Abstract
Comparison of 3-dimensional protein folds is a core problem in molecular biology. The Contact Map Overlap (CMO) scheme provides one of the most common measures for protein structure similarity. Maximizing CMO is, however, NP-hard. To approximately solve CMO, we combine softassign and dynamic programming. Softassign approximately solves the maximum common subgraph (MCS) problem. Dynamic programming converts the MCS solution to a solution of the CMO problem. We present and discuss experiments using proteins with up to 1500 residues. The results indicate that the proposed method is extremely fast compared to other methods, scales well with increasing problem size, and is useful for comparing similar protein structures.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Caprara, A., Lancia, G.: Structural alignment of large-size proteins via Lagrangianrelaxation. In: RECOMB, pp. 100–108 (2002)
Caprara, A., Carr, R., Istrail, S., Lancia, G., Walenz, B.: 1001 optimal pdb structure alignments: Integer programming methods for finding the maximum contact map overlap. Journal of Computational Biology 11(1), 27–52 (2004)
Carr, R., Hart, W., Krasnogor, N., Hirst, J., Burke, E.K., Smith, J.: Alignment of protein structures with a memetic evolutionary algorithm. In: GECCO’02: Proceedings of the Genetic and Evolutionary Computation Conference, pp. 1027–1034. Morgan Kaufmann, San Francisco (2002)
Finch, A.M., Wilson, R.C., Hancock, E.R.: An energy function and continuous edit process for graph matching. Neural Computation 10(7), 1873–1894 (1998)
Godzik, A., Kolinski, A., Skolnick, J.: Topology fingerprint approach to the inverse protein folding problem. Journal of Molecular Biology 5(1), 227–238 (1992)
Godzik, A., Skolnick, J.: Flexible algorithm for direct multiple alignment of protein structures and sequences. Computer Applications in the Biosciences 10(6), 587–596 (1994)
Gold, S., Rangarajan, A.: A graduated assignment algorithm for graph matching. IEEE Transactions on Pattern Analysis and Machine Intelligence 18(4), 377–388 (1996)
Goldman, D.: Algorithmic Aspects of Protein Folding and Protein Structure Similarity. PhD thesis, University of California, Berkerly (2000)
Goldman, D., Istrail, S., Papadimitriou, C.H.: Algorithmic aspects of protein structure similarity. In: 40th Annual Symposium on Foundations of Computer Science, pp. 512–521. IEEE Computer Society Press, Los Alamitos (1999)
Holm, L., Sander, C.: Protein structure comparison by alignment of distance matrices. Journal of Molecular Biology 233, 123–138 (1993)
Ishii, S., Sato, M.: Doubly constrained network for combinatorial optimization. Neurocomputing 43, 239–257 (2002)
Kabash, W.: A solution for the best rotation to relate two sets of vectors. Acta Crystallographica A32(5), 922–923 (1978)
Krasnogor, N.: Self generating metaheuristics in bioinformatics: The proteins structure comparison case. Genetic Programming and Evolvable Machines 5(2), 181–201 (2004)
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 ’01: Proceedings of the fifth annual international conference on Computational biology, pp. 193–202. ACM Press, NewYork (2001)
Lozano, M.A., Escolano, F.: A significant improvement of softassign with diffusion kernels. In: Fred, A., Caelli, T.M., Duin, R.P.W., Campilho, A., de Ridder, D. (eds.) Structural, Syntactic, and Statistical Pattern Recognition. LNCS, vol. 3138, pp. 76–84. Springer, Heidelberg (2004)
Sinkhorn, R.: A relationship between arbitrary positive matrices and doubly stochastic matrices. Annals of Mathematical Statistics 35(2), 876–879 (1964)
Strickl, D.M., Barnes, E., Sokol, J.S.: Optimal protein structure alignment using maximum cliques. Operations Research 53(3), 389–402 (2005)
Xie, W., Sahinidis, N.V.: A branch-and-reduce algorithm for the contact map overlap problem. In: Apostolico, A., Guerra, C., Istrail, S., Pevzner, P., Waterman, M. (eds.) RECOMB 2006. LNCS (LNBI), vol. 3909, pp. 516–529. Springer, Heidelberg (2006)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer Berlin Heidelberg
About this paper
Cite this paper
Jain, B.J., Lappe, M. (2007). Joining Softassign and Dynamic Programming for the Contact Map Overlap Problem. In: Hochreiter, S., Wagner, R. (eds) Bioinformatics Research and Development. BIRD 2007. Lecture Notes in Computer Science(), vol 4414. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71233-6_32
Download citation
DOI: https://doi.org/10.1007/978-3-540-71233-6_32
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-71232-9
Online ISBN: 978-3-540-71233-6
eBook Packages: Computer ScienceComputer Science (R0)