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Difference Maps (difference + map)
Selected AbstractsFitting atomic models into electron-microscopy mapsACTA CRYSTALLOGRAPHICA SECTION D, Issue 10 2000Michael G. Rossmann Combining X-ray crystallographically determined atomic structures of component domains or subunits with cryo-electron microscopic three-dimensional images at around 22,Å resolution can produce structural information that is accurate to about 2.2,Å resolution. In an initial step, it is necessary to determine accurately the absolute scale and absolute hand of the cryo-electron microscopy map, the former of which can be off by up to 5%. It is also necessary to determine the relative height of density by using a suitable scaling function. Difference maps can identify, for instance, sites of glycosylation, the position of which helps to fit the component structures into the EM density maps. Examples are given from the analysis of alphaviruses, rhinovirus,receptor interactions and poliovirus,receptor interactions. [source] Detecting corpus callosum abnormalities in autism subtype using planar conformal mappingINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 2 2010Ye Duan Abstract A number of studies have documented that autism has a neurobiological basis, but the anatomical extent of these neurobiological abnormalities is largely unknown. In this paper, we apply advanced computational techniques to extract 3D models of the corpus callosum (CC) and subsequently analyze local shape variations in a homogeneous group of autistic children. Besides the traditional volumetric analysis, we explore additional phenotypic traits based on the oriented bounding rectangle of the CC. In shape analysis, a new conformal parameterization is applied in our shape analysis work, which maps the surface onto a planar domain. Surface matching among different individual meshes is achieved by aligning the planar domains of individual meshes. Shape differences of the CC between autistic patients and the controls are computed using Hotelling T2 two-sample metric followed by a permutation test. The raw and corrected p -values are shown in the results. Additional visualization of the group difference is provided via mean difference map. Copyright © 2009 John Wiley & Sons, Ltd. [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] 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] The endoproteinase furin contains two essential Ca2+ ions stabilizing its N-terminus and the unique S1 specificity pocketACTA CRYSTALLOGRAPHICA SECTION D, Issue 5 2005Manuel E. Than The mammalian prohormone/proprotein convertase (PC) furin is responsible for the maturation of a great variety of homeostatic but also many pathogenic proteins within the secretory pathway and the endosomal pathway and at the cell surface. Similar to other members of the PC family, furin requires calcium for catalytic activity. In a previous paper, the structural association of the catalytic and the P-domain of furin was shown and data were presented indicating two or three calcium-binding sites. The exact number and the three-dimensional localization of the essential calcium sites within furin have now been determined by collecting X-ray diffraction data on either side of the Ca,K absorption edge and by calculating a novel type of double difference map from these anomalous scattering data. Two calcium ions were unambiguously identified: the purely structural Ca-1 also conserved in the bacterial digestive subtilisins and the Ca-2 site specific to PCs and essential for the formation of the P1 specificity-determining S1-binding pocket. In addition, these anomalous diffraction data show that no tightly bound K+ sites exist in furin. [source] Quantitative assessment of the effect of basis set superposition error on the electron density of molecular complexes by means of quantum molecular similarity measuresINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 11 2009Pedro Salvador Abstract The Chemical Hamiltonian Approach (CHA) method is applied to obtain Basis Set Superposition Error (BSSE)-free molecular orbitals at the Hartree,Fock (HF) and Density Functional Theory (DFT) levels of theory. To assess qualitatively the effect of the BSSE on the first-order electron density, we had previously applied Bader's analysis of the intermolecular critical points located on the electron density, as well as density difference maps for several hydrogen bonded complexes. In this work, Quantum Molecular Similarity Measures are probed as an alternative avenue to properly quantify the electronic relaxation due to the BSSE removal by means of distance indices between the uncorrected and corrected charge densities. It is shown that BSSE contamination is more important at the DFT level of theory, and in some cases, changes on the topology of the electron density are observed upon BSSE correction. Inclusion of diffuse functions have been found to dramatically decrease the BSSE effect in both geometry and electron density. The CHA method represents a good compromise to obtain accurate results with small basis sets. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009 [source] DFT calculations of light-induced excited states and comparison with time-resolved crystallographic resultsINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 5 2005Philip Coppens Abstract DFT calculations of the ground and first excited states of several transition metal complexes have been performed to complement time-resolved diffraction experiments. The results from different functionals and relativistic treatments are tested against both diffraction and spectroscopic values. Calculations of the d8,d8 complex [Pt2(pyrophosphite)4]4, quantitatively reproduce metal,metal shortening on excitation to the triplet state and support bond formation between the two metal centers, as do calculations on [Rh2(1,3-diisocyanopropane)4]2+. Results on homoleptic and heteroleptic copper(I) 2,9-dimethyl,1,10-phenanthroline (dmp) complexes, which are investigated because of their potential for solar energy capture, confirm considerable molecular deformations on excitation. The distortion calculated for the isolated complex [Cu(dmp)(dmpe)]+ (dmpe=1,2-bis(dimethylphosphino)ethane) is significantly larger than observed in the crystal, indicating the constraining effect of the crystalline environment. The change in the net charge of the Cu atom upon photo-induced metal-to-ligand charge transfer is less than 0.2 e, showing the limitations of the formal Cu(I),Cu(II) designation. Electron density difference maps show a pronounced change in electronic structure of the Cu atom on excitation. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005 [source] Use of Cr K, radiation to enhance the signal from anomalous scatterers including sulfurJOURNAL OF APPLIED CRYSTALLOGRAPHY, Issue 3-2 2000Witek Kwiatkowski The anomalous signals from scatterers such as sulfur (S) and arsenic (As) were compared in diffraction data sets collected from an X-ray source with three different targets, Au, Cu and Cr, on a multi-target rotating anode. HIV-1 integrase crystals served as the test case for this study. The crystalline specimen of HIV-1 integrase contains in each protein molecule two As atoms, each covalently bound to a cysteine S atom, and two additional S atoms derived from methionine. It was found that the Cr K, radiation gave the clearest peaks in anomalous difference Fourier maps, although the signal-to-noise ratios of the anomalous signal for the Cu K, and Cr K, data were similar but better than that for Au L,. This result was in spite of the fourfold higher flux from the Cu anode versus the Cr anode. For all three X-ray wavelengths, anomalous difference Fourier maps calculated with bias-removed phases derived from the known atomic model revealed clear peaks at the two As sites. However, only in the map calculated using the Cr K, data were both peaks of the expected ellipsoidal shape, enveloping the As atom and the adjacent S atom. None of the S sites was apparent in difference maps calculated using the Au L, data. The ability to enhance the S-derived anomalous signal using Cr K, radiation has particularly useful applications in the structure determination of proteins, for example in resolving ambiguities in the chain tracing of a protein with numerous disulfide bonds and in assigning amino acid identities. Additionally, anomalous difference Patterson maps calculated from the Cr K, data were sufficiently clear to identify the As-related peaks. These results form the groundwork for in-house phase determination with the multi-wavelength anomalous diffraction method. [source] Elevating tensor rank increases anisotropy in brain areas associated with intra-voxel orientational heterogeneity (IVOH): a generalised DTI (GDTI) studyNMR IN BIOMEDICINE, Issue 1 2008L. Minati Abstract Rank-2 tensors are unable to represent multi-modal diffusion associated with intra-voxel orientational heterogeneity (IVOH), which occurs where axons are incoherently oriented, such as where bundles intersect or diverge. Under this condition, they are oblate or spheroidally shaped, resulting in artefactually low anisotropy, potentially masking reduced axonal density, myelinisation and integrity. Higher rank tensors can represent multi-modal diffusion, and suitable metrics such as generalised anisotropy (GA) and scaled entropy (SE) have been introduced. The effect of tensor rank was studied through simulations, and analysing high angular resolution diffusion imaging (HARDI) data from two volunteers, fit with rank-2, rank-4 and rank-6 tensors. The variation of GA and SE as a function of rank was investigated through difference maps and region of interest (ROI)-based comparisons. Results were correlated with orientation distribution functions (ODF) reconstructed with q-ball, and with colour-maps of the principal and second eigenvectors. Simulations revealed that rank-4 tensors are able to represent multi-modal diffusion, and that increasing rank further has a minor effect on measurements. IVOH was detected in subcortical regions of the corona radiata, along the superior longitudinal fasciculus, in the radiations of the genu of the corpus callosum, in peritrigonal white matter and along the inferior fronto-occipital and longitudinal fascicula. In these regions, elevating tensor rank increased anisotropy. This was also true for the corpus callosum, cingulum and anterior limb of the internal capsule, where increasing tensor rank resulted in patterns that, although mono-modal, were more anisotropic. In these regions the second eigenvector was coherently oriented. As rank-4 tensors have only 15 distinct elements, they can be determined without acquiring a large number of directions. By removing artefactual underestimation of anisotropy, their use may increase the sensitivity to pathological change. Copyright © 2007 John Wiley & Sons, Ltd. [source] An X-ray diffraction study of partially ordered electron density in clathrates of Dianin's compound that include simple carboxylic acidsACTA CRYSTALLOGRAPHICA SECTION B, Issue 1 2003Ronald W. H. Small The nature of the inclusions in ten clathrate complexes of Dianin's compound have been investigated by the use of electron-density difference maps. The guest species are the first eight straight-chain carboxylic acids, formic to octanoic, a branched-chain acid (dimethylacetic acid) and trifluoroacetic acid. The point-group symmetry of the clathrate cavity, , is satisfied by partial occupation of symmetry-related sites by two included molecules in the case of formic, acetic and trifluoroacetic acids and by a single molecule in the remainder. Hydrogen-bonding requirements in the case of formic and acetic acids are satisfied by dimer formation; in the trifluoroacetic acid complex the two acid molecules form hydrogen bonds to framework O atoms at either end of the cavity. The adoption of gauche conformations in heptanoic and octanoic acid chains shortens them sufficiently that they fit the cavity with only slight distortion. [source] | ||||||||||