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Experimental Data
Least Square
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Probability Theory
Protein Structure
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Bayesian Weighting for Macromolecular Crystallographic Refinement
Bayesian Weighting for Macromolecular Crystallographic Refinement,10.1107/S0907444996001473,Acta Crystallographica Section Dbiological Crystallograph
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Bayesian Weighting for Macromolecular Crystallographic Refinement
(
Citations: 2
)
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THOMAS C. TERWILLIGER
,
JOEL BERENDZEN
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 uncertain ties. 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. effect on the accuracies of the refined models. Identical protein structures refined in different laboratories, for example, typically differ by 0.20.3,& r.m.s. (Kuriyan et al., 1986; Daopin, Davies, Schlunegger & Griitter, 1994). We wish to find an approach to atomic refinement that is robust with respect to incompleteness of the working model and that returns the most likely set of model parameters, given the
experimental data
(structure factors) and certain
prior knowledge
about the system (e.g., bond lengths). We shall employ the Bayesian formulation of probability theory, which is eminently suited to this task. We begin by describing the general
statistical approach
and show that, given certain simplifying assumptions, it leads to familiar least squares refinement with a somewhatmodified weighting scheme for the
experimental data
involving the r.m.s. discrepancies between calculated and observed structure factors. We have applied this scheme, termed 'Bayesian weighting', to macromolecular crystallographic model cases involving simulated and measured data and shown that application of the method can yield a model that is considerably more accurate than methods based on uniform weighting or experimental uncertainties alone.
Journal:
Acta Crystallographica Section Dbiological Crystallography  ACTA CRYSTALLOGR DBIOL CRYST
, vol. 52, no. 4, pp. 743748, 1996
DOI:
10.1107/S0907444996001473
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References
(2)
Data Reduction and Error Analysis for the Physical Sciences
(
Citations: 1900
)
P. R. Bevington
,
D. K. Robinson
Published in 1992.
Bayesian inference in statistical analysis
(
Citations: 1612
)
G. E. R Box
,
G. C. Tiao
Published in 1973.
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Citations
(2)
Crystal Structures of MyoglobinLigand Complexes at NearAtomic Resolution
(
Citations: 124
)
Jaroslav Vojtěchovský
,
Kelvin Chu
,
Joel Berendzen
,
Robert M. Sweet
,
Ilme Schlichting
Journal:
Biophysical Journal  BIOPHYS J
, vol. 77, no. 4, pp. 21532174, 1999
Current Methods and Optimization Algorithms for the Refinement of XRay Crystal Structures
(
Citations: 1
)
Juan Francisco Van Der Maelen Uria
Journal:
Crystallography Reviews
, vol. 7, no. 2, pp. 125180, 1999