An efficient multiple protein structure comparison method and its application to structure clustering and outlier detection

Despite many years of research, comparing multiple protein structures simultaneously (multiple structure comparison) is still a challenging problem. Most of the previous studies have focused on similarities among subsets of residues (or atoms) from a group of proteins (local structure alignment) by minimizing some similarity scores based on root mean square deviation (RMSD) of the aligned residues. In this paper, we designed a novel mathematical and statistical framework for multiple global structure comparison (MGSC). Under this framework, a formal geodesic distance is defined for any pair of protein structures and a mean structure can be estimated for a group of protein structures. The multiple structure comparison is then conveniently performed by comparing each individual structure with the mean structure. The formal distance facilitates consistent and accurate clustering of protein structures. An efficient clustering algorithm was designed based on the developed method. Probability models can be built for groups of protein structures and used in hypothesis testing. A robust outlier detection algorithm was designed to illustrate the potential applications of the framework.