Acta Crystallographica Section A: Foundations and Advances最新文献

Diffraction intensities from a crystallographic experiment include contributions from the entire unit cell of the crystal: the macromolecule, the solvent around it and eventually other compounds. These contributions cannot typically be well described by an atomic model alone, i.e. using point scatterers. Indeed, entities such as disordered (bulk) solvent, semi-ordered solvent (e.g. lipid belts in membrane proteins, ligands, ion channels) and disordered polymer loops require other types of modeling than a collection of individual atoms. This results in the model structure factors containing multiple contributions. Most macromolecular applications assume two-component structure factors: one component arising from the atomic model and the second one describing the bulk solvent. A more accurate and detailed modeling of the disordered regions of the crystal will naturally require more than two components in the structure factors, which presents algorithmic and computational challenges. Here an efficient solution of this problem is proposed. All algorithms described in this work have been implemented in the computational crystallography toolbox (CCTBX) and are also available within Phenix software. These algorithms are rather general and do not use any assumptions about molecule type or size nor about those of its components.

As an alternative approach to X-ray crystallography and single-particle cryo-electron microscopy, single-molecule electron diffraction has a better signal-to-noise ratio and the potential to increase the resolution of protein models. This technology requires collection of numerous diffraction patterns, which can lead to congestion of data collection pipelines. However, only a minority of the diffraction data are useful for structure determination because the chances of hitting a protein of interest with a narrow electron beam may be small. This necessitates novel concepts for quick and accurate data selection. For this purpose, a set of machine learning algorithms for diffraction data classification has been implemented and tested. The proposed pre-processing and analysis workflow efficiently distinguished between amorphous ice and carbon support, providing proof of the principle of machine learning based identification of positions of interest. While limited in its current context, this approach exploits inherent characteristics of narrow electron beam diffraction patterns and can be extended for protein data classification and feature extraction.

The paper by Gopalan [(2020). Acta Cryst. A76, 318-327] presented an enumeration of the 41 physical quantity types in non-relativistic physics, in arbitrary dimensions, based on the formalism of Clifford algebra. Gopalan considered three antisymmetries: spatial inversion, 1, time reversal, 1', and wedge reversion, 1^†. A consideration of the set of all seven antisymmetries (1, 1', 1^†, 1'^†, 1^†, 1', 1'^†) leads to an extension of the results obtained by Gopalan. It is shown that there are 51 types of physical quantities with distinct symmetry properties in total.

Automatic crystal orientation determination and orientation mapping are important tools for research on polycrystalline materials. The most common methods of automatic orientation determination rely on detecting and indexing individual diffraction reflections, but these methods have not been used for orientation mapping of quasicrystalline materials. The paper describes the necessary changes to existing software designed for orientation determination of periodic crystals so that it can be applied to quasicrystals. The changes are implemented in one such program. The functioning of the modified program is illustrated by an example orientation map of an icosahedral polycrystal.

To avoid the time-consuming and often monotonous task of manual inspection of crystallization plates, a Python-based program to automatically detect crystals in crystallization wells employing deep learning techniques was developed. The program uses manually scored crystallization trials deposited in a database of an in-house crystallization robot as a training set. Since the success rate of such a system is able to catch up with manual inspection by trained persons, it will become an important tool for crystallographers working on biological samples. Four network architectures were compared and the SqueezeNet architecture performed best. In detecting crystals AlexNet accomplished a better result, but with a lower threshold the mean value for crystal detection was improved for SqueezeNet. Two assumptions were made about the imaging rate. With these two extremes it was found that an image processing rate of at least two times, but up to 58 times in the worst case, would be needed to reach the maximum imaging rate according to the deep learning network architecture employed for real-time classification. To avoid high workloads for the control computer of the CrystalMation system, the computing is distributed over several workstations, participating voluntarily, by the grid programming system from the Berkeley Open Infrastructure for Network Computing (BOINC). The outcome of the program is redistributed into the database as automatic real-time scores (ARTscore). These are immediately visible as colored frames around each crystallization well image of the inspection program. In addition, regions of droplets with the highest scoring probability found by the system are also available as images.

Wyckoff sequences are a way of encoding combinatorial information about crystal structures of a given symmetry. In particular, they offer an easy access to the calculation of a crystal structure's combinatorial, coordinational and configurational complexity, taking into account the individual multiplicities (combinatorial degrees of freedom) and arities (coordinational degrees of freedom) associated with each Wyckoff position. However, distinct Wyckoff sequences can yield the same total numbers of combinatorial and coordinational degrees of freedom. In this case, they share the same value for their Shannon entropy based subdivision complexity. The enumeration of Wyckoff sequences with this property is a combinatorial problem solved in this work, first in the general case of fixed subdivision complexity but non-specified Wyckoff sequence length, and second for the restricted case of Wyckoff sequences of both fixed subdivision complexity and fixed Wyckoff sequence length. The combinatorial results are accompanied by calculations of the combinatorial, coordinational, configurational and subdivision complexities, performed on Wyckoff sequences representing actual crystal structures.

In a pilot study, electron-density (ED) and ED Laplacian distributions were reconstructed for the challenging case of CaB₆ (Pearson symbol cP7) with conceptually fractional B-B bonds from quantum-chemically calculated structure-factor sets with resolutions 0.5 Å^-1 ≤ [sin(θ)/λ]_max ≤ 5.0 Å^-1 by means of Fourier-synthesis techniques. Convergence of norm deviations of the distributions obtained with respect to the reference ones was obtained in the valence region of the unit cell. The QTAIM (quantum theory of atoms in molecules) atomic charges, and the ED and ED Laplacian values at the characteristic critical points of the Fourier-synthesized distributions have been analysed for each resolution and found to display a convergent behaviour with increasing resolution. The presented method(exponent) (ME) type of Fourier-synthesis approach can qualitatively reconstruct all characteristic chemical bonding features of the ED from valence-electron structure-factor sets with resolutions of about 1.2 Å^-1 and beyond, and from all-electron structure-factor sets with resolutions of about 2.0 Å^-1 and beyond. Application of the ME type of Fourier-synthesis approach for reconstruction of ED and ED Laplacian distributions at experimental resolution is proposed to complement the usual extrapolation to infinite resolution in Hansen-Coppens multipole model derived static ED distributions.

It is shown that from a skewed, skeletal (edges and vertices), truncated octahedron, skewed skeletons can be derived of the other four convex parallelohedra found by Fedorov in 1885. In addition, three new nonconvex parallelohedra are produced, a counterexample to a statement by Grünbaum. This opens several new ways to view atomic positions in crystals, and new avenues in geometry.

Boris Gruber made fundamental contributions to the study of crystal lattices, leading to a finer classification of lattice types than those of Paul Niggli and Boris Delaunay before him.

The previously described approach for determination of the relativistic atomic X-ray scattering factors (XRSFs) at the Dirac-Hartree-Fock level [Olukayode et al. (2023). Acta Cryst. A79, 59-79] has been used to evaluate the XRSFs for a total of 318 species including all chemically relevant cations [Greenwood & Earnshaw (1997). Chemistry of the Elements], six monovalent anions (O^-, F^-, Cl^-, Br^-, I^-, At^-), the ns¹np³ excited (valence) states of carbon and silicon, and several exotic cations (Db⁵⁺, Sg⁶⁺, Bh⁷⁺, Hs⁸⁺ and Cn²⁺) for which the chemical compounds have been recently identified, thus significantly extending the coverage relative to all the earlier studies. Unlike the data currently recommended by the International Union of Crystallography (IUCr) [Maslen et al. (2006). International Tables for Crystallography, Vol. C, Section 6.1.1, pp. 554-589], which originate from different levels of theory including the non-relativistic Hartree-Fock and correlated methods, as well as the relativistic Dirac-Slater calculations, the re-determined XRSFs come from a uniform treatment of all species within the same relativistic B-spline Dirac-Hartree-Fock approach [Zatsarinny & Froese Fischer (2016). Comput. Phys. Comm. 202, 287-303] that includes the Breit interaction correction and the Fermi nuclear charge density model. While it was not possible to compare the quality of the generated wavefunctions with that from the previous studies due to a lack (to the best of our knowledge) of such data in the literature, a careful comparison of the total electronic energies and the estimated atomic ionization energies with experimental and theoretical values from other studies instils confidence in the quality of the calculations. A combination of the B-spline approach and a fine radial grid allowed for a precise determination of the XRSFs for each species in the entire 0 ≤ sin θ/λ ≤ 6 Å^-1 range, thus avoiding the necessity for extrapolation in the 2 ≤ sin θ/λ ≤ 6 Å^-1 interval which, as was shown in the first study, may lead to inconsistencies. In contrast to the Rez et al. work [Acta Cryst. (1994), A50, 481-497], no additional approximations were introduced when calculating wavefunctions for the anions. The conventional and extended expansions were employed to produce interpolating functions for each species in both the 0 ≤ sin θ/λ ≤ 2 Å^-1 and 2 ≤ sin θ/λ ≤ 6 Å^-1 intervals, with the extended expansions offering a significantly better accuracy at a minimal computational overhead. The combined results of this and the previous study may be used to update the XRSFs for neutral atoms and ions listed in Vol. C of the 2006 edition of International Tables for Crystallography.