Fluctuation x-ray scattering from biological particles in frozen solution by using synchrotron radiation

A workflow for single-particle structure determination via iterative phasing of rotational invariants in fluctuation X-ray scattering

Fluctuation X-ray scattering (FXS) offers a complementary approach for nano- and bioparticle imaging with an X-ray free-electron laser (XFEL), by extracting structural information from correlations in scattered XFEL pulses. Here a workflow is presented for single-particle structure determination using FXS. The workflow includes procedures for extracting the rotational invariants from FXS patterns, performing structure reconstructions via iterative phasing of the invariants, and aligning and averaging multiple reconstructions. The reconstruction pipeline is implemented in the open-source software xFrame and its functionality is demonstrated on several simulated structures.

Structure determination using high-order spatial correlations in single-particle X-ray scattering

Single-particle imaging using X-ray free-electron lasers (XFELs) is a promising technique for observing nanoscale biological samples under near-physiological conditions. However, as the sample's orientation in each diffraction pattern is unknown, advanced algorithms are required to reconstruct the 3D diffraction intensity volume and subsequently the sample's density model. While most approaches perform 3D reconstruction via determining the orientation of each diffraction pattern, a correlation-based approach utilizes the averaged spatial correlations of diffraction intensities over all patterns, making it well suited for processing experimental data with a poor signal-to-noise ratio of individual patterns. Here, a method is proposed to determine the 3D structure of a sample by analyzing the double, triple and quadruple spatial correlations in diffraction patterns. This ab initio method can reconstruct the basic shape of an irregular unsymmetric 3D sample without requiring any prior knowledge of the sample. The impact of background and noise on correlations is investigated and corrected to ensure the success of reconstruction under simulated experimental conditions. Additionally, the feasibility of using the correlation-based approach to process incomplete partial diffraction patterns is demonstrated. The proposed method is a variable addition to existing algorithms for 3D reconstruction and will further promote the development and adoption of XFEL single-particle imaging techniques.

Angular X-ray cross-correlation analysis applied to the scattering data in 3D reciprocal space from a single crystal

An application of angular X-ray cross-correlation analysis (AXCCA) to the scattered intensity distribution measured in 3D reciprocal space from a single-crystalline sample is proposed in this work. Contrary to the conventional application of AXCCA, when averaging over many 2D diffraction patterns collected from different randomly oriented samples is required, the proposed approach provides an insight into the structure of a single specimen. This is particularly useful in studies of defect-rich samples that are unlikely to have the same structure. The application of the method is shown on an example of a qualitative structure determination of a colloidal crystal from simulated as well as experimentally measured 3D scattered intensity distributions.

Preferred orientation and its effects on intensity-correlation measurements

Intensity-correlation measurements allow access to nanostructural information on a range of ordered and disordered materials beyond traditional pair-correlation methods. In real space, this information can be expressed in terms of a pair-angle distribution function (PADF) which encodes three- and four-body distances and angles. To date, correlation-based techniques have not been applied to the analysis of microstructural effects, such as preferred orientation, which are typically investigated by texture analysis. Preferred orientation is regarded as a potential source of error in intensity-correlation experiments and complicates interpretation of the results. Here, the theory of preferred orientation in intensity-correlation techniques is developed, connecting it to the established theory of texture analysis. The preferred-orientation effect is found to scale with the number of crystalline domains in the beam, surpassing the nanostructural signal when the number of domains becomes large. Experimental demonstrations are presented of the orientation-dominant and nanostructure-dominant cases using PADF analysis. The results show that even minor deviations from uniform orientation produce the strongest angular correlation signals when the number of crystalline domains in the beam is large.

GPU-accelerated multitiered iterative phasing algorithm for fluctuation X-ray scattering

The multitiered iterative phasing (MTIP) algorithm is used to determine the biological structures of macromolecules from fluctuation scattering data. It is an iterative algorithm that reconstructs the electron density of the sample by matching the computed fluctuation X-ray scattering data to the external observations, and by simultaneously enforcing constraints in real and Fourier space. This paper presents the first ever MTIP algorithm acceleration efforts on contemporary graphics processing units (GPUs). The Compute Unified Device Architecture (CUDA) programming model is used to accelerate the MTIP algorithm on NVIDIA GPUs. The computational performance of the CUDA-based MTIP algorithm implementation outperforms the CPU-based version by an order of magnitude. Furthermore, the Heterogeneous-Compute Interface for Portability (HIP) runtime APIs are used to demonstrate portability by accelerating the MTIP algorithm across NVIDIA and AMD GPUs.

Characterizing crystalline defects in single nanoparticles from angular correlations of single-shot diffracted X-rays

Characterizing and controlling the uniformity of nanoparticles is crucial for their application in science and technology because crystalline defects in the nanoparticles strongly affect their unique properties. Recently, ultra-short and ultra-bright X-ray pulses provided by X-ray free-electron lasers (XFELs) opened up the possibility of structure determination of nanometre-scale matter with Å spatial resolution. However, it is often difficult to reconstruct the 3D structural information from single-shot X-ray diffraction patterns owing to the random orientation of the particles. This report proposes an analysis approach for characterizing defects in nanoparticles using wide-angle X-ray scattering (WAXS) data from free-flying single nanoparticles. The analysis method is based on the concept of correlated X-ray scattering, in which correlations of scattered X-ray are used to recover detailed structural information. WAXS experiments of xenon nanoparticles, or clusters, were conducted at an XFEL facility in Japan by using the SPring-8 Ångstrom compact free-electron laser (SACLA). Bragg spots in the recorded single-shot X-ray diffraction patterns showed clear angular correlations, which offered significant structural information on the nanoparticles. The experimental angular correlations were reproduced by numerical simulation in which kinematical theory of diffraction was combined with geometric calculations. We also explain the diffuse scattering intensity as being due to the stacking faults in the xenon clusters.

Fluctuation X-ray scattering from nanorods in solution reveals weak temperature-dependent orientational ordering

Higher-order statistical analysis of X-ray scattering from dilute solutions of polydisperse goethite nanorods was performed and revealed structural information which is inaccessible by conventional small-angle scattering. For instance, a pronounced temperature dependence of the correlated scattering from suspension was observed. The higher-order scattering terms deviate from those expected for a perfectly isotropic distribution of particle orientations, demonstrating that the method can reveal faint orientational order in apparently disordered systems. The observation of correlated scattering from polydisperse particle solutions is also encouraging for future free-electron laser experiments aimed at extracting high-resolution structural information from systems with low particle heterogeneity.

Ab initio structure determination from experimental fluctuation X-ray scattering data

Fluctuation X-ray scattering is a biophysical structural characterization technique that overcomes low data-to-parameter ratios encountered in traditional X-ray methods used for studying noncrystalline samples. By collecting a series of ultrashort X-ray exposures on an ensemble of particles at a free-electron laser, information-dense experimental data can be extracted that ultimately result in structures with a greater level of detail than can be obtained using traditional X-ray scattering methods. In this article we demonstrate the practical feasibility of this technique by introducing data-processing techniques and advanced noise-filtering methods that reduce the required data collection time to less than a few minutes. This will ultimately allow one to visualize details of structural dynamics that may be inaccessible through traditional methods.

Fluctuation X-ray scattering (FXS) is an emerging experimental technique in which X-ray solution scattering data are collected from particles in solution using ultrashort X-ray exposures generated by a free-electron laser (FEL). FXS experiments overcome the low data-to-parameter ratios associated with traditional solution scattering measurements by providing several orders of magnitude more information in the final processed data. Here we demonstrate the practical feasibility of FEL-based FXS on a biological multiple-particle system and describe data-processing techniques required to extract robust FXS data and significantly reduce the required number of snapshots needed by introducing an iterative noise-filtering technique. We showcase a successful ab initio electron density reconstruction from such an experiment, studying the Paramecium bursaria Chlorella virus (PBCV-1).

Correlations in Scattered X-Ray Laser Pulses Reveal Nanoscale Structural Features of Viruses

We use extremely bright and ultrashort pulses from an x-ray free-electron laser (XFEL) to measure correlations in x rays scattered from individual bioparticles. This allows us to go beyond the traditional crystallography and single-particle imaging approaches for structure investigations. We employ angular correlations to recover the three-dimensional (3D) structure of nanoscale viruses from x-ray diffraction data measured at the Linac Coherent Light Source. Correlations provide us with a comprehensive structural fingerprint of a 3D virus, which we use both for model-based and ab initio structure recovery. The analyses reveal a clear indication that the structure of the viruses deviates from the expected perfect icosahedral symmetry. Our results anticipate exciting opportunities for XFEL studies of the structure and dynamics of nanoscale objects by means of angular correlations.

The Linac Coherent Light Source: Recent Developments and Future Plans

The development of X-ray free-electron lasers (XFELs) has launched a new era in X-ray science by providing ultrafast coherent X-ray pulses with a peak brightness that is approximately one billion times higher than previous X-ray sources. The Linac Coherent Light Source (LCLS) facility at the SLAC National Accelerator Laboratory, the world’s first hard X-ray FEL, has already demonstrated a tremendous scientific impact across broad areas of science. Here, a few of the more recent representative highlights from LCLS are presented in the areas of atomic, molecular, and optical science; chemistry; condensed matter physics; matter in extreme conditions; and biology. This paper also outlines the near term upgrade (LCLS-II) and motivating science opportunities for ultrafast X-rays in the 0.25–5 keV range at repetition rates up to 1 MHz. Future plans to extend the X-ray energy reach to beyond 13 keV (<1 Å) at high repetition rate (LCLS-II-HE) are envisioned, motivated by compelling new science of structural dynamics at the atomic scale.

Orientational order of liquids and glasses via fluctuation diffraction

Liquids, glasses and other amorphous matter lack long-range order, which makes them notoriously difficult to study. Local atomic order is partially revealed by measuring the distribution of pairwise atomic distances, but this measurement is insensitive to orientational order and unable to provide a complete picture of diverse amorphous phenomena, such as supercooling and the glass transition. Fluctuation scattering with electrons and X-rays is able provide this orientational sensitivity, but it is difficult to obtain clear structural interpretations of fluctuation data. Here we show that the interpretation of fluctuation diffraction data can be simplified by converting it into a real-space angular distribution function. We calculate this function from simulated diffraction of amorphous nickel, generated with a classical molecular dynamics simulation of the quenching of a high temperature liquid state. We compare the results of the amorphous case to the initial liquid state and to the ideal f.c.c. lattice structure of nickel. We show that the extracted angular distributions are rich in information about orientational order and bond angles. The diffraction fluctuations are potentially measurable with electron sources and also with the brightest X-ray sources, like X-ray free-electron lasers.

Angular correlations of photons from solution diffraction at a free-electron laser encode molecular structure

During X-ray exposure of a molecular solution, photons scattered from the same molecule are correlated. If molecular motion is insignificant during exposure, then differences in momentum transfer between correlated photons are direct measurements of the molecular structure. In conventional small- and wide-angle solution scattering, photon correlations are ignored. This report presents advances in a new biomolecular structural analysis technique, correlated X-ray scattering (CXS), which uses angular intensity correlations to recover hidden structural details from molecules in solution. Due to its intense rapid pulses, an X-ray free electron laser (XFEL) is an excellent tool for CXS experiments. A protocol is outlined for analysis of a CXS data set comprising a total of half a million X-ray exposures of solutions of small gold nanoparticles recorded at the Spring-8 Ångström Compact XFEL facility (SACLA). From the scattered intensities and their correlations, two populations of nanoparticle domains within the solution are distinguished: small twinned, and large probably non-twinned domains. It is shown analytically how, in a solution measurement, twinning information is only accessible via intensity correlations, demonstrating how CXS reveals atomic-level information from a disordered solution of like molecules.

Iterative phasing for fluctuation X-ray scattering

Fluctuation X-ray scattering (FXS) is an extension of small- and wide-angle X-ray scattering in which the X-ray snapshots are taken below rotational diffusion times. This technique, performed using a free electron laser or ultrabright synchrotron source, provides significantly more experimental information compared with traditional solution scattering methods. We develop a multitiered iterative phasing algorithm to determine the underlying structure of the scattering object from FXS data.

Operational properties of fluctuation X-ray scattering data

X-ray scattering images collected on timescales shorter than rotation diffusion times using a (partially) coherent beam result in a significant increase in information content in the scattered data. These measurements, named fluctuation X-ray scattering (FXS), are typically performed on an X-ray free-electron laser (XFEL) and can provide fundamental insights into the structure of biological molecules, engineered nanoparticles or energy-related mesoscopic materials beyond what can be obtained with standard X-ray scattering techniques. In order to understand, use and validate experimental FXS data, the availability of basic data characteristics and operational properties is essential, but has been absent up to this point. In this communication, an intuitive view of the nature of FXS data and their properties is provided, the effect of FXS data on the derived structural models is highlighted, and generalizations of the Guinier and Porod laws that can ultimately be used to plan experiments and assess the quality of experimental data are presented.

Biostructural Science Inspired by Next-Generation X-Ray Sources

Next-generation synchrotron radiation sources, such as X-ray free-electron lasers, energy recovery linacs, and ultra-low-emittance storage rings, are catalyzing novel methods of biomolecular microcrystallography and solution scattering. These methods are described and future trends are predicted. Importantly, there is a growing realization that serial microcrystallography and certain cutting-edge solution scattering experiments can be performed at existing storage ring sources by utilizing new technology. In this sense, next-generation sources are serving two distinct functions, namely, provision of new capabilities that require the newer sources and inspiration of new methods that can be performed at existing sources.

Observation of correlated X-ray scattering at atomic resolution

Tools to study disordered systems with local structural order, such as proteins in solution, remain limited. Such understanding is essential for e.g. rational drug design. Correlated X-ray scattering (CXS) has recently attracted new interest as a way to leverage next-generation light sources to study such disordered matter. The CXS experiment measures angular correlations of the intensity caused by the scattering of X-rays from an ensemble of identical particles, with disordered orientation and position. Averaging over 15 496 snapshot images obtained by exposing a sample of silver nanoparticles in solution to a micro-focused synchrotron radiation beam, we report on experimental efforts to obtain CXS signal from an ensemble in three dimensions. A correlation function was measured at wide angles corresponding to atomic resolution that matches theoretical predictions. These preliminary results suggest that other CXS experiments on disordered ensembles—such as proteins in solution—may be feasible in the future.

A microfabricated fixed path length silicon sample holder improves background subtraction for cryoSAXS

The application of small-angle X-ray scattering (SAXS) for high-throughput characterization of biological macromolecules in solution is limited by radiation damage. By cryocooling samples, radiation damage and required sample volumes can be reduced by orders of magnitude. However, the challenges of reproducibly creating the identically sized vitrified samples necessary for conventional background subtraction limit the widespread adoption of this method. Fixed path length silicon sample holders for cryoSAXS have been microfabricated to address these challenges. They have low background scattering and X-ray absorption, require only 640 nl of sample, and allow reproducible sample cooling. Data collected in the sample holders from a nominal illuminated sample volume of 2.5 nl are reproducible down to q ≃ 0.02 Å^-1, agree with previous cryoSAXS work and are of sufficient quality for reconstructions that match measured crystal structures. These sample holders thus allow faster, more routine cryoSAXS data collection. Additional development is required to reduce sample fracturing and improve data quality at low q.

Characteristics of angular cross correlations studied by light scattering from two-dimensional microsphere films

Recently the analysis of scattering patterns by angular cross-correlation analysis (CCA) was introduced to reveal the orientational order in disordered samples with special focus to future applications on x-ray free-electron laser facilities. We apply this CCA approach to ultra-small-angle light-scattering data obtained from two-dimensional monolayers of microspheres. The films were studied in addition by optical microscopy. This combined approach allows to calculate the cross-correlations of the scattering patterns, characterized by the orientational correlation function Ψ(l)(q), as well as to obtain the real-space structure of the monolayers. We show that CCA is sensitive to the orientational order of monolayers formed by the microspheres which are not directly visible from the scattering patterns. By mixing microspheres of different radii the sizes of ordered monolayer domains is reduced. For these samples it is shown that Ψ(l)(q) quantitatively describes the degree of hexagonal order of the two-dimensional films. The experimental CCA results are compared with calculations based on the microscopy images. Both techniques show qualitatively similar features. Differences can be attributed to the wave-front distortion of the laser beam in the experiment. This effect is discussed by investigating the effect of different wave fronts on the cross-correlation analysis results. The so-determined characteristics of the cross-correlation analysis will be also relevant for future x-ray-based studies.

Component particle structure in heterogeneous disordered ensembles extracted from high-throughput fluctuation x-ray scattering

The ring angular correlation function is a characteristic feature determined by the particle structure. Averaging over a large number of ring angular correlation functions calculated from x-ray diffraction patterns will cancel out the cross correlations between different particles and converge to the autocorrelation functions of single particles. Applied on heterogeneous disordered ensembles, the retrieved function is a linear combination of a single-particle autocorrelation function multiplied by the molar ratios in a heterogeneous system. Using this relation, the ring angular correlation functions of the individual component particles in the heterogeneous system can be retrieved through the high throughput fluctuation x-ray scattering technique. This method is demonstrated with a simulated heterogeneous system composed of nanorods, nanoprism, and nanorice.

Structure determination of Pt-coated Au dumbbells via fluctuation X-ray scattering

A fluctuation X-ray scattering experiment has been carried out on platinum-coated gold nanoparticles randomly oriented on a substrate. A complete algorithm for determining the electron density of an individual particle from diffraction patterns of many particles randomly oriented about a single axis is demonstrated. This algorithm operates on angular correlations among the measured intensity distributions and recovers the angular correlation functions of a single particle from measured diffraction patterns. Taking advantage of the cylindrical symmetry of the nanoparticles, a cylindrical slice model is proposed to reconstruct the structure of the nanoparticles by fitting the experimental ring angular auto-correlation and small-angle scattering data obtained from many scattering patterns. The physical meaning of the refined structure is discussed in terms of their statistical distributions of the shape and electron density profile.

X-ray cross correlation analysis uncovers hidden local symmetries in disordered matter

We explore the different local symmetries in colloidal glasses beyond the standard pair correlation analysis. Using our newly developed X-ray cross correlation analysis (XCCA) concept together with brilliant coherent X-ray sources, we have been able to access and classify the otherwise hidden local order within disorder. The emerging local symmetries are coupled to distinct momentum transfer (Q) values, which do not coincide with the maxima of the amorphous structure factor. Four-, 6-, 10- and, most prevalently, 5-fold symmetries are observed. The observation of dynamical evolution of these symmetries forms a connection to dynamical heterogeneities in glasses, which is far beyond conventional diffraction analysis. The XCCA concept opens up a fascinating view into the world of disorder and will definitely allow, with the advent of free electron X-ray lasers, an accurate and systematic experimental characterization of the structure of the liquid and glass states.