The crystal structure of the incommensurate modulated phase of potassium guaninate monohydrate has been solved on the basis of high-pressure single-crystal X-ray diffraction data. The modulated structure was described as a `mosaic' sequence of three different local configurations of two neighbouring guaninate rings. In contrast to known examples of incommensurate modulated organic compounds, the modulation functions of all atoms are discontinuous. This is the first example of the experimental detection of an incommensurate modulated crystal structure that can be modelled using the special `soliton mode' modulation function proposed by Aramburu et al. [(1995), J. Phys. Condens. Matter, 7, 6187–6196].

Through a combination of magnetic susceptibility, specific heat, and neutron powder diffraction measurements we have revealed a sequence of four magnetic phase transitions in the columnar quadruple perovskite Er2CuMnMn4O12. A key feature of the quadruple perovskite structural framework is the complex interplay of multiple magnetic sublattices via frustrated exchange topologies and competing magnetic anisotropies. It is shown that in Er2CuMnMn4O12, this phenomenology gives rise to multiple spin-reorientation transitions driven by the competition of easy-axis single ion anisotropy and the Dzyaloshinskii–Moriya interaction; both within the manganese B-site sublattice. At low temperature, one Er sublattice orders due to a finite f-d exchange field aligned parallel to its Ising axis, while the other Er sublattice remains non-magnetic until a final, symmetry-breaking phase transition into the ground state. This non-trivial low-temperature interplay of transition metal and rare-earth sublattices, as well as an observed k = (0, 0, ½) periodicity in both manganese spin canting and Er ordering, raises future challenges to develop a complete understanding of the R2CuMnMn4O12 family.

Accurate modeling of conformational energies is key to the crystal structure prediction of conformational polymorphs. Focusing on molecules XXXI and XXXII from the seventh blind test of crystal structure prediction, this study employs various electronic structure methods up to the level of domain-local pair natural orbital coupled cluster singles and doubles with perturbative triples [DLPNO-CCSD(T1)] to benchmark the conformational energies and to assess their impact on the crystal energy landscapes. Molecule XXXI proves to be a relatively straightforward case, with the conformational energies from generalized gradient approximation (GGA) functional B86bPBE-XDM changing only modestly when using more advanced density functionals such as PBE0-D4, ωB97M-V, and revDSD-PBEP86-D4, dispersion-corrected second-order Møller–Plesset perturbation theory (SCS-MP2D), or DLPNO-CCSD(T1). In contrast, the conformational energies of molecule XXXII prove difficult to determine reliably, and variations in the computed conformational energies appreciably impact the crystal energy landscape. Even high-level methods such as revDSD-PBEP86-D4 and SCS-MP2D exhibit significant disagreements with the DLPNO-CCSD(T1) benchmarks for molecule XXXII, highlighting the difficulty of predicting conformational energies for complex, drug-like molecules. The best-converged predicted crystal energy landscape obtained here for molecule XXXII disagrees significantly with what has been inferred about the solid-form landscape experimentally. The identified limitations of the calculations are probably insufficient to account for the discrepancies between theory and experiment on molecule XXXII, and further investigation of the experimental solid-form landscape would be valuable. Finally, assessment of several semi-empirical methods finds r2SCAN-3c to be the most promising, with conformational energy accuracy intermediate between the GGA and hybrid functionals and a low computational cost.

The seventh blind test of crystal structure prediction (CSP) methods substantially increased the level of complexity of the target compounds relative to the previous tests organized by the Cambridge Crystallographic Data Centre. In this work, the performance of density-functional methods is assessed using numerical atomic orbitals and the exchange-hole dipole moment dispersion correction (XDM) for the energy-ranking phase of the seventh blind test. Overall, excellent performance was seen for the two rigid molecules (XXVII, XXVIII) and for the organic salt (XXXIII). However, for the agrochemical (XXXI) and pharmaceutical (XXXII) targets, the experimental polymorphs were ranked fairly high in energy amongst the provided candidate structures and inclusion of thermal free-energy corrections from the lattice vibrations was found to be essential for compound XXXI. Based on these results, it is proposed that the importance of vibrational free-energy corrections increases with the number of rotatable bonds.

A novel approach to computationally enhance the sampling of molecular crystal structures is proposed and tested. This method is based on the use of extended variables coupled to a Monte Carlo based crystal polymorph generator. Inspired by the established technique of quasi-random sampling of polymorphs using the rigid molecule constraint, this approach represents molecular clusters as extended variables within a thermal reservoir. Polymorph unit-cell variables are generated using pseudo-random sampling. Within this framework, a harmonic coupling between the extended variables and polymorph configurations is established. The extended variables remain fixed during the inner loop dedicated to polymorph sampling, enforcing a stepwise propagation of the extended variables to maintain system exploration. The final processing step results in a polymorph energy landscape, where the raw structures sampled to create the extended variable trajectory are re-optimized without the thermal coupling term. The foundational principles of this approach are described and its effectiveness using both a Metropolis Monte Carlo type algorithm and modifications that incorporate replica exchange is demonstrated. A comparison is provided with pseudo-random sampling of polymorphs for the molecule coumarin. The choice to test a design of this algorithm as relevant for enhanced sampling of crystal structures was due to the obvious relation between molecular structure variables and corresponding crystal polymorphs as representative of the inherent vapor to crystal transitions that exist in nature. Additionally, it is shown that the trajectories of extended variables can be harnessed to extract fluctuation properties that can lead to valuable insights. A novel thermodynamic variable is introduced: the free energy difference between ensembles of Z' = 1 and Z' = 2 crystal polymorphs.

A seventh blind test of crystal structure prediction has been organized by the Cambridge Crystallographic Data Centre. The results are presented in two parts, with this second part focusing on methods for ranking crystal structures in order of stability. The exercise involved standardized sets of structures seeded from a range of structure generation methods. Participants from 22 groups applied several periodic DFT-D methods, machine learned potentials, force fields derived from empirical data or quantum chemical calculations, and various combinations of the above. In addition, one non-energy-based scoring function was used. Results showed that periodic DFT-D methods overall agreed with experimental data within expected error margins, while one machine learned model, applying system-specific AIMnet potentials, agreed with experiment in many cases demonstrating promise as an efficient alternative to DFT-based methods. For target XXXII, a consensus was reached across periodic DFT methods, with consistently high predicted energies of experimental forms relative to the global minimum (above 4 kJ mol−1 at both low and ambient temperatures) suggesting a more stable polymorph is likely not yet observed. The calculation of free energies at ambient temperatures offered improvement of predictions only in some cases (for targets XXVII and XXXI). Several avenues for future research have been suggested, highlighting the need for greater efficiency considering the vast amounts of resources utilized in many cases.

A seventh blind test of crystal structure prediction was organized by the Cambridge Crystallographic Data Centre featuring seven target systems of varying complexity: a silicon and iodine-containing molecule, a copper coordination complex, a near-rigid molecule, a cocrystal, a polymorphic small agrochemical, a highly flexible polymorphic drug candidate, and a polymorphic morpholine salt. In this first of two parts focusing on structure generation methods, many crystal structure prediction (CSP) methods performed well for the small but flexible agrochemical compound, successfully reproducing the experimentally observed crystal structures, while few groups were successful for the systems of higher complexity. A powder X-ray diffraction (PXRD) assisted exercise demonstrated the use of CSP in successfully determining a crystal structure from a low-quality PXRD pattern. The use of CSP in the prediction of likely cocrystal stoichiometry was also explored, demonstrating multiple possible approaches. Crystallographic disorder emerged as an important theme throughout the test as both a challenge for analysis and a major achievement where two groups blindly predicted the existence of disorder for the first time. Additionally, large-scale comparisons of the sets of predicted crystal structures also showed that some methods yield sets that largely contain the same crystal structures.

The synthesis of a chiral isothiourea, namely, (4aR,8aR)-3-phenyl-4a,5,6,7,8,8a-hexahydrobenzo[4,5]imidazo[2,1-b]thiazol-9-ium bromide, C15H17N2S+·Br−, with potential organocatalytic and anti-inflammatory activity is reported. The preparation of the heterocycle of interest was carried out in two high-yielding steps. The hydrobromide salt of the isothiourea of interest provided suitable crystals for X-ray diffraction analysis, the results of which are reported. Salient observations from this analysis are the near perpendicular arrangement of the phenyl ring and the mean plane of the heterocycle. This conformational characteristic may be relevant with regard the stereoselectivity induced by the chiral isothiourea in asymmetric reactions. Furthermore, evidence was found for the existence of an S...Br− halogen bond.

We report the structural characterization of a new quaternary telluride, Ba2Y0.87(1)Mn1.71(1)Te5, which was synthesized by the direct reaction of the elements inside a vacuum-sealed fused-silica tube. The quaternary phase is the first member of the Ba–M–Mn–Te system (M = Sc and Y). The composition and structure of the phase were elucidated using SEM–EDX (scanning electron microscopy–energy dispersive X-ray spectrometry) and single-crystal X-ray diffraction (SCXRD) studies. The title phase is nonstoichiometric and crystallizes in the monoclinic system (space group C2/m) having the refined unit-cell parameters a = 15.1466 (8), b = 4.5782 (3), c = 10.6060 (7) Å and β = 116.956 (2)°, with two formula units (Z = 2). The pseudo-two-dimensional crystal structure of Ba2Y0.87(1)Mn1.71(1)Te5 consists of distorted YTe6 octahedra and MnTe4 tetrahedra as the building blocks of the structure. The YTe6 octahedra are arranged to form infinite one-dimensional chains by sharing edges along the [010] direction. These chains are further connected to the MnTe4 tetrahedra along the c axis to create layered two-dimensional polyanionic [Y0.87(1)Mn1.71(1)Te5]4− units. The stuffing of Ba2+ cations in between the layers of [Y0.87(1)Mn1.71(1)Te5]4− anions brings the charge neutrality of the structure. Each Ba atom in the structure sits at the centre of a distorted monocapped trigonal prism-like polyhedron of seven Te atoms.

Hydraulic fracking exposes shale plays to acidic hydraulic fracking fluid (HFF), releasing toxic uranium (U) along with the desired oil and gas. With no existing methods to ensure U remains sequestered in the shale, this study sought to add organic ligands to HFF to explore potential U retention in shale plays. To test this possibility, incubations were set up in which uranyl acetate and one organic bipyridine ligand (either 2,2'-, 2,3'-, 2,4'-, or 4,4'-bipyridine) were added to pristine HFF as the crystallization medium. After several months and complete evaporation of all volatiles, bulk yellow crystalline material was obtained from the incubations, three of which yielded crystals suitable for single-crystal analysis, resulting in two novel structures and a high-quality structure of a previously described compound. The UO2VI acetate complexes bis(acetato-κ2O,O')(2,2'-bipyridine-κ2N,N')dioxidouranium(VI), [U(C2H3O2)2O2(C10H8N2)2] or [2,2'-bipyridine]UVIO2(CH3CO2)2, (I), and bis(acetato-κ2O,O')(2,4'-bipyridine-κN1')dioxidouranium(VI), [U(C2H3O2)2O2(C10H8N2)2] or [2,4'-bipyridine]2UVIO2(CH3CO2)2, (III), contain eight-coordinate UVI in a pseudo-hexagonal bipyramidal coordination geometry and are molecular, packing via weak C—H...O/N interactions, whereas catena-poly[bis(2,3'-bipyridinium) [di-μ-acetato-μ3-hydroxido-μ-hydroxido-di-μ3-oxido-hexaoxidotriuranium(VI)]–2,3'-bipyridine–water (1/1/1)], (C10H9N2)2[U3(C2H3O2)2O8(OH)2]·C10H8N2·H2O or {[2,3'-bipyridinium]2[2,3'-bipyridine][(UVIO2)3(O)2(OH)2(CH3CO2)2·H2O]}n, (II), forms an ionic one-dimensional polymer with seven-coordinate pentagonal bipyramidal UVI centers and hydrogen-bonding interactions within each chain. The formation of these crystals could indicate the potential for bipyridine to bind with U in shale during fracking, which will be explored in a future study via ICP-MS (inductively coupled plasma mass spectrometry) analyses of U concentration in HFF/bipyridine/shale incubations. The variation seen here between the molecular structures may indicate variance in the ability of bipyridine isomers to form complexes with U, which could impact their ability to retain U within shale in the context of fracking.

Parameters in analytical models for X-ray form factors of ions f0(s), based on the inverse Mott–Bethe formula involving a variable number of Gaussians, are determined for a wide range of published data sets {s, f0(s)}. The models reproduce the calculated form-factor values close to what is expected from a uniform statistical distribution with limits determined by their precision. For different ions associated with the same atom, the number of Gaussians in the models decreases with increasing net positive charge.

Three-dimensional electron diffraction (3D-ED) is a powerful technique for crystallographic characterization of nanometre-sized crystals that are too small for X-ray diffraction. For accurate crystal structure refinement, however, it is important that the Bragg diffracted intensities are treated dynamically. Bloch wave simulations are often used in 3D-ED, but can be computationally expensive for large unit cell crystals due to the large number of diffracted beams. Proposed here is an alternative method, the `scattering cluster algorithm' (SCA), that replaces the eigen-decomposition operation in Bloch waves with a simpler matrix multiplication. The underlying principle of SCA is that the intensity of a given Bragg reflection is largely determined by intensity transfer (i.e. `scattering') from a cluster of neighbouring diffracted beams. However, the penalty for using matrix multiplication is that the sample must be divided into a series of thin slices and the diffracted beams calculated iteratively, similar to the multislice approach. Therefore, SCA is more suitable for thin specimens. The accuracy and speed of SCA are demonstrated on tri-iso­propyl silane (TIPS) pentacene and rubrene, two exemplar organic materials with large unit cells.

The strong interaction of high-energy electrons with a crystal results in both dynamical elastic scattering and inelastic events, particularly phonon and plasmon excitation, which have relatively large cross sections. For accurate crystal structure refinement it is therefore important to uncover the impact of inelastic scattering on the Bragg beam intensities. Here a combined Bloch wave–Monte Carlo method is used to simulate phonon and plasmon scattering in crystals. The simulated thermal and plasmon diffuse scattering are consistent with experimental results. The simulations also confirm the empirical observation of a weaker unscattered beam intensity with increasing energy loss in the low-loss regime, while the Bragg-diffracted beam intensities do not change significantly. The beam intensities include the diffuse scattered background and have been normalized to adjust for the inelastic scattering cross section. It is speculated that the random azimuthal scattering angle during inelastic events transfers part of the unscattered beam intensity to the inner Bragg reflections. Inelastic scattering should not significantly influence crystal structure refinement, provided there are no artefacts from any background subtraction, since the relative intensity of the diffracted beams (which includes the diffuse scattering) remains approximately constant in the low energy loss regime.

In electron diffraction, thermal atomic motion produces incoherent scattering over a relatively wide angular range, which appears as a diffuse background that is usually subtracted from measurements of Bragg spot intensities in structure solution methods. The transfer of electron flux from Bragg spots to diffuse scatter is modelled using complex scattering factors f + if' in the Bloch wave methodology. In a two-beam Einstein model the imaginary `absorptive' scattering factor f' can be obtained by the evaluation of an integral containing f over all possible scattering angles. While more sophisticated models of diffuse scatter are widely used in the electron microscopy community, it is argued in this paper that this simple model is appropriate for current structure solution and refinement methods. The two-beam model is a straightforward numerical calculation, but even this simplistic approach can become time consuming for simulations of materials with large numbers of atoms in the unit cell and/or many incident beam orientations. Here, a parameterized form of f' is provided for 103 elements as neutral, spherical atoms that reduces calculation time considerably.

The bulk solvent is a major component of biomacromolecular crystals that contributes significantly to the observed diffraction intensities. Accurate modelling of the bulk solvent has been recognized as important for many crystallographic calculations. Owing to its simplicity and modelling power, the flat (mask-based) bulk-solvent model is used by most modern crystallographic software packages to account for disordered solvent. In this model, the bulk-solvent contribution is defined by a binary mask and a scale (scattering) function. The mask is calculated on a regular grid using the atomic model coordinates and their chemical types. The grid step and two radii, solvent and shrinkage, are the three parameters that govern the mask calculation. They are highly correlated and their choice is a compromise between the computer time needed to calculate the mask and the accuracy of the mask. It is demonstrated here that this choice can be optimized using a unique value of 0.6 Å for the grid step irrespective of the data resolution, and the radii values adjusted correspondingly. The improved values were tested on a large sample of Protein Data Bank entries derived from X-ray diffraction data and are now used in the computational crystallography toolbox (CCTBX) and in Phenix as the default choice.

Small-angle X-ray scattering (SAXS) is widely used to analyze the shape and size of nanoparticles in solution. A multitude of models, describing the SAXS intensity resulting from nanoparticles of various shapes, have been developed by the scientific community and are used for data analysis. Choosing the optimal model is a crucial step in data analysis, which can be difficult and time-consuming, especially for non-expert users. An algorithm is proposed, based on machine learning, representation learning and SAXS-specific preprocessing methods, which instantly selects the nanoparticle model best suited to describe SAXS data. The different algorithms compared are trained and evaluated on a simulated database. This database includes 75 000 scattering spectra from nine nanoparticle models, and realistically simulates two distinct device configurations. It will be made freely available to serve as a basis of comparison for future work. Deploying a universal solution for automatic nanoparticle model selection is a challenge made more difficult by the diversity of SAXS instruments and their flexible settings. The poor transferability of classification rules learned on one device configuration to another is highlighted. It is shown that training on several device configurations enables the algorithm to be generalized, without degrading performance compared with configuration-specific training. Finally, the classification algorithm is evaluated on a real data set obtained by performing SAXS experiments on nanoparticles for each of the instrumental configurations, which have been characterized by transmission electron microscopy. This data set, although very limited, allows estimation of the transferability of the classification rules learned on simulated data to real data.

A novel automated high-throughput screening approach, ClusterFinder, is reported for finding candidate structures for atomic pair distribution function (PDF) structural refinements. Finding starting models for PDF refinements is notoriously difficult when the PDF originates from nanoclusters or small nanoparticles. The reported ClusterFinder algorithm can screen 104 to 105 candidate structures from structural databases such as the Inorganic Crystal Structure Database (ICSD) in minutes, using the crystal structures as templates in which it looks for atomic clusters that result in a PDF similar to the target measured PDF. The algorithm returns a rank-ordered list of clusters for further assessment by the user. The algorithm has performed well for simulated and measured PDFs of metal–oxido clusters such as Keggin clusters. This is therefore a powerful approach to finding structural cluster candidates in a modelling campaign for PDFs of nanoparticles and nanoclusters.

Recent advances in quantum crystallography have shown that, beyond conventional charge density refinement, a one-electron reduced density matrix (1-RDM) satisfying N-representability conditions can be reconstructed using jointly experimental X-ray structure factors and directional Compton profiles (DCP) through semidefinite programming. So far, such reconstruction methods for 1-RDM, not constrained to idempotency, have been tested only on a toy model system (CO2). In this work, a new method is assessed on crystalline urea [CO(NH2)2] using static (0 K) and dynamic (50 K) artificial experimental data. An improved model, including symmetry constraints and frozen core-electron contribution, is introduced to better handle the increasing system complexity. Reconstructed 1-RDMs, deformation densities and DCP anisotropy are analysed, and it is demonstrated that the changes in the model significantly improve the reconstruction quality, even when there is insufficient information and data corruption. The robustness of the model and the strategy are thus shown to be well adapted to address the reconstruction problem from actual experimental scattering data.

Monoclinic ferroelectric phases are prevalent in various functional materials, most notably mixed-ion perovskite oxides. These phases can manifest as regularly ordered long-range crystallographic structures or as macroscopic averages of the self-assembled tetragonal/rhombohedral nanodomains. The structural and physical properties of monoclinic ferroelectric phases play a pivotal role when exploring the interplay between ferroelectricity, ferroelasticity, giant piezoelectricity and multiferroicity in crystals, ceramics and epitaxial thin films. However, the complex nature of this subject presents challenges, particularly in deciphering the microstructures of monoclinic domains. In Paper I [Biran & Gorfman (2024). Acta Cryst. A80, 112–128] the geometrical principles governing the connection of domain microstructures formed by pairing MAB type monoclinic domains were elucidated. Specifically, a catalog was established of `permissible domain walls', where `permissible', as originally introduced by Fousek & Janovec [J. Appl. Phys. (1969), 40, 135–142], denotes a mismatch-free connection between two monoclinic domains along the corresponding domain wall. The present article continues the prior work by elaborating on the formalisms of permissible domain walls to describe domain microstructures formed by pairing the MC type monoclinic domains. Similarly to Paper I, 84 permissible domain walls are presented for MC type domains. Each permissible domain wall is characterized by Miller indices, the transformation matrix between the crystallographic basis vectors of the domains and, crucially, the expected separation of Bragg peaks diffracted from the matched pair of domains. All these parameters are provided in an analytical form for easy and intuitive interpretation of the results. Additionally, 2D illustrations are provided for selected instances of permissible domain walls. The findings can prove valuable for various domain-related calculations, investigations involving X-ray diffraction for domain analysis and the description of domain-related physical properties.

In Part I of this series, all topologically possible 1-periodic infinite graphs (chain graphs) representing chains of tetrahedra with up to 6–8 vertices (tetrahedra) per repeat unit were generated. This paper examines possible restraints on embedding these chain graphs into Euclidean space such that they are compatible with the metrics of chains of tetrahedra in observed crystal structures. Chain-silicate minerals with T = Si4+ (plus P5+, V5+, As5+, Al3+, Fe3+, B3+, Be2+, Zn2+ and Mg2+) have a grand nearest-neighbour 〈T–T〉 distance of 3.06±0.15 Å and a minimum T⋯T separation of 3.71 Å between non-nearest-neighbour tetrahedra, and in order for embedded chain graphs (called unit-distance graphs) to be possible atomic arrangements in crystals, they must conform to these metrics, a process termed equalization. It is shown that equalization of all acyclic chain graphs is possible in 2D and 3D, and that equalization of most cyclic chain graphs is possible in 3D but not necessarily in 2D. All unique ways in which non-isomorphic vertices may be moved are designated modes of geometric modification. If a mode (m) is applied to an equalized unit-distance graph such that a new geometrically distinct unit-distance graph is produced without changing the lengths of any edges, the mode is designated as valid (mv); if a new geometrically distinct unit-distance graph cannot be produced, the mode is invalid (mi). The parameters mv and mi are used to define ranges of rigidity of the unit-distance graphs, and are related to the edge-to-vertex ratio, e/n, of the parent chain graph. The program GraphT–T was developed to embed any chain graph into Euclidean space subject to the metric restraints on T–T and T⋯T. Embedding a selection of chain graphs with differing e/n ratios shows that the principal reason why many topologically possible chains cannot occur in crystal structures is due to violation of the requirement that T⋯T > 3.71 Å. Such a restraint becomes increasingly restrictive as e/n increases and indicates why chains with stoichiometry TO<2.5 do not occur in crystal structures.

Following the work of Day & Hawthorne [Acta Cryst. (2022), A78, 212–233] and Day et al. [Acta Cryst. (2024), A80, 258–281], the program GraphT–T has been developed to embed graphical representations of observed and hypothetical chains of (SiO4)4− tetrahedra into 2D and 3D Euclidean space. During embedding, the distance between linked vertices (T–T distances) and the distance between unlinked vertices (T⋯T separations) in the resultant unit-distance graph are restrained to the average observed distance between linked Si tetrahedra (3.06±0.15 Å) and the minimum separation between unlinked vertices is restrained to be equal to or greater than the minimum distance between unlinked Si tetrahedra (3.713 Å) in silicate minerals. The notional interactions between vertices are described by a 3D spring-force algorithm in which the attractive forces between linked vertices behave according to Hooke's law and the repulsive forces between unlinked vertices behave according to Coulomb's law. Embedding parameters (i.e. spring coefficient, k, and Coulomb's constant, K) are iteratively refined during embedding to determine if it is possible to embed a given graph to produce a unit-distance graph with T–T distances and T⋯T separations that are compatible with the observed T–T distances and T⋯T separations in crystal structures. The resultant unit-distance graphs are denoted as compatible and may form crystal structures if and only if all distances between linked vertices (T–T distances) agree with the average observed distance between linked Si tetrahedra (3.06±0.15 Å) and the minimum separation between unlinked vertices is equal to or greater than the minimum distance between unlinked Si tetrahedra (3.713 Å) in silicate minerals. If the unit-distance graph does not satisfy these conditions, it is considered incompatible and the corresponding chain of tetrahedra is unlikely to form crystal structures. Using GraphT–T, Day et al. [Acta Cryst. (2024), A80, 258–281] have shown that several topological properties of chain graphs influence the flexibility (and rigidity) of the corresponding chains of Si tetrahedra and may explain why particular compatible chain arrangements (and the minerals in which they occur) are more common than others and/or why incompatible chain arrangements do not occur in crystals despite being topologically possible.

Analytical calculations of absorption corrections for X-ray powder diffraction experiments on non-ideal samples with surface roughness, porosity or absorption contrasts from multiple phases require complex mathematical models to represent their material distribution. In a computational approach to this problem, a practicable ray-tracing algorithm is formulated which is capable of simulating angle-dependent absorption corrections in reflection geometry for any given rasterized sample model. Single or multiphase systems with arbitrary surface roughness, porosity and spatial distribution of the phases in any combination can be modeled on a voxel grid by assigning respective values to each voxel. The absorption corrections are calculated by tracing the attenuation of X-rays along their individual paths via a modified shear-warp algorithm. The algorithm is presented in detail and the results of simulated absorption corrections on samples with various surface modulations are discussed in the context of published experimental results.

The atomic pair distribution function (PDF) is a real-space representation of the structure of a material. Experimental PDFs are obtained using a Fourier transform from total scattering data which may or may not have Bragg diffraction peaks. The determination of Bragg peak resolution in scattering data from the fundamental physical parameters of the diffractometer used is well established, but after the Fourier transform from reciprocal to direct space, these contributions are harder to identify. Starting from an existing definition of the resolution function of large-area detectors for X-ray diffraction, this approach is expanded into direct space. The effect of instrumental parameters on PDF peak resolution is developed mathematically, then studied with modelling and comparison with experimental PDFs of LaB6 from measurements made in different-sized capillaries.

The superstructure spots that appear in diffraction patterns of tilted perovskites are well documented and easily calculated using crystallographic software. Here, by considering a distortion mode as a perturbation of the prototype perovskite structure, it is shown how the structure-factor equation yields Boolean conditions for the presence of superstructure reflections. This approach may have some advantages for the analysis of electron diffraction patterns of perovskites.

Conjugation is the process by which plasmids, including those that carry antibiotic-resistance genes, are mobilized from one bacterium (the donor) to another (the recipient). The conjugation efficiency of IncF-like plasmids relies on the formation of mating-pair stabilization via intimate interactions between outer membrane proteins on the donor (a plasmid-encoded TraN isoform) and recipient bacteria. Conjugation of the R100-1 plasmid into Escherichia coli and Klebsiella pneumoniae (KP) recipients relies on pairing between the plasmid-encoded TraNα in the donor and OmpW in the recipient. Here, the crystal structure of K. pneumoniae OmpW (OmpWKP) is reported at 3.2 Å resolution. OmpWKP forms an eight-stranded β-barrel flanked by extracellular loops. The structures of E. coli OmpW (OmpWEC) and OmpWKP show high conservation despite sequence variability in the extracellular loops.

Protein tyrosine phosphatase 1B (PTP1B) plays important roles in cellular homeostasis and is a highly validated therapeutic target for multiple human ailments, including diabetes, obesity and breast cancer. However, much remains to be learned about how conformational changes may convey information through the structure of PTP1B to enable allosteric regulation by ligands or functional responses to mutations. High-resolution X-ray crystallography can offer unique windows into protein conformational ensembles, but comparison of even high-resolution structures is often complicated by differences between data sets, including non-isomorphism. Here, the highest resolution crystal structure of apo wild-type (WT) PTP1B to date is presented out of a total of ∼350 PTP1B structures in the PDB. This structure is in a crystal form that is rare for PTP1B, with two unique copies of the protein that exhibit distinct patterns of conformational heterogeneity, allowing a controlled comparison of local disorder across the two chains within the same asymmetric unit. The conformational differences between these chains are interrogated in the apo structure and between several recently reported high-resolution ligand-bound structures. Electron-density maps in a high-resolution structure of a recently reported activating double mutant are also examined, and unmodeled alternate conformations in the mutant structure are discovered that coincide with regions of enhanced conformational heterogeneity in the new WT structure. These results validate the notion that these mutations operate by enhancing local dynamics, and suggest a latent susceptibility to such changes in the WT enzyme. Together, these new data and analysis provide a detailed view of the conformational ensemble of PTP1B and highlight the utility of high-resolution crystallography for elucidating conformational heterogeneity with potential relevance for function.

Human tRNA (uracil-5-)-methyltransferase 2 homolog A (TRMT2A) is the dedicated enzyme for the methylation of uridine 54 in transfer RNA (tRNA). Human TRMT2A has also been described as a modifier of polyglutamine (polyQ)-derived neuronal toxicity. The corresponding human polyQ pathologies include Huntington's disease and constitute a family of devastating neuro­degenerative diseases. A polyQ tract in the corresponding disease-linked protein causes neuronal death and symptoms such as impaired motor function, as well as cognitive impairment. In polyQ disease models, silencing of TRMT2A reduced polyQ-associated cell death and polyQ protein aggregation, suggesting this protein as a valid drug target against this class of disorders. In this paper, the 1.6 Å resolution crystal structure of the RNA-recognition motif (RRM) from Drosophila melanogaster, which is a homolog of human TRMT2A, is described and analysed.

Sorghum, a short-day tropical plant, has been adapted for temperate grain production, in particular through the selection of variants at the MATURITY loci (Ma1–Ma6) that reduce photoperiod sensitivity. Ma3 encodes phytochrome B (phyB), a red/far-red photochromic biliprotein photoreceptor. The multi-domain gene product, comprising 1178 amino acids, autocatalytically binds the phytochromobilin chromophore to form the photoactive holophytochrome (Sb.phyB). This study describes the development of an efficient heterologous overproduction system which allows the production of large quantities of various holoprotein constructs, along with purification and crystallization procedures. Crystals of the Pr (red-light-absorbing) forms of NPGP, PGP and PG (residues 1–655, 114–655 and 114–458, respectively), each C-terminally tagged with His6, were successfully produced. While NPGP crystals did not diffract, those of PGP and PG diffracted to 6 and 2.1 Å resolution, respectively. Moving the tag to the N-terminus and replacing phytochromobilin with phycocyanobilin as the ligand produced PG crystals that diffracted to 1.8 Å resolution. These results demonstrate that the diffraction quality of challenging protein crystals can be improved by removing flexible regions, shifting fusion tags and altering small-molecule ligands.

The GTPase FlhF, a signal recognition particle (SRP)-type enzyme, is pivotal for spatial–numerical control and bacterial flagella assembly across diverse species, including pathogens. This study presents the X-ray structure of FlhF in its GDP-bound state at a resolution of 2.28 Å. The structure exhibits the classical N- and G-domain fold, consistent with related SRP GTPases such as Ffh and FtsY. Comparative analysis with GTP-loaded FlhF elucidates the conformational changes associated with GTP hydrolysis. These topological reconfigurations are similarly evident in Ffh and FtsY, and play a pivotal role in regulating the functions of these hydrolases.

Molybdenum- or tungsten-dependent formate dehydrogenases have emerged as significant catalysts for the chemical reduction of CO2 to formate, with biotechnological applications envisaged in climate-change mitigation. The role of Met405 in the active site of Desulfovibrio vulgaris formate dehydrogenase AB (DvFdhAB) has remained elusive. However, its proximity to the metal site and the conformational change that it undergoes between the resting and active forms suggests a functional role. In this work, the M405S variant was engineered, which allowed the active-site geometry in the absence of methionine Sδ interactions with the metal site to be revealed and the role of Met405 in catalysis to be probed. This variant displayed reduced activity in both formate oxidation and CO2 reduction, together with an increased sensitivity to oxygen inactivation.

Imaging scaffolds composed of designed protein cages fused to designed ankyrin repeat proteins (DARPins) have enabled the structure determination of small proteins by cryogenic electron microscopy (cryo-EM). One particularly well characterized scaffold type is a symmetric tetrahedral assembly composed of 24 subunits, 12 A and 12 B, which has three cargo-binding DARPins positioned on each vertex. Here, the X-ray crystal structure of a representative tetrahedral scaffold in the apo state is reported at 3.8 Å resolution. The X-ray crystal structure complements recent cryo-EM findings on a closely related scaffold, while also suggesting potential utility for crystallographic investigations. As observed in this crystal structure, one of the three DARPins, which serve as modular adaptors for binding diverse `cargo' proteins, present on each of the vertices is oriented towards a large solvent channel. The crystal lattice is unusually porous, suggesting that it may be possible to soak crystals of the scaffold with small (≤30 kDa) protein cargo ligands and subsequently determine cage–cargo structures via X-ray crystallography. The results suggest the possibility that cryo-EM scaffolds may be repurposed for structure determination by X-ray crystallography, thus extending the utility of electron-microscopy scaffold designs for alternative structural biology applications.

Ribulose-1,5-bisphosphate carboxylase/oxygenase (RuBisCO) is the enzyme responsible for the first step of carbon dioxide (CO2) fixation in plants, which proceeds via the carboxylation of ribulose 1,5-biphosphate. Because of the enormous importance of this reaction in agriculture and the environment, there is considerable interest in the mechanism of fixation of CO2 by RuBisCO. Here, a serial synchrotron crystallography structure of spinach RuBisCO is reported at 2.3 Å resolution. This structure is consistent with earlier single-crystal X-ray structures of this enzyme and the results are a good starting point for a further push towards time-resolved serial synchrotron crystallography in order to better understand the mechanism of the reaction.

Mycobacterium tuberculosis can reside and persist in deep tissues; latent tuberculosis can evade immune detection and has a unique mechanism to convert it into active disease through reactivation. M. tuberculosis Rv1421 (MtRv1421) is a hypothetical protein that has been proposed to be involved in nucleotide binding-related metabolism in cell-growth and cell-division processes. However, due to a lack of structural information, the detailed function of MtRv1421 remains unclear. In this study, a truncated N-terminal domain (NTD) of MtRv1421, which contains a Walker A/B-like motif, was purified and crystallized using PEG 400 as a precipitant. The crystal of MtRv1421-NTD diffracted to a resolution of 1.7 Å and was considered to belong to either the C-centered monoclinic space group C2 or the I-centered orthorhombic space group I222, with unit-cell parameters a = 124.01, b = 58.55, c = 84.87 Å, β = 133.12° or a = 58.53, b = 84.86, c = 90.52 Å, respectively. The asymmetric units of the C2 or I222 crystals contained two or one monomers, respectively. In terms of the binding ability of MtRv1421-NTD to various ligands, uridine diphosphate (UDP) and UDP-N-acetylglucosamine significantly increased the melting temperature of MtRv1421-NTD, which indicates structural stabilization through the binding of these ligands. Altogether, the results reveal that a UDP moiety may be required for the interaction of MtRv1421-NTD as a nucleotide-binding protein with its ligand.

Pseudoalteromonas fuliginea sp. PS47 is a recently identified marine bacterium that has extensive enzymatic machinery to metabolize polysaccharides, including a locus that targets pectin-like substrates. This locus contains a gene (locus tag EU509_03255) that encodes a pectin-degrading lyase, called PfPL1, that belongs to polysaccharide lyase family 1 (PL1). The 2.2 Å resolution X-ray crystal structure of PfPL1 reveals the compact parallel β-helix fold of the PL1 family. The back side of the core parallel β-helix opposite to the active site is a meandering set of five α-helices joined by lengthy loops. A comparison of the active site with those of other PL1 enzymes suggests a catalytic mechanism that is independent of metal ions, such as Ca2+, but that substrate recognition may require metal ions. Overall, this work provides the first structural insight into a pectinase of marine origin and the first structure of a PL1 enzyme in subfamily 2.

The third complementary-determining regions of the heavy-chain (CDR3H) variable regions (VH) of some cattle antibodies are highly extended, consisting of 48 or more residues. These `ultralong' CDR3Hs form β-ribbon stalks that protrude from the surface of the antibody with a disulfide cross-linked knob region at their apex that dominates antigen interactions over the other CDR loops. The structure of the Fab fragment of a naturally paired bovine ultralong antibody (D08), identified by single B-cell sequencing, has been determined to 1.6 Å resolution. By swapping the D08 native light chain with that of an unrelated antigen-unknown ultralong antibody, it is shown that interactions between the CDR3s of the variable domains potentially affect the fine positioning of the ultralong CDR3H; however, comparison with other crystallo­graphic structures shows that crystalline packing is also a major contributor. It is concluded that, on balance, the exact positioning of ultralong CDR3H loops is most likely to be due to the constraints of crystal packing.

Preparation of biomacromolecules for structural biology studies is a complex and time-consuming process. The goal is to produce a highly concentrated, highly pure product that is often shipped to large facilities with tools to prepare the samples for crystallization trials or for measurements at synchrotrons and cryoEM centers. The aim of this article is to provide guidance and to discuss general considerations for shipping biomacromolecular samples. Details are also provided about shipping samples for specific experiment types, including solution- and cryogenic-based techniques. These guidelines are provided with the hope that the time and energy invested in sample preparation is not lost due to shipping logistics.

Brucella ovis is an etiologic agent of ovine epididymitis and brucellosis that causes global devastation in sheep, rams, goats, small ruminants and deer. There are no cost-effective methods for the worldwide eradication of ovine brucellosis. B. ovis and other protein targets from various Brucella species are currently in the pipeline for high-throughput structural analysis at the Seattle Structural Genomics Center for Infectious Disease (SSGCID), with the aim of identifying new therapeutic targets. Furthermore, the wealth of structures generated are effective tools for teaching scientific communication, structural science and biochemistry. One of these structures, B. ovis leucine-, isoleucine-, valine-, threonine- and alanine-binding protein (BoLBP), is a putative periplasmic amino acid-binding protein. BoLBP shares less than 29% sequence identity with any other structure in the Protein Data Bank. The production, crystallization and high-resolution structures of BoLBP are reported. BoLBP is a prototypical bacterial periplasmic amino acid-binding protein with the characteristic Venus flytrap topology of two globular domains encapsulating a large central cavity containing the peptide-binding region. The central cavity contains small molecules usurped from the crystallization milieu. The reported structures reveal the conformational flexibility of the central cavity in the absence of bound peptides. The structural similarity to other LBPs can be exploited to accelerate drug repurposing.

Crystallographic fragment screening has become a pivotal technique in structure-based drug design, particularly for bacterial targets with a crucial role in infectious disease mechanisms. The enzyme CdaA, which synthesizes an essential second messenger cyclic di-AMP (c-di-AMP) in many pathogenic bacteria, has emerged as a promising candidate for the development of novel antibiotics. To identify crystals suitable for fragment screening, CdaA enzymes from Streptococcus pneumoniae, Bacillus subtilis and Enterococcus faecium were purified and crystallized. Crystals of B. subtilis CdaA, which diffracted to the highest resolution of 1.1 Å, were used to perform the screening of 96 fragments, yielding data sets with resolutions spanning from 1.08 to 1.87 Å. A total of 24 structural hits across eight different sites were identified. Four fragments bind to regions that are highly conserved among pathogenic bacteria, specifically the active site (three fragments) and the dimerization interface (one fragment). The coordinates of the three active-site fragments were used to perform an in silico drug-repurposing screen using the OpenEye suite and the DrugBank database. This screen identified tenofovir, an approved drug, that is predicted to interact with the ATP-binding region of CdaA. Its inhibitory potential against pathogenic E. faecium CdaA has been confirmed by ITC measurements. These findings not only demonstrate the feasibility of this approach for identifying lead compounds for the design of novel antibacterial agents, but also pave the way for further fragment-based lead-optimization efforts targeting CdaA.

Glucose-6-phosphate dehydrogenase (G6PD) is the first enzyme in the pentose phosphate pathway. It has been extensively studied by biochemical and structural techniques. 13 X-ray crystal structures and five electron cryo-microscopy structures in the PDB are focused on in this topical review. Two F420-dependent glucose-6-phosphate dehydrogenase (FGD) structures are also reported. The significant differences between human and parasite G6PDs can be exploited to find selective drugs against infections such as malaria and leishmaniasis. Furthermore, G6PD is a prognostic marker in several cancer types and is also considered to be a tumour target. On the other hand, FGD is considered to be a target against Mycobacterium tuberculosis and possesses a high biotechnological potential in biocatalysis and bioremediation.

Porphyromonas gingivalis is a major pathogenic oral bacterium that is responsible for periodontal disease. It is linked to chronic periodontitis, gingivitis and aggressive periodontitis. P. gingivalis exerts its pathogenic effects through mechanisms such as immune evasion and tissue destruction, primarily by secreting various factors, including cysteine proteases such as gingipain K (Kgp), gingipain R (RgpA and RgpB) and PrtH (UniProtKB ID P46071). Virulence proteins comprise multiple domains, including the pro-peptide region, catalytic domain, K domain, R domain and DUF2436 domain. While there is a growing database of knowledge on virulence proteins and domains, there was no prior evidence or information regarding the structure and biological function of the well conserved DUF2436 domain. In this study, the DUF2436 domain of PrtH from P. gingivalis (PgDUF2436) was determined at 2.21 Å resolution, revealing a noncanonical β-jelly-roll sandwich topology with two antiparallel β-sheets and one short α-helix. Although the structure of PgDUF2436 was determined by the molecular-replacement method using an AlphaFold model structure as a template, there were significant differences in the positions of β1 between the AlphaFold model and the experimentally determined PgDUF2436 structure. The Basic Local Alignment Search Tool sequence-similarity search program showed no sequentially similar proteins in the Protein Data Bank. However, DaliLite search results using structure-based alignment revealed that the PgDUF2436 structure has structural similarity Z-scores of 5.9–5.4 with the C-terminal domain of AlgF, the D4 domain of cytolysin, IglE and the extracellular domain structure of PepT2. This study has elucidated the structure of the DUF2436 domain for the first time and a comparative analysis with similar structures has been performed.

Plasmodium vivax is a major cause of malaria, which poses an increased health burden on approximately one third of the world's population due to climate change. Primaquine, the preferred treatment for P. vivax malaria, is contraindicated in individuals with glucose-6-phosphate dehydrogenase (G6PD) deficiency, a common genetic cause of hemolytic anemia, that affects ∼2.5% of the world's population and ∼8% of the population in areas of the world where P. vivax malaria is endemic. The Seattle Structural Genomics Center for Infectious Disease (SSGCID) conducted a structure–function analysis of P. vivax N-myristoyltransferase (PvNMT) as part of efforts to develop alternative malaria drugs. PvNMT catalyzes the attachment of myristate to the N-terminal glycine of many proteins, and this critical post-translational modification is required for the survival of P. vivax. The first step is the formation of a PvNMT–myristoyl–CoA binary complex that can bind to peptides. Understanding how inhibitors prevent protein binding will facilitate the development of PvNMT as a viable drug target. NMTs are secreted in all life stages of malarial parasites, making them attractive targets, unlike current antimalarials that are only effective during the plasmodial erythrocytic stages. The 2.3 Å resolution crystal structure of the ternary complex of PvNMT with myristoyl-CoA and a novel inhibitor is reported. One asymmetric unit contains two monomers. The structure reveals notable differences between the PvNMT and human enzymes and similarities to other plasmodial NMTs that can be exploited to develop new antimalarials.

Guanosine 5'-monophosphate (GMP) synthetase (GuaA) catalyzes the last step of GMP synthesis in the purine nucleotide biosynthetic pathway. This enzyme catalyzes a reaction in which xanthine 5'-monophosphate (XMP) is converted to GMP in the presence of Gln and ATP through an adenyl-XMP intermediate. A structure of an XMP-bound form of GuaA from the domain Bacteria has not yet been determined. In this study, the crystal structure of an XMP-bound form of GuaA from the thermophilic bacterium Thermus thermophilus HB8 (TtGuaA) was determined at a resolution of 2.20 Å and that of an apo form of TtGuaA was determined at 2.10 Å resolution. TtGuaA forms a homodimer, and the monomer is composed of three domains, which is a typical structure for GuaA. Disordered regions in the crystal structure were obtained from the AlphaFold2-predicted model structure, and a model with substrates (Gln, XMP and ATP) was constructed for molecular-dynamics (MD) simulations. The structural fluctuations of the TtGuaA dimer as well as the interactions between the active-site residues were analyzed by MD simulations.

Proliferating cell nuclear antigen (PCNA) plays a critical role in DNA replication by enhancing the activity of various proteins involved in replication. In this study, the crystal structure of ApePCNA1, one of three PCNAs from the thermophilic archaeon Aeropyrum pernix, was elucidated. ApePCNA1 was cloned and expressed in Escherichia coli and the protein was purified and crystallized. The resulting crystal structure determined at 2.00 Å resolution revealed that ApePCNA1 does not form a trimeric ring, unlike PCNAs from other domains of life. It has unique structural features, including a long interdomain-connecting loop and a PIP-box-like sequence at the N-terminus, indicating potential interactions with other proteins. These findings provide insights into the functional mechanisms of PCNAs in archaea and their evolutionary conservation across different domains of life. A modified medium and protocol were used to express recombinant protein containing the lac operon. The expression of the target protein increased and the total incubation time decreased when using this system compared with those of previous expression protocols.

The crystal structure of the intracellular domain of transforming growth factor β type I receptor (TβR1) in complex with the competitive inhibitor SB505124 is presented. The study provides insights into the structure and function of TβR1 in complex with SB505124, and as such offers molecular-level understanding of the inhibition of this critical signalling pathway. The potential of SB505124 as an avenue for therapy in cancer treatment is discussed on basis of the results.

Cryogenic electron microscopy (cryoEM) is a rapidly growing structural biology modality that has been successful in revealing molecular details of biological systems. However, unlike established biophysical and analytical techniques with calibration standards, cryoEM has lacked comprehensive biological test samples. Here, a cryoEM calibration sample consisting of a mixture of compatible macromolecules is introduced that can not only be used for resolution optimization, but also provides multiple reference points for evaluating instrument performance, data quality and image-processing workflows in a single experiment. This combined test specimen provides researchers with a reference point for validating their cryoEM pipeline, benchmarking their methodologies and testing new algorithms.

The reciprocal of a non-primitive unit cell is not a unit cell and the basis vectors do not correspond to cell lengths.

Animations, videos and 3D models have been designed to visualize the effects of symmetry operators on selected cases of crystal structures, pointing out the relationship with the diagrams published in International Tables for Crystallography, Vol. A.

Fixed targets (`chips') offer efficient, high-throughput microcrystal delivery for serial crystallography at synchrotrons and X-ray free-electron lasers (XFELs). Within this family, sheet-on-sheet (SOS) chips offer noteworthy advantages in cost, adaptability, universality and ease of crystal loading. We describe our latest generation of SOS devices, which are now in active use at both synchrotrons and XFELs.

This review summarizes the methodological aspects of laboratory X-ray powder micro-diffraction and demonstrates the assets of the method in the research of painted artworks for evaluation of their provenance or diagnosing their degradation.

This study validates the feasibility of applying a smearing method for the multi-slit very small angle neutron scattering instrument (MS-VSANS) at the China Spallation Neutron Source. Through analysis limited to a vertical range of 8 mm, the study demonstrates consistency between the predicted smearing function and experimental data, marking a significant milestone in utilizing real data from such instruments.