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  • National Academy of Sciences  (17)
  • International Union of Crystallography (IUCr)  (10)
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  • 1
    Electronic Resource
    Electronic Resource
    Simple statistics for intensity data from twinned specimens (1988)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 44 (1988), S. 142-144 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The statistics of intensity data from hemihedrally twinned specimens are analyzed in terms of a new parameter and are shown to take a simple form in both the centrosymmetric and non-centrosymmetric cases. This analysis provides a sensitive method for determining the twinning fraction. The effects of intensity measurement errors on the observed statistics are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767387009632
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  • 2
    Electronic Resource
    Electronic Resource
    An isomorphous replacement method for phasing twinned structures (1987)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 43 (1987), S. 30-36 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A linear least-squares formulation of the method of isomorphous replacement is presented. With data from untwinned crystals, this approach is shown to be equivalent to the phasing representation developed by Hendrickson & Lattman [Acta Cryst. (1970). B26, 136-143]. A general method for calculating the most probable phase is described and applied to the higher- dimensional problem of phase determination for twinned structures. A method for calculating the best phase with intensity data from twinned crystals is also presented. The dependences of these phasing procedures on the number of derivatives and accuracy of the data sets are evaluated in test calculations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767387099951
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  • 3
    Electronic Resource
    Electronic Resource
    Simultaneous search for symmetry-related molecules in cross-rotation functions (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 309-314 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: In a typical cross-rotation function, the Patterson function of a single search molecule is compared with an observed Patterson function, which contains a set of symmetry-related intramolecular vector sets. In principle, it is better to search for the symmetry- related molecules simultaneously, and Nordman [Am. Crystallogr. Assoc. (1986), Hamilton, Ontario, Program Abstr. p. 36] has reported success with an algorithm of this type. In this paper, the differences between the ordinary search and a simultaneous search are investigated, and it is shown that the combined presence of crystallographic symmetry and approximate symmetry of a search model may lead to significant bias in conventional rotation functions. The nature and magnitude of this symmetry bias are discussed. An efficient algorithm is derived for generating a modified unbiased cross-rotation function map from conventional rotation functions. Two examples are described that demonstrate improvement in the quality of the rotation function maps and the ability to obtain physically meaningful correlation coefficients.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767388013388
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  • 4
    Electronic Resource
    Electronic Resource
    Determination of the correct reference frame from an atomic coordinate list (1990)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 46 (1990), S. 625-626 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A simple method is described for determining the reference coordinate system of a list of atomic coordinates. The reference system is characterized by finding the optimal metric tensor on the basis of the expected bond lengths. The ability to identify the correct frame of reference is important for structures solved in non-orthogonal unit cells.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767390002793
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  • 5
    Electronic Resource
    Electronic Resource
    The asymmetric regions of rotation functions between Patterson functions of arbitrarily high symmetry (1993)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 49 (1993), S. 138-141 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Rotation functions between Patterson functions can be calculated and analyzed more efficiently when it is possible to consider only a unique or asymmetric region of rotation space. Previous authors have succeeded in characterizing the symmetries and asymmetric units of rotation functions between Patterson functions whose symmetries are less than cubic. Here we describe a simple and general solution that applies to rotation functions between Patterson functions of any symmetry, including cubic. The method relies on partitioning rotation space into Dirichlet domains.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767392008110
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  • 6
    Electronic Resource
    Electronic Resource
    Structure determination of plastocyanin from a specimen with a hemihedral twinning fraction of one-half (1993)
    Copenhagen : International Union of Crystallography (IUCr)
    Acta crystallographica 49 (1993), S. 375-380 
    Details
    ISSN: 1399-0047
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The structure determination of a macromolecule from a hemihedrally twinned crystal specimen with a twinning fraction of one-half is described. Twinning was detected by analysis of crystal-packing density and intensity statistics. The structure was solved using molecular replacement, and the positioned search model was used to overcome the twinning by a novel method of `detwinning' the observed data. Estimates of the unobservable crystallographic intensities from each of the twin domains were obtained and used to refine the model. The structure of a new algal plastocyanin from Chlamydomonas reinhardtii was determined by this method to 1.6 Å resolution with a `twinned' R factor of 15.6%. Additional data from a crystal specimen with a low twinning fraction were used to establish the accuracy of the structure solution from the perfectly twinned data, and to finalize the refinement to 1.5 Å resolution and a true R factor of 16.8%. Methods for detecting twinning and obtaining a molecular-replacement solution in the presence of twinning are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S090744499300294X
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  • 7
    Electronic Resource
    Electronic Resource
    Crystals of the Carotenoid Protein from Arthrospira maxima Containing Uniformly Oriented Pigment Molecules (1997)
    Copenhagen : International Union of Crystallography (IUCr)
    Acta crystallographica 53 (1997), S. 720-723 
    Details
    ISSN: 1399-0047
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Crystals of a carotenoid protein from the cyanobacterium Arthrospira maxima have been grown in space group C2 with unit-cell dimensions a = 219.6, b = 40.3, c = 75.5 Å and β = 95.5°. The crystals diffract X-rays to 2.3 Å resolution and display unusual optical properties in polarized light that suggest that all of the carotenoid molecules in the crystals are oriented similarly. A slight increase in the concentration of a crystallization additive in the mother liquor induces macroscopic twinning, which is also visible when the crystals are illuminated with polarized light.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0907444997006999
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  • 8
    Electronic Resource
    Electronic Resource
    Intensity-based domain refinement of oriented but unpositioned molecular replacement models (1990)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 46 (1990), S. 352-359 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A program is described that performs least-squares group refinement of oriented molecular replacement models whose positions in the unit cell are unknown. The program (INTREF) is designed to produce improved models for use in a translation function by optimizing the orientations and relative translations of the model domains. The molecular contents of the asymmetric unit are refined as a small number of rigid bodies whose origins relative to each other may be unknown. More than one molecule in the asymmetric unit can be accommodated. The refinement seeks to minimize the residual error between the observed and calculated intensities that have been modified to produce the equivalent of a radial weighting in Patterson space. Calculated intensities include contributions from all symmetry-related molecules, enabling meaningful refinement in high-symmetry space groups. Derivatives of the intensities with respect to the rigid-body parameters are evaluated numerically using fast Fourier transforms and the shifts are obtained by non-linear least-squares analysis. Results with test cases show that the program is capable of adjusting the orientations and relative translations of protein domains to give models that more closely resemble the known structures. Consequently, the resulting models produce more accurate and more interpretable results in translation functions. The importance of including all crystallographically related molecules and of downweighting the contribution of the longer-radius region of the Patterson function is demonstrated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767389013073
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  • 9
    Electronic Resource
    Electronic Resource
    Versatile rigid-body and group refinement in real space (1988)
    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 21 (1988), S. 925-928 
    Details
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: A procedure is described for performing least-squares rigid-body or group refinements in real space. The necessary derivatives are obtained from gradients in a difference Fourier map [Jack & Levitt (1978). Acta Cryst. A34, 931–935] allowing the use of fast Fourier transforms for rapid calculations. The computation time is nearly independent of the number of rigid groups being refined. The orientational transformation of the molecule or group is represented in a linear matrix form. The inherent non-linearity is treated outside of the refinement calculations, and trigonometric calculations are avoided. The linear approximation provides versatility in the types of constraints that may be applied during the refinement. Errors in unit-cell parameters may be detected through the strain component of the transformation matrix. The results of refinement of two protein structures are described as examples.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0021889888007927
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  • 10
    Electronic Resource
    Electronic Resource
    Statistics for rotation functions (1993)
    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 26 (1993), S. 448-449 
    Details
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: Equations and justification are provided to compensate for the non-Euclidean nature of rotation space in statistical calculations with rotation functions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0021889892011622
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