Spectroscopic and computational studies of nitrile hydratase: insights into geometric and electronic structure and the mechanism of amide synthesis

In addition to its activation of coordinated nitriles, nitrile hydratase utilizes a coordinated sulfenate ligand as a well-oriented nucleophile to form a five-membered intermediate which subsequently undergoes attack by H2O to ultimately form the amide product.


Introduction
Nitriles produced by plants and animals are a source of carbon and nitrogen for some microorganisms. Nitrile hydratases (NHases) are enzymes found in bacteria that catalyze the hydrolysis of nitriles to amides as part of the nitrile degradation pathway. 1 NHases have been used industrially as catalysts for the production of methacrylonitrile and nicotinamide, 2 and have also been used in the synthesis of chiral amides 3 and possess the potential to treat industrial wastewater. 4 As shown in Fig. 1A, NHases possess an active site that uses either lowspin (LS) Fe III or LS Co III complexed to a very unusual ligand set. 5,6 This set is comprised of two deprotonated backbone amides or amidates, a cysteine thiolate, cysteine-derived posttranslationally modied sulfenic/sulfenate (Cys-SO(H)) and sulnate (Cys-SO 2 À ) groups, and an exogenous ligand (X). The protonation state of the Cys-SO(H) group in the active form of the enzyme has not been unambiguously determined, with conicting spectroscopic evidence for the sulfenate and sulfenic acid forms in the literature. 7,8 NHases are ab heterodimers with the metal ligand residues residing in the a subunit. The Cys-SO 2 À and Cys-SO(H) residues H-bond with two arginines on the b subunit, as shown in Fig. 1B. 5,6 For the Fe III NHase of Rhodococcus erythropolis N771 bArg56 (Fig. 1B) was found to be essential for catalysis. In Co III NHases the sixth ligand (X in Fig. 1A) is derived from water, 6 whereas Fe III NHase produced in the dark has a NO bound to Fe that is photolytically cleaved to produce the active form containing a water-derived ligand ( Fig. 2A). [9][10][11] If le exposed to air for a sufficient period of time, the Cys-SO(H) ligand is oxidized to Cys-SO 2 À and the enzyme becomes inactive (Fig. 2B). 12 However, butyric acid may be added to act as a protecting agent, binding to Fe and inhibiting further oxidation of the Cys-SO(H) group (Fig. 2C). [13][14][15] Butyric acid has also been found to be a competitive inhibitor, which becomes more strongly inhibiting with decreasing pH. 16 This indicates that it is the protonated form of the acid that stabilizes the enzyme (although from EPR data and DFT calculations (vide infra) the proton transfers to the sulfenate group upon butyric acid coordination to NHase Fe III ). The catalytic mechanism by which these enzymes operate has not yet been fully elucidated. The fact that the coordinated butyrate acts as a competitive inhibitor suggests that nitrile is activated for nucleophilic attack by coordination to metal, which has provided support for the mechanism of a water attacking this coordinated nitrile with a base accepting a proton as shown in Fig. 3A. [17][18][19][20] Recently, a crystallographic study by Holz and coworkers 21 showing that alkyl boronic acids, also competitive inhibitors, bind to the active site metal of NHase and are nucleophilically attacked by the sulfenate oxygen. This led to the proposal that the RSO(H) itself is the nucleophile that attacks the coordinated nitrile C as shown in Fig. 3B, activating it for nucleophilic attack by water on either the C or S atoms ( Fig. 3C and D, respectively). 21 A related mechanism has been proposed 22 that involves the axial thiolate acting as the initial nucleophile and the subsequent formation of a disulde bond, as shown in Fig. 3E. The protonation states of the water-derived and Cys-SO(H) ligands in the active form of the enzyme are not well dened, and their determination is important in understanding the mechanism of nitrile hydrolysis.
It is also important to note that a second-sphere mechanism involving nucleophilic attack on an uncoordinated nitrile in the active site pocket by a coordinated hydroxide has been proposed and found to have a theoretically similar barrier to coordinated nitrile activation via DFT calculations. 20,23 However, such a mechanism is not in agreement with the crystallographic results involving boronic acids described above. 21 In this study we use electronic paramagnetic resonance (EPR), absorption, and magnetic circular dichroism (MCD) spectroscopies to determine the geometric and electronic structures of the paramagnetic LS Fe III NHase from Rhodococcus erythropolis N771 in its butyrate-bound (NHaseBA) and active  (NHaseAq) forms. EPR spectra of the oxidized, inactive form of NHase (NHaseOX) further allow us to characterize the protonated and deprotonated forms of NHaseAq. Due to the relatively complex nature of the NHase ligand set with regard to possible ligand-to-metal charge transfer (LMCT) transitions, band assignment is assisted through a density functional theory (DFT) computational investigation of a series of LS Co III complexes [(en) 2 Co(XCH 2 CH 2 NH 2 )-N,S] 2+/3+ (Fig. 4) and their hypothetical LS Fe III counterparts, where X is a thiolate, sulfenate, sulfenic acid, or sulnate group. [24][25][26] These results provide insight into the relative energy ordering of the LMCT transitions for the different sulfur ligands. We use the subsequently assigned experimental data to calibrate DFT models of the butyrate bound and active forms of NHase and to extend these computational models to examine potential mechanisms for nitrile hydrolysis. These results provide insight into the electronic structure of the unusual active site of NHases and the mechanistic strategy developed by this class of enzymes.

Results and discussion
EPR spectroscopy of NHaseBA, NHaseAq, and NHaseOx EPR powder pattern spectra of LS Fe III systems generally exhibit 3 features around g eff z 2.0. 27 The g values are sensitive to the ligand environment, and can allow the determination of the number of species in a given sample, as well as their relative abundance and a quantitative analysis of the ground state. The EPR spectra of NHaseBA at pH 7.5 and NHaseAq at pH 6.5, 7.5, and 8.5 are shown in Fig. 5. NHaseBA (Fig. 5, blue) is a clean single species with g values of 2.28, 2.14 and 1.97. NHaseAq at pH 7.5, on the other hand, is a mixture of 2 species (Fig. 5, green). At pH 8.5 the minor species component has increased in relative contribution (Fig. 5, purple). Simulations of the spectra (see ESI †) indicate that at pH 7.5 NHaseAq is a 74%/26% AE 5% mixture, with the major species having g values of 2.20, 2.13, and 1.99, and the minor species having g values of 2.22, 2.14 and 1.98. These are indicated in Fig. 5. On going from pH 7.5 to 8.5 the ratio changes to 52%/48% AE 5%. Buffer exchanging the sample back to pH 7.5 leads to the original EPR spectrum (data not shown). These results indicate that the NHaseAq active site possesses a deprotonatable ligand with a pK a z 8.5. On going from pH 7.5 to 6.5 (Fig. 5, orange), the EPR spectrum of NHa-seAq shows that the high-pH minor species (above) has disappeared, and has been replaced by a third species with g values of 2.28, 2.14 and 1.97. The pH 6.5 sample is comprised of approximately 28% of this low-pH minor form and 72% of the major form, indicating a second deprotonatable ligand with a pK a z 6.1. This value is identical to the pK a determined for the sulfenate of the alkyl hydroperoxide reductase AhpC. 28 Again, increasing the pH back to 7.5 restores the pH 7.5 spectrum, showing that the process is reversible (data now shown).
EPR spectra of NHaseOx at pH 6.5, 7.5 and 8.5 are shown in Fig. 6. Spectra taken at 7.5 (red) and 8.5 (purple) indicate there is an acid-base equilibrium present for NHaseOx similar to that of NHaseAq with a pK a > 7 (a shoulder to the low eld side of g ¼ 2.2 (arrow) increases in intensity on going from pH 7.5 to 8.5). However, on going from pH 7.5 to 6.5 (cyan), no third species is observed. This implies that the moiety in NHaseAq with a pK a of 6.1 is the Cys-SO(H) group, and that at the active form present under functional conditions possesses a deprotonated sulfenate ligand. As sulnic acids generally have pK a values of approximately 2, 29 this means that the moiety in NHaseAq with a pK a of 8.5 is the water-derived ligand, and that under  functional conditions NHaseAq also possess a coordinated water ligand (X in Fig. 1A).

NIR MCD spectra of NHaseBA and NHaseAq: low energy d-d transitions
Octahedral LS Fe III species possess a (t 2g ) 5 ground conguration giving a threefold orbitally degenerate 2 T 2g ground state, which in the rhombic ligand environment of a protein site splits in energy and leads to two t 2g / t 2g (dp / dp) transitions at #5000 cm À1 . The orbitally degenerate doublet excited states also split to produce a manifold of t 2g / e g (dp / ds) transitions from z15 000 to 30 000 cm À1 , although the higherenergy ligand eld (LF) transitions are frequently obscured by the intense LMCT transitions and may be difficult to detect. 27 The 1.5 K, 7 T NIR MCD spectra of NHaseBA and NHaseAq at pD 7.5 are shown in Fig. 7A and B, respectively. The spectrum of NHaseBA has a band at z5600 cm À1 corresponding to the highest energy dp-dp transition, as well as a band at z10 600 cm À1 , which corresponds to the lowest energy dp-ds transition. 30 The shoulder of the z13 600 cm À1 Cys-Sp / dp LMCT is also visible as a tail in the higher energy region of this spectrum (vide infra). The spectrum of NHaseAq shows two bands at low energy, one with añ max < 5000 cm À1 (Gaussian t at z4700 cm À1 ) and another withñ max z 6300 cm À1 . Thus the dp-dp transitions of NHaseAq are raised in energy relative to those of NHaseBA. The lowest energy dp / ds transition of NHaseAq is also higher than that of NHaseBA at z11 000 cm À1 .

Assignment of t 2g orbital splittings
As the ground states of six-coordinate LS Fe III active sites are derived from the 2 T 2g states of O h , in addition to the low symmetry splitting of the dp orbitals considered above they have in-state orbital angular momentum and thus undergo instate spin-orbit coupling (SOC). This in-state coupling has a signicant effect on the experimental EPR g values of a complex. A system of equations developed by Taylor includes this SOC and allows for the determination of the energy splitting of the t 2g orbitals as well as the order and sign of the experimental g values. 31 The t 2g orbital energies of a given site are dened by the tetragonal splitting, D, of the d xy orbital from the {d xz , d yz }  pair, and the rhombic splitting, V, of the d xz and d yz orbitals. The quantity |V/2D| is a measure of the rhombicity of the LS Fe III site, with a value of zero indicating a purely axial system and a value of 1/3 being the rhombic limit in which the t 2g orbital splittings are equal. The assigned g values, energy splitting parameters, and predicted transitions for NHaseBA and NHaseAq are given in Table 1. The values of a, b, and c are the coefficients of the d yz , d xz , and d xy orbitals, respectively, in the half-occupied dp ground state. The predicted dp-dp transition energies of NHaseBA (z2800 cm À1 and 5300 cm À1 ) and NHaseAq (z3900 cm À1 and 6200 cm À1 ) compare well with the experimental values (z5600 cm À1 for NHaseBA, the lowest energy dp / dp transition being below the detection limit of the instrumentation, and z4700 cm À1 and 6200 cm À1 for NHaseAq), indicating that the Taylor method provides an accurate description of the t 2g dp orbital energies. The negative values of D for NHaseBA and NHaseAq indicate that d xy is the half-occupied orbital for both of these forms of the enzyme. This is reected in the coefficients where c is dominant. The |V/2D| value for NHaseBA indicates that this form has a strongly rhombic Fe III site, whereas the value of NHaseAq indicates that its site is closer to axial.

LS Co III and Fe III models: bonding interactions and their associated LMCT transitions
The unusual ligation of NHase allows a number of different possible CT transitions, whose nature and energy order need to be claried. One may initially anticipate thiolate p / dp*, amidate p / dp*, and thiolate/sulfenate/sulfenic/sulnate s / ds* CT transitions as potentially occurring within the accessible spectral range for UV-Vis absorption (z11 000-33 000 cm À1 ). It has been previously shown through resonance Raman spectroscopy 32 that the thiolate p / dp* CT transition for butyrate-free Fe NHases occurs at z14 700 cm À1 (680 nm) and shis to z14 100 cm À1 (710 nm) upon butyrate binding. 16 The LS Fe III cyanide-bound form of superoxide reductase (SOR) also exhibits a thiolate p / dp at $15 200 cm À1 . 33 Resonance Raman spectroscopy identied amidate p / dp CT transitions in ferric bleomycin (FeBLM) and activated bleomycin (ABLM) at z26 400 cm À1 and z27 300 cm À1 , respectively. 30 NHase has two amidates, whose proximity leads to in-phase (+) and out-ofphase (À) combinations of ligand donor orbitals p + and p À as shown in Fig. 8. Therefore, it is reasonable for two amidate pdp* CT transitions to contribute to the spectrum of NHase in the z26 000 cm À1 energy region.
There has been an interesting study of the UV-Vis absorption spectra of a series of LS Co III complexes [(en) 2 Co(XCH 2 CH 2 -NH 2 )-N,S] 2+/3+ , where X is S À , S-coordinated SO À , S-coordinated SOH, and S-coordinated SO 2 À . [24][25][26] This series provides a complete set of spectroscopic data for the thiolate-based ligands of interest for which the computational extension to the hypothetical LS Fe III forms is straightforward. The observed LMCT's are given in Table 2. For LS Co III (d 6 ) these can only be Ls / ds* CT transitions as there is no electron hole in the dp manifold. The thiolate and sulnate complexes exhibit LMCT transitions at z35 000 cm À1 , with the latter lower in energy by 800 cm À1 . The sulfenate complex, however, exhibits a lower energy LMCT transition at 27 400 cm À1 , in addition to a transition at 35 200 cm À1 . Addition of protons diminishes the intensity of the lower energy transition, while addition of BF 3 eliminates it entirely. 26,34 TD-DFT calculations were performed on the LS Co III complexes and their LS Fe III counterparts, with the predicted transition energies listed in Table 2. Contours of the ligand donor molecular orbitals involved in these transitions are shown in Fig. 9. The thiolate ligand has two S 3p orbitals for bonding to metal (the third 3p orbital is involved in bonding to C), one and NHaseAq (B) at pD 7.5. Experimental data are in blue, the fit is in black dashes, red dashed curves denote d-d transitions and the green dashed curve denotes the thiolate-to-dp LMCT. Table 1 Predicted g values, dp coefficients, dp splitting parameters and dp-dp transitions for NHaseBA and NHaseAq from the Taylor method. Splitting parameter and transition values are in cm À1 Form  Co III transition energies agree qualitatively with the experimental results. The thiolate s / ds* transition predicted by TD-DFT is higher in energy than the corresponding sulnate by 2700 cm À1 , vs. 800 cm À1 in the experimental data. The TD-DFT sulfenate s IP / ds* transition is lower in energy than the thiolate s and sulnate transitions at 29 800 cm À1 , comparable to the experimental value of 27 400 cm À1 . A sulfenate s OOP / ds* transition is predicted at 34 900 cm À1 , but this transition will not be observed in an NHase active site with a deprotonated sulfenate group. The protonated sulfenate complex possesses a calculated RSOH s IP / ds* at 39 200 cm À1 , comparable to the analogous transition in the thiolate complex. A calculated RSOH s OOP / ds* transition occurs at a signicantly higher energy of 42 800 cm À1 , which is beyond the protein cutoff for spectroscopy on an enzyme (z33 000 cm À1 ).
In order to extend the above ndings to the LS Fe III site of NHase, Fe III was computationally substituted for Co III in the starting structures of the 4 model complexes above and reoptimized (with an S ¼ 1/2 ground state). These hypothetical Fe III complexes have TD-DFT transitions that are comparable to their Co III counterparts, with the Fe III transitions at higher energy due to the lower Z eff of Fe III leading to a higher energy d orbital manifold relative to Co III . The Fe III thiolate complex also has a dp* hole due to the LS d 5 conguration leading to a RS À p / dp* transition at 19 600 cm À1 from TD-DFT, or about 5000 cm À1 higher in energy than the corresponding transitions of NHaseBA, NHaseAq and cyanide-bound SOR. Scaling the other Fe III TD-DFT calculated transition energies by a similar amount gives predicted deprotonated sulfenate s IP / ds* transition at z28 000 cm À1 and sulfenate/thiolate/sulnate s transitions predicted at 33 000-36 000 cm À1 for NHaseBA and NHaseAq. The relative energy order for the LMCT transitions in NHase is therefore predicted to be Cys-S À p / dp* (experimentally assigned by resonance Raman at z15 000 cm À1 ) < amidate p / dp* z Cys-SO À s IP / ds* < Cys-SO 2 À s IP / ds* < Cys-S À s IP / ds* < Cys-SOH s IP / ds*. It should be noted that the Cys-SO À s IP MO is the highest in energy among the occupied Sbased ligands, and has considerable O character (48% O vs. 32% S in the Fe III model), indicating that it has the potential to be a good nucleophile (vide infra).

UV-Vis low-temperature absorption and MCD spectroscopy of NHaseBA and NHaseAq
The 5 K absorption spectrum and 5 K, 7 T MCD spectrum of NHaseBA are given in Fig. 10A and B, respectively. A list of band Fig. 8 The diamidate moiety in NHase (left) and its in-phase (center) and out-of-phase (right) p MO combinations. energies, 3 and D3 values, and C/D ratios is given in Table 3. Temperature dependence indicates the MCD transitions are all C terms of a paramagnetic complex. The C/D ratio of a transition is proportional to its D3/3 value, and is generally higher for d-d than CT transitions. 35 The Cys-S À p / dp* LMCT transition occurs at 13 600 cm À1 (band a) from resonance Raman spectroscopy. 32 The transitions at 15 700, 17 500, 19 500 and 21 800 cm À1 (bands b, c, d, and e, respectively) are determined by their relative lower 3 values (and higher D3 in MCD) as dp / ds* ligand eld transitions. As NHaseBA has a protonated sulfenate group, the intense in absorption, and therefore CT in nature, transitions at 24 700 and 27 000 cm À1 (bands f and g) are ascribed to amidate p / dp* transitions, while the 30 000 cm À1 (band h) transition is assigned to the Cys-SO 2 À s / ds* CT transition. The LS nature of the Fe III site implies strong ligand bonds and relatively high covalency, which can lead to signicant ligand character in the d-based molecular orbitals and increased absorption intensity for the d-d transitions through LF excited state mixing with CT transitions. The CT transitions of NHaseBA generally have low C/D ratios, except for the Cys-S À p / dp* (band a in Fig. 10) and amidate p + / dp* (band f in Fig. 10) transitions which have signicant MCD intensities of opposite sign. This can be explained by the two transitions interacting through SOC to form a pseudo-A term in MCD. The pseudo-A term requires 2 perpendicularly polarized transitions to SOC in a third mutually orthogonal direction. 36 From the DFT results given in the ESI, † the Cys-S À p / dp* CT transition is y-polarized with the Cys-S À p donor MO having d xz character, while the amidate p + / dp* transition is x-polarized with the amidate p + donor MO having d yz character. The d xz and d yz characters of these two donor MOs couple by the L z component of the angular momentum operator and therefore spin-orbit couple to produce the pseudo-A-term.
The absorption and MCD spectra of NHaseAq are given in Fig. 11. A list of band energies, 3 and D3 values, and C/D ratios is given in Table 4. The spectra in Fig. 11 are similar to those in Fig. 10, but with more absorption intensity in the 25 000-30 000 cm À1 region associated with the butyrate being replaced by H 2 O and Cys-SOH deprotonated to Cys-SO À . NHaseAq possesses a Cys-S À p / dp* LMCT transition at 14 300 cm À1 (band a) which is shied up from that of NHaseBA by 700 cm À1 and is similar to the results previously found in the room temperature absorption spectra for other NHases. 14 The dp / ds* LF transitions of NHaseAq (bands b-e) are also shied up in energy relative to that of NHaseBA, consistent with the LF effects on the dp splitting. The amidate p / dp* CT transitions (band f) are also shied higher in energy relative to NHaseBA at z27 500 cm À1 . Instead of two features, however, one broad feature is observed with higher intensity than the two amidate p / dp* CT transitions of NHaseBA (z2100 M À1 cm À1 for each NHaseBA transition vs. 3200 M À1 cm À1 for the NHaseAq transition). It is possible that the Cys-SO À s / ds* transition (predicted to be in this energy region from the model complex DFT calculations, vide supra) overlaps with the two amidate p / dp* transitions to form this broad, intense feature. The transition in the NHaseAq spectra at z30 600 cm À1 (band g) is similar in energy and intensity to band h in NHaseBA and is reasonably assigned to the Cys-SO 2 À s / ds* CT transition.
DFT and TD-DFT calculations: EPR parameters, dp orbital splittings and ground state wave functions The DFT optimized structures of NHaseBA and NHaseAq are shown in Fig. 12 (note that both are based on crystal structures).
Optimization of an NHaseBA structure with a sulfenate and protonated butyric acid ligand leads to the proton moving to the sulfenate group. NHaseAq contains an exogenous water that is H bonding with both the sulfenate oxygen and the coordinated water ligand. The B3LYP, BP86, and BP86 with 10% Hartree- Experimental data are in black, the total fit is in dashed gray, and dashed Gaussian curves denote Cys-S À p / dp (a, green), dp / ds (b-e, black), amidate p / dp (f-g, red) and Cys-SO 2 À s / ds (h, blue) transitions. Fock (HF) functionals were tested by optimizing the NHaseBA and NHaseAq structures in the S ¼ 1/2, S ¼ 3/2, and S ¼ 5/2 states to determine if each functional correctly predicted the ground state spin (S ¼ 1/2). The values of DH(1/2 / 3/2) and DH(1/2 / 5/2) for the different functionals are given in Table 5. The B3LYP functional predicts the S ¼ 1/2 and S ¼ 3/2 states are virtually isoenthalpic for both NHaseBA and NHaseAq, rendering this functional unsuitable for modeling the NHase active site. While the BP86 with 10% HF functional predicts an S ¼ 1/2 ground state for both NHaseBA and NHaseAq, it predicts Cys-S À p / dp CT transitions of 16 400 cm À1 for both NHaseBA and NHaseAq, whereas the pure BP86 functional predicts the NHaseAq transition to be 500 cm À1 higher in energy than the NHaseBA transition (vide infra), which is very close to the 700 cm À1 difference observed experimentally. The pure GGA BP86 functional was therefore used for all subsequent calculations.
The ORCA program was used to calculate the EPR g values for the NHaseBA and NHaseAq models as listed in Table 6. Signicant deviations from the largest experimental g value for each form of NHase are calculated consistent with past results that DFT tends to underestimate the largest g value. 37 The calculated g tensor directions for both the NHaseBA and NHa-seAq models indicate that the x direction is approximately along the amidate N-Fe-sulfenate S bond axis, the y direction is pointing along the thiolate S-Fe-butyrate/water O bond axis and the z direction is effectively pointing along the amidate N-Fe-sulnate S bond axis (see ESI †).
The minority spin b molecular orbital energy diagrams for NHaseBA and NHaseAq are given in Fig. 13 le and right, respectively. Contour plots for all MOs in Fig. 13 are supplied in the ESI. † For both forms of the enzyme the calculated halfoccupied t 2g orbital is d xy (perpendicular to the amidate Nsulfenate S axis) 206b for NHaseBA and 200b for NHaseAq in Fig. 14 (le and right, respectively). For both MOs d xy interacts most strongly with the Cys-S À p orbital, but also interacts with the amidate p orbitals trans to the sulfenate group. The thiolate ligand of NHase is therefore the strongest p donor ligand in this enzyme. The implications of this strong donor bonding interaction will be considered further in the Discussion. From Fig. 13, the unoccupied s* orbitals are d x 2 Ày 2 and d z 2, with the d z 2 Experimental data are in black, the total fit is in dashed gray, and dashed Gaussian curves denote Cys-S À p / dp (a, green), dp / ds (b-e, black), amidate p / dp/Cys-SO À s / ds (f, orange) and Cys-SO 2 À s / ds (g, blue) transitions. orbital highest in energy. These two ds orbitals are split by z6000 cm À1 in NHaseBA and z6300 cm À1 in NHaseAq. The sulnate and its trans amidate both overlap with d z 2 and are therefore the strongest s donors in the active site.
DFT and TD-DFT calculations: dp / ds* LF and CT transitions From Fig. 13, closest in energy to the Fe d orbital manifold for both active site models is the Cys-S À p orbital, as would be expected from its p bonding nature and the relatively low electronegativity of the S valence 3p orbitals. For the NHaseBA model, the next highest-energy MO is the diamidate in-phase, p + , combination, with the out-of-phase, p À , combination at lower energy. The Cys-SO 2 À s orbital (Fig. 9) is sandwiched between the p + and p À MOs. For NHaseBA, below p À lies the Cys-SOH s and the Cys-S À s MOs are lowest in energy. For the NHaseAq model, the next MO below the thiolate p is the Cys-SO À s donor orbital. The removal of the proton from the coordinated sulfenic acid signicantly raises the energy of this orbital, reected in the low energy Cys-SO À s / ds* CT transition of the Co III sulfenate complex that was eliminated upon protonation of the sulfenate group (vide supra). The high energy of this Cys-SO À MO has implications for this ligand's capacity as a nucleophile (vide infra). Below the Cys-SO À s lie the amidate p + and p À MOs followed by the Cys-SO 2 À s and Cys-S À s MOs.
Thus the calculated energy ordering of the different S ligands reasonably parallels the order determined experimentally for the model complexes.
The experimentally-determined and TD-DFT-predicted transitions for NHaseBA and NHaseAq are given in Fig. 15 le and right, respectively. The predicted dp / dp* transitions for NHaseBA are at 3600 and 6900 cm À1 , similar in energy to the experimentally determined (from Taylor analysis and NIR MCD data) values of 2800 and 5300 cm À1 . The same is true for NHaseAq, with calculated values of 4300 and 7200 cm À1 compared to experimental values of 3900 and 6200 cm À1 . The calculations correctly predict the increase in the dp / dp LF transition energies upon replacing the butyrate ligand with water, and the values of |V/2D| determined from these TD-DFT transitions (0.31 for NHaseBA and 0.25 for NHaseAq) agree well with the experimental values (0.32 and 0.23, respectively). The calculated dp / ds* LF energies for NHaseBA range from 10 200 to 18 900 cm À1 , which compares reasonably well to the experimental range of 10 600 to 21 800 cm À1 . The corresponding dp / ds* transition energies for the NHaseAq model range from 10 900 to 19 400 cm À1 , similar to the experimental transitions of 11 000 to 23 900 cm À1 . The calculated dp / ds* transitions shi up in energy upon replacing butyrate with water, as is observed experimentally, which indicates an increase in 10Dq, reecting replacement of the p donor butyrate in NHaseBA by water.
The calculated Cys-S À p / dp CT transitions are at 11 800 cm À1 for NHaseBA and 12 300 cm À1 for NHaseAq. These values are in the range of those determined experimentally (13 600 cm À1 for NHaseBA and 14 300 cm À1 for NHaseAq), and the increase in transition energy upon substituting a water ligand for butyrate is correctly predicted. The calculated amidate p / dp* transition energies for NHaseBA (16 200 and 19 700 cm À1 ) and NHaseAq (18 800 and 20 600 cm À1 ) are signicantly lower than their experimental counterparts (z26 000 cm À1 for NHaseBA and z27 000 cm À1 NHaseAq), perhaps reecting a large self-interaction error for the anionic ligands. 38 The models do, however, correctly predict that the amidate-based transitions of NHaseAq are shied up in energy relative to those of NHaseBA. For NHaseBA the calculated Cys-SOH s / ds and Cys-SO 2 À s / ds CT transitions are 31 900 and 33 600 cm À1 , respectively. From the model studies it was predicted that the Cys-SOH-based transition would lie to higher energy, but in this system the Cys-SO 2 À transition is to the higher energy d z 2 orbital while the Cys-SOH transition is to the lower energy d x 2 Ày 2 orbital. In the TD-DFT calculation of NHa-seAq, the Cys-SO À -based transition at 25 200 cm À1 is 6000 cm À1 lower in energy relative to that of Cys-SOH in NHaseBA. This is consistent with the experimental Cys-SOH s / ds* CT  Lines are colored purple for dp / dp, black for dp / ds, green for Cys-S À p / dp, red for amidate p / dp, orange for Cys-SOH/-SO À s / ds and blue for Cys-SO 2 À s / ds. The transition at z27 000 cm À1 in the upper-right plot is marked half red, half orange to denote the overlap of the amidate dp / dp and Cys-SO À s / ds transitions. transition of NHaseBA being unobserved and the broad, intense transition of NHaseAq at 27 500 cm À1 arising from the overlap of the amidate p / dp* and Cys-SO À s / ds* CT transitions. The lower energy CT transition for sulfenate vs. sulfenic acid indicates an increase in the sulfenate frontier MO energy with deprotonation and a consequent increase in its nucleophilic character. While TD-DFT calculations of the CT excited states are shied relative to experiment, their ordering and energy shis between enzyme forms are consistent with experiment. Also, the functional used predicts the correct LS ground state and from the Taylor analysis above the ground state parameters are well described. The functional (BP86) and basis set employed above were thus used to evaluate possible mechanisms of nitrile hydration by this unusual LS Fe III active site.

Reaction coordinate calculations
Nucleophilic attack on coordinated acetonitrile by water with the sulfenate group acting as a proton acceptor was explored as described previously. 20 This is shown in blue in the energy diagram in Fig. 16, with corresponding structures in Fig. 17, top. At the transition state, the proton is approximately equidistant between the water and sulfenate oxygens. The electronic energy of the transition state lies 16.7 kcal mol À1 above the ground state, similar to the value of 20.2 kcal mol À1 obtained previously. 20 Complete transfer of the proton to the sulfenate group leads to a coordinated amidate tautomer structure 11.3 kcal mol À1 above the starting structure, labeled as 'SOH' in Fig. 16. Rotation of the amidate tautomer around the Fe-N axis leads to the abstraction of the proton of sulfenic acid by amidate tautomer N, generating the coordinated amide tautomer at À14.4 kcal mol À1 relative to the starting coordinated nitrile structure. Tautomerization/dissociation of the product amide and regeneration of the active form of NHase leads to a net energy change of À10.4 kcal mol À1 . For the reaction of two water molecules with free acetonitrile, one water acting as nucleophile and the other as proton acceptor, 20 the electronic energy of the transition state is 27.4 kcal mol À1 , or approximately 11 kcal mol À1 higher than for water attack on NHase LS Fe III -coordinated nitrile. Thus the combination of activation of nitrile by coordination to metal and the better nucleophilic character of sulfenate relative to water lowers the energy barrier by z11 kcal mol À1 .
Alternatively, the sulfenate group can act as the nucleophile towards the coordinated nitrile to form a cyclic intermediate. 21 Fig. 16 Reaction coordinates for attack on coordinated nitrile by water (blue) and attack on coordinated nitrile by sulfenate (green). All energies are in kcal mol À1 . Fig. 17 Structures listed for the reaction coordinates of Fig. 16 and 18. All distances are inÅ.
The reaction coordinate and associated structures for this process are also shown in Fig. 16 and 17, center, respectively. The process of direct attack by sulfenate on nitrile (shown in green in Fig. 16) has a barrier of only 2.6 kcal mol À1 , signicantly lower than the barrier for nucleophilic attack on nitrile by water (16.7 kcal mol À1 , blue in Fig. 16). The cyclic species formed by attack of the sulfenate is effectively isoenergetic with the starting structure.
Subsequent attack by water on the cyclic species can occur at the (formerly) nitrile carbon or at the (formerly) sulfenate sulfur. Attempts to produce a transition state for attack at the nitrile carbon led only to cleavage of the sulfenate-O bond, with no transfer of a proton from attacking water to the O now bound to C. Also, the energy was approximately 28 kcal mol À1 higher than the starting structure for a water O-nitrile C distance of 1.8Å. Nucleophilic attack by water on the C of the cyclic species was therefore deemed unfeasible. However, nucleophilic attack by water on the S of the cyclic structure did lead to cleavage of the sulfenate S-O bond and generation of a coordinated amidate tautomer (SOH) similar to the nucleophilic attack by water on (uncyclized) coordinated nitrile. The reaction coordinate for this attack at S is given in Fig. 18, and structures of the transition state and end point before and aer amidate tautomer rotation are given in Fig. 17 Fig. 19) indicate that the transition state proceeds towards the reactants and products. The barrier for attack at the S of the cyclized species is 14.4 kcal mol À1 , or 2.3 kcal mol À1 lower than that of attack at coordinated, uncyclized C in Fig. 16. At the transition state (one imaginary frequency, conrmed to be on the IRC), the proton transfer is similar to that of an attack on uncyclized nitrile. Interestingly, in the transition state for attack on the S of the cyclized species, the sulfenate S-axial thiolate S distance has shortened to 2.3Å, indicating some bonding  between these atoms (a Mayer bond order of 0.53 between the sulfenate S-axial thiolate S was calculated, whereas the S-S bond in dimethyl disulde has a calculated Mayer bond order of 1.61). This is similar to a recent computational study proposing a mechanism involving nucleophilic attack by the axial thiolate upon the sulfur of the cyclic intermediate, resulting in the formation of a disulde bond. 22 In the computed mechanism at the bottom of Fig. 17 and 18 the S-S interaction aids in stabilizing the transition state and lowering the barrier for this reaction step involving H 2 O attack on the cyclic S. Aer amidate tautomer rotation and proton shiing the S-S distance increases to 3.1Å and the bonding interaction is eliminated. The nature of the activation of the coordinated nitrile and the cyclic structure are explored below.

Conclusions
The EPR and UV-Vis MCD spectra of NHaseBA and NHaseAq in this study have shown that the LS Fe III site of NHase, which has a protonated sulfenate group when butyrate is coordinated to metal, has a deprotonated sulfenate group and coordinated water ligand in the active form as shown in Fig. 20. For both forms, the active site (including the positively charged bArg56 and bArg141 that are H-bonding to the sulfenate and sulnate ligands) has zero net charge therefore the NHase active site maintains charge neutrality and the coordinated sulfenate can easily change protonation state at functional pHs (here determined to have a pK a of 6.1 and deprotonated in the active form of the site). From the EPR, UV-Vis LT Abs and UV-Vis/NIR MCD spectroscopic data coupled to DFT calculations the highest energy, half-occupied dp orbital for both NHase forms is strongly p bonding to the cysteine thiolate ligand, and the sulfenate ligand possesses a high-energy occupied s IP MO with signicant O character (Fig. 9), implying signicant nucleophilic capability for this ligand. These spectrally evaluated structural and electronic properties of the NHase active site provide insight into its reactivity.
Using EPR, NIR MCD, and UV-Vis LT-Abs and MCD spectroscopic data, computational models of NHaseBA and NHa-seAq were developed which qualitatively reproduce the spectroscopic features and geometric and electronic structures of the two enzyme forms. These ndings show that the computational models provide a reasonable basis for evaluating possible NHase catalytic mechanisms. The ve negatively charged protein-derived ligands combined with the nearby positively charged bArg56 and bArg141 residues lead to a relatively high pK a for the bound H 2 O, allowing its displacement and nitrile substitution. Upon coordination to the LS Fe III the nitrile is activated for nucleophilic attack: (a) the C^N bond becomes more polarized such that the C atom has an increased electrostatic interaction with the nucleophile, (b) the nitrile frontier p* LUMO has more C character, leading to better overlap with the HOMO of the nucleophile, and (c) the energy of the nitrile p* MO is decreased, leading to better covalent interaction. DFT calculations on free acetonitrile and acetonitrile bound to the Fe III of NHase show that upon coordination to LS Fe III the positive charge on the nitrile C increases from +0.12 to +0.21, the C character in the acetonitrile p* LUMO increases from 53% to 59% and the energy decreases by z0.2 eV. This activation is shown in Fig. 21, le and center.
The NHase active site also possesses a good internal nucleophile in the coordinated sulfenate ligand. This is shown in Fig. 21, center. The occupied sulfenate S-O s IP MO may act as a donor and is higher in energy than the water MO by z1.6 eV. It is negatively charged, and is well-oriented for overlap with the nitrile p* acceptor orbital. Sulfenate can therefore attack the nitrile C to form the cyclic species shown in Fig. 21, right. This cyclic species has an unoccupied sulfenate S-O s* FMO which is z3 eV lower than the p* orbital of the uncyclized coordinated nitrile, leading to favorable attack by water at S and a lower reaction barrier than for attack by water on the coordinated, uncyclized nitrile.
Alternatively, the axial thiolate could act as a nucleophile as previously predicted. 22 In this reported mechanism, the barriers for formation of the cyclic intermediate and the disulde intermediate are the largest and of similar energy, indicating that both should be observed over the course of enzyme turnover. Holz and coworkers reported stopped ow data for an Fe NHase enzyme with substoichiometric nitrile reactant, which showed intermediates with a blue shi in the Cys-S À p / dp CT transition of approximately 1100 cm À1 . 39 TD-DFT calculations on the cyclic intermediate both in this work and on the structure in ref. 22 showed Cys-S À p / dp CT transitions approximately 4000 cm À1 higher in energy than NHaseAq, whereas the disulde intermediate of ref . 22 showed no transition in the z12 000-18 000 cm À1 region. As the z14 300-15 400 cm À1 band does not disappear over the course of the  stopped-ow experiment, the presence of a disulde intermediate does not appear likely.
The ligand set and spin state of NHase are unusual relative to the other mononuclear non-heme iron enzymes. Most are ferrous enzymes that activate O 2 and utilize histidine, glutamate, and aspartate residues to coordinate the metal and facilitate the redox reaction. In the intradiol dioxygenases an Fe III with Tyr ligands is active, but this is high spin and this spin state and its change along the reaction coordinate are important in activating the singlet substrate for the spin-forbidden reaction with 3 O 2 . 40 In order to determine the contribution of the low spin state on the nitrile-bound form of NHase, geometry optimizations were performed on models of this complex with S ¼ 3/2 and 5/2 ground states. Whereas the nitrile N-Fe bond length in the S ¼ 1/2 spin state is z1.9Å, this length is z2.6Å in the S ¼ 3/2 state and z2.4Å in the S ¼ 5/2 state, indicating that the bonds are very weak to nonexistent. Indeed, the nitrile N-Fe bond dissociation energies for the S ¼ 1/2, S ¼ 3/2, and S ¼ 5/2 forms are +6.6, À2.3, and À7.0 kcal mol À1 respectively, indicating that the low spin state of NHase is required to assist in the coordination and activation of nitrile substrates.
In order to explore the effects of the NHase ligands on the spin state and activity of the enzyme, DFT calculations were performed on active site models with unoxidized Cys residues, as well as with two His or two acetate ligands replacing the backbone amidates of the WT site. The active site model with all unoxidized thiolates was found to not have an S ¼ 1/2 ground state; the S ¼ 3/2 ground state was lower in energy by 14.2 kcal mol À1 . Geometry optimization of this S ¼ 3/2, structure leads to dissociation of the exogenous ligand and a 5C form that would not be catalytic. Alternatively, the amidate ligands of NHase are not critical to maintaining the low-spin active site. The in silico results with the amidates replaced with weaker donors indicate better activation of coordinated nitriles for nucleophilic attack (i.e. these form stronger Fe III -nitrile bonds). Nature may have selected this deprotonated amide ligand set for its rigidity and chelate ring for orienting the sulfenate ligand for attack on the C of the coordinated nitrile.
Finally, consistent with the EPR g value analysis and LF MCD, the DFT calculations indicate that the axial Cys thiolate is the strongest p donor in the NHase coordination sphere and controls the orientation of the half-occupied dp orbital. This strong p donor trans to coordinated nitrile would not assist in its activation, but may serve to increase both H 2 O and product lability from the LS Fe III site, as was observed by Kovacs et al. for NHase model complexes. 41 This increased lability would be especially important for NHase forms that utilize low-spin Co III , which generally undergoes very slow ligand exchange. The presence of a weak interaction between the thiolate and sulfenate S atoms in the transition state for nucleophilic attack on the S of the cyclic species (Fig. 17, bottom, TS) also indicates that the axial thiolate may serve to lower the energy barrier for nitrile hydrolysis.
In summary, our spectroscopic results have provided new insight into the geometric and electronic structure of NHase, which activates nitriles by coordination to a LS Fe III and contains a sulfenate group that acts as a good nucleophile oriented well for this attack. These spectroscopically-calibrated computational results show that the cyclic intermediate that would be formed in this reaction is activated for nucleophilic attack by water at the S atom leading to formation of the amide product and regeneration of the active site sulfenate. Nature has selected an unusual set of ligands for this enzyme to ensure that the low-spin state necessary for nitrile binding is maintained, and that a rigid chelate ring is present, which properly orients the frontier MO of the sulfenate group for nucleophilic attack on the bound substrate.