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A well-characterized wavefront is important for many x-ray free-electron laser (XFEL) experiments, especially for single-particle imaging (SPI), where individual biomolecules randomly sample a nanometer region of highly focused femtosecond pulses. We demonstrate high-resolution multiple-plane wavefront imaging of an ensemble of XFEL pulses, focused by Kirkpatrick–Baez mirrors, based on mixed-state ptychography, an approach letting us infer and reduce experimental sources of instability. From the recovered wavefront profiles, we show that while local photon fluence correction is crucial and possible for SPI, a small diversity of phase tilts likely has no impact. Our detailed characterization will aid interpretation of data from past and future SPI experiments and provides a basis for further improvements to experimental design and reconstruction algorithms.

Optica 8(1), 15 - 23 (2021). doi:10.1364/OPTICA.410851, Single particle imaging at x-ray free electron lasers (XFELs) has the potential to determine the structure and dynamics of single biomolecules at room temperature. Two major hurdles have prevented this potential from being reached, namely, the collection of sufficient high-quality diffraction patterns and robust computational purification to overcome structural heterogeneity. We report the breaking of both of these barriers using gold nanoparticle test samples, recording around 10 million diffraction patterns at the European XFEL and structurally and orientationally sorting the patterns to obtain better than 3-nm-resolution 3D reconstructions for each of four samples. With these new developments, integrating advancements in x-ray sources, fast-framing detectors, efficient sample delivery, and data analysis algorithms, we illuminate the path towards sub-nanometer biomolecular imaging. The methods developed here can also be extended to characterize ensembles that are inherently diverse to obtain their full structural landscape., Published by OSA, Washington, DC

Communications Physics 3(1), 97 (2020). doi:10.1038/s42005-020-0362-y, 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., Published by Springer Nature, London

Physical chemistry, chemical physics 20(18), 12381 - 12389 (2018). doi:10.1039/C7CP07267H, Single particle imaging (SPI) using X-ray pulses has become increasingly attainable with the advent of high-intensity free electron lasers. Eliminating the need for crystallized samples enables structural studies of molecules previously inaccessible by conventional crystallography. While this emerging technique already demonstrates substantial promise, some obstacles need to be overcome before SPI can reach its full potential. One such problem is determining the spatial orientation of the sample at the time of X-ray interaction. Existing solutions rely on diffraction data and are computationally demanding and sensitive to noise. In this in silico study, we explore the possibility of aiding these methods by mapping the ion distribution as the sample undergoes a Coulomb explosion following the intense ionization. By detecting the ions ejected from the fragmented sample, the orientation of the original sample should be possible to determine. Knowledge of the orientation has been shown earlier to be of substantial advantage in the reconstruction of the original structure. 150 explosions of each of twelve separate systems – four polypeptides with different amounts of surface bound water – were simulated with molecular dynamics (MD) and the average angular distribution of carbon and sulfur ions was investigated independently. The results show that the explosion maps are reproducible in both cases, supporting the idea that orientation information is preserved. Additional water seems to restrict the carbon ion trajectories further through a shielding mechanism, making the maps more distinct. For sulfurs, water has no significant impact on the trajectories, likely due to their higher mass and greater ionization cross section, indicating that they could be of particular interest. Based on these findings, we conclude that explosion data can aid spatial orientation in SPI experiments and could substantially improve the capabilities of the novel technique., Published by RSC Publ., Cambridge

Nature photonics 12(3), 150 - 153 (2018). doi:10.1038/s41566-018-0110-y, Ultrafast X-ray imaging on individual fragile specimens such as aerosols1, metastable particles2, superfluid quantum systems3 and live biospecimens4 provides high-resolution information that is inaccessible with conventional imaging techniques. Coherent X-ray diffractive imaging, however, suffers from intrinsic loss of phase, and therefore structure recovery is often complicated and not always uniquely defined4,5. Here, we introduce the method of in-flight holography, where we use nanoclusters as reference X-ray scatterers to encode relative phase information into diffraction patterns of a virus. The resulting hologram contains an unambiguous three-dimensional map of a virus and two nanoclusters with the highest lateral resolution so far achieved via single shot X-ray holography. Our approach unlocks the benefits of holography for ultrafast X-ray imaging of nanoscale, non-periodic systems and paves the way to direct observation of complex electron dynamics down to the attosecond timescale., Published by Nature Publ. Group, London [u.a.]

The journal of physical chemistry letters 8(18), 4540 - 4544 (2017). doi:10.1021/acs.jpclett.7b02005, Single-particle imaging using X-ray free-electron lasers is an emerging technique that could provide high-resolution structures of macromolecules in the gas phase. One of the largest difficulties in realizing this goal is the unknown orientation of the individual sample molecules at the time of exposure. Preorientation of the molecules has been identified as a possible solution to this problem. Using molecular dynamics simulations, we identify a range of electric field strengths where proteins become oriented without losing their structure. For a number of experimentally relevant cases we show that structure determination is possible only when orientation information is included in the orientation-recovery process. We conclude that nondestructive field orientation of intact proteins is feasible and that it enables a range of new structural investigations with single-particle imaging., Published by ACS, Washington, DC

The prospect of high-resolution three-dimensional (3D) imaging of biological objects was a major part of the science case for constructing X-ray free-electron lasers (FELs). Rather early after the construction of the FLASH facility in Hamburg, the first X-ray FEL, two-dimensional (2D) images of cells were presented. It did, however, take another 9 years for the first non-trivial sample to be imaged in 3D with similar methods. Why is this? And why is it that even now the resolution of this 3D image is almost an order of magnitude worse than the highest resolution achieved in 2D? This chapter gives a detailed explanation of the data analysis required to reconstruct a sample in 3D. These analysis methods took a long time to develop and did not exist at the time when the first FEL data was available. Understanding this set of algorithms also makes it possible to understand if current resolution limits are really a limit to the method or a limit imposed by experimental parameters that are likely to change in the near future. Last, this chapter includes some speculation on the future of the method.

Imaging live cells at a resolution higher than achieved using optical microscopy is a challenge. Ultra-fast coherent diffractive imaging with X-ray free-electron lasers (XFELs) has the potential to achieve sub-nanometer resolution on micron-sized living cells. Our container-free injection method can introduce a beam of live cyanobacteria into the micron-sized focus of the Linac Coherent Light Source (LCLS) to record of diffraction patterns from individual cells, with very low noise at high hit rates (millions of cells/day). We used iterative phase retrieval to derive two-dimensional projection images directly from the diffraction patterns. In a first experiment, we collected diffraction patterns to 33-46 nm full-period resolution, and reconstructed the exit wave front to 76 nm full-period resolution. In a second experiment, we demonstrate that it is indeed possible to record diffraction data to nanometer resolution on live cells with an intense, ultra-short X-ray pulse as predicted earlier. These results are encouraging, and future developments to the XFELs and improvements to the X-ray area-detectors will bring sub-nanometer resolution reconstructions of living cells within reach. Utilizing this type of diffraction data will require the development of new analysis methods and algorithms for studying structure and structural variability in large populations of cells and to create abstract models. Such studies will allow us to understand living cells and populations of cells in new ways.

Scientific data 3, 160058 (2016). doi:10.1038/sdata.2016.58, Structural studies on living cells by conventional methods are limited to low resolution because radiation damage kills cells long before the necessary dose for high resolution can be delivered. X-ray free-electron lasers circumvent this problem by outrunning key damage processes with an ultra-short and extremely bright coherent X-ray pulse. Diffraction-before-destruction experiments provide high-resolution data from cells that are alive when the femtosecond X-ray pulse traverses the sample. This paper presents two data sets from micron-sized cyanobacteria obtained at the Linac Coherent Light Source, containing a total of 199,000 diffraction patterns. Utilizing this type of diffraction data will require the development of new analysis methods and algorithms for studying structure and structural variability in large populations of cells and to create abstract models. Such studies will allow us to understand living cells and populations of cells in new ways. New X-ray lasers, like the European XFEL, will produce billions of pulses per day, and could open new areas in structural sciences., Published by Nature Publ. Group, London

Ultra-intense femtosecond X-ray pulses from X-ray lasers permit structural studies on single particles and biomolecules without crystals. We present a large data set on inherently heterogeneous, polyhedral carboxysome particles. Carboxysomes are cell organelles that vary in size and facilitate up to 40% of Earth’s carbon fixation by cyanobacteria and certain proteobacteria. Variation in size hinders crystallization. Carboxysomes appear icosahedral in the electron microscope. A protein shell encapsulates a large number of Rubisco molecules in paracrystalline arrays inside the organelle. We used carboxysomes with a mean diameter of 115±26 nm from Halothiobacillus neapolitanus. A new aerosol sample-injector allowed us to record 70,000 low-noise diffraction patterns in 12 min. Every diffraction pattern is a unique structure measurement and high-throughput imaging allows sampling the space of structural variability. The different structures can be separated and phased directly from the diffraction data and open a way for accurate, high-throughput studies on structures and structural heterogeneity in biology and elsewhere.

Scientific data 3, 160060 (2016). doi:10.1038/sdata.2016.60, Free-electron lasers (FEL) hold the potential to revolutionize structural biology by producing X-ray pules short enough to outrun radiation damage, thus allowing imaging of biological samples without the limitation from radiation damage. Thus, a major part of the scientific case for the first FELs was three-dimensional (3D) reconstruction of non-crystalline biological objects. In a recent publication we demonstrated the first 3D reconstruction of a biological object from an X-ray FEL using this technique. The sample was the giant Mimivirus, which is one of the largest known viruses with a diameter of 450 nm. Here we present the dataset used for this successful reconstruction. Data-analysis methods for single-particle imaging at FELs are undergoing heavy development but data collection relies on very limited time available through a highly competitive proposal process. This dataset provides experimental data to the entire community and could boost algorithm development and provide a benchmark dataset for new algorithms., Published by Nature Publ. Group, London

There exists a conspicuous gap of knowledge about the organization of life at mesoscopic levels. Ultra-fast coherent diffractive imaging with X-ray free-electron lasers can probe structures at the relevant length scales and may reach sub-nanometer resolution on micron-sized living cells. Here we show that we can introduce a beam of aerosolised cyanobacteria into the focus of the Linac Coherent Light Source and record diffraction patterns from individual living cells at very low noise levels and at high hit ratios. We obtain two-dimensional projection images directly from the diffraction patterns, and present the results as synthetic X-ray Nomarski images calculated from the complex-valued reconstructions. We further demonstrate that it is possible to record diffraction data to nanometer resolution on live cells with X-ray lasers. Extension to sub-nanometer resolution is within reach, although improvements in pulse parameters and X-ray area detectors will be necessary to unlock this potential.

International audience; We present a proof-of-concept three-dimensional reconstruction of the giant mimivirus particle from experimentally measured diffraction patterns from an x-ray free-electron laser. Three-dimensional imaging requires the assembly of many two-dimensional patterns into an internally consistent Fourier volume. Since each particle is randomly oriented when exposed to the x-ray pulse, relative orientations have to be retrieved from the diffraction data alone. We achieve this with a modified version of the expand, maximize and compress algorithm and validate our result using new methods.

We use a Mach-Zehnder type autocorrelator to split and delay XUV pulses from the FLASH soft X-ray laser for triggering and subsequently probing the explosion of aerosolised sugar balls. FLASH was running at 182 eV photon energy with pulses of 70 fs duration. The delay between the pump-probe pulses was varied between zero and 5 ps, and the pulses were focused to reach peak intensities above 1016 W/cm2 with an off-axis parabola. The direct pulse triggered the explosion of single aerosolised sucrose nano-particles, while the delayed pulse probed the exploding structure. The ejected ions were measured by ion time of flight spectrometry, and the particle sizes were measured by coherent diffractive imaging. The results show that sucrose particles of 560-1000 nm diameter retain their size for about 500 fs following the first exposure. Significant sample expansion happens between 500 fs and 1 ps. We present simulations to support these observations.

The first hard X-ray laser, the Linac Coherent Light Source (LCLS), produces 120 shots per second. Particles injected into the X-ray beam are hit randomly and in unknown orientations by the extremely intense X-ray pulses, where the femtosecond-duration X-ray pulses diffract from the sample before the particle structure is significantly changed even though the sample is ultimately destroyed by the deposited X-ray energy. Single particle X-ray diffraction experiments generate data at the FEL repetition rate, resulting in more than 400,000 detector readouts in an hour, the data stream during an experiment contains blank frames mixed with hits on single particles, clusters and contaminants. The diffraction signal is generally weak and it is superimposed on a low but continually fluctuating background signal, originating from photon noise in the beam line and electronic noise from the detector. Meanwhile, explosion of the sample creates fragments with a characteristic signature. Here, we describe methods based on rapid image analysis combined with ion Time-of-Flight (ToF) spectroscopy of the fragments to achieve an efficient, automated and unsupervised sorting of diffraction data. The studies described here form a basis for the development of real-time frame rejection methods, e. g. for the European XFEL, which is expected to produce 100 million pulses per hour. (C)2014 Optical Society of America

We overcome two of the most daunting challenges in single-particle diffractive imaging: collecting many high-quality diffraction patterns on a small amount of sample and separating components from mixed samples. We demonstrate this on carboxysomes, which are polyhedral cell organelles that vary in size and facilitate up to 40% of Earth's carbon fixation. A new aerosol sample-injector allowed us to record 70,000 low-noise diffraction patterns in 12 min with the Linac Coherent Light Source running at 120 Hz. We separate different structures directly from the diffraction data and show that the size distribution is preserved during sample delivery. We automate phase retrieval and avoid reconstruction artefacts caused by missing modes. We attain the highest-resolution reconstructions on the smallest single biological objects imaged with an X-ray laser to date. These advances lay the foundations for accurate, high-throughput structure determination by flash-diffractive imaging and offer a means to study structure and structural heterogeneity in biology and elsewhere.

Characterizing intense, focused x-ray free electron laser (FEL) pulses is crucial for their use in diffractive imaging. We describe how the distribution of average phase tilts and intensities on hard x-ray pulses with peak intensities of 10(21) W/m(2) can be retrieved from an ensemble of diffraction patterns produced by 70 nm-radius polystyrene spheres, in a manner that mimics wavefront sensors. Besides showing that an adaptive geometric correction may be necessary for diffraction data from randomly injected sample sources, our paper demonstrates the possibility of collecting statistics on structured pulses using only the diffraction patterns they generate and highlights the imperative to study its impact on single-particle diffractive imaging.

The structures of biological molecules may soon be determined with X-ray free-electron lasers without crystallization by recording the coherent diffraction patterns of many identical copies of a molecule. Most analysis methods require a measurement of each molecule individually. However, current injection methods deliver particles to the X-ray beam stochastically and the maximum yield of single particle measurements is 37% at optimal concentration. The remaining 63% of pulses intercept no particles or multiple particles. We demonstrate that in the latter case single particle diffraction patterns can be extracted provided the particles are sufficiently separated. The technique has the potential to greatly increase the amount of data available for three-dimensional imaging of identical particles with X-ray lasers.

Optics express 21(23), 28729(2013). doi:10.1364/OE.21.028729, Single shot diffraction imaging experiments via X-ray free- electron lasers can generate as many as hundreds of thousands of diffraction patterns of scattering objects. Recovering the real space contrast of a scat- tering object from these patterns currently requires a reconstruction process with user guidance in a number of steps, introducing severe bottlenecks in data processing. We present a series of measures that replace user guidance with algorithms that reconstruct contrasts in an unsupervised fashion. We demonstrate the feasibility of automating the reconstruction process by generating hundreds of contrasts obtained from soot particle diffraction experiments., Published by Soc., Washington, DC

Profiling structured beams produced by X-ray free-electron lasers (FELs) is crucial to both maximizing signal intensity for weakly scattering targets and interpreting their scattering patterns. Earlier ablative imprint studies describe how to infer the X-ray beam profile from the damage that an attenuated beam inflicts on a substrate. However, the beams in-situ profile is not directly accessible with imprint studies because the damage profile could be different from the actual beam profile. On the other hand, although a Shack-Hartmann sensor is capable of in-situ profiling, its lenses may be quickly damaged at the intense focus of hard X-ray FEL beams. We describe a new approach that probes the in-situ morphology of the intense FEL focus. By studying the translations in diffraction patterns from an ensemble of randomly injected sub-micron latex spheres, we were able to determine the non-Gaussian nature of the intense FEL beam at the Linac Coherent Light Source (SLAC National Laboratory) near the FEL focus. We discuss an experimental application of such a beam-profiling technique, and the limitations we need to overcome before it can be widely applied. © (2012) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.

X-ray free-electron lasers deliver intense femtosecond pulses that promise to yield high resolution diffraction data of nanocrystals before the destruction of the sample by radiation damage. Diffraction intensities of lysozyme nanocrystals collected at the Linac Coherent Light Source using 2 keV photons were used for structure determination by molecular replacement and analyzed for radiation damage as a function of pulse length and fluence. Signatures of radiation damage are observed for pulses as short as 70 fs. Parametric scaling used in conventional crystallography does not account for the observed effects.

Results of coherent diffractive imaging experiments performed with soft X-rays (1-2 keV) at the Linac Coherent Light Source are presented. Both organic and inorganic nano-sized objects were injected into the XFEL beam as an aerosol focused with an aerodynamic lens. The high intensity and femtosecond duration of X-ray pulses produced by the Linac Coherent Light Source allow structural information to be recorded by X-ray diffraction before the particle is destroyed. Images were formed by using iterative methods to phase single shot diffraction patterns. Strategies for improving the reconstruction methods have been developed. This technique opens up exciting opportunities for biological imaging, allowing structure determination without freezing, staining or crystallization.

The start-up of the Linac Coherent Light Source (LCLS), the new femtosecond hard X-ray laser facility in Stanford, California, has brought high expectations of a new era for biological imaging. The intense, ultrashort X-ray pulses allow diffraction imaging of small structures before radiation damage occurs. Two papers in this issue of Nature present proof-of-concept experiments showing the LCLS in action. Chapman et al. tackle structure determination from nanocrystals of macromolecules that cannot be grown in large crystals. They obtain more than three million diffraction patterns from a stream of nanocrystals of the membrane protein photosystem I, and assemble a three-dimensional data set for this protein. Seibert et al. obtain images of a non-crystalline biological sample, mimivirus, by injecting a beam of cooled mimivirus particles into the X-ray beam. The start-up of the new femtosecond hard X-ray laser facility in Stanford, the Linac Coherent Light Source, has brought high expectations for a new era for biological imaging. The intense, ultrashort X-ray pulses allow diffraction imaging of small structures before radiation damage occurs. This new capability is tested for the problem of imaging a non-crystalline biological sample. Images of mimivirus are obtained, the largest known virus with a total diameter of about 0.75 micrometres, by injecting a beam of cooled mimivirus particles into the X-ray beam. The measurements indicate no damage during imaging and prove the concept of this imaging technique. X-ray lasers offer new capabilities in understanding the structure of biological systems, complex materials and matter under extreme conditions1,2,3,4. Very short and extremely bright, coherent X-ray pulses can be used to outrun key damage processes and obtain a single diffraction pattern from a large macromolecule, a virus or a cell before the sample explodes and turns into plasma1. The continuous diffraction pattern of non-crystalline objects permits oversampling and direct phase retrieval2. Here we show that high-quality diffraction data can be obtained with a single X-ray pulse from a non-crystalline biological sample, a single mimivirus particle, which was injected into the pulsed beam of a hard-X-ray free-electron laser, the Linac Coherent Light Source5. Calculations indicate that the energy deposited into the virus by the pulse heated the particle to over 100,000 K after the pulse had left the sample. The reconstructed exit wavefront (image) yielded 32-nm full-period resolution in a single exposure and showed no measurable damage. The reconstruction indicates inhomogeneous arrangement of dense material inside the virion. We expect that significantly higher resolutions will be achieved in such experiments with shorter and brighter photon pulses focused to a smaller area. The resolution in such experiments can be further extended for samples available in multiple identical copies.

In a flash diffraction experiment, a short and extremely intense x-ray pulse illuminates the sample to obtain a diffraction pattern before the onset of significant radiation damage. The over-sampled diffraction pattern permits phase retrieval by iterative phasing methods. Flash diffractive imaging was first demonstrated on an inorganic test object (Chapman et al 2006 Nat. Phys. 2 839‐43). We report here experiments on biological systems where individual cells were imaged, using single, 10‐15 fs soft x-ray pulses at 13.5 nm wavelength from the FLASH free-electron laser in Hamburg. Simulations show that the pulse heated the sample to about 160 000 K but not before an interpretable diffraction pattern could be obtained. The reconstructed projection images return the structures of the intact cells. The simulations suggest that the average displacement of ions and atoms in the hottest surface layers remained below 3 ˚ A during the pulse. (Some figures in this article are in colour only in the electronic version)

Unraveling the complex morphology of functional materials like core-shell nanoparticles and its evolution in different environments is still a challenge. Only recently has the single-particle coherent diffraction imaging (CDI), enabled by the ultrabright femtosecond free-electron laser pulses, provided breakthroughs in understanding mesoscopic morphology of nanoparticulate matter. Here, we report the first CDI results for Co@SiO2 core-shell nanoparticles randomly clustered in large airborne aggregates, obtained using the x-ray free-electron laser at the Linac Coherent Light Source. Our experimental results compare favourably with simulated diffraction patterns for clustered Co@SiO2 nanoparticles with similar to 10 nm core diameter and similar to 30 nm shell outer diameter, which confirms the ability to resolve the mesoscale morphology of complex metastable structures. The findings in this first morphological study of core-shell nanomaterials are a solid base for future time-resolved studies of dynamic phenomena in complex nanoparticulate matter using x-ray lasers.