Abstract
We present a branch-and-bound (bb) algorithm for the multiple sequence alignment problem (MSA), one of the most important problems in computational biology. The upper bound at each bb node is based on a Lagrangian relaxation of an integer linear programming formulation for MSA. Dualizing certain inequalities, the Lagrangian subproblem becomes a pairwise alignment problem, which can be solved efficiently by a dynamic programming approach. Due to a reformulation w.r.t. additionally introduced variables prior to relaxation we improve the convergence rate dramatically while at the same time being able to solve the Lagrangian problem efficiently. Our experiments show that our implementation, although preliminary, outperforms all exact algorithms for the multiple sequence alignment problem. Furthermore, the quality of the alignments is among the best computed so far.
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Althaus E, Caprara A, Lenhof H-P, Reinert K (2002) Multiple sequence alignment with arbitrary gap costs: Computing an optimal solution using polyhedral combinatorics. In: Lengauer T, Lenhof H-P (eds) Proceedings of the European conference on computational biology, Saarbrücken, October 2002. Bioinformatics, vol 18. Oxford University Press, London, pp S4–S16
Althaus E, Caprara A, Lenhof H-P, Reinert K (2006) A branch-and-cut algorithm for multiple sequence alignment. Math Program 105:387–425
Beasley J (1993) Lagrangian relaxation. In: Modern heuristic techniques for combinatorial problems. Blackwell Scientific, Oxford
Caprara A, Fischetti M, Toth P (1999) A heuristic method for the set cover problem. Oper Res 47:730–743
Carrillo H, Lipman DJ (1988) The multiple sequence alignment problem in biology. SIAM J Appl Math 48(5):1073–1082
Delcher A, Kasif S, Fleischmann R, Peterson J, White O, Salzberg S (1999) Alignment of whole genomes. Nucleic Acids Res 27:2369–2376
Edgar RC (2004) Muscle: multiple sequence alignment with high accuracy and high throughput. Nucleic Acids Res 32(5):1792–1797
Elias I (2003) Settling the intractability of multiple alignment. In: Proc. of the 14th ann. int. symp. on algorithms and computation (ISAAC’03). Lecture notes in computer science, vol 2906. Springer, Berlin, pp 352–363
Eppstein D (1990) Sequence comparison with mixed convex and concave costs. J Algorithms 11:85–101
Fisher M (1994) Optimal solutions of vehicle routing problems using minimum k-trees. Oper Res 42:626–642
Garey M, Johnson D (1979) Computers and intractability: a guide to the theory of NP-completeness. Freeman, New York
Gupta S, Kececioglu J, Schaeffer A (1995) Improving the practical space and time efficiency of the shortest-paths approach to sum-of-pairs multiple sequence alignment. J Comput Biol 2:459–472
Gusfield D (1997) Algorithms on strings, trees and sequences: computer science and computational biology. Cambridge University Press, Cambridge
Held M, Karp R (1971) The traveling salesman problem and minimum spanning trees: part II. Math Program 1:6–25
Katoh K, Kuma K, Toh H, Miyata T (2005) MAFFT version 5: improvement in accuracy of multiple sequence alignment. Nucleic Acids 33:511
Larmore L, Schieber B (1990) Online dynamic programming with applications to the prediction of RNA secondary structure. In: Proceedings of the first symposium on discrete algorithms, pp 503–512
Lermen M, Reinert K (2000) The practical use of the \(\mathcal{A}^{*}\) algorithm for exact multiple sequence alignment. J Comput Biol 7(5):655–673
Lipman D, Altschul S, Kececioglu J (1989) A tool for multiple sequence alignment. Proc Nat Acad Sci US Am 86:4412–4415
Lucena A (1993) Steiner problem in graphs: Lagrangean relaxation and cutting-planes. COAL Bull 21:2–7
Mehlhorn K, Näher S (1999) The LEDA platform of combinatorial and geometric computing. Cambridge University Press, Cambridge. See also http://www.mpi-sb.mpg.de/LEDA/
Notredame C, Higgins DG, Heringa J (2000) T-Coffee: a novel method for fast and accurate multiple sequence alignment. J Mol Biol 302(1):205–217
Reinert K (1999) A polyhedral approach to sequence alignment problems. PhD thesis, Universität des Saarlandes, 1999
Reinert K, Lenhof H-P, Mutzel P, Mehlhorn K, Kececioglu J (1997) A branch-and-cut algorithm for multiple sequence alignment. In: Proceedings of the first annual international conference on computational molecular biology (RECOMB-97), pp 241–249
Reinert K, Stoye J, Will T (2000) An iterative method for faster sum-of-pairs multiple sequence alignment. Bioinformatics 16(9):808–814
Sankoff D, Kruskal JB (1983) Time warps, string edits and macromolecules: the theory and practice of sequence comparison. Addison–Wesley, Reading
Subramanian AR, Weyer-Menkhoff J, Kaufmann M, Morgenstern B (2005) DIALIGN-T: An improved algorithm for segment-based multiple sequence alignment. BMC Bioinformatics 6:66
Thompson JD, Higgins DG, Gibson TJ (1994) CLUSTAL W: improving the sensitivity of progressive multiple sequence alignment through sequence weighting, position-specific gap penalties and weight matrix choice. Nucleic Acids Res 22(22):4673–4680
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Althaus, E., Canzar, S. A Lagrangian relaxation approach for the multiple sequence alignment problem. J Comb Optim 16, 127–154 (2008). https://doi.org/10.1007/s10878-008-9139-z
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DOI: https://doi.org/10.1007/s10878-008-9139-z