Making use of coordinate uncertainties in structure comparison
Thomas R. Schneider · Acta Crystallographica Section A Foundations of Crystallography · 2006
The comparison of similar structures is a central step in extracting biological information from structural models. As structural data become available at an ever increasing rate, the set of ’similar structures’ to be taken into account for a specific problem can easily contain tens or hundreds of models. For such a situation, the classical approach of pair wise superposition using the root-mean-square-deviation (r.m.s.d.) between superimposed atoms as the central criterion for similarity is clearly inadequate. We suggest to use the fraction of distances that remain identical within experimental uncertainty in an ensemble as a new criterion for structural similarity. We define a conformational similarity index ’C.S.I.’ as C.S.I. = nid / nall (where nid and nall are the number of equivalent distances that are identical within error and the total number of equivalent distances, respectively). The C.S.I. can be used (1) to evaluate the overall similarity of groups of structures and (2) as a criterion to find subsets of atoms that are similar within experimental uncertainty. In our current implementation of a C.S.I.-based framework for structure analysis, we use Cruickshank’s DPI [1] plus a B-factor based scaling [2] to estimate the coordinate uncertainties of individual atoms. The C.S.I. can be calculated by comparing all CA-CA distances in different models and then used to drive the clustering of models into groups containing models that are identical within error. From these groups, representative models are chosen and analysed further in terms of subsets of atoms leading to a description of a protein in terms of rigid bodies and flexible regions. We demonstrate the approach by analysing the ensemble consisting of crystal structures of protein kinase A as available from the protein data bank. This ensemble contains more than 40 models of the enzyme crystallized in different space groups, with different ligands etc. and shows estimatedmean coordinate uncertainties ranging from less than 0.05 A tomore than 0.5 A. The clustering of the models followed by the analysis in terms of rigid bodies divides the protein into the two known domains and provides an objective basis for optimum superposition and further detailed analysis. A computer program implementing the ideas presented is available from http://schneider.group.ifom-ieo-campus.it/escet.