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.

Entropy-Entropy Compensation between the Protein, Ligand, and Solvent Degrees of Freedom Fine-Tunes Affinity in Ligand Binding to Galectin-3C.

Molecular recognition is fundamental to biological signaling. A central question is how individual interactions between molecular moieties affect the thermodynamics of ligand binding to proteins and how these effects might propagate beyond the immediate neighborhood of the binding site. Here, we investigate this question by introducing minor changes in ligand structure and characterizing the effects of these on ligand affinity to the carbohydrate recognition domain of galectin-3, using a combination of isothermal titration calorimetry, X-ray crystallography, NMR relaxation, and computational approaches including molecular dynamics (MD) simulations and grid inhomogeneous solvation theory (GIST). We studied a congeneric series of ligands with a fluorophenyl-triazole moiety, where the fluorine substituent varies between the ortho, meta, and para positions (denoted O, M, and P). The M and P ligands have similar affinities, whereas the O ligand has 3-fold lower affinity, reflecting differences in binding enthalpy and entropy. The results reveal surprising differences in conformational and solvation entropy among the three complexes. NMR backbone order parameters show that the O-bound protein has reduced conformational entropy compared to the M and P complexes. By contrast, the bound ligand is more flexible in the O complex, as determined by 19F NMR relaxation, ensemble-refined X-ray diffraction data, and MD simulations. Furthermore, GIST calculations indicate that the O-bound complex has less unfavorable solvation entropy compared to the other two complexes. Thus, the results indicate compensatory effects from ligand conformational entropy and water entropy, on the one hand, and protein conformational entropy, on the other hand. Taken together, these different contributions amount to entropy-entropy compensation among the system components involved in ligand binding to a target protein.

A protocol for production of perdeuterated OmpF porin for neutron crystallography.

Hydrogen atoms are at the limit of visibility in X-ray structures even at high resolution. Neutron macromolecular crystallography (NMX) is an unambiguous method to locate hydrogens and study the significance of hydrogen bonding interactions in biological systems. Since NMX requires very large crystals, very few neutron structures of proteins have been determined yet. In addition, the most common hydrogen isotope 1H gives rise to significant background due to its large incoherent scattering cross-section. Therefore, it is advantageous to substitute as many hydrogens as possible with the heavier isotope 2H (deuterium) to reduce the sample volume requirement. While the solvent exchangeable hydrogens can be substituted by dissolving the protein in heavy water, complete deuterium labelling - perdeuteration - requires the protein to be expressed in heavy water with a deuterated carbon source. In this work, we developed an optimized method for large scale production of deuterium-labelled bacterial outer membrane protein F (OmpF) for NMX. OmpF was produced using deuterated media with different carbon sources. Mass spectrometry verified the integrity and level of deuteration of purified OmpF. Perdeuterated OmpF crystals diffracted X-rays to a resolution of 1.9 Å. This work lays the foundation for structural studies of membrane protein by neutron diffraction in future.

Exploring ligand dynamics in protein crystal structures with ensemble refinement.

Understanding the dynamics of ligands bound to proteins is an important task in medicinal chemistry and drug design. However, the dominant technique for determining protein-ligand structures, X-ray crystallography, does not fully account for dynamics and cannot accurately describe the movements of ligands in protein binding sites. In this article, an alternative method, ensemble refinement, is used on six protein-ligand complexes with the aim of understanding the conformational diversity of ligands in protein crystal structures. The results show that ensemble refinement sometimes indicates that the flexibility of parts of the ligand and some protein side chains is larger than that which can be described by a single conformation and atomic displacement parameters. However, since the electron-density maps are comparable and Rfree values are slightly increased, the original crystal structure is still a better model from a statistical point of view. On the other hand, it is shown that molecular-dynamics simulations and automatic generation of alternative conformations in crystallographic refinement confirm that the flexibility of these groups is larger than is observed in standard refinement. Moreover, the flexible groups in ensemble refinement coincide with groups that give high atomic displacement parameters or non-unity occupancy if optimized in standard refinement. Therefore, the conformational diversity indicated by ensemble refinement seems to be qualitatively correct, indicating that ensemble refinement can be an important complement to standard crystallographic refinement as a tool to discover which parts of crystal structures may show extensive flexibility and therefore are poorly described by a single conformation. However, the diversity of the ensembles is often exaggerated (probably partly owing to the rather poor force field employed) and the ensembles should not be trusted in detail.

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 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.

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.

Automated orientation of water molecules in neutron crystallographic structures of proteins.

The structure and function of proteins are strongly affected by the surrounding solvent water, for example through hydrogen bonds and the hydrophobic effect. These interactions depend not only on the position, but also on the orientation, of the water molecules around the protein. Therefore, it is often vital to know the detailed orientations of the surrounding ordered water molecules. Such information can be obtained by neutron crystallography. However, it is tedious and time-consuming to determine the correct orientation of every water molecule in a structure (there are typically several hundred of them), which is presently performed by manual evaluation. Here, a method has been developed that reliably automates the orientation of a water molecules in a simple and relatively fast way. Firstly, a quantitative quality measure, the real-space correlation coefficient, was selected, together with a threshold that allows the identification of water molecules that are oriented. Secondly, the refinement procedure was optimized by varying the refinement method and parameters, thus finding settings that yielded the best results in terms of time and performance. It turned out to be favourable to employ only the neutron data and a fixed protein structure when reorienting the water molecules. Thirdly, a method has been developed that identifies and reorients inadequately oriented water molecules systematically and automatically. The method has been tested on three proteins, galectin-3C, rubredoxin and inorganic pyrophosphatase, and it is shown that it yields improved orientations of the water molecules for all three proteins in a shorter time than manual model building. It also led to an increased number of hydrogen bonds involving water molecules for all proteins.

Optimization of crystallization of biological macromolecules using dialysis combined with temperature control.

A rational way to find the appropriate conditions to grow crystal samples for bio-crystallography is to determine the crystallization phase diagram, which allows precise control of the parameters affecting the crystal growth process. First, the nucleation is induced at supersaturated conditions close to the solubility boundary between the nucleation and metastable regions. Then, crystal growth is further achieved in the metastable zone - which is the optimal location for slow and ordered crystal expansion - by modulation of specific physical parameters. Recently, a prototype of an integrated apparatus for the rational optimization of crystal growth by mapping and manipulating temperature-precipitant-concentration phase diagrams has been constructed. Here, it is demonstrated that a thorough knowledge of the phase diagram is vital in any crystallization experiment. The relevance of the selection of the starting position and the kinetic pathway undertaken in controlling most of the final properties of the synthesized crystals is shown. The rational crystallization optimization strategies developed and presented here allow tailoring of crystal size and diffraction quality, significantly reducing the time, effort and amount of expensive protein material required for structure determination.