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[4Fe-4S] clusters are essential cofactors in many proteins involved in biological redox-active processes. Density functional theory (DFT) methods are widely used to study these clusters. Previous investigations have indicated that there exist two local minima for these clusters in proteins. We perform a detailed study of these minima in five proteins and two oxidation states, using combined quantum mechanical and molecular mechanical (QM/MM) methods. We show that one local minimum (L state) has longer Fe-Fe distances than the other (S state), and that the L state is more stable for all cases studied. We also show that some DFT methods may only obtain the L state, while others may obtain both states. Our work provides new insights into the structural diversity and stability of [4Fe-4S] clusters in proteins, and highlights the importance of reliable DFT methods and geometry optimization. We recommend r 2 SCAN for optimizing [4Fe-4S] clusters in proteins, which gives the most accurate structures for the five proteins studied., (© 2023. The Author(s).)

The DMSO reductase family is the largest and most diverse family of mononuclear molybdenum oxygen-atom-transfer proteins. Their active sites contain a Mo ion coordinated to two molybdopterin ligands, one oxo group in the oxidised state, and one additional, often protein-derived ligand. We have used density-functional theory to evaluate how the fourth ligand (serine, cysteine, selenocysteine, OH - , O 2- , SH - , or S 2- ) affects the geometries, reaction mechanism, reaction energies, and reduction potentials of intermediates in the DMSO reductase reaction. Our results show that there are only small changes in the geometries of the reactant and product states, except from the elongation of the MoX bond as the ionic radius of XO, S, Se increases. The five ligands with a single negative charge gave an identical two-step reaction mechanism, in which DMSO first binds to the reduced active site, after which the SO bond is cleaved, concomitantly with the transfer of two electrons from Mo in a rate-determining second transition state. The five models gave similar activation energies of 69-85kJ/mol, with SH - giving the lowest barrier. In contrast, the O 2- and S 2- ligands gave much higher activation energies (212 and 168kJ/mol) and differing mechanisms (a more symmetric intermediate for O 2- and a one-step reaction without any intermediate for S 2- ). The high activation energies are caused by a less exothermic reaction energy, 13-25kJ/mol, and by a more stable reactant state owing to the strong MoO 2- or MoS 2- bonds., (Copyright © 2017 Elsevier Inc. All rights reserved.)

A series of QM/MM optimizations of the full protein of [Fe] hydrogenase were performed. The FeGP cofactor has been optimized in the water-bound resting state (1), with a side-on bound dihydrogen (2), or as a hydride intermediate (3). For inclusion of H4MPT in the closed structure, advanced multiscale modeling appears to be necessary, especially to obtain reliable distances between CH-H4MPT(+) and the dihydrogen (H2) or hydride (H(-)) ligand in the FeGP cofactor. Inclusion of the full protein is further important for the relative energies of the two intermediates 2 and 3. We finally find that hydride transfer from 3 has a significantly higher barrier than found in previous studies neglecting the full protein environment., (© 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.)

Mössbauer spectroscopy is an indispensable spectroscopic technique and analytical tool in iron coordination chemistry. The linear correlation between the electron density at the nucleus ("contact density") and experimental isomer shifts has been used to link calculated contact densities to experimental isomer shifts. Here we have investigated relativistic methods of systematically increasing sophistication, including the eXact 2-Component (X2C) Hamiltonian and a finite-nucleus model, for the calculation of isomer shifts of iron compounds. While being of similar accuracy as the full four-component treatment, X2C calculations are far more efficient. We find that effects of spin-orbit coupling can safely be neglected, leading to further speedup. Linear correlation plots using effective densities rather than contact densities versus experimental isomer shift lead to a correlation constant a = -0.294 a0(-3) mm s(-1) (PBE functional) which is close to an experimentally derived value. Isomer shifts of similar quality can thus be obtained both with and without fitting, which is not the case if one pursues a priori a non-relativistic model approach. As an application for a biologically relevant system, we have studied three recently proposed [Fe]-hydrogenase intermediates. The structures of these intermediates were extracted from QM/MM calculations using large QM regions surrounded by the full enzyme and a solvation shell of water molecules. We show that a comparison between calculated and experimentally observed isomer shifts can be used to discriminate between different intermediates, whereas calculated atomic charges do not necessarily correlate with Mössbauer isomer shifts. Detailed analysis reveals that the difference in isomer shifts between two intermediates is due to an overlap effect.

A QM/MM investigation of the active-ready (H(ox)) form of [FeFe]-hydrogenase from D. desulfuricans, in which the electronic properties of all Fe-S clusters (H, F and F') have been simultaneously described using DFT, was carried out with the aim of disclosing a possible interplay between the H-cluster and the accessory iron-sulfur clusters in the initial steps of the catalytic process leading to H(2) formation. It turned out that one-electron addition to the active-ready form leads to reduction of the F'-cluster and not of the H-cluster. Protonation of the H-cluster in H(ox) is unlikely, and in any case it would not trigger electron transfer from the accessory Fe(4)S(4) clusters to the active site. Instead, one-electron reduction and protonation of the active-ready form trigger electron transfer within the protein, a key event in the catalytic cycle. In particular, protonation of the H-cluster after one-electron reduction of the enzyme lowers the energy of the lowest unoccupied molecular orbitals localized on the H-cluster to such an extent that a long-range electron transfer from the F'-cluster towards the H-cluster itself is allowed., (Copyright © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.)

Key stereoelectronic properties of Desulfovibrio desulfuricans [FeFe]-hydrogenase (DdH) were investigated by quantum mechanical description of its complete inorganic core, which includes a Fe(6)S(6) active site (the H-cluster), as well as two ancillary Fe(4)S(4) assemblies (the F and F' clusters). The partially oxidized, active-ready form of DdH is able to efficiently bind dihydrogen, thus starting H(2) oxidation catalysis. The calculations allow us to unambiguously assign a mixed Fe(II)Fe(I) state to the catalytic core of the active-ready enzyme and show that H(2) uptake exerts subtle, yet crucial influences on the redox properties of DdH. In fact, H(2) binding can promote electron transfer from the H-cluster to the solvent-exposed F'-cluster, thanks to a 50% decrease of the energy gap between the HOMO (that is localized on the H-cluster) and the LUMO (which is centered on the F'-cluster). Our results also indicate that the binding of the redox partners of DdH in proximity of its F'-cluster can trigger one-electron oxidation of the H(2)-bound enzyme, a process that is expected to have an important role in H(2) activation. Our findings are analyzed not only from a mechanistic perspective, but also in consideration of the physiological role of DdH. In fact, this enzyme is known to be able to catalyze both the oxidation and the evolution of H(2), depending on the cellular metabolic requirements. Hints for the design of targeted mutations that could lead to the enhancement of the oxidizing properties of DdH are proposed and discussed.

In this work, we employ density functional theory to assign vibrational signatures of [FeFe]-hydrogenase intermediates to molecular structures. For this purpose, we perform an exhaustive analysis of structures and harmonic vibrations of a series of CN and CO containing model clusters of the [FeFe]-hydrogenase enzyme active site considering also different charges, counterions, and solvents. The pure density functional BP86 in combination with a triple-ζ polarized basis set produce reliable molecular structures as well as harmonic vibrations. Calculated CN and CO stretching vibrations are analyzed separately. Scaled vibrational frequencies are then applied to assign intermediates in [FeFe]-hydrogenase's reaction cycle. The results nicely complement the previous studies of Darensbourg and Hall, and Zilberman et al. The infrared spectrum of the H(ox) form is in very good agreement with the calculated spectrum of the Fe(I)Fe(II) model complex featuring a free coordination site at the distal Fe atom, as well as, with the calculated spectra of the complexes in which H(2) or H(2)O are coordinated at this site. The spectrum of H(red) measured from Desulfovibrio desulfuricans is compatible with a mixture of a Fe(I)Fe(I) species with all terminal COs, and a Fe(I)Fe(I) species with protonated dtma ligand, while the spectrum of H(red) recently measured from Chlamydomonas reinhardtii is compatible with a mixture of a Fe(I)Fe(I) species with a bridged CO, and a Fe(II)Fe(II) species with a terminal hydride bound to the Fe atom., (© 2011 American Chemical Society)

The presence of Fe-bound cyanide ligands in the active site of the proton-reducing enzymes [FeFe]-hydrogenases has led to the hypothesis that such Brønsted-Lowry bases could be protonated during the catalytic cycle, thus implying that hydrogen isocyanide (HNC) might have a relevant role in such crucial microbial metabolic paths. We present a hybrid quantum mechanical/molecular mechanical (QM/MM) study of the energetics of CN(-) protonation in the enzyme, and of the effects that cyanide protonation can have on [FeFe]-hydrogenase active sites. A detailed analysis of the electronic properties of the models and of the energy profile associated with H(2) evolution clearly shows that such protonation is dysfunctional for the catalytic process. However, the inclusion of the protein matrix surrounding the active site in our QM/MM models allowed us to demonstrate that the amino acid environment was finely selected through evolution, specifically to lower the Brønsted-Lowry basicity of the cyanide ligands. In fact, the conserved hydrogen-bonding network formed by these ligands and the neighboring amino acid residues is able to impede CN(-) protonation, as shown by the fact that the isocyanide forms of [FeFe]-hydrogenases do not correspond to stationary points on the enzyme QM/MM potential-energy surface., (Copyright © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.)

[FeFe]-hydrogenases are highly efficient H(2)-evolving metalloenzymes that include cyanides and carbonyls in the active site. The latter is an Fe(6)S(6) cluster (the so-called H-cluster) that can be subdivided into a binuclear portion carrying the CO and CN(-) groups and a tetranuclear subcluster. The fundamental role of cyanide ligands in increasing the basicity of the H-cluster has been highlighted previously. Here a more subtle but crucial role played by the two CN(-) ligands in the active site of [FeFe]-hydrogenases is disclosed. In fact, QM/MM calculations on all-atom models of the enzyme from Desulfovibrio desulfuricans show that the cyanide groups fine-tune the electronic and redox properties of the active site, affecting both the protonation regiochemistry and electron transfer between the two subclusters of the H-cluster. Despite the crucial role of cyanides in the protein active site, the currently available bioinspired electrocatalysts generally lack CN(-) groups in order to avoid competition between the latter and the catalytic metal centers for proton binding. In this respect, we show that a targeted inclusion of phosphine ligands in hexanuclear biomimetic clusters may restore the electronic and redox features of the wild-type H-cluster.

The active site of the [FeFe] hydrogenases contains two Fe ions bound to one Cys ligand, three CO molecules, two CN(-) ions, and a dithiolate ligand. The nature of the last of these has been much discussed, and it has been suggested that it contains C, N, or O as the bridgehead atom. Most experimental studies indicate a N atom, whereas a recent density functional theory (DFT) study of a crystal structure indicated an O atom. Here, we performed quantum refinement on the same crystal structure with five different models of the dithiolate ligand X(CH(2)S(-))(2), with X = CH(2), NH(2)(+), NH (two conformations), or O; we found that structures with a N bridgehead atom actually provide the best fit to the raw crystallographic data. Quantum refinement is standard crystallographic refinement in which the molecular mechanics force field normally used to supplement the experimental raw data to give a more chemical structure is replaced by more accurate DFT calculations for the active site. Thereby, we obtain structures that are an ideal compromise between DFT and crystallography.

Biotin synthase was the first example of what is now regarded as a distinctive enzyme class within the radical S-adenosylmethionine superfamily, the members of which use Fe/S clusters as the sulphur source in radical sulphur insertion reactions. The crystal structure showed that this enzyme contains a [2Fe-2S] cluster with a highly unusual arginine ligand, besides three normal cysteine ligands. However, the crystal structure is at such a low resolution that neither the exact coordination mode nor the role of this exceptional ligand has been elucidated yet, although it has been shown that it is not essential for enzyme activity. We have used quantum refinement of the crystal structure and combined quantum mechanical and molecular mechanical calculations to explore possible coordination modes and their influences on cluster properties. The investigations show that the protonation state of the arginine ligand has little influence on cluster geometry, so even a positively charged guanidinium moiety would be in close proximity to the iron atom. Nevertheless, the crystallised enzyme most probably contains a deprotonated (neutral) arginine coordinating via the NH group. Furthermore, the Fe...Fe distance seems to be independent of the coordination mode and is in perfect agreement with distances in other structurally characterised [2Fe-2S] clusters. The exceptionally large Fe...Fe distance found in the crystal structure could not be reproduced.

[FeFe]-hydrogenases harbor a {2Fe3S} assembly bearing two CO and two CN- groups, a mu-CO ligand, and a vacant coordination site trans to the mu-CO group. Recent theoretical results obtained studying the isolated {2Fe3S} subsite indicated that one of the CN- ligands can easily move from the crystallographic position to the coordination site trans to the mu-CO group; such an isomerization would have a major impact on substrates and inhibitors binding regiochemistry and, consequently, on the catalytic mechanism. To shed light on this crucial issue, we have carried out hybrid QM/MM and free energy perturbation calculations on the whole enzyme, which demonstrate that the protein environment plays a crucial role and maintains the CN- group fixed in the position observed in the crystal structure; these results strongly support the hypothesis that the vacant coordination site trans to the mu-CO group has a crucial functional relevance both in the context of CO-mediated inhibition of the enzyme and in dihydrogen oxidation/evolution catalysis.