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

High-resolution imaging of organic and inorganic nanoparticles at nanometre-scale resolution by X-ray ensemble diffraction microscopy

Coherent diffraction microscopy (CDM) is a robust direct imaging method due to its unique 2D/3D phase retrieval capacity. Nonetheless, its resolution faces limitations due to a diminished signal-to-noise ratio (SNR) in high-frequency regions. Addressing this challenge, X-ray ensemble diffraction microscopy (XEDM) emerges as a viable solution, ensuring an adequate SNR in high-frequency regions and effectively surmounting resolution constraints. In this article, two experiments were conducted to underscore XEDM's superior spatial resolution capabilities. These experiments employed 55 nm-sized silicon-gold nanoparticles (NPs) and 19 nm-sized nodavirus-like particles (NV-LPs) on the coherent X-ray scattering beamline of the Taiwan Photon Source. The core-shell density distribution of the silicon-gold NPs was successfully obtained with a radial resolution of 3.4 nm per pixel, while NV-LPs in solution were reconstructed at a radial resolution of 1.3 nm per pixel. The structural information was directly retrieved from the diffraction intensities without prior knowledge and was subsequently confirmed through transmission electron microscopy.

Bayesian electron density determination from sparse and noisy single-molecule X-ray scattering images

Single molecule x-ray scattering experiments using free-electron lasers hold the potential to resolve biomolecular structures and structural ensembles. However, molecular electron density determination has so far not been achieved because of low photon counts, high noise levels, and low hit rates. Most approaches therefore focus on large specimen like entire viruses, which scatter sufficiently many photons to allow orientation determination of each image. Small specimens like proteins, however, scatter too few photons for the molecular orientations to be determined. Here, we present a rigorous Bayesian approach to overcome these limitations, additionally taking into account intensity fluctuations, beam polarization, irregular detector shapes, incoherent scattering, and background scattering. We demonstrate using synthetic scattering images that electron density determination of small proteins is possible in this extreme high noise Poisson regime. Tests on published virus data achieved the detector-limited resolution of 9 nm, using only 0.01% of the available photons per image.

A predicted model-aided one-step classification-multireconstruction algorithm for X-ray free-electron laser single-particle imaging

Ultrafast, high-intensity X-ray free-electron lasers can perform diffraction imaging of single protein molecules. Various algorithms have been developed to determine the orientation of each single-particle diffraction pattern and reconstruct the 3D diffraction intensity. Most of these algorithms rely on the premise that all diffraction patterns originate from identical protein molecules. However, in actual experiments, diffraction patterns from multiple different molecules may be collected simultaneously. Here, we propose a predicted model-aided one-step classification-multireconstruction algorithm that can handle mixed diffraction patterns from various molecules. The algorithm uses predicted structures of different protein molecules as templates to classify diffraction patterns based on correlation coefficients and determines orientations using a correlation maximization method. Tests on simulated data demonstrated high accuracy and efficiency in classification and reconstruction.

A predicted model-aided reconstruction algorithm for X-ray free-electron laser single-particle imaging

Ultra-intense, ultra-fast X-ray free-electron lasers (XFELs) enable the imaging of single protein molecules under ambient temperature and pressure. A crucial aspect of structure reconstruction involves determining the relative orientations of each diffraction pattern and recovering the missing phase information. In this paper, we introduce a predicted model-aided algorithm for orientation determination and phase retrieval, which has been tested on various simulated datasets and has shown significant improvements in the success rate, accuracy and efficiency of XFEL data reconstruction.

Crystal structure via fluctuation scattering

Crystallography is a quintessential method for determining the atomic structure of crystals. The most common implementation of crystallography uses single crystals that must be of sufficient size, typically tens of micrometres or larger, depending on the complexity of the crystal structure. The emergence of serial data-collection methods in crystallography, particularly for time-resolved experiments, opens up opportunities to develop new routes to structure determination for nanocrystals and ensembles of crystals. Fluctuation X-ray scattering is a correlation-based approach for single-particle imaging from ensembles of identical particles, but has yet to be applied to crystal structure determination. Here, an iterative algorithm is presented that recovers crystal structure-factor intensities from fluctuation X-ray scattering correlations. The capabilities of this algorithm are demonstrated by recovering the structure of three small-molecule crystals and a protein crystal from simulated fluctuation X-ray scattering correlations. This method could facilitate the recovery of structure-factor intensities from crystals in serial crystallography experiments and relax sample requirements for crystallography experiments.

The pypadf package: computing the pair angle distribution function from fluctuation scattering data

The pair angle distribution function (PADF) is a three- and four-atom correlation function that characterizes the local angular structure of disordered materials, particles or nanocrystalline materials. The PADF can be measured using X-ray or electron fluctuation diffraction data, which can be collected by scanning or flowing a structurally disordered sample through a focused beam. It is a natural generalization of established pair distribution methods, which do not provide angular information. The software package pypadf provides tools to calculate the PADF from fluctuation diffraction data. The package includes tools for calculating the intensity correlation function, which is a necessary step in the PADF calculation and also the basis for other fluctuation scattering analysis techniques.

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.

Enhancing electrospray ionization efficiency for particle transmission through an aerodynamic lens stack

This work investigates the performance of the electrospray aerosol generator at the European X-ray Free Electron Laser (EuXFEL). This generator is, together with an aerodynamic lens stack that transports the particles into the X-ray interaction vacuum chamber, the method of choice to deliver particles for single-particle coherent diffractive imaging (SPI) experiments at the EuXFEL. For these experiments to be successful, it is necessary to achieve high transmission of particles from solution into the vacuum interaction region. Particle transmission is highly dependent on efficient neutralization of the charged aerosol generated by the electrospray mechanism as well as the geometry in the vicinity of the Taylor cone. We report absolute particle transmission values for different neutralizers and geometries while keeping the conditions suitable for SPI experiments. Our findings reveal that a vacuum ultraviolet ionizer demonstrates a transmission efficiency approximately seven times greater than the soft X-ray ionizer used previously. Combined with an optimized orifice size on the counter electrode, we achieve >40% particle transmission from solution into the X-ray interaction region. These findings offer valuable insights for optimizing electrospray aerosol generator configurations and data rates for SPI experiments.

Characterization of Biological Samples Using Ultra-Short and Ultra-Bright XFEL Pulses

The advent of X-ray Free Electron Lasers (XFELs) has ushered in a transformative era in the field of structural biology, materials science, and ultrafast physics. These state-of-the-art facilities generate ultra-bright, femtosecond-long X-ray pulses, allowing researchers to delve into the structure and dynamics of molecular systems with unprecedented temporal and spatial resolutions. The unique properties of XFEL pulses have opened new avenues for scientific exploration that were previously considered unattainable. One of the most notable applications of XFELs is in structural biology. Traditional X-ray crystallography, while instrumental in determining the structures of countless biomolecules, often requires large, high-quality crystals and may not capture highly transient states of proteins. XFELs, with their ability to produce diffraction patterns from nanocrystals or even single particles, have provided solutions to these challenges. XFEL has expanded the toolbox of structural biologists by enabling structural determination approaches such as Single Particle Imaging (SPI) and Serial X-ray Crystallography (SFX). Despite their remarkable capabilities, the journey of XFELs is still in its nascent stages, with ongoing advancements aimed at improving their coherence, pulse duration, and wavelength tunability.

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.

Preparation and characterization of inactivated tick-borne encephalitis virus samples for single-particle imaging at the European XFEL

X-ray imaging of virus particles at the European XFEL could eventually allow their complete structures to be solved, potentially approaching the resolution of other structural virology methods. To achieve this ambitious goal with today's technologies, about 1 ml of purified virus suspension containing at least 1012 particles per millilitre is required. Such large amounts of concentrated suspension have never before been obtained for enveloped viruses. Tick-borne encephalitis virus (TBEV) represents an attractive model system for the development of enveloped virus purification and concentration protocols, given the availability of large amounts of inactivated virus material provided by vaccine-manufacturing facilities. Here, the development of a TBEV vaccine purification and concentration scheme is presented combined with a quality-control protocol that allows substantial amounts of highly concentrated non-aggregated suspension to be obtained. Preliminary single-particle imaging experiments were performed for this sample at the European XFEL, showing distinct diffraction patterns.

Thinner than a knife's edge: 3D-printed liquid sheet jet technology for solution phase XFEL experiments

In this commentary, we explore the pioneering implementation of 3D-printed thin liquid sheet devices for advanced X-ray scattering and spectroscopy experiments at high-repetition rate XFELs.

3D-printed sheet jet for stable megahertz liquid sample delivery at X-ray free-electron lasers

X-ray free-electron lasers (XFELs) can probe chemical and biological reactions as they unfold with unprecedented spatial and temporal resolution. A principal challenge in this pursuit involves the delivery of samples to the X-ray interaction point in such a way that produces data of the highest possible quality and with maximal efficiency. This is hampered by intrinsic constraints posed by the light source and operation within a beamline environment. For liquid samples, the solution typically involves some form of high-speed liquid jet, capable of keeping up with the rate of X-ray pulses. However, conventional jets are not ideal because of radiation-induced explosions of the jet, as well as their cylindrical geometry combined with the X-ray pointing instability of many beamlines which causes the interaction volume to differ for every pulse. This complicates data analysis and contributes to measurement errors. An alternative geometry is a liquid sheet jet which, with its constant thickness over large areas, eliminates the problems related to X-ray pointing. Since liquid sheets can be made very thin, the radiation-induced explosion is reduced, boosting their stability. These are especially attractive for experiments which benefit from small interaction volumes such as fluctuation X-ray scattering and several types of spectroscopy. Although their use has increased for soft X-ray applications in recent years, there has not yet been wide-scale adoption at XFELs. Here, gas-accelerated liquid sheet jet sample injection is demonstrated at the European XFEL SPB/SFX nano focus beamline. Its performance relative to a conventional liquid jet is evaluated and superior performance across several key factors has been found. This includes a thickness profile ranging from hundreds of nanometres to 60 nm, a fourfold increase in background stability and favorable radiation-induced explosion dynamics at high repetition rates up to 1.13 MHz. Its minute thickness also suggests that ultrafast single-particle solution scattering is a possibility.

Form factor determination of biological molecules with X-ray free electron laser small-angle scattering (XFEL-SAS)

Free-electron lasers (FEL) are revolutionizing X-ray-based structural biology methods. While protein crystallography is already routinely performed at FELs, Small Angle X-ray Scattering (SAXS) studies of biological macromolecules are not as prevalent. SAXS allows the study of the shape and overall structure of proteins and nucleic acids in solution, in a quasi-native environment. In solution, chemical and biophysical parameters that have an influence on the structure and dynamics of molecules can be varied and their effect on conformational changes can be monitored in time-resolved XFEL and SAXS experiments. We report here the collection of scattering form factors of proteins in solution using FEL X-rays. The form factors correspond to the scattering signal of the protein ensemble alone; the scattering contributions from the solvent and the instrument are separately measured and accurately subtracted. The experiment was done using a liquid jet for sample delivery. These results pave the way for time-resolved studies and measurements from dilute samples, capitalizing on the intense and short FEL X-ray pulses.

Water layer and radiation damage effects on the orientation recovery of proteins in single-particle imaging at an X-ray free-electron laser

The noise caused by sample heterogeneity (including sample solvent) has been identified as one of the determinant factors for a successful X-ray single-particle imaging experiment. It influences both the radiation damage process that occurs during illumination as well as the scattering patterns captured by the detector. Here, we investigate the impact of water layer thickness and radiation damage on orientation recovery from diffraction patterns of the nitrogenase iron protein. Orientation recovery is a critical step for single-particle imaging. It enables to sort a set of diffraction patterns scattered by identical particles placed at unknown orientations and assemble them into a 3D reciprocal space volume. The recovery quality is characterized by a "disconcurrence" metric. Our results show that while a water layer mitigates protein damage, the noise generated by the scattering from it can introduce challenges for orientation recovery and is anticipated to cause problems in the phase retrieval process to extract the desired protein structure. Compared to these disadvantageous effects due to the thick water layer, the effects of radiation damage on the orientation recovery are relatively small. Therefore, minimizing the amount of residual sample solvent should be considered a crucial step in improving the fidelity and resolution of X-ray single-particle imaging experiments.

Exploring fingerprints of ultrafast structural dynamics in molecular solutions with an X-ray laser

We apply ultrashort X-ray laser pulses to track optically excited structural dynamics of [Ir2(dimen)4]2+ molecules in solution. In our exploratory study we determine angular correlations in the scattered X-rays, which comprise a complex fingerprint of the ultrafast dynamics. Model-assisted analysis of the experimental correlation data allows us to elucidate various aspects of the photoinduced changes in the excited molecular ensembles. We unambiguously identify that in our experiment the photoinduced transition dipole moments in [Ir2(dimen)4]2+ molecules are oriented perpendicular to the Ir-Ir bond. The analysis also shows that the ground state conformer of [Ir2(dimen)4]2+ with a larger Ir-Ir distance is mostly responsible for the formation of the excited state. We also reveal that the ensemble of solute molecules can be characterized with a substantial structural heterogeneity due to solvent influence. The proposed X-ray correlation approach offers an alternative path for studies of ultrafast structural dynamics of molecular ensembles in the liquid and gas phases.

Autocorrelation analysis for cryo-EM with sparsity constraints: Improved sample complexity and projection-based algorithms

The number of noisy images required for molecular reconstruction in single-particle cryoelectron microscopy (cryo-EM) is governed by the autocorrelations of the observed, randomly oriented, noisy projection images. In this work, we consider the effect of imposing sparsity priors on the molecule. We use techniques from signal processing, optimization, and applied algebraic geometry to obtain theoretical and computational contributions for this challenging nonlinear inverse problem with sparsity constraints. We prove that molecular structures modeled as sums of Gaussians are uniquely determined by the second-order autocorrelation of their projection images, implying that the sample complexity is proportional to the square of the variance of the noise. This theory improves upon the nonsparse case, where the third-order autocorrelation is required for uniformly oriented particle images and the sample complexity scales with the cube of the noise variance. Furthermore, we build a computational framework to reconstruct molecular structures which are sparse in the wavelet basis. This method combines the sparse representation for the molecule with projection-based techniques used for phase retrieval in X-ray crystallography.

Structural studies of protein-nucleic acid complexes: A brief overview of the selected techniques

Protein-nucleic acid complexes are involved in all vital processes, including replication, transcription, translation, regulation of gene expression and cell metabolism. Knowledge of the biological functions and molecular mechanisms beyond the activity of the macromolecular complexes can be determined from their tertiary structures. Undoubtably, performing structural studies of protein-nucleic acid complexes is challenging, mainly because these types of complexes are often unstable. In addition, their individual components may display extremely different surface charges, causing the complexes to precipitate at higher concentrations used in many structural studies. Due to the variety of protein-nucleic acid complexes and their different biophysical properties, no simple and universal guideline exists that helps scientists chose a method to successfully determine the structure of a specific protein-nucleic acid complex. In this review, we provide a summary of the following experimental methods, which can be applied to study the structures of protein-nucleic acid complexes: X-ray and neutron crystallography, nuclear magnetic resonance (NMR) spectroscopy, cryogenic electron microscopy (cryo-EM), atomic force microscopy (AFM), small angle scattering (SAS) methods, circular dichroism (CD) and infrared (IR) spectroscopy. Each method is discussed regarding its historical context, advancements over the past decades and recent years, and weaknesses and strengths. When a single method does not provide satisfactory data on the selected protein-nucleic acid complex, a combination of several methods should be considered as a hybrid approach; thus, specific structural problems can be solved when studying protein-nucleic acid complexes.

Molecular size dependence on achievable resolution from XFEL single-particle 3D reconstruction

Single-particle analysis using x-ray free-electron lasers (XFELs) is a novel method for obtaining structural information of samples in a state close to nature. In particular, it is suitable for observing the inner structure of large biomolecules by taking advantage of the high transmittance of x-rays. However, systematic studies on the resolution achievable for large molecules are lacking. In this study, the molecular size dependence of the resolution of a three-dimensional (3D) structure resulting from XFEL single-particle reconstruction is evaluated using synthetic data. Evidently, 3D structures of larger molecules can be restored with higher detail (defined relative to the molecular sizes) than smaller ones; however, reconstruction with high absolute resolution (defined in nm^-1) is challenging. Our results provide useful information for the experimental design of 3D structure reconstruction using coherent x-ray diffraction patterns of single-particles.

The structure of tick-borne encephalitis virus determined at X-ray free-electron lasers. Simulations

The study of virus structures by X-ray free-electron lasers (XFELs) has attracted increased attention in recent decades. Such experiments are based on the collection of 2D diffraction patterns measured at the detector following the application of femtosecond X-ray pulses to biological samples. To prepare an experiment at the European XFEL, the diffraction data for the tick-borne encephalitis virus (TBEV) was simulated with different parameters and the optimal values were identified. Following the necessary steps of a well established data-processing pipeline, the structure of TBEV was obtained. In the structure determination presented, a priori knowledge of the simulated virus orientations was used. The efficiency of the proposed pipeline was demonstrated.

Expected resolution limits of x-ray free-electron laser single-particle imaging for realistic source and detector properties

The unprecedented intensity of x-ray free-electron laser sources has enabled single-particle x-ray diffraction imaging (SPI) of various biological specimens in both two-dimensional projection and three dimensions (3D). The potential of studying protein dynamics in their native conditions, without crystallization or chemical staining, has encouraged researchers to aim for increasingly higher resolutions with this technique. The currently achievable resolution of SPI is limited to the sub-10 nanometer range, mainly due to background effects, such as instrumental noise and parasitic scattering from the carrier gas used for sample delivery. Recent theoretical studies have quantified the effects of x-ray pulse parameters, as well as the required number of diffraction patterns to achieve a certain resolution, in a 3D reconstruction, although the effects of detector noise and the random particle orientation in each diffraction snapshot were not taken into account. In this work, we show these shortcomings and address limitations on achievable image resolution imposed by the adaptive gain integrating pixel detector noise.

Skopi: a simulation package for diffractive imaging of noncrystalline biomolecules

X-ray free-electron lasers (XFELs) have the ability to produce ultra-bright femtosecond X-ray pulses for coherent diffraction imaging of biomolecules. While the development of methods and algorithms for macromolecular crystallography is now mature, XFEL experiments involving aerosolized or solvated biomolecular samples offer new challenges in terms of both experimental design and data processing. Skopi is a simulation package that can generate single-hit diffraction images for reconstruction algorithms, multi-hit diffraction images of aggregated particles for training machine learning classifiers using labeled data, diffraction images of randomly distributed particles for fluctuation X-ray scattering algorithms, and diffraction images of reference and target particles for holographic reconstruction algorithms. Skopi is a resource to aid feasibility studies and advance the development of algorithms for noncrystalline experiments at XFEL facilities.

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.

Random conical tilt reconstruction without particle picking in cryo-electron microscopy

A method is proposed to reconstruct the 3D molecular structure from micrographs collected at just one sample tilt angle in the random conical tilt scheme in cryo-electron microscopy. The method uses autocorrelation analysis on the micrographs to estimate features of the molecule which are invariant under certain nuisance parameters such as the positions of molecular projections in the micrographs. This enables the molecular structure to be reconstructed directly from micrographs, completely circumventing the need for particle picking. Reconstructions are demonstrated with simulated data and the effect of the missing-cone region is investigated. These results show promise to reduce the size limit for single-particle reconstruction in cryo-electron microscopy.

Super-resolution multi-reference alignment

We study super-resolution multi-reference alignment, the problem of estimating a signal from many circularly shifted, down-sampled and noisy observations. We focus on the low SNR regime, and show that a signal inℝ M is uniquely determined when the number L of samples per observation is of the order of the square root of the signal's length ( L = O ( M ) ). Phrased more informally, one can square the resolution. This result holds if the number of observations is proportional to 1/SNR3. In contrast, with fewer observations recovery is impossible even when the observations are not down-sampled (L = M). The analysis combines tools from statistical signal processing and invariant theory. We design an expectation-maximization algorithm and demonstrate that it can super-resolve the signal in challenging SNR regimes.

Unsupervised learning approaches to characterizing heterogeneous samples using X-ray single-particle imaging

One of the outstanding analytical problems in X-ray single-particle imaging (SPI) is the classification of structural heterogeneity, which is especially difficult given the low signal-to-noise ratios of individual patterns and the fact that even identical objects can yield patterns that vary greatly when orientation is taken into consideration. Proposed here are two methods which explicitly account for this orientation-induced variation and can robustly determine the structural landscape of a sample ensemble. The first, termed common-line principal component analysis (PCA), provides a rough classification which is essentially parameter free and can be run automatically on any SPI dataset. The second method, utilizing variation auto-encoders (VAEs), can generate 3D structures of the objects at any point in the structural landscape. Both these methods are implemented in combination with the noise-tolerant expand-maximize-compress (EMC) algorithm and its utility is demonstrated by applying it to an experimental dataset from gold nanoparticles with only a few thousand photons per pattern. Both discrete structural classes and continuous deformations are recovered. These developments diverge from previous approaches of extracting reproducible subsets of patterns from a dataset and open up the possibility of moving beyond the study of homogeneous sample sets to addressing open questions on topics such as nanocrystal growth and dynamics, as well as phase transitions which have not been externally triggered.

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.

Imaging of femtosecond bond breaking and charge dynamics in ultracharged peptides

X-ray free-electrons lasers have revolutionized the method of imaging biological macromolecules such as proteins, viruses and cells by opening the door to structural determination of both single particles and crystals at room temperature. By utilizing high intensity X-ray pulses on femtosecond timescales, the effects of radiation damage can be reduced. Achieving high resolution structures will likely require knowledge of how radiation damage affects the structure on an atomic scale, since the experimentally obtained electron densities will be reconstructed in the presence of radiation damage. Detailed understanding of the expected damage scenarios provides further information, in addition to guiding possible corrections that may need to be made to obtain a damage free reconstruction. In this work, we have quantified the effects of ionizing photon-matter interactions using first principles molecular dynamics. We utilize density functional theory to calculate bond breaking and charge dynamics in three ultracharged molecules and two different structural conformations that are important to the structural integrity of biological macromolecules, comparing to our previous studies on amino acids. The effects of the ultracharged states and subsequent bond breaking in real space are studied in reciprocal space using coherent diffractive imaging of an ensemble of aligned biomolecules in the gas phase.

Low-energy electron holography imaging of conformational variability of single-antibody molecules from electrospray ion beam deposition

Molecular imaging at the single-molecule level of large and flexible proteins such as monoclonal IgG antibodies is possible by low-energy electron holography after chemically selective sample preparation by native electrospray ion beam deposition (ES-IBD) from native solution conditions. The single-molecule nature of the measurement allows the mapping of the structural variability of the molecules that originates from their intrinsic flexibility and from different adsorption geometries. Additionally, we can distinguish gas-phase–related conformations and conformations induced by the landing of the molecules on the surface. Our results underpin the relation between the gas-phase structure of protein ions created by native electrospray ionization (ESI) and the native protein structure and are of relevance for structural biology applications in the gas phase.

Imaging of proteins at the single-molecule level can reveal conformational variability, which is essential for the understanding of biomolecules. To this end, a biologically relevant state of the sample must be retained during both sample preparation and imaging. Native electrospray ionization (ESI) can transfer even the largest protein complexes into the gas phase while preserving their stoichiometry and overall shape. High-resolution imaging of protein structures following native ESI is thus of fundamental interest for establishing the relation between gas phase and solution structure. Taking advantage of low-energy electron holography’s (LEEH) unique capability of imaging individual proteins with subnanometer resolution, we investigate the conformational flexibility of Herceptin, a monoclonal IgG antibody, deposited by native electrospray mass-selected ion beam deposition (ES-IBD) on graphene. Images reconstructed from holograms reveal a large variety of conformers. Some of these conformations can be mapped to the crystallographic structure of IgG, while others suggest that a compact, gas-phase–related conformation, adopted by the molecules during ES-IBD, is retained. We can steer the ratio of those two types of conformations by changing the landing energy of the protein on the single-layer graphene surface. Overall, we show that LEEH can elucidate the conformational heterogeneity of inherently flexible proteins, exemplified here by IgG antibodies, and thereby distinguish gas-phase collapse from rearrangement on surfaces.

In a flash of light: X-ray free electron lasers meet native mass spectrometry

During the last years, X-ray free electron lasers (XFELs) have emerged as X-ray sources of unparalleled brightness, delivering extreme amounts of photons in femtosecond pulses. As such, they have opened up completely new possibilities in drug discovery and structural biology, including studying high resolution biomolecular structures and their functioning in a time resolved manner, and diffractive imaging of single particles without the need for their crystallization. In this perspective, we briefly review the operation of XFELs, their immediate uses for drug discovery and focus on the potentially revolutionary single particle diffractive imaging technique and the challenges which remain to be overcome to fully realize its potential to provide high resolution structures without the need for crystallization, freezing or the need to keep proteins stable at extreme concentrations for long periods of time. As the issues have been to a large extent sample delivery related, we outline a way for native mass spectrometry to overcome these and enable so far impossible research with a potentially huge impact on structural biology and drug discovery, such as studying structures of transient intermediate species in viral life cycles or during functioning of molecular machines.

Wilson statistics: derivation, generalization and applications to electron cryomicroscopy

The power spectrum of proteins at high frequencies is remarkably well described by the flat Wilson statistics. Wilson statistics therefore plays a significant role in X-ray crystallography and more recently in electron cryomicroscopy (cryo-EM). Specifically, modern computational methods for three-dimensional map sharpening and atomic modelling of macromolecules by single-particle cryo-EM are based on Wilson statistics. Here the first rigorous mathematical derivation of Wilson statistics is provided. The derivation pinpoints the regime of validity of Wilson statistics in terms of the size of the macromolecule. Moreover, the analysis naturally leads to generalizations of the statistics to covariance and higher-order spectra. These in turn provide a theoretical foundation for assumptions underlying the widespread Bayesian inference framework for three-dimensional refinement and for explaining the limitations of autocorrelation-based methods in cryo-EM.

Cross-correlation analysis of X-ray photon correlation spectroscopy to extract rotational diffusion coefficients

X-ray photon correlation spectroscopy (XPCS) is a powerful technique that can probe a broad range of space and time scales and will become increasingly powerful due to coming advancements in coherence. Assessing translational and rotational diffusion is a key quantity in analyzing material structures and dynamics, with applications across molecular biology, drug discovery, and materials science. While methods for estimating translational diffusion coefficients from XPCS data are well-developed, there are no algorithms for measuring the rotational diffusion. Here, we present a mathematical formulation and algorithm based on angular-temporal cross-correlations for extracting this rotational information, providing tools for data analysis of XPCS. Although we focus on XPCS, the proposed method can be applied to other experimental techniques due to its generality.

Coefficients for translational and rotational diffusion characterize the Brownian motion of particles. Emerging X-ray photon correlation spectroscopy (XPCS) experiments probe a broad range of length scales and time scales and are well-suited for investigation of Brownian motion. While methods for estimating the translational diffusion coefficients from XPCS are well-developed, there are no algorithms for measuring the rotational diffusion coefficients based on XPCS, even though the required raw data are accessible from such experiments. In this paper, we propose angular-temporal cross-correlation analysis of XPCS data and show that this information can be used to design a numerical algorithm (Multi-Tiered Estimation for Correlation Spectroscopy [MTECS]) for predicting the rotational diffusion coefficient utilizing the cross-correlation: This approach is applicable to other wavelengths beyond this regime. We verify the accuracy of this algorithmic approach across a range of simulated data.

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.

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.

Protein orientation in time-dependent electric fields: orientation before destruction

Proteins often have nonzero electric dipole moments, making them interact with external electric fields and offering a means for controlling their orientation. One application that is known to benefit from orientation control is single-particle imaging with x-ray free-electron lasers, in which diffraction is recorded from proteins in the gas phase to determine their structures. To this point, theoretical investigations into this phenomenon have assumed that the field experienced by the proteins is constant or a perfect step function, whereas any real-world pulse will be smooth. Here, we explore the possibility of orienting gas-phase proteins using time-dependent electric fields. We performed ab initio simulations to estimate the field strength required to break protein bonds, with 45 V/nm as a breaking point value. We then simulated ubiquitin in time-dependent electric fields using classical molecular dynamics. The minimal field strength required for orientation within 10 ns was on the order of 0.5 V/nm. Although high fields can be destructive for the structure, the structures in our simulations were preserved until orientation was achieved regardless of field strength, a principle we denote “orientation before destruction.”

An advanced workflow for single-particle imaging with the limited data at an X-ray free-electron laser

An improved analysis for single-particle imaging (SPI) experiments, using the limited data, is presented here. Results are based on a study of bacteriophage PR772 performed at the Atomic, Molecular and Optical Science instrument at the Linac Coherent Light Source as part of the SPI initiative. Existing methods were modified to cope with the shortcomings of the experimental data: inaccessibility of information from half of the detector and a small fraction of single hits. The general SPI analysis workflow was upgraded with the expectation-maximization based classification of diffraction patterns and mode decomposition on the final virus-structure determination step. The presented processing pipeline allowed us to determine the 3D structure of bacteriophage PR772 without symmetry constraints with a spatial resolution of 6.9 nm. The obtained resolution was limited by the scattering intensity during the experiment and the relatively small number of single hits.

Slowing down of dynamics and orientational order preceding crystallization in hard-sphere systems

Despite intensive studies in the past decades, the local structure of disordered matter remains widely unknown. We show the results of a coherent x-ray scattering study revealing higher-order correlations in dense colloidal hard-sphere systems in the vicinity of their crystallization and glass transition. With increasing volume fraction, we observe a strong increase in correlations at both medium-range and next-neighbor distances in the supercooled state, both invisible to conventional scattering techniques. Next-neighbor correlations are indicative of ordered precursor clusters preceding crystallization. Furthermore, the increase in such correlations is accompanied by a marked slowing down of the dynamics, proving experimentally a direct relation between orientational order and sample dynamics in a soft matter system. In contrast, correlations continuously increase for nonequilibrated, glassy samples, suggesting that orientational order is reached before the sample slows down to reach (quasi-)equilibrium.

Flash X-ray diffraction imaging in 3D: a proposed analysis pipeline

Modern Flash X-ray diffraction Imaging (FXI) acquires diffraction signals from single biomolecules at a high repetition rate from X-ray Free Electron Lasers (XFELs), easily obtaining millions of 2D diffraction patterns from a single experiment. Due to the stochastic nature of FXI experiments and the massive volumes of data, retrieving 3D electron densities from raw 2D diffraction patterns is a challenging and time-consuming task. We propose a semi-automatic data analysis pipeline for FXI experiments, which includes four steps: hit-finding and preliminary filtering, pattern classification, 3D Fourier reconstruction, and post-analysis. We also include a recently developed bootstrap methodology in the post-analysis step for uncertainty analysis and quality control. To achieve the best possible resolution, we further suggest using background subtraction, signal windowing, and convex optimization techniques when retrieving the Fourier phases in the post-analysis step. As an application example, we quantified the 3D electron structure of the PR772 virus using the proposed data analysis pipeline. The retrieved structure was above the detector edge resolution and clearly showed the pseudo-icosahedral capsid of the PR772.

The Sensitivity of the Pair-Angle Distribution Function to Protein Structure

The continued development of X-ray free-electron lasers and serial crystallography techniques has opened up new experimental frontiers. Nanoscale dynamical processes such as crystal growth can now be probed at unprecedented time and spatial resolutions. Pair-angle distribution function (PADF) analysis is a correlation-based technique that has the potential to extend the limits of current serial crystallography experiments, by relaxing the requirements for crystal order, size and number density per exposure. However, unlike traditional crystallographic methods, the PADF technique does not recover the electron density directly. Instead it encodes substantial information about local three-dimensional structure in the form of three- and four-body correlations. It is not yet known how protein structure maps into the many-body PADF correlations. In this paper, we explore the relationship between the PADF and protein conformation. We calculate correlations in reciprocal and real space for model systems exhibiting increasing degrees of order and secondary structural complexity, from disordered polypeptides, single alpha helices, helix bundles and finally a folded 100 kilodalton protein. These models systems inform us about the distinctive angular correlations generated by bonding, polypeptide chains, secondary structure and tertiary structure. They further indicate the potential to use angular correlations as a sensitive measure of conformation change that is complementary to existing structural analysis techniques.

Perspectives on single particle imaging with x rays at the advent of high repetition rate x-ray free electron laser sources

X-ray free electron lasers (XFELs) now routinely produce millijoule level pulses of x-ray photons with tens of femtoseconds duration. Such x-ray intensities gave rise to the idea that weakly scattering particles-perhaps single biomolecules or viruses-could be investigated free of radiation damage. Here, we examine elements from the past decade of so-called single particle imaging with hard XFELs. We look at the progress made to date and identify some future possible directions for the field. In particular, we summarize the presently achieved resolutions as well as identifying the bottlenecks and enabling technologies to future resolution improvement, which in turn enables application to samples of scientific interest.

Steerable ePCA: Rotationally Invariant Exponential Family PCA

In photon-limited imaging, the pixel intensities are affected by photon count noise. Many applications require an accurate estimation of the covariance of the underlying 2-D clean images. For example, in X-ray free electron laser (XFEL) single molecule imaging, the covariance matrix of 2-D diffraction images is used to reconstruct the 3-D molecular structure. Accurate estimation of the covariance from low-photon-count images must take into account that pixel intensities are Poisson distributed, hence the classical sample covariance estimator is highly biased. Moreover, in single molecule imaging, including in-plane rotated copies of all images could further improve the accuracy of covariance estimation. In this paper we introduce an efficient and accurate algorithm for covariance matrix estimation of count noise 2-D images, including their uniform planar rotations and possibly reflections. Our procedure, steerable ePCA, combines in a novel way two recently introduced innovations. The first is a methodology for principal component analysis (PCA) for Poisson distributions, and more generally, exponential family distributions, called ePCA. The second is steerable PCA, a fast and accurate procedure for including all planar rotations when performing PCA. The resulting principal components are invariant to the rotation and reflection of the input images. We demonstrate the efficiency and accuracy of steerable ePCA in numerical experiments involving simulated XFEL datasets and rotated face images from Yale Face Database B.

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.

Design of a liquid cell toward three-dimensional imaging of unidirectionally-aligned particles in solution using X-ray free-electron lasers

A liquid cell was designed for coherent diffractive imaging measurements at high tilt angles and tested at SACLA.

Low-signal limit of X-ray single particle diffractive imaging

An outstanding question in X-ray single particle imaging experiments has been the feasibility of imaging sub 10-nm-sized biomolecules under realistic experimental conditions where very few photons are expected to be measured in a single snapshot and instrument background may be significant relative to particle scattering. While analyses of simulated data have shown that the determination of an average image should be feasible using Bayesian methods such as the EMC algorithm, this has yet to be demonstrated using experimental data containing realistic non-isotropic instrument background, sample variability and other experimental factors. In this work, we show that the orientation and phase retrieval steps work at photon counts diluted to the signal levels one expects from smaller molecules or with weaker pulses, using data from experimental measurements of 60-nm PR772 viruses. Even when the signal is reduced to a fraction as little as 1/256, the virus electron density determined using ab initio phasing is of almost the same quality as the high-signal data. However, we are still limited by the total number of patterns collected, which may soon be mitigated by the advent of high repetition-rate sources like the European XFEL and LCLS-II.

Angular X-Ray Cross-Correlation Analysis (AXCCA): Basic Concepts and Recent Applications to Soft Matter and Nanomaterials

Angular X-ray cross-correlation analysis (AXCCA) is a technique which allows quantitative measurement of the angular anisotropy of X-ray diffraction patterns and provides insights into the orientational order in the system under investigation. This method is based on the evaluation of the angular cross-correlation function of the scattered intensity distribution on a two-dimensional (2D) detector and further averaging over many diffraction patterns for enhancement of the anisotropic signal. Over the last decade, AXCCA was successfully used to study the anisotropy in various soft matter systems, such as solutions of anisotropic particles, liquid crystals, colloidal crystals, superlattices composed by nanoparticles, etc. This review provides an introduction to the technique and gives a survey of the recent experimental work in which AXCCA in combination with micro- or nanofocused X-ray microscopy was used to study the orientational order in various soft matter systems.

Multi-target detection with application to cryo-electron microscopy

We consider the multi-target detection problem of recovering a set of signals that appear multiple times at unknown locations in a noisy measurement. In the low noise regime, one can estimate the signals by first detecting occurrences, then clustering and averaging them. In the high noise regime, however, neither detection nor clustering can be performed reliably, so that strategies along these lines are destined to fail. Notwithstanding, using autocorrelation analysis, we show that the impossibility to detect and cluster signal occurrences in the presence of high noise does not necessarily preclude signal estimation. Specifically, to estimate the signals, we derive simple relations between the autocorrelations of the observation and those of the signals. These autocorrelations can be estimated accurately at any noise level given a sufficiently long measurement. To recover the signals from the observed autocorrelations, we solve a set of polynomial equations through nonlinear least-squares. We provide analysis regarding well-posedness of the task, and demonstrate numerically the effectiveness of the method in a variety of settings. The main goal of this work is to provide theoretical and numerical support for a recently proposed framework to image 3D structures of biological macromolecules using cryo-electron microscopy in extreme noise levels.

Structural mass spectrometry goes viral

Over the last 20 years, mass spectrometry (MS), with its ability to analyze small sample amounts with high speed and sensitivity, has more and more entered the field of structural virology, aiming to investigate the structure and dynamics of viral proteins as close to their native environment as possible. The use of non-perturbing labels in hydrogen-deuterium exchange MS allows for the analysis of interactions between viral proteins and host cell factors as well as their dynamic responses to the environment. Cross-linking MS, on the other hand, can analyze interactions in viral protein complexes and identify virus-host interactions in cells. Native MS allows transferring viral proteins, complexes and capsids into the gas phase and has broken boundaries to overcome size limitations, so that now even the analysis of intact virions is possible. Different MS approaches not only inform about size, stability, interactions and dynamics of virus assemblies, but also bridge the gap to other biophysical techniques, providing valuable constraints for integrative structural modeling of viral complex assemblies that are often inaccessible by single technique approaches. In this review, recent advances are highlighted, clearly showing that structural MS approaches in virology are moving towards systems biology and ever more experiments are performed on cellular level.

Deep neural networks for classifying complex features in diffraction images

Intense short-wavelength pulses from free-electron lasers and high-harmonic-generation sources enable diffractive imaging of individual nanosized objects with a single x-ray laser shot. The enormous data sets with up to several million diffraction patterns present a severe problem for data analysis because of the high dimensionality of imaging data. Feature recognition and selection is a crucial step to reduce the dimensionality. Usually, custom-made algorithms are developed at a considerable effort to approximate the particular features connected to an individual specimen, but because they face different experimental conditions, these approaches do not generalize well. On the other hand, deep neural networks are the principal instrument for today's revolution in automated image recognition, a development that has not been adapted to its full potential for data analysis in science. We recently published [Langbehn et al., Phys. Rev. Lett. 121, 255301 (2018)PRLTAO0031-900710.1103/PhysRevLett.121.255301] the application of a deep neural network as a feature extractor for wide-angle diffraction images of helium nanodroplets. Here we present the setup, our modifications, and the training process of the deep neural network for diffraction image classification and its systematic bench marking. We find that deep neural networks significantly outperform previous attempts for sorting and classifying complex diffraction patterns and are a significant improvement for the much-needed assistance during postprocessing of large amounts of experimental coherent diffraction imaging data.