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Bayesian Weighting for Macromolecular Crystallographic Refinement

Bayesian Weighting for Macromolecular Crystallographic Refinement,10.1107/S0907444996001473,Acta Crystallographica Section D-biological Crystallograph

Bayesian Weighting for Macromolecular Crystallographic Refinement   (Citations: 2)
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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 0.2-0.3,& 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 somewhat-modified 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.
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