A new solution to the curved Ewald sphere problem for 3D image reconstruction in electron microscopy.

We develop an algorithm capable of imaging a three-dimensional object given a collection of two-dimensional images of that object that are significantly influenced by the curvature of the Ewald sphere. These two-dimensional images cannot be approximated as projections of the object. Such an algorithm is useful in cryo-electron microscopy where larger samples, higher resolution, or lower energy electron beams are desired, all of which contribute to the significance of Ewald curvature.

Quantitative agreement between dynamical rocking curves in ultrafast electron diffraction for x-ray lasers.

Electron diffraction through a thin patterned silicon membrane can be used to create complex spatial modulations in electron distributions. By precisely varying parameters such as crystallographic orientation and wafer thickness, the intensity of reflections in the diffraction plane can be controlled and by placing an aperture to block all but one spot, we can form an image with different parts of the patterned membrane, as is done for bright-field imaging in microscopy. The patterned electron beams can then be used to control phase and amplitude of subsequent x-ray emission, enabling novel coherent x-ray methods. The electrons themselves can also be used for femtosecond time resolved diffraction and microscopy. As a first step toward patterned beams, we demonstrate experimentally and through simulation the ability to accurately predict and control diffraction spot intensities. We simulate MeV transmission electron diffraction patterns using the multislice method for various crystallographic orientations of a single crystal Si(001) membrane near beam normal. The resulting intensity maps of the Bragg reflections are compared to experimental results obtained at the Accelerator Structure Test Area Ultrafast Electron Diffraction (ASTA UED) facility at SLAC. Furthermore, the fraction of inelastic and elastic scattering of the initial charge is estimated along with the absorption of the membrane to determine the contrast that would be seen in a patterned version of the Si(001) membrane.

Dynamics of rare gas solids irradiated by electron beams.

The remarkable success of x-ray free-electron lasers and their ability to image biological macromolecules while outrunning secondary radiation damage due to photoelectrons, by using femtosecond pulses, raise the question of whether this can be done using pulsed high-energy electron beams. In this paper, we use excited state molecular dynamics simulations, with tabulated potentials, for rare gas solids to investigate the effect of radiation damage due to inelastic scattering (by plasmons, excitons, and heat) on the pair distribution function. We use electron energy loss spectra to characterize the electronic excitations responsible for radiation damage.

Short-wavelength free-electron laser sources and science: a review.

This review is focused on free-electron lasers (FELs) in the hard to soft x-ray regime. The aim is to provide newcomers to the area with insights into: the basic physics of FELs, the qualities of the radiation they produce, the challenges of transmitting that radiation to end users and the diversity of current scientific applications. Initial consideration is given to FEL theory in order to provide the foundation for discussion of FEL output properties and the technical challenges of short-wavelength FELs. This is followed by an overview of existing x-ray FEL facilities, future facilities and FEL frontiers. To provide a context for information in the above sections, a detailed comparison of the photon pulse characteristics of FEL sources with those of other sources of high brightness x-rays is made. A brief summary of FEL beamline design and photon diagnostics then precedes an overview of FEL scientific applications. Recent highlights are covered in sections on structural biology, atomic and molecular physics, photochemistry, non-linear spectroscopy, shock physics, solid density plasmas. A short industrial perspective is also included to emphasise potential in this area.

XFELs for structure and dynamics in biology.

The development and application of the free-electron X-ray laser (XFEL) to structure and dynamics in biology since its inception in 2009 are reviewed. The research opportunities which result from the ability to outrun most radiation-damage effects are outlined, and some grand challenges are suggested. By avoiding the need to cool samples to minimize damage, the XFEL has permitted atomic resolution imaging of molecular processes on the 100 fs timescale under near-physiological conditions and in the correct thermal bath in which molecular machines operate. Radiation damage, comparisons of XFEL and synchrotron work, single-particle diffraction, fast solution scattering, pump-probe studies on photosensitive proteins, mix-and-inject experiments, caged molecules, pH jump and other reaction-initiation methods, and the study of molecular machines are all discussed. Sample-delivery methods and data-analysis algorithms for the various modes, from serial femtosecond crystallo-graphy to fast solution scattering, fluctuation X-ray scattering, mixing jet experiments and single-particle diffraction, are also reviewed.

Structures of riboswitch RNA reaction states by mix-and-inject XFEL serial crystallography.

Riboswitches are structural RNA elements that are generally located in the 5' untranslated region of messenger RNA. During regulation of gene expression, ligand binding to the aptamer domain of a riboswitch triggers a signal to the downstream expression platform. A complete understanding of the structural basis of this mechanism requires the ability to study structural changes over time. Here we use femtosecond X-ray free electron laser (XFEL) pulses to obtain structural measurements from crystals so small that diffusion of a ligand can be timed to initiate a reaction before diffraction. We demonstrate this approach by determining four structures of the adenine riboswitch aptamer domain during the course of a reaction, involving two unbound apo structures, one ligand-bound intermediate, and the final ligand-bound conformation. These structures support a reaction mechanism model with at least four states and illustrate the structural basis of signal transmission. The three-way junction and the P1 switch helix of the two apo conformers are notably different from those in the ligand-bound conformation. Our time-resolved crystallographic measurements with a 10-second delay captured the structure of an intermediate with changes in the binding pocket that accommodate the ligand. With at least a 10-minute delay, the RNA molecules were fully converted to the ligand-bound state, in which the substantial conformational changes resulted in conversion of the space group. Such notable changes in crystallo highlight the important opportunities that micro- and nanocrystals may offer in these and similar time-resolved diffraction studies. Together, these results demonstrate the potential of 'mix-and-inject' time-resolved serial crystallography to study biochemically important interactions between biomacromolecules and ligands, including those that involve large conformational changes.

The linac coherent light source single particle imaging road map.

Intense femtosecond x-ray pulses from free-electron laser sources allow the imaging of individual particles in a single shot. Early experiments at the Linac Coherent Light Source (LCLS) have led to rapid progress in the field and, so far, coherent diffractive images have been recorded from biological specimens, aerosols, and quantum systems with a few-tens-of-nanometers resolution. In March 2014, LCLS held a workshop to discuss the scientific and technical challenges for reaching the ultimate goal of atomic resolution with single-shot coherent diffractive imaging. This paper summarizes the workshop findings and presents the roadmap toward reaching atomic resolution, 3D imaging at free-electron laser sources.

The extraction of single-particle diffraction patterns from a multiple-particle diffraction pattern.

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.

Lawrence Bragg, microdiffraction and X-ray lasers.

We trace the historical development of W. L. Bragg's `law' and the key experimental observation which made it possible using polychromatic radiation at a time when neither X-ray wavelengths nor cell constants were known. This led, through his phasing and solving large mineral structures (without use of a computer), to work on metals, proteins, bubble rafts and his X-ray microscope. The relationship of this to early X-ray microdiffraction is outlined, followed by a brief review of electron microdiffraction methods, where electron-probe sizes smaller than one unit cell can be formed with an interesting `failure' of Bragg's law. We end with a review of recent femtosecond X-ray `snapshot' diffraction from protein nanocrystals, using an X-ray laser which generates pulses so short that they terminate before radiation damage can commence, yet subsequently destroy the sample. In this way, using short pulses instead of freezing, the nexus between dose, resolution and crystal size has been broken, opening the way to time-resolved diffraction without damage for a stream of identical particles.

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.

X-ray lasers for structural and dynamic biology.

Research opportunities and techniques are reviewed for the application of hard x-ray pulsed free-electron lasers (XFEL) to structural biology. These include the imaging of protein nanocrystals, single particles such as viruses, pump--probe experiments for time-resolved nanocrystallography, and snapshot wide-angle x-ray scattering (WAXS) from molecules in solution. The use of femtosecond exposure times, rather than freezing of samples, as a means of minimizing radiation damage is shown to open up new opportunities for the molecular imaging of biochemical reactions at room temperature in solution. This is possible using a 'diffract-and-destroy' mode in which the incident pulse terminates before radiation damage begins. Methods for delivering hundreds of hydrated bioparticles per second (in random orientations) to a pulsed x-ray beam are described. New data analysis approaches are outlined for the correlated fluctuations in fast WAXS, for protein nanocrystals just a few molecules on a side, and for the continuous x-ray scattering from a single virus. Methods for determining the orientation of a molecule from its diffraction pattern are reviewed. Methods for the preparation of protein nanocrystals are also reviewed. New opportunities for solving the phase problem for XFEL data are outlined. A summary of the latest results is given, which now extend to atomic resolution for nanocrystals. Possibilities for time-resolved chemistry using fast WAXS (solution scattering) from mixtures is reviewed, toward the general goal of making molecular movies of biochemical processes.

Injector for scattering measurements on fully solvated biospecies.

We describe a liquid jet injector system developed to deliver fully solvated microscopic target species into a probe beam under either vacuum or ambient conditions. The injector was designed specifically for x-ray scattering studies of biological nanospecies using x-ray free electron lasers and third generation synchrotrons, but is of interest to any application in which microscopic samples must be delivered in a fully solvated state and with microscopic precision. By utilizing a gas dynamic virtual nozzle (GDVN) to generate a sample-containing liquid jet of diameter ranging from 300 nm to 20 µm, the injector avoids the clogging problems associated in this size range with conventional Rayleigh jets. A differential pumping system incorporated into the injector shields the experimental chamber from the gas load of the GDVN, making the injector compatible with high vacuum systems. The injector houses a fiber-optically coupled pump laser to illuminate the jet for pump-probe experiments and a hermetically sealed microscope to observe the liquid jet for diagnostics and alignment during operation. This injector system has now been used during several experimental runs at the Linac Coherent Light Source. Recent refinements in GDVN design are also presented.

New light on disordered ensembles: ab initio structure determination of one particle from scattering fluctuations of many copies.

We report on the first experimental ab initio reconstruction of an image of a single particle from fluctuations in the scattering from an ensemble of copies, randomly oriented about an axis. The method is applicable to identical particles frozen in space or time (as by snapshot diffraction from an x-ray free electron laser). These fluctuations enhance information obtainable from an experiment such as conventional small angle x-ray scattering.

Towards ETEM serial crystallography: Electron diffraction from liquid jets.

A sufficiently thin column of liquid was produced to permit penetration with a 200 keV electron beam as evidenced by the observation of diffraction rings due to the intermolecular spacing of the liquid samples. For liquid thickness below 800 nm, the diffraction rings became visible above the inelastic background. Studies were carried out in the environmental chamber of a transmission electron microscope using water and isopropanol.

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.

Combined structure-factor phase measurement and theoretical calculations for mapping of chemical bonds in GaN.

For non-centrosymmetric crystals, the refinement of charge-density maps requires highly accurate measurements of structure-factor phase, which can now be obtained using the extinction-free convergent-beam electron microdiffraction method. We report here accurate low-order structure-factor phases and amplitudes for gallium nitride (GaN) in the wurtzite structure. The measurement accuracy is up to 0.1% for amplitude and 0.2 degrees for phases. By combining these with high-order structure factors from electronic structure calculation, charge-density maps were obtained. Fine bonding features suggest that the Ga-N bonds are polar and covalent, with charge transfer from Ga to N; however, the polarity effect is extremely small.

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.

Two-wavelength inversion of multiply scattered soft X-ray intensities to charge density.

A method is described for reconstructing the two-dimensional real-space charge density of an isolated object from measurement of the soft X-ray transmission diffraction pattern when it is affected by strong multiple scattering. The Bloch-wave scattering-matrix approach is used to show that the diffracted amplitude depends only on a simple product of X-ray wavelength and sample thickness (unlike the case of relativistic electron diffraction) under reasonable approximations. The multislice formulation then gives the effect of a small change in wavelength, which involves only single scattering. Dynamical diffraction patterns are recorded at two adjacent wavelengths, phased by iterative methods, transformed to real space and divided to give a single-scattering wavefunction. This can then be used to produce a charge-density map. The extension of the method to tomography is discussed. Consideration is first also given to the possibility that absorption due to the photoelectric effect may be so severe for soft X-rays that multiple elastic scattering becomes so much less probable than photoelectric absorption that it may be neglected entirely. A discussion of signs in soft X-ray, positron and electron multiple-scattering theory is given.

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.