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  • 1
    Electronic Resource
    Electronic Resource
    Reliability of maximum likelihood-based figures of merit (2000)
    Springer
    Crystallography reports 45 (2000), S. 195-198 
    Details
    ISSN: 1063-7745
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract Various schemes for determining the maximum likelihood-based figures of merit for phases of structure factors have been considered. It is shown that the use of the likelihood function of all the available structure factors provides the adequate estimates of the accuracy of phases calculated for the atomic models with independent errors in the coordinates, but, at the same time, systematically overestimates the figures of merit for models preliminarily refined in the reciprocal space. It is shown that the use of the marginal likelihood function calculated from the control set of reflections allows the elimination of the systematic bias estimates. A method for reducing the statistical dispersion of the estimates based on a small number of control reflections is suggested.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1134/1.171161
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  • 2
    Electronic Resource
    Electronic Resource
    Improvement of protein phases by coarse model modification (1984)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 40 (1984), S. 269-277 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A procedure is suggested for the refinement of a set of protein phases and for its extension to a higher resolution, which is a development of the approach of Agarwal & Isaacs [Proc. Natl Acad. Sci. USA, (1977), 74, 2835-2839]. A new set of phases is obtained by combining the starting phases with those calculated from a stereochemically non-conditioned coarse 'atomic' model which is automatically constructed and subjected to a least-squares refinement in reciprocal space. The method has been tested with actinidin data generated from atomic coordinates. Starting from the phases calculated to 3 Å resolution and the amplitudes calculated to 2 Å resolution a new set of phases was obtained with a mean error of 31° for 12 713 non-centrosymmetric reflections in the range to 2 Å. The refinement of the phases to 3 Å, resolution for γ-crystallin IIIb from calf lens and its extension to 2.7 Å resolution resulted in a noticeable improvement in the electron density map.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767384000544
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  • 3
    Electronic Resource
    Electronic Resource
    Atomic structure of the Serratia marcescens endonuclease at 1.1 Å resolution and the enzyme reaction mechanism (2000)
    Copenhagen : International Union of Crystallography (IUCr)
    Acta crystallographica 56 (2000), S. 567-572 
    Details
    ISSN: 1399-0047
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The three-dimensional crystal structure of Serratia marcescens endonuclease has been refined at 1.1 Å resolution to an R factor of 12.9% and an Rfree of 15.6% with the use of anisotropic temperature factors. The model contains 3694 non-H atoms, 715 water molecules, four sulfate ions and two Mg2+-binding sites at the active sites of the homodimeric protein. It is shown that the magnesium ion linked to the active-site Asn119 of each monomer is surrounded by five water molecules and shows an octahedral coordination geometry. The temperature factors for the bound Mg2+ ions in the A and B subunits are 7.08 and 4.60 Å2, respectively, and the average temperature factors for the surrounding water molecules are 12.13 and 10.3 Å2, respectively. In comparison with earlier structures, alternative side-chain conformations are defined for 51 residues of the dimer, including the essential active-site residue Arg57. A plausible mechanism of enzyme function is proposed based on the high-resolution S. marcescens nuclease structure, the functional characteristics of the natural and mutational forms of the enzyme and consideration of its structural analogy with homing endonuclease I-PpoI.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S090744490000322X
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  • 4
    Electronic Resource
    Electronic Resource
    Program construction for macromolecule atomic model refinement based on the fast Fourier transform and fast differentiation algorithms; erratum (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 57-57 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: In Lunin & Urzhumtsev [Acta Cryst. (1985), A41, 327-333] references to Lifshitz (Agarwal, 1981) on pages 327 and 329 should be amended to Lifchitz (Agarwal, 1981).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767386099889
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  • 5
    Electronic Resource
    Electronic Resource
    Electron-denisty histograms and the phase problem (1993)
    Copenhagen : International Union of Crystallography (IUCr)
    Acta crystallographica 49 (1993), S. 90-99 
    Details
    ISSN: 1399-0047
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The specific properties of the range of possible electron-density values may serve as useful additional information for the determination and refinement of structure-factor phases. Fourier synthesis histograms (showing the spectra of frequencies of different possible values) produce the most adequate representation of these properties. The mathematical background and practical uses of these histograms are discussed. The investigation provides new information on some traditional methods of phase refinement, including density-modification procedures, maximization of Cochran's integral value and other techniques.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0907444992009247
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  • 6
    Electronic Resource
    Electronic Resource
    Program construction for macromolecule atomic model refinement based on the fast Fourier transform and fast differentiation algorithms (1985)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 41 (1985), S. 327-333 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Structure refinement may be considered as a minimization of a function R(χ) of a large number of refineable parameters. A new type of function incorporating phase probability distribution is proposed. The minimization of the function utilizing gradient methods requires the computation of gradient ∇R, as well as the product of the gradient and the matrix of second derivatives with some direction. The algorithm of Kim, Nesterov & Cherkassky [Dokl. Akad. Nauk SSSR (1984), 275, 1306-1309] adapted to macromolecular structure refinement takes about four times longer for the computation of these values compared to the computation of the value of the minimized function. The matrix of second derivatives is used without any approximation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S010876738500071X
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  • 7
    Electronic Resource
    Electronic Resource
    Use of the information on electron density distribution in macromolecules (1988)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 44 (1988), S. 144-150 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A new type of information on the distribution of electron density in crystals of biological macromolecules is proposed. This is a quasihistogram of the image of the function of electron density distribution at a finite resolution. It is shown how this information should be used to restore the values of low-angle structure factors whose amplitudes have not been measured during X-ray experiments.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767387009784
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  • 8
    Electronic Resource
    Electronic Resource
    Bounding a molecule in a noisy synthesis (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 34-39 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A method of bounding a protein molecule in a very noisy synthesis is considered. It consists of two steps. In the first step ('nonlinear filtration') basic points are chosen that are most likely to belong to the region of the molecule. In the second step ('linear filtration') a compact region with the maximal concentration of these points is searched. Various modifications of the method are analysed. It is shown that the molecular region in a finite-resolution synthesis contains not only the highest positive maxima of the density distribution but also the deepest negative minima.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767388008955
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  • 9
    Electronic Resource
    Electronic Resource
    Mean phase error and the map-correlation coefficient (1993)
    Copenhagen : International Union of Crystallography (IUCr)
    Acta crystallographica 49 (1993), S. 530-533 
    Details
    ISSN: 1399-0047
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: In judging the effectiveness of methods of solving crystal structures, or in phase refinement and development, two criteria are commonly used. The first is the mean phase error, which may be weighted in some way, and the second is the map correlation coefficient which describes the similarity of a map with estimated phases to that with true phases. It is shown that these two measures are directly related and that given the individual phase errors the map correlation coefficient may be found without the need to calculate a map. Various aspects of this connection are examined, including the map correlation coefficient when weights are used for calculating maps and the conditions under which phase extension leads to maps with a higher map correlation coefficient – which involves a balance between the advantage of employing more data and the disadvantage that the extra data may have a higher average phase error.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0907444993005852
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  • 10
    Electronic Resource
    Electronic Resource
    Phase improvement in protein crystallography using a mixed electron density model (1985)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 41 (1985), S. 166-171 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The proposed technique for phase improvement is based on the refinement of a so-called mixed electron density model. This model consists of two parts. The first is a partial stereochemically correct atomic model of the protein molecule related to the interpreted part of electron density of the unit cell. The second is an artificial atomic model describing the uninterpreted part of the residual electron density of the unit cell. The conventional free-atom crystallographic refinement of such a mixed model results in phase improvement. No attention is paid to the structural sense of the refined atomic positions of the mixed electron density model. This method of phase improvement has been applied for eye lens protein γ-crystallin IIIb at 2.7 Å resolution. A starting partial model of the molecule contained about 56% of the total number of residues. Phase refinement is done in two stages. Each stage leads to a significant increase in the quality of the electron density map, so that the partial atomic model of the protein molecule can be improved and expanded.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767385000332
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