Twinning in Zr-Based Metal-Organic Framework Crystals

Ab initio structure determination of new metal-organic framework (MOF) compounds is generally done by single crystal X-ray diffraction, but this technique can yield incorrect crystal structures if crystal twinning is overlooked. Herein, the crystal structures of three Zirconium-based MOFs, that are especially prone to twinning, have been determined from twinned crystals. These twin laws (and others) could potentially occur in many MOFs or related network structures, and the methods and tools described herein to detect and treat twinning could be useful to resolve the structures of affected crystals. Our results highlight the prevalence (and sometimes inevitability) of twinning in certain Zr-MOFs. Of special importance are the works of Howard Flack which, in addition to fundamental advances in crystallography, provide accessible tools for inexperienced crystallographers to take twinning into account in structure elucidation.

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.

Euhedral crystals of Na2TiGeO5 with switchable translucency and reorientable microstructure

Crystal twinning in euhedral crystals reveals anomalous optical properties.

Continuous diffraction of molecules and disordered molecular crystals

The intensities of far-field diffraction patterns of orientationally aligned molecules obey Wilson statistics, whether those molecules are in isolation (giving rise to a continuous diffraction pattern) or arranged in a crystal (giving rise to Bragg peaks). Ensembles of molecules in several orientations, but uncorrelated in position, give rise to the incoherent sum of the diffraction from those objects, modifying the statistics in a similar way as crystal twinning modifies the distribution of Bragg intensities. This situation arises in the continuous diffraction of laser-aligned molecules or translationally disordered molecular crystals. This paper develops the analysis of the intensity statistics of such continuous diffraction to obtain parameters such as scaling, beam coherence and the number of contributing independent object orientations. When measured, continuous molecular diffraction is generally weak and accompanied by a background that far exceeds the strength of the signal. Instead of just relying upon the smallest measured intensities or their mean value to guide the subtraction of the background, it is shown how all measured values can be utilized to estimate the background, noise and signal, by employing a modified `noisy Wilson' distribution that explicitly includes the background. Parameters relating to the background and signal quantities can be estimated from the moments of the measured intensities. The analysis method is demonstrated on previously published continuous diffraction data measured from crystals of photosystem II [Ayyeret al.(2016),Nature,530, 202–206].

Pitfalls in metal–organic framework crystallography: towards more accurate crystal structures

Proper handling of pore-occupying species and crystal twinning in structure determination of porous metal–organic frameworks by single crystal X-ray diffraction.

Data collection with a tailored X-ray beam size at 2.69 Å wavelength (4.6 keV): sulfur SAD phasing of Cdc23Nterm

The capability to reach wavelengths of up to 3.1 Å at the newly established EMBL P13 beamline at PETRA III, the new third-generation synchrotron at DESY in Hamburg, provides the opportunity to explore very long wavelengths to harness the sulfur anomalous signal for phase determination. Data collection at λ = 2.69 Å (4.6 keV) allowed the crystal structure determination by sulfur SAD phasing of Cdc23Nterm, a subunit of the multimeric anaphase-promoting complex (APC/C). At this energy, Cdc23Ntermhas an expected Bijvoet ratio 〈|Fanom|〉/〈F〉 of 2.2%, with 282 residues, including six cysteines and five methionine residues, and two molecules in the asymmetric unit (65.4 kDa; 12 Cys and ten Met residues). Selectively illuminating two separate portions of the same crystal with an X-ray beam of 50 µm in diameter allowed crystal twinning to be overcome. The crystals diffracted to 3.1 Å resolution, with unit-cell parametersa=b= 61.2,c = 151.5 Å, and belonged to space groupP43. The refined structure to 3.1 Å resolution has anRfactor of 18.7% and anRfreeof 25.9%. This paper reports the structure solution, related methods and a discussion of the instrumentation.

Phasing and structure of bestrophin-1: a case study in the use of heavy-atom cluster compounds with multi-subunit transmembrane proteins

The purification and three-dimensional crystallization of membrane proteins are commonly affected by a cumulation of pathologies that are less prevalent in their soluble counterparts. This may include severe anisotropy, poor spot shape, poor to moderate-resolution diffraction, crystal twinning, translational pseudo-symmetry and poor uptake of heavy atoms for derivatization. Such challenges must be circumvented by adaptations in the approach to crystallization and/or phasing. Here, an example of a protein that exhibited all of the above-mentioned complications is presented. Bestrophin-1 is a eukaryotic calcium-activated chloride channel, the structure of which was recently determined in complex with monoclonal antibody fragments using SAD phasing with tantalum bromide clusters (Ta6Br12·Br2). Some of the obstacles to obtaining improved diffraction and phasing for this particular channel are discussed, as well as the approach and adaptations that were key to determining the structure.