Showing papers in "Acta Crystallographica Section A in 2017"

Crystallography online by the Bilbao Crystallographic Server

Abstract: Received January 7, 2011; Revised April 19, 2011 The Bilbao Crystallographic Server is a web site with crystallographic databases and programs available online (www.cryst.ehu.es). It has been operating for more than ten years and new applications are being added regularly. The programs available on the server do not need a local installation and can be used free of charge. The server gives access to general information related to crystallographic symmetry groups (generators, general and special positions, maximal subgroups, Brillouin zones, etc.). Apart from the simple tools for retrieving the stored data, there are programs for the analysis of group-subgroup relations between space groups. There are also software package studying specific problems of solid-state physics, structural chemistry and crystallography.

Near-atomic resolution visualization of human transcription promoter opening

Abstract: In eukaryotic transcription initiation, a large multi-subunit pre-initiation complex (PIC) that assembles at the core promoter is required for the opening of the duplex DNA and identification of the start site for transcription by RNA polymerase II. Here we use cryo-electron microscropy (cryo-EM) to determine near-atomic resolution structures of the human PIC in a closed state (engaged with duplex DNA), an open state (engaged with a transcription bubble), and an initially transcribing complex (containing six base pairs of DNA-RNA hybrid). Our studies provide structures for previously uncharacterized components of the PIC, such as TFIIE and TFIIH, and segments of TFIIA, TFIIB and TFIIF. Comparison of the different structures reveals the sequential conformational changes that accompany the transition from each state to the next throughout the transcription initiation process. This analysis illustrates the key role of TFIIB in transcription bubble stabilization and provides strong structural support for a translocase activity of XPB.

The European X-ray Free-Electron Laser

Abstract: The European X-ray Free Electron Laser is being commissioned in the spring of 2017 and will start first user operation in the fall. First lasing is expected in the summer. It will be the world’s first hard X-ray laser facility based on superconducting accelerator technology and will deliver an unprecedented X-ray beam to the user community with a high repetition rate. First users are expected to come in the fall of 2017 on the FXE instrument for ultra-fast x-ray spectroscopy and x-ray scattering and on the SPB/SFX instrument for diffractive imaging and structural determination for single particles, clusters and biomolecules. In 2018 four more instruments will be taken into operation covering a wide range of scientific fields. In the talk a full description of the facility will be given including a report of the status of the commissioning.

Structures of riboswitch RNA reaction states by mix-and-inject XFEL serial crystallography

Abstract: Riboswitches are structural RNA elements that are generally located in the 5' untranslated region of messenger RNA. During regulation of gene expression, ligand binding to the aptamer domain of a riboswitch triggers a signal to the downstream expression platform. A complete understanding of the structural basis of this mechanism requires the ability to study structural changes over time. Here we use femtosecond X-ray free electron laser (XFEL) pulses to obtain structural measurements from crystals so small that diffusion of a ligand can be timed to initiate a reaction before diffraction. We demonstrate this approach by determining four structures of the adenine riboswitch aptamer domain during the course of a reaction, involving two unbound apo structures, one ligand-bound intermediate, and the final ligand-bound conformation. These structures support a reaction mechanism model with at least four states and illustrate the structural basis of signal transmission. The three-way junction and the P1 switch helix of the two apo conformers are notably different from those in the ligand-bound conformation. Our time-resolved crystallographic measurements with a 10-second delay captured the structure of an intermediate with changes in the binding pocket that accommodate the ligand. With at least a 10-minute delay, the RNA molecules were fully converted to the ligand-bound state, in which the substantial conformational changes resulted in conversion of the space group. Such notable changes in crystallo highlight the important opportunities that micro- and nanocrystals may offer in these and similar time-resolved diffraction studies. Together, these results demonstrate the potential of 'mix-and-inject' time-resolved serial crystallography to study biochemically important interactions between biomacromolecules and ligands, including those that involve large conformational changes.

A Theoretical Investigation of Orientation Relationships and Transformation Strains in Steels

Abstract: The identification of orientation relationships (ORs) plays a crucial role in the understanding of solid phase transformations. In steels, the most common models of ORs are the ones by Nishiyama–Wassermann (NW) and Kurdjumov– Sachs (KS). The defining feature of these and other OR models is the matching of directions and planes in the parent face-centred cubic gamma phase to ones in the product body-centred cubic/tetragonal alpha\alpha' phase. In this article a novel method that identifies transformation strains with ORs is introduced and used to develop a new strain-based approach to phase-transformation models in steels. Using this approach, it is shown that the transformation strains that leave a close-packed plane in the gamma phase and a close-packed direction within that plane unrotated are precisely those giving rise to the NW and KS ORs when a cubic product phase is considered. Further, it is outlined how, by choosing different pairs of unrotated planes and directions, other common ORs such as the ones by Pitsch and Greninger–Troiano can be derived. One of the advantages of our approach is that it leads to a natural generalization of the NW, KS and other ORs for different ratios of tetragonality r of the product body-centred tetragonal alpha' phase. These generalized ORs predict a sharpening of the transformation textures with increasing tetragonality and are thus in qualitative agreement with experiments on steels with varying alloy concentration

Photochromic metal–organic frameworks for inkless and erasable printing

Abstract: Inkless and erasable printing is the key solution towards a more sustainable paper industry, in terms of reducing paper wastages and the associated environmental hazards from waste paper processing. However, only a few cases have been reported in the literature where inkless printing has been tested in some practical systems. In an attempt to address this solution, we used photochromic metal–organic frameworks (MOFs) and tested their capability as inkless and erasable printing media. The printing was performed using sunlight as the light source on MOF-coated papers. The resulting printing had good resolution and stability, and was capable of being read both by the human eye and smart electronic devices; furthermore, the paper could be reused for several cycles without any significant loss in intensity. Interestingly, different coloured printing with a similar efficiency was achieved by varying the structure of the MOF.

Upconverting nanoparticles working as primary thermometers in different media

Abstract: Lanthanide-doped nanoparticles have recently emerged as very attractive multifunctional systems with potential for simultaneous thermal sensing and bio-imaging, due to near-infrared excitation and emission in the visible and near infrared spectral regions [1]. Non-invasive luminescent nanothermometry becomes popular in the last decade due to the limitations of traditional contact thermometers to operate at scales below 100 μm, as required by current technological demands in areas such as microelectronics, microoptics, photonics, microfluidics, and nanomedicine [2]. Generally, the usual calibration procedure of luminescent thermometers requires an independent measurement of the temperature to allow the corresponding conversion between the thermometry parameter (usually relative intensities) and temperature. A new calibration procedure is, then, necessary whenever the thermometer operates in a different medium, as other variables, such as the ionic strength, pH, pressure, or atmosphere composition impact the thermometric parameter. However, recording multiple calibrations in different medium is a time-consuming task and is not always possible (e.g., at the submicrometric scale). In general, a unique calibration relation is assumed to be valid, independently of the medium, which is a central bottleneck of secondary luminescent thermometers. Here we show that the temperature calibration curve of upconverting luminescent thermometers can be predicted by the Boltzmann distribution, independently of the medium where the material operates. We illustrate this concept using SrF2:Yb/Er upconverting nanoparticles in powder and in water suspensions that are primary Yb/Er co-doped luminescent nanothermometers. The maximum relative thermal sensitivity of the primary thermometer in the physiological temperature range (302–385 K) in two distinct mediums (powder and water suspension) is 1.159 ± 0.004%K−1.

Three-dimensional single-cell imaging with X-ray waveguides in the holographic regime

Abstract: X-ray tomography at the level of single biological cells is possible in a low-dose regime, based on full-field holographic recordings, with phase contrast originating from free-space wave propagation. Building upon recent progress in cellular imaging based on the illumination by quasi-point sources provided by X-ray waveguides, here this approach is extended in several ways. First, the phase-retrieval algorithms are extended by an optimized deterministic inversion, based on a multi-distance recording. Second, different advanced forms of iterative phase retrieval are used, operational for single-distance and multi-distance recordings. Results are compared for several different preparations of macrophage cells, for different staining and labelling. As a result, it is shown that phase retrieval is no longer a bottleneck for holographic imaging of cells, and how advanced schemes can be implemented to cope also with high noise and inconsistencies in the data.

A first-prototype multi-determinant X-ray constrained wavefunction approach: the X-ray constrained extremely localized molecular orbital–valence bond method

Abstract: All the current variants of Jayatilaka's X-ray constrained wavefunction (XCW) approach work within the framework of the single-determinant wavefunction ansatz. In this paper, a first-prototype multi-determinant XCW technique is proposed. The strategy assumes that the desired XCW is written as a valence-bond-like expansion in terms of pre-determined single Slater determinants constructed with extremely localized molecular orbitals. The method, which can be particularly suitable to investigate systems with a multi-reference character, has been applied to determine the weights of the resonance structures of naphthalene at different temperatures by exploiting experimental high-resolution X-ray diffraction data. The results obtained have shown that the explicit consideration of experimental structure factors in the determination of the resonance structure weights may lead to results significantly different compared with those resulting only from the simple energy minimization.

How many photons are needed to reconstruct random objects in coherent X-ray diffractive imaging?

Abstract: This paper presents an investigation of the reconstructibility of coherent X-ray diffractive imaging diffraction patterns for a class of binary random `bitmap' objects. Combining analytical results and numerical simulations, the critical fluence per bitmap pixel is determined, for arbitrary contrast values (absorption level and phase shift), both for the optical near- and far-field. This work extends previous investigations based on information theory, enabling a comparison of the amount of information carried by single photons in different diffraction regimes. The experimental results show an order-of-magnitude agreement.

International Tables for Crystallography, Volume A, Space-group symmetry. 6th edition. Edited by Mois I. Aroyo. Wiley, 2016. Pp. xxi + 873. Price GBP 295.00, EUR 354.00 (hardcover). ISBN 978-0-470-97423-0.

Abstract: HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. International Tables for Crystallography, Volume A, Space-group symmetry . Massimo Nespolo

HU multimerization shift controls nucleoid compaction

Abstract: Molecular mechanisms controlling functional bacterial chromosome (nucleoid) compaction and organization are surprisingly enigmatic but partly depend on conserved, histone-like proteins HUαα and HUαβ and their interactions that span the nanoscale and mesoscale from protein-DNA complexes to the bacterial chromosome and nucleoid structure. We determined the crystal structures of these chromosome-associated proteins in complex with native duplex DNA. Distinct DNA binding modes of HUαα and HUαβ elucidate fundamental features of bacterial chromosome packing that regulate gene transcription. By combining crystal structures with solution x-ray scattering results, we determined architectures of HU-DNA nucleoproteins in solution under near-physiological conditions. These macromolecular conformations and interactions result in contraction at the cellular level based on in vivo imaging of native unlabeled nucleoid by soft x-ray tomography upon HUβ and ectopic HUα38 expression. Structural characterization of charge-altered HUαα-DNA complexes reveals an HU molecular switch that is suitable for condensing nucleoid and reprogramming noninvasive Escherichia coli into an invasive form. Collective findings suggest that shifts between networking and cooperative and noncooperative DNA-dependent HU multimerization control DNA compaction and supercoiling independently of cellular topoisomerase activity. By integrating x-ray crystal structures, x-ray scattering, mutational tests, and x-ray imaging that span from protein-DNA complexes to the bacterial chromosome and nucleoid structure, we show that defined dynamic HU interaction networks can promote nucleoid reorganization and transcriptional regulation as efficient general microbial mechanisms to help synchronize genetic responses to cell cycle, changing environments, and pathogenesis.

Non-crystallographic symmetry of liquid metal, flat crystallographic faults and polymorph transformation of the M7C3 carbide.

Abstract: The fine lamellar fault structure of primary M7C3 carbide particles in the heat-resistant Fe-Cr-Ni-C alloy of the HP series (0.45C-25Cr-35Ni) in the cast condition has been revealed using transmission electron microscopy. The lamellar fault structure is regarded as an inheritance of the initial melt structure. A one-to-one correspondence between the crystal structures of M7C3, M5C2, M3C and M23C6 carbides and constructions of the projective 103 Desargues configuration and its subconfigurations is shown. Mutual mapping between 103 Desargues subconfigurations determines transformations of the ten-vertex equal-edged triangulated clusters appearing as building units of these carbides.

Dynamic quantum crystallography: lattice-dynamical models refined against diffraction data. II. Applications to L-alanine, naphthalene and xylitol.

Abstract: In the first paper of this series [Hoser & Madsen (2016). Acta Cryst. A72, 206–214], a new approach was introduced which enables the refinement of frequencies of normal modes obtained from ab initio periodic computations against single-crystal diffraction data. In this contribution, the performance of this approach is tested by refinement against data in the temperature range from 23 to 205 K on the molecular crystals of l-alanine, naphthalene and xylitol. The models, which are lattice-dynamical models derived at the Γ point of the Brillouin zone, are able to describe the atomic vibrations of l-alanine and naphthalene to a level where the residual densities are similar to those obtained from the independent atom model. For the more flexible molecule xylitol, larger deviations are found. Hydrogen ADPs (anisotropic displacement parameters) derived from the models are in similar or better agreement with neutron diffraction results than ADPs obtained by other procedures. The heat capacity calculated after normal mode refinement for naphthalene is in reasonable agreement with the heat capacity obtained from calorimetric measurements (to less than 1 cal mol−1 K−1 below 300 K), with deviations at higher temperatures indicating anharmonicity. Standard uncertainties and correlation of the refined parameters have been derived based on a Monte Carlo procedure. The uncertainties are quite small and probably underestimated.

ADDIE: ADvanced DIffraction Environment – a software environment for analyzing neutron diffraction data

Abstract: ADDIE is a software environment that aims to provide an intuitive graphical user interface for executing, managing, and visualizing total scattering neutron powder diffraction data. ADDIE is the current data reduction software being developed and used at the Nanoscale-Ordered Materials Diffractometer (NOMAD)[1], a time-of-flight powder diffractometer at the Spallation Neutron Source (SNS) at Oak Ridge National Laboratory. In ADDIE, the user is provided with a workflow that begins with selection of standard, normalization, and background datasets for sample data corrections. Options are available to perform inelastic (Placzek), absorption, and multiple scattering data corrections. After initial data reduction of individual runs, the user can analyze datasets and perform summing of selected runs to provide datasets of better statistical significance. From the summed spectrum, the user can visualize the by-bank Bragg peak data to determine the average structure of materials while simultaneously visualizing the S(Q) and G(r) data. Finally, the user can output the optimized spectra to different file formats that feed into multiple data modelling programs. One of the major goals of ADDIE is to deliver an accessible, simultaneous view of Bragg data, the total scattering structure factor S(Q), and the pair distribution function G(r) for data analysis. Another major goal is ease of optimization of the Fourier transform from S(Q) to G(r) via pre-defined filter functions and adjustable limits on Qmin and Qmax. A Python interface is integrated into the visualization window with the Mantid framework[2] to provide the ability for user-defined extensions and manipulations of the datasets. The current development of ADDIE is directed towards the ability to access metadata of datasets from multiple databases at the SNS; filtering neutron events by certain sample conditions to aid in in-situ experiments; provide input files for other data reduction software for benchmarking and comparison; and increase the portfolio of output formats to support different data modelling software. Overall, ADDIE aims to deliver an optimal user experience, increase the connectivity between data reduction and modelling software, and to optimize the data analysis process in neutron diffraction experiments. [1] J. Neuefeind, M. Feygenson, J. Carruth, R. Hoffman, and K. K. Chipley. The Nanoscale Ordered MAterials Diffractometer NOMAD at the Spallation Neutron Source SNS. Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms. 287:68-75, 2012. [2] O. Arnolda, b, J.C. Bilheuxc, J.M. Borregueroc, A. Butsa, S.I. Campbellc, L. Chapona, d, M. Doucetc, N. Drapera, b, R. Ferraz Leald, M.A. Gigga, b, V.E. Lynchc, A. Markvardsena, D.J. Mikkelsone, c, R.L. Mikkelsone, c, R. Millerf, K. Palmena, P. Parkera, G. Passosa, T.G. Perringa, P.F. Petersonc, S. Renc, M.A. Reuterc, A.T. Savicic, , , J.W. Taylora, R.J. Taylorc, g, R. Tolchenova, b, W. Zhouc, J. Zikovskyc.. Mantid—Data analysis and visualization package for neutron scattering and μSR experiments. Equipment. 764:156-166, 2014. Acta Cryst. (2017). A73, a377

High-resolution X-ray diffraction with no sample preparation

Abstract: It is shown that energy-dispersive X-ray diffraction (EDXRD) implemented in a back-reflection geometry is extremely insensitive to sample morphology and positioning even in a high-resolution configuration. This technique allows high-quality X-ray diffraction analysis of samples that have not been prepared and is therefore completely non-destructive. The experimental technique was implemented on beamline B18 at the Diamond Light Source synchrotron in Oxfordshire, UK. The majority of the experiments in this study were performed with pre-characterized geological materials in order to elucidate the characteristics of this novel technique and to develop the analysis methods. Results are presented that demonstrate phase identification, the derivation of precise unit-cell parameters and extraction of microstructural information on unprepared rock samples and other sample types. A particular highlight was the identification of a specific polytype of a muscovite in an unprepared mica schist sample, avoiding the time-consuming and difficult preparation steps normally required to make this type of identification. The technique was also demonstrated in application to a small number of fossil and archaeological samples. Back-reflection EDXRD implemented in a high-resolution configuration shows great potential in the crystallographic analysis of cultural heritage artefacts for the purposes of scientific research such as provenancing, as well as contributing to the formulation of conservation strategies. Possibilities for moving the technique from the synchrotron into museums are discussed. The avoidance of the need to extract samples from high-value and rare objects is a highly significant advantage, applicable also in other potential research areas such as palaeontology, and the study of meteorites and planetary materials brought to Earth by sample-return missions.

Structural basis of protein translocation by the Vps4-Vta1 AAA ATPase

Abstract: Many important cellular membrane fission reactions are driven by ESCRT pathways, which culminate in disassembly of ESCRTIII polymers by the AAA ATPase Vps4. We report a 4.3Å resolution cryo-EM structure of the active Vps4 hexamer with its cofactor Vta1, ADP·BeFx, and an ESCRT-III substrate peptide. Four Vps4 subunits form a helix whose interfaces are consistent with ATP-binding, is stabilized by Vta1, and binds the substrate peptide. The fifth subunit approximately continues this helix but appears to be dissociating. The final Vps4 subunit completes a notched-washer configuration as if transitioning between the ends of the helix. We propose that ATP binding propagates growth at one end of the helix while hydrolysis promotes disassembly at the other end, so that Vps4 “walks” along ESCRT-III until it encounters the ordered N-terminal domain to destabilize the ESCRT-III lattice. This model may be generally applicable to other protein-translocating AAA ATPases.

The phase problem for one-dimensional crystals.

Abstract: The phase problem for diffraction amplitudes measured from a one-dimensional crystal is examined. In the absence of any a priori information, the solution to this problem is shown to be unique up to a parameterized, low-dimensional set of solutions. Minimal additional a priori information is expected to render the solution unique. The effects of additional information such as positivity, molecular envelope and helical symmetry on uniqueness are characterized. The results are pertinent to structural studies of polymeric and rod-like biomolecular assemblies that form one-dimensional, rather than three-dimensional, crystals. This shows the potential for ab initio phasing of diffraction data from single such assemblies measured using new X-ray free-electron laser sources. Such an approach would circumvent the complicated inversion of cylindrically averaged diffraction that is necessary in traditional X-ray fibre diffraction analysis.

Hard-sphere displacive model of deformation twinning in hexagonal close-packed metals. Revisiting the case of the (56°, a) contraction twins in magnesium.

Abstract: Contraction twinning in magnesium alloys leads to new grains that are misoriented from the parent grain by a rotation (56°, a). The classical shear theory of deformation twinning does not specify the atomic displacements and does not explain why contraction twinning is less frequent than extension twinning. The paper proposes a new displacive model in line with our previous work on martensitic transformations and extension twinning. A continuous angular distortion matrix that transforms the initial hexagonal close-packed (h.c.p.) crystal into a final h.c.p. crystal is determined such that the atoms move as hard spheres and reach the final positions expected by the orientation relationship. The calculations prove that the distortion is not a simple shear when it is considered in its continuity. The ({0{\overline 1}1}) plane is untilted and restored, but it is not fully invariant because some interatomic distances in this plane evolve during the distortion process; the unit volume also increases up to 5% before coming back to its initial value when the twinning distortion is complete. Then, the distortion takes the form of a simple shear on the ({0{\overline 1}1}) plane with a shear along the direction [{18,{\overline 5},{\overline 5}}] of amplitude 0.358. Experiments are proposed to validate or disprove the model.

Asymmetry in serial femtosecond crystallography data

Abstract: Serial crystallography is an increasingly important approach to protein crystallography that exploits both X-ray free-electron laser (XFEL) and synchrotron radiation. Serial crystallography recovers complete X-ray diffraction data by processing and merging diffraction images from thousands of randomly oriented non-uniform microcrystals, of which all observations are partial Bragg reflections. Random fluctuations in the XFEL pulse energy spectrum, variations in the size and shape of microcrystals, integrating over millions of weak partial observations and instabilities in the XFEL beam position lead to new types of experimental errors. The quality of Bragg intensity estimates deriving from serial crystallography is therefore contingent upon assumptions made while modeling these data. Here it is observed that serial femtosecond crystallography (SFX) Bragg reflections do not follow a unimodal Gaussian distribution and it is recommended that an idealized assumption of single Gaussian peak profiles be relaxed to incorporate apparent asymmetries when processing SFX data. The phenomenon is illustrated by re-analyzing data collected from microcrystals of the Blastochloris viridis photosynthetic reaction center and comparing these intensity observations with conventional synchrotron data. The results show that skewness in the SFX observations captures the essence of the Wilson plot and an empirical treatment is suggested that can help to separate the diffraction Bragg intensity from the background.

Atomic structure of granulin determined from native nanocrystalline granulovirus using an X-ray free-electron laser

Abstract: 57 To understand how molecules function in biological systems, new methods are required to obtain 58 atomic resolution structures from biological material under physiological conditions. Intense 59 femtosecond-duration pulses from X-ray free-electron lasers (XFELs) can outrun most damage 60 3 processes, vastly increasing the tolerable dose before the specimen is destroyed. This in turn allows 61 structure determination from crystals much smaller and more radiation sensitive than previously 62 considered possible, allowing data collection from room temperature structures and avoiding structural 63 changes due to cooling. Regardless, high-resolution structures obtained from XFEL data mostly use 64 crystals far larger than 1 3 in volume, while the X-ray beam is often attenuated to protect the 65 detector from damage caused by intense Bragg spots. Here, we describe the 2 Å resolution structure of 66 native nanocrystalline granulovirus occlusion bodies (OBs) that are less than 0.016 3 in volume 67 using the full power of the Linac Coherent Light Source (LCLS) and a dose up to 1.3 GGy per crystal. 68 The crystalline shell of granulovirus OBs consists, on average, of about 9,000 unit cells, representing 69 the smallest protein crystals to yield a high-resolution structure by X-ray crystallography to date. The 70 XFEL structure shows little to no evidence of radiation damage and is more complete than a model 71 determined using synchrotron data from recombinantly produced, much larger, cryo-cooled 72 granulovirus granulin microcrystals. Our measurements suggest that it should be possible, under ideal 73 experimental conditions, to obtain data from protein crystals with only 100 unit cells in volume using 74 currently available XFELs and suggest that single-molecule imaging of individual biomolecules could 75 almost be within reach. 76

RCSB Protein Data Bank: structural biology views for basic and applied research

Abstract: Users can perform simple searches from the top search bar (e.g., ID, name, sequence, ligand) or build complex combinations of search parameters using Advanced Search. Information from DrugBank is integrated with PDB data to facilitate searches for drugs and drug targets. Other classification systems are used to organize PDB structures in hierarchical trees for browsing and searching (e.g., mpstruc, Gene Ontology, Enzyme Classification).

Edge-2-transitive trinodal polyhedra and 2-periodic tilings.

Abstract: All trinodal, edge-2-transitive polyhedra and 2-periodic tilings are enumerated and described. These are of special interest for the design and synthesis of materials such as metal-organic polyhedra and frameworks.

Macromolecular structure determination using X-ray FELs

Abstract: The pulses from X-ray free-electron lasers are a billion times brighter than the brightest synchrotron beams available today. When focused to micron dimensions, such a pulse destroys any material, but if the pulse is short enough then the effect on the scattering pattern due to this interaction can be avoided. This mode of “diffraction before destruction” yields high-resolution structural information from proteins that cannot be grown into large enough crystals or are too radiation sensitive for high-resolution crystallography [1]. This has opened up a new methodology of serial femtosecond crystallography for radiation damage-free structures without the need for cryogenic cooling of the sample. The ability to record diffraction of biological materials using extremely intense and spatially coherent X-ray pulses has also been of interest for imaging non-crystalline samples, such as virus particles and single molecules [2]. Such singleparticle imaging is being developed but is challenging due to the very low signal levels (compared to background sources) of tiny non-crystalline particles. There is a very significant advantage of measuring continuous diffraction from non-crystalline objects since it contains vastly more information than is encoded by the Bragg peaks in diffraction patterns of crystals. The increase in information makes it possible to directly determine the diffraction phases, overcoming the well-known phase problem in crystallography.

A general algorithm for generating isotropy subgroups in superspace

Abstract: This paper presents a general algorithm for generating the isotropy subgroups of superspace extensions of crystallographic space groups involving arbitrary superpositions of multi-k order parameters from incommensurate and commensurate k vectors. Several examples are presented in detail in order to illuminate each step of the algorithm. The practical outcome is that one can now start with any commensurate parent crystal structure and generate a structure model for any conceivable incommensurate modulation of that parent, fully parameterized in terms of order parameters of irreducible representations at the relevant wavevectors. The resulting modulated structures have (3 + d)-dimensional superspace-group symmetry. Because incommensurate structures are now commonly encountered in the context of many scientifically and technologically important functional materials, the opportunity to apply the powerful methods of group representation theory to this broader class of structural distortions is very timely.