Experimental 3D coherent diffractive imaging from photon-sparse random projections

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.

Bragg coherent diffraction imaging with the CITIUS charge-integrating detector

The CITIUS detector is a next-generation high-speed X-ray imaging detector. It has integrating-type pixels and is designed to show a consistent linear response at a frame rate of 17.4 kHz, which results in a saturation count rate of over 30 Mcps pixel-1 when operating at an acquisition duty cycle close to 100%, and up to 20 times higher with special extended acquisition modes. Here, its application for Bragg coherent diffraction imaging is demonstrated by taking advantage of the fourth-generation Extremely Brilliant Source of the European Synchrotron (ESRF-EBS, Grenoble, France). The CITIUS detector outperformed a photon-counting detector, similar spatial resolution being achieved (20 ± 6 nm versus 22 ± 9 nm) with greatly reduced acquisition times (23 s versus 200 s). It is also shown how the CITIUS detector can be expected to perform during dynamic Bragg coherent diffraction imaging measurements. Finally, the current limitations of the CITIUS detector and further optimizations for coherent imaging techniques are discussed.

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.

Single-Image Super-Resolution Improvement of X-ray Single-Particle Diffraction Images Using a Convolutional Neural Network

Femtosecond X-ray pulse lasers are promising probes for the elucidation of the multiconformational states of biomolecules because they enable snapshots of single biomolecules to be observed as coherent diffraction images. Multi-image processing using an X-ray free-electron laser has proven to be a successful structural analysis method for viruses. However, the performance of single-particle analysis (SPA) for flexible biomolecules with sizes ≤100 nm remains difficult. Owing to the multiconformational states of biomolecules and noisy character of diffraction images, diffraction image improvement by multi-image processing is often ineffective for such molecules. Herein, a single-image super-resolution (SR) model was constructed using an SR convolutional neural network (SRCNN). Data preparation was performed in silico to consider the actual observation situation with unknown molecular orientations and the fluctuation of molecular structure and incident X-ray intensity. It was demonstrated that the trained SRCNN model improved the single-particle diffraction image quality, corresponding to an observed image with an incident X-ray intensity (approximately three to seven times higher than the original X-ray intensity), while retaining the individuality of the diffraction images. The feasibility of SPA for flexible biomolecules with sizes ≤100 nm was dramatically increased by introducing the SRCNN improvement at the beginning of the various structural analysis schemes.

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.

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.

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.

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.

Coarse-Grained Diffraction Template Matching Model to Retrieve Multiconformational Models for Biomolecule Structures from Noisy Diffraction Patterns

Biomolecular imaging using X-ray free-electron lasers (XFELs) has been successfully applied to serial femtosecond crystallography. However, the application of single-particle analysis for structure determination using XFELs with 100 nm or smaller biomolecules has two practical problems: the incomplete diffraction data sets for reconstructing 3D assembled structures and the heterogeneous conformational states of samples. A new diffraction template matching method is thus presented here to retrieve a plausible 3D structural model based on single noisy target diffraction patterns, assuming candidate structures. Two concepts are introduced here: prompt candidate diffraction, generated by enhanced sampled coarse-grain (CG) candidate structures, and efficient molecular orientation searching for matching based on Bayesian optimization. A CG model-based diffraction-matching protocol is proposed that achieves a 100-fold speed increase compared to exhaustive diffraction matching using an all-atom model. The conditions that enable multiconformational analysis were also investigated by simulated diffraction data for various conformational states of chromatin and ribosomes. The proposed method can enable multiconformational analysis, with a structural resolution of at least 20 Å for 270-800 Å flexible biomolecules, in experimental single-particle structure analyses that employ XFELs.