Nanoscale x-ray imaging with high spectral sensitivity using fluorescence intensity correlations.

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.

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.

Form factor determination of biological molecules with X-ray free electron laser small-angle scattering (XFEL-SAS).

Free-electron lasers (FEL) are revolutionizing X-ray-based structural biology methods. While protein crystallography is already routinely performed at FELs, Small Angle X-ray Scattering (SAXS) studies of biological macromolecules are not as prevalent. SAXS allows the study of the shape and overall structure of proteins and nucleic acids in solution, in a quasi-native environment. In solution, chemical and biophysical parameters that have an influence on the structure and dynamics of molecules can be varied and their effect on conformational changes can be monitored in time-resolved XFEL and SAXS experiments. We report here the collection of scattering form factors of proteins in solution using FEL X-rays. The form factors correspond to the scattering signal of the protein ensemble alone; the scattering contributions from the solvent and the instrument are separately measured and accurately subtracted. The experiment was done using a liquid jet for sample delivery. These results pave the way for time-resolved studies and measurements from dilute samples, capitalizing on the intense and short FEL X-ray pulses.

Ab initio spatial phase retrieval via intensity triple correlations.

Second-order intensity correlations from incoherent emitters can reveal the Fourier transform modulus of their spatial distribution, but retrieving the phase to enable completely general Fourier inversion to real space remains challenging. Phase retrieval via the third-order intensity correlations has relied on special emitter configurations which simplified an unaddressed sign problem in the computation. Without a complete treatment of this sign problem, the general case of retrieving the Fourier phase from a truly arbitrary configuration of emitters is not possible. In this paper, a general method for ab initio phase retrieval via the intensity triple correlations is described. Simulations demonstrate accurate phase retrieval for clusters of incoherent emitters which could be applied to imaging stars or fluorescent atoms and molecules. With this work, it is now finally tractable to perform Fourier inversion directly and reconstruct images of arbitrary arrays of independent emitters via far-field intensity correlations alone.

Time-Resolved Single-Particle X-ray Scattering Reveals Electron-Density Gradients As Coherent Plasmonic-Nanoparticle-Oscillation Source.

Dynamics of optically excited plasmonic nanoparticles are presently understood as a series of scattering events involving the initiation of nanoparticle breathing oscillations. According to established models, these are caused by statistical heat transfer from thermalized electrons to the lattice. An additional contribution by hot-electron pressure accounts for phase mismatches between theory and experimental observations. However, direct experimental studies resolving the breathing-oscillation excitation are still missing. We used optical transient-absorption spectroscopy and time-resolved single-particle X-ray diffractive imaging to access the electron system and lattice. The time-resolved single-particle imaging data provided structural information directly on the onset of the breathing oscillation and confirmed the need for an additional excitation mechanism for thermal expansion. We developed a new model that reproduces all of our experimental observations. We identified optically induced electron density gradients as the initial driving source.

Imaging via Correlation of X-Ray Fluorescence Photons.

We demonstrate that x-ray fluorescence emission, which cannot maintain a stationary interference pattern, can be used to obtain images of structures by recording photon-photon correlations in the manner of the stellar intensity interferometry of Hanbury Brown and Twiss. This is achieved utilizing femtosecond-duration pulses of a hard x-ray free-electron laser to generate the emission in exposures comparable to the coherence time of the fluorescence. Iterative phasing of the photon correlation map generated a model-free real-space image of the structure of the emitters. Since fluorescence can dominate coherent scattering, this may enable imaging uncrystallised macromolecules.

Speckle contrast of interfering fluorescence X-rays.

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.

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.

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.

Diffraction data from aerosolized Coliphage PR772 virus particles imaged with the Linac Coherent Light Source.

Single Particle Imaging (SPI) with intense coherent X-ray pulses from X-ray free-electron lasers (XFELs) has the potential to produce molecular structures without the need for crystallization or freezing. Here we present a dataset of 285,944 diffraction patterns from aerosolized Coliphage PR772 virus particles injected into the femtosecond X-ray pulses of the Linac Coherent Light Source (LCLS). Additional exposures with background information are also deposited. The diffraction data were collected at the Atomic, Molecular and Optical Science Instrument (AMO) of the LCLS in 4 experimental beam times during a period of four years. The photon energy was either 1.2 or 1.7 keV and the pulse energy was between 2 and 4 mJ in a focal spot of about 1.3 µm x 1.7 µm full width at half maximum (FWHM). The X-ray laser pulses captured the particles in random orientations. The data offer insight into aerosolised virus particles in the gas phase, contain information relevant to improving experimental parameters, and provide a basis for developing algorithms for image analysis and reconstruction.

Segmented flow generator for serial crystallography at the European X-ray free electron laser.

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.

Low-signal limit of X-ray single particle diffractive imaging.

An outstanding question in X-ray single particle imaging experiments has been the feasibility of imaging sub 10-nm-sized biomolecules under realistic experimental conditions where very few photons are expected to be measured in a single snapshot and instrument background may be significant relative to particle scattering. While analyses of simulated data have shown that the determination of an average image should be feasible using Bayesian methods such as the EMC algorithm, this has yet to be demonstrated using experimental data containing realistic non-isotropic instrument background, sample variability and other experimental factors. In this work, we show that the orientation and phase retrieval steps work at photon counts diluted to the signal levels one expects from smaller molecules or with weaker pulses, using data from experimental measurements of 60-nm PR772 viruses. Even when the signal is reduced to a fraction as little as 1/256, the virus electron density determined using ab initio phasing is of almost the same quality as the high-signal data. However, we are still limited by the total number of patterns collected, which may soon be mitigated by the advent of high repetition-rate sources like the European XFEL and LCLS-II.

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.

Single-particle imaging without symmetry constraints at an X-ray free-electron laser.

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.

Megahertz serial crystallography.

The new European X-ray Free-Electron Laser is the first X-ray free-electron laser capable of delivering X-ray pulses with a megahertz inter-pulse spacing, more than four orders of magnitude higher than previously possible. However, to date, it has been unclear whether it would indeed be possible to measure high-quality diffraction data at megahertz pulse repetition rates. Here, we show that high-quality structures can indeed be obtained using currently available operating conditions at the European XFEL. We present two complete data sets, one from the well-known model system lysozyme and the other from a so far unknown complex of a ß-lactamase from K. pneumoniae involved in antibiotic resistance. This result opens up megahertz serial femtosecond crystallography (SFX) as a tool for reliable structure determination, substrate screening and the efficient measurement of the evolution and dynamics of molecular structures using megahertz repetition rate pulses available at this new class of X-ray laser source.

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.

Femtosecond X-ray coherent diffraction of aligned amyloid fibrils on low background graphene.

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.

Analysis of XFEL serial diffraction data from individual crystalline fibrils.

Serial diffraction data collected at the Linac Coherent Light Source from crystalline amyloid fibrils delivered in a liquid jet show that the fibrils are well oriented in the jet. At low fibril concentrations, diffraction patterns are recorded from single fibrils; these patterns are weak and contain only a few reflections. Methods are developed for determining the orientation of patterns in reciprocal space and merging them in three dimensions. This allows the individual structure amplitudes to be calculated, thus overcoming the limitations of orientation and cylindrical averaging in conventional fibre diffraction analysis. The advantages of this technique should allow structural studies of fibrous systems in biology that are inaccessible using existing techniques.

Incoherent Diffractive Imaging via Intensity Correlations of Hard X Rays.

Established x-ray diffraction methods allow for high-resolution structure determination of crystals, crystallized protein structures, or even single molecules. While these techniques rely on coherent scattering, incoherent processes like fluorescence emission-often the predominant scattering mechanism-are generally considered detrimental for imaging applications. Here, we show that intensity correlations of incoherently scattered x-ray radiation can be used to image the full 3D arrangement of the scattering atoms with significantly higher resolution compared to conventional coherent diffraction imaging and crystallography, including additional three-dimensional information in Fourier space for a single sample orientation. We present a number of properties of incoherent diffractive imaging that are conceptually superior to those of coherent methods.

Continuous diffraction of molecules and disordered molecular crystals.

The intensities of far-field diffraction patterns of orientationally aligned molecules obey Wilson statistics, whether those molecules are in isolation (giving rise to a continuous diffraction pattern) or arranged in a crystal (giving rise to Bragg peaks). Ensembles of molecules in several orientations, but uncorrelated in position, give rise to the incoherent sum of the diffraction from those objects, modifying the statistics in a similar way as crystal twinning modifies the distribution of Bragg intensities. This situation arises in the continuous diffraction of laser-aligned molecules or translationally disordered molecular crystals. This paper develops the analysis of the intensity statistics of such continuous diffraction to obtain parameters such as scaling, beam coherence and the number of contributing independent object orientations. When measured, continuous molecular diffraction is generally weak and accompanied by a background that far exceeds the strength of the signal. Instead of just relying upon the smallest measured intensities or their mean value to guide the subtraction of the background, it is shown how all measured values can be utilized to estimate the background, noise and signal, by employing a modified 'noisy Wilson' distribution that explicitly includes the background. Parameters relating to the background and signal quantities can be estimated from the moments of the measured intensities. The analysis method is demonstrated on previously published continuous diffraction data measured from crystals of photosystem II [Ayyer et al. (2016 ▸), Nature, 530, 202-206].