Single-particle XFEL 3D reconstruction of ribosome-size particles based on Fourier slice matching: requirements to reach subnanometer resolution

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.

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.

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.

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.

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.

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.

Reconstruction of Three-Dimensional Conformations of Bacterial ClpB from High-Speed Atomic-Force-Microscopy Images

ClpB belongs to the cellular disaggretase machinery involved in rescuing misfolded or aggregated proteins during heat or other cellular shocks. The function of this protein relies on the interconversion between different conformations in its native condition. A recent high-speed-atomic-force-microscopy (HS-AFM) experiment on ClpB from Thermus thermophilus shows four predominant conformational classes, namely, open, closed, spiral, and half-spiral. Analyses of AFM images provide only partial structural information regarding the molecular surface, and thus computational modeling of three-dimensional (3D) structures of these conformations should help interpret dynamical events related to ClpB functions. In this study, we reconstruct 3D models of ClpB from HS-AFM images in different conformational classes. We have applied our recently developed computational method based on a low-resolution representation of 3D structure using a Gaussian mixture model, combined with a Monte-Carlo sampling algorithm to optimize the agreement with target AFM images. After conformational sampling, we obtained models that reflect conformational variety embedded within the AFM images. From these reconstructed 3D models, we described, in terms of relative domain arrangement, the different types of ClpB oligomeric conformations observed by HS-AFM experiments. In particular, we highlighted the slippage of the monomeric components around the seam. This study demonstrates that such details of information, necessary for annotating the different conformational states involved in the ClpB function, can be obtained by combining HS-AFM images, even with limited resolution, and computational modeling.

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.

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.

Parameter optimization for 3D-reconstruction from XFEL diffraction patterns based on Fourier slice matching

Single-particle analysis (SPA) by X-ray free electron laser (XFEL) is a novel method that can observe biomolecules and living tissue that are difficult to crystallize in a state close to nature. To reconstruct three-dimensional (3D) molecular structure from two-dimensional (2D) XFEL diffraction patterns, we have to estimate the incident beam angle to the molecule for each pattern to assemble the 3D-diffraction intensity distribution using interpolation, and retrieve the phase information. In this study, we investigated the optimal parameter sets to assemble the 3D-diffraction intensity distribution from simulated 2D-diffraction patterns of ribosome. In particular, we examined how the parameters need to be adjusted for diffraction patterns with different binning sizes and beam intensities to obtain the highest resolution of molecular structure phase retrieved from the 3D-diffraction intensity. We found that resolution of restored molecular structure is sensitive to the interpolation parameters. Using the optimal parameter set, a linear oversampling ratio of around four is found to be sufficient for correct angle estimation and phase retrieval from the diffraction patterns of SPA by XFEL.

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

The routine atomic resolution structure determination of single particles is expected to have profound implications for probing structure-function relationships in systems ranging from energy-storage materials to biological molecules. Extremely bright ultrashort-pulse X-ray sources - X-ray free-electron lasers (XFELs) - provide X-rays that can be used to probe ensembles of nearly identical nanoscale particles. When combined with coherent diffractive imaging, these objects can be imaged; however, as the resolution of the images approaches the atomic scale, the measured data are increasingly difficult to obtain and, during an X-ray pulse, the number of photons incident on the 2D detector is much smaller than the number of pixels. This latter concern, the signal 'sparsity', materially impedes the application of the method. An experimental analog using a conventional X-ray source is demonstrated and yields signal levels comparable with those expected from single biomolecules illuminated by focused XFEL pulses. The analog experiment provides an invaluable cross check on the fidelity of the reconstructed data that is not available during XFEL experiments. Using these experimental data, it is established that a sparsity of order 1.3 × 10-3 photons per pixel per frame can be overcome, lending vital insight to the solution of the atomic resolution XFEL single-particle imaging problem by experimentally demonstrating 3D coherent diffractive imaging from photon-sparse random projections.

Role of Computational Methods in Going beyond X-ray Crystallography to Explore Protein Structure and Dynamics

Protein structural biology came a long way since the determination of the first three-dimensional structure of myoglobin about six decades ago. Across this period, X-ray crystallography was the most important experimental method for gaining atomic-resolution insight into protein structures. However, as the role of dynamics gained importance in the function of proteins, the limitations of X-ray crystallography in not being able to capture dynamics came to the forefront. Computational methods proved to be immensely successful in understanding protein dynamics in solution, and they continue to improve in terms of both the scale and the types of systems that can be studied. In this review, we briefly discuss the limitations of X-ray crystallography in studying protein dynamics, and then provide an overview of different computational methods that are instrumental in understanding the dynamics of proteins and biomacromolecular complexes.

Gaussian mixture model for coarse-grained modeling from XFEL

We explore the advantage of Gaussian mixture model (GMM) for interpretation of single particle diffraction patterns from X-ray free electron laser (XFEL) experiments. GMM approximates a biomolecular shape by the superposition of Gaussian distributions. As the Fourier transformation of GMM can be quickly performed, we can efficiently simulate XFEL diffraction patterns from approximated structure models. We report that the resolution that GMM can accurately reproduce is proportional to the cubic root of the number of Gaussians used in the modeling. This behavior can be attributed to the correspondence between the number of adjustable parameters in GMM and the amount of sampling points in diffraction space. Furthermore, GMMs can successfully be used to perform angular assignment and to detect conformational variation. These results demonstrate that GMMs serve as useful coarse-grained models for hybrid approach in XFEL single particle experiments.