Classification and assessment of retrieved electron density maps in coherent X-ray diffraction imaging using multivariate analysis

Similarity score for screening phase-retrieved maps in X-ray diffraction imaging - characterization in reciprocal space

X-ray diffraction imaging (XDI) is utilized for visualizing the structures of non-crystalline particles in material sciences and biology. In the structural analysis, phase-retrieval (PR) algorithms are applied to the diffraction amplitude data alone to reconstruct the electron density map of a specimen particle projected along the direction of the incident X-rays. However, PR calculations may not lead to good convergence because of a lack of diffraction patterns in small-angle regions and Poisson noise in X-ray detection. Therefore, the PR calculation is still a bottleneck for the efficient application of XDI in the structural analyses of non-crystalline particles. For screening maps from hundreds of trial PR calculations, we have been using a score and measuring the similarity between a pair of retrieved maps. Empirically, probable maps approximating the particle structures gave a score smaller than a threshold value, but the reasons for the effectiveness of the score are still unclear. In this study, the score is characterized in terms of the phase differences between the structure factors of the retrieved maps, the usefulness of the score in screening the maps retrieved from experimental diffraction patterns is demonstrated, and the effective resolution of similarity-score-selected maps is discussed.

Protocol using similarity score and improved shrink-wrap algorithm for better convergence of phase-retrieval calculation in X-ray diffraction imaging

In X-ray diffraction imaging (XDI), electron density maps of a targeted particle are reconstructed computationally from the diffraction pattern alone using phase-retrieval (PR) algorithms. However, the PR calculations sometimes fail to yield realistic electron density maps that approximate the structure of the particle. This occurs due to the absence of structure amplitudes at and near the zero-scattering angle and the presence of Poisson noise in weak diffraction patterns. Consequently, the PR calculation becomes a bottleneck for XDI structure analyses. Here, a protocol to efficiently yield realistic maps is proposed. The protocol is based on the empirical observation that realistic maps tend to yield low similarity scores, as suggested in our prior study [Sekiguchi et al. (2017), J. Synchrotron Rad. 24, 1024-1038]. Among independently and concurrently executed PR calculations, the protocol modifies all maps using the electron-density maps exhibiting low similarity scores. This approach, along with a new protocol for estimating particle shape, improved the probability of obtaining realistic maps for diffraction patterns from various aggregates of colloidal gold particles, as compared with PR calculations performed without the protocol. Consequently, the protocol has the potential to reduce computational costs in PR calculations and enable efficient XDI structure analysis of non-crystalline particles using synchrotron X-rays and X-ray free-electron laser pulses.

Ultrastructure and fractal property of chromosomes in close-to-native yeast nuclei visualized using X-ray laser diffraction

Genome compaction and activity in the nucleus depend on spatiotemporal changes in the organization of chromatins in chromosomes. However, the direct imaging of the chromosome structures in the nuclei has been difficult and challenging. Herein, we directly visualized the structure of chromosomes in frozen-hydrated nuclei of budding yeast in the interphase using X-ray laser diffraction. The reconstructed projection electron density maps revealed inhomogeneous distributions of chromosomes, such as a 300 nm assembly and fibrous substructures in the elliptic-circular shaped nuclei of approximately 800 nm. In addition, from the diffraction patterns, we confirmed the absence of regular arrangements of chromosomes and chromatins with 400-20 nm spacing, and demonstrated that chromosomes were composed of self-similarly assembled substructural domains with an average radius of gyration of 58 nm and smooth surfaces. Based on these analyses, we constructed putative models to discuss the organization of 16 chromosomes, carrying DNA of 4.1 mm in 800 nm ellipsoid of the nucleus at the interphase. We anticipate the structural parameters on the fractal property of chromosomes and the experimental images to be a starting point for constructing more sophisticated 3D structural models of the nucleus.

Quantitative analysis of the effect of radiation on mitochondria structure using coherent diffraction imaging with a clustering algorithm

Radiation damage and a low signal-to-noise ratio are the primary factors that limit spatial resolution in coherent diffraction imaging (CDI) of biomaterials using X-ray sources. Introduced here is a clustering algorithm named ConvRe based on deep learning, and it is applied to obtain accurate and consistent image reconstruction from noisy diffraction patterns of weakly scattering biomaterials. To investigate the impact of X-ray radiation on soft biomaterials, CDI experiments were performed on mitochondria from human embryonic kidney cells using synchrotron radiation. Benefiting from the new algorithm, structural changes in the mitochondria induced by X-ray radiation damage were quantitatively characterized and analysed at the nanoscale with different radiation doses. This work also provides a promising approach for improving the imaging quality of biomaterials with XFEL-based plane-wave CDI.

Common architectures in cyanobacteria Prochlorococcus cells visualized by X-ray diffraction imaging using X-ray free electron laser

Visualization of intracellular structures and their spatial organization inside cells without any modification is essential to understand the mechanisms underlying the biological functions of cells. Here, we investigated the intracellular structure of cyanobacteria Prochlorococcus in the interphase by X-ray diffraction imaging using X-ray free-electron laser. A number of diffraction patterns from single cells smaller than 1 µm in size were collected with high signal-to-noise ratio with a resolution of up to 30 nm. From diffraction patterns, a set of electron density maps projected along the direction of the incident X-ray were retrieved with high reliability. The most characteristic structure found to be common among the cells was a C-shaped arrangement of 100-nm sized high-density spots, which surrounded a low-density area of 100 nm. Furthermore, a three-dimensional map reconstructed from the projection maps of individual cells was non-uniform, indicating the presence of common structures among cyanobacteria cells in the interphase. By referring to the fluorescent images for distributions of thylakoid membranes, nucleoids, and carboxysomes, we inferred and represented their spatial arrangements in the three-dimensional map. The arrangement allowed us to discuss the relevance of the intracellular organization to the biological functions of cyanobacteria.

Methods and application of coherent X-ray diffraction imaging of noncrystalline particles

Microscopic imaging techniques have been developed to visualize events occurring in biological cells. Coherent X-ray diffraction imaging is one of the techniques applicable to structural analyses of cells and organelles, which have never been crystallized. In the experiment, a single noncrystalline particle is illuminated by an X-ray beam with almost complete spatial coherence. The structure of the particle projected along the direction of the beam is, in principle, retrieved from a finely recorded diffraction pattern alone by using iterative phase-retrieval algorithms. Here, we describe fundamental theory and experimental methods of coherent X-ray diffraction imaging and the recent application in structural studies of noncrystalline specimens by using X-rays available at Super Photon Ring of 8-Gev and SPring-8 Angstrom Compact Free Electron Laser in Japan.

Diffraction apparatus and procedure in tomography X-ray diffraction imaging for biological cells at cryogenic temperature using synchrotron X-ray radiation

X-ray diffraction imaging is a technique for visualizing the structure of biological cells. In X-ray diffraction imaging experiments using synchrotron radiation, cryogenic conditions are necessary in order to reduce radiation damage in the biological cells. Frozen-hydrated biological specimens kept at cryogenic temperatures are also free from drying and bubbling, which occurs in wet specimens under vacuum conditions. In a previous study, the diffraction apparatus KOTOBUKI-1 [Nakasako et al. (2013), Rev. Sci. Instrum. 84, 093705] was constructed for X-ray diffraction imaging at cryogenic temperatures by utilizing a cryogenic pot, which is a cooling device developed in low-temperature physics. In this study a new cryogenic pot, suitable for tomography experiments, has been developed. The pot can rotate a biological cell over an angular range of ±170° against the direction of the incident X-ray beam. Herein, the details and the performance of the pot and miscellaneous devices are reported, along with established experimental procedures including specimen preparation. The apparatus has been used in tomography experiments for visualizing the three-dimensional structure of a Cyanidioschyzon merolae cell with an approximate size of 5 µm at a resolution of 136 nm. Based on the experimental results, the necessary improvements for future experiments and the resolution limit achievable under experimental conditions within a maximum tolerable dose are discussed.

Growth of Cuprous Oxide Particles in Liquid-Phase Synthesis Investigated by X-ray Laser Diffraction

Cuprous oxide (Cu₂O) particles obtained by surfactant-assisted liquid-phase synthesis have cuboid shapes but the internal structures are difficult to be visualized by electron microscopy. Herein, we investigated the internal structures of numerous individual Cu₂O particles with submicrometer dimensions by X-ray diffraction imaging (XDI) using X-ray free-electron laser (XFEL) pulses. The reconstructed two-dimensional electron density maps, which displayed inhomogeneous internal structures, were divided into five classes characterized by the positions and shapes of high and low electron density areas. Further analysis of the maps in each class by a manifold learning algorithm revealed that the internal structures of Cu₂O particles varied in correlation with total electron density while retaining the characteristics within each class. On the basis of the analyses, we proposed a growth mechanism to yield the inhomogeneity in the internal structures of Cu₂O particles in surfactant-mediated liquid-phase synthesis.

Atmospheric coherent X-ray diffraction imaging for in situ structural analysis at SPring-8 Hyogo beamline BL24XU

Coherent X-ray diffraction imaging (CXDI) is a promising technique for non-destructive structural analysis of micrometre-sized non-crystalline samples at nanometre resolutions. This article describes an atmospheric CXDI system developed at SPring-8 Hyogo beamline BL24XU for in situ structural analysis and designed for experiments at a photon energy of 8 keV. This relatively high X-ray energy enables experiments to be conducted under ambient atmospheric conditions, which is advantageous for the visualization of samples in native states. The illumination condition with pinhole-slit optics is optimized according to wave propagation calculations based on the Fresnel-Kirchhoff diffraction formula so that the sample is irradiated by X-rays with a plane wavefront and high photon flux of ∼1 × 10¹⁰ photons/16 µmø(FWHM)/s. This work demonstrates the imaging performance of the atmospheric CXDI system by visualizing internal voids of sub-micrometre-sized colloidal gold particles at a resolution of 29.1 nm. A CXDI experiment with a single macroporous silica particle under controlled humidity was also performed by installing a home-made humidity control device in the system. The in situ observation of changes in diffraction patterns according to humidity variation and reconstruction of projected electron-density maps at 5.2% RH (relative humidity) and 82.6% RH at resolutions of 133 and 217 nm, respectively, were accomplished.

A protocol for searching the most probable phase-retrieved maps in coherent X-ray diffraction imaging by exploiting the relationship between convergence of the retrieved phase and success of calculation

Coherent X-ray diffraction imaging (CXDI) is a technique for visualizing the structures of non-crystalline particles with size in the submicrometer to micrometer range in material sciences and biology. In the structural analysis of CXDI, the electron density map of a specimen particle projected along the direction of the incident X-rays can be reconstructed only from the diffraction pattern by using phase-retrieval (PR) algorithms. However, in practice, the reconstruction, relying entirely on the computational procedure, sometimes fails because diffraction patterns miss the data in small-angle regions owing to the beam stop and saturation of the detector pixels, and are modified by Poisson noise in X-ray detection. To date, X-ray free-electron lasers have allowed us to collect a large number of diffraction patterns within a short period of time. Therefore, the reconstruction of correct electron density maps is the bottleneck for efficiently conducting structure analyses of non-crystalline particles. To automatically address the correctness of retrieved electron density maps, a data analysis protocol to extract the most probable electron density maps from a set of maps retrieved from 1000 different random seeds for a single diffraction pattern is proposed. Through monitoring the variations of the phase values during PR calculations, the tendency for the PR calculations to succeed when the retrieved phase sets converged on a certain value was found. On the other hand, if the phase set was in persistent variation, the PR calculation tended to fail to yield the correct electron density map. To quantify this tendency, here a figure of merit for the variation of the phase values during PR calculation is introduced. In addition, a PR protocol to evaluate the similarity between a map of the highest figure of merit and other independently reconstructed maps is proposed. The protocol is implemented and practically examined in the structure analyses for diffraction patterns from aggregates of gold colloidal particles. Furthermore, the feasibility of the protocol in the structure analysis of organelles from biological cells is examined.

XFELs for structure and dynamics in biology

The development and application of the free-electron X-ray laser (XFEL) to structure and dynamics in biology since its inception in 2009 are reviewed. The research opportunities which result from the ability to outrun most radiation-damage effects are outlined, and some grand challenges are suggested. By avoiding the need to cool samples to minimize damage, the XFEL has permitted atomic resolution imaging of molecular processes on the 100 fs timescale under near-physiological conditions and in the correct thermal bath in which molecular machines operate. Radiation damage, comparisons of XFEL and synchrotron work, single-particle diffraction, fast solution scattering, pump-probe studies on photosensitive proteins, mix-and-inject experiments, caged molecules, pH jump and other reaction-initiation methods, and the study of molecular machines are all discussed. Sample-delivery methods and data-analysis algorithms for the various modes, from serial femtosecond crystallo-graphy to fast solution scattering, fluctuation X-ray scattering, mixing jet experiments and single-particle diffraction, are also reviewed.

Three-dimensional reconstruction for coherent diffraction patterns obtained by XFEL

The three-dimensional (3D) structural analysis of single particles using an X-ray free-electron laser (XFEL) is a new structural biology technique that enables observations of molecules that are difficult to crystallize, such as flexible biomolecular complexes and living tissue in the state close to physiological conditions. In order to restore the 3D structure from the diffraction patterns obtained by the XFEL, computational algorithms are necessary as the orientation of the incident beam with respect to the sample needs to be estimated. A program package for XFEL single-particle analysis based on the Xmipp software package, that is commonly used for image processing in 3D cryo-electron microscopy, has been developed. The reconstruction program has been tested using diffraction patterns of an aerosol nanoparticle obtained by tomographic coherent X-ray diffraction microscopy.

Enhancing resolution in coherent x-ray diffraction imaging

Achieving a resolution near 1 nm is a critical issue in coherent x-ray diffraction imaging (CDI) for applications in materials and biology. Albeit with various advantages of CDI based on synchrotrons and newly developed x-ray free electron lasers, its applications would be limited without improving resolution well below 10 nm. Here, we review the issues and efforts in improving CDI resolution including various methods for resolution determination. Enhancing diffraction signal at large diffraction angles, with the aid of interference between neighboring strong scatterers or templates, is reviewed and discussed in terms of increasing signal-to-noise ratio. In addition, we discuss errors in image reconstruction algorithms-caused by the discreteness of the Fourier transformations involved-which degrade the spatial resolution, and suggest ways to correct them. We expect this review to be useful for applications of CDI in imaging weakly scattering soft matters using coherent x-ray sources including x-ray free electron lasers.

Common structural features of toxic intermediates from α-synuclein and GroES fibrillogenesis detected using cryogenic coherent X-ray diffraction imaging

The aggregation and deposition of α-synuclein (αSyn) in neuronal cells is correlated to pathogenesis of Parkinson's disease. Although the mechanism of αSyn aggregation and fibril formation has been studied extensively, the structural hallmarks that are directly responsible for toxicity toward cells are still under debate. Here, we have compared the structural characteristics of the toxic intermediate molecular species of αSyn and similar toxic species of another protein, GroES, using coherent X-ray diffraction analysis. Using coherent X-ray free electron laser pulses of SACLA, we analysed αSyn and GroES fibril intermediate species and characterized various aggregate structures. Unlike previous studies where an annular oligomeric form of αSyn was identified, particle reconstruction from scattering traces suggested that the specific forms of the toxic particles were varied, with the sizes of the particles falling within a specific range. We did however discover a common structural feature in both αSyn and GroES samples; the edges of the detected particles were nearly parallel and produced a characteristic diffraction pattern in the diffraction experiments. The presence of parallel-edged particles in toxic intermediates of αSyn and GroES fibrillogenesis pointed towards a plausible common molecular interface that leads to the formation of mature fibrils.

Specimen preparation for cryogenic coherent X-ray diffraction imaging of biological cells and cellular organelles by using the X-ray free-electron laser at SACLA

Coherent X-ray diffraction imaging (CXDI) allows internal structures of biological cells and cellular organelles to be analyzed. CXDI experiments have been conducted at 66 K for frozen-hydrated biological specimens at the SPring-8 Angstrom Compact Free-Electron Laser facility (SACLA). In these cryogenic CXDI experiments using X-ray free-electron laser (XFEL) pulses, specimen particles dispersed on thin membranes of specimen disks are transferred into the vacuum chamber of a diffraction apparatus. Because focused single XFEL pulses destroy specimen particles at the atomic level, diffraction patterns are collected through raster scanning the specimen disks to provide fresh specimen particles in the irradiation area. The efficiency of diffraction data collection in cryogenic experiments depends on the quality of the prepared specimens. Here, detailed procedures for preparing frozen-hydrated biological specimens, particularly thin membranes and devices developed in our laboratory, are reported. In addition, the quality of the frozen-hydrated specimens are evaluated by analyzing the characteristics of the collected diffraction patterns. Based on the experimental results, the internal structures of the frozen-hydrated specimens and the future development for efficient diffraction data collection are discussed.

TAKASAGO-6 apparatus for cryogenic coherent X-ray diffraction imaging of biological non-crystalline particles using X-ray free electron laser at SACLA

Coherent X-ray diffraction imaging (CXDI) is a technique for structure analyses of non-crystalline particles with dimensions ranging from micrometer to sub-micrometer. We have developed a diffraction apparatus named TAKASAGO-6 for use in single-shot CXDI experiments of frozen-hydrated non-crystalline biological particles at cryogenic temperature with X-ray free electron laser pulses provided at a repetition rate of 30 Hz from the SPring-8 Angstrom Compact free-electron LAser. Specimen particles are flash-cooled after being dispersed on thin membranes supported by specially designed disks. The apparatus is equipped with a high-speed translation stage with a cryogenic pot for raster-scanning of the disks at a speed higher than 25 μm/33 ms. In addition, we use devices assisting the easy transfer of cooled specimens from liquid-nitrogen storages to the cryogenic pot. In the current experimental procedure, more than 20 000 diffraction patterns can be collected within 1 h. Here we report the key components and performance of the diffraction apparatus. Based on the efficiency of the diffraction data collection and the structure analyses of metal particles, biological cells, and cellular organelles, we discuss the future application of this diffraction apparatus for structure analyses of biological specimens.

Cryogenic coherent X-ray diffraction imaging of biological samples at SACLA: a correlative approach with cryo-electron and light microscopy

Coherent X-ray diffraction imaging at cryogenic temperature (cryo-CXDI) allows the analysis of internal structures of unstained, non-crystalline, whole biological samples in micrometre to sub-micrometre dimensions. Targets include cells and cell organelles. This approach involves preparing frozen-hydrated samples under controlled humidity, transferring the samples to a cryo-stage inside a vacuum chamber of a diffractometer, and then exposing the samples to coherent X-rays. Since 2012, cryo-coherent diffraction imaging (CDI) experiments have been carried out with the X-ray free-electron laser (XFEL) at the SPring-8 Ångstrom Compact free-electron LAser (SACLA) facility in Japan. Complementary use of cryo-electron microscopy and/or light microscopy is highly beneficial for both pre-checking samples and studying the integrity or nature of the sample. This article reports the authors' experience in cryo-XFEL-CDI of biological cells and organelles at SACLA, and describes an attempt towards reliable and higher-resolution reconstructions, including signal enhancement with strong scatterers and Patterson-search phasing.