CSDL Home IEEE/ACM Transactions on Computational Biology and Bioinformatics 2011 vol.8 Issue No.05 - September/October

Subscribe

Issue No.05 - September/October (2011 vol.8)

pp: 1296-1308

René van Bevern , Friedrich-Schiller-Universität Jena, Jena

Michael R. Fellows , Charles Darwin University, Darwin

Christian Komusiewicz , Friedrich-Schiller-Universität Jena, Jena

Nadja Betzler , Friedrich-Schiller-Universität Jena, Jena

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/TCBB.2011.19

ABSTRACT

We study the NP-hard List-Colored Graph Motif problem which, given an undirected list-colored graph G=(V,E) and a multiset M of colors, asks for maximum-cardinality sets S\subseteq V and M^{\prime }\subseteq M such that G[S] is connected and contains exactly (with respect to multiplicity) the colors in M^{\prime }. List-Colored Graph Motif has applications in the analysis of biological networks. We study List-Colored Graph Motif with respect to three different parameterizations. For the parameters motif size \vert M\vert and solution size \vert S\vert, we present fixed-parameter algorithms, whereas for the parameter \vert V\vert -\vert M\vert, we show W[1]-hardness for general instances and achieve fixed-parameter tractability for a special case of List-Colored Graph Motif. We implemented the fixed-parameter algorithms for parameters \vert M\vert and \vert S\vert, developed further speed-up heuristics for these algorithms, and applied them in the context of querying protein-interaction networks, demonstrating their usefulness for realistic instances. Furthermore, we show that extending the request for motif connectedness to stronger demands, such as biconnectedness or bridge-connectedness leads to W[1]-hard problems when the parameter is the motif size \vert M\vert

INDEX TERMS

Parameterized complexity, color-coding, list-colored graphs, pattern matching in graphs, protein-interaction networks.

CITATION

René van Bevern, Michael R. Fellows, Christian Komusiewicz, Nadja Betzler, "Parameterized Algorithmics for Finding Connected Motifs in Biological Networks",

*IEEE/ACM Transactions on Computational Biology and Bioinformatics*, vol.8, no. 5, pp. 1296-1308, September/October 2011, doi:10.1109/TCBB.2011.19REFERENCES

- [1] E. Alm and A.P. Arkin, “Biological Networks,”
Current Opinion in Structural Biology, vol. 13, no. 2, pp. 193-202, 2003.- [2] N. Alon, R. Yuster, and U. Zwick, “Color-coding,”
J. ACM, vol. 42, no. 4, pp. 844-856, 1995.- [3] D. Barrell, E. Dimmer, R.P. Huntley, D. Binns, C. O'Donovan, and R. Apweiler, “The GOA Database in 2009—An Integrated Gene Ontology Annotation Resource,”
Nucleic Acids Research, vol. 37, pp. 396-403, 2009/2010.- [4] N. Betzler, M.R. Fellows, C. Komusiewicz, and R. Niedermeier, “Parameterized Algorithms and Hardness Results for Some Graph Motif Problems,”
Proc. 19th Ann. Symp. Combinatorial Pattern Matching (CPM '08), LNCS, vol. 5029, pp. 31-43, 2008.- [5] A. Björklund, T. Husfeldt, P. Kaski, and M. Koivisto, “Fourier Meets Möbius: Fast Subset Convolution,”
Proc. 39th Ann. ACM Symp. Theory of Computing (STOC '07), pp. 67-74, 2007.- [6] G. Blin, F. Sikora, and S. Vialette, “GraMoFoNe: A Cytoscape Plugin for Querying Motifs without Topology in Protein-Protein Interactions networks,”
Proc. Second Int'l Conf. Bioinformatics and Computational Biology (BICoB '10), pp. 38-43, 2010.- [7] E.I. Boyle, S. Weng, J. Gollub, H. Jin, D. Botstein, J.M. Cherry, and G. Sherlock, “GO::TermFinder-Open Source Software for Accessing Gene Ontology Information and Finding Significantly Enriched Gene Ontology Terms Associated with a List of Genes,”
Bioinformatics, vol. 20, no. 18, pp. 3710-3715, 2004.- [8] S. Bruckner, F. Hüffner, R.M. Karp, R. Shamir, and R. Sharan, “Torque: Topology-Free Querying of Protein Interaction Networks,”
Nucleic Acids Research, vol. 37, pp. W106-W108, 2009.- [9] S. Bruckner, F. Hüffner, R.M. Karp, R. Shamir, and R. Sharan, “Topology-Free Querying of Protein Interaction Networks,”
J. Computational Biology, vol. 17, no. 3, pp. 237-252, 2010.- [10] M. Cesati, “Perfect Code is W[1]-Complete,”
Information Processing Letters, vol. 81, pp. 163-168, 2002.- [11] J. Chen and J. Meng, “On Parameterized Intractability: Hardness and Completeness,”
The Computer J., vol. 51, no. 1, pp. 39-59, 2008.- [12] Y. Chen, J. Flum, and M. Grohe, “Machine-Based Methods in Parameterized Complexity Theory,”
Theoretical Computer Science, vol. 339, nos. 2/3, pp. 167-199, 2005.- [13] R. Dondi, G. Fertin, and S. Vialette, “Weak Pattern Matching in Colored Graphs: Minimizing the Number of Connected Components,”
Proc. 10th Italian Conf. Theoretical Computer Science (ICTCS '07), vol. 4596, pp. 27-38, 2007.- [14] R. Dondi, G. Fertin, and S. Vialette, “Maximum Motif Problem in Vertex-Colored Graphs,”
Proc. 20th Ann. Symp. Combinatorial Pattern Matching (CPM '09), LNCS, vol. 5577, pp. 221-235, 2009.- [15] B. Dost, T. Shlomi, N. Gupta, E. Ruppin, V. Bafna, and R. Sharan, “Qnet: A Tool for Querying Protein Interaction Networks,”
J. Computational Biology, vol. 15, no. 7, pp. 913-925, 2008.- [16] R.G. Downey and M.R. Fellows,
Parameterized Complexity. Springer, 1999.- [17] M.R. Fellows, “Towards Fully Multivariate Algorithmics: Some New Results and Directions in Parameter Ecology,”
Proc. 20th Int'l Workshop Combinatorial Algorithms (IWOCA '09), LNCS, vol. 5874, pp. 2-10, 2009.- [18] M.R. Fellows, G. Fertin, D. Hermelin, and S. Vialette, “Upper and Lower Bounds for Finding Connected Motifs in Vertex-Colored Graphs,”
J. Computer and System Sciences, vol. 77, no. 4, pp. 799-811, 2011.- [19] J. Flum and M. Grohe,
Parameterized Complexity Theory. Springer, 2006.- [20] S. Guillemot and F. Sikora, “Finding and Counting Vertex-Colored Subtrees,”
Proc. 35th Int'l Symp. Math. Foundations of Computer Science (MFCS '10), LNCS, vol. 6281, pp. 405-416, 2010.- [21] J. Guo, R. Niedermeier, and S. Wernicke, “Parameterized Complexity of Vertex Cover Variants,”
Theory of Computing Systems, vol. 41, no. 3, pp. 501-520, 2007.- [22] F. Hüffner, S. Wernicke, and T. Zichner, “FASPAD: Fast Signaling Pathway Detection,”
Bioinformatics, vol. 23, no. 13, pp. 1708-1709, 2007.- [23] F. Hüffner, S. Wernicke, and T. Zichner, “Algorithm Engineering for Color-Coding with Applications to Signaling Pathway Detection,”
Algorithmica, vol. 52, no. 2, pp. 114-132, 2008.- [24] V. Lacroix, C.G. Fernandes, and M.-F. Sagot, “Motif Search in Graphs: Application to Metabolic Networks,”
IEEE/ACM Trans. Computational Biology and Bioinformatics, vol. 3, no. 4, pp. 360-368, Oct.-Dec. 2006.- [25] R. Niedermeier,
Invitation to Fixed-Parameter Algorithms. Oxford Univ. Press, 2006.- [26] R. Niedermeier, “Reflections on Multivariate Algorithmics and Problem Parameterization,”
Proc. 27th Int'l Symp. Theoretical Aspects of Computer Science (STACS '10), pp. 17-32, 2010.- [27] J. Scott, T. Ideker, R.M. Karp, and R. Sharan, “Efficient Algorithms for Detecting Signaling Pathways in Protein Interaction Networks,”
J. Computational Biology, vol. 13, no. 2, pp. 133-144, 2006.- [28] SGD project, Saccharomyces genome database, http:/ downloads.yeastgenome.org/. 2010.
- [29] R. Sharan and T. Ideker, “Modeling Cellular Machinery through Biological Network Comparison,”
Nature Biotechnology, vol. 24, pp. 427-433, Apr. 2006.- [30] S. Shen-Orr, R. Milo, S. Mangan, and U. Alon, “Network Motifs in the Transcriptional Regulation Network of Escherichia Coli,”
Nature Genetics, vol. 31, no. 1, pp. 64-68, 2002.- [31] S. Tweedie, M. Ashburner, K. Falls, P. Leyland, P. McQuilton, S. Marygold, G.H. Millburn, D. Osumi-Sutherland, A. Schroeder, R. Seal, and H. Zhang, “Flybase: Enhancing Drosophila Gene Ontology annotations,”
Nucleic Acids Research, vol. 37, pp. 555-559, 2009/2010.- [32] S. Wernicke, “Efficient Detection of Network Motifs,”
IEEE/ACM Trans. Computational Biology and Bioinformatics, vol. 3, no. 4, pp. 347-359, Oct.-Dec. 2006. |