Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Gibrat, J.-F., Madej, T., Bryant, S.H.: Surprising similarities in structure comparison. Curr. Opin. Struct. Biol. 6, 377–385 (1996)
Caprara, A., Carr, R., Israil, S., Lancia, G., Walenz, B.: 1001 Optimal PDB Structure Alignments: Integer Programming Methods for Finding the Maximum Contact Map Overlap. J. Comput. Biol. 11(1), 27–52 (2004)
Halperin, I., Ma, B., Wolfson, H., et al.: Principles of docking: An overview of search algorithms and a guide to scoring functions. Proteins Struct. Funct. Genet. 47, 409–443 (2002)
Godzik, A.: The Structural alignment between two proteins: is there a unique answer? Protein Science 5, 1325–1338 (1996)
Goldman, D., Israil, S., Papadimitriu, C.: Algorithmic aspects of protein structure similarity. In: IEEE Symp. Found. Comput. Sci., pp. 512–522 (1999)
Caprara, A., Lancia, G.: Structural Alignment of Large-Size Protein via Lagrangian Relaxation. In: RECOMB 2002, pp. 100–108 (2002)
Lancia, G., Istrail, S.: Protein Structure Comparison: Algorithms and Applications. Prot. Str. Anal. Des., 1–33 (2003)
Carr, R., Lancia, G.: Compact optimization can outperform separation: A case study in structural proteomics. 4OR 2, 221–233 (2004)
Agarwal, P.K., Mustafa, N.H., Wang, Y.: Fast Molecular Shape Matching Using Contact Maps. J. Comput. Biol. 14(2), 131–147 (2007)
Xu, J., Jiao, F., Berger, B.: A parametrized Algorithm for Protein Structure Alignment. In: Apostolico, A., Guerra, C., Istrail, S., Pevzner, P.A., Waterman, M. (eds.) RECOMB 2006. LNCS (LNBI), vol. 3909, pp. 488–499. Springer, Heidelberg (2006)
Garey, M., Johnson, D.: Computers and Intractability: A Guide to the Theory of NP-completness. Freeman and company, New York (1979)
Crescenzi, P., Kann, V.: A compendium of NP optimization problems, http://www.nada.kth.se/~viggo/problemlist/
Strickland, D.M., Barnes, E., Sokol, J.S.: Optimal Protein Structure Alignment Using Maximum Cliques. Oper. Res. 53, 389–402 (2005)
Xie, W., Sahinidis, N.: A Reduction-Based Exact Algorithm for the Contact Map Overlap Problem. J. Comput. Biol. 14, 637–654 (2007)
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)
Andonov, R., Balev, S., Yanev, N.: Protein threading: From mathematical models to parallel implementations. INFORMS J. on Comput. 16(4) (2004)
Veber, P., Yanev, N., Andonov, R., Poirriez, V.: Optimal protein threading by cost-splitting. In: Casadio, R., Myers, G. (eds.) WABI 2005. LNCS (LNBI), vol. 3692, pp. 365–375. Springer, Heidelberg (2005)
Yanev, N., Veber, P., Andonov, R., Balev, S.: Lagrangian approaches for a class of matching problems. Comp. and Math. with Appl. 55(5), 1054–1067 (2008)
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)
Lerman, I.C.: Likelihood linkage analysis (LLA) classification method (Around an example treated by hand). Biochimie, Elsevier Editions 75, 379–397 (1993)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Andonov, R., Yanev, N., Malod-Dognin, N. (2008). An Efficient Lagrangian Relaxation for the Contact Map Overlap Problem. In: Crandall, K.A., Lagergren, J. (eds) Algorithms in Bioinformatics. WABI 2008. Lecture Notes in Computer Science(), vol 5251. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87361-7_14
Download citation
DOI: https://doi.org/10.1007/978-3-540-87361-7_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-87360-0
Online ISBN: 978-3-540-87361-7
eBook Packages: Computer ScienceComputer Science (R0)