The three-dimensional structures of macromolecules and their complexes are predominantly elucidated by X-ray protein crystallography. A major limitation is access to high-quality crystals, to ensure X-ray diffraction extends to sufficiently large scattering angles and hence yields sufficiently high-resolution information that the crystal structure can be solved. The observation that crystals with shrunken unit-cell volumes and tighter macromolecular packing often produce higher-resolution Bragg peaks1,2 hints that crystallographic resolution for some macromolecules may be limited not by their heterogeneity but rather by a deviation of strict positional ordering of the crystalline lattice. Such displacements of molecules from the ideal lattice give rise to a continuous diffraction pattern, equal to the incoherent sum of diffraction from rigid single molecular complexes aligned along several discrete crystallographic orientations and hence with an increased information content3. Although such continuous diffraction patterns have long been observed—and are of interest as a source of information about the dynamics of proteins4 —they have not been used for structure determination. Here we show for crystals of the integral membrane protein complex photosystem II that lattice disorder increases the information content and the resolution of the diffraction pattern well beyond the 4.5 Å limit of measurable Bragg peaks, which allows us to directly phase5 the pattern. With the molecular envelope conventionally determined at 4.5 Å as a constraint, we then obtain a static image of the photosystem II dimer at 3.5 Å resolution. This result shows that continuous diffraction can be used to overcome long-supposed resolution limits of macromolecular crystallography, with a method that puts great value in commonly encountered imperfect crystals and opens up the possibility for model-free phasing6,7.

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 β-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.

Data-processing workflow for single-particle imaging experiments at X-ray free-electron lasers is presented. The analysis developed here revealed nanoscale features of the PR772 virus with a resolution better than 10 nm and without any symmetry constraints.

We report the 3D structure determination of gold nanoparticles (AuNPs) by X-ray single particle imaging (SPI). Around 10 million diffraction patterns from gold nanoparticles were measured in less than 100 hours of beam time, more than 100 times the amount of data in any single prior SPI experiment, using the new capabilities of the European X-ray free electron laser which allow measurements of 1500 frames per second. A classification and structural sorting method was developed to disentangle the heterogeneity of the particles and to obtain a resolution of better than 3 nm. With these new experimental and analytical developments, we have entered a new era for the SPI method and the path towards close-to-atomic resolution imaging of biomolecules is apparent.

Single-particle imaging (SPI) with X-ray free-electron lasers has the potential to change fundamentally how biomacromolecules are imaged. The structure would be derived from millions of diffraction patterns, each from a different copy of the macromolecule before it is torn apart by radiation damage. The challenges posed by the resultant data stream are staggering: millions of incomplete, noisy and un-oriented patterns have to be computationally assembled into a threedimensional intensity map and then phase reconstructed. In this paper, the Dragonfly software package is described, based on a parallel implementation of the expand-maximize-compress reconstruction algorithm that is well suited for this task. Auxiliary modules to simulate SPI data streams are also included to assess the feasibility of proposed SPI experiments at the Linac Coherent Light Source, Stanford, California, USA.

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. DOI: 10.1103/PhysRevLett.119.053401 The advent of accelerator-driven x-ray free-electron lasers (FEL) has opened new avenues for high-resolution x-ray structure determination via coherent diffractive imaging (CDI) methods that go far beyond conventional x-ray crystallography [1][2][3][4][5][6][7][8][9][10][11]. In these methods, it is assumed that a fixed phase relation between the incoming and scattered photons exists and the first-order coherence of the radiation field is maintained throughout the imaging procedure. This produces a stationary interference pattern upon measurement of large numbers of photons, a central paradigm of the field since its foundation more than one hundred years ago. Incoherence induced by, e.g., time-varying wavefront distortions or incoherent scattering processes like fluorescence emission or Compton scattering, is generally considered detrimental in this approach, as the scattered photons on average generate a constant intensity distribution producing a background that reduces the fidelity of CDI measurements [12][13][14].The situation is fundamentally altered if the photons are recorded within their coherence time τ c , i.e., a time interval short with respect to the temporal phase fluctuations of the radiation field. Over such short times, the relative phases of the scattered photons can be considered as stable, allowing the observation of a stationary fringe pattern. The pattern will fluctuate and spatially vary over times longer than τ c , yet the autocorrelation of the intensity distribution calculated for each short exposure is insensitive to the spatial pattern variations and will continuously build up when averaging over many short measurements.It was this approach that led Hanbury Brown and Twiss (HBT) to their landmark experiment in stellar interferometry to overcome atmospheric fluctuations and determine the diameter of stars via intensity correlations [15]. Based on the discovery of photon bunching of thermal light [16], the HBT experiment initiated a paradigm shift towards a quantum statistical description of light and is nowadays regarded as one of the founding pillars for the development of modern quantum optics [17]. T...

Single-particle diffraction from X-ray Free Electron Lasers offers the potential for molecular structure determination without the need for crystallization. In an effort to further develop the technique, we present a dataset of coherent soft X-ray diffraction images of Coliphage PR772 virus, collected at the Atomic Molecular Optics (AMO) beamline with pnCCD detectors in the LAMP instrument at the Linac Coherent Light Source. The diameter of PR772 ranges from 65–70 nm, which is considerably smaller than the previously reported ~600 nm diameter Mimivirus. This reflects continued progress in XFEL-based single-particle imaging towards the single molecular imaging regime. The data set contains significantly more single particle hits than collected in previous experiments, enabling the development of improved statistical analysis, reconstruction algorithms, and quantitative metrics to determine resolution and self-consistency.

Sample delivery is a major challenge to performing serial crystallography experiments at upcoming high-repetition-rate X-ray free-electron lasers. The feasibility of using gas-driven liquid jets for this purpose at the FLASH facility in Hamburg has been studied.