Evaluation of phase accuracy via topological and geometrical analysis of electron-density maps

An empirical function is developed to measure the protein-like character of electron-density maps. The function is based upon a systematic analysis of numerous local and global map properties or descriptors. Local descriptors measure the occurrence throughout the unit cell of unique patterns on various defined templates, while global descriptors enumerate topological characteristics that define the connectivity and complexity of electron-density isosurfaces. We examine how these quantitative descriptors vary as error is introduced into the phase sets used to generate maps. Informative descriptors are combined in an optimal fashion to arrive at a predictive function. When the topological and geometrical analysis is applied to protein maps generated from phase sets with varying amounts of error, the function is able to estimate changes in average phase error with an accuracy of better than 10 degrees. Additionally, when used to monitor maps generated with experimental phases from different heavy-atom models, the analysis clearly distinguishes between the correct heavy-atom substructure solution and incorrect heavy-atom solutions. The function is also evaluated as a tool to monitor changes in map quality and phase error before and after density-modification procedures.