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  • 1
    Electronic Resource
    Electronic Resource
    Improving Crystallographic Macromolecular Images: The Real-Space Approach (1987)
    Palo Alto, Calif. : Annual Reviews
    Annual Review of Biophysics and Biomolecular Structure 16 (1987), S. 351-373 
    Details
    ISSN: 0084-6589
    Source: Annual Reviews Electronic Back Volume Collection 1932-2001ff
    Topics: Biology , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1146/annurev.bb.16.060187.002031
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  • 2
    Electronic Resource
    Electronic Resource
    Programs for translation searches with two independent models simultaneously (1994)
    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 27 (1994), S. 122-124 
    Details
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: Programs to carry out translation searches for the molecular replacement method using two independent models simultaneously have been developed. Both correlation-coefficient distributions and packing functions can be calculated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0021889893005849
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  • 3
    Electronic Resource
    Electronic Resource
    Improving and extending the phases of medium- and low-resolution macromolecular structure factors by density modification (1981)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 37 (1981), S. 669-677 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Non-negativity of the electron density function and constancy of the solvent regions were exploited to improve 2633 phases of crystalline yeast tRNAfMet (P6422, a = 115.3, c = 137.9 Å, z = 12), which had been obtained by multiple isomorphous replacement (MIR) in the resolution zone 14-4.5 Å. Phases were also determined for an additional 912 reflections not previously phased by MIR from the resolution range 100 to 4 Å, the very limits of the diffraction pattern. An iterative procedure was employed in which phases for each cycle were calculated from a density map modified by imposing the above constraints and were combined with the observed amplitudes to produce a new and improved map. Initially phases calculated in each cycle were merged with the original MIR phase probability curve; convergence was achieved in seven cycles. The phases were then released from the MIR analysis by using just the calculated phases until a second convergence was achieved (four cycles). The average difference between the experimental phases and phases calculated from the refined coordinates was reduced from 68° for the original MIR analysis to 43° by the use of these real-space direct methods. Phases determined solely by density modification were as accurate as the original MIR phase set. The map calculated with improved and extended phases was dramatically superior to the MIR map and even approached in quality the map produced with phases calculated from the refined molecular coordinates.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0567739481001526
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  • 4
    Electronic Resource
    Electronic Resource
    A new determinantal theory for solving the phase problem using stereochemical information (1982)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 38 (1982), S. 401-407 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A priori structural information is incorporated into determinantal phasing techniques to improve phase prediction accuracy in resolution ranges where atomic or isotropic group-scatterer assumptions are not valid. For this purpose a conditional joint probability distribution to triplet order for any set of normalized structure factors of space groups P1 and P\bar 1 is derived. The covariance of two normalized structure factors from the original set is calculated. A more general conditional joint probability distribution, involving covariance matrices of any order, is further derived. Numerical tests are performed employing ideal models consisting of several atomic groups of known stereochemistry but with random positions and orientations. The results indicate that the inclusion of stereochemical information improves the accuracy of phase prediction. The relative merit of this strategy in either one of or both normalization and covariance calculations for different resolutions is discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0567739482000928
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  • 5
    Electronic Resource
    Electronic Resource
    Approaches to Very Low Resolution Phasing of the Ribosome 50S Particle from Thermus thermophilus by the Few-Atoms-Models and Molecular-Replacement Methods (1996)
    Copenhagen : International Union of Crystallography (IUCr)
    Acta crystallographica 52 (1996), S. 1092-1097 
    Details
    ISSN: 1399-0047
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Estimates for the phases of the X-ray diffraction data from the 50S ribosomal particle of Thermus thermophilus has been made to an effective resolution around 80 Å using the few-atoms-modes ab initio technique [Lunin, Lunina, Petrova, Vernoslova, Urzhumtsev & Podjarny (1995). Acta Cryst. D51, 896–903]. This technique models the density with a small number of Gaussian spheres to generate a large number of possible phase sets and then uses clustering algorithms to identify the best ones. Independently, an envelope obtained from electron-micrograph image reconstruction [Yonath, Leonard & Wittmann (1987). Science, 236, 813–816] was oriented and positioned using the molecular-replacement technique, specially adapted to the very low resolution case [Urzhumtsev & Podjarny (1995). Acta Cryst. D51, 888–895]. The two methods show similar packing arrangements.The electron density calculated by the few-atoms-models technique without any assumption on the number of molecules in asymmetric unit or on their shape shows recognizable features of the particle.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0907444996005537
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  • 6
    Electronic Resource
    Electronic Resource
    On the Ab Initio Solution of the Phase Problem for Macromolecules at Very Low Resolution. II. Generalized Likelihood Based Approach to Cluster Discrimination (1998)
    Copenhagen : International Union of Crystallography (IUCr)
    Acta crystallographica 54 (1998), S. 726-734 
    Details
    ISSN: 1399-0047
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The multisolution strategies for direct phasing at very low resolution, such as the few atoms model technique, result in a number of alternative phase sets, each of them arising from a cluster of closely related models. Use of a Monte-Carlo type computer procedure is suggested to choose between the possible phase sets. It consists of generating a large number of pseudo-atom models inside the mask defined by a trial phase set and the use of histograms of magnitude correlation to evaluate the masks. It is shown that the procedure may be considered as a generalization of the statistical maximum-likelihood principle and may be used as a powerful supplementary tool in the likelihood-based approaches to the phase problem solution.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0907444997012456
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  • 7
    Electronic Resource
    Electronic Resource
    A multivariate joint probability for phase determination (1973)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 29 (1973), S. 609-615 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A multivariate conditional joint probability distribution of a set of K normalized structure factors has been developed using a novel approach. The covariance matrix of the distribution is calculated for all the space groups in terms of linear combinations of specific unitary structure factors. It is shown that if any number of off-diagonal elements are set arbitrarily to zero, an approximation is obtained to the covariance matrix which corresponds to a particular set of a priori conditions. The importance of this result in practical phase-determining methods is pointed out. Group theory is used to obtain results valid for all space groups. The multivariate distribution is used to calculate more general versions of the Cochran and Woolfson sign probability and the Karle and Hauptman tangent formulae.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0567739473001579
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  • 8
    Electronic Resource
    Electronic Resource
    Phasing low-resolution macromolecular structure factors by matricial direct methods (1981)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 37 (1981), S. 662-668 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Matricial direct methods were used to phase 28 strong low-resolution (100-19 Å) structure factors of crystalline yeast tRNAfMet (P6422, z = 12) which had not been phased by multiple isomorphous replacement (MIR). The starting phase set was composed of 107 terms in the resolution range 32-14 Å which had been phased by MIR. Extending the phase set to the strong low-resolution terms significantly improved the electron-density map. The goal of establishing a well defined molecular boundary was clearly achieved and provided the basis of a successful structure determination to 4.0 Å resolution. The phases determined by direct methods deviated from the phases subsequently calculated from the refined atomic coordinates by an unweighted average value of 73°; 36% of these were determined with a figure of merit greater than 0.75 and showed a discrepancy of only 44°. The accuracy of the phases determined by matricial methods compared favorably with those of the starting MIR phase set. An analysis of the resolution dependence of the intensities suggests plausible substructures as the basis of the normalization leading to the successful extension of phases to very low resolution.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0567739481001514
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  • 9
    Electronic Resource
    Electronic Resource
    Ab initio low-resolution phasing in crystallography of macromolecules by maximization of likelihood (2000)
    Copenhagen : International Union of Crystallography (IUCr)
    Acta crystallographica 56 (2000), S. 1245-1252 
    Details
    ISSN: 1399-0047
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Statistical likelihood criteria were tested to select the true (or closest to true) structure-factor phases from an ensemble of phase sets. To define the criterion value for a given trial phase set, the trial `molecular region' is defined as a region consisting of the points with the highest values in the Fourier synthesis calculated with the observed magnitudes and the trial set of phases. The structure studied is considered as composed of atoms randomly placed inside the trial molecular region. The figure of merit is defined as the likelihood corresponding to this hypothesis, i.e. the probability that the structure-factor magnitudes calculated (from the positions of atoms randomly placed into the trial region) are equal to the observed magnitudes. The concept of generalized likelihood is introduced to make the calculations more straightforward. The tests performed for known structures with the use of experimentally observed magnitudes show that in general it is impossible to unambiguously determine the best phases among a `population' of trial phase sets. Nevertheless, the random generation of a great number of phase sets and the selection of phase sets with high likelihood values give a collection of variants with a higher concentration of `good' phase sets than those found in the original population. Averaging the selected phase sets gives a starting solution of the low-resolution phase problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0907444900009343
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  • 10
    Electronic Resource
    Electronic Resource
    On the ab initio solution of the phase problem for macromolecules at very low resolution: the few atoms model method (1995)
    Copenhagen : International Union of Crystallography (IUCr)
    Acta crystallographica 51 (1995), S. 896-903 
    Details
    ISSN: 1399-0047
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A method is proposed for the solution of the phase problem at very low resolution for macromolecules. It generates randomly a very large number of models, each consisting of a few (two to ten) pseudo-atoms. The corresponding amplitudes are used for selecting a subset of `best' models by choosing those with the highest correlation with experimental values. The phases calculated from these `best' models are analysed by a clusterization procedure leading to a few possible solutions, from which the correct one can be recognized by simple additional criteria. This method has been successfully applied to the neutron diffraction data of the AspRS–tRNAAsp complex at 50 Å resolution and to data calculated from a model ribosome crystal at 60 Å resolution.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0907444995005075
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