Inactivation of [Fe-Fe]-Hydrogenase by O₂. Thermodynamics and Frontier Molecular Orbitals Analyses

Abstract

The oxidation of H-cluster in gas phase, and in aqueous enzyme phase, has been investigated by means of quantum mechanics (QM) and combined quantum mechanics-molecular mechanics (QM/MM). Several potential reaction pathways (in the above mentioned chemical environments) have been studied, wherein only the aqueous enzyme phase has been found to lead to an inhibited hydroxylated cluster. Specifically, the inhibitory process occurs at the distal iron (Fe_d) of the catalytic H-cluster (which is also the atom involved in H₂ synthesis). The processes involved in the H-cluster oxidative pathways are O₂ binding, e^- transfer, protonation, and H₂O removal.

We found that oxygen binding is non-spontaneous in gas phase, and spontaneous for aqueous enzyme phase where both Fe atoms have oxidation state II; however, it is spontaneous for the partially oxidized and reduced clusters in both phases. Hence, in the protein environment the hydroxylated H-cluster is obtained by means of completely exergonic reaction pathway starting with proton transfer.

A unifying endeavor has been carried out for the purpose of understanding the thermodynamic results vis-à-vis several other performed electronic structural methods, such as frontier molecular orbitals (FMO), natural bond orbital partial charges (NBO), and H-cluster geometrical analysis. An interesting result of the FMO examination (for gas phase) is that an e^- is transferred to LUMO_α rather than to SOMO_β, which is unexpected because SOMO_β usually resides in a lower energy rather than LUMO_α for open-shell clusters.

Introduction

[Fe-Fe]-hydrogenases as well as [Ni-Fe]-hydrogenases are enzymes that are implicated in H₂ metabolism (2H⁺ + 2e^- ⇆ H₂), which occurs in anaerobic media. Of these two bi-metal enzymes, only [Fe-Fe]-hydrogenases are viable for H₂ production, with a reactivity of up to 2 orders of magnitude larger than [Ni-Fe]- hydrogenases ^1,2. In hydrogenases, H₂ evolution, emerging from proton reduction (2H⁺ + 2e^- → H₂), is essential in pyruvate fermentation, and in the disposal of excess electrons. Low-molecular weight biomolecules such as ferredoxins, cytochrome C3, and cytochrome C6 can act as physiological electron acceptors or donors³.

The hydrogenase H-cluster (Scheme 1) is the active site which is comprised of two subunits, the 2Fe subunit, and the cubane, [Fe₄-S₄]²⁺, subunit. The 2Fe subunit is composed of two iron atoms (Fe_p-Fe_d, i.e., proximal and distal iron) that are bridged by di(thiomethyl)amine (DTMA) chain, and are coordinated by endogenous ligands, i.e., two cyanides, two terminal carbonyls, and a bridging carbonyl (CO_b). Moreover, the S_γ (of Cys³⁸²) is the connecting atom from an Fe atom of the (proximal) cubane subunit and the Fe_p of the 2Fe subunit.

Scheme 1.

The H-cluster and its subunits, i.e., the cubane, and the 2Fe subunit.

The reason for studying biological H₂ production is because the eventual elucidation of the mechanism (for hydrogen synthesis) may benefit researchers produce clean fuel, using certain anaerobic prokaryotes^4-8.

Previous Density Functional Theory (DFT) as well as hybrid quantum mechanics/ molecular mechanics (QM/MM) calculations^2,9-16 have been successful in clarifying some aspects of the catalytic properties of the H-cluster.

As in similar computational studies^2,9, cysteine is substituted with CH₃-S^-, whereas cubane is replaced^* with a H⁺.

Furthermore, computational and experimental^2,9,14,16-41 [Fe-Fe]-hydrogenase H-cluster (and synthetic H-cluster-like compounds) research sheds light on the potential redox states of the 2Fe H-cluster subunit, Fe_p-Fe_d, where Fe_p^I-Fe_d^I is the reduced 2Fe H-cluster subunit, Fe_p^II-Fe_d^I is the partially oxidized enzyme subunit, and Fe_p^II-Fe_d^II is the fully oxidized, inactive enzyme H-cluster subunit.

The fully oxidized H-cluster, Fe_p^II-Fe_d^II, has a H₂O molecule or an OH^- bound to the Fe_d^II. In our previous investigation²¹, we have inferred that a vacant (fully oxidized) Fe_p^II-Fe_d^II (1, Figure 1) could also be a viable intermediate in H₂ synthesis. Regardless of the 2Fe H-cluster subunit redox states, the proximal cubane [more precisely, a cuboid (point group: D₂d)] always retains a 2+ oxidation state, [Fe₄-S₄]²⁺.

Figure 1.

Reaction pathways I - IV: Oxidation mechanisms of H-clusters that are fully oxidized (1), partially oxidized (5), and reduced (6). The charges and multiplicities are given in square brackets. The first energy value is for gas phase, and the second is for ONIOM calculations. Fe_p is the proximal iron, and Fe_d is the distal iron.

The partially oxidized H-cluster (Fe_p^II-Fe_d^I, 5, Figure 1), H_ox, is the active form of the hydrogenase enzyme^†. The reduced H-cluster (Fe_p^I-Fe_d^I, 6, Figure 1) has both iron atoms in oxidation states I (being an intermediate in H₂ metabolism). According to Liu and Hu⁹, 6 is the cluster having great affinity for protonation (6 → 8), in capturing a proton from the side chain of a near by amino-acid, such as Lys²³⁷.

X-ray crystallography and spectroscopic studies of hydrogenases, with the latter having been obtained from Clostridium pasteurianum (CPI)⁴³ and Desulfovibrio desulfuricans (DdH)³¹, led to a better understanding of the biochemical roles of these enzymes. The X-ray crystal structure of CPI hydrogenase shows an oxygen species that may be OH^-, or H₂O bound to the Fe_d of the H-cluster. Based on the computational results of Liu and Hu² (CPI has OH^- in its inactive form according to X-ray crystal structure), we endeavor to ascertain whether the air oxidized H-cluster (Fe_p-Fe_d-O₂) converts to Fe_p-Fe_d-OH species²¹.

Our investigation is composed of three different subdivisions. 1). Thermodynamic analysis, for every reaction path mechanism (Figures 1 - 3), implicated in the eventual H-cluster 14 inhibition by means of O₂ → OH^-. 2). Electronic analysis, for the same paths, which deals with Natural Bond Orbitals (NBO), as well as Frontier Molecular Orbitals (FMO). 3). Geometrical analysis carried out only for appropriate bond breaking, and bond formation.

Figure 3.

Reaction mechanism for reduction, protonation, and H₂O removal from the inhibited [Fe-Fe]-hydrogenase H-cluster. Here, the H₂O is being eliminated from an open-shell cluster. (The charges, multiplicities, and energy values are presented as in Figure 1.)

From the investigated subdivisions, thermodynamics analysis (Figure 2, and 3) is of pivotal importance since it shows that there is just an exergonic path from H-cluster 9′ to the hydroxylated cluster 14 occurring in the aqueous enzyme phase. However, from the thermodynamic results (Figure 1), it is observed that most reaction steps proceed exergonically (except 1 → 2, gas phase), leading to the oxidized cluster 9. Moreover, at the end of each path, every vacant H-cluster 1, 5, and 6, in spite of its oxidation states, becomes aerobically inactivated, 9.

Figure 2.

Reaction mechanism for isomerization, protonation, H₂O elimination, and reduction of the inhibited [Fe-Fe]-hydrogenase H-cluster. The H₂O is being removed from a closed-shell cluster. (The charges, multiplicities, and energy values are presented as in Figure 1.)

Thus, this paper is organized as follows: in the Methods we describe the QM/MM partitioning, and the methods used for calculations (e.g., QM Hamiltonian, basis sets, and the force field parameters). Then, in the Results and Discussion, we present the computational results organized into subsections that present and discuss thermodynamic results, geometrical, and electronic data for different steps of the reaction pathways, such as oxygen binding, reduction, oxidation, and water elimination. Finally, in the Conclusion we give a summary of our findings.

Methods

In the current study, both QM [DFT (in gas phase)] and QM/MM [DFT/UFF⁴⁴ (in aqueous enzyme phase)] methodologies have been used. The ONIOM⁴⁵ method (DFT for the QM region, and the universal force field, UFF, for the MM region, implemented in Gaussian03⁴⁶) has been applied to determine the reaction thermodynamics, i.e., ΔG, for the inactivation pathways of the H-cluster, and the [Fe-Fe]-hydrogenase H-cluster (positioned within the enzyme matrix). Subsequently, the DFT results have been compared with the ONIOM calculations. The electronic structure of the hydrogenase active site (except the proximal cubane) is investigated by quantum mechanics (Gaussian 03) using DFT method (B3LYP functional^47,48), and QM/MM with 6-31+G(d,p) basis set. For Fe an effective-core potential with a double zeta polarization basis set (LANL2DZ^49,50) was used for DFT gas phase calculations, and a 6-31+G(d,p) basis set for the ONIOM calculations. In accordance with experimental and in-silico data low spin states (singlet, and doublet), and low oxidation states (I, and II) have been selected for the Fe atoms^2,14,35. Gromacs program^51,52 was employed to add hydrogen atoms, water, and counter ions to the X-ray crystal structure of DdH [Brookhaven Protein Data Bank id.1HFE]. Hydrogen atoms and a 1 nm layer of water (2043 molecules) have been added to the PDB DdH structure. Moreover, Na⁺ ions have been randomly inserted into the solvent to neutralize the negative charges encountered therein, e.g., the -2 a.u. found on the cubane/cysteine moieties^‡53. For both basic and acidic amino acids, charges were assigned by Gromacs algorithm to be at pH 7. ONIOM geometry optimizations have been performed on the DdH, with the low layer (MM region) being frozen^*, with the exception of the proximal cubane, while the high layer (QM) had only the iron atoms, Fe_p-Fe_d, and the N₃, (of the DTMA bridge) kept frozen; “freezing atoms” is practiced to reduce computational time. The low layer consists of all the hydrogenase amino acids as well as its constituent cubanes, i.e., proximal, medial, and distal. The high layer is comprised of 2Fe subunit, (which is the moiety of the H-cluster), and C_β and S_γ (appertaining to the bridging Cys³⁸²). Moreover, two linking hydrogen atoms were added between C_α and C_β of Cys³⁸², and between S_γ and an Fe atom of the proximal cubane. The charge equilibration method of the UFF was used to describe the electrostatic interactions within the low layer of the system⁵⁴. The DdH partial charges were obtained using the charge equilibration method, whereas the solvent charges were acquired from literature⁵⁴ (q_O = -0.706 a.u. and q_H = 0.353 a.u.).

Results and Discussion

H-cluster Thermodynamics for O₂ Binding, Reduction, and Protonation

Figure 1 illustrates different O₂ inhibition pathways of the hydrogenase H-cluster; the H-clusters, 1, 5, 6, and 8^2,9,21, of the pathways are obtained in the reversible catalysis of H₂. Reaction 1 → 2 (path I) is endergonic for the gas phase (ΔG_gas = +9.8 kcal/mol; gas = gas phase) when O₂ binds to the fully oxidized H-cluster (1). ONIOM calculations, on the other hand, show that O₂ binding occurs exergonically (ΔG_QM/MM = -16.6 kcal/mol), shedding light on the sensitivity of hydrogenases to O₂⁵⁵.

Reduction 2 → 3 (ΔG_gas = -110.2 kcal/mol) as well as protonation 3 → 4 (ΔG_gas = -136.0 kcal/mol) proceed exergonically; ONIOM calculations, for the hydrogenase matrix, show that e^- transfer is considerably less exergonic (ΔG_QM/MM = -80.4 kcal/mol) relative to protonation which is more exergonic (ΔG_QM/MM = -154.1 kcal/mol). The free energy differences, in gas vs. aqueous enzyme phases for reactions 2 → 3 and 3 → 4, ensue from the effect of the electric field of the protein on the H-clusters 2, 3, and 4, and from the different phase geometries.

Cluster 4 undergoes reduction, and it (4 → 9) proceeds exergonically in both gas and aqueous hydrogenase phase (ΔG_gas = -79.1 kcal/mol; ΔG_QM/MM = -78.3 kcal/mol).

Path II starts with the partially oxidized H-cluster 5, (Fe_p^II-Fe_d^I). The binding of O₂ to Fe^I (Fe_d^I-O₂), 5 → 3, is firmer (ΔG_gas = -36.1 kcal/mol) than for Fe^II in 1 → 2 (Fe_d^II-O₂, path I). In contrast, ONIOM results show that O₂ binds to the partially oxidized H-cluster (Fe_p^II-Fe_d^I, ΔG_QM/MM = -7.9 kcal/mol) as well as to the fully oxidized cluster (Fe_p^II-Fe_d^II, ΔG_QM/MM = -16.6 kcal/mol, 1 → 2, path I). The remaining two reactions 3 → 4, and 4 → 9 (path II) are the same as the last two steps of path I.

In path III, 6 → 7, which starts with the fully reduced H-cluster 6, (Fe_p^I-Fe_d^I), the reaction spontaneity (ΔG_gas = -36.0 kcal/mol) is almost identical to the free energies of reaction 5 → 3. The gas phase free energy similarity may ensue because both loci of oxygen binding (Fe_d^I-O₂) are on similar oxidized species, Fe_d^I. However, ONIOM calculations show smaller reaction spontaneity difference between aqueous enzyme (ΔG_QM/MM = -20.7 kcal/mol) and gas phase results (ΔG_gas = -36.0 kcal/mol, 6 → 7), than for O₂ binding in path I and II. In path III, protonation (7 → 9) is, once again, largely exergonic for both phases (ΔG_gas = -241.9 kcal/mol; ΔG_QM/MM = -244.9 kcal/mol). Moreover, from all of Figure 1, the above ONIOM calculations show the highest H⁺ affinity because H-cluster 7 has a charge of -2 a.u., and also the H⁺ binds to a rather electronegative atom, viz., oxygen.

In the final path (IV), protonation 6 → 8 is the second most exergonic reaction in gas phase (ΔG_gas = -220.6 kcal/mol) mostly because of the over-all charge of -2 on the H-cluster 6. ONIOM data (as in 7 → 9) show very high H⁺ affinity (ΔG_QM/MM = -219.2 kcal/mol) for the hydrogenase H-cluster (in spite of the fact that the H⁺ is seized by the Fe_d as opposed to the more electronegative Fe_d-O₂, 7 → 9), which is comparatively similar to the gas phase result (ΔG_gas = -220.6 kcal/mol).

In the last step (8 → 9; path IV), O₂ is interposed between Fe_d and the hydride (Fe_d^I-O₂-H, 9). For this insertion reaction, the O₂ binding occurs exergonically in both ONIOM (ΔG_QM/MM = -46.4 kcal/mol) and the gas phase (ΔG_gas = -57.3 kcal/mol) results.

N.B., path IV shows that oxidation of Fe_p-Fe_d H-cluster is similar^* to the Ni_p-Fe_d hydrogenase H-cluster obtained from experimental data⁵⁶.

From the above thermodynamic results, most reaction steps proceed exergonically (except 1 → 2, gas phase), leading to oxidized cluster 9. At the end of every path, each vacant H-cluster 1, 5, or 6, in spite of its oxidation states, becomes aerobically inactivated.

NBO Charges and Geometry Adjustment of Intermediates in the Oxidation of H-cluster

The atoms of the vacant H-clusters 1, 5, and 6 have slightly different natural bond orbital (NBO) charge distributions. For instance, for cluster 1 the NBO charges of Fe_p-Fe_d are q^g_Fep^** = 0.137 a.u. (q^e_Fep = -0.230 a.u.) and q^g_Fed = -0.096 a.u. (q^e_Fed = 0.187 a.u.), whereas in 5, the sign of the partial charges are reversed only in gas phase, i.e. q^g_Fep = -0.024 a.u. (q^e_Fep = -0.227 a.u.) and q^g_Fed = 0.078 a.u. (q^e_Fed = 0.061 a.u.). Then, the NBO charges for the Fe_p-Fe_d in cluster 6 (in both phases) are more negative, q^g_Fep = -0.104 a.u. (q^e_Fep = -0.297 a.u.), and q^g_Fed = -0.117 a.u. (q^e_Fed = -0.160 a.u.) because both metals are in a reduced state (Figure 1), unlike clusters 1 and 5. Regarding charges on the nitrogen, N₃, (of the DTMA bridge), similarities are seen amongst clusters 1, 5, and 6; the NBO charges for N₃ are approximately -0.700 a.u., making this amine (within the above H-clusters) a relatively important H⁺ acceptor/donor (vs. amino acids with similar function in the juxtaposed enzyme matrix, e.g., Lys²³⁷) as suggested by Liu and Hu⁹. The non-bridging S_γ (of Cys³⁸²) has the following charges: for 1 q^g_Sγ = 0.204 a.u. (q^e_Sγ = 0.474 a.u.), for 5 q^g_Sγ = 0.142 a.u. (q^e_Sγ = 0.425 a.u.), and for 6 q^g_Sγ = 0.079 a.u. (q^e_Sγ = 0.285 a.u.). Comparing clusters 1, 5 and 6, a sequential drop in NBO charges for Fe_p and S_γ is observed.

When H-cluster 1 is in an oxidized state (in gas phase), Fe_p^II- Fe_d^II, the CO_b shifts⁹ towards the Fe_d^II, and becomes bonded to Fe_d^II. The shifted CO_b bond distance (measured from its bridging carbon, C_b, to the iron atoms) between C_b—Fe_p^II is 3.067 Å, whereas C_b—Fe_d^II is 1.819 Å. When the carbonyl is close to Fe_d^II, CO_b-Fe_d^II, the fully oxidized H-cluster 1 becomes relatively stable vs. the quasi-symmetric cluster²¹ (ΔH = 14 kcal/mol), which is also shown by the NBO charge on C_b in CO_b, (0.664 a.u.). This may be due to repulsion of charges between q^g_Cb (0.664 a.u.) and q^g_Fep (0.137 a.u.), whereas for the clusters 5 and 6, the partial charges (q^g_Cb = 0.462 a.u., and q^g_Cb = 0.466 a.u., respectively) are less then in 1 because CO_b is bonded to both iron atoms. However, in the enzyme phase less shifting of the bridging carbonyl occurs, with the charges on C_b being similar (q^e_Cb = 0.536 a.u. for 1, q^e_Cb = 0.497 a.u. for 5, and q^e_Cb = 0.493 a.u. for 6). Comparing the reaction spontaneity for O₂ binding (in gas phase), which renders clusters 2, 3, and 7, one may observe that 3 and 7 are more stable than 2. The reason for this stability is essentially due to the formation of a hydrogen bond between the exogenous O₂ and the hydrogen H₉ (bonded to N₃ of the DTMA bridge) in both 3 and 7. The O₁—H₉ bond distance is 2.016 Å in 3, and O₂—H₉ bond distance is 1.765 Å in 7, which correlates with the NBO charges on the mentioned oxygens and hydrogens; the partial charges on oxygens are q^g_O1 = -0.235 a.u. in 3, and q^g_O2 = -0.493 a.u. in 7, whereas the charge on H₉ is 0.439 a.u. in 3, and 0.454 a.u. in 7. Note that CO_b is located almost symmetrically in clusters 2, 3, and 7. Structurally, clusters 4 and 9 are similar in view of the fact that both possess a hydrogen bond (H₉…O₁), whereas CO_b is found to reside quasi-symmetrically in 9, but asymmetrically in 4 bonded only to Fe_p^II. In the enzyme phase both hydrogen bonds (in clusters 3 and 7) are formed between H₉ and O₂ of the exogenous oxygen (q^e_O2 = -0.210 a.u. in 3, q^e_O2 = -0.452 a.u. in 7, q^e_H9 = 0.443 a.u. in 3, and q^e_H9 = 0.445 a.u. in 7; O₂—H₉ bond distance is 1.890 Å in 3, and O₂—H₉ bond distance is 1.760 Å in 7).

Thermodynamics and NBO charges relationship for H₂O Removal from the Oxidized H-cluster

Figure 2 depicts a series of reactions (9 → 9′, 9′ → 10, 10 → 11, 11 → 12, 12 → 13, and 13 → 14), which present the net conversion of 9 to 14. The compounds 9 and 9′ are isomers; 9′ is more stable by 47.2 kcal/mol, [which may be, to a certain extent, attributed to the hydrogen bond formation between H₂O and the N₃ of DTMA bridge (N₃…H-OH; i.e., 2 bonds being broken vs. 3 being formed for 9 → 9′, respectively)]. The hydrogen bond length, N₃…H, is 1.939 Å (and the angle formed by N₃…H-O is 168.7°). The distance between the iron atoms is larger in 9′ (2.796 Å) than in 9 (2.605 Å). During reaction 9 → 9′, CO_b moves away from Fe_p^II [i.e., for C_b-Fe_p^II 2.225 Å (9) → 2.771 Å (9′)]. Also, in Figure 2 (hydrogenase H-cluster 9, and 9′), ONIOM geometry optimizations for 9, and 9′ resulted in the same structure for the hydrogenase H-clusters (ΔG_QM/MM corresponding to 9 → 9′ is 0 kcal/mol). The protonation of 9′ (9′ → 10) produces a quaternary ammonium ion (NR₄⁺) within the DTMA bridge, which is exergonic for both phases, viz., ΔG_gas = -130.7 kcal/mol, and ΔG_QM/MM = -138.4 kcal/mol. To wit, the observed high reaction spontaneity for both phases is attributed to the negatively charged H-cluster 9′. In 10 → 11, H₂O is removed from N₃ by means of hydrogen bond breaking; this reaction (vs. 9′ → 10) occurs slightly endergonically in gas phase (ΔG_gas = +3.3 kcal/mol), while for QM/MM results, the H₂O removal step, 10 → 11, is exergonic (ΔG_QM/MM = -24.1 kcal/mol).

Reduction 11 → 12 (Figure 2) is subjected to an increase in the partial charge of the exogenous oxygen (q^g_O1 = -0.568 a.u. (11) → -0.594 a.u. (12); ΔG_gas = -72.8 kcal/mol). Regarding geometrical changes in 11 → 12, the bond distance between Fe_p^II-Fe_d^I is increasing from 2.792 Å to 3.261 Å, while the CO_b departs from Fe_p^II [for C_b-Fe_p^II 2.766 Å (11) → 3.183 Å (12)]. For the aqueous enzyme phase result, 11 → 12 occurs with a relatively large free energy (ΔG_QM/MM = -95.4 kcal/mol; compared to other neutral H-cluster reductions), versus the gas phase outcome (ΔG_gas = -72.8 kcal/mol); the charge remains constant on the exogenous oxygen [q^e_O1 = -0.530 a.u. (11) → -0.527 a.u. (12)]. Due to excess electron density accumulation on O₁ (12), the latter readily captures a proton (12 → 13; ΔG_gas = -148.9 kcal/mol). ONIOM calculations, 12 → 13, confirm the high H⁺ affinity (in Figure 2, ΔG_QM/MM = -141.6 kcal/mol) for the hydrogenase H-cluster, which is close to the gas phase result (ΔG_gas = -148.9 kcal/mol). The free energy differences between the given protonations, 12 → 13 vs. 9′ → 10, may arise because of the greater stability of cluster 13 vs.10.

Finally, in Figure 2, an e^- is acquired by the hydroxyl group (13 → 14; ΔG_gas = -77.4 kcal/mol; ΔG_QM/MM = -86.3 kcal/mol). Note that the H-cluster 14^2,21 is the starting compound in the reactivation pathway that ends in the reduced H-cluster 6 (Fe_p^I-Fe_d^I).

In Figure 3, an alternative pathway (9′ → 15, 15 → 16, 16 → 12, 12 → 13, and 13 → 14) has been investigated. The pathway starts with a reductive step, rather than with a protonation. Reaction 9′ → 15 is slightly exergonic for the gas phase (ΔG_gas = -1.8 kcal/mol), while ONIOM calculations indicate an endergonic process (ΔG_QM/MM = +25.6 kcal/mol). 9′ → 15 is another O₂ inhibitory step (in addition to 10 → 11 for the gas phase, Figure 2) which seems to explain the O₂ sensitivity of wild type DdH. Therefore, mutagenic studies ought to be performed on [Fe-Fe]-hydrogenase H-cluster 9′ to eliminate its inhibitory path (viz., 9′ → 15). When a H⁺ is in the vicinity of H-cluster 15, 15 → 16 proceeds with the greatest spontaneity (of Figures 2 and 3) in gas phase (ΔG_gas = -199.7 kcal/mol) because 15 has a net charge of -2 a.u. Note that the ONIOM findings, for step 15 → 16, confirm the highest free energy (ΔG_QM/MM = -259.9 kcal/mol) of all the potential reaction mechanisms analyzed for the [Fe-Fe]-hydrogenase H-cluster, while the gas phase result is about 60 kcal/mol less exergonic. Water elimination in gas phase, (16 → 12) is slightly endergonic (ΔG_gas = +1.3 kcal/mol), whereas for the aqueous enzyme phase it is significantly exergonic (ΔG _QM/MM = -23.6 kcal/mol). Note that both 10 (Figure 2) and 16 (Figure 3) lead to the same compound (12) by H₂O elimination. The thermodynamic data are similar for both reactions, 10 → 11 and 16 → 12, because Fe_d is found in the same oxidation state (Fe_d^I) in both 10 and 16, but Fe_p (being further away from the focal catalytic locus, Fe_d) has different oxidation states [Fe_p^II (10); Fe_p^I (16)]. The in silico ONIOM result of the H₂O removal step (Figure 3, 16 → 12), is exergonic (ΔG_QM/MM = -23.6 kcal/mol), just like in step 10 → 11, (Figure 2, ΔG_QM/MM = -24.1 kcal/mol). Also, close free energies are observed for the gas phases of 16 → 12 (ΔG_gas = +1.3 kcal/mol) and 10 → 11 (ΔG_gas = +3.3 kcal/mol). Next, reactions 12 → 13, and 13 → 14 proceed exergonically [(ΔG_gas = -148.9 kcal/mol; ΔG_QM/MM = -141.6 kcal/mol), and (ΔG_gas = -77.4 kcal/mol; ΔG_QM/MM = -86.3 kcal/mol), respectively], just as (previously discussed) in Figure 2. The following reactions, 10 → 11 (Figure 2) and 16 → 12 (Figure 3), show that the entire (oxidative inhibitory H-cluster) path has difficulties proceeding to 14 in gas phase.

From the above, it can be seen that there is only one exergonic path (Figure 2) from the oxidized H-cluster 9′ to the hydroxylated cluster 14 in aqueous enzyme phase. A path starts with H⁺ transfer (Figure 2), while the other begins by e^- transfer (Figure 3). The gas phase H₂O elimination, from the oxidized H-cluster, proceeds endergonically in both pathways (Figure 2 and 3).

Frontier Molecular Orbital Analysis

Electronic contributions are now presented for both phases, which are adduced by the frontier molecular orbitals in conjunction with the previously presented free energies.

Upon reduction of open-shell H-clusters, it is observed that an e^- is obtained by a semi-occupied molecular orbital (SOMO), while the closed-shell clusters receive an e^- into the lowest virtual molecular orbital (LUMO). However, when a H⁺ is in the proximity of an open-shell H-cluster, it can form a σ-bond probably through the interaction of the e^- in the highest occupied molecular orbital (HOMO), or through the contributions of both HOMO and SOMO, with the proviso that the SOMO is sufficiently low in energy relative to HOMO. Alternatively, when a H⁺ is near a closed-shell cluster, the σ-bond probably ensues mainly due to the contribution of e^-s from HOMO with the H⁺.

Gas phase thermodynamic properties, of the reactions in Figs. 1, 2, and 3, are being examined with regard to frontier molecular orbitals (FMO). Thus, in 2 the LUMO (Figure 4) is mostly localized on the exogenous O₂ and N₃, which is also corroborated by an increase of NBO charges on O₂ and N₃ in 3 upon reduction of H-cluster 2 [q^g_O1 = -0.046 a.u. (2) → -0.235 a.u. (3); q^g_N3 = -0.568 a.u. (2) → -0.717 a.u. (3)].

Figure 4.

Frontier molecular orbitals (gas phase) for H-clusters LUMO (2), HOMO_α (3), HOMO_β (3), LUMO_α (4), LUMO_β (4), SOMO_α (4), SOMO_β (4), HOMO (6), and HOMO (7) (where the atom colors, of the H-clusters, are O = red, C = grey, N = blue, S = yellow, Fe = burgundy, and H = white).

Aqueous enzyme phase thermodynamic properties are next being examined for the reactions of Figs. 1, 2, and 3 relative to the frontier molecular orbitals (FMO).

For 2, LUMO [Figure 6, (compare to Figure 4 in gas phase)] is mostly localized on S_γ of Cys³⁸² (as opposed to cluster 2 in gas phase) owing to the electronic contribution of the proximal cubane. Additionally, the localization of LUMO is supported by a decrease of NBO charge on S_γ in 3 upon reduction of H-cluster 2 [q^e_Sγ = 0.471 a.u. (2) → 0.388 a.u. (3)].

Figure 6.

Frontier molecular orbitals (aqueous enzyme phase) for H-clusters LUMO (2), HOMO_α (3), HOMO_β (3), LUMO_α (4), LUMO_β (4), SOMO_α (4), SOMO_β (4), HOMO (6), and HOMO (7).

For open-shell clusters, unrestricted B3LYP calculations have been performed which resulted in different quantum mechanical (QM) energies and molecular orbital (MO) coefficients for α and β electrons.

In gas phase, the HOMO_α (the lower energy HOMO containing a spin up e^-) of 3 is predominantly localized on the exogenous O₂, where the protonation also occurs. However, the HOMO_β (the higher energy HOMO with its spin down e^-) is localized on the DTMA bridge (Figure 4).

For the aqueous enzyme phase, the HOMO_α of 3 is less localized on the exogenous O₂ (relative to the gas phase situation), but this orbital is essentially localized on the DTMA bridge.

The HOMO_β, relative to the gas phase electronic distribution, is more localized on the exogenous O₂ (Figure 6), supporting the greater spontaneity of H⁺ transfer (3 → 4).

The SOMO_α of compound 4, in gas phase, is mostly localized on the DTMA bridge, and, to some extent, on the exogenous O₂ and the Fe atoms (Figure 4). SOMO_β is more delocalized than SOMO_α. Following the e^- transfer 4 → 9, the main change in partial charges occurs on the iron atoms [q^g_Fep = -0.141 a.u. (4) → -0.003 a.u. (9); q^g_Fed = 0.464 a.u. (4) → 0.025 a.u. (9)]. The change in NBO charges in 4 → 9 can be corroborated by LUMO_α (4; Figure 4). It is noteworthy that the e^- is transferred into the LUMO_α (-0.15381 Hartrees), for its energy is lower than that of SOMO_β (-0.14425 Hartrees). For the hydrogenase, LUMO_α (4, Figure 6) is also lower in energy than SOMO_β (4, Figure 6) (E_LUMOα^Enzyme = -0.35944 Hartrees, E_SOMOβ^Enzyme = -0.35907 Hartrees), implying that the e^- is transferred to and localized on S_γ of Cys³⁸². However, this difference in electron localization is not reflected in the reaction thermodynamics, because 4 → 9 is similarily exergonic in both phases.

The HOMO of 6, in gas phase, is localized on the Fe_d and the CO_b, whereas the HOMO of 7 is primarily localized on the exogenous O₂ but is less diffused over CO_b (Figure 4). The proton binds with high affinity to Fe_d of H-clusters 6 (Path IV) and 7 (Path III) because the HOMO orbitals of these clusters are localized on Fe_d and exogenous O₂, respectively. In particular, 7 manifestly displays where protonation occurs, viz., on the exogenous O₂ (Figure 1).

In aqueous enzyme phase, similar electron orbital distributions are encountered for clusters 6 (Path IV) and 7 (Path III), except that S_γ (of Cys³⁸²) incurs MO distributions, which may be sustained by the proximal cubane (that facilitates the e^- transfer).

The HOMO of 9′, is delocalized throughout the cluster and, has smaller proton affinity in comparison to 6 and 7. However, higher HOMO 9′ amplitude is found on the exogenous O₁, DTMA bridge, and the two irons which may explain why the N₃ is being protonated in this case.

For cluster 11, the LUMO is more localized over the Fe_p than on Fe_d, extending from the irons towards the CO_b via a linear combination between the e_g orbitals of the iron atoms with the CO_b π orbitals⁹, thus the e^- transfer, 11 → 12, changes the oxidation state of Fe_p. However, for ONIOM, the LUMO is localized on S_γ which is being bereft of e^-s via an inductive effect of the vicinal cubanes [q^e_Sγ = 0.464 a.u. (11) vs. 0.333 a.u. (12)].

Both HOMO_α and HOMO_β, of 12, are generally localized on the Fe_p (Figure 5). However, in this case, the protonation does not occur at the Fe_d, instead it occurs at the exogenous O₁ since its NBO charge is very negative, i.e., q^g_O1 = -0.594 a.u. as opposed to q^g_Fed = 0.126 a.u. On the other hand, for the aqueous enzyme phase, both HOMO_α and HOMO_β, of 12, differ in their distribution, especially HOMO_α having orbital amplitude on the exogenous oxygen, making it a good H⁺ acceptor.

Figure 5.

Frontier molecular orbitals (gas phase) for H-clusters HOMO (9′), LUMO (9′), LUMO (11), HOMO_α (12), HOMO_β (12), SOMO_α (12), LUMO_α (13), SOMO_β (13), and HOMO_α (15).

Cluster 13 is an open-shell cluster, so upon its reduction an e^- may either enter a LUMO_α, or a SOMO_β depending on their relative orbital energies. In the reductive process of H-cluster 13 (for gas phase), the in silico data explicitly shows that the orbital energy of LUMO_α (E_LUMOα^gas = -0.14850 Hartrees) is lower than the energy of SOMO_β (E_SOMOβ^gas = -0.13886 Hartrees). Nevertheless, these energies are almost identical in the aqueous enzyme phase (E_LUMOα^enzyme = -0.35177 Hartrees, E_SOMOβ^enzyme = -0.35185 Hartrees). Thus, upon reduction of cluster 13, the e^- could enter into LUMO_α (Figures 5 and 7 of both phases). Upon analysis of the NBO charges of clusters 13 and 14, the OH^- and Fe_d of 14 acquire most of the partial charge ceded by Fe_p during the reductive process 13 → 14.

Figure 7.

Frontier molecular orbitals (aqueous enzyme phase) for H-clusters HOMO (9), LUMO (9), LUMO (11), HOMO_α (12), HOMO_β (12), SOMO_α (12), LUMO_α (13), SOMO_β (13), and HOMO_α (15).

Finally, in gas phase H-cluster 15 undergoes a protonation reaction on N₃, which is substantiated by the NBO negative charge decrease, for both phases, on N₃ [q^g_N3 = -0.267 a.u. (15) → -0.187 a.u. (16)], while in protein environment the exogenous O₂ is protonated [q^e_O2 = -0.510 a.u. (15) → -1.024 a.u. (16)].

Conclusion

Several possible pathways have been investigated for the oxidation of [Fe-Fe]-hydrogenase H-cluster, and they all proceed spontaneously to cluster, 9. Each pathway is initiated by an intermediate (1, 5, 6, and 8) of the catalytic cycles in H₂ metabolism.

In gas phase, O₂ binding is endergonic for the fully oxidized H-cluster 1 and exergonic for 8; however, it is exergonic for the partially oxidized 5 and reduced 6 clusters. But for aqueous enzyme phase, the O₂ binding is exergonic for all oxidation states. This suggests that the fully oxidized state of the H-cluster 1 in enzyme environment is more sensitive to O₂ inhibition.

Our calculations show that in the protein environment (Figure 2, and 3) the hydroxylated H-cluster 14, which is the end product of hydrogenase inhibition^*, is obtained from 9 via the fully exergonic reaction pathway that starts by means of protonation (Figure 2). Antithetically, the reaction pathway that is initiated by means of reduction (Figure 3, aqueous enzyme phase) does not proceed to the hydroxylated H-cluster 14 due to this very endergonic step (ΔG_QM/MM = +25.6 kcal/mol ).

The inhibitory steps in gas phase (Figure 2, and 3) consist of water removal from a closed shell, 10, and an open shell, 16, H-cluster (ΔG_gas = +3.3 and +1.3 kcal/mol, respectively), while in the aqueous enzyme phase there is one inhibitory step, i.e., an e^- transfer from an open shell H-cluster (9′, ΔG_QM/MM = +25.6 kcal/mol ).

From gas phase geometrical analysis CO_b shows a displacement away from Fe_p^II (9 → 9′), but in the aqueous enzyme phase this CO_b translocation is not observed; the observed different phase behavior in the protein environment may be due to the imposed immobility on the iron atoms (by means of “freezing” them).

For the gas phase, cluster 11, LUMO is more localized over the Fe_p than on Fe_d, extending from the iron atoms towards the CO_b via a linear combination between the e_g orbitals of the iron atoms with the CO_b π orbitals⁹, thus the e^- transfer, 11 → 12, changes the oxidation state of Fe_p. However, for the protein environment, the LUMO is localized on S_γ which is being bereft of e^-s via an inductive effect of the vicinal cubanes [q^e_Sγ = 0.464 a.u. (11) vs. 0.333 a.u. (12)].

Lastly, an interesting result from the FMO gas phase analysis is that an e^- is transferred to the LUMO_α rather than to the virtual SOMO_β, which is rather unexpected since the virtual SOMO_β usually resides in a lower energy state than LUMO_α for open-shell compounds. We also found that O₂ inhibited [Fe-Fe]-hydrogenase H-cluster has OH^- bonded to the Fe_d, and that OH^- is the end product of O₂ metabolism, with all aqueous enzyme phase reaction pathways proceeding exergonically.