Abstract
In metabolomics and other fields dealing with small compounds, mass spectrometry is applied as sensitive high-throughput technique. Recently, fragmentation trees have been proposed to automatically analyze the fragmentation mass spectra recorded by such instruments. Computationally, this leads to the problem of finding a maximum weight subtree in an edge weighted and vertex colored graph, such that every color appears at most once in the solution.
We introduce new heuristics and an exact algorithm for this Maximum Colorful Subtree problem, and evaluate them against existing algorithms on real-world datasets. Our tree completion heuristic consistently scores better than other heuristics, while the integer programming-based algorithm produces optimal trees with modest running times. Our fast and accurate heuristic can help to determine molecular formulas based on fragmentation trees. On the other hand, optimal trees from the integer linear program are useful if structure is relevant, e.g., for tree alignments.
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References
Björklund, A., Husfeldt, T., Kaski, P., Koivisto, M.: Fourier meets Möbius: fast subset convolution. In: Proc. of ACM Symposium on Theory of Computing (STOC 2007), pp. 67–74. ACM Press, New York (2007)
Böcker, S., Rasche, F.: Towards de novo identification of metabolites by analyzing tandem mass spectra. Bioinformatics 24, I49–I55 (2008)
Dondi, R., Fertin, G., Vialette, S.: Maximum Motif Problem in Vertex-Colored Graphs. In: Kucherov, G., Ukkonen, E. (eds.) CPM 2009. LNCS, vol. 5577, pp. 221–235. Springer, Heidelberg (2009)
Dreyfus, S.E., Wagner, R.A.: The Steiner problem in graphs. Networks 1(3), 195–207 (1972)
Fellows, M.R., Gramm, J., Niedermeier, R.: On the parameterized intractability of motif search problems. Combinatorica 26(2), 141–167 (2006)
Fernie, A.R., Trethewey, R.N., Krotzky, A.J., Willmitzer, L.: Metabolite profiling: from diagnostics to systems biology. Nat. Rev. Mol. Cell Biol. 5(9), 763–769 (2004)
Guillemot, S., Sikora, F.: Finding and Counting Vertex-Colored Subtrees. In: Hliněný, P., Kučera, A. (eds.) MFCS 2010. LNCS, vol. 6281, pp. 405–416. Springer, Heidelberg (2010)
Hill, D.W., Kertesz, T.M., Fontaine, D., Friedman, R., Grant, D.F.: Mass spectral metabonomics beyond elemental formula: Chemical database querying by matching experimental with computational fragmentation spectra. Anal. Chem. 80(14), 5574–5582 (2008)
Ito, T.: Finding maximum weight arborescence in an edge-weighted DAG. Theoretical Computer Science – Stack Exchange, http://cstheory.stackexchange.com/q/4088/189 (retrieved: October 12, 2011)
Koutis, I., Williams, R.: Limits and Applications of Group Algebras for Parameterized Problems. In: Albers, S., Marchetti-Spaccamela, A., Matias, Y., Nikoletseas, S., Thomas, W. (eds.) ICALP 2009. LNCS, vol. 5555, pp. 653–664. Springer, Heidelberg (2009)
Li, J.W.-H., Vederas, J.C.: Drug discovery and natural products: end of an era or an endless frontier? Science 325(5937), 161–165 (2009)
Ljubić, I., Weiskircher, R., Pferschy, U., Klau, G.W., Mutzel, P., Fischetti, M.: Solving the prize-collecting Steiner tree problem to optimality. In: Proc. of Algorithm Engineering and Experiments (ALENEX 2005), pp. 68–76. SIAM (2005)
Oberacher, H., Pavlic, M., Libiseller, K., Schubert, B., Sulyok, M., Schuhmacher, R., Csaszar, E., Köfeler, H.C.: On the inter-instrument and inter-laboratory transferability of a tandem mass spectral reference library: 1. results of an Austrian multicenter study. J. Mass Spectrom. 44(4), 485–493 (2009)
Rasche, F., Scheubert, K., Hufsky, F., Zichner, T., Kai, M., Svatoš, A., Böcker, S.: Identifying the unknowns by aligning fragmentation trees (October 2011) (manuscript)
Rasche, F., Svatoš, A., Maddula, R.K., Böttcher, C., Böcker, S.: Computing fragmentation trees from tandem mass spectrometry data. Anal. Chem. 83, 1243–1251 (2011)
Scheubert, K., Hufsky, F., Rasche, F., Böcker, S.: Computing fragmentation trees from metabolite multiple mass spectrometry data. J. Comput. Biol. 18(11), 1383–1397 (2011)
Scheubert, K., Hufsky, F., Rasche, F., Böcker, S.: Computing Fragmentation Trees from Metabolite Multiple Mass Spectrometry Data. In: Bafna, V., Sahinalp, S.C. (eds.) RECOMB 2011. LNCS, vol. 6577, pp. 377–391. Springer, Heidelberg (2011)
Sikora, F.: An (almost complete) state of the art around the graph motif problem. Technical report, Université Paris-Est, France (2010), http://www-igm.univ-mlv.fr/~fsikora/pub/GraphMotif-Resume.pdf
Sikora, F.: Aspects algorithmiques de la comparaison d’éléments biologiques. PhD thesis, Université Paris-Est (2011)
Xu, K., Li, W.: Many hard examples in exact phase transitions. Theor. Comput. Sci. 355(3), 291–302 (2006)
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Rauf, I., Rasche, F., Nicolas, F., Böcker, S. (2012). Finding Maximum Colorful Subtrees in Practice. In: Chor, B. (eds) Research in Computational Molecular Biology. RECOMB 2012. Lecture Notes in Computer Science(), vol 7262. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29627-7_22
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DOI: https://doi.org/10.1007/978-3-642-29627-7_22
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