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  • 1
    Electronic Resource
    Electronic Resource
    s.l. : American Chemical Society
    Analytical chemistry 28 (1956), S. 1045-1046 
    ISSN: 1520-6882
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    s.l. : American Chemical Society
    Analytical chemistry 23 (1951), S. 826-830 
    ISSN: 1520-6882
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 37 (1981), S. 548-552 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A new relationship between products of two structure factors with coefficients calculated as the Fourier transform of a modified Patterson function is presented. The relation is alternatively expressed in terms of triple phase invariants and also a new weighted form of Sayre's equation [Sayre (1952). Acta Cryst. 5, 60-65] emerges as a special case. The advantages of the new equations with respect to Sayre's equation are discussed and, with simple one-dimensional models, examples of direct calculation of the cosines of triple-phase invariants are included.
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  • 4
    Electronic Resource
    Electronic Resource
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 41 (1985), S. 286-290 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The application of the condition that a true set of phases for a substantial subset of normalized structure factors should satisfy Sayre's equation leads to a phase-refining equation called the Sayre tangent formula. Phases refined by this formula tend to satisfy Sayre's equation for a subset of E's containing some of large magnitude and some of small (ideally zero) magnitude. Trials indicate that the new formula, incorporated into a computer program SAYTAN, is more effective than MULTAN80, especially for symmorphic structures.
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  • 5
    Electronic Resource
    Electronic Resource
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 44 (1988), S. 353-357 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The Sayre-equation tangent formula (SETF) develops sets of phases tending to satisfy Sayre's equations for both large and small normalized structure factors. There are two components in the SETF, corresponding to contributions from phase triplets and quartets respectively. The development of objective algorithms for properly weighting these components and for gradually building up the quartet contribution has enabled the SETF, within the procedure SAYTAN, to be incorporated into MULTAN87, the latest version of the package. Examples of tests of MULTAN87 and its use in solving unknown structures are given.
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  • 6
    Electronic Resource
    Electronic Resource
    Copenhagen : International Union of Crystallography (IUCr)
    Acta crystallographica 52 (1996), S. 252-256 
    ISSN: 1399-0047
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: In the conventional histogram-matching technique for phase extension and refinement for proteins a simple one-to-one transformation is made in the protein region to modify calculated density so that it will have some target histogram in addition to solvent flattening. This work describes an investigation where the density modification takes into account not only the current calculated density at a grid point but also some characteristic of the environment of the grid point within some distance R. This characteristic can be one of the local maximum density, the local minimum density or the local variance of density. The grid points are divided into ten groups, each containing the same number of grid points, for ten different ranges of value of the local characteristic. The ten groups are modified to give different histograms, each corresponding to that obtained under the same circumstances from a structure similar to the one under investigation. This process is referred to as the double-histogram matching method. Other processes which have been investigated are the weighting of structure factors when calculating maps with estimated phases and also the use of a factor to dampen the change of density and so control the refinement process. Two protein structures were used in numerical trials, RNApl [Bezborodova, Ermekbaeva, Shlyapnikov, Polyakov & Bezborodov (1988). Biokhimiya, 53, 965–973] and 2-Zn insulin [Baker, Blundell, Cutfield, Cutfield, Dodson, Dodson, Hodgkin, Hubbard, lsaacs, Reynolds, Sakabe, Sakabe & Vijayan (1988). Philos. Trans. R. Soc. London Ser. B, 319, 456--469]. Comparison of the proposed procedures with the normal histogram-matching technique without structure-factor weighting or damping gives mean phase errors reduced by up to 10° with map correlation coefficients improved by as much as 0.14. Compared to the normal histogram used with weighting of structure factors and damping, the improvement due to the use of the double-histogram method is usually of order 4° in mean phase error and an increase of 0.06–0.08 in the map correlation coefficient. It is concluded that the most reliable results are found with the local-maximum condition and with R in the range 0.5–0.6 Å.
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  • 7
    Electronic Resource
    Electronic Resource
    Copenhagen : International Union of Crystallography (IUCr)
    Acta crystallographica 52 (1996), S. 1119-1124 
    ISSN: 1399-0047
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Several techniques for extending and refining phases for macromolecular structures have been incorporated into a program package PERP. In addition to previously employed techniques such as solvent flattening and histogram matching, PERP includes a new way of applying the Sayre equation [Refaat, Tate & Woolfson (1995). Acta Cryst. D51, 1036–1040], low-density elimination [Shiono & Woolfson (1992). Acta Cryst. A48, 451–456] and two double-histogram methods [Refaat, Tate & Woolfson (1996). Acta Cryst. D52, 252–256]. PERP is an easy-to-use package controlled by keywords and provided with default parameters that usually give near-optimum results. Examples are given of refinement, and also extension and refinement, for six known protein structures with a variety of characteristics. In each case PERP gives a very satisfactory outcome as measured by improvements in the mean-phase-error and conventional map-correlation coefficient. The main conclusion is that the several methods used in sequence give more effective extension and refinement than using any single method alone.
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    Copenhagen : International Union of Crystallography (IUCr)
    Acta crystallographica 51 (1995), S. 1036-1040 
    ISSN: 1399-0047
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: An algorithm is described for refining a set of phases to agree with the Sayre equation. All operations are carried out using Fourier transforms with modest computer-store requirements even for very large systems. The procedure is tested with two moderate-sized proteins, one containing heavy atoms, and is found to give good refinement with data at more than atomic resolution (1.17 Å) and useful, if less good, refinement when the data resolution is lower (1.5 Å). It is concluded that at atomic resolution, or slightly below, the Sayre equation still has something to offer both for phase refinement and phase extension, especially if used cautiously with weighted multiple isomorphous replacement phases acting as a constraint on the phase changes. Even when the Sayre equation on its own refines phases badly, or not at all, it may still make an important contribution in conjunction with other real-space refinement procedures.
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  • 9
    Electronic Resource
    Electronic Resource
    Amsterdam : Elsevier
    Biochimica et Biophysica Acta (BBA)/Biomembranes 551 (1989), S. 382-388 
    ISSN: 0005-2736
    Keywords: (Sarcoplasmic reticulum) ; ATP effects ; Ca^2^+ release ; Chelometric dyes
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Biology , Chemistry and Pharmacology , Medicine , Physics
    Type of Medium: Electronic Resource
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  • 10
    Electronic Resource
    Electronic Resource
    Amsterdam : Elsevier
    Computer Physics Communications 35 (1984), S. C-13 
    ISSN: 0010-4655
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Computer Science , Physics
    Type of Medium: Electronic Resource
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