Abstract
BackgroundOwing to rapid expansion of protein structure databases in recent years, methods of structure comparison are becoming increasingly effective and important in revealing novel information on functional properties of proteins and their roles in the grand scheme of evolutionary biology. Currently, the structural similarity between two proteins is measured by the root-mean-square-deviation (RMSD) in their best-superimposed atomic coordinates. RMSD is the golden rule of measuring structural similarity when the structures are nearly identical; it, however, fails to detect the higher order topological similarities in proteins evolved into different shapes. We propose new algorithms for extracting geometrical invariants of proteins that can be effectively used to identify homologous protein structures or topologies in order to quantify both close and remote structural similarities.ResultsWe measure structural similarity between proteins by correlating the principle components of their secondary structure interaction matrix. In our approach, the Principle Component Correlation (PCC) analysis, a symmetric interaction matrix for a protein structure is constructed with relationship parameters between secondary elements that can take the form of distance, orientation, or other relevant structural invariants. When using a distance-based construction in the presence or absence of encoded N to C terminal sense, there are strong correlations between the principle components of interaction matrices of structurally or topologically similar proteins.ConclusionThe PCC method is extensively tested for protein structures that belong to the same topological class but are significantly different by RMSD measure. The PCC analysis can also differentiate proteins having similar shapes but different topological arrangements. Additionally, we demonstrate that when using two independently defined interaction matrices, comparison of their maximum eigenvalues can be highly effective in clustering structurally or topologically similar proteins. We believe that the PCC analysis of interaction matrix is highly flexible in adopting various structural parameters for protein structure comparison.
Highlights
Owing to rapid expansion of protein structure databases in recent years, methods of structure comparison are becoming increasingly effective and important in revealing novel information on functional properties of proteins and their roles in the grand scheme of evolutionary biology
We measure structural similarity between proteins by correlating the principle components of their secondary structure interaction matrix. In this method, referred here as the principle component correlation (PCC) analysis, the symmetric matrix for an individual protein is constructed with relationship parameters between secondary elements that can take the form of distance, orientation, or other relevant structural invariants
The atomic coordinates were retrieved from protein structure database (PDB) with accession codes 1A4F, 1A6G, 1COL (A), 1DDB (A), 1F16 (A), 1G5M (A), 1GJH (A), 1MAZ, 1MDT (A), and 2BID (A), where (A) means chain A
Summary
Owing to rapid expansion of protein structure databases in recent years, methods of structure comparison are becoming increasingly effective and important in revealing novel information on functional properties of proteins and their roles in the grand scheme of evolutionary biology. We propose new algorithms for extracting geometrical invariants of proteins that can be effectively used to identify homologous protein structures or topologies in order to quantify both close and remote structural similarities. Large sets of protein structures are accumulated in the public domain databases for which we know little about their biological roles. This shortfall calls for the development of cost-effective computational methods to predict protein function based on three-dimensional structures, with the aim of providing preliminary information to guide biological experiments later
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