Individual Diffraction Patterns Research Articles

Data reduction for serial crystallography using a robust peak finder.

A peak-finding algorithm for serial crystallography (SX) data analysis based on the principle of 'robust statistics' has been developed. Methods which are statistically robust are generally more insensitive to any departures from model assumptions and are particularly effective when analysing mixtures of probability distributions. For example, these methods enable the discretization of data into a group comprising inliers (i.e. the background noise) and another group comprising outliers (i.e. Bragg peaks). Our robust statistics algorithm has two key advantages, which are demonstrated through testing using multiple SX data sets. First, it is relatively insensitive to the exact value of the input parameters and hence requires minimal optimization. This is critical for the algorithm to be able to run unsupervised, allowing for automated selection or 'vetoing' of SX diffraction data. Secondly, the processing of individual diffraction patterns can be easily parallelized. This means that it can analyse data from multiple detector modules simultaneously, making it ideally suited to real-time data processing. These characteristics mean that the robust peak finder (RPF) algorithm will be particularly beneficial for the new class of MHz X-ray free-electron laser sources, which generate large amounts of data in a short period of time.

Protocol for Retrieving Three-Dimensional Biological Shapes for a Few XFEL Single-Particle Diffraction Patterns.

X-ray free-electron laser (XFEL) scattering promises to probe single biomolecular complexes without crystallization, enabling the study of biomolecular structures under near-physiological conditions at room temperature. However, such structural determination of biomolecules is extremely challenging thus far. In addition to the large numbers of diffraction patterns required, the orientation of each diffraction pattern needs to be accurately estimated and the missing phase information needs to be recovered for three-dimensional (3D) structure reconstruction. Given the current limitations to the amount and resolution of the data available from single-particle XFEL scattering experiments, we propose an alternative approach to find plausible 3D biological shapes from a limited number of diffraction patterns to serve as a starting point for further analyses. In our proposed strategy, small sets of input (e.g., five) XFEL diffraction patterns were matched against a library of diffraction patterns simulated from 1628 electron microscopy (EM) models to find potential matching 3D models that are consistent with the input diffraction patterns. This approach was tested for three example cases: EMD-3457 (Thermoplasma acidophilum 20S proteasome), EMD-5141 (Escherichia coli 70S ribosome complex), and EMD-5152 (budding yeast Nup84 complex). We observed that choosing the best strategy to define matching regions on the diffraction patterns is critical for identifying correctly matching diffraction patterns. While increasing the number of input diffraction patterns improved the matches in some cases, we found that the resulting matches are more dependent on the uniqueness or complexity of the shape as captured in the individual input diffraction patterns and the availability of a similar 3D biological shape in the search library. The protocol could be useful for finding candidate models for a limited amount of low-resolution data, even when insufficient for reconstruction, performing a quick exploration of new data upon collection, and the analysis of the conformational heterogeneity of the particle of interest as captured within the diffraction patterns.

PinkIndexer - a universal indexer for pink-beam X-ray and electron diffraction snapshots.

A crystallographic indexing algorithm, pinkIndexer, is presented for the analysis of snapshot diffraction patterns. It can be used in a variety of contexts including measurements made with a monochromatic radiation source, a polychromatic source or with radiation of very short wavelength. As such, the algorithm is particularly suited to automated data processing for two emerging measurement techniques for macromolecular structure determination: serial pink-beam X-ray crystallography and serial electron crystallography, which until now lacked reliable programs for analyzing many individual diffraction patterns from crystals of uncorrelated orientation. The algorithm requires approximate knowledge of the unit-cell parameters of the crystal, but not the wavelengths associated with each Bragg spot. The use of pinkIndexer is demonstrated by obtaining 1005 lattices from a published pink-beam serial crystallography data set that had previously yielded 140 indexed lattices. Additionally, in tests on experimental serial crystallography diffraction data recorded with quasi-monochromatic X-rays and with electrons the algorithm indexed more patterns than other programs tested.

Algorithm for characterizing the subcellular structures of nanometer-sized biological specimens in a solution using x-ray free-electron lasers

Coherent diffraction imaging using third generation synchrotron sources and x-ray free-electron lasers has been demonstrated to be an excellent tool for revealing the inner structures of a single particle. The primary challenge in imaging pure, tiny, and isolated biological specimens is obtaining a reliable reconstruction from diffraction data that have a poor signal-to-noise ratio. Thus, we developed a robust method that yields the internal density distribution of liposome vesicles immersed in a solution. By combining the guided hybrid input-output method and a new order parameter defined by the consistency of the reconstruction, we, without prior knowledge, retrieved both pure and drug-containing liposome vesicles from individual diffraction patterns. This result is currently the smallest noncrystalline biological specimen resolved by single-shot coherent diffraction microscopy.

NLPAR: Non-local smoothing for enhanced EBSD pattern indexing

Due to continued advances in phosphor sensitivity and camera technology, electron backscattered diffraction (EBSD) within a scanning electron microscope (SEM) has become an increasingly popular method for determining crystal orientations within a given microstructure. Concurrent advances in computational processing have also made it possible to store each individual diffraction pattern as it is collected, which has allowed more complex algorithms to be deployed for post-processing and indexing patterns. This paper proposes a new post-processing technique for pattern enhancement that aids in re-indexing by leveraging a non-local smoothing kernel whose weights are based on the exponential decay of the Euclidean distance between patterns. The advantage of this approach is its ability to utilize very large smoothing kernels without losing integrity near interface boundaries and while still operating on timescales comparable to traditional indexing approaches. Using an Inconel 600 nickel alloy sample, the capabilities and performance of the proposed approach are compared to other indexing schemes, including neighbor pattern averaging with re-indexing (NPAR) and a dictionary-based approach. The results demonstrate that the proposed method consistently produces a higher index success rate (ISR) than NPAR and comparable ISRs to the dictionary-based approach, a method with orders-of-magnitude greater computational demands. Source code for the NLPAR algorithm is available at https://github.com/USNavalResearchLaboratory/NLPAR

Femtosecond X-ray coherent diffraction of aligned amyloid fibrils on low background graphene

Here we present a new approach to diffraction imaging of amyloid fibrils, combining a free-standing graphene support and single nanofocused X-ray pulses of femtosecond duration from an X-ray free-electron laser. Due to the very low background scattering from the graphene support and mutual alignment of filaments, diffraction from tobacco mosaic virus (TMV) filaments and amyloid protofibrils is obtained to 2.7 Å and 2.4 Å resolution in single diffraction patterns, respectively. Some TMV diffraction patterns exhibit asymmetry that indicates the presence of a limited number of axial rotations in the XFEL focus. Signal-to-noise levels from individual diffraction patterns are enhanced using computational alignment and merging, giving patterns that are superior to those obtainable from synchrotron radiation sources. We anticipate that our approach will be a starting point for further investigations into unsolved structures of filaments and other weakly scattering objects.

Direct derivation (DD) of weight fractions of individual crystalline phases from observed intensities and chemical composition data: incorporation of the DD method into the whole-powder-pattern fitting procedure

A formula for quantitative phase analysis (QPA), called the intensity–composition (IC) formula, can be used for deriving weight fractions of individual crystalline phases in a mixture from sets of observed integrated intensities, measured in a wide 2θ range, with chemical composition data [Toraya (2016). J. Appl. Cryst. 49, 1508–1516; Toraya (2017). J. Appl. Cryst. 50, 820–829]. In this study, the IC formula has been incorporated into the whole-powder-pattern fitting (WPPF) procedure to conduct QPA. The fitting function for calculating the profile intensity at each step of the scattering angle consists of three sub-functions that represent the individual component diffraction patterns. The first sub-function calculates the diffraction pattern using a set of integrated intensities, the parameter values of which are determined by the least-squares fitting of the whole-powder pattern as is usually done by the whole-powder-pattern decomposition (WPPD) method. The second sub-function uses a set of integrated intensity parameters, which are preliminarily prepared by WPPD or may be calculated from a crystal structure model. These intensity parameters, multiplied by a scale factor, are fixed at their original values while the scale factor is adjusted in WPPF. The third sub-function uses an observed or calculated diffraction pattern multiplied by a scale factor. This diffraction pattern can be fitted directly by adjusting the scale factor. Therefore, one can fit patterns consisting of heavily broadened and degraded diffraction lines, like those of clay minerals, without being concerned with the problem of peak overlap in decomposing the diffraction pattern. The IC formula uses the total sums of the intensities under the diffraction patterns of individual phases as observed data sets; therefore, it can equally treat these intensity data sets irrespective of differences in the profile models used by the three sub-functions. The three sub-functions can arbitrarily be chosen and linearly combined, and then they can simultaneously be fitted to the observed diffraction pattern of a target mixture. The capability of the above method has been demonstrated with QPA of mixtures consisting of α-quartz, albite and kaolinite. Theories of currently used QPA techniques are reviewed from a viewpoint of the present theory and they can be interpreted as being based on the same principle, whereby the total observed intensities of individual phases are divided by the standard reference intensity per unit weight.

Scratch iridescence

The surface of metal, glass and plastic objects is often characterized by microscopic scratches caused by manufacturing and/or wear. A closer look onto such scratches reveals iridescent colors with a complex dependency on viewing and lighting conditions. The physics behind this phenomenon is well understood; it is caused by diffraction of the incident light by surface features on the order of the optical wavelength. Existing analytic models are able to reproduce spatially unresolved microstructure such as the iridescent appearance of compact disks and similar materials. Spatially resolved scratches, on the other hand, have proven elusive due to the highly complex wave-optical light transport simulations needed to account for their appearance. In this paper, we propose a wave-optical shading model based on non-paraxial scalar diffraction theory to render this class of effects. Our model expresses surface roughness as a collection of line segments. To shade a point on the surface, the individual diffraction patterns for contributing scratch segments are computed analytically and superimposed coherently. This provides natural transitions from localized glint-like iridescence to smooth BRDFs representing the superposition of many reflections at large viewing distances. We demonstrate that our model is capable of recreating the overall appearance as well as characteristic detail effects observed on real-world examples.

Direct identification of monolayer rhenium diselenide by an individual diffraction pattern

In the current extensive studies of transition metal dichalcogenides (TMDCs), compared to hexagonal layered materials, like graphene, hBN and MoS2, low symmetry layered 2D crystals showed great potential for applications in anisotropic devices. Rhenium diselenide (ReSe2) has the bulk space group P1 and belongs to triclinic crystal system with a deformed cadmium iodide type structure. Here we unambiguously determined monolayer and its vertical orientation of rhenium diselenide membrane with an individual electron diffraction pattern, which could be applicable to low symmetry crystal systems, including both triclinic and monoclinic lattices, as long as their third unit-cell basis vector is not perpendicular to basal plane. Atomically resolved image from probe corrected annular dark field scanning transmission electron microscope (ADF-STEM) was employed to validate layer number. Finally, experimental results were well explained by kinematical electron diffraction theory and corresponding simulations.

Following DNA Compaction During the Cell Cycle by X-ray Nanodiffraction.

X-ray imaging of intact biological cells is emerging as a complementary method to visible light or electron microscopy. Owing to the high penetration depth and small wavelength of X-rays, it is possible to resolve subcellular structures at a resolution of a few nanometers. Here, we apply scanning X-ray nanodiffraction in combination with time-lapse bright-field microscopy to nuclei of 3T3 fibroblasts and thus relate the observed structures to specific phases in the cell division cycle. We scan the sample at a step size of 250 nm and analyze the individual diffraction patterns according to a generalized Porod's law. Thus, we obtain information on the aggregation state of the nuclear DNA at a real space resolution on the order of the step size and in parallel structural information on the order of few nanometers. We are able to distinguish nucleoli, heterochromatin, and euchromatin in the nuclei and follow the compaction and decompaction during the cell division cycle.

Measuring Protein Binding to Individual Hydrogel Nanoparticles with Single-Nanoparticle Surface Plasmon Resonance Imaging Microscopy

The specific binding and uptake of protein molecules to individual hydrogel nanoparticles is measured with real-time single-nanoparticle surface plasmon resonance imaging (SPRI) microscopy. Nanoparticles that adsorb onto chemically modified gold thin films interact with traveling surface plasmon polaritons and create individual point diffraction patterns in the SPRI microscopy differential reflectivity images. The intensity of each point diffraction pattern depends on the integrated refractive index of the nanoparticle; an increase in this single nanoparticle point diffraction intensity (Δ%RNP) is observed for nanoparticles that bind proteins. SPRI adsorption measurements can be used to measure an average increase in Δ%RNP that can be correlated with bulk dynamic light scattering measurements. Moreover, the distribution of Δ%RNP values observed for individual nanoparticles can be used to learn more about the nature of the protein–nanoparticle interaction. As a first example, the binding of the lectin Concanavalin A to 180 nm N-Isopropylacrylamide hydrogel nanoparticles that incorporate a small percentage of mannose sugar monomer units is characterized.

Quantitative anomalous powder diffraction analysis of cation disorder in kesterite semiconductors

Kesterite-type compound semiconductors, containing copper and zinc, have photovoltaic properties depending on cation distribution in the crystal structure. Anomalous diffraction allows discrimination of isoelectronic cations, in principle allowing a straightforward determination of site occupation factors from data collected at multiple energies close to the X-ray absorption edges of copper and zinc. However, extremely strong correlation between structural parameters precludes this. We present a recipe based on the direct dependency between refined occupation factors and atomic scattering power, which allows to lift the correlations and to detect issues of individual diffraction patterns or assumptions in the model, thereby allowing for reliable quantitative analysis of the Cu/Zn distribution.

Revealing the structure of stereociliary actin by X-ray nanoimaging.

Hair cell stereocilia are crucial for hearing and the sense of balance. They include an array of accurately packed, parallel actin filaments and act as levers, which transform mechanical deformation into neuronal signals. The length of vestibular stereocilia reaches several micrometers, whereas, for individual microfilaments, the diameter and therefore the characteristic length scale in the lateral direction is on the order of a few nanometers. These orders of magnitude render X-rays an ideal tool for investigating actin packing, and numerous studies on reconstituted in vitro systems have revealed important information. Here we report on the characterization of intact stereocilia using two nanoscale X-ray techniques. We use X-ray ptychography to image stereocilia with quantitative phase contrast and high dose efficiency, showing stereocilia with diameters and lengths in the expected range. We further employ X-ray nanodiffraction using a nanofocused X-ray beam on the same order of magnitude as the width of a stereocilium. Despite the small probe volume we can clearly visualize the stereocilia bundles. From the individual diffraction patterns we determine the local orientation of the actin structures and can clearly correlate them with the corresponding visible-light fluorescence images. Furthermore, azimuthal integration of individual diffraction patterns reveals distinct intensity curves, showing modulations of the signal, which reflect the relevant length scales and pronounced order in the biological system. The applied techniques are not limited to the studies on stereocilia but have the potential of being applied to many biological and soft-matter systems, in particular if a pronounced degree of order is present.

Cellular Diffraction: Scanning X-Ray Nanodiffraction from Living Cells

Cellular diffraction, or scanning x-ray nanodiffraction applied to cells, is a new technique that promises insight into cellular organization at length scales of 1–200 nm, covering the features of molecules and organelles. Filling a niche between the length scales probed by optical and electron microscopy, cellular diffraction rasters a nanofocused x-ray beam across living cells in an aqueous medium and records a two-dimensional image of, for instance, the small-angle scattering signal at each position. This results in a real-space image of the cell where the contrast is based on the average intensity of the small-angle x-ray scattering (SAXS) signal (dark-field image), or phase contrast, or other modalities such as the x-ray fluorescence intensity, with spatial resolution determined by the step-size of the raster scan ranging from submicron to a few microns. But the individual diffraction patterns can also be analyzed, providing higher-resolution limited by the signal/noise of the scattering pattern, currently ∼6 nm. With the cells bound to a solid support, the SAXS patterns do not result from isotropic averaging of the scatterers, and no staining or labeling is required for the technique. The development of cellular diffraction is spearheaded by two groups from the Institute for X-Ray Physics at the University of Gottingen, led by Sarah Koster and Tim Salditt, who exploit recent advances in x-ray detectors, x-ray optics, and microfluidics in order to apply scanning SAXS imaging (1) to hydrated, living cells and address subcellular dimensions. In a collaborative first effort at beamline ID13 of the European Synchrotron Radiation Facility, they imaged freeze-dried epithelial cells and saw distinctive scattering from the network of keratin fibers in the cell (2). More recent work using a specially developed instrument and beamline P10 of PETRA III imaged both fixed and live cells. The Koster team, together with collaborators from the European Synchrotron Radiation Facility, HASYLAB, and Ghent University, observed that the azimuthally averaged SAXS signal from the cells follows a power-law decay, with different exponents for living and fixed cells (3). Moreover, the scattering decays more rapidly after repeated exposure, so the value of the exponent serves as a diagnostic for beam damage in the sample. This issue of the Biophysical Journal contains a report from the Salditt team and collaborators from the Max Planck Institute for Dynamics and Self-Organization about their studies on living and fixed amoeboid cells (4), one which provides the best realization yet of the full potential of this exciting new technique. Chemotaxis in amoeboids is accomplished by extending pseudopods with controlled polymerization of actin fibers and the retraction of receding edges by depolymerization of actin and contraction of myosin motor proteins, but the details of the actin networks remain unknown. The molecular signature of this mechanism is revealed by cellular diffraction, which shows highly anisotropic scattering streaks resulting from oriented fiber bundles in the periphery of the cell. Using an automated algorithm to convert this anisotropy to a contrast neatly outlines the advancing edges of the cell. Further modeling of the scattering streaks is necessary to characterize quantitatively the nature of the fiber bundles that give rise to the SAXS signal, but the richness of the data should allow the extraction of meaningful parameters such as the number of fibers in the bundle, their spacing, and the density of cross-links. The authors note that their data and instrument are both complementary to and compatible with x-ray coherent diffraction imaging, so that with suitable modifications, users could first apply coherent diffraction imaging to image the whole cell and then scanning nanodiffraction to examine particular regions in greater detail. Indeed, the team has already demonstrated this approach by examining freeze-dried bacterial cells with both ptychography and cellular diffraction at the coherent SAXS beamline of the Swiss Light Source (5). With the synchrotron community preparing for fourth-generation facilities that approach the diffraction limit, which will greatly improve the coherence of the x-ray beam and the ability to focus the beam (6), cellular diffraction will surely grow in application and impact.

Scanning electron microscopy and transmitted electron backscatter diffraction examination of asbestos standard reference materials, amphibole particles of differing morphology, and particle phase discrimination from talc ores.

Since 1972, when the US Occupational Health and Safety Administration established the first limits on occupational exposure to asbestos fibers, numerous analytical methods employing several microscopy techniques have been developed to identify a group of minerals defined by legislation as asbestos. While transmission electron microscopy (TEM) is implemented in standardized analytical methods, these methods specify the use of selected area electron diffraction. Because of this constraint, the diffraction data a TEM can provide are often underutilized due to challenges associated with collecting and interpreting individual diffraction patterns. It has been shown that transmission electron backscatter diffraction (tEBSD) produces diffraction patterns nearly identical to electron backscatter diffraction, but from smaller crystal domains. This paper explores the utility of tEBSD for characterization of asbestiform particles from reference asbestos materials, a suite of amphibole minerals of varying morphologies to determine if there is a correlation between mineral habit (i.e., crystal form), microscopic particle shape preferred orientation, and mineral specimens from an industrial talc deposit to provide a case study of the utility and limitations of the technique.

MicroED: Three Dimensional Electron Crystallography of Protein Micro-Crystals

We demonstrate that it is feasible to determine high-resolution protein structures by electron crystallography of three-dimensional crystals in an electron cryo-microscope (CryoEM). Lysozyme microcrystals were frozen on an electron microscopy grid, and electron diffraction data collected to 1.7Å resolution. We developed a data collection protocol to collect a full-tilt series in electron diffraction to atomic resolution. A single tilt series contains up to 90 individual diffraction patterns collected from a single crystal with tilt angle increment of 0.1 - 10and a total accumulated electron dose less than 10 electrons per angstrom squared. We indexed the data from three crystals and used them for structure determination of lysozyme by molecular replacement followed by crystallographic refinement to 2.9Å resolution. In this seminar I will present our initial proof of principle study and highlight the major advances since the first publication.

Processing method for near-field in-line holograms (Fresnel number ≥1)

Liquid–liquid extraction is used in many industrial processes. Such processes involve liquid–liquid flows, called emulsions, which can be successfully characterized by especially suited holographic techniques. Because the droplets are millimeter size, a near-field diffraction regime is observed. This regime departs from conventional holography and requires adapted numerical solutions. Due to droplets transparency, positioning could not be achieved by usual focusing methods based on research of singularities. The only suitable method is based on calculating an indicator. To be effective a segmentation of the image into individual diffraction patterns is needed. As initial reconstruction can lead to errors, to further improve robustness, the hologram restitution is checked, and then the four parameters, radius and position, are optimized to fit the acquired hologram. If some missing droplets are found, they are identified and included. As a result about slightly less than twice as many drops are included, leading to a shadow density of 20%. Outlooks are regarding the adaptation to cylindrical geometry of industrial columns and a two channel system to improve the maximum hold-up to be measured.

Three-dimensional electron crystallography of protein microcrystals

We demonstrate that it is feasible to determine high-resolution protein structures by electron crystallography of three-dimensional crystals in an electron cryo-microscope (CryoEM). Lysozyme microcrystals were frozen on an electron microscopy grid, and electron diffraction data collected to 1.7 Å resolution. We developed a data collection protocol to collect a full-tilt series in electron diffraction to atomic resolution. A single tilt series contains up to 90 individual diffraction patterns collected from a single crystal with tilt angle increment of 0.1-1° and a total accumulated electron dose less than 10 electrons per angstrom squared. We indexed the data from three crystals and used them for structure determination of lysozyme by molecular replacement followed by crystallographic refinement to 2.9 Å resolution. This proof of principle paves the way for the implementation of a new technique, which we name 'MicroED', that may have wide applicability in structural biology. DOI: http://dx.doi.org/10.7554/eLife.01345.001.

X-ray nano-diffraction on cytoskeletal networks

The nano-scale structure of cytoskeletal biopolymers as well as sophisticated superstructures determine the versatile cellular shapes and specific mechanical properties. One example is keratin intermediate filaments in epithelial cells, which form thick bundles that can further organize in a cross-linked network. To study the native structure of keratin bundles in whole cells, high-resolution techniques are required, which do at the same time achieve high penetration depths. We employ scanning x-ray diffraction using a nano-focused x-ray beam to study the structure of keratin in freeze-dried eukaryotic cells. By scanning the sample through the beam we obtain x-ray dark-field images with a resolution of the order of the beam size, which clearly show the keratin network. Each individual diffraction pattern is further analyzed to yield insight into the local sample structure, which allows us to determine the local structure orientation. Due to the small beam size we access the structure in a small sample volume without performing the ensemble average over one complete cell.

Introducing an Optimized Method for Obtaining X-ray Diffraction Patterns of Biological Tissues

Introduction Individual X-Ray diffraction patterns of biological tissues are obtained via interference of coherent scattering with their electrons. Many scientists have distinguished normal and cancerous breast tissue, bone density, and urinary stone types using the X-Ray diffraction patterns resulting from coherent scattering. The goal of this study was to introduce an optimized method for obtaining X-ray diffraction patterns of different types from biological tissues. Materials and Methods A special tool constituting primary and scatter collimators as well as a sample holder was designed and built. All measurements were done using an X-ray tube, the above-mentioned tool, and a semiconductor detector (HPGe). The X-ray diffraction patterns of some tissue-equivalent materials (acrylic, polyethylene, nylon, and calcium carbonate) and biological tissues (adipose, muscle, and bone) were obtained. Results The corresponding peak positions for adipose, muscle, bone, acrylic, polyethylene, nylon, and calcium carbonate in corresponding X-ray diffraction patterns are located in 1.1±0.055 nm-1, 1.41±0.072, 1.6±0.08 nm-1, 0.8±0.04 nm-1, 1.03±0.051 nm-1, 1.22±0.061 nm-1, and 1.7 ± 0.085 nm-1, respectively. Conclusion The X-ray diffraction patterns obtained in this study were in good agreement relative to previous measurements in terms of peak position. This study introduces a useful setup for extraction of X-ray diffraction patterns from different biological tissues.