Showing papers in "Acta Crystallographica Section A in 1992"
TL;DR: In this paper, a reduction of model bias in macromolecular crystallography through various omit-map techniques has been investigated, including simulated-annealing refinement and conjugate-gradient minimization.
Abstract: Reduction of model bias in macromolecular crystallography through various omit-map techniques has been investigated. The two cases studied were the p21 protein complexed with GDP at 2.25 A resolution and the AN02 Fab fragment of an anti-dinitrophenyl-spin-label murine monoclonal antibody complexed with its hapten at 2.9 A resolution. In the former case, the correct model was compared to a partially incorrect model consisting of an exchanged pair of β strands along with rearrangement of the connecting loops whereas, in the latter case, the correct placement of an active-site tryptophan side chain was compared to an incorrect rotamer conformation. Partial structures were created by omission of spherical regions around the incorrect region. Omit maps without refinement of the partial structure showed a large degree of model bias. Model bias could be reduced significantly by refinement of the partial structure. Simulated-annealing refinement of the partial structure showed the best results, followed by conjugate-gradient minimization with or without prior randomization of the partial structure. To avoid compensation for missing atoms during simulated-annealing refinement of the partial structure, a suitable `boundary' region was restrained to the starting coordinates. Model bias removal by iterative density modification was not successful in that it reduced density for both the correct and incorrect conformations.
389 citations
TL;DR: In this article, a general method for estimating the expected contribution of statistical error to the pair distribution function (PDF) is introduced for the first time, based on a model structure.
Abstract: Pair distribution function (PDF) analysis of neutron or X-ray powder diffraction data is a useful technique for analysis of short-range structure in both amorphous and crystalline materials. Errors in PDF determinations may arise from several sources: termination of the Fourier transform, lack of instrument resolution, counting statistics and inaccurate corrections for experimental artifacts. Estimates of the amount of error from termination and instrument resolution are computed using a model structure. A general method for estimating the expected contribution of statistical error to the PDF is introduced for the first time. The effect of termination varies with the type of material and with the amplitude of lattice vibrations but, in general, termination with Q > 30 A produces minimal errors. Broadening of the diffraction pattern produces negligible effect for conventional instrumentation. With moderate data-collection times, the statistical errors can be reduced to reasonable levels. Pulsed-neutron diffraction can provide accurate and precise PDF measurements, as is demonstrated in this work by the agreement between model and experimental results for polycrystalline aluminium.
269 citations
TL;DR: In this paper, the theoretical and experimental aspects of generalized atomic displacement parameters (ADP's) in crystalline matter are summarized and a more frequent comparison of theoretical calculations and experimental determinations of generalized ADP's is advocated.
Abstract: An attempt is made to summarize both theoretical and experimental aspects of generalized atomic displacement parameters (ADP's) in crystalline matter. Generalized displacement parameters are used to describe the weakening of Bragg intensities via the anharmonic (static or thermal) Debye–Waller factor (DWF) and its real-space counterpart, the generalized atomic probability density function (p.d.f.). The lattice dynamical base of the harmonic and anharmonic thermal DWF is discussed. It is pointed out that the static DWF frequently contains higher-order terms. The mathematical base for an experimental determination of generalized ADP's is given. The most popular current formulations (one-particle potential and statistical approaches) are reviewed and their individual limitations are discussed. Likewise the demands put on the quality and extent of experimental data are assessed. Some aids to the interpretation of generalized ADP's established by crystallographic least-squares procedures are given and a Monte-Carlo method for the calculation of errors in p.d.f. maps is presented. Finally, some prospects for future work are outlined and a more frequent comparison of theoretical calculations and experimental determinations of generalized ADP's is advocated.
168 citations
TL;DR: A novel method of function minimization that combines the power of the diagonal approximation to the normal matrix with conjugate directions is described and approaches closer to the local minimum than the methods that are commonly used in macromolecular refinement.
Abstract: A novel method of function minimization that combines the power of the diagonal approximation to the normal matrix with conjugate directions is described. This method approaches closer to the local minimum than the methods that are commonly used in macromolecular refinement. The weaknesses of the current methods are analyzed to explain the advantage of the conjugate-direction method.
144 citations
TL;DR: In this article, a method is presented for the rapid, objective and automatic comparison of selected parts of protein surfaces as a function of resolution using differences and correlations of Fourier coefficients.
Abstract: Resolution is a crucial parameter to consider in making surface comparisons. A method is presented here for the rapid, objective and automatic comparison of selected parts of protein surfaces as a function of resolution using differences and correlations of Fourier coefficients. A test-case application of this procedure to the surfaces of five immunoglobulin antigen-combining sites allowed them to be partitioned into two categories.
116 citations
TL;DR: A method is presented to calculate the electrostatic potential, the electric field and the electric-field gradient in a crystal from the atomic multipole expansion of the experimental charge density, as described by the Hansen-Coppens formalism.
Abstract: A method is presented to calculate the electrostatic potential, the electric field and the electric field gradient in a crystal from the atomic multipole expansion of the experimental charge density, as described by the Hansen-Coppens formalism [Hansen & Coppens (1978), Acta Cryst. A34, 909–921]. The electrostatic properties are expressed in terms of the positions and the charge-density parameters of the individual atoms. Contributions due to the procrystal charge density and the deformation charge density are compared. The method is illustrated by the calculation of the electrostatic potential maps of fully deuterated benzene and of iron(II) tetraphenylporphyrin.
86 citations
TL;DR: In this article, a density-modification procedure for phase extension and refinement is described which replaces all density less than one-fifth of the height of a light-atom peak by zero.
Abstract: A density-modification procedure for phase extension and refinement is described which replaces all density less than one-fifth of the height of a light-atom peak by zero. Its effectiveness is demonstrated by applications to a small and a medium-size protein structure. With high-resolution data, for the small protein, it is possible to extend and refine from 3 to 1 A with a mean phase error less than 30°. Successful phase extension from 4 A is also possible. In general it is shown that phase extension to high resolution gives less error than extension to lower resolution. It has also been shown that for a small protein it is possible to obtain an ab initio solution of the structure by refining from a complete set of random phases for all reflexions.
75 citations
TL;DR: The potential, symmetry and Foppl arrangement for distributing up to 60 point charges on the surface of a sphere so that the Coulombic potential is a minimum is given in this paper.
Abstract: The potential, symmetry and Foppl arrangement are given for distributing up to 60 point charges on the surface of a sphere so that the Coulombic potential is a minimum. Some new configurations are described and a general comparison made with the hard-sphere case.
61 citations
TL;DR: A description of 4-connected nets with one kind of vertex in which the shortest rings containing each pair of edges are N-rings (N > 4) is given in this article.
Abstract: A description is given of 4-connected nets with one kind of vertex in which the shortest rings containing each pair of edges are N-rings (N > 4). Eleven uniform nets (66) are identified; seven of these are believed to be new. A further thirteen nets with one type of vertex and without 3- or 4-rings are described; nine of these are also believed to be new
58 citations
TL;DR: An explicit parametrization algorithm for the simplest class of triply periodic minimal surfaces (the ''regular'' class) for which the Weierstrass function specifying the complex plane representation has a simple product form is reported in this paper.
Abstract: An explicit parametrization algorithm is reported for the simplest class of triply periodic minimal surfaces (the `regular' class) for which the Weierstrass function specifying the complex plane representation has a simple product form. As the Gauss map links triply periodic minimal surfaces with spherical tessellations, the set of Schwarz triangular tilings of the sphere is used as the basis of an exhaustive listing of all such possible branch-point distributions, and hence surfaces, in this class. The symmetry and geometry of the resulting surfaces are determined by the locations and orders of these branch points.
57 citations
TL;DR: In this paper, a derivation of triply periodic minimal surfaces of monoclinic symmetry and higher that fall within the regular class (including those containing self-intersections) is given.
Abstract: A derivation is given of the set of triply periodic minimal surfaces of monoclinic symmetry and higher that fall within the regular class (including those containing self-intersections). The Gauss maps, Weierstrass parametrizations and asymmetric units of each surface are included. Triclinic relatives of monoclinic surfaces are also discussed. Some minimal surfaces that lack translational order but exhibit orientational symmetry also naturally appear within this derivation.
TL;DR: In this article, it was shown that the reflectivity of X-rays at smooth and fiat surfaces gives the dispersive correction f′(E) to the atomic form factor with an accuracy comparable to that obtained by X-ray interferometry.
Abstract: It is shown in this paper that the reflectivity of X-rays at smooth and fiat surfaces gives the dispersive correction f′(E) to the atomic form factor with an accuracy comparable to that obtained by X-ray interferometry. A detailed set of values of f′(E) in the energy range 7–27 keV is given for Ni, Cu, CuO, Ta, LiTaO3, Pt and Au, together with the corresponding linear absorption coefficients μ/ρ. Whenever comparison is possible the values of f′(E) agree very well with those obtained by interferometry or by Kramers–Kronig transformation. Data calculated according to Cromer & Liberman [J. Chem. Phys. (1970). 53, 1891–1898] agree well with our data far from absorption edges. At the edges there are substantial differences because the calculations do not take into account the structure of the edges, their chemical shift in compounds and the EXAFS structure above the edges. Below absorption edges the values of f′(E) for metals and their oxides are equal, provided the chemical shift in the position of the edges is taken care of. This feature is interesting in anomalous scattering experiments, where the variation off' with energy is used to vary the scattering contrast of a given atomic species. Once f′(E) is known, X-ray reflectivity measurements can be used to determine the density and the thickness of layers on fiat substrates. In addition, the roughness of the air-layer and layer-substrate interfaces have been determined with high precision in the metals and oxides mentioned above.
TL;DR: In this paper, an ensemble of vecteurs unitaires dans les groupes de superespace pour les cristaux composites is discussed, in order to simplify leur desciption and de donner a methode systematique d'analyse similaire a celle utilisee for l'analysis des structures modulees.
Abstract: Discussion sur un ensemble de vecteurs unitaires dans les groupes de superespace pour les cristaux composites, afin de simplifier leur desciption et de donner une methode systematique d'analyse similaire a celle utilisee pour l'analyse des structures modulees. Cet ensemble est generalement different de l'ensemble standard pour les structures modulees
TL;DR: In this paper, the authors present a space-group-frequency table of observed structures based on some of the fundamental aspects of chirality, and they advocate the retention of all the 230 space groups.
Abstract: In compiling the space-group-frequency table of observed structures, retention of all the 230 space groups is advocated. This is based on some of the fundamental aspects of chirality. For cases both with space-group chirality (case A, e.g. P41, P43 etc.) and without (case B, e.g. P21, P212121), possible asymmetric distribution of observed structures over mirror equivalents cannot be ruled out. The need to specify a possible physical attribute to characterize a given crystal and correlate this to the absolute structure in case B is pointed out.
TL;DR: 3D electron crystallography, developed by biophysicists to study proteins, has been used to investigate the crystal structure of staurolite and has great potential in crystal structure determinations of small domains in heterogeneous crystals which are inaccessible to X-ray analysis.
Abstract: Resolution of better than 2 A has been obtained in many crystals by high-resolution electron microscopy. Although this resolution is sufficient to resolve interatomic spacings, structures are traditionally interpreted by comparing experimental images with contrast calculations. A drawback of this method is that images are 2D projections in which information is invariably obscured by overlap of atoms. 3D electron crystallography, developed by biophysicists to study proteins, has been used to investigate the crystal structure of staurolite. Amplitudes and phases of structure factors are obtained experimentally from high-resolution images (Jeol ARM 1000 at the National Center for Electron Microscopy at LBL), taken in different directions from thin regions where dynamic scattering is minimal. From images in five orientations (containing 59 independent reflections to a resolution of 1.38 A), a 3D electron potential map is constructed which resolves clearly all cations (Al, Si, Fe, including those with partial occupancy) and all O atoms. This method has great potential in crystal structure determinations of small domains in heterogeneous crystals which are inaccessible to X-ray analysis. It is estimated that 3D structure determinations should be possible on regions only about ten unit cells wide and should resolve not only atom positions but also site occupancies. The method is also applicable to space-group determination.
TL;DR: A method is discussed for finding the transformations that mutually superpose an arbitrary number of structures in the least-squares sense given specified atom-to-atom correspondence.
Abstract: The study of families of protein structures is important in analysing the results of NMR structure determinations and in investigating mechanisms of molecular evolution at the level of conformation. A method is discussed for finding the transformations that mutually superpose an arbitrary number of structures in the least-squares sense given specified atom-to-atom correspondence.
TL;DR: A description is given of nineteen 4-connected nets with one kind of vertex and containing 3-rings that are believed to be new.
Abstract: A description is given of nineteen 4-connected nets with one kind of vertex and containing 3-rings. Many of them are believed to be new.
TL;DR: In this paper, the problem of recovering the structure factors that contribute to a zone-axis convergent-beam diffraction pattern is discussed and an automated matching procedure that minimizes the sum-of-squares difference between experimental and simulated patterns is applied.
Abstract: The problem of recovering the structure factors that contribute to a zone-axis convergent-beam diffraction pattern is discussed. It is shown that an automated matching procedure that minimizes the sum-of-squares difference between experimental and simulated patterns is effective whether one is refining accurate structure factors in a known crystal or attempting ab initio structure determination. The details of the minimization method are analysed and it is shown that a quasi-Newton method that uses analytically derived gradients is particularly effective when several structure factors are varied. The inversion method for ab initio structure determination is tested on the [110] axis of GaP, using simulated patterns as ideal 'experimental' data.
TL;DR: In this paper, the authors used statistical dynamical theory to model the thickness dependence of the Bragg reflections measured on an absolute scale with 316'V γ-radiation and determined the size of the SiO2 precipitates in Czochralski-grown silicon.
Abstract: A homogeneous distribution of SiO2 precipitates in Czochralski-grown silicon containing different amounts of oxygen were produced by annealing the dislocation-free crystals at 1023 K. The resulting long-range strain field modifies the integrated reflecting power R of the Bragg reflections measured on an absolute scale with 316 keV γ-radiation. The thickness dependence of R has been modelled using the results of statistical dynamical theory. The assumption made in Kato's original theory, where the correlation length Γ for the wave-field amplitudes is proportional to the extinction length, has to be abandoned. Recent modifications to statistical dynamical theory by Becker & Al Haddad [Acta Cryst. (1990). A46, 123–139] lead to excellent agreement with the present experimental results. Furthermore, in the present case, the correlation length τ, describing short-range correlation in the fluctuations of the phase factor caused by the displacement field of the defects, turns out to be very small, so that the contribution of the mixed term to the integrated reflecting power could be neglected. Therefore, the defect scattering is characterized by the static Debye–Waller factor alone, which was determined accurately from the thickness dependence of the measured integrated reflecting power. From the ratio of the static Debye–Waller factors determined for different orders of reflection, the sizes of the SiO2 precipitates have been calculated and the results are in very good agreement with the values determined directly from small-angle neutron scattering on the same samples.
TL;DR: Electron diffraction intensity data were collected from thin epitaxially oriented crystals of copper perbromophthalocyanine in a projection down molecular columns and the structure was determined by Fourier refinement after three heavy-atom positions were identified in an initial potential map.
Abstract: Electron diffraction intensity data were collected at 1200 kV from thin epitaxically oriented crystals of copper perbromophthalocyanine (C32Br16CuN8) in a projection down molecular columns. Measured cell constants for the projection with cmm symmetry are d100 = 17.88 (9), b = 26.46 (15) A. The structure was determined by Fourier refinement after three heavy-atom positions were identified in an initial potential map. In addition to the copper and halogens, all light-atom positions were found. Although the final R value for all data is 0.41, n-beam dynamical calculations for crystal thicknesses corresponding to the estimated sample dimension account for the observed amplitudes that deviate most from their kinematical values.
TL;DR: In this paper, the relationship between the intensity distributions of the crystal truncation rod (CTR) scattering and the surface roughness of a crystal is discussed by developing a kinematic theory for the CTR scattering so as to reflect the two-dimensional aspect of the surface.
Abstract: The relationship between the intensity distributions of the crystal truncation rod (CTR) scattering and the surface roughness of a crystal is discussed by developing a kinematic theory for the CTR scattering so as to reflect the two-dimensional aspect of the surface. The intensity of the CTR scattering elongated from a Bragg point is shown to be reduced by a factor |Γ(q)|2 for a surface possessing some roughness, where Γ(q) is defined by a simple Fourier summation of γp, the relative area with the same step height p on a surface, i.e. Γ(q) = p = 0∞ γp exp (2πipq), with Σp γp = 1, q being the distance in reciprocal space from the Bragg point along the CTR scattering. A pair-correlation function between the steps can, therefore, be obtained by a simple Fourier integral of the roughness damping factor |Γ(q)|2. For the case where γp has a Gaussian distribution around the average step height, |Γ(q)|2 is approximated by the well known Debye–Waller-like factor, exp (−4π2〈Δp2〉q2), where 〈Δp2〉 is the mean square deviation of step height in units of the lattice spacing. The intensity formulae proposed so far by several authors are also discussed on the basis of the above factor.
TL;DR: Conditions that would permit the complete structure determination of spherical viruses that have high internal symmetry were examined starting only from an initial spherical shell model, and an error of 1.6 A caused noticeable phasing error at a resolution greater than 20 A.
Abstract: Conditions that would permit the complete structure determination of spherical viruses that have high internal symmetry were examined starting only from an initial spherical shell model. Problems were considered that might arise due to the following. 1. Creation of centric phases due to the simple shell model and its position in the unit cell. The centric symmetry can generally be broken on averaging an initial electron density map based on observed structure amplitudes, provided that the internal molecular symmetry is sufficiently non-parallel to the crystallographic symmetry. 2. Choice of the average model shell radius. Some incorrect radii led to the Babinet opposite solution (electron density is negative instead of positive). Phases derived from other models with incorrect radii failed to converge to the correct solution. 3. Error in structure amplitude measurements. 4. Lack of a complete data set. 5. Error in positioning the initial spherical-shell model within the crystal unit cell. It was found that an error of 1.6 A caused noticeable phasing error at a resolution greater than 20 A.
TL;DR: Extension de methodes de determination automatique de structures en utilisant les pics de Patterson and une nouvelle version du program d'ordinateur XFPS as discussed by the authors.
Abstract: Extension de methodes de determination automatique de structures en utilisant les pics de Patterson et une nouvelle version du programme d'ordinateur XFPS. Les resultats d'essais de calculs ont ete compares a ceux de SHELX86. Environ 80% des structures a atome lourd peuvent etre resolues automatiquement.
TL;DR: In this paper, a systematic and precise X-ray diffraction intensity measurement has been carried out using a spherical single-crystal of gallium arsenide at 300 K.
Abstract: The introduction of dispersion corrections in the generalized structure-factor expression for the zinc blende structure leads to the breakdown of Friedel's law for all even-index reflections, owing to bonding or anharmonicity in these crystals. A systematic and precise X-ray diffraction intensity measurement has been carried out using a spherical single-crystal of gallium arsenide at 300 K. Least-squares refinement of the experimental data yields the Debye–Waller factors BGa = 0.62 (2), BAs + 0.49 (2) A2 for the harmonic model and BGa = 0.670 (3), BAs = 0.470 (2) A2 and individual anharmonic thermal factors BGa = 3.15 (59) × 10−18 and BAs= 8.92 (182) × 10−18 J A−3 for the anharmonic model. The residual index for the discrepancy between measured and calculated structure factors in the present work is R = 1.237% for the harmonic model and R = 1.229% for the anharmonic model. The present work reveals excellent agreement in both sign and magnitude of the Bijvoet inequalities for a large number of reflections. Covalent charge transfer has also been deduced from the experimental measurements on a few quasi-forbidden Bragg reflections showing a net transfer of charge from Ga to As.
TL;DR: A new method is presented by which theheavy-atom parameters of isomorphous derivatives are refined against solvent-flattened phases and is shown to enhance convergence of the parameters by decoupling heavy-atom-parameter adjustment from parent-phase calculation.
Abstract: Solvent flattening of macromolecular MIR electron density maps is frequently used to improve the quality of the phases and the interpretability of resultant electron density maps. A new method is presented by which the heavy-atom parameters of isomorphous derivatives are refined against these same solvent-flattened phases and is shown to enhance convergence of the parameters by decoupling heavy-atom-parameter adjustment from parent-phase calculation. This approach is described here in the first example of its application in the solution of the glutaminyl-tRNA synthetase-tRNAGln-ATP co-crystal structure.
TL;DR: In this paper, it is shown how parameters such as radii, DNA density and particle positions can be determined and refined from diffraction data with sufficient precision to start phase extension from 20 A resolution for a virus of approximately 122 A radius.
Abstract: The structure determination of canine parvovirus depended on the extension of phases calculated initially from a spherical-shell model [Tsao, Chapman, Wu, Agbandje, Keller & Rossmann (1992). Acta Cryst. B48, 75-88]. Such ab initio phasing holds the promise of obviating initial experimental phasing by isomorphous or molecular replacement, thereby expediting the structure determinations of spherical virus capsids. In this paper, it is shown how parameters such as radii, DNA density and particle positions may be determined and refined from diffraction data with sufficient precision to start phase extension from 20 A resolution for a virus of approximately 122 A radius.
TL;DR: In this paper, the form of the tensor describing the piezomagnetoelectric effect of non-centrosymmetric point groups with space-time inversion was investigated.
Abstract: Taking time reversal into account there are 122 crystallographic Shubnikov point groups and 21 limiting Shubnikov point groups containing ∞-fold rotation axes. The restrictions on the form of the tensor describing the piezomagnetoelectric effect are given for all these groups and compared with results of other authors. Antiferromagnetic materials with non-centrosymmetric point groups containing space-time inversion are suitable candidates for measuring the piezomagnetoelectric effect.
TL;DR: In this paper, the origins of these diffuse features are explained using both real-space and modulation-wave approaches, by concentrating on a Monte Carlo simulated two-dimensional binary alloy.
Abstract: Diffuse intensity absences, on reciprocal planes that pass through the Bragg positions, have been observed in diffraction patterns of Zr0.61Y0.39O1.81 and (Ta2O5).7%(WO3). These absences, occurring on planes normal to near-neighbour directions and high-lighted by sheets of diffuse intensity on either side, are shown to result naturally from atomic size effect distortions. The origins of these diffuse features are explained, using both real-space and modulation-wave approaches, by concentrating on a Monte Carlo simulated two-dimensional binary alloy. These absences, which should be characteristic of systems that distort via the size effect, result from intensity components that do not depend on scattering-factor differences and so will be most prominent when the atomic species have similar scattering powers, thus suppressing the normal size effect intensity component [Warren, Averbach & Roberts (1951). J. Appl. Phys. 22, 1493–1496].
TL;DR: In this paper, the authors analyzed X-ray diffraction data on LiH and LiD measured at three different temperatures and measured in terms of multipolar radial densities searching for phenomenological indications on the nature of bonding.
Abstract: Accurate X-ray diffraction data on LiH and LiD measured at three different temperatures are analysed in terms of multipolar radial densities searching for phenomenological indications on the nature of bonding. The average spherical charge density around the atomic positions shows typical features of an ionic crystal. The central peaks are slightly contracted compared with superimposed free ions. The Li + peak contains, however, a small but significant excess of electrons, and the H-/D- peak is low and diffuse. Li + is spherical and its Debye-Waller parameters agree with the neutron diffraction values obtained by Vidal& Vidal-Valat [Acta Cryst. (1986), B42, 131137]. This indicates that, within the experimental accuracy, Li + is rigid. The non-spherical multipoles are significantly stronger in the hydrogen than in the deuterium derivative. They accumulate charge along the (100) directions giving a phenomenological indication of 'long-distance covalency' of H-H and D-D bonding with Li ÷ ions embedded in the middle but not contributing to the covalency. The significant deviation of the charge distribution of the anion in LiH from that in LiD indicates breakdown of the Born-Oppenheimer approximation due to coupling of the vibrations and the electronic states, which is much stronger in LiH. This is the first case - and probably the only possible - where such a breakdown can be seen by X-ray diffraction.
TL;DR: In this paper, the modulated structure in (Sr, Ca)14Cu24O41 has been studied using electron diffraction and high-resolution microscopy, and the structure can be considered as consisting of two interpenetrating substructures.
Abstract: The modulated structure in (Sr, Ca)14Cu24O41 has been studied using electron diffraction and high-resolution microscopy. The structure can be considered as consisting of two interpenetrating substructures. The first sheet-like substructure is shown to be hardly modulated while the second substructure, consisting of c-oriented chains, contains most of the modulation. High-resolution electron microscopy allows either separate imaging of the two substructures or identification of the misfit between them.