Structure Refinement Procedure Research Articles

The Transform Class in SPARX and EMAN2

We describe the Transform Class in SPARX/EMAN2 that is designed to handle rigid body motions of two- and three-dimensional data. We describe relationships between Eulerian angles conventions used in different electron microscopy software packages, as well as give examples of the simple scripts that execute conversions of Eulerian angles between these packages and handle other related tasks. The Transform Class is also responsible for generating point-group symmetry operations as well as generating quasi-evenly distributed points on the sphere (which is used in creating reference projections for structure refinement procedures in single particle reconstruction). We discuss how this is carried out internally in the code, and how symmetry operations are accessed through the SPARX interactive interface. We present a comprehensive description of symmetry operations for all point-group symmetries, as implemented in the class. Finally, we provide solutions to a number of typical problems associated with rotation operations—alignment of markers for dual-axis tomography, delineations of asymmetric subunits, quasi-uniform distribution of projection directions and such, and provide examples how these problems are solved using operations in the Transform Class.

3D Structure Elucidation Using NMR Chemical Shifts

AbstractFor Abstract see ChemInform Abstract in Full Text.

Combining EXAFS and x-ray powder diffraction to solve structures containing heavy atoms

Determination of structures using x-ray powder diffraction is complicated if the reflection intensities are mainly influenced by the scattering from heavy atoms and the atomic coordinates of light atoms remain uncertain. A method like EXAFS, which is sensitive to short range order, gives reliable atomic distances in the surroundings of heavy atoms with a precision of ±0.02 Å. The probability for obtaining the complete structure from x-ray powder diffraction increases if one includes parameters derived from EXAFS measurements as restraints during the procedure of structure solving. We demonstrate the potential of combining EXAFS and x-ray powder diffraction by solving the structure UO2[H2AsO4]2·H2O. The procedure starts with the determination of space group and cell parameters from XRD powder data. In a second step the absolute values of the structure factor |F| are separated by iterating a decomposition formula. The heavy atom positions are determined by direct methods. In the third step atomic distances of coordination polyhedra are estimated using EXAFS. Subsequently, the complete coordination geometries around the heavy atoms including reliable distances are used as restraints in the structure solving and refinement procedure.

Impact of urea on water structure: a clue to its properties as a denaturant?

A new investigation of the structure of urea–water solutions at a mole ratio of 1 urea to 4 water molecules is described. Neutron diffraction is used in conjunction with isotope labelling on the water and urea hydrogen atoms and on the nitrogen atom of urea. The diffraction data are analysed using the empirical potential structure refinement procedure to yield a set of site–site radial distribution functions and spatial density functions that are consistent with the diffraction data. The results are discussed in relation to recent and past X-ray and neutron diffraction experiments and theoretical studies of this system. It is found that urea incorporates readily into water, forming pronounced hydrogen bonds with water at both the amine and carbonyl headgroups. In addition the urea also hydrogen bonds to itself, forming chains or clusters consisting of up to approximately 60 urea molecules in a cluster. There, is however, little or no evidence of urea segregating itself from water, in marked contrast to a recent study of the methanol–water system. This behaviour is discussed in the context of the great propensity of urea to effect protein denaturation.

Some structure and magnetic effects of Ga incorporation on α-FeOOH

The effects of Ga incorporation on goethite were investigated by using X-ray diffractometry (XRD), particle-induced X-ray emission (PIXE), susceptibility measurements and Mössbauer spectroscopy (MS). Samples Ga x Fe 1− x OOH were prepared with x=0.00, 0.01, 0.03, 0.05, 0.10, 0.35 and 0.70. All the samples are single-phase and an accurate observation of the structure refinement procedure makes clear the sample-dependent structural behaviour. A model is proposed in which the main effect of Ga incorporation is to reduce the crystallite dimensions.

Determination of site population in olivine: Warnings on X-ray data treatment and refinement

Leverage analysis enables identification of reflections with the greatest influence on the estimate of each refined variable, and thus may be an important tool to improve standard structure-refinement procedures, especially in the case of minerals with complex composition. In this work, leverage analysis was used to investigate in detail the influence of each reflection in high-resolution X-ray diffraction data collected from olivine, a mineral often used to model order-disorder processes and to calculate temperatures of closure and cooling rates of host rocks. Particular attention was paid to the estimate of the scattering power at the cation sites, that are crucial for the above studies. Various procedures for data correction and refinement were also investigated, and the different possible choices were compared to choose the strategy that provides the best results. The presence of high-leverage weak reflections in olivine strongly suggests that systematic data truncation according to intensity threshold should be avoided. The estimates of the site-scatterings obtained under the different conditions tested are very close (always ≤3 σ); they are often smaller than those which may be obtained from electron-microprobe analysis under different experimental conditions or on inhomogeneous (zoned) crystals. Chemical data should thus not be routinely used to constrain the refinement procedure and/or to optimize final site-populations, provided that appro- priate errors are given; on the other hand, they are valuable to appreciate the presence and the amounts of very minor, sometimes unexpected, substituents. Our tests show that precision better than 0.001 in site-occupancy determination (sometimes claimed in the literature) is probably not achieved.

(Fe, Mg) distribution in olivine effects of data collection and refinement strategies

Determination of cation distributions in minerals is crucial for any thermodynamic application. In order to explore to what extent the choice of X-ray data collection, reduction, and structure refinement procedures might influence obtained site occupancies, a methodological and interlaboratory study was undertaken. Two single crystals of olivine (Fo 90 and Fo 45 ) were used to collect diffraction data up to 2𝛉 = 110° (Mo K α) in three Italian laboratories with different single-crystal diffractometers (Sℐℰℳℰ𝒩𝒮 Aℰ𝒟II, Pℋℐℒ𝒫𝒮 PW1100, K𝒰ℳ𝒜 KM4). In each laboratory, several data collections (12 and 10 for samples Fo 90 and Fo 45 , respectively) were carried out for each crystal, changing crystal mounting and measurement strategies for every experiment. All data were refined using the Strucsy, Orfls and Shelxl-93 programs with various refinement models, refinement strategies and weighting schemes, for a total number of 240 and 204 refinements for samples Fo 90 and Fo 45 , respectively. The main results are as follows. Atomic coordinates obtained by refining data sets at various resolutions with different refinement programs and crystal mountings do not change significantly. The structural geometry is therefore not affected by either resolution or refinement strategy. When refining a single set of data with different programs, the differences obtained for M1 and M2 site occupancies are up to 0.02 and 0.03 for both Fo 90 and Fo 45 crystals due to changing refinement models (valence states, extinction correction) and refinement strategy. When all the data sets collected in the three laboratories were refined with the same program (Shelxl-93), the results only suffered from different crystal mountings and experimental apparatus, and showed differences in M1 and M2 site occupancies up to 0.017. Considering both cases b and c, we observed differences which are approximately ten times the e.s.d.’s of the single values. The use of scattering curves with no pre-established ionization for Si and O led to better agreement between crystallographic site occupancies and chemical data.

The radial distribution functions of water and ice from 220 to 673 K and at pressures up to 400 MPa

Neutron diffraction data for water and ice in the form of OO, OH and HH partial structure factors now exist over a temperature range 220–673 K, and at pressures up to ∼400 MPa. In order for these data to be useful for comparing with different computer simulations and theories of water, it is first necessary to Fourier transform them to the corresponding site–site radial distribution functions. The process of doing this is not straightforward because of the inherent systematic uncertainties in the data, which arise primarily in the case of neutron scattering, from the inelasticity or recoil effects that can distort the experimental data. In this paper, it is shown that the empirical potential structure refinement procedure, which attempts to fit a three-dimensional ensemble of water molecules to all three partial structure factors simultaneously, leads to improved reliability in the extracted radial distribution functions. There are still some uncertainties, primarily associated with the hardness of the repulsive core of the intermolecular potential, which current data are not precise enough to resolve. The derived empirical potentials show some variability associated with particular experiments. General trends can be discerned however which indicate polarisation effects may be significant when effective intermolecular potentials are used over a wide temperature and density range.

The contrast factors of dislocations in cubic crystals: the dislocation model of strain anisotropy in practice

It has been shown recently that in many cases strain anisotropy in powder diffraction can be well accounted for by the dislocation model of the mean square strain. The practical application assumes knowledge of the individual contrast factorsCof dislocations related to particular Burgers, line and diffraction vectors or to the average contrast factorsC¯. A simple procedure for the experimental determination ofC¯has been worked out, enabling the determination of the character of the dislocations in terms of a simple parameterq. The values of the individualCfactors were determined numerically for a wide range of elastic constants for cubic crystals. TheC¯factors andqparameters were parametrized by simple analytical functions, which can be used in a straightforward manner in numerical analyses, ase.g.in Rietveld structure refinement procedures.

The Effect of Dislocation Contrast on X-Ray Line Profiles in Untextured Polycrystals

Anisotropic strain broadening in X-ray line profile analysis means that the width of diffraction profiles of Bragg reflections is not a monotonous function of the diffraction angle. The lack of a physically sound model makes the interpretation of line broadening and the structure refinement procedure of Rietveld often difficult or even impossible. A simple and straightforward procedure is presented for the rationalisation of anisotropic strain broadening in terms of the anisotropic contrast effect of dislocations or dislocation-like lattice defects. The procedure makes the evaluation of particle size or coherent domain size, and the density and arrangement of dislocations rather simple with a high precision, especially in the case of untextured polycrystals or when dislocation population on the possible slip systems is uniform. Three illustrative examples of severely deformed microcrystalline copper, the Rb 3 C 60 f.c.c. fullerite and a ball-milled iron powder show the effectiveness of the procedure.

Structural Investigation of Solute−Solute Interactions in Aqueous Solutions of Tertiary Butanol

Hydrogen/deuterium isotopic substitution neutron diffraction techniques have been used to measure the solute-solute intermolecular structural correlations in 0.06, 0.11, and 0.16 mole fraction tertiary butanol-water solutions. Empirical potential structure refinement (EPSR) procedures have been used to extract detailed information relating to the intermolecular structure in these systems. A trend from hydrophobic to hydrophilic character of the solute-solute correlations as a function of solute concentration is observed. Of particular note is the domination of nonpolar to nonpolar solute contacts at 0.06 mole fraction concentration compared with a more complex mixture of nonpolar and polar solute-solute intermolecular contact configurations at the higher alcohol concentration.

Reliability of atom column positions in a ternary system determined by quantitative high‐resolution transmission electron microscopy

Employing an iterative structure refinement procedure, we have determined the atomistic structure of the Σ3 (111) grain boundary in strontium titanate (SrTiO3) from high‐resolution transmission electron microscopy (HRTEM) images. This grain boundary serves as a model system to study the effect of column occupancies on the reliability of the column positions. In this paper we introduce a method to derive confidence regions for the positions of individual atom columns at crystal defects. Based on a statistical approach we first determine the reliabilities of different types of atom columns in regions of unfaulted crystal. Next we extrapolate these reliabilities to obtain the reliabilities of individual atom columns at the grain boundary. The method accounts correctly for random errors and promises to be generally applicable provided that repetitive units of unfaulted crystal structure are contained in the HRTEM image. Under the conditions of the present study, the reliability of a column position correlates with the projected electrostatic potential of the column. Accordingly, the reliabilities of the column positions at the boundary vary with the column type: 0.008 nm for Sr–O columns, 0.014 nm for Ti columns, and 0.018 nm for O–O columns.

Orthopyroxene from the Serra de Mage Meteorite; a structure-refinement procedure for a Pbca phase coexisting with a C2/c exsolved phase

An X-ray structure-refinement procedure was developed to characterize orthopyroxene from the Serra de Mage meteorite. In the studied sample, the orthorhombic phase coexists with exsolution lamellae of C2/c augite, parallel to (100), with a~px ==a!ug, [lOl]~px == c!ugob~px==b!ug. Diffraction maxima of the monoclinic phase overlap those of the orthorhombic phase with h + l = 2n, yielding violations of the extinction conditions for space group Pbca and simulating the lower symmetry space group P2lca. Structural parameters of the Pbca phase together with the WCpxparameter, which expresses the fraction of the C2k phase present, were refined first. Fe values were calculated using the equation Fe = y(1 - Wcpx)[Fe]&'x + Wcpx[Fc1~p with [Fc1cpx values taken from the structure refinement of an augite, Observed Fo values were then corrected by subtracting the calculated contribution of the monoclinic phase with use of the equation F~orr = y[Fo)2 - [Fc1~pxW Cpx and used for a further refinement of the orthorhombic phase. The final residual indices, Rob were 2.11 and 1.78%for two crystals with different augite contents. This refinement procedure confirms Pbca as the correct space group and provides more accurate structural parameters for the Serra de Mage orthopyroxene.

PRO_LIGAND: An approach to de novo molecular design. 3. A genetic algorithm for structure refinement

Recently, the development of computer programs which permit the de novo design of molecular structures satisfying a set of steric and chemical constraints has become a burgeoning area of research and many operational systems have been reported in the literature. Experience with PRO-LIGAND-the de novo design methodology embodied in our in-house molecular design and simulation system PRO-METHEUS-has suggested that the addition of a genetic algorithm (GA) structure refinement procedure can 'add value' to an already useful tool. Starting with the set of designed molecules as an initial population, the GA can combine features from both high- and low-scoring structures and, over a number of generations, produce individuals of better score than any of the starting structures. This paper describes how we have implemented such a procedure and demonstrates its efficacy in improving two sets of molecules generated by different de novo design projects.

Best-fit experimental scattering factors derived with least-squares crystal structure refinement procedures

Best-fit experimental scattering factors derived with least-squares crystal structure refinement procedures

Automated NMR structure refinement via NOE peak volumes. Application to a dodecamer DNA duplex

In NMR structure determination, the initial estimation of distances from NOE cross peaks usually involves the use of a two-spin approximation and the resulting distance geometry initial structures satisfy a set of initial distances that contain some spin-diffusion errors. In order to account for spin diffusion in a multiple-spin system, NOE back-calculation methods are frequently employed, using either numerical integration ( I, 2) or relaxation-matrix methods (3). Iterative back-calculation structure refinements have been carried out by visual comparison of simulated cross-peak intensities (4-6) and by full relaxation-matrix methods ( 7-10) to produce refined structures whose simulated spectra better match the experimental spectra. For visual comparison against experimental data, simulated spectra are generated with the appropriate chemical shifts, linewidths, and lineshapes. NOESY cross-peak volumes depend not only on peak height but also on linewidths and lineshapes (multiplet splitting) that, if incorrect, can lead to volume errors in matching peaks of similar intensity. The relaxation-matrix approaches IRMA ( 7, 8) and MORASS ( 10) use a “hybrid matrix,” that is, a combination of experimental volumes and simulated volumes generated from the coordinates of the current model structure. In the hybrid-matrix approach, distance constraints are not determined by the actual intensity differences between experimental and calculated cross peaks, but by the distance matrix derived from the hybrid volume matrix; because of this, the hybrid-matrix method does not minimize the R factor (the average NOE intensity difference between experimental and calculated cross-peak volumes) very rapidly or efficiently. For example, Koning et al. (8) reported that the average R factor for a simulation of an octamer DNA duplex was about 0.5 after the first cycle of refinement and improved relatively little during further iterations. Furthermore, the relaxation-matrix structural-refinement procedure is confined to fully resolved NOE cross peaks (unless independent spectral deconvolution methods are applied to partially overlapped peaks), while visual inspection can interpolate partially overlapped multiple peaks reasonably accurately. We have developed an automated back-calculation refinement method that operates on all NOE cross peaks, including overlapped cross peaks, by using experimental

A potential gene target in HIV-1: rationale, selection of a conserved sequence, and determination of NMR distance and torsion angle constraints.

Recently, the capability for determining the high-resolution, sequence-dependent structure of oligonucleotides in solution via careful analysis of multidimensional NMR spectra and structure refinement procedures has been developed. Consequently, the rationale for selection of a genome sequence as a target for drug design based on the detailed three-dimensional structure of the target is presented. The concept is illustrated by the successful search for a highly conserved region of the HIV-1 genome's long terminal repeat which could serve as a molecular target. A compound which could selectively bind the target sequence could inhibit both RNA transcription from the integrated provirus and the reverse transcription process. Of 148 unique HIV-1 sequences examined, 147 exhibit a 21-base conserved sequence (nucleotides 70-90 in HIVHXB2R) in the R region of the long terminal repeat. The only exception, a minor constituent for one individual, has a change in the penultimate base. A 13 base pair duplex sequence, [d(AGCTTGCCTTGAG).d(CTCAAGGCAAGCT)], from this conserved region was selected and synthesized for NMR structure studies. Phase-sensitive proton two-dimensional nuclear Overhauser enhancement (2D NOE) and double-quantum-filtered correlation (2QF-COSY) spectra were obtained at 500 MHz for the DNA duplex. Exchangeable and nonexchangeable proton resonances were assigned. Quantitative assessments of the 2D NOE cross-peak intensities for different mixing times were carried out using conventional Fourier transform NMR and the maximum likelihood method (MLM). Distance constraints, along with upper and lower bounds, were obtained from the 2D NOE intensities using the iterative complete relaxation matrix algorithm MARDIGRAS. Distances entailing both exchangeable and nonexchangeable protons were determined: 7-11 experimental distance constraints per residue including interresidue and interstrand distances. Simulations of the scalar coupling effects manifest in 2QF-COSY cross-peaks by means of the program SPHINX/LINSHA were compared with experimental data to yield torsion angle constraints for the sugar rings. A single conformer was inadequate to describe any of the sugar puckers, but a rapid two-state equilibrium with one conformer strongly dominant (75-95%) provided a good fit of the 2QF-COSY cross-peaks. The sugar pucker of the major conformer exhibited significant variability for the various nucleotides but was roughly 2'-endo. Though derived independently and subject to different time-averaging effects, the 2QF-COSY and 2D NOE results are in accord.

The structural phase transition in anthracene—TCNB

Abstract The problem of the orientational disorder in mixed stack charge transfer crystals has been addressed. X-ray diffraction data in the HT phase of A-TCNB are reported. They were analysed using conventional structure-refinement procedures and utilizing symmetry-adapted functions. For the HT phase, the orientational probability function allowed us to characterize as dynamic the disorder of the anthracene molecules. The soft mode was measured by Raman and coherent neutron scattering. Measurement by Brillouin scattering of the elastic constant C11 led to another determination of the soft mode. The behaviour of this soft mode allows one to conclude the existence of a mixed regime (between displacive and order-disorder) for the LT phase of A-TCNB.

Quantitative X-Ray Structure Determination of Superlattices and Interfaces

AbstractWe present a general procedure for quantitative structural refinement of superlattice structures. To analyze a wide range of superlattices, we have derived a general kinematical diffraction formula that includes random, continuous and discrete fluctuations from the average structure. By implementing a non-linear fitting algorithm to fit the entire x-ray diffraction profile, refined parameters that describe the average superlattice structure, and deviations from this average are obtained. The structural refinement procedure is applied to a crystalline/crystalline Mo/Ni superlattices and crystalline/amorphous Pb/Ge superlattices. Roughness introduced artificially during growth in Mo/Ni superlattices is shown to be accurately reproduced by the refinement.

Structure of Arc represser in solution: evidence for a family of β-sheet DNA-binding proteins

The Arc repressor, which is involved in the switch between lysis and lysogeny of Salmonella bacteriophage P22, does not belong to any of the known classes of DNA-binding proteins. Mutagenesis studies show that the DNA-binding region is located in the 15 N-terminal amino-acid residues. We have now determined the three-dimensional structure of the Arc dimer from an extensive set of interproton-distance data obtained from 1H NMR spectroscopy. A priori, intra- and inter-monomer nuclear Overhauser effects (NOEs) cannot be distinguished for a symmetric dimer. But by using the homology with the Escherichia coli Met repressor we could interpret the NOEs unambiguously in an iterative structure refinement procedure. The final structure satisfies a large set of NOE constraints (1,352 for the dimer). It shows a strongly intertwined dimer, in which residues 8-14 of different monomers form an antiparallel beta-sheet. A model for the Arc repressor-operator complex can account for all available biochemical and genetic data. In this model two Arc dimers bind with their beta-sheet regions in successive major grooves on one side of the DNA helix, similar to the Met repressor interaction. Thus, Arc and Met repressors are members of the same family of proteins, which contain an antiparallel beta-sheet as the DNA-binding motif.