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  • 1
    Electronic Resource
    Electronic Resource
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 39 (1983), S. 512-515 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Statistical methodology originally introduced by French & Wilson [Acta Cryst. (1978). A34, 517-525] for the treatment of negative-intensity observations is shown to be useful for the estimation of anomalous-scattering differences. The general principles of this method are described, along with applications to data from a lead derivative of the enzyme carboxypeptidase A.
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  • 2
    Electronic Resource
    Electronic Resource
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 43 (1987), S. 30-36 
    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.
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  • 3
    Electronic Resource
    Electronic Resource
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 39 (1983), S. 94-97 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The least-squares refinement of macromolecular structures is characterized by a low ratio of observed data to refined parameters. Efforts have been made to compensate for this problem by incorporating subsidiary restraints into the observational equations. In this paper, a method is proposed and examples given for the introduction of additional observations into a least- squares refinement in the form of experimental phase information.
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  • 4
    Electronic Resource
    Electronic Resource
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 36 (1980), S. 578-581 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A simple test based on intensity statistics is presented for the detection of twinning by merohedry. Using relationships derived in the text, the twinning fraction of a crystal may be estimated from the intensity probability distribution. Unlike most methods for the detection of twinning, application of this test does not require knowledge of the twinning operation. Two possible mechanisms for increasing the apparent diffraction symmetry of a crystal, twinning by merohedry and crystal disorder, may be distinguished in certain cases by these procedures.
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  • 5
    Electronic Resource
    Electronic Resource
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 38 (1982), S. 201-207 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A general theory of X-ray intensity statistics for twins by merohedry is developed based on mathematical analogy of this problem to a one-dimensional random walk. Probability distribution functions are derived (a) for intensities from a single twinned specimen, and (b) for the differences in intensities from two separate twinned specimens. Theoretical values of a discrepancy index between observed intensities from a twin, and calculated intensities from both correct and incorrect structural models are evaluated. A new method for determining volume fractions of crystals in a twin is also proposed, based on the distribution of differences in intensities between twin-related reflections. These results have implications for the treatment of isomorphous replacement data collected from twins by hemihedry.
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  • 6
    Electronic Resource
    Electronic Resource
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 39 (1983), S. 916-920 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The progress of phase refinement by non-crystallographic symmetry averaging is often described by the behavior of a crystallographic R factor expressing agreement between the observed structure factors and structure factors calculated from an averaged electron density map. An upper limit for this R factor is evaluated for the case of incorrectly positioned non-crystallographic symmetry operators. Depending on the degree of non-crystallographic symmetry, the upper limit on R varies from 0.29 to 0.3, for acentric structures. Incorrect structures with the correct non-crystallographic symmetry are anticipated to converge to even lower values of R. In all cases, R values calculated for incorrect structures will be significantly lower than the value of 0.586 characteristic of wrong structures lacking non-crystallographic symmetry [Wilson (1950). Acta Cryst. 3, 397-399].
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  • 7
    Electronic Resource
    Electronic Resource
    Copenhagen : International Union of Crystallography (IUCr)
    Acta crystallographica 50 (1994), S. 596-602 
    ISSN: 1399-0047
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Cytochrome c2 serves as the secondary electron donor that reduces the photo-oxidized bacteriochlorophyll dimer in photosynthetic bacteria. Cytochrome c2 from Rhodobacter sphaeroides has been crystallized in three different forms. At high ionic strength, crystals of a hexagonal space group (P6122) were obtained, while at low ionic strength, triclinic (P1) and tetragonal (P41212) crystals were formed. The three-dimensional structures of the cytochrome in all three crystal forms have been determined by X-ray diffraction at resolutions of 2.20 Å (hexagonal), 1.95 Å, (triclinic) and 1.53 Å (tetragonal). The most significant difference observed was the binding of an imidazole molecule to the iron atom of the heme group in the hexagonal structure. This binding displaces the sulfur atom of Met l00, which forms the axial ligand in the triclinic and tetragonal structures.
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  • 8
    Electronic Resource
    Electronic Resource
    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 30 (1997), S. 190-194 
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: This paper demonstrates for the first time a method for preparing cryocooled xenon-derivatized protein crystals. The method is based upon the hypothesis and subsequent observation that the diffusion of a xenon atom from a tight binding site following depressurization occurs on a timescale of minutes. We have observed significant changes in diffraction intensities from myoglobin crystals for up to 5 min following depressurization from 1 MPa of xenon. In accordance with this observation, a xenon-derivatized myoglobin crystal was cryocooled at 9̃5 K within 20 s of complete depressurization. A crystallographic data set was then collected to 2.0 Å resolution and isomorphous and anomalous difference Patterson maps revealed the presence of a well ordered xenon site with an occupancy of approximately 0.5. Phasing statistics for this site were of good quality and demonstrate the practicality of this method. The ability to cryocool xenon-derivatized crystals will make this heavy-atom substitution method even more useful for single-isomorphous-replacement and multiple-isomorphous-replacement phasing of macromolecules.
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  • 9
    Electronic Resource
    Electronic Resource
    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 21 (1988), S. 925-928 
    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.
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  • 10
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: A simple device for studying crystalline samples under moderate gas pressure (0.1–10 MPa) has been developed. The device employs a modified Cajon ultra-torr fitting to ensure a gas-tight seal around an X-ray capillary. The cell accommodates standard X-ray capillaries that require no modification. The device is straightforward to utilize and samples can be mounted with routine techniques and pressurized in a matter of seconds. In a subsequent development, a complete purging and pressurization system has been designed and constructed for use on beamline 7-1 at the Stanford Synchrotron Radiation Laboratory. This paper describes the construction of both the pressure cell and the delivery system and presents results of the use of this cell for the preparation of xenon derivatives to be used in phase determination by the multiple isomorphous replacement method.
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