An Efficient Lagrangian Relaxation for the Contact Map Overlap Problem
Among the measures for quantifying the similarity between protein 3-D structures, contact map overlap (CMO) maximization deserved sustained attention during past decade. Despite this large involvement, the known algorithms possess a modest performance and are not applicable for large scale comparison.
This paper offers a clear advance in this respect. We present a new integer programming model for CMO and propose an exact B&B algorithm with bounds obtained by a novel Lagrangian relaxation. The efficiency of the approach is demonstrated on a popular small benchmark (Skolnick set, 40 domains). On this set our algorithm significantly outperforms the best existing exact algorithms. Many hard CMO instances have been solved for the first time. To assess furthermore our approach, we constructed a large scale set of 300 protein domains. Computing the similarity measure for any of the 44850 couples, we obtained a classification in excellent agreement with SCOP.
KeywordsProtein structure alignment contact map overlap combinatorial optimization integer programming branch and bound Lagrangian relaxation
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- 5.Goldman, D., Israil, S., Papadimitriu, C.: Algorithmic aspects of protein structure similarity. In: IEEE Symp. Found. Comput. Sci., pp. 512–522 (1999)Google Scholar
- 6.Caprara, A., Lancia, G.: Structural Alignment of Large-Size Protein via Lagrangian Relaxation. In: RECOMB 2002, pp. 100–108 (2002)Google Scholar
- 7.Lancia, G., Istrail, S.: Protein Structure Comparison: Algorithms and Applications. Prot. Str. Anal. Des., 1–33 (2003)Google Scholar
- 11.Garey, M., Johnson, D.: Computers and Intractability: A Guide to the Theory of NP-completness. Freeman and company, New York (1979)Google Scholar
- 12.Crescenzi, P., Kann, V.: A compendium of NP optimization problems, http://www.nada.kth.se/~viggo/problemlist/
- 15.Bauer, M., Klau, G.W., Reinert, K.: Fast and Accurate Structural RNA Alignment by Progressive Lagrangian Optimization. In: R. Berthold, M., Glen, R.C., Diederichs, K., Kohlbacher, O., Fischer, I. (eds.) CompLife 2005. LNCS (LNBI), vol. 3695, pp. 217–228. Springer, Heidelberg (2005)CrossRefGoogle Scholar
- 16.Andonov, R., Balev, S., Yanev, N.: Protein threading: From mathematical models to parallel implementations. INFORMS J. on Comput. 16(4) (2004)Google Scholar
- 19.Andreeva, A., Howorth, D., Chandonia, J.-M., Brenner, S.E., Hubbard, T.J.P., Chothia, C., Murzin, A.G.: Data growth and its impact on the SCOP database: new developments. Nucl. Acid Res (2007)Google Scholar
- 20.Lerman, I.C.: Likelihood linkage analysis (LLA) classification method (Around an example treated by hand). Biochimie, Elsevier Editions 75, 379–397 (1993)Google Scholar