway proceeds via C−C bond breaking over TS3C2, followed by C−O bond formation to give the anhydride. The spin-down partner of the spin-coupled pair for the transition state shows contributions from the oxyl radical as well as from the C−C σ-bonding orbital, reminiscent of the HOMO of unbound QHPCA shown in Figure 10. This analysis indicates that the extradiol and intradiol pathways involve fundamentally different EDOs. In the extradiol pathway, the electron comes from substrate π-system, whereas for intradiol cleavage the electron originates from a hybrid of the C1−C2 σ-bonding orbital and the OC1 and OC2 lone pairs. Influence of the Metal Center and the Coordination Sphere on the Selectivity of Step 2. In order to better understand what factors dictate the extradiol/intradiol selectivity of step 2, the problem was again studied systematically. Starting from the quasi-intermediate the extradiol and intradiol pathways were explored for (1) the isolated substrate, (2) the first coordination sphere, and (3) the second coordination sphere with a similar approach to that used for the study of step 1. Previous work17b has shown that the salt bridge between Arg243 and the substrate reduces the electron donating ability of the latter and leads to longer metal− substrate bond lengths. Therefore, all models include Arg243. His248 has been suggested to influence intradiol/extradiol selectivity,8c,17b so it was also included in the systematic study. The relative energies of the barriers to extradiol and intradiol cleavage are summarized in Table 3. For the unbound substrate, the intradiol pathway was found to be effectively barrierless. Although relaxed surface scans showed a barrier of 2 to 4 kJ mol−1 on the potential energy surface, no transition state could be located. The extradiol

elegantly explain how HPCD directs the reaction not to yield the distal extradiol product for the native substrate (Figure 5). Selectivity of Step 2. After the hydroperoxo bridge is generated, the second step at which the selectivity is important is electrophilic attack of the oxyl radical generated by the O−O bond cleavage on the aromatic ring to form either an epoxide (extradiol pathway) or an anhydride (intradiol pathway) (Figure 3). The oxyl radical is not a local minimum on the reaction profile, but as it is the point at which the pathways diverge, it is a useful point of reference. Once formed this oxyl radical can attack either at C3 to give an epoxide followed by ring opening to form a lactone, or at C1 to insert the O2-atom in the C1−C2 bond to form an anhydride. Starting from BrC2, the formation of the epoxide along the extradiol pathway has been investigated previously and found to be barrierless.8a Along the intradiol channel, a transition state associated with the C1−C2 bond cleavage was located, which is 28 kJ mol−1 above the energy of the quasi-intermediate, in good agreement with the recent QM/MM study.8d Therefore, the extradiol pathway is kinetically favored in the native enzyme. These results are similar to those calculated for the manganese enzyme,8b for which a barrier of approximately 17 kJ mol−1 was calculated for intradiol cleavage and a negligible barrier for extradiol cleavage.8b As the oxyl quasi-intermediate is the last common point of the extradiol and intradiol pathways, it is useful to have an estimate of its energy. This was achieved by fixing the C3−O2 bond at 2.2 Å. This quasi-intermediate is best described as having an FeIII center antiferromagnetically coupled to an oxyl radical, and is estimated to lie 30 kJ mol−1 below TS2C2 in energy. The singly occupied molecular orbital (SOMO) in the spin-down manifold shown in Figure 10 represents the unpaired electron of the oxyl radical. Along the extradiol pathway from TS2C2 to the quasiintermediate and then epoxide, no significant changes in the metal center have been observed. Instead the electronic structure changes take place predominantly in the substrate and the O2 moiety as evidenced by the major changes occurring in the spin-down partner of the spin-coupled pair. These orbitals are shown in Figure 10, along with the high lying occupied MOs from the isolated substrate for comparison. At this point, the substrate has been transformed to a Q derivative. I


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Inorganic Chemistry

relative to the extradiol EDO, the barrier generally increases. In fact, the results show a linear correlation except for models that do not include His200 (including the isolated substrate). When these models are removed from the data, an R2 value of 0.948 is obtained. This supports the idea that the second sphere residues tune the electronic properties of the substrate to direct the extradiol or intradiol pathway. The reason why the results for the models without His200 deviate from linearity is discussed below. Of the second sphere residues, Tyr257 is the only one that forms a hydrogen bond directly with the substrate, at OC2, an oxygen donor to the metal. The intradiol EDO has significantly more OC2 character than the extradiol EDO and is therefore stabilized to a greater extent when Tyr257 is present, thereby increasing the preference for the extradiol pathway. The remaining second sphere residues form hydrogen bonds with the oxygen moiety and tune the relative energies of the EDOs indirectly by modulating the metal−ligand interactions, which in turn influences the metal−substrate interaction. His200 forms a hydrogen bond with the hydroxide bound to the metal. His248 hydrogen bonds with the first coordination sphere residue Glu267 and is also within π stacking distance of the substrate aromatic ring. The influence of these residues on the electronic structure is evident from Table 3, which reveals that removing His248 or His200 decreases the energy gap between the extradiol and intradiol EDOs. This effect is more pronounced for His248. The potential energy surfaces for O−O and C−C cleavage are more complex when His200 is removed from the model. His200 not only is crucial for proton transfer in step 1 but also maintains a hydrogen bond with the Fe−OH moiety once the O−O bond is broken. When His200 is removed from the model, the OH group rotates during O−O bond scission and hydrogen bonds with the oxyl radical. This rotation costs approximately 10 kJ mol−1; however, once it has occurred, both C1−C2 bond cleavage and the extradiol pathway are essentially barrierless. If this rotation is prevented, the barrier to intradiol cleavage is significantly higher at 29.2 kJ mol−1. Consequently, the presence of this new pathway explains why the models with His200 removed do not follow the linear relationship. This result demonstrates that His200 influences not only the relative energies of the relevant EDOs but also the mechanism. As shown in Figure 6, the C1 pathway (Figure 5) is largely blocked at the stage of formation of BrC1. However, the mechanistic investigation on step 2 starting from BrC1 sheds more insights into how HPCD controls the product regiospecificity. The formation of the extradiol epoxide from BrC1 is also calculated to be barrierless. The transition state for intradiol cleavage lies only 2 kJ mol−1 above the energy of the oxyl quasi-intermediate on the potential energy surface, and the barrier changes to −1.2 kJ mol−1 on the free energy surface. Therefore, intradiol cleavage is predicted to be competitive with the extradiol pathway if step 1 proceeded via the attack at C1. This is an interesting result, as it suggests that the selectivity of step 2 is largely determined by the result of step 1. That is, if the entire reaction was initiated via the C1 pathway, both extradiol and intradiol products would be likely to be observed, while only the extradiol product is favored for the C2 pathway (for more details see the Supporting Information.). The same situation is found for the reaction with 2,3-DHB. Starting from BrC1, C−C bond cleavage is calculated to have a negligible barrier, while the formation of the extradiol epoxide now has a barrier of approximately 6 kJ mol−1; extradiol cleavage is

Table 3. Calculated Potential Energies of Barriers to the Extradiol and Intradiol Pathways in kJ mol−1 Relative to the Quasi-Intermediate and the Relative Energy of the Extradiol and Intradiol EDOs (in Hartrees)a TSextra substrate only WT enzyme with native subs (without His200) (without Tyr257) (without His248) (without His248 and Tyr257) (without His248, Tyr257, and His200) (without Tyr257 and His200) (without His248, His200, Tyr257, and Asn157) a

TSintra

ΔE(extra/ intradiol EDOs)

34.6 (28.4) ∼10 20.5 (14.3) 20.5 (16.7) 15.1 (18.6) ∼3 (∼4)

0.02121 −0.02773 −0.02240 −0.01539 −0.01871 −0.02113 −0.02034

10.0 (5.9) 0.9 (0.0)

−0.01407 −0.02050

∼38

Free energies shown in parentheses.

pathway, however, was found to have a barrier of approximately 38 kJ mol−1. This is a complete reversal of the behavior seen in the enzyme, and is consistent with earlier studies.17b Therefore, only intradiol cleavage is expected for the isolated substrate. More importantly, the intradiol product is stabilized by 90 kJ mol−1 relative to the extradiol product. Likewise, in the enzyme, intradiol cleavage is also predicted to be thermodynamically favored with the generated anhydride preferred by 50 kJ mol−1 over the formation of the extradiol epoxide. This indicates that, unlike step 1, step 2 is under kinetic rather than thermodynamic control. Interestingly, for models including the first coordination sphere, the preference for the intradiol pathway is lost. Both extradiol and intradiol routes were found to be effectively barrierless. To gain more insight into the product selectivity change from the isolated substrate to the models including the first coordination sphere, it is useful to look at the electronic structure changes upon the substrate binding. For the unbound substrate, the HOMO (shown in Figure 10) is the EDO associated with the intradiol pathway, and the EDO responsible for extradiol cleavage lies lower in energy, consistent with the predicted preference for intradiol cleavage. Coordination to the metal reverses this ordering, and the extradiol EDO becomes the substrate HOMO; thus, extradiol behavior is then energetically favored. The reason for the change in the energy ordering of the EDOs can be readily attributed to the interaction of the substrate with the metal. The extradiol EDO is primarily localized on the aromatic ring with relatively small contributions on the oxygen donors. The intradiol EDO, however, has a substantial contribution from the in-plane OC1 and OC2 lone pairs and is stabilized by coordination to a metal. In this study, for all models including the metal center the extradiol pathway was found to be barrierless. The barrier to intradiol cleavage, on the other hand, varies from approximately 1 kJ mol−1 for the model including only the first coordination sphere to 28 kJ mol−1 for the full cluster model. Furthermore, the deletion of every residue was found to have an influence, differing from previous computational studies.8c,17b Since a higher barrier to intradiol cleavage appears due to a higher lying intradiol EDO, the energy separations between the extradiol and intradiol EDOs were recorded for the models used in Table 3. A plot of intradiol barriers against the relative energies of the extradiol and intradiol EDOs (Figure S6) demonstrates that, as long as the intradiol EDO is stabilized J


Article

Inorganic Chemistry

techniques through investigating two key steps: (1) attack of superoxide on the substrate to form a hydroperoxo bridge and (2) O−O bond cleavage and subsequent attack of an oxyl radical on the substrate. The selectivity at both steps was investigated through a systematic study of the role of the substrate, and the first and second coordination spheres. For step 1, the superoxide may attack two positions: either C1 or C2. For this step the second sphere residues His200 and Tyr257 were found to determine which of these two sites is favored. Tyr257 forms a hydrogen bond with the substrate at OC2. This hydrogen bond stabilizes the C2OC2 π* orbital, making it a better electron accepting orbital (EAO), and enhances the overlap between the EAO and the electron donating orbital (EDO); therefore, both effects work in synergy to direct the nucleophilic attack at C2. The importance of His200 in acid/base catalysis15 has been well documented; however, its role in influencing the selectivity has been, until now, less well understood. In the accepted reaction mechanism His200 plays an important role in proton transfer from the substrate to the superoxide species. This study shows that it is also carefully positioned to favor the nucleophilic attack of the generated hydroperoxide on C2 in step 1. In step 2, for the isolated substrate intradiol cleavage was found to be both thermodynamically and kinetically preferred. In the enzyme active site intradiol cleavage is still predicted to be thermodynamically favored; however, the active site controls the kinetics of the reaction through coordinating the substrate to the metal center and through hydrogen bonding with key second sphere residues. Importantly, the results of this study indicate that the selectivity depends on the relative energy of the EDOs. When the oxyl radical attacks the substrate, the electron may come either from the substrate π-system (extradiol pathway) or from an orbital with substantial C−C σ-bonding character (intradiol pathway). Coordination to the metal center and hydrogen bonds with key residues influence the relative energies of these two orbitals. Three second sphere residues were found to have an important influence on the selectivity at step 2: Tyr257, His200, and His248. All three were found to influence the relative energies of the EDOs. Of these Tyr257 has the greatest electronic effect through the hydrogen bond with OC2 of the substrate. His200 is important both electronically and geometrically. When His200 is removed from the model, an alternative pathway to intradiol ring opening becomes energetically accessible. His248 exerts both steric and electronic influence as it is positioned within the π stacking distance of the substrate aromatic ring. If all three residues are removed from the model, the preference for extradiol cleavage is almost completely lost. Taken together, the results of this study demonstrate that Tyr257 and His200 play pivotal roles in governing the product regiospecificity in both steps 1 and 2.

favored if the reaction proceeds via BrC2. Similar to step 1, a definite conclusion about the effect of the substrate on the regiospecificity of step 2 cannot be reached, because of the small energy gaps delivered by the computations; nevertheless these results do offer some insight into the differences and similarities between the substrates. In summary, for step 2 the system was found to be under kinetic control and the relative barriers for extradiol or intradiol cleavage determine the final reaction outcome. For the unbound substrate, intradiol cleavage is highly preferred. However, upon coordination to the metal center, this product selectivity is completely lost. The second coordination sphere was found to tune the electronic structure of the substrate to direct the extradiol pathway. Three key second sphere residues are found to play an important role: Tyr257, His200, and His248. For the model in which all three residues were removed, the barrier to intradiol cleavage was reduced to approximately 4 kJ mol−1, significantly lower than that calculated for the full active site. These models with residues deleted do not reflect the behavior of the corresponding mutations as they may result in major shifts in the active site. They do, however, probe the role of the residues in the active site of the native enzyme. Unlike His200 and Tyr257, removal of His248 may cause drastic geometric arrangements of Glu267, which may then form a new hydrogen bond with the substrate, likely changing the reaction energetics. For both steps, the importance of Tyr257 lies in its ability to modulate the energy of the substrate orbitals. Experimental results for the Tyr257Phe mutant provide a useful comparison to our computational findings. For Tyr257Phe, despite the reaction involving different intermediates, the proximal extradiol product is still observed albeit at a much slower reaction rate.7g This is in general consistent with the results of the current work, as the proximal extradiol pathway is calculated to be preferred even in the absence of Tyr257. Interestingly, the electronic structure of Tyr257Phe-HPCAInt2 is the same as that computed for TS1C2 in the reaction with the wide-type enzyme. Starting from TS1C2, the nucleophilic attack of the hydroperoxo on Q HPCA (step 1b) takes place spontaneously, because BrC2 lies 34.2 kJ mol−1 lower in energy than TS1C2. In step 1 Tyr257 is found to appreciably increase the driving force for formation of BrC1; thus, one may expect that replacing Tyr with Phe should considerably slow step 1b due to lack of sufficient driving force. The experimental investigations showed that this is indeed the case. 7g Furthermore, the high inertness of the FeII-QHPCA complex in Tyr257Phe may explain why this species was found to be an intermediate instead of a transition state. An interesting prediction arising from this study is that if both His200 and Tyr257 were not present in the enzyme active site, intradiol cleavage may be possible in this enzyme even with the native substrate, provided that the enzyme still turns over. Our theoretical results show that the enzyme active site is designed to reverse the natural tendency of intradiol cleavage toward extradiol ring opening, using hydrogen bonds with key second sphere residues. The importance of the hydrogen bonding in determining the selectivity of the enzyme perhaps explains the influence of solvent and changes in the ligand backbone on the reactivity and selectivity of model complexes.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.5b02978. Tables of coordinates of optimized structure and analysis of the electronic structure of key intermediate (PDF)

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CONCLUSIONS In this study, intradiol vs proximal extradiol regiospecificity of extradiol dioxygenases was explored using computational

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. K


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The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We acknowledge the financial support from the German Science Foundation (DFG), the University of Bonn, the MaxPlanck Society, and the Humboldt foundation in the form of a postdoctoral fellowship for G.J.C. We also acknowledge the NCI National Facility in Canberra, Australia, which is supported by the Australian Commonwealth Government, for computational resources.

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