Measured Diffraction Data Research Articles

Atomic resolution studies of S1 nuclease complexes reveal details of RNA interaction with the enzyme despite multiple lattice-translocation defects

S1 nuclease from Aspergillus oryzae is a single-strand-specific nuclease from the S1/P1 family that is utilized in biochemistry and biotechnology. S1 nuclease is active on both RNA and DNA but with differing catalytic efficiencies. This study clarifies its catalytic properties using a thorough comparison of differences in thebinding of RNA and DNA in the active site of S1 nuclease based on X-ray structures, including two newly solved complexes of S1 nuclease with the products of RNA cleavage at atomic resolution. Conclusions derived from this comparison are valid for the whole S1/P1 nuclease family. For proper model building and refinement, multiple lattice-translocation defects present in the measured diffraction data needed to be solved. Two different approaches were tested and compared. Correction of the measured intensities proved to be superior to the use of the dislocation model of asymmetric units with partial occupancy of individual chains. As the crystals suffered from multiple lattice translocations, equations for their correction were derived de novo. The presented approach to the correction of multiple lattice-translocation defects may help to solve similar problems in the field of protein X-ray crystallography.

Ab initio reconstruction from one-dimensional crystal diffraction data.

Filamentary and rod-like assemblies are ubiquitous in biological systems, and single such assemblies can form one-dimensional (1D) crystals. New, intense X-ray sources, such as X-ray free-electron lasers, make it feasible to measure diffraction data from single 1D crystals. Such experiments would present some advantages, since cylindrical averaging of the diffraction data in conventional fiber diffraction analysis is avoided, there is coherent signal amplification relative to single-particle imaging, and the diffraction data are oversampled compared with those from a 3D crystal so that the phase problem is better determined than for a 3D crystal [Millane (2017). Acta Cryst. A73, 140-150]. Phasing of 1D crystal diffraction data is examined, by simulation, using an iterative projection algorithm. Ab initio phasing is feasible with realistic noise levels and little envelope information is required if a shrink-wrap algorithm is also incorporated. Some practical aspects of the proposed experiments are explored.

Editorial

Editorial

Michael Mark Woolfson. 9 January 1927—23 December 2019

Michael Woolfson contributed enormously to the theory and practice of X-ray crystallography for almost 60 years. He extended the theory of ‘direct methods’, which provided a general solution of the crystallographic phase problem from the measured diffraction data alone, and provided tools to exploit this theory. Software developed in his laboratory, such as the computer package MULTAN, was responsible for about half of the structures determined around the world in the 1970s and 1980s. His parallel work on the origin of the Solar System renewed interest in the Capture theory, and he contributed numerous stimulating ideas to the general study of the origin and dynamical evolution of the Solar System. Michael was a great educator and mentor for both undergraduates and young researchers, and many of these went on to make significant scientific contributions.

X-ray diffraction data from shock-compressed copper: Some consequences of metallurgical texture

We report the measurements of in situ Debye–Scherrer x-ray diffraction from copper foils shock compressed at the Orion laser facility to pressure in the range of 10–40 GPa. Our objective was to record distortion (variation of scattering angle at peak intensity, 2θ, with azimuthal position, φ, around the diffraction ring) of the Debye–Scherrer rings. We intended to measure the anisotropy of elastic strain and infer the effective strength of copper at a high strain rate. However, our measured diffraction data from all crystallographic reflection planes considered together are not consistent with a simple model that assumes homogeneous elastic strain. Consideration of both the β-fiber metallurgical texture of the rolled copper foil that we used as the sample material and the measured diffraction linewidths provides an empirical understanding of the data. We extend our understanding by using a Taylor-type, single-crystal plasticity model in which the total strain of each grain is assumed to be identical to that of the whole sample. This model reproduces many features of our experimental data and points to the importance of accounting for the plastic anisotropy of single-crystal grains, which can, in turn, lead to inter-grain elastic strain inhomogeneity and complex distortions of the diffraction rings.

Temperature-dependent structure of methanol-water mixtures on cooling: X-ray and neutron diffraction and molecular dynamics simulations

Methanol-water liquid mixtures have been investigated by high-energy synchrotron X-ray and neutron diffraction at low temperatures. We are thus able to report the first complete sets of both X-ray and neutron weighted total scattering structure factors over the entire composition range (at 12 different methanol concentrations (xM) from 10 to 100 mol%) and at temperatures from ambient down to the freezing points of the mixtures. The new diffraction data may later be used as reference in future theoretical and simulation studies. The measured data are interpreted by molecular dynamics simulations, in which the all atom OPLS/AA force field model for methanol is combined with both the SPC/E and TIP4P/2005 water potentials. Although the TIP4P/2005 water model was found to be somewhat more successful, both combinations provide at least semi-quantitative agreement with measured diffraction data. From the simulated particle configurations, partial radial distribution functions, as well as various distributions of the number of hydrogen bonds have been determined. As a general trend, the average number of hydrogen bonds increases upon cooling. However, the number of hydrogen bonds between methanol molecules slightly decreases with lowering temperatures in the concentration range between ca. 30 and 60 mol% alcohol content. The same is valid for water-water hydrogen bonds above 70 mol% of methanol content, from room temperature down to 193 K.

A routine for the determination of the microstructure of stacking-faulted nickel cobalt aluminium hydroxide precursors for lithium nickel cobalt aluminium oxide battery materials.

The microstructures of six stacking-faulted industrially produced cobalt- and aluminium-bearing nickel layered double hydroxide (LDH) samples that are used as precursors for Li(Ni1-x-yCo x Al y )O2 battery materials were investigated. Shifts from the brucite-type (AγB)□(AγB)□ stacking pattern to the CdCl2-type (AγB)□(CβA)□(BαC)□ and the CrOOH-type (BγA)□(AβC)□(CαB)□ stacking order, as well as random intercalation of water molecules and carbonate ions, were found to be the main features of the microstructures. A recursive routine for generating and averaging supercells of stacking-faulted layered substances implemented in the TOPAS software was used to calculate diffraction patterns of the LDH phases as a function of the degree of faulting and to refine them against the measured diffraction data. The microstructures of the precursor materials were described by a model containing three parameters: transition probabilities for generating CdCl2-type and CrOOH-type faults and a transition probability for the random intercalation of water/carbonate layers. Automated series of simulations and refinements were performed, in which the transition probabilities were modified incrementally and thus the microstructures optimized by a grid search. All samples were found to exhibit the same fraction of CdCl2-type and CrOOH-type stacking faults, which indicates that they have identical Ni, Co and Al contents. Different degrees of interstratification faulting were determined, which could be correlated to different heights of intercalation-water-related mass-loss steps in the thermal analyses.

Time filtering of event based neutron scattering data: A pathway to study the dynamic structural responses of materials.

Time-resolved diffraction has become a vital tool for probing dynamic responses to an applied stimulus. Such experiments traditionally use hardware solutions to histogram measured data into their respective bin. We will show that a major advantage of event-based data acquisition, which time-stamps measured diffraction data with 100 ns accuracy, is much preferred over hardware histogramming of the data by enabling postprocessing for advanced custom binning using a software solution. This approach is made even more powerful by coupling measured diffraction data with metadata about the applied stimuli and material response. In this work, we present a time-filter approach that leverages the power of event-based diffraction collection to reduce stroboscopic data measured over many hours into equally weighted segments that represent subsets of the response to a single cycle of the applied stimulus. We demonstrate this approach by observing ferroelectric/ferroelastic domain wall motion during electric field cycling of BaTiO3. The developed approach can readily be expanded to investigate other dynamic phenomena using complex sample environments.

Diffraction Effects and Compensation in Passive Acoustic Mapping.

Over the last decade, a variety of noninvasive techniques have been developed to monitor therapeutic ultrasound procedures in support of safety or efficacy assessments. One class of methods employs diagnostic ultrasound arrays to sense acoustic emissions, thereby providing a means to passively detect, localize, and quantify the strength of nonlinear sources, including cavitation. Real array element diffraction patterns may differ substantially from those presumed in existing beamforming algorithms. However, diffraction compensation has received limited treatment in passive and active imaging, and measured diffraction data have yet to be used for array response correction. The objectives of this paper were to identify differences between ideal and real element diffraction patterns, and to quantify the impact of diffraction correction on cavitation mapping beamformer performance. These objectives were addressed by performing calibration measurements on a diagnostic linear array, using the results to calculate diffraction correction terms, and applying the corrections to cavitation emission data collected from soft tissue phantom experiments. Measured diffraction patterns were found to differ significantly from those of ideal element forms, particularly at higher frequencies and shorter distances from the array. Diffraction compensation of array data resulted in cavitation energy estimates elevated by as much as a factor of 5, accompanied by the elimination of a substantial bias between two established beamforming algorithms. These results illustrate the importance of using measured array responses to validate analytical field models and to minimize observation biases in imaging applications where quantitative analyses are critical for assessment of therapeutic safety and efficacy.

Study of stability of microstructure and residual strain after thermal loading of plasma sprayed YSZ by through surface neutron scanning

Yttria stabilized zirconia (YSZ) is often applied as thermal barrier coating on metal parts as e.g. turbine blades made of nickel base super alloys. The coating process in combination with the preconditioning of the substrate material induces characteristic residual stress distributions in the coating system consisting of topcoat, bondcoat and the substrate material. Knowledge about the residual stress depth distribution in the coating and at the interfaces down to the substrate material is essential for the assessment of the mechanical integrity and the reliability of the coating. In this regard the stability of the microstructure and the residual stresses is of particular interest; hence this forms the scope of our investigations. Yttria (8 wt.%) stabilized zirconia with a NiCoCrAlY bondcoat was deposited by atmospheric plasma spraying (APS) at different spray conditions on a nickel base super alloy substrate material. The coatings were subjected to different heat-treatment processes, i.e. static aging and cyclic thermal loadings. Through surface scanning using neutron diffraction was carried out for the as sprayed condition and for the thermally loaded samples. Based on the measured diffraction data the stability of the microstructure (phases) and the residual strain/stresses through the depths of the coating system were assessed.

Theoretical study of the structure of lead zirconate–titanate PbZr0.6Ti0.4O3

A model of the structure of the piezoelectric ceramic lead zirconate–titanate PbZr1–x Ti x O3 (PZT) is proposed. The model is based on ab initio calculations for possible local structures using the density functional theory (DFT) approach. A comparison of the calculated neutron diffraction data for local structures and the measured diffraction data obtained for actual powder samples shows there is a partially established long-range crystalline order in the material, in the sublattice of Zr and Ti cations.

Comparison of interatomic potentials of water via structure factors reconstructed from simulated partial radial distribution functions: a reverse Monte Carlo based approach

Neutron- and x-ray weighted total structure factors of liquid water have been calculated on the basis of the intermolecular parts of partial radial distribution functions resulting from various computer simulations. The approach includes reverse Monte Carlo (RMC) modelling of these partials, using realistic flexible molecules, and the calculation of experimental diffraction data, including the intramolecular contributions, from the RMC particle configurations. The procedure has been applied to ten sets of intermolecular partial radial distribution functions obtained from various computer simulations, including one set from an ab initio molecular dynamics, of water. It is found that modern polarizable water potentials, such as SWM4-DP and BK3 are the most successful in reproducing measured diffraction data.

Phononic and Phasonic Debye-Waller Factors for 1D Quasicrystals

The main purpose of crystallography is to solve and refine crystal structures based on measured diffraction data. One of important corrections crucial in the refinement process is the Debye–Waller factor correction for phonons in physical, and phasons in perpendicular space. In our paper we show the limitations of the standard approaches to the Debye–Waller correction in case of quasicrystals and propose new approach based on the statistical method. For the model 1D quasicrystal we show that in case of phonons there is no significant objection against classical (exponential) Debye–Waller factor, however using different forms can slightly improve the results of a refinement. In case of phasons the classical formula gives no rise to the efficiency of the refinement and completely new approach is required. We propose a redefinition of the Debye–Waller factor in terms of the statistical approach and show its effectiveness.

Advancing X-ray scattering metrology using inverse genetic algorithms.

We compare the speed and effectiveness of two genetic optimization algorithms to the results of statistical sampling via a Markov chain Monte Carlo algorithm to find which is the most robust method for determining real space structure in periodic gratings measured using critical dimension small angle X-ray scattering. Both a covariance matrix adaptation evolutionary strategy and differential evolution algorithm are implemented and compared using various objective functions. The algorithms and objective functions are used to minimize differences between diffraction simulations and measured diffraction data. These simulations are parameterized with an electron density model known to roughly correspond to the real space structure of our nanogratings. The study shows that for X-ray scattering data, the covariance matrix adaptation coupled with a mean-absolute error log objective function is the most efficient combination of algorithm and goodness of fit criterion for finding structures with little foreknowledge about the underlying fine scale structure features of the nanograting.

Pressure-induced structures of Si-doped HfO2

The effect of hydrostatic pressure on the structure of Si-doped HfO2 (Si:HfO2) was studied by using a diamond anvil cell in combination with high-energy X-ray diffraction at a synchrotron source. Diffraction data were measured in situ during compression up to pressures of 31 GPa. Si:HfO2 with 3, 5, and 9 at. % Si were found to undergo a monoclinic to orthorhombic transition at pressures between 7 and 15 GPa. Whole pattern analysis was carried out using nonpolar (Pbca) and polar (Pca21) crystallographic models to investigate the symmetry of the observed high-pressure orthorhombic phase. Rietveld refinement results cannot discriminate a reliable difference between the Pbca and Pca21 structures as they nearly equally model the measured diffraction data. The pressure dependent lattice parameters, relative volume, and spontaneous strain are reported.

Macromolecular crystallographic estructure refinement

Model refinement is a key step in crystallographic structure determination that ensures final atomic structure of macromolecule represents measured diffraction data as good as possible. Several decades have been put into developing methods and computational tools to streamline this step. In this manuscript we provide a brief overview of major milestones of crystallographic computing and methods development pertinent to structure refinement.

In-situ observation of bulk 3D grain evolution during plastic deformation in polycrystalline Cu

We present a non-destructive in-situ measurement of three-dimensional (3D) microstructure evolution of 99.995% pure polycrystalline copper during tensile loading using synchrotron radiation. Spatially resolved three-dimensional crystallographic orientation fields are reconstructed from the measured diffraction data obtained from a near-field high-energy X-ray diffraction microscopy (nf-HEDM), and the evolution of about 5000 3D bulk grains is tracked through multiple stages of deformation. Spatially resolved observation of macroscopic texture change, anisotropic deformation development, and the correspondence of different crystallographic parameters to defect accumulation are illustrated. Moreover, correlations between different crystallographic parameters, such as crystal rotation evolution, short- and long-range orientation gradient development, microstructural features, and grain size effects are investigated. The current state of data mining tools available to analyze large and complicated diffraction data is presented and challenges associated with extracting meaningful information from these datasets are discussed.

Optical diffractometry of anisotropic holographic structure composed of liquid crystal and polymer phases with extended Bragg modes

Diffraction spectra at several Bragg modes of holographic polymer dispersed liquid crystals (HPDLCs) were measured individually for two orthogonal polarizations at temperatures below and above nematic-to-isotropic point. Then optical structures of the HPDLCs were quantitatively analyzed based on advanced two-wave coupled wave theory by fitting calculations consistently all at once to the measured diffraction data at not only the first Bragg mode but also the higher order ones, which has never been demonstrated before. The present analysis provided the microscopic information such as the polarization and temperature dependences on harmonic sinusoidal profiles of refractive-index modulation along grating vector, and was examined in validity by comparison with phase-separated morphology observed by scanning electron microscopy. The present analysis allowed you to find the technologically-advanced information, that is, the controllability of fine configuration of LC/polymer phase distribution and the optical anisotropy in the fabrication process.

Reconstructing an icosahedral virus from single-particle diffraction experiments

The first experimental data from single-particle scattering experiments from free electron lasers (FELs) are now becoming available. The first such experiments are being performed on relatively large objects such as viruses, which produce relatively low-resolution, low-noise diffraction patterns in so-called "diffract-and-destroy" experiments. We describe a very simple test on the angular correlations of measured diffraction data to determine if the scattering is from an icosahedral particle. If this is confirmed, the efficient algorithm proposed can then combine diffraction data from multiple shots of particles in random unknown orientations to generate a full 3D image of the icosahedral particle. We demonstrate this with a simulation for the satellite tobacco necrosis virus (STNV), the atomic coordinates of whose asymmetric unit is given in Protein Data Bank entry 2BUK.

Semi-automated protein crystal mounting device for the sulfur single-wavelength anomalous diffraction method

Use of longer-wavelength X-rays has advantages for the detection of small anomalous signals from light atoms, such as sulfur, in protein molecules. However, the accuracy of the measured diffraction data decreases at longer wavelengths because of the greater X-ray absorption. The capillary-top mounting method (formerly the loopless mounting method) makes it possible to eliminate frozen solution around the protein crystal and reduces systematic errors in the evaluation of small anomalous differences. However, use of this method requires custom-made tools and a large amount of skill. Here, the development of a device that can freeze the protein crystal semi-automatically using the capillary-top mounting method is described. This device can pick up the protein crystal from the crystallization drop using a micro-manipulator, and further procedures, such as withdrawal of the solution around the crystal by suction and subsequent flash freezing of the protein crystal, are carried out automatically. This device makes it easy for structural biologists to use the capillary-top mounting method for sulfur single-wavelength anomalous diffraction phasing using longer-wavelength X-rays.