Toward atomic resolution diffractive imaging of isolated molecules with X-ray free-electron lasers.

We give a detailed account of the theoretical analysis and the experimental results of an X-ray-diffraction experiment on quantum-state selected and strongly laser-aligned gas-phase ensembles of the prototypical large asymmetric rotor molecule 2,5-diiodobenzonitrile, performed at the Linac Coherent Light Source [Phys. Rev. Lett.112, 083002 (2014)]. This experiment is the first step toward coherent diffractive imaging of structures and structural dynamics of isolated molecules at atomic resolution, i.e., picometers and femtoseconds, using X-ray free-electron lasers.

Ultrafast X-ray probing of water structure below the homogeneous ice nucleation temperature.

Water has a number of anomalous physical properties, and some of these become drastically enhanced on supercooling below the freezing point. Particular interest has focused on thermodynamic response functions that can be described using a normal component and an anomalous component that seems to diverge at about 228 kelvin (refs 1-3). This has prompted debate about conflicting theories that aim to explain many of the anomalous thermodynamic properties of water. One popular theory attributes the divergence to a phase transition between two forms of liquid water occurring in the 'no man's land' that lies below the homogeneous ice nucleation temperature (TH) at approximately 232 kelvin and above about 160 kelvin, and where rapid ice crystallization has prevented any measurements of the bulk liquid phase. In fact, the reliable determination of the structure of liquid water typically requires temperatures above about 250 kelvin. Water crystallization has been inhibited by using nanoconfinement, nanodroplets and association with biomolecules to give liquid samples at temperatures below TH, but such measurements rely on nanoscopic volumes of water where the interaction with the confining surfaces makes the relevance to bulk water unclear. Here we demonstrate that femtosecond X-ray laser pulses can be used to probe the structure of liquid water in micrometre-sized droplets that have been evaporatively cooled below TH. We find experimental evidence for the existence of metastable bulk liquid water down to temperatures of 227(-1)(+2) kelvin in the previously largely unexplored no man's land. We observe a continuous and accelerating increase in structural ordering on supercooling to approximately 229 kelvin, where the number of droplets containing ice crystals increases rapidly. But a few droplets remain liquid for about a millisecond even at this temperature. The hope now is that these observations and our detailed structural data will help identify those theories that best describe and explain the behaviour of water.

Single-particle structure determination by correlations of snapshot X-ray diffraction patterns.

Diffractive imaging with free-electron lasers allows structure determination from ensembles of weakly scattering identical nanoparticles. The ultra-short, ultra-bright X-ray pulses provide snapshots of the randomly oriented particles frozen in time, and terminate before the onset of structural damage. As signal strength diminishes for small particles, the synthesis of a three-dimensional diffraction volume requires simultaneous involvement of all data. Here we report the first application of a three-dimensional spatial frequency correlation analysis to carry out this synthesis from noisy single-particle femtosecond X-ray diffraction patterns of nearly identical samples in random and unknown orientations, collected at the Linac Coherent Light Source. Our demonstration uses unsupported test particles created via aerosol self-assembly, and composed of two polystyrene spheres of equal diameter. The correlation analysis avoids the need for orientation determination entirely. This method may be applied to the structural determination of biological macromolecules in solution.

Fractal morphology, imaging and mass spectrometry of single aerosol particles in flight.

The morphology of micrometre-size particulate matter is of critical importance in fields ranging from toxicology to climate science, yet these properties are surprisingly difficult to measure in the particles' native environment. Electron microscopy requires collection of particles on a substrate; visible light scattering provides insufficient resolution; and X-ray synchrotron studies have been limited to ensembles of particles. Here we demonstrate an in situ method for imaging individual sub-micrometre particles to nanometre resolution in their native environment, using intense, coherent X-ray pulses from the Linac Coherent Light Source free-electron laser. We introduced individual aerosol particles into the pulsed X-ray beam, which is sufficiently intense that diffraction from individual particles can be measured for morphological analysis. At the same time, ion fragments ejected from the beam were analysed using mass spectrometry, to determine the composition of single aerosol particles. Our results show the extent of internal dilation symmetry of individual soot particles subject to non-equilibrium aggregation, and the surprisingly large variability in their fractal dimensions. More broadly, our methods can be extended to resolve both static and dynamic morphology of general ensembles of disordered particles. Such general morphology has implications in topics such as solvent accessibilities in proteins, vibrational energy transfer by the hydrodynamic interaction of amino acids, and large-scale production of nanoscale structures by flame synthesis.

Femtosecond dark-field imaging with an X-ray free electron laser.

The emergence of femtosecond diffractive imaging with X-ray lasers has enabled pioneering structural studies of isolated particles, such as viruses, at nanometer length scales. However, the issue of missing low frequency data significantly limits the potential of X-ray lasers to reveal sub-nanometer details of micrometer-sized samples. We have developed a new technique of dark-field coherent diffractive imaging to simultaneously overcome the missing data issue and enable us to harness the unique contrast mechanisms available in dark-field microscopy. Images of airborne particulate matter (soot) up to two microns in length were obtained using single-shot diffraction patterns obtained at the Linac Coherent Light Source, four times the size of objects previously imaged in similar experiments. This technique opens the door to femtosecond diffractive imaging of a wide range of micrometer-sized materials that exhibit irreproducible complexity down to the nanoscale, including airborne particulate matter, small cells, bacteria and gold-labeled biological samples.

X-ray diffraction from membrane protein nanocrystals.

Membrane proteins constitute > 30% of the proteins in an average cell, and yet the number of currently known structures of unique membrane proteins is < 300. To develop new concepts for membrane protein structure determination, we have explored the serial nanocrystallography method, in which fully hydrated protein nanocrystals are delivered to an x-ray beam within a liquid jet at room temperature. As a model system, we have collected x-ray powder diffraction data from the integral membrane protein Photosystem I, which consists of 36 subunits and 381 cofactors. Data were collected from crystals ranging in size from 100 nm to 2 µm. The results demonstrate that there are membrane protein crystals that contain < 100 unit cells (200 total molecules) and that 3D crystals of membrane proteins, which contain < 200 molecules, may be suitable for structural investigation. Serial nanocrystallography overcomes the problem of x-ray damage, which is currently one of the major limitations for x-ray structure determination of small crystals. By combining serial nanocrystallography with x-ray free-electron laser sources in the future, it may be possible to produce molecular-resolution electron-density maps using membrane protein crystals that contain only a few hundred or thousand unit cells.

Reconstruction from a single diffraction pattern of azimuthally projected electron density of molecules aligned parallel to a single axis.

Diffraction from the individual molecules of a molecular beam, aligned parallel to a single axis by a strong electric field or other means, has been proposed as a means of structure determination of individual molecules. As in fiber diffraction, all the information extractable is contained in a diffraction pattern from incidence of the diffracting beam normal to the molecular alignment axis. The limited size of the object results in continuous diffraction patterns characterized by neither Bragg spots nor layer lines. Equations relating the scattered amplitudes to the molecular electron density may be conveniently formulated in terms of cylindrical harmonics. For simulated diffraction patterns from short C nanotubes aligned along their axes, iterative solution of the equation for the zeroth-order cylindrical harmonic and its inverse with appropriate constraints in real and reciprocal space enables the phasing of the measured amplitudes, and hence a reconstruction of the azimuthal projection of the molecule.

Molecular structure determination from x-ray scattering patterns of laser-aligned symmetric-top molecules.

We investigate the molecular structure information contained in the x-ray diffraction patterns of an ensemble of rigid CF(3)Br molecules aligned by an intense laser pulse at finite rotational temperature. The diffraction patterns are calculated at an x-ray photon energy of 20 keV to probe molecular structure at angstrom-scale resolution. We find that a structural reconstruction algorithm based on iterative phase retrieval fails to extract a reliable structure. However, the high atomic number of Br compared with C or F allows each diffraction pattern to be treated as a hologram. Using this approach, the azimuthal projection of the molecular electron density about the alignment axis may be retrieved.

An assessment of the resolution limitation due to radiation-damage in x-ray diffraction microscopy.

X-ray diffraction microscopy (XDM) is a new form of x-ray imaging that is being practiced at several third-generation synchrotron-radiation x-ray facilities. Nine years have elapsed since the technique was first introduced and it has made rapid progress in demonstrating high-resolution three-dimensional imaging and promises few-nm resolution with much larger samples than can be imaged in the transmission electron microscope. Both life- and materials-science applications of XDM are intended, and it is expected that the principal limitation to resolution will be radiation damage for life science and the coherent power of available x-ray sources for material science. In this paper we address the question of the role of radiation damage. We use a statistical analysis based on the so-called "dose fractionation theorem" of Hegerl and Hoppe to calculate the dose needed to make an image of a single life-science sample by XDM with a given resolution. We find that for simply-shaped objects the needed dose scales with the inverse fourth power of the resolution and present experimental evidence to support this finding. To determine the maximum tolerable dose we have assembled a number of data taken from the literature plus some measurements of our own which cover ranges of resolution that are not well covered otherwise. The conclusion of this study is that, based on the natural contrast between protein and water and "Rose-criterion" image quality, one should be able to image a frozen-hydrated biological sample using XDM at a resolution of about 10 nm.

Tomographic femtosecond x-ray diffractive imaging.

A method is proposed for obtaining three simultaneous projections of a target from a single radiation pulse, which also allows the relative orientation of successive targets to be determined. The method has application to femtosecond x-ray diffraction, and does not require solution of the phase problem. We show that the principal axes of a compact charge-density distribution can be obtained from projections of its autocorrelation function, which is directly accessible in diffraction experiments. The results may have more general application to time resolved tomographic pump-probe experiments and time-series imaging.

Powder diffraction from a continuous microjet of submicrometer protein crystals.

Atomic-resolution structures from small proteins have recently been determined from high-quality powder diffraction patterns using a combination of stereochemical restraints and Rietveld refinement [Von Dreele (2007), J. Appl. Cryst. 40, 133-143; Margiolaki et al. (2007), J. Am. Chem. Soc. 129, 11865-11871]. While powder diffraction data have been obtained from batch samples of small crystal-suspensions, which are exposed to X-rays for long periods of time and undergo significant radiation damage, the proof-of-concept that protein powder diffraction data from nanocrystals of a membrane protein can be obtained using a continuous microjet is shown. This flow-focusing aerojet has been developed to deliver a solution of hydrated protein nanocrystals to an X-ray beam for diffraction analysis. This method requires neither the crushing of larger polycrystalline samples nor any techniques to avoid radiation damage such as cryocooling. Apparatus to record protein powder diffraction in this manner has been commissioned, and in this paper the first powder diffraction patterns from a membrane protein, photosystem I, with crystallite sizes of less than 500 nm are presented. These preliminary patterns show the lowest-order reflections, which agree quantitatively with theoretical calculations of the powder profile. The results also serve to test our aerojet injector system, with future application to femtosecond diffraction in free-electron X-ray laser schemes, and for serial crystallography using a single-file beam of aligned hydrated molecules.

Dose, exposure time and resolution in serial X-ray crystallography.

The resolution of X-ray diffraction microscopy is limited by the maximum dose that can be delivered prior to sample damage. In the proposed serial crystallography method, the damage problem is addressed by distributing the total dose over many identical hydrated macromolecules running continuously in a single-file train across a continuous X-ray beam, and resolution is then limited only by the available molecular and X-ray fluxes and molecular alignment. Orientation of the diffracting molecules is achieved by laser alignment. The incident X-ray fluence (energy/area) is evaluated that is required to obtain a given resolution from (i) an analytical model, giving the count rate at the maximum scattering angle for a model protein, (ii) explicit simulation of diffraction patterns for a GroEL-GroES protein complex, and (iii) the spatial frequency cut-off of the transfer function following iterative solution of the phase problem, and reconstruction of an electron density map in the projection approximation. These calculations include counting shot noise and multiple starts of the phasing algorithm. The results indicate counting time and the number of proteins needed within the beam at any instant for a given resolution and X-ray flux. An inverse fourth-power dependence of exposure time on resolution is confirmed, with important implications for all coherent X-ray imaging. It is found that multiple single-file protein beams will be needed for sub-nanometer resolution on current third-generation synchrotrons, but not on fourth-generation designs, where reconstruction of secondary protein structure at a resolution of 7 A should be possible with relatively short exposures.

Damped and thermal motion of laser-aligned hydrated macromolecule beams for diffraction.

We consider a monodispersed Rayleigh droplet beam of water droplets doped with proteins. An intense infrared laser is used to align these droplets. The arrangement has been proposed for electron- and x-ray-diffraction studies of proteins which are difficult to crystallize. This paper considers the effect of thermal fluctuations on the angular spread of alignment in thermal equilibrium, and relaxation phenomena, particularly the damping of oscillations excited as the molecules enter the field. The possibility of adiabatic alignment is also considered. We find that damping times in a high-pressure gas cell as used in x-ray-diffraction experiments are short compared with the time taken for molecules to traverse the beam and that a suitably shaped field might be used for electron-diffraction experiments in vacuum to provide adiabatic alignment, thus obviating the need for a damping gas cell.