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  • 1
    Electronic Resource
    Electronic Resource
    Copenhagen : International Union of Crystallography (IUCr)
    Acta crystallographica 52 (1996), S. 743-748 
    ISSN: 1399-0047
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A simple weighting scheme for atomic refinement is discussed. The approach, called `Bayesian weighting', is designed to be robust with respect to the bias that arises from the incomplete nature of the atomic model, which in macromolecular crystallography is typically quite serious. Bayesian weights are based on the mean-squared residual errors over shells of resolution, with centric and acentric reflections considered separately and with allowances made for experimental uncertainties. Use of Bayesian weighting is shown in test cases typical for macromolecular crystallography to improve the accuracy of the refined coordinates when compared with schemes employing unit weights or experimental variances.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Copenhagen : International Union of Crystallography (IUCr)
    Acta crystallographica 52 (1996), S. 1004-1011 
    ISSN: 1399-0047
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Interest in a pair of highly isomorphous structures often focuses on the differences between them. In cases where substantial correlated model errors exist or where there are differences in the quality of the two experimental data sets (cases quite common in macromolecular crystallography), independent refinement of the two structures does not lead to the most accurate estimate of the differences between them. An alternative procedure that has proven effective in some such cases is difference refinement, in which the residual between observed and calculated differences in structure-factor amplitudes between the two structures is minimized. A Bayesian approach has been used to extend the range of applicability of difference refinement to cases where there is only partial correlation in model errors and where the overlap between the data sets is limited. The resulting method, Bayesian difference refinement, uses residuals to be minimized that vary smoothly between difference refinement and independent refinement. When the errors in the two structural models are very similar, difference refinement is used; when they are very different, independent refinement is used; and when they are partially correlated, a combination of the two is used. The procedure is very simple to apply and does not significantly increase the computational demands of refinement.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Copenhagen : International Union of Crystallography (IUCr)
    Acta crystallographica 53 (1997), S. 571-579 
    ISSN: 1399-0047
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A Bayesian treatment for phase calculation in the multiwavelength anomalous diffraction (MAD) technique is presented. This approach explicitly treats effects of errors correlated among measurements at different wavelengths and between Bijvoet pairs. The resulting method, which is called Bayesian correlated MAD phasing, gives proper statistical consideration to all data and does not give special treatment to data from a particular wavelength. Results obtained using Bayesian correlated MAD phasing and two other strategies on both a model test case and on data obtained in two actual MAD experiments are compared. Although all procedures performed well when the completeness of the data was high, it is shown that Bayesian correlated MAD phasing is more robust with respect to incompleteness of data than the other methods are. At 60% completeness the improvement over other methods for the examples given was nearly 50% in the correlation coefficients, and made a substantial difference in the interpretability of an electron-density map.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Copenhagen : International Union of Crystallography (IUCr)
    Acta crystallographica 52 (1996), S. 749-757 
    ISSN: 1399-0047
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Substantial highly correlated differences sometimes exist between a series of heavy-atom derivatives of a macromolecule and the native structure. Use of such a series of derivatives for phase determination by multiple isomorphous replacement (MIR) has been difficult because MIR analysis has treated errors as independent. A simple Bayesian approach has been used to derive probability distributions for the phase in the case where a group of MIR derivatives have correlated errors. The utility of the resulting `correlated-phasing' method has been examined by applying it to both simulated and real MIR data sets that contain sizeable correlated errors and it has been found that it can dramatically improve MIR phase estimates in these cases. Correlated phasing is applicable to situations where derivatives exhibit substantial correlated changes in protein conformation or crystal packing or where correlated errors in heavy-atom models are large. Correlated phasing does not substantially increase the complexity of phase computation and is suitable for routine use.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Copenhagen : International Union of Crystallography (IUCr)
    Acta crystallographica 51 (1995), S. 609-618 
    ISSN: 1399-0047
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: There are many examples in macromolecular crystallography where interest focuses on the differences between a previously determined `native' structure and a nearly isomorphous `variant'. In such cases, a useful approach to atomic refinement of the variant structure is through weighted least-squares minimization of the residual between the observed and calculated differences in amplitudes of structure factors, a strategy first used in the refinement of deoxycobalt hemoglobin [Fermi, Perutz, Dickinson & Chien (1982). J. Mol. Biol. 155, 495–505] and termed `difference refinement'. For cases in which the modeling errors for the native and variant structures are correlated, theoretical arguments indicate that difference refinement should lead to improved estimates of structural differences when compared with conventional independent refinement. Tests employing simulated peptide data sets and real data from a wild-type protein and a mutant show that difference refinement can substantially reduce errors in the differences between structures when compared with independent refinement. The algorithm is very easy to implement and does not increase the computational demands of refinement.
    Type of Medium: Electronic Resource
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  • 6
    ISSN: 0301-4622
    Keywords: CO stretching band ; Conformational substate hierarchy ; Control mechanism ; Myoglobin ; Protein dynamics ; Protein relaxation
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Biology , Chemistry and Pharmacology , Physics
    Type of Medium: Electronic Resource
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