Abstract
Contact maps are a model to capture the core information in the structure of biological molecules, e.g., proteins. A contact map consists of an ordered set S of elements (representing a protein’s sequence of amino acids), and a set A of element pairs of S, called arcs (representing amino acids which are closely neighbored in the structure). Given two contact maps (S,A) and (S p ,A p ) with |A|≥ |A p |, the Contact Map Pattern Matching (CMPM) problem asks whether the “pattern” (S p ,A p ) “occurs” in (S,A), i.e., informally stated, whether there is a subset of |A p | arcs in A whose arc structure coincides with A p . CMPM captures the biological question of finding structural motifs in protein structures. In general, CMPM is NP-hard. In this paper, we show that CMPM is solvable in O(|A|6|A p |2) time when the pattern is \(\{<,\between\}\)-structured, i.e., when each two arcs in the pattern are disjoint or crossing. Our algorithm extends to other closely related models. In particular, it answers an open question raised by Vialette that, rephrased in terms of contact maps, asked whether CMPM for \(\{<,\between\}\)-structured patterns is NP-hard or solvable in polynomial time. Our result stands in sharp contrast to the NP-hardness of closely related problems. We provide experimental results which show that contact maps derived from real protein structures can be processed efficiently.
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
Alber, J., Gramm, J., Guo, J., Niedermeier, R.: Computing the similarity of two sequences with nested arc annotations. Theoretical Computer Science 312, 337–358 (2004)
Berman, H.M., et al.: The Protein Data Bank. Nucleic Acids Research 28, 235–242 (2000), http://www.rcsb.org/pdb/
Blin, G., Fertin, G., Vialette, S.: New results for the 2-interval pattern problem. In: Proc. of the 15th CPM. LNCS, Springer, Heidelberg (2004) (to appear)
Evans, P.A.: Finding common subsequences with arcs and pseudoknots. In: Crochemore, M., Paterson, M. (eds.) CPM 1999. LNCS, vol. 1645, pp. 270–280. Springer, Heidelberg (1999)
Gramm, J., Guo, J., Niedermeier, R.: Pattern matching for arc-annotated sequences. In: Agrawal, M., Seth, A.K. (eds.) FSTTCS 2002. LNCS, vol. 2556, pp. 182–193. Springer, Heidelberg (2002)
Goldman, D., Istrail, S., Papadimitriou, C.H.: Algorithmic aspects of protein structure similarity. In: Proc. of the 40th FOCS, pp. 512–521. IEEE Computer Society, Los Alamitos (1999)
Harrison, M.A.: Introduction to Formal Language Theory. Addison-Wesley, Reading (1978)
Jiang, T., Lin, G.-H., Ma, B., Zhang, K.: The Longest Common Subsequence problem for arc-annotated sequences. In: Giancarlo, R., Sankoff, D. (eds.) CPM 2000. LNCS, vol. 1848, pp. 154–165. Springer, Heidelberg (2000)
Lancia, G., Carr, R., Walenz, B., Istrail, S.: 1001 optimal PDB structure alignments: Integer Programming methods for finding the maximum contact map overlap. Journal of Computational Biology 11(1), 27–52 (2004)
Orengo, C.A., Michie, A.D., Jones, S., Jones, D.T., Swindells, M.B., Thornton, J.M.: CATH – A Hierarchic Classification of Protein Domain Structures. Structure 5(8), 1093–1108 (1997), http://www.biochem.ucl.ac.uk/bsm/cath/
Wang, Z., Zhang, K.: RNA secondary structure prediction. In: Jiang, T., et al. (eds.) Current Topics in Computational Molecular Biology, pp. 345–364. MIT Press, Cambridge (2002)
Vialette, S.: On the computational complexity of 2-interval pattern matching problems. Theoretical Computer Science 312(2-3), 223–249 (2004)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Gramm, J. (2004). A Polynomial-Time Algorithm for the Matching of Crossing Contact-Map Patterns. In: Jonassen, I., Kim, J. (eds) Algorithms in Bioinformatics. WABI 2004. Lecture Notes in Computer Science(), vol 3240. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30219-3_4
Download citation
DOI: https://doi.org/10.1007/978-3-540-30219-3_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-23018-2
Online ISBN: 978-3-540-30219-3
eBook Packages: Springer Book Archive