An Eigendecomposition Method for Protein Structure Alignment

Abstract

AbstractThe alignment of two protein structures is a fundamental problem in structural bioinformatics. Their structural similarity carries with it the connotation of similar functional behavior that could be exploited in various applications. In this paper, we model a protein as a polygonal chain of α carbon residues in three dimension and investigate the application of an eigendecomposition method due to Umeyama to the protein structure alignment problem. This method allows us to reduce the structural alignment problem to an approximate weighted graph matching problem.The paper introduces two new algorithms, EDAlign res and EDAlign sse , for pairwise protein structure alignment. E DAlign res identifies the best structural alignment of two equal length proteins by refining the correspondence obtained from eigendecomposition and to maximize similarity measure, TM-score, for the refined correspondence. EDAlign sse , on the other hand, does not require the input proteins to be of equal length. It works in three stages: (1) identifies a correspondence between secondary structure elements (i.e SSE-pairs); (2) identifies a correspondence between residues within SSE-pairs; (3) applies a rigid transformation to report structural alignment in space. The latter two steps are repeated until there is no further improvement in the alignment. We report the TM-score and cRMSD as measures of structural similarity. These new methods are able to report sequence and topology independent alignments, with similarity scores that are comparable to those of the state-of-the-art algorithms such as, TM align and SuperPose.KeywordsRoot Mean Square DeviationRigid TransformationNucleic Acid ResearchPolygonal ChainProtein Structure ComparisonThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.