The interpretation of protein structures based on graph theory and contact map
Mahnaz Habibi1, Changiz Eslahchi1, Mehdi Sadeghi2, Hamid Pezashk3,4,5
1Faculty of Mathematics, Shahid-Beheshti University, GC, Tehran, Iran; 2National Institute of Genetic Engineering and Biotechnology, Tehran, Iran; 3School of Mathematics, Statistics and Computer Sciences, College of Science, University of Tehran, Tehran, Iran; 4Center of Excellence in Biomathematics, College of Science, University of Tehran, Tehran, Iran; 5Bioinformatics Group, School of Computer Science, IPM, Tehran, Iran
Purpose: The analysis of a protein’s structure allowing detailed exploration of the protein’s biological function is one of the most challenging problems in bioinformatics. There are efficient algorithms to calculate main properties of a protein structure, such as packing density, buried or surface residues, and accessible surface area. But these algorithms need the three-dimensional (3D) coordinates of the proteins.
Methods: We used the contact map of a protein to construct a graph. By considering several features of the corresponding graph, we proposed some algorithms to discuss the above-mentioned properties of a protein. We also introduced a new measure for the hydrophobicity of an amino acid by defining an average degree for the amino acid as a vertex on the graph.
Results: We compared our results with those obtained by some other existing algorithms. We found strong correlations between the popular methods, which use 3D coordinates, and our methods, which only use a predicted contact map.
Conclusion: Many features of a protein can be predicted without having 3D coordinates, based on the contact map of the protein. The programs are freely available from http://www.bioinf.cs.ipm.ir/softwares/asa/asa.rar.
Keywords: accessible surface area, buried residue, surface residue, packing density, hydrophobic
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