Abstract
Data on molecular interactions is increasing at a tremendous pace, while the development of solid methods for analyzing this network data is lagging behind. This holds in particular for the field of comparative network analysis, where one wants to identify commonalities between biological networks. Since biological functionality primarily operates at the network level, there is a clear need for topology-aware comparison methods. In this paper we present a method for global network alignment that is fast and robust, and can flexibly deal with various scoring schemes taking both node-to-node correspondences as well as network topologies into account. It is based on an integer linear programming formulation, generalizing the well-studied quadratic assignment problem. We obtain strong upper and lower bounds for the problem by improving a Lagrangian relaxation approach and introduce the software tool natalie 2.0, a publicly available implementation of our method. In an extensive computational study on protein interaction networks for six different species, we find that our new method outperforms alternative state-of-the-art methods with respect to quality and running time. An extended version of this paper including proofs and pseudo code is available at http://arxiv.org/pdf/1108.4358v1 .
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Adams, W.P., Johnson, T.: Improved linear programming-based lower bounds for the quadratic assignment problem. DIMACS Series in Discrete Mathematics and Theoretical Computer Science (1994)
Alon, U.: Network motifs: theory and experimental approaches. Nat. Rev. Genet. 8(6), 450–461 (2007)
Ashburner, M., Ball, C.A., Blake, J.A., et al.: Gene ontology: tool for the unification of biology. Nat. Genet. 25 (2000)
Ay, F., Kellis, M., Kahveci, T.: SubMAP: Aligning Metabolic Pathways with Subnetwork Mappings.. J. Comput. Biol. 18(3), 219–235 (2011)
Caprara, A., Fischetti, M., Toth, P.: A heuristic method for the set cover problem. Oper. Res. 47, 730–743 (1999)
Edmonds, J.: Path, trees, and flowers. Canadian J. Math. 17, 449–467 (1965)
Edmonds, J., Karp, R.M.: Theoretical improvements in algorithmic efficiency for network flow problems. J.ACM 19, 248–264 (1972)
Flannick, J., Novak, A., Srinivasan, B.S., McAdams, H.H., Batzoglou, S.: Graemlin: general and robust alignment of multiple large interaction networks.. Genome Res. 16(9), 1169–1181 (2006)
Guignard, M.: Lagrangean relaxation. Top 11, 151–200 (2003)
Held, M., Karp, R.M.: The traveling-salesman problem and minimum spanning trees: Part II. Math. Program 1, 6–25 (1971)
Jaeger, S., Sers, C., Leser, U.: Combining modularity, conservation, and interactions of proteins significantly increases precision and coverage of protein function prediction. BMC Genomics 11(1), 717 (2010)
Kanehisa, M., Goto, S., Hattori, M., et al.: From genomics to chemical genomics: new developments in KEGG. Nucleic Acids Res. 34, 354–357 (2006)
Karp, R.M.: Reducibility among combinatorial problems. In: Miller, R.E., Thatcher, J.W. (eds.) Complexity of Computer Computations, pp. 85–103. Plenum Press (1972)
Kelley, B.P., Sharan, R., Karp, R.M., et al.: Conserved pathways within bacteria and yeast as revealed by global protein network alignment. P. Natl. Acad. Sci. USA 100(20), 11394–11399 (2003)
Klau, G.W.: A new graph-based method for pairwise global network alignment.. BMC Bioinform. 10(suppl.1), S59 (2009)
Koyutürk, M., Kim, Y., Topkara, U., et al.: Pairwise alignment of protein interaction networks.. J. Comput. Biol. 13(2), 182–199 (2006)
Kuchaiev, O., Milenkovic, T., Memisevic, V., Hayes, W., Przulj, N.: Topological network alignment uncovers biological function and phylogeny.. J. R. Soc. Interface 7(50), 1341–1354 (2010)
Kuhn, H.W.: The Hungarian method for the assignment problem. Nav. Res. Logist. Q 2(1-2), 83–97 (1955)
Lawler, E.L.: The quadratic assignment problem. Manage. Sci. 9(4), 586–599 (1963)
Munkres, J.: Algorithms for the assignment and transportation problems. SIAM J. Appl. Math. 5, 32–38 (1957)
Sharan, R., Ideker, T.: Modeling cellular machinery through biological network comparison.. Nat. Biotechnol. 24(4), 427–433 (2006)
Sharan, R., Ideker, T., Kelley, B., Shamir, R., Karp, R.M.: Identification of protein complexes by comparative analysis of yeast and bacterial protein interaction data. J. Comput. Biol. 12(6), 835–846 (2005)
Singh, R., Xu, J., Berger, B.: Global alignment of multiple protein interaction networks with application to functional orthology detection.. P. Natl. Acad. Sci. USA 105(35), 12763–12768 (2008)
Szklarczyk, D., Franceschini, A., Kuhn, M., et al.: The STRING database in 2011: functional interaction networks of proteins, globally integrated and scored. Nucleic Acids Res. 39, 561–568 (2010)
Wohlers, I., Andonov, R., Klau, G.W.: Algorithm engineering for optimal alignment of protein structure distance matrices. Optim. Lett. (2011)
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El-Kebir, M., Heringa, J., Klau, G.W. (2011). Lagrangian Relaxation Applied to Sparse Global Network Alignment. In: Loog, M., Wessels, L., Reinders, M.J.T., de Ridder, D. (eds) Pattern Recognition in Bioinformatics. PRIB 2011. Lecture Notes in Computer Science(), vol 7036. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24855-9_20
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DOI: https://doi.org/10.1007/978-3-642-24855-9_20
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