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X-ray free-electron lasers offer unique capabilities for measuring the structure and dynamics of biomolecules, helping us understand the basic building blocks of life. Notably, high-repetition-rate free-electron lasers enable single particle imaging, where individual, weakly scattering biomolecules are imaged under near-physiological conditions with the opportunity to access fleeting states that cannot be captured in cryogenic or crystallized conditions. Existing X-ray single particle reconstruction algorithms, which estimate the particle orientation for each image independently, are slow and memory-intensive when handling the massive datasets generated by emerging free-electron lasers. Here, we introduce X-RAI ( X - R ay single particle imaging with A mortized I nference), an online reconstruction framework that estimates the structure of 3D macromolecules from large X-ray single particle datasets. X-RAI consists of a convolutional encoder, which amortizes pose estimation over large datasets, as well as a physics-based decoder, which employs an implicit neural representation to enable high-quality 3D reconstruction in an end-to-end, self-supervised manner. We demonstrate that X-RAI achieves state-of-the-art performance for small-scale datasets in simulation and challenging experimental settings and demonstrate its unprecedented ability to process large datasets containing millions of diffraction images in an online fashion. These abilities signify a paradigm shift in X-ray single particle imaging towards real-time reconstruction. The authors devise an algorithm to reconstruct proteins from X-ray single particle data, unlocking the ability to process datasets online, in a single pass. The technique matches or outperforms existing methods in simulation and on experimental data.

This paper introduces spectral incoherent diffractive imaging (SIDI) as a novel method for achieving dark-field imaging of nanostructures with heterogeneous oxidation states. With SIDI, shifts in photoemission profiles can be spatially resolved, enabling the independent imaging of the underlying emitter distributions contributing to each spectral line. In the x-ray domain, this approach offers unique insights beyond the conventional combination of diffraction and x-ray emission spectroscopy. When applied at x-ray free-electron lasers, SIDI promises to be a versatile tool for investigating a broad range of systems, offering unprecedented opportunities for detailed characterization of heterogeneous nanostructures for catalysis and energy storage, including of their ultrafast dynamics.

Intensity interferometry is a well known method in astronomy. Recently, a related method called incoherent diffractive imaging (IDI) was proposed to apply intensity correlations of x-ray fluorescence radiation to determine the 3D arrangement of the emitting atoms in a sample. Here we discuss inherent sources of noise affecting IDI and derive a model to estimate the dependence of the signal to noise ratio (SNR) on the photon counts per pixel, the temporal coherence (or number of modes), and the shape of the imaged object. Simulations in two- and three-dimensions have been performed to validate the predictions of the model. We find that contrary to coherent imaging methods, higher intensities and higher detected counts do not always correspond to a larger SNR. Also, larger and more complex objects generally yield a poorer SNR despite the higher measured counts. The framework developed here should be a valuable guide to future experimental design.

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.

Serial femtosecond crystallography (SFX) with X-ray free electron lasers (XFELs) allows structure determination of membrane proteins and time-resolved crystallography. Common liquid sample delivery continuously jets the protein crystal suspension into the path of the XFEL, wasting a vast amount of sample due to the pulsed nature of all current XFEL sources. The European XFEL (EuXFEL) delivers femtosecond (fs) X-ray pulses in trains spaced 100 ms apart whereas pulses within trains are currently separated by 889 ns. Therefore, continuous sample delivery via fast jets wastes >99% of sample. Here, we introduce a microfluidic device delivering crystal laden droplets segmented with an immiscible oil reducing sample waste and demonstrate droplet injection at the EuXFEL compatible with high pressure liquid delivery of an SFX experiment. While achieving ~60% reduction in sample waste, we determine the structure of the enzyme 3-deoxy-D- manno -octulosonate-8-phosphate synthase from microcrystals delivered in droplets revealing distinct structural features not previously reported. Due to the pulsed nature of X-ray free electron laser (XFEL) instruments the majority of protein crystals, which are injected using continuous jet injection techniques are wasted. Here, the authors present a microfluidic device to deliver aqueous protein crystal laden droplets segmented with an immiscible oil and demonstrate that with this device an approx. 60% reduction in sample waste was achieved for data collection of 3-deoxy-D-manno-octulosonate 8-phosphate synthase crystals at the EuXFEL.

The emergence of high repetition-rate X-ray free-electron lasers (XFELs) powered by superconducting accelerator technology enables the measurement of significantly more experimental data per day than was previously possible. The European XFEL is expected to provide 27,000 pulses per second, over two orders of magnitude more than any other XFEL. The increased pulse rate is a key enabling factor for single-particle X-ray diffractive imaging, which relies on averaging the weak diffraction signal from single biological particles. Taking full advantage of this new capability requires that all experimental steps, from sample preparation and delivery to the acquisition of diffraction patterns, are compatible with the increased pulse repetition rate. Here, we show that single-particle imaging can be performed using X-ray pulses at megahertz repetition rates. The results obtained pave the way towards exploiting high repetition-rate X-ray free-electron lasers for single-particle imaging at their full repetition rate. Diffractive imaging of single-particle nanoscale systems has so far been hindered by low hit probabilities and repetition rates. Here, single-particle imaging of nanospheres and viruses at megahertz repetition rates is demonstrated at the European X-ray Free-Electron Laser (XFEL) for the first time.

The analysis of a single-particle imaging (SPI) experiment performed at the AMO beamline at LCLS as part of the SPI initiative is presented here. A workflow for the three-dimensional virus reconstruction of the PR772 bacteriophage from measured single-particle data is developed. It consists of several well defined steps including single-hit diffraction data classification, refined filtering of the classified data, reconstruction of three-dimensional scattered intensity from the experimental diffraction patterns by orientation determination and a final three-dimensional reconstruction of the virus electron density without symmetry constraints. The analysis developed here revealed and quantified nanoscale features of the PR772 virus measured in this experiment, with the obtained resolution better than 10 nm, with a clear indication that the structure was compressed in one direction and, as such, deviates from ideal icosahedral symmetry.

With the development of X‐ray free‐electron lasers (XFELs), producing pulses of femtosecond durations comparable with the coherence times of X‐ray fluorescence, it has become possible to observe intensity–intensity correlations due to the interference of emission from independent atoms. This has been used to compare durations of X‐ray pulses and to measure the size of a focusedX‐ray beam, for example. Here it is shown that it is also possible to observe the interference of fluorescence photons through the measurement of the speckle contrast of angle‐resolved fluorescence patterns. Speckle contrast is often used as a measure of the degree of coherence of the incident beam or the fluctuations of the illuminated sample as determined from X‐ray diffraction patterns formed by elastic scattering, rather than from fluorescence patterns as addressed here. Commonly used approaches to estimate speckle contrast were found to suffer when applied to XFEL‐generated fluorescence patterns due to low photon counts and a significant variation of the excitation pulse energy from shot to shot. A new method to reliably estimate speckle contrast under such conditions, using a weighting scheme, is introduced. The method is demonstrated by comparing the speckle contrast of fluorescence observed with pulses of 3 fs to 15 fs duration. Methods are developed to quantify the degree of coherence of fluorescently emitted X‐rays from short‐pulse XFEL excitations. Applications to 3 fs and 15 fs excitations are shown.

Here we present a new approach to diffraction imaging of amyloid fibrils, combining a free-standing graphene support and single nanofocused X-ray pulses of femtosecond duration from an X-ray free-electron laser. Due to the very low background scattering from the graphene support and mutual alignment of filaments, diffraction from tobacco mosaic virus (TMV) filaments and amyloid protofibrils is obtained to 2.7 Å and 2.4 Å resolution in single diffraction patterns, respectively. Some TMV diffraction patterns exhibit asymmetry that indicates the presence of a limited number of axial rotations in the XFEL focus. Signal-to-noise levels from individual diffraction patterns are enhanced using computational alignment and merging, giving patterns that are superior to those obtainable from synchrotron radiation sources. We anticipate that our approach will be a starting point for further investigations into unsolved structures of filaments and other weakly scattering objects. The structures of amyloid fibres are currently primarily studied through solid state NMR and cryo-EM. Here the authors present a free-standing graphene support device that allows diffraction imaging of non-crystalline amyloid fibrils with single X-ray pulses from an X-ray free-electron laser.

Single-stranded RNA viruses co-assemble their capsid with the genome, and variations in capsid structures can have significant functional relevance. In particular, viruses need to respond to a dehydrating environment to prevent genomic degradation and remain active upon rehydration. Theoretical work has predicted low-energy buckling transitions in icosahedral capsids, which could protect the virus from further dehydration. However, there has been no direct experimental evidence, nor a molecular mechanism, for such behavior. Here, we observe this transition using X-ray single particle imaging of MS2 bacteriophages after aerosolization. Using a combination of machine learning tools, we classify hundreds of thousands of single-particle diffraction patterns to learn the structural landscape of the capsid morphology as a function of time spent in the aerosol phase. We found a previously unreported compact conformation as well as intermediate structures that suggest an incoherent buckling transition that does not preserve icosahedral symmetry. Finally, we propose a mechanism for this buckling, where a single 19-residue loop is destabilized, leading to the large observed morphological change. Our results provide experimental evidence for a mechanism by which viral capsids may protect themselves from dehydration upon aerosolization. In the process, these findings also demonstrate the power of single-particle X-ray imaging and machine learning methods in studying biomolecular structural dynamics.