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.

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 Refinement Does Not Support Dinuclear Copper Sites in Crystal Structures of Particulate Methane Monooxygenase.

Particulate methane monooxygenase (pMMO) is one of the few enzymes that can activate methane. The metal content of this enzyme has been highly controversial, with suggestions of a dinuclear Fe site or mono-, di-, or trinuclear Cu sites. Crystal structures have shown a mono- or dinuclear Cu site, but the resolution was low and the geometry of the dinuclear site unusual. We have employed quantum refinement (crystallographic refinement enhanced with quantum-mechanical calculations) to improve the structure of the active site. We compared a number of different mono- and dinuclear geometries, in some cases enhanced with more protein ligands or one or two water molecules, to determine which structure fits two sets of crystallographic raw data best. In all cases, the best results were obtained with mononuclear Cu sites, occasionally with an extra water molecule. Thus, we conclude that there is no crystallographic support for a dinuclear Cu site in pMMO.

Quantum refinement in real and reciprocal space using the Phenix and ORCA software.

X-ray and neutron crystallography, as well as cryogenic electron microscopy (cryo-EM), are the most common methods to obtain atomic structures of biological macromolecules. A feature they all have in common is that, at typical resolutions, the experimental data need to be supplemented by empirical restraints, ensuring that the final structure is chemically reasonable. The restraints are accurate for amino acids and nucleic acids, but often less accurate for substrates, inhibitors, small-molecule ligands and metal sites, for which experimental data are scarce or empirical potentials are harder to formulate. This can be solved using quantum mechanical calculations for a small but interesting part of the structure. Such an approach, called quantum refinement, has been shown to improve structures locally, allow the determination of the protonation and oxidation states of ligands and metals, and discriminate between different interpretations of the structure. Here, we present a new implementation of quantum refinement interfacing the widely used structure-refinement software Phenix and the freely available quantum mechanical software ORCA. Through application to manganese superoxide dismutase and V- and Fe-nitrogenase, we show that the approach works effectively for X-ray and neutron crystal structures, that old results can be reproduced and structural discrimination can be performed. We discuss how the weight factor between the experimental data and the empirical restraints should be selected and how quantum mechanical quality measures such as strain energies should be calculated. We also present an application of quantum refinement to cryo-EM data for particulate methane monooxygenase and show that this may be the method of choice for metal sites in such structures because no accurate empirical restraints are currently available for metals.

Combining crystallography with quantum mechanics.

In standard crystallographic refinement of biomacromolecules, the crystallographic raw data are supplemented by empirical restraints that ensure that the structure makes chemical sense. These restraints are typically accurate for amino acids and nucleic acids, but less so for cofactors, substrates, inhibitors, ligands and metal sites. In quantum refinement, this potential is replaced by more accurate quantum mechanical (QM) calculations. Several implementations have been presented, differing in the level of QM and whether it is used for the entire structure or only for a site of particular interest. It has been shown that the method can improve and correct errors in crystal structures and that it can be used to determine protonation and tautomeric states of various ligands and to decide what is really seen in the structure by refining different interpretations and using standard crystallographic and QM quality measures to decide which fits the structure best.

Computationally enhanced X-ray diffraction analysis of a gold(III) complex interacting with the human telomeric DNA G-quadruplex. Unravelling non-unique ligand positioning.

The crystal structure of the human telomeric DNA Tel24 G-quadruplex (Tel24 = TAG3(T2AG3)3T) in complex with the novel [AuL] species (with L = 2,4,6-tris(2-pyrimidyl)-1,3,5-triazine - TPymT-α) was solved by a novel joint molecular mechanical (MM)/quantum mechanical (QM) innovative approach. The quantum-refinement crystallographic method (crystallographic refinement enhanced with quantum mechanical calculation) was adapted to treat the [AuL]/G-quadruplex structure, where each gold complex in the binding site was found spread over four equally occupied positions. The four positions were first determined by docking restrained to the crystallographically determined metal ions' coordinates. Then, the quantum refinement method was used to resolve the poorly defined density around the ligands and improve the crystallographic determination, revealing that the binding preferences of this metallodrug toward Tel24 G-quadruplex arise from a combined effect of pyrimidine stacking, metal-guanine interactions and charge-charge neutralizing action of the π-acid triazine. The occurrence of interaction in solution with the Tel24 G-quadruplex DNA was further proved through DNA melting experiments, which showed a slight destabilisation of the quadruplex upon adduct formation.

Quantum-refinement studies of the bidentate ligand of V­nitrogenase and the protonation state of CO-inhibited Mo­nitrogenase.

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 V­nitrogenase is carbonate, rather than bicarbonate or nitrate. Second, we study the CO-inhibited structure of Mo­nitrogenase. 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.

Triosephosphate isomerase: the perfect enzyme, but how does it work?

Insights are offered on the study by Kelpsas et al. [IUCrJ (2021). 8, 633-643], who have combined neutron and X-ray crystallography then QM (quantum mechanics) calculations on triosephosphate isomerase (TIM). The authors dissect three possible enzyme mechanisms of TIM that have arisen in the decades since the first X-ray crystal structure of this enzyme was published in 1975.

Neutron structures of Leishmania mexicana triosephosphate isomerase in complex with reaction-intermediate mimics shed light on the proton-shuttling steps.

Triosephosphate isomerase (TIM) is a key enzyme in glycolysis that catalyses the interconversion of glyceraldehyde 3-phosphate and dihydroxy-acetone phosphate. This simple reaction involves the shuttling of protons mediated by protolysable side chains. The catalytic power of TIM is thought to stem from its ability to facilitate the deprotonation of a carbon next to a carbonyl group to generate an enediolate intermediate. The enediolate intermediate is believed to be mimicked by the inhibitor 2-phosphoglycolate (PGA) and the subsequent enediol intermediate by phosphoglycolohydroxamate (PGH). Here, neutron structures of Leishmania mexicana TIM have been determined with both inhibitors, and joint neutron/X-ray refinement followed by quantum refinement has been performed. The structures show that in the PGA complex the postulated general base Glu167 is protonated, while in the PGH complex it remains deprotonated. The deuteron is clearly localized on Glu167 in the PGA-TIM structure, suggesting an asymmetric hydrogen bond instead of a low-barrier hydrogen bond. The full picture of the active-site protonation states allowed an investigation of the reaction mechanism using density-functional theory calculations.

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.

Real-space quantum-based refinement for cryo-EM: Q|R#3.

Electron cryo-microscopy (cryo-EM) is rapidly becoming a major competitor to X-ray crystallography, especially for large structures that are difficult or impossible to crystallize. While recent spectacular technological improvements have led to significantly higher resolution three-dimensional reconstructions, the average quality of cryo-EM maps is still at the low-resolution end of the range compared with crystallography. A long-standing challenge for atomic model refinement has been the production of stereochemically meaningful models for this resolution regime. Here, it is demonstrated that including accurate model geometry restraints derived from ab initio quantum-chemical calculations (HF-D3/6-31G) can improve the refinement of an example structure (chain A of PDB entry 3j63). The robustness of the procedure is tested for additional structures with up to 7000 atoms (PDB entry 3a5x and chain C of PDB entry 5fn5) using the less expensive semi-empirical (GFN1-xTB) model. The necessary algorithms enabling real-space quantum refinement have been implemented in the latest version of qr.refine and are described here.

Including crystallographic symmetry in quantum-based refinement: Q|R#2.

Three-dimensional structure models refined using low-resolution data from crystallographic or electron cryo-microscopy experiments can benefit from high-quality restraints derived from quantum-chemical methods. However, nonperiodic atom-centered quantum-chemistry codes do not inherently account for nearest-neighbor interactions of crystallographic symmetry-related copies in a satisfactory way. Here, these nearest-neighbor effects have been included in the model by expanding to a super-cell and then truncating the super-cell to only include residues from neighboring cells that are interacting with the asymmetric unit. In this way, the fragmentation approach can adequately and efficiently include nearest-neighbor effects. It has previously been shown that a moderately sized X-ray structure can be treated using quantum methods if a fragmentation approach is applied. In this study, a target protein (PDB entry 4gif) was partitioned into a number of large fragments. The use of large fragments (typically hundreds of atoms) is tractable when a GPU-based package such as TeraChem is employed or cheaper (semi-empirical) methods are used. The QM calculations were run at the HF-D3/6-31G level. The models refined using a recently developed semi-empirical method (GFN2-xTB) were compared and contrasted. To validate the refinement procedure for a non-P1 structure, a standard set of crystallographic metrics were used. The robustness of the implementation is shown by refining 13 additional protein models across multiple space groups and a summary of the refinement metrics is presented.

Refinement of protein structures using a combination of quantum-mechanical calculations with neutron and X-ray crystallographic data.

Neutron crystallography is a powerful method to determine the positions of H atoms in macromolecular structures. However, it is sometimes hard to judge what would constitute a chemically reasonable model, and the geometry of H atoms depends more on the surroundings (for example the formation of hydrogen bonds) than heavy atoms, so that the empirical geometry information for the H atoms used to supplement the experimental data is often less accurate. These problems may be reduced by using quantum-mechanical calculations. A method has therefore been developed to combine quantum-mechanical calculations with joint crystallographic refinement against X-ray and neutron data. A first validation of this method is provided by re-refining the structure of the galectin-3 carbohydrate-recognition domain in complex with lactose. The geometry is improved, in particular for water molecules, for which the method leads to better-resolved hydrogen-bonding interactions. The method has also been applied to the active copper site of lytic polysaccharide monooxygenase and shows that the protonation state of the amino-terminal histidine residue can be determined.

Solving the scalability issue in quantum-based refinement: Q|R#1.

Accurately refining biomacromolecules using a quantum-chemical method is challenging because the cost of a quantum-chemical calculation scales approximately as nm, where n is the number of atoms and m (≥3) is based on the quantum method of choice. This fundamental problem means that quantum-chemical calculations become intractable when the size of the system requires more computational resources than are available. In the development of the software package called Q|R, this issue is referred to as Q|R#1. A divide-and-conquer approach has been developed that fragments the atomic model into small manageable pieces in order to solve Q|R#1. Firstly, the atomic model of a crystal structure is analyzed to detect noncovalent interactions between residues, and the results of the analysis are represented as an interaction graph. Secondly, a graph-clustering algorithm is used to partition the interaction graph into a set of clusters in such a way as to minimize disruption to the noncovalent interaction network. Thirdly, the environment surrounding each individual cluster is analyzed and any residue that is interacting with a particular cluster is assigned to the buffer region of that particular cluster. A fragment is defined as a cluster plus its buffer region. The gradients for all atoms from each of the fragments are computed, and only the gradients from each cluster are combined to create the total gradients. A quantum-based refinement is carried out using the total gradients as chemical restraints. In order to validate this interaction graph-based fragmentation approach in Q|R, the entire atomic model of an amyloid cross-ß spine crystal structure (PDB entry 2oNA) was refined.

Q|R: quantum-based refinement.

Quantum-based refinement utilizes chemical restraints derived from quantum-chemical methods instead of the standard parameterized library-based restraints used in refinement packages. The motivation is twofold: firstly, the restraints have the potential to be more accurate, and secondly, the restraints can be more easily applied to new molecules such as drugs or novel cofactors. Here, a new project called Q|R aimed at developing quantum-based refinement of biomacromolecules is under active development by researchers at Shanghai University together with PHENIX developers. The central focus of this long-term project is to develop software that is built on top of open-source components. A development version of Q|R was used to compare quantum-based refinements with standard refinement using a small model system.

QM/MM Calculations on Proteins.

In this chapter, I discuss combined quantum mechanics (QM) and molecular mechanics (MM; QM/MM) calculations for proteins. In QM/MM, a small but interesting part of the protein is treated by accurate QM methods, whereas the remainder is treated by faster MM methods. The prime problems with QM/MM calculations are bonds between the QM and MM systems, the selection of the QM system, and the local-minima problem. The two first problems can be solved by the big-QM approach, including in the QM calculation all groups within 4.5-6Å of the active site and all buried charges in the protein. The third problem can be solved by calculating free energies. It is important to study QM/MM energy components to ensure that the results are stable and reliable. They can also be used to understand the reaction and the effect of the surroundings, eg, by dividing the catalytic effect into bonded, van der Waals, electrostatic, and geometric components and to deduce which parts of the protein contribute most to the catalysis. It should be ensured that the QM calculations are reliable and converged by extending the basis set to quadruple-zeta quality, including a proper treatment of dispersion, as well as years experience and method development calculations with both pure and hybrid density functional theory methods. If the latter give differing results, calibration with high-level QM methods is needed. Reactions that change the net charge should be avoided. QM/MM calculations can be combined with experimental methods.