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A method of combining interactive molecular graphics with restrained least-squares refinement is described. This enables a researcher using the interactive computer graphics terminal to weight the shifts applied to the individual atoms in following cycles of refinement according to the confidence in their positions. The weights are incorporated into the least-squares procedure using the Marquardt factor which was originally introduced to handle the ill-conditioned case [Moss & Morffew (1982). Comput. Chem. 6, 1-3; Marquardt (1963). SIAM J. Appl. Math. 11, 431-441]. The described refinement strategy has been implemented at Birkbeck College, London, and, using avian pancreatic polypeptide (APP) as test data, some refinements have been carried out. In order to compare the results of these refinements, histograms have been drawn that show the distribution of distances between the corresponding atoms in the different models. These histograms show that the model is improved by including the 'confidence' weighting. An improvement of 7.5% was achieved in the mean distance between the corresponding atoms in the fully refined model and a model resulting from four cycles of restrained least squares. When the 'confidence' weighting was included this improvement rose to 14-0%.
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