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Phase Problem (phase + problem)
Selected AbstractsTeaching crystallography to undergraduate physical chemistry studentsJOURNAL OF APPLIED CRYSTALLOGRAPHY, Issue 5-2 2010Virginia B. Pett Teaching goals, laboratory experiments and homework assignments are described for teaching crystallography as part of two undergraduate physical chemistry courses. A two-week teaching module is suggested for introductory physical chemistry, including six to eight classroom sessions, several laboratory experiences and a 3,h computer-based session, to acquaint undergraduate physical chemistry students with crystals, diffraction patterns, the mathematics of structure determination by X-ray diffraction, data collection, structure solution and the chemical insights available from crystal structure information. Student projects and laboratory work for three to four weeks of an advanced physical chemistry course are presented. Topics such as symmetry operators, space groups, systematic extinctions, methods of solving the phase problem, the Patterson map, anomalous scattering, synchrotron radiation, crystallographic refinement, hydrogen bonding and neutron diffraction all lead to the goal of understanding and evaluating a crystallographic journal article. Many of the ideas presented here could also be adapted for inorganic chemistry courses. [source] Combining solution wide-angle X-ray scattering and crystallography: determination of molecular envelope and heavy-atom sitesJOURNAL OF APPLIED CRYSTALLOGRAPHY, Issue 2 2009Xinguo Hong Solving the phase problem remains central to crystallographic structure determination. A six-dimensional search method of molecular replacement (FSEARCH) can be used to locate a low-resolution molecular envelope determined from small-angle X-ray scattering (SAXS) within the crystallographic unit cell. This method has now been applied using the higher-resolution envelope provided by combining SAXS and WAXS (wide-angle X-ray scattering) data. The method was tested on horse hemoglobin, using the most probable model selected from a set of a dozen bead models constructed from SAXS/WAXS data using the program GASBOR at 5,Å resolution (qmax = 1.25,Å,1) to phase a set of single-crystal diffraction data. It was found that inclusion of WAXS data is essential for correctly locating the molecular envelope in the crystal unit cell, as well as for locating heavy-atom sites. An anomalous difference map was calculated using phases out to 8,Å resolution from the correctly positioned envelope; four distinct peaks at the 3.2, level were identified, which agree well with the four iron sites of the known structure (Protein Data Bank code 1ns9). In contrast, no peaks could be found close to the iron sites if the molecular envelope was constructed using the data from SAXS alone (qmax = 0.25,Å,1). The initial phases can be used as a starting point for a variety of phase-extension techniques, successful application of which will result in complete phasing of a crystallographic data set and determination of the internal structure of a macromolecule to atomic resolution. It is anticipated that the combination of FSEARCH and WAXS techniques will facilitate the initial structure determination of proteins and provide a good foundation for further structure refinement. [source] New opportunities in biological and chemical crystallographyJOURNAL OF SYNCHROTRON RADIATION, Issue 1 2002John R. Helliwell Banerjee [Proc. R. Soc. (1933), 141, 188,193] offered a new way of approaching the crystallographic phase problem which not only broke new ground beyond the `trial and error' structure solution method of that time but also heralded the extremely powerful direct methods of crystallography of the modern era from the 1970s onwards in chemical crystallography. Some 200000 crystal structures are known today. More complex crystal structures such as proteins required new experimental and theoretical methods to solve the phase problem. These are still evolving, and new methods and results involving synchrotron radiation at softer X-ray wavelengths (2,Å) are reported. In addition, an overview is given of the new opportunities that are possible for biological and chemical crystallography, especially via harnessing synchrotron radiation and neutron beams. [source] Coherent nano-area electron diffractionMICROSCOPY RESEARCH AND TECHNIQUE, Issue 5-6 2004J.M. Zuo We describe the new coherent nano-area electron diffraction (NED) and its application for structure determination of individual nanostructures. The study is motivated by the challenge and the general lack of analytical techniques for characterizing nanometer-sized, heterogeneous phases. We show that by focusing electrons on the focal plane of the pre-objective lens using a 3rd condenser lens and a small condense aperture, it is possible to achieve a nanometer-sized highly parallel illumination or probe. The high angular resolution of diffraction pattern from the parallel illumination allows over-sampling and consequently the solution of phase problem based on the recently developed ab initio phase retrieval technique. From this, a high-contrast and high-resolution image can be reconstructed at resolution beyond the performance limit of the image-forming objective lens. The significance of NED for nanostructure characterization will be exemplified by single-wall carbon nanotubes and small metallic clusters. Imaging from diffraction patterns, or diffractive imaging, will be demonstrated using double-wall carbon nanotubes. Microsc. Res. Tech. 64:347,355, 2004. © 2004 Wiley-Liss, Inc. [source] Retrieving low- and medium-resolution structural features of macromolecules directly from the diffraction intensities , a real-space approach to the X-ray phase problemACTA CRYSTALLOGRAPHICA SECTION A, Issue 6 2008Wu-Pei Su A simple mathematical algorithm is proposed to generate electron-density functions whose Fourier amplitudes match the diffraction intensities. The function is by construction everywhere positive. Using appropriate averaging procedures, the high-density regions of such functions could yield important structural information about macromolecular crystals. Trial calculations on protein crystals show that the protein envelope plus other structural motifs such as barrels and secondary structures could be recognized in the density maps. As such, the algorithm could provide a basis for new phasing methods or supplement existing phasing methods. [source] Phase and amplitude recovery and diffraction image generation method: structure of Sb/Au(110),,3,×,,3R54.7° from surface X-ray diffractionACTA CRYSTALLOGRAPHICA SECTION A, Issue 3 2007R. Fung The discovery that the phase problem of diffraction from non-periodic objects may be solved by oversampling the diffraction intensities in reciprocal space with respect to a Nyquist criterion has opened up new vistas for structure determination by diffraction methods. A similar principle may be applied to the problem of surface X-ray diffraction (SXRD), where, owing to the breaking of a crystal periodicity normal to its surface, diffraction data consist of a set of superstructure rods (SRs) due to scattering from the parts of the surface whose structure is different from that of the truncated bulk and of crystal truncation rods (CTRs), formed by interfering contributions from the surface and the bulk. A phase and amplitude recovery and diffraction image generation method (PARADIGM) is described that provides a prescription for finding the unmeasured amplitudes and phases of the surface contributions to the CTRs in addition to the phases of the SRs, directly from the diffraction data. The resulting `diffraction image' is the basis of a determination of the previously unknown multidomain structure of Sb/Au(110),,3,×,,3R54.7°. [source] The algebraic approach to the phase problemACTA CRYSTALLOGRAPHICA SECTION A, Issue 5 2005A. Cervellino A rather detailed report is presented on the present status of the algebraic approach to the phase problem in the case of an ideal crystal in order to make clear that some points must still be proven for it to apply to neutron scattering. To make this extension, the most important results that were previously obtained in the case of X-ray scattering are derived again by a different procedure. By so doing, the three-dimensional case is treated explicitly, the polynomial equations in a single variable whose roots determine the positions of the scattering centres are explicitly reported and the procedure is shown to generalize to neutron scattering, overcoming the difficulty related to the non-positivity of the scattering density. In this way, it is fully proven that the atomicity assumption removes the phase ambiguity in the sense that the full diffraction pattern of an ideal crystal can uniquely be reconstructed from a suitable finite portion of it in both X-ray and neutron scattering. The procedures able to isolate these portions that contain the pattern's full information are also given. [source] Solution of the crystallographic phase problem by iterated projectionsACTA CRYSTALLOGRAPHICA SECTION A, Issue 3 2003Veit Elser An algorithm for determining crystal structures from diffraction data is described which does not rely on the usual reciprocal-space formulations of atomicity. The new algorithm implements atomicity constraints in real space, as well as intensity constraints in reciprocal space, by projections that restore each constraint with the minimal modification of the scattering density. To recover the true density, the two projections are combined into a single operation, the difference map, which is iterated until the magnitude of the density modification becomes acceptably small. The resulting density, when acted upon by a single additional operation, is by construction a density that satisfies both intensity and atomicity constraints. Numerical experiments have yielded solutions for atomic resolution X-ray data sets with over 400 non-hydrogen atoms, as well as for neutron data, where positivity of the density cannot be invoked. [source] An evolutionary computational approach to the phase problem in macromolecular X-ray crystallographyACTA CRYSTALLOGRAPHICA SECTION A, Issue 3 2001Gordon Webster The ab initio computation of the molecular envelopes of two proteins exclusively from their corresponding diffraction amplitudes demonstrates that an efficient and inherently parallel evolutionary search algorithm can assist in the direct phasing of macromolecules for which almost no a priori structural information is available. The applicability of this evolutionary computational approach is general and should not be limited to the examples described nor to extremes of data resolution, symmetry or structural size. [source] Features of the secondary structure of a protein molecule from powder diffraction dataACTA CRYSTALLOGRAPHICA SECTION D, Issue 7 2010Sebastian Basso Protein powder diffraction is shown to be suitable for obtaining de novo solutions to the phase problem at low resolution via phasing methods such as the isomorphous replacement method. Two heavy-atom derivatives (a gadolinium derivative and a holmium derivative) of the tetragonal form of hen egg-white lysozyme were crystallized at room temperature. Using synchrotron radiation, high-quality powder patterns were collected in which pH-induced anisotropic lattice-parameter changes were exploited in order to reduce the challenging and powder-specific problem of overlapping reflections. The phasing power of two heavy-atom derivatives in a multiple isomorphous replacement analysis enabled molecular structural information to be obtained up to approximately 5.3,Å resolution. At such a resolution, features of the secondary structure of the lysozyme molecule can be accurately located using programs dedicated to that effect. In addition, the quoted resolution is sufficient to determine the correct hand of the heavy-atom substructure which leads to an electron-density map representing the protein molecule of proper chirality. [source] The interdependence of wavelength, redundancy and dose in sulfur SAD experimentsACTA CRYSTALLOGRAPHICA SECTION D, Issue 12 2008Michele Cianci In the last decade, the popularity of sulfur SAD anomalous dispersion experiments has spread rapidly among synchrotron users as a quick and streamlined way of solving the phase problem in macromolecular crystallography. On beamline 10 at SRS (Daresbury Laboratory, UK), a versatile design has allowed test data sets to be collected at six wavelengths between 0.979 and 2.290,Å in order to evaluate the importance and the interdependence of experimental variables such as the Bijvoet ratio, wavelength, resolution limit, data redundancy and absorbed X-ray dose in the sample per data set. All the samples used in the experiments were high-quality hen egg-white lysozyme crystals. X-radiation damage was found to affect disulfide bridges after the crystals had been given a total dose of 0.20 × 107,Gy. However, with such a total dose, it was still possible in all cases to find a strategy to collect data sets to determine the sulfur substructure and produce good-quality phases by choosing an optimum combination of wavelength, exposure time and redundancy. A ,|,ano|/,(,ano), greater than 1.5 for all resolution shells was a necessary requirement for successful sulfur SAD substructure location. Provided this is achieved, it seems possible to find an optimum compromise between wavelength, redundancy and dose to provide phasing information. The choice of the wavelength should then follow the sample composition and the diffracting properties of the crystal. For strongly diffracting crystals, wavelengths equal or shorter than 1.540,Å can be selected to capture the available data (provided the Bijvoet ratio is reasonable), while a longer wavelength, to gain as high a Bijvoet ratio as possible, must be used for more weakly diffracting crystals. These results suggest that an approach to a sulfur SAD experiment based on a complete description of the crystal system and the instrument for data collection is useful. [source] Crystallization and preliminary X-ray diffraction study of mammalian mitochondrial seryl-tRNA synthetaseACTA CRYSTALLOGRAPHICA SECTION D, Issue 7 2004Sarin Chimnaronk The mitochondrial seryl-tRNA synthetase (mt SerRS) from Bos taurus was overexpressed in Escherichia coli and crystallized using the sitting-drop vapour-diffusion method. Crystals grew in a very narrow range of conditions using PEG 8000 as precipitant at room temperature. An appropriate concentration of lithium sulfate was critical for crystal nucleation. Crystals diffracted well beyond a resolution of 1.6,Å and were found to belong to the orthorhombic space group C2221, with unit-cell parameters a = 79.89, b = 230.42, c = 135.60,Å. There is one dimer (Mr, 113,kDa) in the asymmetric unit, with a solvent content of 55%. Efforts to solve the phase problem by molecular replacement are under way. [source] Crystallization and preliminary crystallographic characterization of GumK, a membrane-associated glucuronosyltransferase from Xanthomonas campestris required for xanthan polysaccharide synthesisACTA CRYSTALLOGRAPHICA SECTION F (ELECTRONIC), Issue 9 2006Máximo Barreras GumK is a membrane-associated inverting glucuronosyltransferase that is part of the biosynthetic route of xanthan, an industrially important exopolysaccharide produced by Xanthomonas campestris. The enzyme catalyzes the fourth glycosylation step in the pentasaccharide-P-P-polyisoprenyl assembly, an oligosaccharide diphosphate lipid intermediate in xanthan biosynthesis. GumK has marginal homology to other glycosyltransferases (GTs). It belongs to the CAZy family GT 70, for which no structure is currently available, and indirect biochemical evidence suggests that it also belongs to the GT-B structural superfamily. Crystals of recombinant GumK from X. campestris have been grown that diffract to 1.9,Å resolution. Knowledge of the crystal structure of GumK will help in understanding xanthan biosynthesis and its regulation and will also allow a subsequent rational approach to enzyme design and engineering. The multiwavelength anomalous diffraction approach will be used to solve the phase problem. [source] Crystallization and preliminary X-ray crystallographic analysis of agkicetin-C from Deinagkistrodon acutus venomACTA CRYSTALLOGRAPHICA SECTION F (ELECTRONIC), Issue 1 2005Gufeng Xu The crystallization and preliminary crystallographic analysis of agkicetin-C, a well known platelet glycoprotein Ib (GPIb) antagonist from the venom of Deinagkistrodon acutus found in Anhui Province, China is reported. Crystals of agkicetin-C suitable for structure determination were obtained from 1.8,M ammonium sulfate, 40,mM MES pH 6.5 with 2%(v/v) PEG 400. Interestingly, low buffer concentrations of MES seem to be necessary for crystal growth. The crystals of agkicetin-C belong to space group C2, with unit-cell parameters a = 177.5, b = 97.7, c = 106.8,Å, , = 118.5°, and diffract to 2.4,Å resolution. Solution of the phase problem by the molecular-replacement method shows that there are four agkicetin-C molecules in the asymmetric unit, with a VM value of 3.4,Å3,Da,1, which corresponds to a high solvent content of approximately 64%. Self-rotation function calculations show a single well defined non-crystallographic twofold axis with features that may represent additional elements of non-crystallographic symmetry. [source] Use of novel selenomethionine-resistant yeast to produce selenomethionyl protein suitable for structural analysisFEMS YEAST RESEARCH, Issue 3 2009Toshihiko Kitajima Abstract Yeast is widely used to determine the tertiary structure of eukaryotic proteins, because of its ability to undergo post-translational modifications such as glycosylation. A mutant lacking S -adenosylmethionine synthesis has been reported as a suitable host for producing selenomethionine derivatives, which can help solve phase problems in protein crystallography. However, the mutant required external addition of S -adenosylmethionine for cell proliferation. Here, a selenomethionine-resistant Pichia pastoris mutant that showed S -adenosylmethionine autotrophy was isolated. Human lysozyme expressed by the mutant under the control of constitutive promoter contained selenomethionine at 65% occupancy, sufficient for use as a selenomethionine derivative for single-wavelength anomalous dispersion phasing. [source] | ||||||||||