Maximum Cliques in Protein Structure Comparison
Computing the similarity between two protein structures is a crucial task in molecular biology, and has been extensively investigated. Many protein structure comparison methods can be modeled as maximum clique problems in specific k-partite graphs, referred here as alignment graphs. In this paper, we propose a new protein structure comparison method based on internal distances (DAST), which main characteristic is that it generates alignments having RMSD smaller than any previously given threshold. DAST is posed as a maximum clique problem in an alignment graph, and in order to compute DAST’s alignments, we also design an algorithm (ACF) for solving such maximum clique problems. We compare ACF with one of the fastest clique finder, recently conceived by Östergȧrd. On a popular benchmark (the Skolnick set) we observe that ACF is about 20 times faster in average than the Östergȧrd’s algorithm. We then successfully use DAST’s alignments to obtain automatic classification in very good agreement with SCOP.
Keywordsprotein structure comparison maximum clique problem k-partite graphs combinatorial optimization branch and bound
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- 1.Godzik, A.: The structural alignment between two proteins: Is there a unique answer? Protein Science (7), 1325–1338 (1996)Google Scholar
- 2.Sierk, M., Kleywegt, G.: Déjà vu all over again: Finding and analyzing protein structure similarities. Structure 12(12), 2103–2111 (2004)Google Scholar
- 3.Konc, J., Janezic, D.: An efficient branch-and-bound algorithm for finding a maximum clique. Discrete Mathematics and Theoretical Computer Science 58, 220 (2003)Google Scholar
- 4.Tomita, E., Seki, T.: An improved branch and bound algorithm for the maximum clique problem. Communications in Mathematical and in Computer Chemistry / MATCH 58, 569–590 (2007)Google Scholar
- 8.Karp, R.: Reducibility among combinatorial problems. Complexity of Computer Computations 6, 85–103 (1972)Google Scholar
- 9.Bomze, I., Budinich, M., Pardalos, P., Pelillo, M.: The maximum clique problem. Handbook of Combinatorial Optimization (1999)Google Scholar
- 11.Godzik, A., Skolnick, J.: Flexible algorithm for direct multiple alignment of protein structures and sequences. CABIOS 10, 587–596 (1994)Google Scholar
- 16.Lancia, G., Carr, R., Walenz, B., Istrail, S.: 101 optimal pdb structure alignments: a branch-and-cut algorithm for the maximum contact map overlap problem. In: RECOMB 2001: Proceedings of the fifth annual international conference on Computational biology, pp. 193–202 (2001)Google Scholar