Single-particle imaging by x-ray free-electron lasers-How many snapshots are needed?

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.

Structural biology in the age of X-ray free-electron lasers and exascale computing

Serial femtosecond X-ray crystallography has emerged as a powerful method for investigating biomolecular structure and dynamics. With the new generation of X-ray free-electron lasers, which generate ultrabright X-ray pulses at megahertz repetition rates, we can now rapidly probe ultrafast conformational changes and charge movement in biomolecules. Over the last year, another innovation has been the deployment of Frontier, the world's first exascale supercomputer. Synergizing extremely high repetition rate X-ray light sources and exascale computing has the potential to accelerate discovery in biomolecular sciences. Here we outline our perspective on each of these remarkable innovations individually, and the opportunities and challenges in yoking them within an integrated research infrastructure.

Helium-electrospray improves sample delivery in X-ray single-particle imaging experiments

Imaging the structure and observing the dynamics of isolated proteins using single-particle X-ray diffractive imaging (SPI) is one of the potential applications of X-ray free-electron lasers (XFELs). Currently, SPI experiments on isolated proteins are limited by three factors: low signal strength, limited data and high background from gas scattering. The last two factors are largely due to the shortcomings of the aerosol sample delivery methods in use. Here we present our modified electrospray ionization (ESI) source, which we dubbed helium-ESI (He-ESI). With it, we increased particle delivery into the interaction region by a factor of 10, for 26 nm-sized biological particles, and decreased the gas load in the interaction chamber corresponding to an 80% reduction in gas scattering when compared to the original ESI. These improvements have the potential to significantly increase the quality and quantity of SPI diffraction patterns in future experiments using He-ESI, resulting in higher-resolution structures.

Blue and red in the protein world: Photoactive yellow protein and phytochromes as revealed by time-resolved crystallography

Time-resolved crystallography (TRX) is a method designed to investigate functional motions of biological macromolecules on all time scales. Originally a synchrotron-based method, TRX is enabled by the development of TR Laue crystallography (TRLX). TR serial crystallography (TR-SX) is an extension of TRLX. As the foundations of TRLX were evolving from the late 1980s to the turn of the millennium, TR-SX has been inspired by the development of Free Electron Lasers for hard X-rays. Extremely intense, ultrashort x-ray pulses could probe micro and nanocrystals, but at the same time, they inflicted radiation damage that necessitated the replacement by a new crystal. Consequently, a large number of microcrystals are exposed to X-rays one by one in a serial fashion. With TR-SX methods, one of the largest obstacles of previous approaches, namely, the unsurmountable challenges associated with the investigation of non-cyclic (irreversible) reactions, can be overcome. This article describes successes and transformative contributions to the TRX field by Keith Moffat and his collaborators, highlighting two major projects on protein photoreceptors initiated in the Moffat lab at the turn of the millennium.

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.

Single-Molecule X-ray Scattering Used to Visualize the Conformation Distribution of Biological Molecules via Single-Object Scattering Sampling

Biological macromolecules, the fundamental building blocks of life, exhibit dynamic structures in their natural environment. Traditional structure determination techniques often oversimplify these multifarious conformational spectra by capturing only ensemble- and time-averaged molecular structures. Addressing this gap, in this work, we extend the application of the single-object scattering sampling (SOSS) method to diverse biological molecules, including RNAs and proteins. Our approach, referred to as "Bio-SOSS", leverages ultrashort X-ray pulses to capture instantaneous structures. In Bio-SOSS, we employ two gold nanoparticles (AuNPs) as labels, which provide strong contrast in the X-ray scattering signal, to ensure precise distance determinations between labeled sites. We generated hypothetical Bio-SOSS images for RNAs, proteins, and an RNA-protein complex, each labeled with two AuNPs at specified positions. Subsequently, to validate the accuracy of Bio-SOSS, we extracted distances between these nanoparticle labels from the images and compared them with the actual values used to generate the Bio-SOSS images. Specifically, for a representative RNA (1KXK), the standard deviation in distance discrepancies between molecular dynamics snapshots and Bio-SOSS retrievals was found to be optimally around 0.2 Å, typically within 1 Å under practical experimental conditions at state-of-the-art X-ray free-electron laser facilities. Furthermore, we conducted an in-depth analysis of how various experimental factors, such as AuNP size, X-ray properties, and detector geometry, influence the accuracy of Bio-SOSS. This comprehensive investigation highlights the practicality and potential of Bio-SOSS in accurately capturing the diverse conformation spectrum of biological macromolecules, paving the way for deeper insights into their dynamic natures.

A phenomenological model of the X-ray pulse statistics of a high-repetition-rate X-ray free-electron laser

Many coherent imaging applications that utilize ultrafast X-ray free-electron laser (XFEL) radiation pulses are highly sensitive to fluctuations in the shot-to-shot statistical properties of the source. Understanding and modelling these fluctuations are key to successful experiment planning and necessary to maximize the potential of XFEL facilities. Current models of XFEL radiation and their shot-to-shot statistics are based on theoretical descriptions of the source and are limited in their ability to capture the shot-to-shot intensity fluctuations observed experimentally. The lack of accurate temporal statistics in simulations that utilize these models is a significant barrier to optimizing and interpreting data from XFEL coherent diffraction experiments. Presented here is a phenomenological model of XFEL radiation that is capable of capturing the shot-to-shot statistics observed experimentally using a simple time-dependent approximation of the pulse wavefront. The model is applied to reproduce non-stationary shot-to-shot intensity fluctuations observed at the European XFEL, whilst accurately representing the single-shot properties predicted by FEL theory. Compared with previous models, this approach provides a simple, robust and computationally inexpensive method of generating statistical representations of XFEL radiation.

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.

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.

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.

Optimizing the geometry of aerodynamic lens injectors for single-particle coherent diffractive imaging of gold nanoparticles

Single-particle X-ray diffractive imaging (SPI) of small (bio-)nanoparticles (NPs) requires optimized injectors to collect sufficient diffraction patterns to allow for the reconstruction of the NP structure with high resolution. Typically, aerodynamic lens-stack injectors are used for NP injection. However, current injectors were developed for larger NPs (>100 nm), and their ability to generate high-density NP beams suffers with decreasing NP size. Here, an aerodynamic lens-stack injector with variable geometry and a geometry-optimization procedure are presented. The optimization for 50 nm gold-NP (AuNP) injection using a numerical-simulation infrastructure capable of calculating the carrier-gas flow and the particle trajectories through the injector is also introduced. The simulations were experimentally validated using spherical AuNPs and sucrose NPs. In addition, the optimized injector was compared with the standard-installation 'Uppsala injector' for AuNPs. Results for these heavy particles showed a shift in the particle-beam focus position rather than a change in beam size, which results in a lower gas background for the optimized injector. Optimized aerodynamic lens-stack injectors will allow one to increase NP beam density, reduce the gas background, discover the limits of current injectors and contribute to structure determination of small NPs using SPI.

Comparison of EMC and CM methods for orienting diffraction images in single-particle imaging experiments

In single-particle imaging (SPI) experiments, diffraction patterns of identical particles are recorded. The particles are injected into the X-ray free-electron laser (XFEL) beam in random orientations. The crucial step of the data processing of SPI is finding the orientations of the recorded diffraction patterns in reciprocal space and reconstructing the 3D intensity distribution. Here, two orientation methods are compared: the expansion maximization compression (EMC) algorithm and the correlation maximization (CM) algorithm. To investigate the efficiency, reliability and accuracy of the methods at various XFEL pulse fluences, simulated diffraction patterns of biological molecules are used.

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.

Features and futures of X-ray free-electron lasers

Linear accelerator-based free-electron lasers (FELs) are the leading source of fully coherent X-rays with ultra-high peak powers and ultra-short pulse lengths. Current X-ray FEL facilities have proved their worth as useful tools for diverse scientific applications. In this paper, we present an overview of the features and future prospects of X-ray FELs, including the working principles and properties of X-ray FELs, the operational status of different FEL facilities worldwide, the applications supported by such facilities, and the current developments and outlook for X-ray FEL-based research.

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X-ray free-electron lasers (XFELs) generate X-ray by electrons flying through a periodic magnetic field.

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XFELs are the leading X-ray sources with ultra-high brightness and ultra-short duration.

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XFELs can be launched from either the shot noise of the electron beam or the seed.

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XFEL-laser collision is proposed to learn the nature of vacuum at SHINE.

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XFELs are being combined with intense lasers and synchrotron radiation light sources.

X-ray-Based Techniques to Study the Nano-Bio Interface

X-ray-based analytics are routinely applied in many fields, including physics, chemistry, materials science, and engineering. The full potential of such techniques in the life sciences and medicine, however, has not yet been fully exploited. We highlight current and upcoming advances in this direction. We describe different X-ray-based methodologies (including those performed at synchrotron light sources and X-ray free-electron lasers) and their potentials for application to investigate the nano-bio interface. The discussion is predominantly guided by asking how such methods could better help to understand and to improve nanoparticle-based drug delivery, though the concepts also apply to nano-bio interactions in general. We discuss current limitations and how they might be overcome, particularly for future use in vivo.

High-resolution crystal structures of transient intermediates in the phytochrome photocycle

Phytochromes are red/far-red light photoreceptors in bacteria to plants, which elicit a variety of important physiological responses. They display a reversible photocycle between the resting Pr state and the light-activated Pfr state. Light signals are transduced as structural change through the entire protein to modulate its activity. It is unknown how the Pr-to-Pfr interconversion occurs, as the structure of intermediates remains notoriously elusive. Here, we present short-lived crystal structures of the photosensory core modules of the bacteriophytochrome from myxobacterium Stigmatella aurantiaca captured by an X-ray free electron laser 5 ns and 33 ms after light illumination of the Pr state. We observe large structural displacements of the covalently bound bilin chromophore, which trigger a bifurcated signaling pathway that extends through the entire protein. The snapshots show with atomic precision how the signal progresses from the chromophore, explaining how plants, bacteria, and fungi sense red light.

An encryption-decryption framework to validating single-particle imaging

We propose an encryption-decryption framework for validating diffraction intensity volumes reconstructed using single-particle imaging (SPI) with X-ray free-electron lasers (XFELs) when the ground truth volume is absent. This conceptual framework exploits each reconstructed volumes' ability to decipher latent variables (e.g. orientations) of unseen sentinel diffraction patterns. Using this framework, we quantify novel measures of orientation disconcurrence, inconsistency, and disagreement between the decryptions by two independently reconstructed volumes. We also study how these measures can be used to define data sufficiency and its relation to spatial resolution, and the practical consequences of focusing XFEL pulses to smaller foci. This conceptual framework overcomes critical ambiguities in using Fourier Shell Correlation (FSC) as a validation measure for SPI. Finally, we show how this encryption-decryption framework naturally leads to an information-theoretic reformulation of the resolving power of XFEL-SPI, which we hope will lead to principled frameworks for experiment and instrument design.

Selecting XFEL single-particle snapshots by geometric machine learning

A promising new route for structural biology is single-particle imaging with an X-ray Free-Electron Laser (XFEL). This method has the advantage that the samples do not require crystallization and can be examined at room temperature. However, high-resolution structures can only be obtained from a sufficiently large number of diffraction patterns of individual molecules, so-called single particles. Here, we present a method that allows for efficient identification of single particles in very large XFEL datasets, operates at low signal levels, and is tolerant to background. This method uses supervised Geometric Machine Learning (GML) to extract low-dimensional feature vectors from a training dataset, fuse test datasets into the feature space of training datasets, and separate the data into binary distributions of "single particles" and "non-single particles." As a proof of principle, we tested simulated and experimental datasets of the Coliphage PR772 virus. We created a training dataset and classified three types of test datasets: First, a noise-free simulated test dataset, which gave near perfect separation. Second, simulated test datasets that were modified to reflect different levels of photon counts and background noise. These modified datasets were used to quantify the predictive limits of our approach. Third, an experimental dataset collected at the Stanford Linear Accelerator Center. The single-particle identification for this experimental dataset was compared with previously published results and it was found that GML covers a wide photon-count range, outperforming other single-particle identification methods. Moreover, a major advantage of GML is its ability to retrieve single particles in the presence of structural variability.

Pump-Probe Time-Resolved Serial Femtosecond Crystallography at X-Ray Free Electron Lasers

With time-resolved crystallography (TRX), it is possible to follow the reaction dynamics in biological macromolecules by investigating the structure of transient states along the reaction coordinate. X-ray free electron lasers (XFELs) have enabled TRX experiments on previously uncharted femtosecond timescales. Here, we review the recent developments, opportunities, and challenges of pump-probe TRX at XFELs.

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.