Resolving Nonequilibrium Shape Variations among Millions of Gold Nanoparticles.

Nanoparticles, exhibiting functionally relevant structural heterogeneity, are at the forefront of cutting-edge research. Now, high-throughput single-particle imaging (SPI) with X-ray free-electron lasers (XFELs) creates opportunities for recovering the shape distributions of millions of particles that exhibit functionally relevant structural heterogeneity. To realize this potential, three challenges have to be overcome: (1) simultaneous parametrization of structural variability in real and reciprocal spaces; (2) efficiently inferring the latent parameters of each SPI measurement; (3) scaling up comparisons between 105 structural models and 106 XFEL-SPI measurements. Here, we describe how we overcame these three challenges to resolve the nonequilibrium shape distributions within millions of gold nanoparticles imaged at the European XFEL. These shape distributions allowed us to quantify the degree of asymmetry in these particles, discover a relatively stable "shape envelope" among nanoparticles, discern finite-size effects related to shape-controlling surfactants, and extrapolate nanoparticles' shapes to their idealized thermodynamic limit. Ultimately, these demonstrations show that XFEL SPI can help transform nanoparticle shape characterization from anecdotally interesting to statistically meaningful.

Enhanced EMC-Advantages of partially known orientations in x-ray single particle imaging.

Single particle imaging of proteins in the gas phase with x-ray free-electron lasers holds great potential to study fast protein dynamics, but is currently limited by weak and noisy data. A further challenge is to discover the proteins' orientation as each protein is randomly oriented when exposed to x-rays. Algorithms such as the expand, maximize, and compress (EMC) exist that can solve the orientation problem and reconstruct the three-dimensional diffraction intensity space, given sufficient measurements. If information about orientation were known, for example, by using an electric field to orient the particles, the reconstruction would benefit and potentially reach better results. We used simulated diffraction experiments to test how the reconstructions from EMC improve with particles' orientation to a preferred axis. Our reconstructions converged to correct maps of the three-dimensional diffraction space with fewer measurements if biased orientation information was considered. Even for a moderate bias, there was still significant improvement. Biased orientations also substantially improved the results in the case of missing central information, in particular in the case of small datasets. The effects were even more significant when adding a background with 50% the strength of the averaged diffraction signal photons to the diffraction patterns, sometimes reducing the data requirement for convergence by a factor of 10. This demonstrates the usefulness of having biased orientation information in single particle imaging experiments, even for a weaker bias than what was previously known. This could be a key component in overcoming the problems with background noise that currently plague these experiments.

Introduction to the virtual collection of papers on Artificial neural networks: applications in X-ray photon science and crystallography.

Artificial intelligence is more present than ever, both in our society in general and in science. At the center of this development has been the concept of deep learning, the use of artificial neural networks that are many layers deep and can often reproduce human-like behavior much better than other machine-learning techniques. The articles in this collection are some recent examples of its application for X-ray photon science and crystallography that have been published in Journal of Applied Crystallography.

Observation of a single protein by ultrafast X-ray diffraction.

The idea of using ultrashort X-ray pulses to obtain images of single proteins frozen in time has fascinated and inspired many. It was one of the arguments for building X-ray free-electron lasers. According to theory, the extremely intense pulses provide sufficient signal to dispense with using crystals as an amplifier, and the ultrashort pulse duration permits capturing the diffraction data before the sample inevitably explodes. This was first demonstrated on biological samples a decade ago on the giant mimivirus. Since then, a large collaboration has been pushing the limit of the smallest sample that can be imaged. The ability to capture snapshots on the timescale of atomic vibrations, while keeping the sample at room temperature, may allow probing the entire conformational phase space of macromolecules. Here we show the first observation of an X-ray diffraction pattern from a single protein, that of Escherichia coli GroEL which at 14 nm in diameter is the smallest biological sample ever imaged by X-rays, and demonstrate that the concept of diffraction before destruction extends to single proteins. From the pattern, it is possible to determine the approximate orientation of the protein. Our experiment demonstrates the feasibility of ultrafast imaging of single proteins, opening the way to single-molecule time-resolved studies on the femtosecond timescale.

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.

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.

Noise reduction and mask removal neural network for X-ray single-particle imaging.

Free-electron lasers could enable X-ray imaging of single biological macromolecules and the study of protein dynamics, paving the way for a powerful new imaging tool in structural biology, but a low signal-to-noise ratio and missing regions in the detectors, colloquially termed 'masks', affect data collection and hamper real-time evaluation of experimental data. In this article, the challenges posed by noise and masks are tackled by introducing a neural network pipeline that aims to restore diffraction intensities. For training and testing of the model, a data set of diffraction patterns was simulated from 10 900 different proteins with molecular weights within the range of 10-100 kDa and collected at a photon energy of 8 keV. The method is compared with a simple low-pass filtering algorithm based on autocorrelation constraints. The results show an improvement in the mean-squared error of roughly two orders of magnitude in the presence of masks compared with the noisy data. The algorithm was also tested at increasing mask width, leading to the conclusion that demasking can achieve good results when the mask is smaller than half of the central speckle of the pattern. The results highlight the competitiveness of this model for data processing and the feasibility of restoring diffraction intensities from unknown structures in real time using deep learning methods. Finally, an example is shown of this preprocessing making orientation recovery more reliable, especially for data sets containing very few patterns, using the expansion-maximization-compression algorithm.

Erratum: Experimental strategies for imaging bioparticles with femtosecond hard X-ray pulses. Corrigendum.

[This corrects the article DOI: 10.1107/S2052252517003591.].

Ab initio phasing of the diffraction of crystals with translational disorder.

To date X-ray protein crystallography is the most successful technique available for the determination of high-resolution 3D structures of biological molecules and their complexes. In X-ray protein crystallography the structure of a protein is refined against the set of observed Bragg reflections from a protein crystal. The resolution of the refined protein structure is limited by the highest angle at which Bragg reflections can be observed. In addition, the Bragg reflections alone are typically insufficient (by a factor of two) to determine the structure ab initio, and so prior information is required. Crystals formed from an imperfect packing of the protein molecules may also exhibit continuous diffraction between and beyond these Bragg reflections. When this is due to random displacements of the molecules from each crystal lattice site, the continuous diffraction provides the necessary information to determine the protein structure without prior knowledge, to a resolution that is not limited by the angular extent of the observed Bragg reflections but instead by that of the diffraction as a whole. This article presents an iterative projection algorithm that simultaneously uses the continuous diffraction as well as the Bragg reflections for the determination of protein structures. The viability of this method is demonstrated on simulated crystal diffraction.

Considerations for three-dimensional image reconstruction from experimental data in coherent diffractive imaging.

Diffraction before destruction using X-ray free-electron lasers (XFELs) has the potential to determine radiation-damage-free structures without the need for crystallization. This article presents the three-dimensional reconstruction of the Melbournevirus from single-particle X-ray diffraction patterns collected at the LINAC Coherent Light Source (LCLS) as well as reconstructions from simulated data exploring the consequences of different kinds of experimental sources of noise. The reconstruction from experimental data suffers from a strong artifact in the center of the particle. This could be reproduced with simulated data by adding experimental background to the diffraction patterns. In those simulations, the relative density of the artifact increases linearly with background strength. This suggests that the artifact originates from the Fourier transform of the relatively flat background, concentrating all power in a central feature of limited extent. We support these findings by significantly reducing the artifact through background removal before the phase-retrieval step. Large amounts of blurring in the diffraction patterns were also found to introduce diffuse artifacts, which could easily be mistaken as biologically relevant features. Other sources of noise such as sample heterogeneity and variation of pulse energy did not significantly degrade the quality of the reconstructions. Larger data volumes, made possible by the recent inauguration of high repetition-rate XFELs, allow for increased signal-to-background ratio and provide a way to minimize these artifacts. The anticipated development of three-dimensional Fourier-volume-assembly algorithms which are background aware is an alternative and complementary solution, which maximizes the use of data.

Rapid sample delivery for megahertz serial crystallography at X-ray FELs.

Liquid microjets are a common means of delivering protein crystals to the focus of X-ray free-electron lasers (FELs) for serial femtosecond crystallography measurements. The high X-ray intensity in the focus initiates an explosion of the microjet and sample. With the advent of X-ray FELs with megahertz rates, the typical velocities of these jets must be increased significantly in order to replenish the damaged material in time for the subsequent measurement with the next X-ray pulse. This work reports the results of a megahertz serial diffraction experiment at the FLASH FEL facility using 4.3 nm radiation. The operation of gas-dynamic nozzles that produce liquid microjets with velocities greater than 80 m s-1 was demonstrated. Furthermore, this article provides optical images of X-ray-induced explosions together with Bragg diffraction from protein microcrystals exposed to trains of X-ray pulses repeating at rates of up to 4.5 MHz. The results indicate the feasibility for megahertz serial crystallography measurements with hard X-rays and give guidance for the design of such experiments.

Reproducibility of single protein explosions induced by X-ray lasers.

Single particle imaging (SPI) using X-ray pulses has become increasingly attainable with the advent of high-intensity free electron lasers. Eliminating the need for crystallized samples enables structural studies of molecules previously inaccessible by conventional crystallography. While this emerging technique already demonstrates substantial promise, some obstacles need to be overcome before SPI can reach its full potential. One such problem is determining the spatial orientation of the sample at the time of X-ray interaction. Existing solutions rely on diffraction data and are computationally demanding and sensitive to noise. In this in silico study, we explore the possibility of aiding these methods by mapping the ion distribution as the sample undergoes a Coulomb explosion following the intense ionization. By detecting the ions ejected from the fragmented sample, the orientation of the original sample should be possible to determine. Knowledge of the orientation has been shown earlier to be of substantial advantage in the reconstruction of the original structure. 150 explosions of each of twelve separate systems - four polypeptides with different amounts of surface bound water - were simulated with molecular dynamics (MD) and the average angular distribution of carbon and sulfur ions was investigated independently. The results show that the explosion maps are reproducible in both cases, supporting the idea that orientation information is preserved. Additional water seems to restrict the carbon ion trajectories further through a shielding mechanism, making the maps more distinct. For sulfurs, water has no significant impact on the trajectories, likely due to their higher mass and greater ionization cross section, indicating that they could be of particular interest. Based on these findings, we conclude that explosion data can aid spatial orientation in SPI experiments and could substantially improve the capabilities of the novel technique.

Controlling Protein Orientation in Vacuum Using Electric Fields.

Single-particle imaging using X-ray free-electron lasers is an emerging technique that could provide high-resolution structures of macromolecules in the gas phase. One of the largest difficulties in realizing this goal is the unknown orientation of the individual sample molecules at the time of exposure. Preorientation of the molecules has been identified as a possible solution to this problem. Using molecular dynamics simulations, we identify a range of electric field strengths where proteins become oriented without losing their structure. For a number of experimentally relevant cases we show that structure determination is possible only when orientation information is included in the orientation-recovery process. We conclude that nondestructive field orientation of intact proteins is feasible and that it enables a range of new structural investigations with single-particle imaging.

Coherent soft X-ray diffraction imaging of coliphage PR772 at the Linac coherent light source.

Single-particle diffraction from X-ray Free Electron Lasers offers the potential for molecular structure determination without the need for crystallization. In an effort to further develop the technique, we present a dataset of coherent soft X-ray diffraction images of Coliphage PR772 virus, collected at the Atomic Molecular Optics (AMO) beamline with pnCCD detectors in the LAMP instrument at the Linac Coherent Light Source. The diameter of PR772 ranges from 65-70 nm, which is considerably smaller than the previously reported ~600 nm diameter Mimivirus. This reflects continued progress in XFEL-based single-particle imaging towards the single molecular imaging regime. The data set contains significantly more single particle hits than collected in previous experiments, enabling the development of improved statistical analysis, reconstruction algorithms, and quantitative metrics to determine resolution and self-consistency.

Experimental strategies for imaging bioparticles with femtosecond hard X-ray pulses.

This study explores the capabilities of the Coherent X-ray Imaging Instrument at the Linac Coherent Light Source to image small biological samples. The weak signal from small samples puts a significant demand on the experiment. Aerosolized Omono River virus particles of ∼40 nm in diameter were injected into the submicrometre X-ray focus at a reduced pressure. Diffraction patterns were recorded on two area detectors. The statistical nature of the measurements from many individual particles provided information about the intensity profile of the X-ray beam, phase variations in the wavefront and the size distribution of the injected particles. The results point to a wider than expected size distribution (from ∼35 to ∼300 nm in diameter). This is likely to be owing to nonvolatile contaminants from larger droplets during aerosolization and droplet evaporation. The results suggest that the concentration of nonvolatile contaminants and the ratio between the volumes of the initial droplet and the sample particles is critical in such studies. The maximum beam intensity in the focus was found to be 1.9 × 1012 photons per µm2 per pulse. The full-width of the focus at half-maximum was estimated to be 500 nm (assuming 20% beamline transmission), and this width is larger than expected. Under these conditions, the diffraction signal from a sample-sized particle remained above the average background to a resolution of 4.25 nm. The results suggest that reducing the size of the initial droplets during aerosolization is necessary to bring small particles into the scope of detailed structural studies with X-ray lasers.

Open data set of live cyanobacterial cells imaged using an X-ray laser.

Structural studies on living cells by conventional methods are limited to low resolution because radiation damage kills cells long before the necessary dose for high resolution can be delivered. X-ray free-electron lasers circumvent this problem by outrunning key damage processes with an ultra-short and extremely bright coherent X-ray pulse. Diffraction-before-destruction experiments provide high-resolution data from cells that are alive when the femtosecond X-ray pulse traverses the sample. This paper presents two data sets from micron-sized cyanobacteria obtained at the Linac Coherent Light Source, containing a total of 199,000 diffraction patterns. Utilizing this type of diffraction data will require the development of new analysis methods and algorithms for studying structure and structural variability in large populations of cells and to create abstract models. Such studies will allow us to understand living cells and populations of cells in new ways. New X-ray lasers, like the European XFEL, will produce billions of pulses per day, and could open new areas in structural sciences.

Condor: a simulation tool for flash X-ray imaging.

Flash X-ray imaging has the potential to determine structures down to molecular resolution without the need for crystallization. The ability to accurately predict the diffraction signal and to identify the optimal experimental configuration within the limits of the instrument is important for successful data collection. This article introduces Condor, an open-source simulation tool to predict X-ray far-field scattering amplitudes of isolated particles for customized experimental designs and samples, which the user defines by an atomic or a refractive index model. The software enables researchers to test whether their envisaged imaging experiment is feasible, and to optimize critical parameters for reaching the best possible result. It also aims to support researchers who intend to create or advance reconstruction algorithms by simulating realistic test data. Condor is designed to be easy to use and can be either installed as a Python package or used from its web interface (http://lmb.icm.uu.se/condor). X-ray free-electron lasers have high running costs and beam time at these facilities is precious. Data quality can be substantially improved by using simulations to guide the experimental design and simplify data analysis.

Single-shot diffraction data from the Mimivirus particle using an X-ray free-electron laser.

Free-electron lasers (FEL) hold the potential to revolutionize structural biology by producing X-ray pules short enough to outrun radiation damage, thus allowing imaging of biological samples without the limitation from radiation damage. Thus, a major part of the scientific case for the first FELs was three-dimensional (3D) reconstruction of non-crystalline biological objects. In a recent publication we demonstrated the first 3D reconstruction of a biological object from an X-ray FEL using this technique. The sample was the giant Mimivirus, which is one of the largest known viruses with a diameter of 450 nm. Here we present the dataset used for this successful reconstruction. Data-analysis methods for single-particle imaging at FELs are undergoing heavy development but data collection relies on very limited time available through a highly competitive proposal process. This dataset provides experimental data to the entire community and could boost algorithm development and provide a benchmark dataset for new algorithms.

A data set from flash X-ray imaging of carboxysomes.

Ultra-intense femtosecond X-ray pulses from X-ray lasers permit structural studies on single particles and biomolecules without crystals. We present a large data set on inherently heterogeneous, polyhedral carboxysome particles. Carboxysomes are cell organelles that vary in size and facilitate up to 40% of Earth's carbon fixation by cyanobacteria and certain proteobacteria. Variation in size hinders crystallization. Carboxysomes appear icosahedral in the electron microscope. A protein shell encapsulates a large number of Rubisco molecules in paracrystalline arrays inside the organelle. We used carboxysomes with a mean diameter of 115±26 nm from Halothiobacillus neapolitanus. A new aerosol sample-injector allowed us to record 70,000 low-noise diffraction patterns in 12 min. Every diffraction pattern is a unique structure measurement and high-throughput imaging allows sampling the space of structural variability. The different structures can be separated and phased directly from the diffraction data and open a way for accurate, high-throughput studies on structures and structural heterogeneity in biology and elsewhere.

Three-dimensional reconstruction of the giant mimivirus particle with an x-ray free-electron laser.

We present a proof-of-concept three-dimensional reconstruction of the giant mimivirus particle from experimentally measured diffraction patterns from an x-ray free-electron laser. Three-dimensional imaging requires the assembly of many two-dimensional patterns into an internally consistent Fourier volume. Since each particle is randomly oriented when exposed to the x-ray pulse, relative orientations have to be retrieved from the diffraction data alone. We achieve this with a modified version of the expand, maximize and compress algorithm and validate our result using new methods.