An approach to three-dimensional structures of biomolecules by using single-molecule diffraction images

A predicted model-aided reconstruction algorithm for X-ray free-electron laser single-particle imaging

Ultra-intense, ultra-fast X-ray free-electron lasers (XFELs) enable the imaging of single protein molecules under ambient temperature and pressure. A crucial aspect of structure reconstruction involves determining the relative orientations of each diffraction pattern and recovering the missing phase information. In this paper, we introduce a predicted model-aided algorithm for orientation determination and phase retrieval, which has been tested on various simulated datasets and has shown significant improvements in the success rate, accuracy and efficiency of XFEL data reconstruction.

Nanocrystalline protein domains via salting-out

Protein salting-out is a well established phenomenon that in many cases leads to amorphous structures and protein gels, which are usually not considered to be useful for protein structure determination. Here, microstructural measurements of several different salted-out protein dense phases are reported, including of lysozyme, ribonuclease A and an IgG1, showing that salted-out protein gels unexpectedly contain highly ordered protein nanostructures that assemble hierarchically to create the gel. The nanocrystalline domains are approximately 10-100 nm in size, are shown to have structures commensurate with those of bulk crystals and grow on time scales in the order of an hour to a day. Beyond revealing the rich, hierarchical nanoscale to mesoscale structure of protein gels, the nanocrystals that these phases contain are candidates for structural biology on next-generation X-ray free-electron lasers, which may enable the study of biological macromolecules that are difficult or impossible to crystallize in bulk.

Orientation and Alignment dynamics of polar molecule driven by shaped laser pulses

We review the theoretical status of intense laser induced orientation and alignment-a field of study which lies at the interface of intense laser physics and chemical dynamics and having potential applications such as high harmonic generation, nano-scale processing and control of chemical reactions. The evolution of the rotational wave packet and its dynamics leading to orientation and alignment is the topic of the present discussion. The major part of this article primarily presents an overview of recent theoretical progress in controlling the orientation and alignment dynamics of a molecule by means of shaped laser pulses. The various theoretical approaches that lead to orientation and alignment such as static electrostatic field in combination with laser field(s), combination of orienting and aligning field, combination of aligning fields, combination of orienting fields, application of train of pulses etc. are discussed. It is observed that the train of pulses is quite an efficient tool for increasing the orientation or alignment of a molecule without causing the molecule to ionize. The orientation and alignment both can occur in adiabatic and non-adiabatic conditions with the rotational period of the molecule taken under consideration. The discussion is mostly limited to non-adiabatic rotational excitation (NAREX) i.e. cases in which the pulse duration is shorter than the rotational period of the molecule. We have emphasised on the so called half-cycle pulse (HCP) and square pulse (SQP). The effect of ramped pulses and of collision on the various laser parameters is also studied. We summarize the current discussion by presenting a consistent theoretical approach for describing the action of such pulses on movement of molecules. The impact of a particular pulse shape on the post-pulse dynamics is also calculated and analysed. In addition to this, the roles played by various laser parameters including the laser frequency, the pulse duration and the system temperature etc. are illustrated and discussed. The concept of alignment is extended from one-dimensional alignment to three-dimensional alignment with the proper choice of molecule and the polarised light. We conclude the article by discussing the potential applications of intense laser orientation and alignment.

Signatures of electronic and nuclear coherences in ultrafast molecular x-ray and electron diffraction

Femtosecond x-ray and electron diffraction hold promise to image the evolving structures of single molecules. We present a unified quantum-electrodynamical formulation of diffraction signals, based on the exact many-body nuclear + electronic wavefunction that can be extracted from quantum chemistry simulations. This gives a framework for analyzing various approximate molecular dynamics simulations. We show that the complete description of ultrafast diffraction signals contains interesting contributions involving mixed elastic and inelastic scattered photons that are usually masked by other larger contributions and are neglected. These terms include overlaps of nuclear wavepackets between different electronic states that provide an electronic decoherence mechanism and are important for the time-resolved imaging of conical intersections.

PyNX: high-performance computing toolkit for coherent X-ray imaging based on operators

The open-source PyNX toolkit has been extended to provide tools for coherent X-ray imaging data analysis and simulation. All calculations can be executed on graphical processing units (GPUs) to achieve high-performance computing speeds. The toolkit can be used for coherent diffraction imaging (CDI), ptychography and wavefront propagation, in the far- or near-field regime. Moreover, all imaging operations (propagation, projections, algorithm cycles…) can be implemented in Python as simple mathematical operators, an approach which can be used to easily combine basic algorithms in a tailored chain. Calculations can also be distributed to multiple GPUs, e.g. for large ptychography data sets. Command-line scripts are available for on-line CDI and ptychography analysis, either from raw beamline data sets or using the coherent X-ray imaging data format.

Continuous scanning for Bragg coherent X-ray imaging

We explore the use of continuous scanning during data acquisition for Bragg coherent diffraction imaging, i.e., where the sample is in continuous motion. The fidelity of continuous scanning Bragg coherent diffraction imaging is demonstrated on a single Pt nanoparticle in a flow reactor at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$400\,^\circ \hbox {C}$$\end{document}400∘C in an Ar-based gas flowed at 50 ml/min. We show a reduction of 30% in total scan time compared to conventional step-by-step scanning. The reconstructed Bragg electron density, phase, displacement and strain fields are in excellent agreement with the results obtained from conventional step-by-step scanning. Continuous scanning will allow to minimise sample instability under the beam and will become increasingly important at diffraction-limited storage ring light sources.

Methods and application of coherent X-ray diffraction imaging of noncrystalline particles

Microscopic imaging techniques have been developed to visualize events occurring in biological cells. Coherent X-ray diffraction imaging is one of the techniques applicable to structural analyses of cells and organelles, which have never been crystallized. In the experiment, a single noncrystalline particle is illuminated by an X-ray beam with almost complete spatial coherence. The structure of the particle projected along the direction of the beam is, in principle, retrieved from a finely recorded diffraction pattern alone by using iterative phase-retrieval algorithms. Here, we describe fundamental theory and experimental methods of coherent X-ray diffraction imaging and the recent application in structural studies of noncrystalline specimens by using X-rays available at Super Photon Ring of 8-Gev and SPring-8 Angstrom Compact Free Electron Laser in Japan.

Free log-likelihood as an unbiased metric for coherent diffraction imaging

Coherent Diffraction Imaging (CDI), a technique where an object is reconstructed from a single (2D or 3D) diffraction pattern, recovers the lost diffraction phases without a priori knowledge of the extent (support) of the object. The uncertainty of the object support can lead to over-fitting and prevents an unambiguous metric evaluation of solutions. We propose to use a ‘free’ log-likelihood indicator, where a small percentage of points are masked from the reconstruction algorithms, as an unbiased metric to evaluate the validity of computed solutions, independent of the sample studied. We also show how a set of solutions can be analysed through an eigen-decomposition to yield a better estimate of the real object. Example analysis on experimental data is presented both for a test pattern dataset, and the diffraction pattern from a live cyanobacteria cell. The method allows the validation of reconstructions on a wide range of materials (hard condensed or biological), and should be particularly relevant for 4th generation synchrotrons and X-ray free electron lasers, where large, high-throughput datasets require a method for unsupervised data evaluation.

X-Ray Free-Electron Lasers for the Structure and Dynamics of Macromolecules

X-ray free-electron lasers provide femtosecond-duration pulses of hard X-rays with a peak brightness approximately one billion times greater than is available at synchrotron radiation facilities. One motivation for the development of such X-ray sources was the proposal to obtain structures of macromolecules, macromolecular complexes, and virus particles, without the need for crystallization, through diffraction measurements of single noncrystalline objects. Initial explorations of this idea and of outrunning radiation damage with femtosecond pulses led to the development of serial crystallography and the ability to obtain high-resolution structures of small crystals without the need for cryogenic cooling. This technique allows the understanding of conformational dynamics and enzymatics and the resolution of intermediate states in reactions over timescales of 100 fs to minutes. The promise of more photons per atom recorded in a diffraction pattern than electrons per atom contributing to an electron micrograph may enable diffraction measurements of single molecules, although challenges remain.

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.

Incorporating particle symmetry into orientation determination in single-particle imaging

In coherent-diffraction-imaging experiments X-ray diffraction patterns of identical particles are recorded. The particles are injected into the X-ray free-electron laser (XFEL) beam in random orientations. If the particle has symmetry, finding the orientation of a pattern can be ambiguous. With some modifications, the correlation-maximization method can find the relative orientations of the diffraction patterns for the case of symmetric particles as well. After convergence, the correlation maps show the symmetry of the particle and can be used to determine the symmetry elements and their orientations. The C factor, slightly modified for the symmetric case, can indicate the consistency of the assembled three-dimensional intensity distribution.

Iterative phase retrieval in coherent diffractive imaging: practical issues

In this work, issues in phase retrieval in the coherent diffractive imaging (CDI) technique, from discussion on parameters for setting up a CDI experiment to evaluation of the goodness of the final reconstruction, are discussed. The distribution of objects under study by CDI often cannot be cross-validated by another imaging technique. It is therefore important to make sure that the developed CDI procedure delivers an artifact-free object reconstruction. Critical issues that can lead to artifacts are presented and recipes on how to avoid them are provided.

Single-pulse enhanced coherent diffraction imaging of bacteria with an X-ray free-electron laser

High-resolution imaging offers one of the most promising approaches for exploring and understanding the structure and function of biomaterials and biological systems. X-ray free-electron lasers (XFELs) combined with coherent diffraction imaging can theoretically provide high-resolution spatial information regarding biological materials using a single XFEL pulse. Currently, the application of this method suffers from the low scattering cross-section of biomaterials and X-ray damage to the sample. However, XFELs can provide pulses of such short duration that the data can be collected using the “diffract and destroy” approach before the effects of radiation damage on the data become significant. These experiments combine the use of enhanced coherent diffraction imaging with single-shot XFEL radiation to investigate the cellular architecture of Staphylococcus aureus with and without labeling by gold (Au) nanoclusters. The resolution of the images reconstructed from these diffraction patterns were twice as high or more for gold-labeled samples, demonstrating that this enhancement method provides a promising approach for the high-resolution imaging of biomaterials and biological systems.

Coherent diffraction imaging: consistency of the assembled three-dimensional distribution

The short pulses of X-ray free-electron lasers can produce diffraction patterns with structural information before radiation damage destroys the particle. From the recorded diffraction patterns the structure of particles or molecules can be determined on the nano- or even atomic scale. In a coherent diffraction imaging experiment thousands of diffraction patterns of identical particles are recorded and assembled into a three-dimensional distribution which is subsequently used to solve the structure of the particle. It is essential to know, but not always obvious, that the assembled three-dimensional reciprocal-space intensity distribution is really consistent with the measured diffraction patterns. This paper shows that, with the use of correlation maps and a single parameter calculated from them, the consistency of the three-dimensional distribution can be reliably validated.

Three-dimensional propagation in near-field tomographic X-ray phase retrieval

An extension of phase retrieval algorithms for near-field X-ray (propagation) imaging to three dimensions is presented, enhancing the quality of the reconstruction by exploiting previously unused three-dimensional consistency constraints.

This paper presents an extension of phase retrieval algorithms for near-field X-ray (propagation) imaging to three dimensions, enhancing the quality of the reconstruction by exploiting previously unused three-dimensional consistency constraints. The approach is based on a novel three-dimensional propagator and is derived for the case of optically weak objects. It can be easily implemented in current phase retrieval architectures, is computationally efficient and reduces the need for restrictive prior assumptions, resulting in superior reconstruction quality.

Single-molecule imaging with longer X-ray laser pulses

During the last five years, serial femtosecond crystallography using X-ray laser pulses has been developed into a powerful technique for determining the atomic structures of protein molecules from micrometre- and sub-micrometre-sized crystals. One of the key reasons for this success is the 'self-gating' pulse effect, whereby the X-ray laser pulses do not need to outrun all radiation damage processes. Instead, X-ray-induced damage terminates the Bragg diffraction prior to the pulse completing its passage through the sample, as if the Bragg diffraction were generated by a shorter pulse of equal intensity. As a result, serial femtosecond crystallography does not need to be performed with pulses as short as 5-10 fs, but can succeed for pulses 50-100 fs in duration. It is shown here that a similar gating effect applies to single-molecule diffraction with respect to spatially uncorrelated damage processes like ionization and ion diffusion. The effect is clearly seen in calculations of the diffraction contrast, by calculating the diffraction of the average structure separately to the diffraction from statistical fluctuations of the structure due to damage ('damage noise'). The results suggest that sub-nanometre single-molecule imaging with 30-50 fs pulses, like those produced at currently operating facilities, should not yet be ruled out. The theory presented opens up new experimental avenues to measure the impact of damage on single-particle diffraction, which is needed to test damage models and to identify optimal imaging conditions.

Classification of projection images of proteins with structural polymorphism by manifold: a simulation study for x-ray free-electron laser diffraction imaging

Coherent x-ray diffraction imaging (CXDI) enables us to visualize noncrystalline sample particles with micrometer to submicrometer dimensions. Using x-ray free-electron laser (XFEL) sources, two-dimensional diffraction patterns are collected from fresh samples supplied to the irradiation area in the "diffraction-before-destruction" scheme. A recent significant increase in the intensity of the XFEL pulse is promising and will allow us to visualize the three-dimensional structures of proteins using XFEL-CXDI in the future. For the protocol proposed for molecular structure determination using future XFEL-CXDI [T. Oroguchi and M. Nakasako, Phys. Rev. E 87, 022712 (2013)10.1103/PhysRevE.87.022712], we require an algorithm that can classify the data in accordance with the structural polymorphism of proteins arising from their conformational dynamics. However, most of the algorithms proposed primarily require the numbers of conformational classes, and then the results are biased by the numbers. To improve this point, here we examine whether a method based on the manifold concept can classify simulated XFEL-CXDI data with respect to the structural polymorphism of a protein that predominantly adopts two states. After random sampling of the conformations of the two states and in-between states from the trajectories of molecular dynamics simulations, a diffraction pattern is calculated from each conformation. Classification was performed by using our custom-made program suite named enma, in which the diffusion map (DM) method developed based on the manifold concept was implemented. We successfully classify most of the projection electron density maps phase retrieved from diffraction patterns into each of the two states and in-between conformations without the knowledge of the number of conformational classes. We also examined the classification of the projection electron density maps of each of the three states with respect to the Euler angle. The present results suggest that the DM method is imperative for future applications of XFEL-CXDI experiments for proteins, and clarify issues to be taken care of in the future application.

Beyond crystallography: diffractive imaging using coherent x-ray light sources

X-ray crystallography has been central to the development of many fields of science over the past century. It has now matured to a point that as long as good-quality crystals are available, their atomic structure can be routinely determined in three dimensions. However, many samples in physics, chemistry, materials science, nanoscience, geology, and biology are noncrystalline, and thus their three-dimensional structures are not accessible by traditional x-ray crystallography. Overcoming this hurdle has required the development of new coherent imaging methods to harness new coherent x-ray light sources. Here we review the revolutionary advances that are transforming x-ray sources and imaging in the 21st century.

Serial crystallography for the masses?

Serial crystallography should be possible with a much wider range of radiation sources as Ayyer et al. [IUCrJ (2015), 2, 29-34] show that crystallographic intensities can be recovered from randomly oriented frames which are too sparse for indexing.

X-ray imaging of chemically active valence electrons during a pericyclic reaction

Time-resolved imaging of chemically active valence electron densities is a long-sought goal, as these electrons dictate the course of chemical reactions. However, X-ray scattering is always dominated by the core and inert valence electrons, making time-resolved X-ray imaging of chemically active valence electron densities extremely challenging. Here we demonstrate an effective and robust method, which emphasizes the information encoded in weakly scattered photons, to image chemically active valence electron densities. The degenerate Cope rearrangement of semibullvalene, a pericyclic reaction, is used as an example to visually illustrate our approach. Our work also provides experimental access to the long-standing problem of synchronous versus asynchronous bond formation and breaking during pericyclic reactions.

X-ray scattering experiments give details of the electrons in a system, although typically this is dominated by core and inert valence electrons. Here, the authors report a method to follow changes in the chemically active valence electrons, and use it to study the reaction mechanism of a pericyclic reaction.

Visualization of ATP synthase dimers in mitochondria by electron cryo-tomography

Electron cryo-tomography is a powerful tool in structural biology, capable of visualizing the three-dimensional structure of biological samples, such as cells, organelles, membrane vesicles, or viruses at molecular detail. To achieve this, the aqueous sample is rapidly vitrified in liquid ethane, which preserves it in a close-to-native, frozen-hydrated state. In the electron microscope, tilt series are recorded at liquid nitrogen temperature, from which 3D tomograms are reconstructed. The signal-to-noise ratio of the tomographic volume is inherently low. Recognizable, recurring features are enhanced by subtomogram averaging, by which individual subvolumes are cut out, aligned and averaged to reduce noise. In this way, 3D maps with a resolution of 2 nm or better can be obtained. A fit of available high-resolution structures to the 3D volume then produces atomic models of protein complexes in their native environment. Here we show how we use electron cryo-tomography to study the in situ organization of large membrane protein complexes in mitochondria. We find that ATP synthases are organized in rows of dimers along highly curved apices of the inner membrane cristae, whereas complex I is randomly distributed in the membrane regions on either side of the rows. By subtomogram averaging we obtained a structure of the mitochondrial ATP synthase dimer within the cristae membrane.

Bayesian orientation estimate and structure information from sparse single-molecule x-ray diffraction images

We developed a Bayesian method to extract macromolecular structure information from sparse single-molecule x-ray free-electron laser diffraction images. The method addresses two possible scenarios. First, using a "seed" structural model, the molecular orientation is determined for each of the provided diffraction images, which are then averaged in three-dimensional reciprocal space. Subsequently, the real space electron density is determined using a relaxed averaged alternating reflections algorithm. In the second approach, the probability that the "seed" model fits to the given set of diffraction images as a whole is determined and used to distinguish between proposed structures. We show that for a given x-ray intensity, unexpectedly, the achievable resolution increases with molecular mass such that structure determination should be more challenging for small molecules than for larger ones. For a sufficiently large number of recorded photons (>200) per diffraction image an M^{1/6} scaling is seen. Using synthetic diffraction data for a small glutathione molecule as a challenging test case, successful determination of electron density was demonstrated for 20000 diffraction patterns with random orientations and an average of 82 elastically scattered and recorded photons per image, also in the presence of up to 50% background noise. The second scenario is exemplified and assessed for three biomolecules of different sizes. In all cases, determining the probability of a structure given set of diffraction patterns allowed successful discrimination between different conformations of the test molecules. A structure model of the glutathione tripeptide was refined in a Monte Carlo simulation from a random starting conformation. Further, effective distinguishing between three differently arranged immunoglobulin domains of a titin molecule and also different states of a ribosome in a tRNA translocation process was demonstrated. These results show that the proposed method is robust and enables structure determination from sparse and noisy x-ray diffraction images of single molecules spanning a wide range of molecular masses.

Applications of direct methods in protein crystallography for dealing with diffraction data down to 5 Å resolution

Apart from solving the heavy-atom substructure in proteins and ab initio phasing of protein diffraction data at atomic resolution, direct methods have also been successfully combined with other protein crystallographic methods in dealing with diffraction data far below atomic resolution, leading to significantly improved results. In this respect, direct methods provide phase constraints in reciprocal space within a dual-space iterative framework rather than solve the phase problem independently. Applications of this type of direct methods to difficult SAD phasing, model completion and low-resolution phase extension will be described in detail.

Data processing software suite SITENNO for coherent X-ray diffraction imaging using the X-ray free-electron laser SACLA

Coherent X-ray diffraction imaging is a promising technique for visualizing the structures of non-crystalline particles with dimensions of micrometers to sub-micrometers. Recently, X-ray free-electron laser sources have enabled efficient experiments in the `diffraction before destruction' scheme. Diffraction experiments have been conducted at SPring-8 Angstrom Compact free-electron LAser (SACLA) using the custom-made diffraction apparatus KOTOBUKI-1 and two multiport CCD detectors. In the experiments, ten thousands of single-shot diffraction patterns can be collected within several hours. Then, diffraction patterns with significant levels of intensity suitable for structural analysis must be found, direct-beam positions in diffraction patterns determined, diffraction patterns from the two CCD detectors merged, and phase-retrieval calculations for structural analyses performed. A software suite named SITENNO has been developed to semi-automatically apply the four-step processing to a huge number of diffraction data. Here, details of the algorithm used in the suite are described and the performance for approximately 9000 diffraction patterns collected from cuboid-shaped copper oxide particles reported. Using the SITENNO suite, it is possible to conduct experiments with data processing immediately after the data collection, and to characterize the size distribution and internal structures of the non-crystalline particles.

Fresnel coherent diffractive imaging of elemental distributions in nanoscale binary compounds

We report quantitative determination of elemental distribution in binary compounds with nano meter scale spatial resolution using x-ray Fresnel coherent diffractive imaging (FCDI). We show that the quantitative magnitude and phase values of the x-ray wave exiting an object determined by FCDI can be utilized to obtain full-field atomic density maps of each element independently. The proposed method was demonstrated by reconstructing the density maps of Pt and NiO in a Pt-NiO binary compound with about 18 nm spatial resolution.

Prospect of Retrieving Vibrational Wave Function by Single-Object Scattering Sampling

The exact shape of wave functions has never been directly measured because an ensemble measurement is often overwhelmed by the contributions of highly populated configurations. In this work, we explore the possibility of directly obtaining vibrational wave functions by single-object scattering sampling (SOSS) using intense, ultrashort X-ray pulses provided by X-ray free electron lasers. Previously, single-molecule diffraction experiments using femtosecond X-ray pulses have been proposed with the prospect of determining three-dimensional structure of macromolecules without the need of single-crystal samples. In contrast to the previous proposals, SOSS is designed for obtaining the structural variations of constantly fluctuating molecules by sampling many single-shot, single-object scattering patterns. From the simulations on iodine molecules adopting various pulse characteristics and molecular parameters, we were able to reconstruct vibrational wave functions of molecular iodine and found that SOSS is feasible under appropriate experimental conditions.

KOTOBUKI-1 apparatus for cryogenic coherent X-ray diffraction imaging

We have developed an experimental apparatus named KOTOBUKI-1 for use in coherent X-ray diffraction imaging experiments of frozen-hydrated non-crystalline particles at cryogenic temperature. For cryogenic specimen stage with small positional fluctuation for a long exposure time of more than several minutes, we here use a cryogenic pot cooled by the evaporation cooling effect for liquid nitrogen. In addition, a loading device is developed to bring specimens stored in liquid nitrogen to the specimen stage in vacuum. The apparatus allows diffraction data collection for frozen-hydrated specimens at 66 K with a positional fluctuation of less than 0.4 μm and provides an experimental environment to easily exchange specimens from liquid nitrogen storage to the specimen stage. The apparatus was developed and utilized in diffraction data collection of non-crystalline particles with dimensions of μm from material and biological sciences, such as metal colloid particles and chloroplast, at BL29XU of SPring-8. Recently, it has been applied for single-shot diffraction data collection of non-crystalline particles with dimensions of sub-μm using X-ray free electron laser at BL3 of SACLA.

Selection and orientation of different particles in single particle imaging

The short pulses of X-ray free electron lasers can produce diffraction patterns with structural information before radiation damage destroys the particle. The particles are injected into the beam in random orientations and they should be identical. However, in real experimental conditions it is not always possible to have identical particles. In this paper we show that the correlation maximization method, developed earlier, is able to select identical particles from a mixture and find their orientations simultaneously.

Lensless coherent imaging of proteins and supramolecular assemblies: Efficient phase retrieval by the charge flipping algorithm

Diffractive imaging using the intense and coherent beam of X-ray free-electron lasers opens new perspectives for structural studies of single nanoparticles and biomolecules. Simulations were carried out to generate 3D oversampled diffraction patterns of non-crystalline biological samples, ranging from peptides and proteins to megadalton complex assemblies, and to recover their molecular structure from nanometer to near-atomic resolutions. Using these simulated data, we show here that iterative reconstruction methods based on standard and variant forms of the charge flipping algorithm, can efficiently solve the phase retrieval problem and extract a unique and reliable molecular structure. Contrary to the case of conventional algorithms, where the estimation and the use of a compact support is imposed, our approach does not require any prior information about the molecular assembly, and is amenable to a wide range of biological assemblies. Importantly, the robustness of this ab initio approach is illustrated by the fact that it tolerates experimental noise and incompleteness of the intensity data at the center of the speckle pattern.

Three-dimensional structure determination protocol for noncrystalline biomolecules using x-ray free-electron laser diffraction imaging

Coherent and intense x-ray pulses generated by x-ray free-electron laser (XFEL) sources are paving the way for structural determination of noncrystalline biomolecules. However, due to the small scattering cross section of electrons for x rays, the available incident x-ray intensity of XFEL sources, which is currently in the range of 10(12)-10(13) photons/μm(2)/pulse, is lower than that necessary to perform single-molecule diffraction experiments for noncrystalline biomolecules even with the molecular masses of megadalton and submicrometer dimensions. Here, we propose an experimental protocol and analysis method for visualizing the structure of those biomolecules by the combined application of coherent x-ray diffraction imaging and three-dimensional reconstruction methods. To compensate the small scattering cross section of biomolecules, in our protocol, a thin vitreous ice plate containing several hundred biomolecules/μm(2) is used as sample, a setup similar to that utilized by single-molecule cryoelectron microscopy. The scattering cross section of such an ice plate is far larger than that of a single particle. The images of biomolecules contained within irradiated areas are then retrieved from each diffraction pattern, and finally provide the three-dimensional electron density model. A realistic atomic simulation using large-scale computations proposed that the three-dimensional structure determination of the 50S ribosomal subunit embedded in a vitreous ice plate is possible at a resolution of 0.8 nm when an x-ray beam of 10(16) photons/500×500 nm(2)/pulse is available.

Assessment of radiation damage in single-shot coherent diffraction of DNA molecules by an extreme-ultraviolet free-electron laser

We have investigated the progress of structural distortions in DNA molecules by single-shot coherent diffraction using extreme-ultraviolet radiation from a free-electron laser. A speckle pattern of DNA molecules was successfully acquired using photons in a single pulse with a 100 fs pulse width. The radiation damage was assessed by a cross correlation, revealing that the first exposure has significantly deformed most of the original structures. Molecules were not completely destroyed by the first single-shot exposure and underwent subsequent distortions through continued exposure, until eventually deforming into a radiation-hard structure.

Emerging opportunities in structural biology with X-ray free-electron lasers

X-ray free-electron lasers (X-FELs) produce X-ray pulses with extremely brilliant peak intensity and ultrashort pulse duration. It has been proposed that radiation damage can be 'outrun' by using an ultra intense and short X-FEL pulse that passes a biological sample before the onset of significant radiation damage. The concept of 'diffraction-before-destruction' has been demonstrated recently at the Linac Coherent Light Source, the first operational hard X-ray FEL, for protein nanocrystals and giant virus particles. The continuous diffraction patterns from single particles allow solving the classical 'phase problem' by the oversampling method with iterative algorithms. If enough data are collected from many identical copies of a (biological) particle, its three-dimensional structure can be reconstructed. We review the current status and future prospects of serial femtosecond crystallography (SFX) and single-particle coherent diffraction imaging (CDI) with X-FELs.

Humidity-controlled preparation of frozen-hydrated biological samples for cryogenic coherent x-ray diffraction microscopy

Coherent x-ray diffraction microscopy (CXDM) has the potential to visualize the structures of micro- to sub-micrometer-sized biological particles, such as cells and organelles, at high resolution. Toward advancing structural studies on the functional states of such particles, here, we developed a system for the preparation of frozen-hydrated biological samples for cryogenic CXDM experiments. The system, which comprised a moist air generator, microscope, micro-injector mounted on a micromanipulator, custom-made sample preparation chamber, and flash-cooling device, allowed for the manipulation of sample particles in the relative humidity range of 20%-94%rh at 293 K to maintain their hydrated and functional states. Here, we report the details of the system and the operation procedure, including its application to the preparation of a frozen-hydrated chloroplast sample. Sample quality was evaluated through a cryogenic CXDM experiment conducted at BL29XUL of SPring-8. Taking the performance of the system and the quality of the sample, the system was suitable to prepare frozen-hydrated biological samples for cryogenic CXDM experiments.

Iterative phase retrieval strategy of transient events

Important nuances of a process or processes in action can be obtained from the phase retrieval of diffraction patterns for analysis of transient events. A significant limitation associated with the iterative approach is that predictive input functions are needed and can result in situations of nonconvergence. In dealing with a transient event recorded as a series of Fourier magnitude patterns, such a hit-and-miss characteristic, on the surface, appears computationally daunting. We report and demonstrate a strategy here that effectively minimizes this by using a prior retrieved frame as the predictive function for the current retrieval process.

Common arc method for diffraction pattern orientation

Very short pulses of X-ray free-electron lasers opened the way to obtaining diffraction signal from single particles beyond the radiation dose limit. For three-dimensional structure reconstruction many patterns are recorded in the object's unknown orientation. A method is described for the orientation of continuous diffraction patterns of non-periodic objects, utilizing intensity correlations in the curved intersections of the corresponding Ewald spheres, and hence named the common arc orientation method. The present implementation of the algorithm optionally takes into account Friedel's law, handles missing data and is capable of determining the point group of symmetric objects. Its performance is demonstrated on simulated diffraction data sets and verification of the results indicates a high orientation accuracy even at low signal levels. The common arc method fills a gap in the wide palette of orientation methods.

Bayesian algorithms for recovering structure from single-particle diffraction snapshots of unknown orientation: a comparison

The advent of X-ray free-electron lasers promises the possibility to determine the structure of individual particles such as microcrystallites, viruses and biomolecules from single-shot diffraction snapshots obtained before the particle is destroyed by the intense femtosecond pulse. This program requires the ability to determine the orientation of the particle giving rise to each snapshot at signal levels as low as ~10(-2) photons per pixel. Two apparently different approaches have recently demonstrated this capability. Here we show they represent different implementations of the same fundamental approach, and identify the primary factors limiting their performance.

Application of a real-space three-dimensional image reconstruction method in the structural analysis of noncrystalline biological macromolecules enveloped by water in coherent x-ray diffraction microscopy

Coherent x-ray diffraction microscopy is a novel technique in the structural analyses of particles that are difficult to crystallize, such as the biological particles composing living cells. As water is indispensable for maintaining particles in functional structures, sufficient hydration of targeted particles is required during sample preparation for diffraction microscopy experiments. However, the water enveloping particles also contributes significantly to the diffraction patterns and reduces the electron-density contrast of the sample particles. In this study, we propose a protocol for the structural analyses of particles in water by applying a three-dimensional reconstruction method in real space for the projection images phase-retrieved from diffraction patterns, together with a developed density modification technique. We examined the feasibility of the protocol through three simulations involving a protein molecule in a vacuum, and enveloped in either a droplet or a cube-shaped water. The simulations were carried out for the diffraction patterns in the reciprocal planes normal to the incident x-ray beam. This assumption and the simulation conditions corresponded to experiments using x-ray wavelengths of shorter than 0.03 Å. The analyses demonstrated that our protocol provided an interpretable electron-density map. Based on the results, we discuss the advantages and limitations of the proposed protocol and its practical application for experimental data. In particular, we examined the influence of Poisson noise in diffraction patterns on the reconstructed three-dimensional electron density in the proposed protocol.

X-ray holographic microscopy with zone plates applied to biological samples in the water window using 3rd harmonic radiation from the free-electron laser FLASH

The imaging of hydrated biological samples - especially in the energy window of 284-540 eV, where water does not obscure the signal of soft organic matter and biologically relevant elements - is of tremendous interest for life sciences. Free-electron lasers can provide highly intense and coherent pulses, which allow single pulse imaging to overcome resolution limits set by radiation damage. One current challenge is to match both the desired energy and the intensity of the light source. We present the first images of dehydrated biological material acquired with 3rd harmonic radiation from FLASH by digital in-line zone plate holography as one step towards the vision of imaging hydrated biological material with photons in the water window. We also demonstrate the first application of ultrathin molecular sheets as suitable substrates for future free-electron laser experiments with biological samples in the form of a rat fibroblast cell and marine biofouling bacteria Cobetia marina.

Coherent diffraction microscopy at SPring-8: instrumentation, data acquisition and data analysis

Since the first demonstration of coherent diffraction microscopy in 1999, this lensless imaging technique has been experimentally refined by continued developments. Here, instrumentation and experimental procedures for measuring oversampled diffraction patterns from non-crystalline specimens using an undulator beamline (BL29XUL) at SPring-8 are presented. In addition, detailed post-experimental data analysis is provided that yields high-quality image reconstructions. As the acquisition of high-quality diffraction patterns is at least as important as the phase-retrieval procedure to guarantee successful image reconstructions, this work will be of interest for those who want to apply this imaging technique to materials science and biological samples.

On the feasibility of nanocrystal imaging using intense and ultrashort X-ray pulses

Structural studies of biological macromolecules are severely limited by radiation damage. Traditional crystallography curbs the effects of damage by spreading damage over many copies of the molecule of interest in the crystal. X-ray lasers offer an additional opportunity for limiting damage by out-running damage processes with ultrashort and very intense X-ray pulses. Such pulses may allow the imaging of single molecules, clusters, or nanoparticles. Coherent flash imaging will also open up new avenues for structural studies on nano- and microcrystalline substances. This paper addresses the theoretical potentials and limitations of nanocrystallography with extremely intense coherent X-ray pulses. We use urea nanocrystals as a model for generic biological substances and simulate the primary and secondary ionization dynamics in the crystalline sample. The results establish conditions for ultrafast single-shot nanocrystallography diffraction experiments as a function of X-ray fluence, pulse duration, and the size of nanocrystals. Nanocrystallography using ultrafast X-ray pulses has the potential to open up a new route in protein crystallography to solve atomic structures of many systems that remain inaccessible using conventional X-ray sources.

Energetics, ionization, and expansion dynamics of atomic clusters irradiated with short intense vacuum-ultraviolet pulses

Kinetic equations are used to model the dynamics of Xe clusters irradiated with short, intense vacuum-ultraviolet pulses. Various cluster size and pulse fluences are considered. It is found that the highly charged ions observed in the experiments are mainly due to Coulomb explosion of the outer cluster shell. Ions within the cluster core predominantly recombine with plasma electrons, forming a large fraction of neutral atoms. To our knowledge, our model is the first and only one that gives an accurate description of all of the experimental data collected from atomic clusters at 100 nm photon wavelength.

Phase retrieval from a single near-field diffraction pattern with a large Fresnel number

A new method of phase retrieval from a single near-field diffraction image with a large Fresnel number is presented and discussed. This method requires only the oversampled diffraction pattern without any other information such as the object envelope. Moreover, we show that the combination with a fast computational method is possible when the linear oversampling ratio is an integer. Numerical simulations are also presented, showing that the method works well with noisy data.

Quantitative imaging of single, unstained viruses with coherent x rays

We report the recording and reconstruction of x-ray diffraction patterns from single, unstained viruses, for the first time. By separating the diffraction pattern of the virus particles from that of their surroundings, we performed quantitative and high-contrast imaging of a single virion. The structure of the viral capsid inside a virion was visualized. This work opens the door for quantitative x-ray imaging of a broad range of specimens from protein machineries and viruses to cellular organelles. Moreover, our experiment is directly transferable to the use of x-ray free electron lasers, and represents an experimental milestone towards the x-ray imaging of large protein complexes.

Extending X-ray crystallography to allow the imaging of noncrystalline materials, cells, and single protein complexes

In 1999, researchers extended X-ray crystallography to allow the imaging of noncrystalline specimens by measuring the X-ray diffraction pattern of a noncrystalline specimen and then directly phasing it using the oversampling method with iterative algorithms. Since then, the field has evolved moving in three important directions. The first is the 3D structural determination of noncrystalline materials, which includes the localization of the defects and strain field inside nanocrystals, and quantitative 3D imaging of disordered materials such as nanoparticles and biomaterials. The second is the 3D imaging of frozen-hydrated whole cells at a resolution of 10 nm or better. A main thrust is to localize specific multiprotein complexes inside cells. The third is the potential of imaging single large protein complexes using extremely intense and ultrashort X-ray pulses. In this article, we review the principles of this methodology, summarize recent developments in each of the three directions, and illustrate a few examples.

Nanoscale imaging of buried structures with elemental specificity using resonant x-ray diffraction microscopy

We report the first demonstration of resonant x-ray diffraction microscopy for element specific imaging of buried structures with a pixel resolution of approximately 15 nm by exploiting the abrupt change in the scattering cross section near electronic resonances. We performed nondestructive and quantitative imaging of buried Bi structures inside a Si crystal by directly phasing coherent x-ray diffraction patterns acquired below and above the Bi M5 edge. We anticipate that resonant x-ray diffraction microscopy will be applied to element and chemical state specific imaging of a broad range of systems including magnetic materials, semiconductors, organic materials, biominerals, and biological specimens.

High numerical aperture tabletop soft x-ray diffraction microscopy with 70-nm resolution

Light microscopy has greatly advanced our understanding of nature. The achievable resolution, however, is limited by optical wavelengths to approximately 200 nm. By using imaging and labeling technologies, resolutions beyond the diffraction limit can be achieved for specialized specimens with techniques such as near-field scanning optical microscopy, stimulated emission depletion microscopy, and photoactivated localization microscopy. Here, we report a versatile soft x-ray diffraction microscope with 70- to 90-nm resolution by using two different tabletop coherent soft x-ray sources-a soft x-ray laser and a high-harmonic source. We also use field curvature correction that allows high numerical aperture imaging and near-diffraction-limited resolution of 1.5lambda. A tabletop soft x-ray diffraction microscope should find broad applications in biology, nanoscience, and materials science because of its simple optical design, high resolution, large depth of field, 3D imaging capability, scalability to shorter wavelengths, and ultrafast temporal resolution.