Dynamical refinement with multipolar electron scattering factors

Dynamical refinement is a well established method for refining crystal structures against 3D electron diffraction (ED) data and its benefits have been discussed in the literature [Palatinus, Petříček & Corrêa, (2015). Acta Cryst. A71, 235-244; Palatinus, Corrêa et al. (2015). Acta Cryst. B71, 740-751]. However, until now, dynamical refinements have only been conducted using the independent atom model (IAM). Recent research has shown that a more accurate description can be achieved by applying the transferable aspherical atom model (TAAM), but this has been limited only to kinematical refinements [Gruza et al. (2020). Acta Cryst. A76, 92-109; Jha et al. (2021). J. Appl. Cryst. 54, 1234-1243]. In this study, we combine dynamical refinement with TAAM for the crystal structure of 1-methyluracil, using data from precession ED. Our results show that this approach improves the residual Fourier electrostatic potential and refinement figures of merit. Furthermore, it leads to systematic changes in the atomic displacement parameters of all atoms and the positions of hydrogen atoms. We found that the refinement results are sensitive to the parameters used in the TAAM modelling process. Though our results show that TAAM offers superior performance compared with IAM in all cases, they also show that TAAM parameters obtained by periodic DFT calculations on the refined structure are superior to the TAAM parameters from the UBDB/MATTS database. It appears that multipolar parameters transferred from the database may not be sufficiently accurate to provide a satisfactory description of all details of the electrostatic potential probed by the 3D ED experiment.

3D electron diffraction goes multipolar

Over 30 years ago, it was shown that bonding between atoms has a noticeable effect on convergent beam electron diffraction patterns. The paper by Olech et al. [(2024). IUCrJ, 11, 309-324] demonstrates that its influence is also clearly present in 3D electron diffraction data, opening up new possibilities for quantum crystallography.

Construction of the single-diamond-structured titania scaffold-Recreation of the holy grail photonic structure

As one of the most stunning biological nanostructures, the single-diamond (SD) surface discovered in beetles and weevils exoskeletons possesses the widest complete photonic bandgap known to date and is renowned as the "holy grail" of photonic materials. However, the synthesis of SD is difficult due to its thermodynamical instability compared to the energetically favoured bicontinuous double diamond and other easily formed lattices; thus, the artificial fabrication of SD has long been a formidable challenge. Herein, we report a bottom-up approach to fabricate SD titania networks via a one-pot cooperative assembly scenario employing the diblock copolymer poly(ethylene oxide)-block-polystyrene as a soft template and titanium diisopropoxide bis(acetylacetonate) as an inorganic precursor in a mixed solvent, in which the SD scaffold was obtained by kinetically controlled nucleation and growth in the skeletal channels of the diamond minimal surface formed by the polymer matrix. Electron crystallography investigations revealed the formation of tetrahedrally connected SD frameworks with the space group Fd [Formula: see text] m in a polycrystalline anatase form. A photonic bandgap calculation showed that the resulting SD structure has a wide and complete bandgap. This work solves the complex synthetic enigmas and offers a frontier in hyperbolic surfaces, biorelevant materials, next-generation optical devices, etc.

Observations of specimen morphology effects on near-zone-axis convergent-beam electron diffraction patterns

This work presents observations of symmetry breakages in the intensity distributions of near-zone-axis convergent-beam electron diffraction (CBED) patterns that can only be explained by the symmetry of the specimen and not the symmetry of the unit cell describing the atomic structure of the material. The specimen is an aluminium-copper-tin alloy containing voids many tens of nanometres in size within continuous single crystals of the aluminium host matrix. Several CBED patterns where the incident beam enters and exits parallel void facets without the incident beam being perpendicular to these facets are examined. The symmetries in their intensity distributions are explained by the specimen morphology alone using a geometric argument based on the multislice theory. This work shows that it is possible to deduce nanoscale morphological information about the specimen in the direction of the electron beam - the elusive third dimension in transmission electron microscopy - from the inspection of CBED patterns.

Molecular replacement for small-molecule crystal structure determination from X-ray and electron diffraction data with reduced resolution

The resolution of 3D electron diffraction (ED) data of small-molecule crystals is often relatively poor, due to either electron-beam radiation damage during data collection or poor crystallinity of the material. Direct methods, used as standard for crystal structure determination, are not applicable when the data resolution falls below the commonly accepted limit of 1.2 Å. Therefore an evaluation was carried out of the performance of molecular replacement (MR) procedures, regularly used for protein structure determination, for structure analysis of small-molecule crystal structures from 3D ED data. In the course of this study, two crystal structures of Bi-3812, a highly potent inhibitor of the oncogenic transcription factor BCL6, were determined: the structure of α-Bi-3812 was determined from single-crystal X-ray data, the structure of β-Bi-3812 from 3D ED data, using direct methods in both cases. These data were subsequently used for MR with different data types, varying the data resolution limit (1, 1.5 and 2 Å) and by using search models consisting of connected or disconnected fragments of BI-3812. MR was successful with 3D ED data at 2 Å resolution using a search model that represented 74% of the complete molecule.

Analysis of diffuse scattering in electron diffraction data for the crystal structure determination of Pigment Orange 13, C32H24Cl2N8O2

The crystallographic study of two polymorphs of the industrial pyrazolone Pigment Orange 13 (P.O.13) is reported. The crystal structure of the β phase was determined using single-crystal X-ray analysis of a tiny needle. The α phase was investigated using three-dimensional electron diffraction. The electron diffraction data contain sharp Bragg reflections and strong diffuse streaks, associated with severe stacking disorder. The structure was solved by careful analysis of the diffuse scattering, and similarities of the unit-cell parameters with the β phase. The structure solution is described in detail and this provides a didactic example of solving molecular crystal structures in the presence of diffuse scattering. Several structural models were constructed and optimized by lattice-energy minimization with dispersion-corrected DFT. A four-layer model was found, which matches the electron diffraction data, including the diffuse scattering, and agrees with X-ray powder data. Additionally, five further phases of P.O.13 are described.

Protein Data Bank: A Comprehensive Review of 3D Structure Holdings and Worldwide Utilization by Researchers, Educators, and Students

The Research Collaboratory for Structural Bioinformatics Protein Data Bank (RCSB PDB), funded by the United States National Science Foundation, National Institutes of Health, and Department of Energy, supports structural biologists and Protein Data Bank (PDB) data users around the world. The RCSB PDB, a founding member of the Worldwide Protein Data Bank (wwPDB) partnership, serves as the US data center for the global PDB archive housing experimentally-determined three-dimensional (3D) structure data for biological macromolecules. As the wwPDB-designated Archive Keeper, RCSB PDB is also responsible for the security of PDB data and weekly update of the archive. RCSB PDB serves tens of thousands of data depositors (using macromolecular crystallography, nuclear magnetic resonance spectroscopy, electron microscopy, and micro-electron diffraction) annually working on all permanently inhabited continents. RCSB PDB makes PDB data available from its research-focused web portal at no charge and without usage restrictions to many millions of PDB data consumers around the globe. It also provides educators, students, and the general public with an introduction to the PDB and related training materials through its outreach and education-focused web portal. This review article describes growth of the PDB, examines evolution of experimental methods for structure determination viewed through the lens of the PDB archive, and provides a detailed accounting of PDB archival holdings and their utilization by researchers, educators, and students worldwide.

The Complex Crystal Structure and Abundant Local Defects of Zeolite EMM-17 Unraveled by Combined Electron Crystallography and Microscopy

In this study, we successfully solve polymorphs A and B of zeolite EMM-17, which can only crystallize in sub-micrometer-sized crystals while containing complex stacking disorders, from the three-dimensional (3D) electron diffraction (ED) data. This is the first time that the atomic structure of this polymorph has been ab initio solved, and the result reveals a unique 10(12)×10(12)×11-ring channel system. Moreover, we acquire the first atomic-resolution images of EMM-17 using integrated differential phase-contrast scanning transmission electron microscopy. The images allow us to directly observe polymorphs B and C and discover a large number of local structural defects. Based on structural features unraveled from the reciprocal-space 3D ED data and real-space images, we propose a series of energetically feasible local structures in EMM-17. We also demonstrate that the unique porous structure of EMM-17 enables efficient kinetic separation of C₆ alkane isomers.

Electron Crystallographic Investigation of Crystals on the Mesostructural Scale

The precise structural solution of crystals on a mesostructural scale is challenging due to the difficulties in obtaining electron diffraction and the complicated relationship between the crystal structure factors (CSFs) and the conventional underfocus phase-contrast transmission electron microscopy (TEM) images due to the large unit cell and the complex structures. Here, we present the structural investigation of mesostructured crystals via the combination of electron crystallographic Fourier synthesis and high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) that only relies on the mass-thickness contrast. The three-dimensional electrostatic potential is reconstructed from the amplitudes and phases extracted from the Fourier transforms of the corresponding HAADF-STEM images and merged into a set of CSFs. This method is verified on silica scaffolds following a shifted double-diamond surface network with space group I41/amd. The results indicate that electron crystallography reconstruction by HAADF-STEM images is more suitable and accurate in determining the structure in comparison with conventional TEM electron crystallography reconstruction. This approach transfers the contrast of mesostructured crystals to images more accurately and the relationship between the Fourier transforms of HAADF-STEM images and the CSFs is more intuitive. It shows great advantages for the structural solution of crystals on the mesostructural scale.

Evolution of standardization and dissemination of cryo-EM structures and data jointly by the community, PDB, and EMDB

Cryogenic electron microscopy (cryo-EM) methods began to be used in the mid-1970s to study thin and periodic arrays of proteins. Following a half-century of development in cryo-specimen preparation, instrumentation, data collection, data processing, and modeling software, cryo-EM has become a routine method for solving structures from large biological assemblies to small biomolecules at near to true atomic resolution. This review explores the critical roles played by the Protein Data Bank (PDB) and Electron Microscopy Data Bank (EMDB) in partnership with the community to develop the necessary infrastructure to archive cryo-EM maps and associated models. Public access to cryo-EM structure data has in turn facilitated better understanding of structure–function relationships and advancement of image processing and modeling tool development. The partnership between the global cryo-EM community and PDB and EMDB leadership has synergistically shaped the standards for metadata, one-stop deposition of maps and models, and validation metrics to assess the quality of cryo-EM structures. The advent of cryo-electron tomography (cryo-ET) for in situ molecular cell structures at a broad resolution range and their correlations with other imaging data introduce new data archival challenges in terms of data size and complexity in the years to come.

Macromolecular crystallography using microcrystal electron diffraction

Microcrystal electron diffraction (MicroED) has recently emerged as a promising method for macromolecular structure determination in structural biology. Since the first protein structure was determined in 2013, the method has been evolving rapidly. Several protein structures have been determined and various studies indicate that MicroED is capable of (i) revealing atomic structures with charges, (ii) solving new protein structures by molecular replacement, (iii) visualizing ligand-binding interactions and (iv) determining membrane-protein structures from microcrystals embedded in lipidic mesophases. However, further development and optimization is required to make MicroED experiments more accurate and more accessible to the structural biology community. Here, we provide an overview of the current status of the field, and highlight the ongoing development, to provide an indication of where the field may be going in the coming years. We anticipate that MicroED will become a robust method for macromolecular structure determination, complementing existing methods in structural biology.

A Comparison of a Direct Electron Detector and a High-Speed Video Camera for a Scanning Precession Electron Diffraction Phase and Orientation Mapping

A scanning precession electron diffraction system has been integrated with a direct electron detector to allow the collection of improved quality diffraction patterns. This has been used on a two-phase α–β titanium alloy (Timetal® 575) for phase and orientation mapping using an existing pattern-matching algorithm and has been compared to the commonly used detector system, which consisted of a high-speed video-camera imaging the small phosphor focusing screen. Noise is appreciably lower with the direct electron detector, and this is especially noticeable further from the diffraction pattern center where the real electron scattering is reduced and both diffraction spots and inelastic scattering between spots are weaker. The results for orientation mapping are a significant improvement in phase and orientation indexing reliability, especially of fine nanoscale laths of α-Ti, where the weak diffracted signal is rather lost in the noise for the optically coupled camera. This was done at a dose of ~19 e−/Å2, and there is clearly a prospect for reducing the current further while still producing indexable patterns. This opens the way for precession diffraction phase and orientation mapping of radiation-sensitive crystalline materials.

Three different Ge environments in a new Sr5CuGe9O24 phase synthesized at high pressure and high temperature

In the framework of expanding the range of copper-based compounds in the pyroxene family, we have synthesized at high pressure and high temperature a powder containing a mixture of a new phase with stoichiometry Sr₅CuGe₉O₂₄ having two identified impurity phases. Electron crystallography showed that the new phase crystallizes in the monoclinic space group P2/c, with unit-cell parameters a = 11.8 Å, b = 8.1 Å, c = 10.3 Å and β = 101.3°. We applied the recently developed low-dose electron diffraction tomography method to solve the structure by direct methods. The obtained structure model contains all 9 independent cation positions and all 13 oxygen positions. A subsequent refinement against powder X-ray diffraction data ascertained the high quality of the structure solution, in particular, the unusual structural arrangement that there are three different environments for Ge in this phase.

New zeolite-like RUB-5 and its related hydrous layer silicate RUB-6 structurally characterized by electron microscopy

This study made use of a recently developed combination of advanced methods to reveal the atomic structure of a disordered nanocrystalline zeolite using exit wave reconstruction, automated diffraction tomography, disorder modelling and diffraction pattern simulation. By applying these methods, it was possible to determine the so far unknown structures of the hydrous layer silicate RUB-6 and the related zeolite-like material RUB-5. The structures of RUB-5 and RUB-6 contain the same dense layer-like building units (LLBUs). In the case of RUB-5, these building units are interconnected via additional SiO4/2 tetrahedra, giving rise to a framework structure with a 2D pore system consisting of intersecting 8-ring channels. In contrast, RUB-6 contains these LLBUs as separate silicate layers terminated by silanol/sil-oxy groups. Both RUB-6 and RUB-5 show stacking disorder with intergrowths of different polymorphs. The unique structure of RUB-6, together with the possibility for an interlayer expansion reaction to form RUB-5, make it a promising candidate for interlayer expansion with various metal sources to include catalytically active reaction centres.

Atomic structures determined from digitally defined nanocrystalline regions

Nanocrystallography has transformed our ability to interrogate the atomic structures of proteins, peptides, organic molecules and materials. By probing atomic level details in ordered sub-10 nm regions of nanocrystals, scanning nanobeam electron diffraction extends the reach of nanocrystallography and in principle obviates the need for diffraction from large portions of one or more crystals. Scanning nanobeam electron diffraction is now applied to determine atomic structures from digitally defined regions of beam-sensitive peptide nanocrystals. Using a direct electron detector, thousands of sparse diffraction patterns over multiple orientations of a given crystal are recorded. Each pattern is assigned to a specific location on a single nanocrystal with axial, lateral and angular coordinates. This approach yields a collection of patterns that represent a tilt series across an angular wedge of reciprocal space: a scanning nanobeam diffraction tomogram. Using this diffraction tomogram, intensities can be digitally extracted from any desired region of a scan in real or diffraction space, exclusive of all other scanned points. Intensities from multiple regions of a crystal or from multiple crystals can be merged to increase data completeness and mitigate missing wedges. It is demonstrated that merged intensities from digitally defined regions of two crystals of a segment from the OsPYL/RCAR5 protein produce fragment-based ab initio solutions that can be refined to atomic resolution, analogous to structures determined by selected-area electron diffraction. In allowing atomic structures to now be determined from digitally outlined regions of a nanocrystal, scanning nanobeam diffraction tomography breaks new ground in nanocrystallography.

A unique insight into the defect structures of bicontinuous mesophases in liquid crystals and hybrid materials

Han et al. [(2020), IUCrJ, 7, 228-237] using advanced electron microscopy and crystallographic modelling rationalise the microstructure of twinning defects in order to visualize mesophase transitions and surface properties of G and D bicontinuous cubic mesostructured silica. This work furthers our understanding of how these phases originate in many natural and synthetic systems.

Crystal twinning of bicontinuous cubic structures

Bicontinuous cubic structures in soft matter consist of two intertwining labyrinths separated by a partitioning layer. Combining experiments, numerical modelling and techniques in differential geometry, we investigate twinning defects in bicontinuous cubic structures. We first demonstrate that a twin boundary is most likely to occur at a plane that cuts the partitioning layer almost perpendicularly, so that the perturbation caused by twinning remains minimal. This principle can be used as a criterion to identify potential twin boundaries, as demonstrated through detailed investigations of mesoporous silica crystals characterized by diamond and gyroid surfaces. We then discuss that a twin boundary can result from a stacking fault in the arrangement of inter-lamellar attachments at an early stage of structure formation. It is further shown that enhanced curvature fluctuations near the twin boundary would cost energy because of geometrical frustration, which would be eased by a crystal distortion that is experimentally observed.

Refinement of organic crystal structures with multipolar electron scattering factors

A revolution in resolution is occurring now in electron microscopy arising from the development of methods for imaging single particles at cryogenic temperatures and obtaining electron diffraction data from nanocrystals of small organic molecules or macromolecules. Near-atomic or even atomic resolution of molecular structures can be achieved. The basis of these methods is the scattering of an electron beam due to the electrostatic potential of the sample. To analyse these high-quality experimental data, it is necessary to use appropriate atomic scattering factors. The independent atom model (IAM) is commonly used although various more advanced models, already known from X-ray diffraction, can also be applied to enhance the analysis. In this study a comparison is presented of IAM and TAAM (transferable aspherical atom model), the latter with the parameters of the Hansen-Coppens multipole model transferred from the University at Buffalo Databank (UBDB). By this method, TAAM takes into account the fact that atoms in molecules are partially charged and are not spherical. Structure refinements were performed on a carbamazepine crystal using electron structure-factor amplitudes determined experimentally [Jones et al. (2018). ACS Cent. Sci. 4, 1587-1592] or modelled with theoretical quantum-mechanical methods. The results show the possibilities and limitations of the TAAM method when applied to electron diffraction. Among others, the method clearly improves model fitting statistics, when compared with IAM, and allows for reliable refinement of atomic thermal parameters. The improvements are more pronounced with poorer-resolution diffraction data.

Electron crystallography

A Special Issue on the topic of Electron Crystallography, now available in the August 2019 issue of Acta Crystallographica, Section B, contains contributions which we hope will interest readers of IUCrJ.

Qualitative Analyses of Polishing and Precoating FIB Milled Crystals for MicroED

Microcrystal electron diffraction (MicroED) leverages the strong interaction between matter and electrons to determine protein structures from vanishingly small crystals. This strong interaction limits the thickness of crystals that can be investigated by MicroED, mainly due to absorption. Recent studies have demonstrated that focused ion-beam (FIB) milling can thin crystals into ideal-sized lamellae; however, it is not clear how to best apply FIB milling for MicroED. Here, the effects of polishing the lamellae, whereby the last few nanometers are milled away using a low-current gallium beam, are explored in both the platinum-precoated and uncoated samples. Our results suggest that precoating samples with a thin layer of platinum followed by polishing the crystal surfaces prior to data collection consistently led to superior results as indicated by higher signal-to-noise ratio, higher resolution, and better refinement statistics. This study lays the foundation for routine and reproducible methodology for sample preparation in MicroED.

Automated electron diffraction tomography - development and applications

Electron diffraction tomography (EDT) has gained increasing interest, starting with the development of automated electron diffraction tomography (ADT) which enables the collection of three-dimensional electron diffraction data from nano-sized crystals suitable for ab initio structure analysis. A basic description of the ADT method, nowadays recognized as a reliable and established method, as well as its special features and general applicability to different transmission electron microscopes is provided. In addition, the usability of ADT for crystal structure analysis of single nano-sized crystals with and without special crystallographic features, such as twinning, modulations and disorder is demonstrated.

Inelastic scattering and solvent scattering reduce dynamical diffraction in biological crystals

Multi-slice simulations of electron diffraction by three-dimensional protein crystals have indicated that structure solution would be severely impeded by dynamical diffraction, especially when crystals are more than a few unit cells thick. In practice, however, dynamical diffraction turned out to be less of a problem than anticipated on the basis of these simulations. Here it is shown that two scattering phenomena, which are usually omitted from multi-slice simulations, reduce the dynamical effect: solvent scattering reduces the phase differences within the exit beam and inelastic scattering followed by elastic scattering results in diffusion of dynamical scattering out of Bragg peaks. Thus, these independent phenomena provide potential reasons for the apparent discrepancy between theory and practice in protein electron crystallography.

Methods for orientation and phase identification of nano-sized embedded secondary phase particles by 4D scanning precession electron diffraction

The diffraction patterns acquired with transmission electron microscopes gather reflections from all crystallites that overlap in the foil thickness. The superimposition renders automated orientation or phase mapping difficult, in particular when secondary phase particles are embedded in a dominant diffracting matrix. Several numerical approaches specifically developed to overcome this issue for 4D scanning precession electron diffraction data sets are described. They consist either in emphasizing the signature of the particles or in subtracting the matrix information out of the collected set of patterns. The different strategies are applied successively to a steel sample containing precipitates that are in Burgers orientation relationship with the matrix and to an aluminium alloy with randomly oriented Mn-rich particles.

3D electron diffraction techniques

3D electron diffraction is an emerging technique for the structural analysis of nanocrystals. The challenges that 3D electron diffraction has to face for providing reliable data for structure solution and the different ways of overcoming these challenges are described. The route from zone axis patterns towards 3D electron diffraction techniques such as precession-assisted electron diffraction tomography, rotation electron diffraction and continuous rotation is also discussed. Finally, the advantages of the new hybrid detectors with high sensitivity and fast readout are demonstrated with a proof of concept experiment of continuous rotation electron diffraction on a natrolite nanocrystal.

Ab initio determination of atomic structure of Zn-Zr precipitates in a Mg-Nd-Zn-Zr alloy

The atomic structure of nanometre-sized Zn-Zr precipitates in a Mg alloy is determined by combining tilt series of micro-beam electron diffraction with atomic resolution Z-contrast imaging. The stoichiometry of the Zn-Zr precipitates is Zn₂Zr₃ with a primitive tetragonal structure (space group P4₂/mnm, a = b = 0.761 nm, c = 0.682 nm). There are 20 atoms in the unit cell of tetragonal Zn₂Zr₃, comprising 12 Zr atoms at the 4d, 4f, 4g positions and eight Zn atoms at the 8j positions.

Nanobeam precession-assisted 3D electron diffraction reveals a new polymorph of hen egg-white lysozyme

Recent advances in 3D electron diffraction have allowed the structure determination of several model proteins from submicrometric crystals, the unit-cell parameters and structures of which could be immediately validated by known models previously obtained by X-ray crystallography. Here, the first new protein structure determined by 3D electron diffraction data is presented: a previously unobserved polymorph of hen egg-white lysozyme. This form, with unit-cell parameters a = 31.9, b = 54.4, c = 71.8 Å, β = 98.8°, grows as needle-shaped submicrometric crystals simply by vapor diffusion starting from previously reported crystallization conditions. Remarkably, the data were collected using a low-dose stepwise experimental setup consisting of a precession-assisted nanobeam of ∼150 nm, which has never previously been applied for solving protein structures. The crystal structure was additionally validated using X-ray synchrotron-radiation sources by both powder diffraction and single-crystal micro-diffraction. 3D electron diffraction can be used for the structural characterization of submicrometric macromolecular crystals and is able to identify novel protein polymorphs that are hardly visible in conventional X-ray diffraction experiments. Additionally, the analysis, which was performed on both nanocrystals and microcrystals from the same crystallization drop, suggests that an integrated view from 3D electron diffraction and X-ray microfocus diffraction can be applied to obtain insights into the molecular dynamics during protein crystal growth.

Homochiral and racemic MicroED structures of a peptide repeat from the ice-nucleation protein InaZ

The ice-nucleation protein InaZ from Pseudomonas syringae contains a large number of degenerate repeats that span more than a quarter of its sequence and include the segment GSTSTA. Ab initio structures of this repeat segment, resolved to 1.1 Å by microfocus X-ray crystallography and to 0.9 Å by the cryo-EM method MicroED, were determined from both racemic and homochiral crystals. The benefits of racemic protein crystals for structure determination by MicroED were evaluated and it was confirmed that the phase restriction introduced by crystal centrosymmetry increases the number of successful trials during the ab initio phasing of the electron diffraction data. Both homochiral and racemic GSTSTA form amyloid-like protofibrils with labile, corrugated antiparallel β-sheets that mate face to back. The racemic GSTSTA protofibril represents a new class of amyloid assembly in which all-left-handed sheets mate with their all-right-handed counterparts. This determination of racemic amyloid assemblies by MicroED reveals complex amyloid architectures and illustrates the racemic advantage in macromolecular crystallography, now with submicrometre-sized crystals.

Extension of the transferable aspherical pseudoatom data bank for the comparison of molecular electrostatic potentials in structure-activity studies

The transferable aspherical pseudoatom data bank, UBDB2018, is extended with over 130 new atom types present in small and biological molecules of great importance in biology and chemistry. UBDB2018 can be applied either as a source of aspherical atomic scattering factors in a standard X-ray experiment (d_min ≃ 0.8 Å) instead of the independent atom model (IAM), and can therefore enhance the final crystal structure geometry and refinement parameters; or as a tool to reconstruct the molecular charge-density distribution and derive the electrostatic properties of chemical systems for which 3D structural data are available. The extended data bank has been extensively tested, with the focus being on the accuracy of the molecular electrostatic potential computed for important drug-like molecules, namely the HIV-1 protease inhibitors. The UBDB allows the reconstruction of the reference B3LYP/6-31G** potentials, with a root-mean-squared error of 0.015 e bohr^-1 computed for entire potential grids which span values from ca 200 e bohr^-1 to ca -0.1 e bohr^-1 and encompass both the inside and outside regions of a molecule. UBDB2018 is shown to be applicable to enhancing the physical meaning of the molecular electrostatic potential descriptors used to construct predictive quantitative structure-activity relationship/quantitative structure-property relationship (QSAR/QSPR) models for drug discovery studies. In addition, it is suggested that electron structure factors computed from UBDB2018 may significantly improve the interpretation of electrostatic potential maps measured experimentally by means of electron diffraction or single-particle cryo-EM methods.

Collection of Continuous Rotation MicroED Data from Ion Beam-Milled Crystals of Any Size

Microcrystal electron diffraction (MicroED) allows for macromolecular structure solution from nanocrystals. To create crystals of suitable size for MicroED data collection, sample preparation typically involves sonication or pipetting a slurry of crystals from a crystallization drop. The resultant crystal fragments are fragile and the quality of the data that can be obtained from them is sensitive to subsequent sample preparation for cryoelectron microscopy as interactions in the water-air interface can damage crystals during blotting. Here, we demonstrate the use of a focused ion beam to generate lamellae of macromolecular protein crystals for continuous rotation MicroED that are of ideal thickness, easy to locate, and require no blotting optimization. In this manner, crystals of nearly any size may be scooped and milled to desired dimensions prior to data collection, thus streamlining the methodology for sample preparation for MicroED.

Rapid Structure Determination of Microcrystalline Molecular Compounds Using Electron Diffraction

Chemists of all fields currently publish about 50 000 crystal structures per year, the vast majority of which are X‐ray structures. We determined two molecular structures by employing electron rather than X‐ray diffraction. For this purpose, an EIGER hybrid pixel detector was fitted to a transmission electron microscope, yielding an electron diffractometer. The structure of a new methylene blue derivative was determined at 0.9 Å resolution from a crystal smaller than 1×2 μm². Several thousand active pharmaceutical ingredients (APIs) are only available as submicrocrystalline powders. To illustrate the potential of electron crystallography for the pharmaceutical industry, we also determined the structure of an API from its pill. We demonstrate that electron crystallography complements X‐ray crystallography and is the technique of choice for all unsolved cases in which submicrometer‐sized crystals were the limiting factor.

Machining protein microcrystals for structure determination by electron diffraction

We demonstrate that ion-beam milling of frozen, hydrated protein crystals to thin lamella preserves the crystal lattice to near-atomic resolution. This provides a vehicle for protein structure determination, bridging the crystal size gap between the nanometer scale of conventional electron diffraction and micron scale of synchrotron microfocus beamlines. The demonstration that atomic information can be retained suggests that milling could provide such detail on sections cut from vitrified cells.

Electron diffraction data processing with DIALS

Electron diffraction is a relatively novel alternative to X-ray crystallography for the structure determination of macromolecules from three-dimensional nanometre-sized crystals. The continuous-rotation method of data collection has been adapted for the electron microscope. However, there are important differences in geometry that must be considered for successful data integration. The wavelength of electrons in a TEM is typically around 40 times shorter than that of X-rays, implying a nearly flat Ewald sphere, and consequently low diffraction angles and a high effective sample-to-detector distance. Nevertheless, the DIALS software package can, with specific adaptations, successfully process continuous-rotation electron diffraction data. Pathologies encountered specifically in electron diffraction make data integration more challenging. Errors can arise from instrumentation, such as beam drift or distorted diffraction patterns from lens imperfections. The diffraction geometry brings additional challenges such as strong correlation between lattice parameters and detector distance. These issues are compounded if calibration is incomplete, leading to uncertainty in experimental geometry, such as the effective detector distance and the rotation rate or direction. Dynamic scattering, absorption, radiation damage and incomplete wedges of data are additional factors that complicate data processing. Here, recent features of DIALS as adapted to electron diffraction processing are shown, including diagnostics for problematic diffraction geometry refinement, refinement of a smoothly varying beam model and corrections for distorted diffraction images. These novel features, combined with the existing tools in DIALS, make data integration and refinement feasible for electron crystallography, even in difficult cases.

Ionic scattering factors of atoms that compose biological molecules

Ionic scattering factors of atoms that compose biological molecules have been computed by the multi-configuration Dirac-Fock method. These ions are chemically unstable and their scattering factors had not been reported except for O-. Yet these factors are required for the estimation of partial charges in protein molecules and nucleic acids. The electron scattering factors of these ions are particularly important as the electron scattering curves vary considerably between neutral and charged atoms in the spatial-resolution range explored in structural biology. The calculated X-ray and electron scattering factors have then been parameterized for the major scattering curve models used in X-ray and electron protein crystallography and single-particle cryo-EM. The X-ray and electron scattering factors and the fitting parameters are presented for future reference.

Analysis of Global and Site-Specific Radiation Damage in Cryo-EM

Micro-crystal electron diffraction (MicroED) combines the efficiency of electron scattering with diffraction to allow structure determination from nano-sized crystalline samples in cryoelectron microscopy (cryo-EM). It has been used to solve structures of a diverse set of biomolecules and materials, in some cases to sub-atomic resolution. However, little is known about the damaging effects of the electron beam on samples during such measurements. We assess global and site-specific damage from electron radiation on nanocrystals of proteinase K and of a prion hepta-peptide and find that the dynamics of electron-induced damage follow well-established trends observed in X-ray crystallography. Metal ions are perturbed, disulfide bonds are broken, and acidic side chains are decarboxylated while the diffracted intensities decay exponentially with increasing exposure. A better understanding of radiation damage in MicroED improves our assessment and processing of all types of cryo-EM data.

Electron crystallography with the EIGER detector

Electron crystallography is a discipline that currently attracts much attention as method for inorganic, organic and macromolecular structure solution. EIGER, a direct-detection hybrid pixel detector developed at the Paul Scherrer Institut, Switzerland, has been tested for electron diffraction in a transmission electron microscope. EIGER features a pixel pitch of 75 × 75 µm2, frame rates up to 23 kHz and a dead time between frames as low as 3 µs. Cluster size and modulation transfer functions of the detector at 100, 200 and 300 keV electron energies are reported and the data quality is demonstrated by structure determination of a SAPO-34 zeotype from electron diffraction data.

From electron crystallography of 2D crystals to MicroED of 3D crystals

Electron crystallography is widespread in material science applications, but for biological samples its use has been restricted to a handful of examples where two-dimensional (2D) crystals or helical samples were studied either by electron diffraction and/or imaging. Electron crystallography in cryoEM, was developed in the mid-1970s and used to solve the structure of several membrane proteins and some soluble proteins. In 2013, a new method for cryoEM was unveiled and named Micro-crystal Electron Diffraction, or MicroED, which is essentially three-dimensional (3D) electron crystallography of microscopic crystals. This method uses truly 3D crystals, that are about a billion times smaller than those typically used for X-ray crystallography, for electron diffraction studies. There are several important differences and some similarities between electron crystallography of 2D crystals and MicroED. In this review, we describe the development of these techniques, their similarities and differences, and offer our opinion of future directions in both fields.

High-Resolution Cryoelectron Microscopy Structure of the Cyclic Nucleotide-Modulated Potassium Channel MloK1 in a Lipid Bilayer

Eukaryotic cyclic nucleotide-modulated channels perform their diverse physiological roles by opening and closing their pores to ions in response to cyclic nucleotide binding. We here present a structural model for the cyclic nucleotide-modulated potassium channel homolog from Mesorhizobium loti, MloK1, determined from 2D crystals in the presence of lipids. Even though crystals diffract electrons to only ∼10 Å, using cryoelectron microscopy (cryo-EM) and recently developed computational methods, we have determined a 3D map of full-length MloK1 in the presence of cyclic AMP (cAMP) at ∼4.5 Å isotropic 3D resolution. The structure provides a clear picture of the arrangement of the cyclic nucleotide-binding domains with respect to both the pore and the putative voltage sensor domains when cAMP is bound, and reveals a potential gating mechanism in the context of the lipid-embedded channel.

Protein structure determination by electron diffraction using a single three-dimensional nanocrystal

Three-dimensional nanometre-sized crystals of macromolecules currently resist structure elucidation by single-crystal X-ray crystallography. Here, a single nanocrystal with a diffracting volume of only 0.14 µm3, i.e. no more than 6 × 105 unit cells, provided sufficient information to determine the structure of a rare dimeric polymorph of hen egg-white lysozyme by electron crystallography. This is at least an order of magnitude smaller than was previously possible. The molecular-replacement solution, based on a monomeric polyalanine model, provided sufficient phasing power to show side-chain density, and automated model building was used to reconstruct the side chains. Diffraction data were acquired using the rotation method with parallel beam diffraction on a Titan Krios transmission electron microscope equipped with a novel in-house-designed 1024 × 1024 pixel Timepix hybrid pixel detector for low-dose diffraction data collection. Favourable detector characteristics include the ability to accurately discriminate single high-energy electrons from X-rays and count them, fast readout to finely sample reciprocal space and a high dynamic range. This work, together with other recent milestones, suggests that electron crystallography can provide an attractive alternative in determining biological structures.

The structure of denisovite, a fibrous nanocrystalline polytypic disordered 'very complex' silicate, studied by a synergistic multi-disciplinary approach employing methods of electron crystallography and X-ray powder diffraction

Denisovite is a rare mineral occurring as aggregates of fibres typically 200-500 nm diameter. It was confirmed as a new mineral in 1984, but important facts about its chemical formula, lattice parameters, symmetry and structure have remained incompletely known since then. Recently obtained results from studies using microprobe analysis, X-ray powder diffraction (XRPD), electron crystallography, modelling and Rietveld refinement will be reported. The electron crystallography methods include transmission electron microscopy (TEM), selected-area electron diffraction (SAED), high-angle annular dark-field imaging (HAADF), high-resolution transmission electron microscopy (HRTEM), precession electron diffraction (PED) and electron diffraction tomography (EDT). A structural model of denisovite was developed from HAADF images and later completed on the basis of quasi-kinematic EDT data by ab initio structure solution using direct methods and least-squares refinement. The model was confirmed by Rietveld refinement. The lattice parameters are a = 31.024 (1), b = 19.554 (1) and c = 7.1441 (5) Å, β = 95.99 (3)°, V = 4310.1 (5) ų and space group P12/a1. The structure consists of three topologically distinct dreier silicate chains, viz. two xonotlite-like dreier double chains, [Si₆O₁₇]^10-, and a tubular loop-branched dreier triple chain, [Si₁₂O₃₀]^12-. The silicate chains occur between three walls of edge-sharing (Ca,Na) octahedra. The chains of silicate tetrahedra and the octahedra walls extend parallel to the z axis and form a layer parallel to (100). Water molecules and K⁺ cations are located at the centre of the tubular silicate chain. The latter also occupy positions close to the centres of eight-membered rings in the silicate chains. The silicate chains are geometrically constrained by neighbouring octahedra walls and present an ambiguity with respect to their z position along these walls, with displacements between neighbouring layers being either Δz = c/4 or -c/4. Such behaviour is typical for polytypic sequences and leads to disorder along [100]. In fact, the diffraction pattern does not show any sharp reflections with l odd, but continuous diffuse streaks parallel to a* instead. Only reflections with l even are sharp. The diffuse scattering is caused by (100) nano-lamellae separated by stacking faults and twin boundaries. The structure can be described according to the order-disorder (OD) theory as a stacking of layers parallel to (100).

Reflections on the value of electron microscopy in the study of heterogeneous catalysts

Electron microscopy (EM) is arguably the single most powerful method of characterizing heterogeneous catalysts. Irrespective of whether they are bulk and multiphasic, or monophasic and monocrystalline, or nanocluster and even single-atom and on a support, their structures in atomic detail can be visualized in two or three dimensions, thanks to high-resolution instruments, with sub-Ångstrom spatial resolutions. Their topography, tomography, phase-purity, composition, as well as the bonding, and valence-states of their constituent atoms and ions and, in favourable circumstances, the short-range and long-range atomic order and dynamics of the catalytically active sites, can all be retrieved by the panoply of variants of modern EM. The latter embrace electron crystallography, rotation and precession electron diffraction, X-ray emission and high-resolution electron energy-loss spectra (EELS). Aberration-corrected (AC) transmission (TEM) and scanning transmission electron microscopy (STEM) have led to a revolution in structure determination. Environmental EM is already playing an increasing role in catalyst characterization, and new advances, involving special cells for the study of solid catalysts in contact with liquid reactants, have recently been deployed.

Two-dimensional crystallization of monomeric bovine cytochrome c oxidase with bound cytochrome c in reconstituted lipid membranes

Mitochondrial cytochrome c oxidase utilizes electrons provided by cytochrome c for the active vectorial transport of protons across the inner mitochondrial membrane through the reduction of molecular oxygen to water. Direct structural evidence on the transient cytochrome c oxidase–cytochrome c complex thus far, however, remains elusive and its physiological relevant oligomeric form is unclear. Here, we report on the 2D crystallization of monomeric bovine cytochrome c oxidase with tightly bound cytochrome c at a molar ratio of 1:1 in reconstituted lipid membranes at the basic pH of 8.5 and low ionic strength.

Two-dimensional crystal structure of aquaporin-4 bound to the inhibitor acetazolamide

Acetazolamide (AZA) reduces the water permeability of aquaporin-4, the predominant water channel in the brain. We determined the structure of aquaporin-4 in the presence of AZA using electron crystallography. Most of the features of the 5-Å density map were consistent with those of the previously determined atomic model. The map showed a protruding density from near the extracellular pore entrance, which most likely represents the bound AZA. Molecular docking simulations supported the location of the protrusion as the likely AZA-binding site. These findings suggest that AZA reduces water conduction by obstructing the pathway at the extracellular entrance without inducing a large conformational change in the protein.

Electron Microscopy and Image Processing: Essential Tools for Structural Analysis of Macromolecules

Macromolecular electron microscopy typically depicts the structures of macromolecular complexes ranging from ∼200 kDa to hundreds of MDa. The amount of specimen required, a few micrograms, is typically 100 to 1000 times less than needed for X-ray crystallography or nuclear magnetic resonance spectroscopy. Micrographs of frozen-hydrated (cryogenic) specimens portray native structures, but the original images are noisy. Computational averaging reduces noise, and three-dimensional reconstructions are calculated by combining different views of free-standing particles ("single-particle analysis"). Electron crystallography is used to characterize two-dimensional arrays of membrane proteins and very small three-dimensional crystals. Under favorable circumstances, near-atomic resolutions are achieved. For structures at somewhat lower resolution, pseudo-atomic models are obtained by fitting high-resolution components into the density. Time-resolved experiments describe dynamic processes. Electron tomography allows reconstruction of pleiomorphic complexes and subcellular structures and modeling of macromolecules in their cellular context. Significant information is also obtained from metal-coated and dehydrated specimens.

A Refined Single-Particle Reconstruction Procedure to Process Two-Dimensional Crystal Images from Transmission Electron Microscopy

Single-particle reconstruction (SPR) and electron crystallography (EC), two major applications in electron microscopy, can be used to determine the structure of membrane proteins. The three-dimensional (3D) map is obtained from separated particles in conventional SPR, but from periodic unit cells in EC. Here, we report a refined SPR procedure for processing 2D crystal images. The method is applied to 2D crystals of melibiose permease, a secondary transporter in Escherichia coli. The current procedure is improved from our previously published one in several aspects. The "gold standard Fourier shell correlation" resolution of our final reconstruction reaches 13 Å, which is significantly better than the previously obtained 17 Å resolution. The choices of different refinement parameters for reconstruction are discussed. Our refined SPR procedure could be applied to determine the structure of other membrane proteins in small or locally distorted 2D crystals, which are not ideal for EC.

Bovine F1Fo ATP synthase monomers bend the lipid bilayer in 2D membrane crystals

We have used a combination of electron cryo-tomography, subtomogram averaging, and electron crystallographic image processing to analyse the structure of intact bovine F₁F_o ATP synthase in 2D membrane crystals. ATPase assays and mass spectrometry analysis of the 2D crystals confirmed that the enzyme complex was complete and active. The structure of the matrix-exposed region was determined at 24 Å resolution by subtomogram averaging and repositioned into the tomographic volume to reveal the crystal packing. F₁F_o ATP synthase complexes are inclined by 16° relative to the crystal plane, resulting in a zigzag topology of the membrane and indicating that monomeric bovine heart F₁F_o ATP synthase by itself is sufficient to deform lipid bilayers. This local membrane curvature is likely to be instrumental in the formation of ATP synthase dimers and dimer rows, and thus for the shaping of mitochondrial cristae.

DOI:http://dx.doi.org/10.7554/eLife.06119.001

Cells use a molecule called adenosine triphosphate (or ATP for short) to power many processes that are vital for life. Animals, plants, and fungi primarily make their ATP in a specialised compartment called the mitochondrion, which is found inside their cells. The mitochondrion is often referred to as the powerhouse of cells as it captures and stores the energy that animals gain from eating food in the molecule ATP. Other enzymes in the cell break apart ATP to release the stored energy, which they use to power various cellular processes.

The interior architecture of the mitochondrion includes a highly folded inner membrane where electrical energy is transformed into chemical energy. The tight folding of the inner membrane is thought to make this process more efficient. An enzyme named ATP synthase performs the final steps of the energy transformation process by producing ATP (ATP synthase literally means ‘ATP maker’). This enzyme sits in pairs along the edges of the inner membrane folds. This raises the question: does the ATP synthase cause the membrane to fold or does this enzyme just ‘prefer’ these folded edges (which are instead caused by something else inside the mitochondrion)?

To investigate this question, Jiko, Davies et al. extracted ATP synthase from the mitochondria of cow hearts and mixed them with modified fat molecules to form a ‘2D membrane crystal’: a membrane containing an ordered pattern of enzymes. An electron microscope was used to generate a three-dimensional volume of the 2D membrane crystal via a process similar to a MRI or CAT scan that one might have in hospital. In the three-dimensional volume of the membrane crystal, Jiko, Davies et al. discovered that instead of being flat as expected, the membrane of the 2D membrane crystal was rippled and that this ripple was caused by the membrane-embedded part of the ATP synthase. The geometry of the ripple exactly matched half of the bend at the edge of the membrane folds in the mitochondrion. Therefore, Jiko, Davies et al. concluded that a pair of ATP synthases, as found in mitochondria, was responsible for defining the tight folds of the inner mitochondrial membrane.

DOI:http://dx.doi.org/10.7554/eLife.06119.002

Electron crystallography of ultrathin 3D protein crystals: atomic model with charges

Membrane proteins and macromolecular complexes often yield crystals too small or too thin for even the modern synchrotron X-ray beam. Electron crystallography could provide a powerful means for structure determination with such undersized crystals, as protein atoms diffract electrons four to five orders of magnitude more strongly than they do X-rays. Furthermore, as electron crystallography yields Coulomb potential maps rather than electron density maps, it could provide a unique method to visualize the charged states of amino acid residues and metals. Here we describe an attempt to develop a methodology for electron crystallography of ultrathin (only a few layers thick) 3D protein crystals and present the Coulomb potential maps at 3.4-Å and 3.2-Å resolution, respectively, obtained from Ca(2+)-ATPase and catalase crystals. These maps demonstrate that it is indeed possible to build atomic models from such crystals and even to determine the charged states of amino acid residues in the Ca(2+)-binding sites of Ca(2+)-ATPase and that of the iron atom in the heme in catalase.

Development of the field of structural physiology

Electron crystallography is especially useful for studying the structure and function of membrane proteins - key molecules with important functions in neural and other cells. Electron crystallography is now an established technique for analyzing the structures of membrane proteins in lipid bilayers that closely simulate their natural biological environment. Utilizing cryo-electron microscopes with helium-cooled specimen stages that were developed through a personal motivation to understand the functions of neural systems from a structural point of view, the structures of membrane proteins can be analyzed at a higher than 3 Å resolution. This review covers four objectives. First, I introduce the new research field of structural physiology. Second, I recount some of the struggles involved in developing cryo-electron microscopes. Third, I review the structural and functional analyses of membrane proteins mainly by electron crystallography using cryo-electron microscopes. Finally, I discuss multifunctional channels named "adhennels" based on structures analyzed using electron and X-ray crystallography.

Solving difficult structures with electron diffraction

Precession electron diffraction has solved a long-standing challenge in electron diffraction. Further progress promises a general technique for structure determination of difficult crystals.