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.

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.

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.

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.

fragHAR: towards ab initio quantum-crystallographic X-ray structure refinement for polypeptides and proteins.

The first ab initio aspherical structure refinement against experimental X-ray structure factors for polypeptides and proteins using a fragmentation approach to break up the protein into residues and solvent, thereby speeding up quantum-crystallographic Hirshfeld atom refinement (HAR) calculations, is described. It it found that the geometric and atomic displacement parameters from the new fragHAR method are essentially unchanged from a HAR on the complete unfragmented system when tested on dipeptides, tripeptides and hexapeptides. The largest changes are for the parameters describing H atoms involved in hydrogen-bond interactions, but it is shown that these discrepancies can be removed by including the interacting fragments as a single larger fragment in the fragmentation scheme. Significant speed-ups are observed for the larger systems. Using this approach, it is possible to perform a highly parallelized HAR in reasonable times for large systems. The method has been implemented in the TONTO software.

Neutron macromolecular crystallography at the European spallation source.

The long-pulse spallation source of the European Spallation Source-a facility under construction in Lund, Sweden-is well suited for macromolecular crystallography experiments. We review briefly the particular properties of the long-pulse source and the associated high-brilliance moderators from the point of view of instrument design. We then outline the design philosophy and current design of the NMX macromolecular diffractometer. We also briefly describe the supporting facilities available for users and finish by an evaluation of the expected performance.

Prospects for membrane protein crystals in NMX.

Adding hydrogen atoms and protonation states to structures of membrane proteins requires successful implementation of neutron macromolecular crystallography (NMX). This information would significantly increase our fundamental understanding of the transport processes membrane proteins undertake. To grow the large crystals needed for NMX studies requires significant amounts of stable protein, but once that challenge is overcome there is no intrinsic property of membrane proteins preventing the growth of large crystals per se. The calcium-transporting P-type ATPase (SERCA) has been thoroughly characterized biochemically and structurally over decades. We have extended our crystallization efforts to assess the feasibility of growing SERCA crystals for NMX-exploring microdialysis and capillary counterdiffusion crystallization techniques as alternatives to the traditional vapor diffusion crystallization experiment. Both methods possess crystallization dynamics favorable for maximizing crystal size and we used them to facilitate the growth of large crystals, validating these approaches for membrane protein crystallization for NMX.

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

Corrections are published for the article by Caldararu et al. [(2019), Acta Cryst. D75, 368-380].

Water structure in solution and crystal molecular dynamics simulations compared to protein crystal structures.

The function of proteins is influenced not only by the atomic structure but also by the detailed structure of the solvent surrounding it. Computational studies of protein structure also critically depend on the water structure around the protein. Herein we compare the water structure obtained from molecular dynamics (MD) simulations of galectin-3 in complex with two ligands to crystallographic water molecules observed in the corresponding crystal structures. We computed MD trajectories both in a water box, which mimics a protein in solution, and in a crystallographic unit cell, which mimics a protein in a crystal. The calculations were compared to crystal structures obtained at both cryogenic and room temperature. Two types of analyses of the MD simulations were performed. First, the positions of the crystallographic water molecules were compared to peaks in the MD density after alignment of the protein in each snapshot. The results of this analysis indicate that all simulations reproduce the crystallographic water structure rather poorly. However, if we define the crystallographic water sites based on their distances to nearby protein atoms and follow these sites throughout the simulations, the MD simulations reproduce the crystallographic water sites much better. This shows that the failure of MD simulations to reproduce the water structure around proteins in crystal structures observed both in this and previous studies is caused by the problem of identifying water sites for a flexible and dynamic protein (traditionally done by overlaying the structures). Our local clustering approach solves the problem and shows that the MD simulations reasonably reproduce the water structure observed in crystals. Furthermore, analysis of the crystal MD simulations indicates a few water molecules that are close to unmodeled electron density peaks in the crystal structures, suggesting that crystal MD could be used as a complementary tool for identifying and modelling water in protein crystallography.

Are crystallographic B-factors suitable for calculating protein conformational entropy?

Conformational entropies are of great interest when studying the binding of small ligands to proteins or the interaction of proteins. Unfortunately, there are no experimental methods available to measure conformational entropies of all groups in a protein. Instead, they are normally estimated from molecular dynamics (MD) simulations, although such methods show problems with convergence and correlation of motions, and depend on the accuracy of the underlying potential-energy function. Crystallographic atomic displacement parameters (also known as B-factors) are available in all crystal structures and contain information about the atomic fluctuations, which can be converted to entropies. We have studied whether B-factors can be employed to extract conformational entropies for proteins by comparing such entropies to those measured by NMR relaxation experiments or obtained from MD simulations in solution or in the crystal. Unfortunately, our results show that B-factor entropies are unreliable, because they include the movement and rotation of the entire protein, they exclude correlation of the movements and they include contributions other than the fluctuations, e.g. static disorder, as well as errors in the model and the scattering factors. We have tried to reduce the first problem by employing translation-libration-screw refinement, the second by employing a description of the correlated movement from MD simulations, and the third by studying only the change in entropy when a pair of ligands binds to the same protein, thoroughly re-refining the structures in exactly the same way and using the same set of alternative conformations. However, the experimental B-factors seem to be incompatible with fluctuations from MD simulations and the precision is too poor to give any reliable entropies.

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.

Perdeuteration, large crystal growth and neutron data collection of Leishmania mexicana triose-phosphate isomerase E65Q variant.

Triose-phosphate isomerase (TIM) catalyses the interconversion of dihydroxyacetone phosphate and glyceraldehyde 3-phosphate. Two catalytic mechanisms have been proposed based on two reaction-intermediate analogues, 2-phosphoglycolate (2PG) and phosphoglycolohydroxamate (PGH), that have been used as mimics of the cis-enediol(ate) intermediate in several studies of TIM. The protonation states that are critical for the mechanistic interpretation of these structures are generally not visible in the X-ray structures. To resolve these questions, it is necessary to determine the hydrogen positions using neutron crystallography. Neutron crystallography requires large crystals and benefits from replacing all hydrogens with deuterium. Leishmania mexicana triose-phosphate isomerase was therefore perdeuterated and large crystals with 2PG and PGH were produced. Neutron diffraction data collected from two crystals with different volumes highlighted the importance of crystal volume, as smaller crystals required longer exposures and resulted in overall worse statistics.

Mechanism of hydrogen peroxide formation by lytic polysaccharide monooxygenase.

Lytic polysaccharide monooxygenases (LPMOs) are copper-containing metalloenzymes that can cleave the glycosidic link in polysaccharides. This could become crucial for production of energy-efficient biofuels from recalcitrant polysaccharides. Although LPMOs are considered oxygenases, recent investigations have shown that H2O2 can also act as a co-substrate for LPMOs. Intriguingly, LPMOs generate H2O2 in the absence of a polysaccharide substrate. Here, we elucidate a new mechanism for H2O2 generation starting from an AA10-LPMO crystal structure with an oxygen species bound, using QM/MM calculations. The reduction level and protonation state of this oxygen-bound intermediate has been unclear. However, this information is crucial to the mechanism. We therefore investigate the oxygen-bound intermediate with quantum refinement (crystallographic refinement enhanced with QM calculations), against both X-ray and neutron data. Quantum refinement calculations suggest a Cu(ii)-O-2 system in the active site of the AA10-LPMO and a neutral protonated -NH2 state for the terminal nitrogen atom, the latter in contrast to the original interpretation. Our QM/MM calculations show that H2O2 generation is possible only from a Cu(i) center and that the most favourable reaction pathway is to involve a nearby glutamate residue, adding two electrons and two protons to the Cu(ii)-O-2 system, followed by dissociation of H2O2.

Interplay between Conformational Entropy and Solvation Entropy in Protein-Ligand Binding.

Understanding the driving forces underlying molecular recognition is of fundamental importance in chemistry and biology. The challenge is to unravel the binding thermodynamics into separate contributions and to interpret these in molecular terms. Entropic contributions to the free energy of binding are particularly difficult to assess in this regard. Here we pinpoint the molecular determinants underlying differences in ligand affinity to the carbohydrate recognition domain of galectin-3, using a combination of isothermal titration calorimetry, X-ray crystallography, NMR relaxation, and molecular dynamics simulations followed by conformational entropy and grid inhomogeneous solvation theory (GIST) analyses. Using a pair of diastereomeric ligands that have essentially identical chemical potential in the unbound state, we reduced the problem of dissecting the thermodynamics to a comparison of the two protein-ligand complexes. While the free energies of binding are nearly equal for the R and S diastereomers, greater differences are observed for the enthalpy and entropy, which consequently exhibit compensatory behavior, ΔΔ H°(R - S) = -5 ± 1 kJ/mol and - TΔΔ S°(R - S) = 3 ± 1 kJ/mol. NMR relaxation experiments and molecular dynamics simulations indicate that the protein in complex with the S-stereoisomer has greater conformational entropy than in the R-complex. GIST calculations reveal additional, but smaller, contributions from solvation entropy, again in favor of the S-complex. Thus, conformational entropy apparently dominates over solvation entropy in dictating the difference in the overall entropy of binding. This case highlights an interplay between conformational entropy and solvation entropy, pointing to both opportunities and challenges in drug design.

Elucidation of Hydrogen Bonding Patterns in Ligand-Free, Lactose- and Glycerol-Bound Galectin-3C by Neutron Crystallography to Guide Drug Design.

The medically important drug target galectin-3 binds galactose-containing moieties on glycoproteins through an intricate pattern of hydrogen bonds to a largely polar surface-exposed binding site. All successful inhibitors of galectin-3 to date have been based on mono- or disaccharide cores closely resembling natural ligands. A detailed understanding of the H-bonding networks in these natural ligands will provide an improved foundation for the design of novel inhibitors. Neutron crystallography is an ideal technique to reveal the geometry of hydrogen bonds because the positions of hydrogen atoms are directly detected rather than being inferred from the positions of heavier atoms as in X-ray crystallography. We present three neutron crystal structures of the C-terminal carbohydrate recognition domain of galectin-3: the ligand-free form and the complexes with the natural substrate lactose and with glycerol, which mimics important interactions made by lactose. The neutron crystal structures reveal unambiguously the exquisite fine-tuning of the hydrogen bonding pattern in the binding site to the natural disaccharide ligand. The ligand-free structure shows that most of these hydrogen bonds are preserved even when the polar groups of the ligand are replaced by water molecules. The protonation states of all histidine residues in the protein are also revealed and correlate well with NMR observations. The structures give a solid starting point for molecular dynamics simulations and computational estimates of ligand binding affinity that will inform future drug design.