Bayesian Difference Refinement

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.