FeMo cofactor of nitrogenase: a density functional study of states M(N), M(OX), M(R), and M(I)

The energetics of N2 reduction by vanadium containing nitrogenase

The main class of nitrogenases has a molybdenum in its cofactor. A mechanism for Mo-nitrogenase has recently been described. In the present study, another class of nitrogenases has been studied, the one with a vanadium instead of a molybdenum in its cofactor. It is generally believed that these classes use the same general mechanism to activate nitrogen. The same methodology has been used here as the one used for Mo-nitrogenase. N2 activation is known to occur after four reductions in the catalytic cycle, in the E4 state. The main features of the mechanism for Mo-nitrogenase found in the previous study are an activation process in four steps prior to catalysis, the release of a sulfide during the activation steps and the formation of H2 from two hydrides in E4, just before N2 is activated. The same features have been found here for V-nitrogenase. A difference is that five steps are needed in the activation process, which explains why the ground state of V-nitrogenase is a triplet (even number) and the one for Mo-nitrogenase is a quartet (odd number). The reason an additional step is needed for V-nitrogenase is that V3+ can be reduced to V2+, in contrast to the case for Mo3+ in Mo-nitrogenase. The fact that V3+ is Jahn-Teller active has important consequences. N2H2 is formed in E4 with reasonably small barriers.

H2 formation from the E2-E4 states of nitrogenase

Nitrogenase is the only enzyme that can cleave the strong triple bond in N2, making nitrogen available for biological lifeforms. The active site is a MoFe7S9C cluster (the FeMo cluster) that binds eight electrons and protons during one catalytic cycle, giving rise to eight intermediate states E0-E7. It is experimentally known that N2 binds to the E4 state and that H2 is a compulsory byproduct of the reaction. However, formation of H2 is also an unproductive side reaction that should be avoided, especially in the early steps of the reaction mechanism (E2 and E3). Here, we study the formation of H2 for various structural interpretations of the E2-E4 states using combined quantum mechanical and molecular mechanical (QM/MM) calculations and four different density-functional theory methods. We find large differences in the predictions of the different methods. B3LYP strongly favours protonation of the central carbide ion and H2 cannot form from such structures. On the other hand, with TPSS, r2SCAN and TPSSh, H2 formation is strongly exothermic for all structures and En and therefore need strict kinetic control to be avoided. For the E2 state, the kinetic barriers for the low-energy structures are high enough to avoid H2 formation. However, for both the E3 and E4 states, all three methods predict that the best structure has two hydride ions bridging the same pair of Fe ions (Fe2 and Fe6) and these two ions can combine to form H2 with an activation barrier of only 29-57 kJ mol-1, corresponding to rates of 7 × 102 to 5 × 107 s-1, i.e. much faster than the turnover rate of the enzyme (1-5 s-1). We have also studied H-atom movements within the FeMo cluster, showing that the various protonation states can quite freely be interconverted (activation barriers of 12-69 kJ mol-1).

On the Shoulders of Giants-Reaching for Nitrogenase

Only a single enzyme system-nitrogenase-carries out the conversion of atmospheric N2 into bioavailable ammonium, an essential prerequisite for all organismic life. The reduction of this inert substrate at ambient conditions poses unique catalytic challenges that strain our mechanistic understanding even after decades of intense research. Structural biology has added its part to this greater tapestry, and in this review, I provide a personal (and highly biased) summary of the parts of the story to which I had the privilege to contribute. It focuses on the crystallographic analysis of the three isoforms of nitrogenases at high resolution and the binding of ligands and inhibitors to the active-site cofactors of the enzyme. In conjunction with the wealth of available biochemical, biophysical, and spectroscopic data on the protein, this has led us to a mechanistic hypothesis based on an elementary mechanism of repetitive hydride formation and insertion.

Protonation of Homocitrate and the E1 State of Fe-Nitrogenase Studied by QM/MM Calculations

Nitrogenase is the only enzyme that can cleave the strong triple bond in N2, making nitrogen available for biological life. There are three isozymes of nitrogenase, differing in the composition of the active site, viz., Mo, V, and Fe-nitrogenase. Recently, the first crystal structure of Fe-nitrogenase was presented. We have performed the first combined quantum mechanical and molecular mechanical (QM/MM) study of Fe-nitrogenase. We show with QM/MM and quantum-refinement calculations that the homocitrate ligand is most likely protonated on the alcohol oxygen in the resting E0 state. The most stable broken-symmetry (BS) states are the same as for Mo-nitrogenase, i.e., the three Noodleman BS7-type states (with a surplus of β spin on the eighth Fe ion), which maximize the number of nearby antiferromagnetically coupled Fe-Fe pairs. For the E1 state, we find that protonation of the S2B μ2 belt sulfide ion is most favorable, 14-117 kJ/mol more stable than structures with a Fe-bound hydride ion (the best has a hydride ion on the Fe2 ion) calculated with four different density-functional theory methods. This is similar to what was found for Mo-nitrogenase, but it does not explain the recent EPR observation that the E1 state of Fe-nitrogenase should contain a photolyzable hydride ion. For the E1 state, many BS states are close in energy, and the preferred BS state differs depending on the position of the extra proton and which density functional is used.

Multireference Protonation Energetics of a Dimeric Model of Nitrogenase Iron-Sulfur Clusters

Characterizing the electronic structure of the iron-sulfur clusters in nitrogenase is necessary to understand their role in the nitrogen fixation process. One challenging task is to determine the protonation state of the intermediates in the nitrogen fixing cycle. Here, we use a dimeric iron-sulfur model to study relative energies of protonation at C, S, or Fe. Using a composite method based on coupled cluster and density matrix renormalization group energetics, we converge the relative energies of four protonated configurations with respect to basis set and correlation level. We find that accurate relative energies require large basis sets as well as a proper treatment of multireference and relativistic effects. We have also tested ten density functional approximations for these systems. Most of them give large errors in their relative energies. The best performing functional in this system is B3LYP, which gives mean absolute and maximum deviations of only 10 and 13 kJ/mol with respect to our correlated wave function estimates, respectively, comparable to the uncertainty in our correlated estimates. Our work provides benchmark results for the calibration of new approximate electronic structure methods and density functionals for these problems.

The E3 state of FeMoco: one hydride, two hydrides or dihydrogen?

Hydrides are present in the reduced states of the iron-molybdenum cofactor (FeMoco) of Mo nitrogenase and are believed to play a key mechanistic role in the dinitrogen reduction reaction catalyzed by the enzyme. Two hydrides are present in the E4 state according to 1H ENDOR and there is likely a single hydride in the E2 redox state. The 2-hydride E4 state has been experimentally observed to bind N2 and it has been speculated that E3 may bind N2 as well. However, the E3 state has not been directly observed and very little is known about its molecular and electronic structure or reactivity. In recent computational studies, we have explored the energy surfaces of the E2 and E4 by QM/MM modelling, and found that the most stable hydride isomers contain bridging or partially bridging hydrides with an open protonated belt sulfide-bridge. In this work we systematically explore the energy surface of the E3 redox state, comparing single hydride and two-hydride isomers with varying coordination and bridging vs. terminal sulfhydryl groups. We also include a model featuring a triply protonated carbide. The results are only mildly dependent on the QM-region size. The three most stable E3 isomers at the r2SCAN level of theory have in common: an open belt sulfide-bridge (terminal sulfhydryl group on Fe6) and either 2 bridging hydrides (between Fe2 and Fe6), 1 bridging-1-terminal hydride (around Fe2 and Fe6) or a dihydrogen ligand bound at the Fe2 site. Analyzing the functional dependency of the results, we find that functionals previously found to predict accurate structures of spin-coupled Fe/Mo dimers and FeMoco (TPSSh, B97-D3, r2SCAN, and B3LYP*) are in generally good agreement about the stability of these 3 E3 isomers. However, B3LYP*, similar to its parent B3LYP method, predicts a triply protonated carbide isomer as the most stable isomer, an unlikely scenario in view of the lack of experimental evidence for carbide protonation occurring in reduced FeMoco states. Distinguishing further between the 3 hydride isomers is difficult and this flexible coordination nature of hydrides suggests that multiple hydride isomers could be present during experimental conditions. N2 binding was explored and resulted in geometries with 2 bridging hydrides and N2 bound to either Fe2 or Fe6 with a local low-spin state on the Fe. N2 binding is predicted to be mildly endothermic, similar to the E2 state, and it seems unlikely that the E3 state is capable of binding N2.

Computational Description of Alkylated Iron-Sulfur Organometallic Clusters

The radical S-adenosyl methionine (SAM) enzyme superfamily has widespread roles in hydrogen atom abstraction reactions of crucial biological importance. In these enzymes, reductive cleavage of SAM bound to a [4Fe-4S]1+ cluster generates the 5'-deoxyadenosyl radical (5'-dAdo•) which ultimately abstracts an H atom from the substrate. However, overwhelming experimental evidence has surprisingly revealed an obligatory organometallic intermediate Ω exhibiting an Fe-C5'-adenosyl bond, whose properties are the target of this theoretical investigation. We report a readily applied, two-configuration version of broken symmetry DFT, denoted 2C-DFT, designed to allow the accurate description of the hyperfine coupling constants and g-tensors of an alkyl group bound to a multimetallic iron-sulfur cluster. This approach has been validated by the excellent agreement of its results both with those of multiconfigurational complete active space self-consistent field computations for a series of model complexes and with the results from electron nuclear double-resonance/electron paramagnetic resonance spectroscopic studies for the crystallographically characterized complex, M-CH3, a [4Fe-4S] cluster with a Fe-CH3 bond. The likewise excellent agreement between spectroscopic results and 2C-DFT computations for Ω confirm its identity as an organometallic complex with a bond between an Fe of the [4Fe-4S] cluster and C5' of the deoxyadenosyl moiety, as first proposed.

Connecting the geometric and electronic structures of the nitrogenase iron-molybdenum cofactor through site-selective 57Fe labelling

Understanding the chemical bonding in the catalytic cofactor of the Mo nitrogenase (FeMo-co) is foundational for building a mechanistic picture of biological nitrogen fixation. A persistent obstacle towards this goal has been that the 57Fe-based spectroscopic data-although rich with information-combines responses from all seven Fe sites, and it has therefore not been possible to map individual spectroscopic responses to specific sites in the three-dimensional structure. Here we have addressed this challenge by incorporating 57Fe into a single site of FeMo-co. Spectroscopic analysis of the resting state informed on the local electronic structure of the terminal Fe1 site, including its oxidation state and spin orientation, and, in turn, on the spin-coupling scheme for the entire cluster. The oxidized resting state and the first intermediate in nitrogen fixation were also characterized, and comparisons with the resting state provided molecular-level insights into the redox chemistry of FeMo-co.

Histidine oxidation in lytic polysaccharide monooxygenase

The lytic polysaccharide monooxygenases (LPMOs) comprise a super-family of copper enzymes that boost the depolymerisation of polysaccharides by oxidatively disrupting the glycosidic bonds connecting the sugar units. Industrial use of LPMOs for cellulose depolymerisation has already begun but is still far from reaching its full potential. One issue is that the LPMOs self-oxidise and thereby deactivate. The mechanism of this self-oxidation is unknown, but histidine residues coordinating to the copper atom are the most susceptible. An unusual methyl modification of the NE2 atom in one of the coordinating histidine residues has been proposed to have a protective role. Furthermore, substrate binding is also known to reduce oxidative damage. We here for the first time investigate the mechanism of histidine oxidation with combined quantum and molecular mechanical (QM/MM) calculations, with outset in intermediates previously shown to form from a reaction with peroxide and a reduced LPMO. We show that an intermediate with a [Cu-O]⁺ moiety is sufficiently potent to oxidise the nearest C-H bond on both histidine residues, but methylation of the NE2 atom of His-1 increases the reaction barrier of this reaction. The substrate further increases the activation barrier. We also investigate a [Cu-OH]²⁺ intermediate with a deprotonated tyrosine radical. This intermediate was previously proposed to have a protective role, and we also find it to have higher barriers than the corresponding a [Cu-O]⁺ intermediate.

Characterization of the Geometrical and Electronic Structures of the Active Site and Its Effects on the Surrounding Environment in Reduced High-Potential Iron-Sulfur Proteins Investigated by the Density Functional Theory Approach

The high-potential iron-sulfur protein (HiPIP) is an electron-transporting protein that functions in the photosynthetic electron-transfer system and possesses a cubane-type [4Fe-4S] cluster in the active center. Characterization of the geometrical and electronic structures of the [4Fe-4S] cluster leads to an understanding of the functions in HiPIP, which are expected to be influenced by the environment surrounding the [4Fe-4S] cluster. This work characterized the geometrical and electronic structures of the [4Fe-4S] cluster in the reduced HiPIP and evaluated their effects on the protein environment using the density functional theory (DFT) approach. DFT calculations showed that the structural asymmetry and spin delocalization between iron atoms allowed for the acquisition of a unique stable geometrical and electronic structure in the open-shell singlet. In addition, the formation of an Fe-Fe bond accompanying the spin delocalization was found to depend on the interatomic distance. A comparison of the calculated stable structures with and without consideration of the amino acids around the [4Fe-4S] cluster demonstrated that the surrounding amino acids stabilized the unique geometrical and electronic structure of the [4Fe-4S] cluster in HiPIP.

Quantum Mechanical Calculations of Redox Potentials of the Metal Clusters in Nitrogenase

We have calculated redox potentials of the two metal clusters in Mo-nitrogenase with quantum mechanical (QM) calculations. We employ an approach calibrated for iron-sulfur clusters with 1-4 Fe ions, involving QM-cluster calculations in continuum solvent and large QM systems (400-500 atoms), based on structures from combined QM and molecular mechanics (QM/MM) geometry optimisations. Calculations on the P-cluster show that we can reproduce the experimental redox potentials within 0.33 V. This is similar to the accuracy obtained for the smaller clusters, although two of the redox reactions involve also proton transfer. The calculated P¹⁺/P^N redox potential is nearly the same independently of whether P¹⁺ is protonated or deprotonated, explaining why redox titrations do not show any pH dependence. For the FeMo cluster, the calculations clearly show that the formal oxidation state of the cluster in the resting E₀ state is MoIIIFe3IIFe4III , in agreement with previous experimental studies and QM calculations. Moreover, the redox potentials of the first five E₀-E₄ states are nearly constant, as is expected if the electrons are delivered by the same site (the P-cluster). However, the redox potentials are insensitive to the formal oxidation states of the Fe ion (i.e., whether the added protons bind to sulfide or Fe ions). Finally, we show that the later (E₄-E₈) states of the reaction mechanism have redox potential that are more positive (i.e., more exothermic) than that of the E₀/E₁ couple.

Subsystem density-functional theory: A reliable tool for spin-density based properties

Subsystem density-functional theory compiles a set of features that allow for efficiently calculating properties of very large open-shell radical systems such as organic radical crystals, proteins, or deoxyribonucleic acid stacks. It is computationally less costly than correlated ab initio wave function approaches and can pragmatically avoid the overdelocalization problem of Kohn-Sham density-functional theory without employing hard constraints on the electron-density. Additionally, subsystem density-functional theory calculations commonly start from isolated fragment electron densities, pragmatically preserving a priori specified subsystem spin-patterns throughout the calculation. Methods based on subsystem density-functional theory have seen a rapid development over the past years and have become important tools for describing open-shell properties. In this Perspective, we address open questions and possible developments toward challenging future applications in connection with subsystem density-functional theory for spin-dependent properties.

Analysis of the Geometric and Electronic Structure of Spin-Coupled Iron-Sulfur Dimers with Broken-Symmetry DFT: Implications for FeMoco

The open-shell electronic structure of iron–sulfur clusters presents considerable challenges to quantum chemistry, with the complex iron–molybdenum cofactor (FeMoco) of nitrogenase representing perhaps the ultimate challenge for either wavefunction or density functional theory. While broken-symmetry density functional theory has seen some success in describing the electronic structure of such cofactors, there is a large exchange–correlation functional dependence in calculations that is not fully understood. In this work, we present a geometric benchmarking test set, FeMoD11, of synthetic spin-coupled Fe–Fe and Mo–Fe dimers, with relevance to the molecular and electronic structure of the Mo-nitrogenase FeMo cofactor. The reference data consists of high-resolution crystal structures of metal dimer compounds in different oxidation states. Multiple density functionals are tested on their ability to reproduce the local geometry, specifically the Fe–Fe/Mo–Fe distance, for both antiferromagnetically coupled and ferromagnetically coupled dimers via the broken-symmetry approach. The metal–metal distance is revealed not only to be highly sensitive to the amount of exact exchange in the functional but also to the specific exchange and correlation functionals. For the antiferromagnetically coupled dimers, the calculated metal–metal distance correlates well with the covalency of the bridging metal–ligand bonds, as revealed via the corresponding orbital analysis, Hirshfeld S/Fe charges, and Fe–S Mayer bond order. Superexchange via bridging ligands is expected to be the dominant interaction in these dimers, and our results suggest that functionals that predict accurate Fe–Fe and Mo–Fe distances describe the overall metal–ligand covalency more accurately and in turn the superexchange of these systems. The best performing density functionals of the 16 tested for the FeMoD11 test set are revealed to be either the nonhybrid functionals r²SCAN and B97-D3 or hybrid functionals with 10–15% exact exchange: TPSSh and B3LYP*. These same four functionals are furthermore found to reproduce the high-resolution X-ray structure of FeMoco well according to quantum mechanics/molecular mechanics (QM/MM) calculations. Almost all nonhybrid functionals systematically underestimate Fe–Fe and Mo–Fe distances (with r²SCAN and B97-D3 being the sole exceptions), while hybrid functionals with >15% exact exchange (including range-separated hybrid functionals) overestimate them. The results overall suggest r²SCAN, B97-D3, TPSSh, and B3LYP* as accurate density functionals for describing the electronic structure of iron–sulfur clusters in general, including the complex FeMoco cluster of nitrogenase.

Thermodynamically Favourable States in the Reaction of Nitrogenase without Dissociation of any Sulfide Ligand

We have used combined quantum mechanical and molecular mechanical (QM/MM) calculations to study the reaction mechanism of nitrogenase, assuming that none of the sulfide ligands dissociates. To avoid the problem that there is no consensus regarding the structure and protonation of the E₄ state, we start from a state where N₂ is bound to the cluster and is protonated to N₂H₂, after dissociation of H₂. We show that the reaction follows an alternating mechanism with HNNH (possibly protonated to HNNH₂) and H₂NNH₂ as intermediates and the two NH₃ products dissociate at the E₇ and E₈ levels. For all intermediates, coordination to Fe6 is preferred, but for the E₄ and E₈ intermediates, binding to Fe2 is competitive. For the E₄, E₅ and E₇ intermediates we find that the substrate may abstract a proton from the hydroxy group of the homocitrate ligand of the FeMo cluster, thereby forming HNNH₂, H₂NNH₂ and NH₃ intermediates. This may explain why homocitrate is a mandatory component of nitrogenase. All steps in the suggested reaction mechanism are thermodynamically favourable compared to protonation of the nearby His‐195 group and in all cases, protonation of the NE2 atom of the latter group is preferred.

Broken-Symmetry Density Functional Theory Analysis of the Ω Intermediate in Radical S-Adenosyl-l-methionine Enzymes: Evidence for a Near-Attack Conformer over an Organometallic Species

Radical S-adenosyl-l-methionine (SAM) enzymes are found in all domains of life and catalyze a wide range of biochemical reactions. Recently, an organometallic intermediate, Ω, has been experimentally implicated in the 5'-deoxyadenosyl radical generation mechanism of the radical SAM superfamily. In this work, we employ broken-symmetry density functional theory to evaluate several structural models of Ω. The results show that the calculated hyperfine coupling constants (HFCCs) for the proposed organometallic structure of Ω are inconsistent with the experiment. In contrast, a near-attack conformer of SAM bound to the catalytic [4Fe-4S] cluster, in which the distance between the unique iron and SAM sulfur is ∼3 Å, yields HFCCs that are all within 1 MHz of the experimental values. These results clarify the structure of the ubiquitous Ω intermediate and suggest a paradigm shift reversal regarding the mechanism of SAM cleavage by members of the radical SAM superfamily.

Accurate 57Fe Mössbauer Parameters from General Gaussian Basis Sets

The prediction of isomer shifts in ⁵⁷Fe Mossbauer spectra is typically achieved by building calibration lines using the values of the density at the nuclear position. Using Slater-type orbital basis or large and specific Gaussian-type orbital basis has been thus far mandatory to achieve accurate predictions with density functional theory methods. In this work, we show that replacing the value of the density at the nucleus by the density integrated in a sphere of radius 0.06 au centered on the Fe nuclei yields excellent calibration lines (r² = 0.976) with a high predictive power (q² = 0.975, MAE = 0.055 mm·s^–1) while using the conventional def2-TZVP basis set and X-ray geometrical parameters. Our data set comprises 69 ⁵⁷Fe-containing compounds and 103 signals. We also find B3LYP performing significantly better than the PW91 functional.

Carbon Monoxide Binding to the Iron-Molybdenum Cofactor of Nitrogenase: a Detailed Quantum Mechanics/Molecular Mechanics Investigation

Carbon monoxide (CO) is a well-known inhibitor of nitrogenase activity. Under turnover conditions, CO binds to FeMoco, the active site of Mo nitrogenase. Time-resolved IR measurements suggest an initial terminal CO at 1904 cm^-1 that converts to a bridging CO at 1715 cm^-1, and an X-ray structure shows that CO can displace one of the bridging belt sulfides of FeMoco. However, the CO-binding redox state(s) of FeMoco (E_n) and the role of the protein environment in stabilizing specific CO-bound intermediates remain elusive. In this work, we carry out an in-depth analysis of the CO-FeMoco interaction based on quantum chemical calculations addressing different aspects of the electronic structure. (1) The local electronic structure of the Fe-CO bond is studied through diamagnetically substituted FeMoco. (2) A cluster model of FeMoco within a polarizable continuum illustrates how CO binding may affect the spin-coupling between the metal centers. (3) A QM/MM model incorporates the explicit influence of the amino acid residues surrounding FeMoco in the MoFe protein. The QM/MM model predicts both a terminal and a bridging CO in the E₁ redox state. The scaled calculated CO frequencies (1922 and 1716 cm^-1, respectively) are in good agreement with the experimentally observed IR bands supporting CO binding to the E₁ state. Alternatively, an E₂ state QM/MM model, which has the same atomic structure as the CO-bound X-ray structure, features a semi-bridging CO with a scaled calculated frequency (1718 cm^-1) similar to the bridging CO in the E₁ model.

The E2 state of FeMoco: Hydride Formation versus Fe Reduction and a Mechanism for H2 Evolution

The iron‐molybdenum cofactor (FeMoco) is responsible for dinitrogen reduction in Mo nitrogenase. Unlike the resting state, E₀, reduced states of FeMoco are much less well characterized. The E₂ state has been proposed to contain a hydride but direct spectroscopic evidence is still lacking. The E₂ state can, however, relax back the E₀ state via a H₂ side‐reaction, implying a hydride intermediate prior to H₂ formation. This E₂→E₀ pathway is one of the primary mechanisms for H₂ formation under low‐electron flux conditions. In this study we present an exploration of the energy surface of the E₂ state. Utilizing both cluster‐continuum and QM/MM calculations, we explore various classes of E₂ models: including terminal hydrides, bridging hydrides with a closed or open sulfide‐bridge, as well as models without. Importantly, we find the hemilability of a protonated belt‐sulfide to strongly influence the stability of hydrides. Surprisingly, non‐hydride models are found to be almost equally favorable as hydride models. While the cluster‐continuum calculations suggest multiple possibilities, QM/MM suggests only two models as contenders for the E₂ state. These models feature either i) a bridging hydride between Fe₂ and Fe₆ and an open sulfide‐bridge with terminal SH on Fe₆ (E₂‐hyd) or ii) a double belt‐sulfide protonated, reduced cofactor without a hydride (E₂‐nonhyd). We suggest both models as contenders for the E₂ redox state and further calculate a mechanism for H₂ evolution. The changes in electronic structure of FeMoco during the proposed redox‐state cycle, E₀→E₁→E₂→E₀, are discussed.

On the Use of Normalized Metrics for Density Sensitivity Analysis in DFT

In the past years, there has been a discussion about how the errors in density functional theory might be related to errors in the self-consistent densities obtained from different density functional approximations. This, in turn, brings up the discussion about the different ways in which we can measure such errors and develop metrics that assess the sensitivity of calculated energies to changes in the density. It is important to realize that there cannot be a unique metric in order to look at this density sensitivity, simultaneously needing size-extensive and size-intensive metrics. In this study, we report two metrics that are widely applicable to any density functional approximation. We also show how they can be used to classify different chemical systems of interest with respect to their sensitivity to small variations in the density.

Postbiosynthetic modification of a precursor to the nitrogenase iron-molybdenum cofactor

Nitrogenases utilize Fe-S clusters to reduce N₂ to NH₃ The large number of Fe sites in their catalytic cofactors has hampered spectroscopic investigations into their electronic structures, mechanisms, and biosyntheses. To facilitate their spectroscopic analysis, we are developing methods for incorporating ⁵⁷Fe into specific sites of nitrogenase cofactors, and we report herein site-selective ⁵⁷Fe labeling of the L-cluster-a carbide-containing, [Fe₈S₉C] precursor to the Mo nitrogenase catalytic cofactor. Treatment of the isolated L-cluster with the chelator ethylenediaminetetraacetate followed by reconstitution with ⁵⁷Fe²⁺ results in ⁵⁷Fe labeling of the terminal Fe sites in high yield and with high selectivity. This protocol enables the generation of L-cluster samples in which either the two terminal or the six belt Fe sites are selectively labeled with ⁵⁷Fe. Mössbauer spectroscopic analysis of these samples bound to the nitrogenase maturase Azotobacter vinelandii NifX reveals differences in the primary coordination sphere of the terminal Fe sites and that one of the terminal sites of the L-cluster binds to H35 of Av NifX. This work provides molecular-level insights into the electronic structure and biosynthesis of the L-cluster and introduces postbiosynthetic modification as a promising strategy for studies of nitrogenase cofactors.

Critical evaluation of a crystal structure of nitrogenase with bound N2 ligands

Recently, a 1.83 Å crystallographic structure of nitrogenase was suggested to show N₂-derived ligands at three sites in the catalytic FeMo cluster, replacing the three [Formula: see text] bridging sulfide ligands (two in one subunit and the third in the other subunit) (Kang et al. in Science 368: 1381-1385, 2020). Naturally, such a structure is sensational, having strong bearings on the reaction mechanism of the enzyme. Therefore, it is highly important to ensure that the interpretation of the structure is correct. Here, we use standard crystallographic refinement and quantum refinement to evaluate the structure. We show that the original crystallographic raw data are strongly anisotropic, with a much lower resolution in certain directions than others. This, together with the questionable use of anisotropic B factors, give atoms an elongated shape, which may look like diatomic atoms. In terms of standard electron-density maps and real-space Z scores, a resting-state structure with no dissociated sulfide ligands fits the raw data better than the interpretation suggested by the crystallographers. The anomalous electron density at 7100 eV is weaker for the putative N₂ ligands, but not lower than for several of the [Formula: see text] bridging sulfide ions and not lower than what can be expected from a statistical analysis of the densities. Therefore, we find no convincing evidence for any N₂ binding to the FeMo cluster. Instead, a standard resting state without any dissociated ligands seems to be the most likely interpretation of the structure. Likewise, we find no support that the homocitrate ligand should show monodentate binding.

Quantum-refinement studies of the bidentate ligand of V‑nitrogenase and the protonation state of CO-inhibited Mo‑nitrogenase

Nitrogenase is the only enzyme that can cleave the triple bond in N₂, making nitrogen available to plants (although the enzyme itself is strictly microbial). It has been studied extensively with both experimental and computational methods, but many details of the reaction mechanism are still unclear. X-ray crystallography is the main source of structural information for biomacromolecules, but it has problems to discern hydrogen atoms or to distinguish between elements with the same number of electrons. These problems can sometimes be alleviated by introducing quantum chemical calculations in the refinement, providing information about the ideal structure (in the same way as the empirical restraints used in standard crystallographic refinement) and comparing different interpretations of the structure with normal crystallographic and quantum mechanical quality measures. We have performed such quantum-refinement calculations to address two important issues for nitrogenase. First, we show that the bidentate ligand of the active-site FeV cluster in V‑nitrogenase is carbonate, rather than bicarbonate or nitrate. Second, we study the CO-inhibited structure of Mo‑nitrogenase. CO binds to a reduced and protonated state of the enzyme by replacing one of the sulfide ions (S2B) in the active-site FeMo cluster. We examined if it is possible to deduce from the crystal structure the location of the protons. Our results indicates that the crystal structure is best modelled as fully deprotonated.

Subsystem density-functional theory for interacting open-shell systems: spin densities and magnetic exchange couplings

We investigate the possibility of describing interacting open-shell systems in high-spin and broken-symmetry (BS) states with subsystem density-functional theory (sDFT). This subsystem method typically starts from the electronic-structure results obtained for individual systems, for which the spin states can be individually defined. Through the confining effect of the embedding potential and/or the use of monomer basis sets, these individual spin states can be preserved in sDFT calculations. This offers the possibility of easy convergence to broken-symmetry states with arbitrary local spin patterns. We show that the resulting spin densities are in very good agreement with successfully converged broken-symmetry Kohn-Sham density-functional theory (KS-DFT) calculations. Yet sDFT can even cure those BS cases where KS-DFT suffers from convergence problems or convergence to undesired spin states. In contrast to KS-DFT, the sDFT-results only show a mild exchange-correlation functional dependence. We also show that magnetic coupling constants from sDFT are not satisfactory with standard approximations for the non-additive kinetic energy. When this component is evaluated "exactly", i.e. based on potential reconstruction, however, the magnetic coupling constants derived from spin-state energy differences are greatly improved. Hence, the interacting radicals studied here represent cases where even (semi-)local approximations for the non-additive kinetic-energy potential work well, while the parent energy functionals do not yield satisfactory results for spin-state energy differences.

Quantum refinement with multiple conformations: application to the P-cluster in nitrogenase

X-ray crystallography is the main source of atomistic information on the structure of proteins. Normal crystal structures are obtained as a compromise between the X-ray scattering data and a set of empirical restraints that ensure chemically reasonable bond lengths and angles. However, such restraints are not always available or accurate for nonstandard parts of the structure, for example substrates, inhibitors and metal sites. The method of quantum refinement, in which these empirical restraints are replaced by quantum-mechanical (QM) calculations, has previously been suggested for small but interesting parts of the protein. Here, this approach is extended to allow for multiple conformations in the QM region by performing separate QM calculations for each conformation. This approach is shown to work properly and leads to improved structures in terms of electron-density maps and real-space difference density Z-scores. It is also shown that the quality of the structures can be gauged using QM strain energies. The approach, called ComQumX-2QM, is applied to the P-cluster in two different crystal structures of the enzyme nitrogenase, i.e. an Fe8S7Cys6 cluster, used for electron transfer. One structure is at a very high resolution (1.0 Å) and shows a mixture of two different oxidation states, the fully reduced PN state (Fe82+, 20%) and the doubly oxidized P2+ state (80%). In the original crystal structure the coordinates differed for only two iron ions, but here it is shown that the two states also show differences in other atoms of up to 0.7 Å. The second structure is at a more modest resolution, 2.1 Å, and was originally suggested to show only the one-electron oxidized state, P1+. Here, it is shown that it is rather a 50/50% mixture of the P1+ and P2+ states and that many of the Fe-Fe and Fe-S distances in the original structure were quite inaccurate (by up to 0.8 Å). This shows that the new ComQumX-2QM approach can be used to sort out what is actually seen in crystal structures with dual conformations and to give locally improved coordinates.

Does the crystal structure of vanadium nitrogenase contain a reaction intermediate? Evidence from quantum refinement

Recently, a crystal structure of V-nitrogenase was presented, showing that one of the µ2 sulphide ions in the active site (S2B) is replaced by a lighter atom, suggested to be NH or NH2, i.e. representing a reaction intermediate. Moreover, a sulphur atom is found 7 Å from the S2B site, suggested to represent a storage site for this ion when it is displaced. We have re-evaluated this structure with quantum refinement, i.e. standard crystallographic refinement in which the empirical restraints (employed to ensure that the final structure makes chemical sense) are replaced by more accurate quantum-mechanical calculations. This allows us to test various interpretations of the structure, employing quantum-mechanical calculations to predict the ideal structure and to use crystallographic measures like the real-space Z-score and electron-density difference maps to decide which structure fits the crystallographic raw data best. We show that the structure contains an OH--bound state, rather than an N2-derived reaction intermediate. Moreover, the structure shows dual conformations in the active site with ~ 14% undissociated S2B ligand, but the storage site seems to be fully occupied, weakening the suggestion that it represents a storage site for the dissociated ligand.

Quantum Mechanics/Molecular Mechanics Study of Resting-State Vanadium Nitrogenase: Molecular and Electronic Structure of the Iron-Vanadium Cofactor

The nitrogenase enzymes are responsible for all biological nitrogen reduction. How this is accomplished at the atomic level, however, has still not been established. The molybdenum-dependent nitrogenase has been extensively studied and is the most active catalyst for dinitrogen reduction of the nitrogenase enzymes. The vanadium-dependent form, on the other hand, displays different reactivity, being capable of CO and CO2 reduction to hydrocarbons. Only recently did a crystal structure of the VFe protein of vanadium nitrogenase become available, paving the way for detailed theoretical studies of the iron-vanadium cofactor (FeVco) within the protein matrix. The crystal structure revealed a bridging 4-atom ligand between two Fe atoms, proposed to be either a CO32- or NO3- ligand. Using a quantum mechanics/molecular mechanics model of the VFe protein, starting from the 1.35 Å crystal structure, we have systematically explored multiple computational models for FeVco, considering either a CO32- or NO3- ligand, three different redox states, and multiple broken-symmetry states. We find that only a [VFe7S8C(CO3)]2- model for FeVco reproduces the crystal structure of FeVco well, as seen in a comparison of the Fe-Fe and V-Fe distances in the computed models. Furthermore, a broken-symmetry solution with Fe2, Fe3, and Fe5 spin-down (BS7-235) is energetically preferred. The electronic structure of the [VFe7S8C(CO3)]2- BS7-235 model is compared to our [MoFe7S9C]- BS7-235 model of FeMoco via localized orbital analysis and is discussed in terms of local oxidation states and different degrees of delocalization. As previously found from Fe X-ray absorption spectroscopy studies, the Fe part of FeVco is reduced compared to FeMoco, and the calculations reveal Fe5 as locally ferrous. This suggests resting-state FeVco to be analogous to an unprotonated E1 state of FeMoco. Furthermore, V-Fe interactions in FeVco are not as strong compared to Mo-Fe interactions in FeMoco. These clear differences in the electronic structures of otherwise similar cofactors suggest an explanation for distinct differences in reactivity.

The Spectroscopy of Nitrogenases

Nitrogenases are responsible for biological nitrogen fixation, a crucial step in the biogeochemical nitrogen cycle. These enzymes utilize a two-component protein system and a series of iron-sulfur clusters to perform this reaction, culminating at the FeMco active site (M = Mo, V, Fe), which is capable of binding and reducing N2 to 2NH3. In this review, we summarize how different spectroscopic approaches have shed light on various aspects of these enzymes, including their structure, mechanism, alternative reactivity, and maturation. Synthetic model chemistry and theory have also played significant roles in developing our present understanding of these systems and are discussed in the context of their contributions to interpreting the nature of nitrogenases. Despite years of significant progress, there is still much to be learned from these enzymes through spectroscopic means, and we highlight where further spectroscopic investigations are needed.

N2H2 binding to the nitrogenase FeMo cluster studied by QM/MM methods

We have made a systematic combined quantum mechanical and molecular mechanical (QM/MM) investigation of possible structures of the N₂ bound state of nitrogenase. We assume that N₂ is immediately protonated to a N₂H₂ state, thereby avoiding the problem of determining the position of the protons in the cluster. We have systematically studied both end-on and side-on structures, as well as both HNNH and NNH₂ states. Our results indicate that the binding of N₂H₂ is determined more by interactions and steric clashes with the surrounding protein than by the intrinsic preferences of the ligand and the cluster. The best binding mode with both the TPSS and B3LYP density-functional theory methods has trans-HNNH terminally bound to Fe2. It is stabilised by stacking of the substrate with His-195 and Ser-278. However, several other structures come rather close in energy (within 3-35 kJ/mol) at least in some calculations: The corresponding cis-HNNH structure terminally bound to Fe2 is second best with B3LYP. A structure with HNNH₂ terminally bound to Fe6 is second most stable with TPSS (where the third proton is transferred to the substrate from the homocitrate ligand). Structures with trans-HNNH, bound to Fe4 or Fe6, or cis-HNNH bound to Fe6 are also rather stable. Finally, with the TPSS functional, a structure with cis-HNNH side-on binding to the Fe3-Fe4-Fe5-Fe7 face of the cluster is also rather low in energy, but all side-on structures are strongly disfavoured by the B3LYP method.

What Is the Structure of the E4 Intermediate in Nitrogenase?

Nitrogenase is the only enzyme that can cleave the strong triple bond in N₂. The active site contains a complicated MoFe₇S₉C cluster. It is believed that it needs to accept four protons and electrons, forming the E₄ state, before it can bind N₂. However, there is no consensus on the atomic structure of the E₄ state. Experimental studies indicate that it should contain two hydride ions bridging two pairs of Fe ions, and it has been suggested that both hydride ions as well as the two protons bind on the same face of the cluster. On the other hand, density functional theory (DFT) studies have indicated that it is energetically more favorable with either three hydride ions or with a triply protonated carbide ion, depending on the DFT functional. We have performed a systematic combined quantum mechanical and molecular mechanical (QM/MM) study of possible E₄ states with two bridging hydride ions. Our calculations suggest that the most favorable structure has hydride ions bridging the Fe2/6 and Fe3/7 ion pairs. In fact, such structures are 14 kJ/mol more stable than structures with three hydride ions, showing that pure DFT functionals give energetically most favorable structures in agreement with experiments. An important reason for this finding is that we have identified a new type of broken-symmetry state that involves only two Fe ions with minority spin, in contrast to the previously studied states with three Fe ions with minority spin. The energetically best structures have the two hydride ions on different faces of the FeMo cluster, whereas better agreement with ENDOR data is obtained if they are on the same face; such structures are only 6–22 kJ/mol less stable.

Resolving the structure of the E1 state of Mo nitrogenase through Mo and Fe K-edge EXAFS and QM/MM calculations

Biological nitrogen fixation is predominately accomplished through Mo nitrogenase, which utilizes a complex MoFe7S9C catalytic cluster to reduce N2 to NH3. This cluster requires the accumulation of three to four reducing equivalents prior to binding N2; however, despite decades of research, the intermediate states formed prior to N2 binding are still poorly understood. Herein, we use Mo and Fe K-edge X-ray absorption spectroscopy and QM/MM calculations to investigate the nature of the E1 state, which is formed following the addition of the first reducing equivalent to Mo nitrogenase. By analyzing the extended X-ray absorption fine structure (EXAFS) region, we provide structural insight into the changes that occur in the metal clusters of the protein when forming the E1 state, and use these metrics to assess a variety of possible models of the E1 state. The combination of our experimental and theoretical results supports that formation of E1 involves an Fe-centered reduction combined with the protonation of a belt-sulfide of the cluster. Hence, these results provide critical experiment and computational insight into the mechanism of this important enzyme.

Electronic landscape of the P-cluster of nitrogenase as revealed through many-electron quantum wavefunction simulations

The electronic structure of the nitrogenase metal cofactors is central to nitrogen fixation. However, the P-cluster and FeMo cofactor, each containing eight Fe atoms, have eluded detailed characterization of their electronic properties. We report on the low-energy electronic states of the P-cluster in three oxidation states through exhaustive many-electron wavefunction simulations enabled by new theoretical methods. The energy scales of orbital and spin excitations overlap, yielding a dense spectrum with features that we trace to the underlying atomic states and recouplings. The clusters exist in superpositions of spin configurations with non-classical spin correlations, complicating interpretation of magnetic spectroscopies, whereas the charges are mostly localized from reorganization of the cluster and its surroundings. On oxidation, the opening of the P-cluster substantially increases the density of states, which is intriguing given its proposed role in electron transfer. These results demonstrate that many-electron simulations stand to provide new insights into the electronic structure of the nitrogenase cofactors.

Extremely large differences in DFT energies for nitrogenase models

Nitrogenase is the only enzyme that can cleave the triple bond in N2, making nitrogen avaiable for other organisms. It contains a complicated MoFe7S9C(homocitrate) cluster in its active site. Many computational studies with density-functional theory (DFT) of the nitrogenase enzyme have been presented, but they do not show any consensus - they do not even agree where the first four protons should be added, forming the central intermediate E4. We show that the prime reason for this is that different DFT methods give relative energies that differ by almost 600 kJ mol-1 for different protonation states. This is 4-30 times more than what is observed for other systems. The reason for this is that in some structures, the hydrogens bind to sulfide or carbide ions as protons, whereas in other structures they bind to the metals as hydride ions, changing the oxidation state of the metals, as well as the Fe-C, Fe-S and Fe-Fe distances. The energies correlate with the amount of Hartree-Fock exchange in the method, indicating a variation in the amount of static correlation in the structures. It is currently unclear which DFT method gives the best results for nitrogenase. We show that non-hybrid DFT functionals and TPSSh give the most accurate structures of the resting active site, whereas B3LYP and PBE0 give the best H2 dissociation energies. However, no DFT method indicates that a structure of E4 with two bridging hydride ions is lowest in energy, as spectroscopic experiments indicate.

Survey of the Geometric and Electronic Structures of the Key Hydrogenated Forms of FeMo-co, the Active Site of the Enzyme Nitrogenase: Principles of the Mechanistically Significant Coordination Chemistry

The enzyme nitrogenase naturally hydrogenates N2 to NH3, achieved through the accumulation of H atoms on FeMo-co, the Fe7MoS9C(homocitrate) cluster that is the catalytically active site. Four intermediates, E1H1, E2H2, E3H3, and E4H4, carry these hydrogen atoms. I report density functional calculations of the numerous possibilities for the geometric and electronic structures of these poly-hydrogenated forms of FeMo-co. This survey involves more than 100 structures, including those with bound H2, and assesses their relative energies and most likely electronic states. Twelve locations for bound H atoms in the active domain of FeMo-co, including Fe–H–Fe and Fe–H–S bridges, are studied. A significant result is that transverse Fe–H–Fe bridges (transverse to the pseudo-threefold axis of FeMo-co and shared with triply-bridging S) are not possible geometrically unless the S is hydrogenated to become doubly-bridging. The favourable Fe–H–Fe bridges are shared with doubly-bridging S. ENDOR data for an E4H4 intermediate trapped at low temperature, and interpretations in terms of the geometrical and electronic structure of E4H4, are assessed in conjunction with the calculated possibilities. The results reported here yield a set of 24 principles for the mechanistically significant coordination chemistry of H and H2 on FeMo-co, in the stages prior to N2 binding.

The mechanism for nitrogenase including all steps

Nitrogen in the air is turned into biologically useful ammonia by the nitrogenase enzyme. The leading member of this group has a cofactor with one molybdenum and seven irons linked together by sulfurs. The structure that binds N₂ has a triply protonated carbide and a rotated homocitrate. Both these structural changes are necessary for the activation.

Computational Methods for Modeling Metalloproteins

Metalloproteins are challenging objects if we want to investigate their chemical reactivity with theoretical approaches such as density functional theory (DFT). The complexity of these biomolecules often requires us to find a compromise between accuracy and feasibility, one that is tailored to the questions we set out to answer. In this chapter, we discuss computational approaches to studying chemical reactions in metalloproteins and how to utilize the information hidden in homologous proteins.

Critical computational analysis illuminates the reductive-elimination mechanism that activates nitrogenase for N2 reduction

Recent spectroscopic, kinetic, photophysical, and thermodynamic measurements show activation of nitrogenase for N₂ → 2NH₃ reduction involves the reductive elimination (re) of H₂ from two [Fe-H-Fe] bridging hydrides bound to the catalytic [7Fe-9S-Mo-C-homocitrate] FeMo-cofactor (FeMo-co). These studies rationalize the Lowe-Thorneley kinetic scheme's proposal of mechanistically obligatory formation of one H₂ for each N₂ reduced. They also provide an overall framework for understanding the mechanism of nitrogen fixation by nitrogenase. However, they directly pose fundamental questions addressed computationally here. We here report an extensive computational investigation of the structure and energetics of possible nitrogenase intermediates using structural models for the active site with a broad range in complexity, while evaluating a diverse set of density functional theory flavors. (i) This shows that to prevent spurious disruption of FeMo-co having accumulated 4[e ^-/H⁺] it is necessary to include: all residues (and water molecules) interacting directly with FeMo-co via specific H-bond interactions; nonspecific local electrostatic interactions; and steric confinement. (ii) These calculations indicate an important role of sulfide hemilability in the overall conversion of E ₀ to a diazene-level intermediate. (iii) Perhaps most importantly, they explain (iiia) how the enzyme mechanistically couples exothermic H₂ formation to endothermic cleavage of the N≡N triple bond in a nearly thermoneutral re/oxidative-addition equilibrium, (iiib) while preventing the "futile" generation of two H₂ without N₂ reduction: hydride re generates an H₂ complex, but H₂ is only lost when displaced by N₂, to form an end-on N₂ complex that proceeds to a diazene-level intermediate.

The Critical E4 State of Nitrogenase Catalysis

The reaction catalyzed by the nitrogenase enzyme involves breaking the stable triple bond of the dinitrogen molecule and is consequently considered among the most challenging reactions in biology. While many aspects regarding its atomic mechanism remain to be elucidated, a kinetic scheme established by David Lowe and Roger Thorneley has remained a gold standard for functional studies of the enzyme for more than 30 years. Recent three-dimensional structures of ligand-bound states of molybdenum- and vanadium-dependent nitrogenases have revealed the actual site of substrate binding on the large active site cofactors of this class of enzymes. The binding mode of an inhibitor and a reaction intermediate further substantiate a hypothesis by Seefeldt, Hoffman, and Dean that the activation of N₂ is made possible by a reductive elimination of H₂ that leaves the cofactor in a super-reduced state that can bind and reduce the inert N₂ molecule. Here we discuss the immediate implications of the structurally observed mode of binding of small molecules to the enzyme with respect to the early stages of the Thorneley-Lowe mechanism of nitrogenase. Four consecutive single-electron reductions give rise to two bridging hydrides at the cluster surface that can recombine to eliminate H₂ and enable the reduced cluster to bind its substrate in a bridging mode.

A bound reaction intermediate sheds light on the mechanism of nitrogenase

Reduction of N₂ by nitrogenases occurs at an organometallic iron cofactor that commonly also contains either molybdenum or vanadium. The well-characterized resting state of the cofactor does not bind substrate, so its mode of action remains enigmatic. Carbon monoxide was recently found to replace a bridging sulfide, but the mechanistic relevance was unclear. Here we report the structural analysis of vanadium nitrogenase with a bound intermediate, interpreted as a μ²-bridging, protonated nitrogen that implies the site and mode of substrate binding to the cofactor. Binding results in a flip of amino acid glutamine 176, which hydrogen-bonds the ligand and creates a holding position for the displaced sulfide. The intermediate likely represents state E₆ or E₇ of the Thorneley-Lowe model and provides clues to the remainder of the catalytic cycle.

Impact of H-termination on the nitrogen reduction reaction of molybdenum carbide as an electrochemical catalyst

H-Terminals can remarkably affect the performance of catalysts in nitrogen reduction.