Near optimal multiple alignment within a band in polynomial time
Multiple sequence alignment is a fundamental problem in computational biology. Because of its notorious difficulties, aligning sequences within a constant band ( c-diagonal) is a popular practice in bioinformatics with good practical results [D. Sankoff, J. Kruskal, Time Warps, String Edits, and Mac...
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| Vydáno v: | Journal of computer and system sciences Ročník 73; číslo 6; s. 997 - 1011 |
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| Abstract | Multiple sequence alignment is a fundamental problem in computational biology. Because of its notorious difficulties, aligning sequences within a constant band (
c-diagonal) is a popular practice in bioinformatics with good practical results [D. Sankoff, J. Kruskal, Time Warps, String Edits, and Macromolecules: The Theory and Practice of Sequence Comparison, Addison–Wesley, 1983; W.R. Pearson, D. Lipman, Improved tools for biological sequence comparison, Proc. Natl. Acad. Sci. USA 85 (1988) 2444–2448; W.R. Pearson, Rapid and sensitive sequence comparison with FASTP and FASTA, Methods Enzymol. 183 (1990) 63–98; W.R. Pearson, Searching protein sequence libraries: Comparison of the sensitivity and selectivity of the Smith–Waterman and FASTA algorithms, Genomics 11 (1991) 635–650; S. Altschul, D. Lipman, Trees, stars, and multiple sequence alignment, SIAM J. Appl. Math. 49 (1989) 197–209; K. Chao, W.R. Pearson, W. Miller, Aligning two sequences within a specified diagonal band, CABIOS 8 (1992) 481–487; J.W. Fickett, Fast optimal alignment, Nucleic Acids Res. 12 (1984) 175–180; E. Ukkonen, Algorithms for approximate string matching, Inform. Control 64 (1985) 100–118; J.L. Spouge, Fast optimal alignment, CABIOS 7 (1991) 1–7]. However, the problem is still NP-hard for multiple sequences. In this paper, we present a theoretical study of this problem. In particular, for arbitrarily small
ϵ
>
0
, we present polynomial time algorithms that produce a multiple alignment (not necessarily
c-diagonal) with cost at most
1
+
ϵ
times the cost of the optimal
c-diagonal alignment, under standard models of both SP alignment and consensus (star) alignment. Our algorithms for consensus alignment allow very general score schemes.
In order to prove our main results, we also present similar results for SP alignment and consensus alignment, allowing only constant number of insertion and deletion gaps (of arbitrary length) per sequence on the average. These results are interesting in their own rights and they improve some results in [M. Li, B. Ma, L. Wang, Finding similar regions in many sequences, in: Proc. 31st ACM Symp. Theory of Computing, Atlanta, 1999, pp. 473–482]. |
|---|---|
| AbstractList | Multiple sequence alignment is a fundamental problem in computational biology. Because of its notorious difficulties, aligning sequences within a constant band (
c-diagonal) is a popular practice in bioinformatics with good practical results [D. Sankoff, J. Kruskal, Time Warps, String Edits, and Macromolecules: The Theory and Practice of Sequence Comparison, Addison–Wesley, 1983; W.R. Pearson, D. Lipman, Improved tools for biological sequence comparison, Proc. Natl. Acad. Sci. USA 85 (1988) 2444–2448; W.R. Pearson, Rapid and sensitive sequence comparison with FASTP and FASTA, Methods Enzymol. 183 (1990) 63–98; W.R. Pearson, Searching protein sequence libraries: Comparison of the sensitivity and selectivity of the Smith–Waterman and FASTA algorithms, Genomics 11 (1991) 635–650; S. Altschul, D. Lipman, Trees, stars, and multiple sequence alignment, SIAM J. Appl. Math. 49 (1989) 197–209; K. Chao, W.R. Pearson, W. Miller, Aligning two sequences within a specified diagonal band, CABIOS 8 (1992) 481–487; J.W. Fickett, Fast optimal alignment, Nucleic Acids Res. 12 (1984) 175–180; E. Ukkonen, Algorithms for approximate string matching, Inform. Control 64 (1985) 100–118; J.L. Spouge, Fast optimal alignment, CABIOS 7 (1991) 1–7]. However, the problem is still NP-hard for multiple sequences. In this paper, we present a theoretical study of this problem. In particular, for arbitrarily small
ϵ
>
0
, we present polynomial time algorithms that produce a multiple alignment (not necessarily
c-diagonal) with cost at most
1
+
ϵ
times the cost of the optimal
c-diagonal alignment, under standard models of both SP alignment and consensus (star) alignment. Our algorithms for consensus alignment allow very general score schemes.
In order to prove our main results, we also present similar results for SP alignment and consensus alignment, allowing only constant number of insertion and deletion gaps (of arbitrary length) per sequence on the average. These results are interesting in their own rights and they improve some results in [M. Li, B. Ma, L. Wang, Finding similar regions in many sequences, in: Proc. 31st ACM Symp. Theory of Computing, Atlanta, 1999, pp. 473–482]. |
| Author | Li, Ming Ma, Bin Wang, Lusheng |
| Author_xml | – sequence: 1 givenname: Bin surname: Ma fullname: Ma, Bin email: bma@uwo.ca organization: Department of Computer Science, University of Western Ontario, London, Ontario N6A 5B7, Canada – sequence: 2 givenname: Lusheng surname: Wang fullname: Wang, Lusheng email: lwang@cs.cityu.edu.hk organization: Department of Computer Science, City University of Hong Kong, Kowloon, Hong Kong – sequence: 3 givenname: Ming surname: Li fullname: Li, Ming email: mli@uwaterloo.ca organization: David R. Cheriton School of Computer Science, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada |
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| Keywords | Multiple sequence alignment within a band Polynomial time approximation algorithms |
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| References_xml | – year: 1995 ident: bib023 article-title: Introduction to Computational Biology – volume: 43 start-page: 425 year: 1991 end-page: 440 ident: bib011 article-title: Optimization, approximation, and complexity classes publication-title: J. Comput. System Sci. – volume: 16 start-page: 302 year: 1996 end-page: 315 ident: bib021 article-title: Approximation algorithms for tree alignment with a given phylogeny publication-title: Algorithmica – volume: 1 start-page: 337 year: 1994 end-page: 348 ident: bib020 article-title: On the complexity of multiple sequence alignment publication-title: J. Comput. Biol. – reference: V. Bafna, E. Lawler, P. Pevzner, Approximation algorithms for multiple sequence alignment, in: Proc. 8th Ann. Combinatorial Pattern Matching Conf. Asilomar, 1994, pp. 43–53 – reference: W. Just, On the computational complexity of gap-0 multiple alignment, manuscript, 1998 – volume: 52 start-page: 1763 year: 1992 end-page: 1779 ident: bib015 article-title: Multiple alignment, communication cost, and graph matching publication-title: SIAM J. Appl. Math. – volume: 12 start-page: 175 year: 1984 end-page: 180 ident: bib006 article-title: Fast optimal alignment publication-title: Nucleic Acids Res. – year: 1995 ident: bib010 article-title: Randomized Algorithms – reference: B.Y. Wu, G. Lancia, V. Bafna, K. Chao, R. Ravi, C.Y. Tang, A polynomial time approximation scheme for minimum routing cost spanning trees, in: Proc. 9th ACM–SIAM Symp. Disc. Alg., San Francisco, 1998, pp. 21–32 – year: 1983 ident: bib016 article-title: Time Warps, String Edits, and Macromolecules: The Theory and Practice of Sequence Comparison – volume: 85 start-page: 2444 year: 1988 end-page: 2448 ident: bib012 article-title: Improved tools for biological sequence comparison publication-title: Proc. Natl. Acad. Sci. USA – reference: J. Kececioglu, H.-P. Lenhof, K. Mehlhorn, P. Mutzel, K. Reinert, M. Vingron, A polyhedral approach to sequence alignment problems, in: P. Pevzner (Ed.), Special Issue on Computational Biology, Discrete Appl. Math. (1999), in press – volume: 49 start-page: 197 year: 1989 end-page: 209 ident: bib001 article-title: Trees, stars, and multiple sequence alignment publication-title: SIAM J. Appl. Math. – volume: 11 start-page: 635 year: 1991 end-page: 650 ident: bib014 article-title: Searching protein sequence libraries: Comparison of the sensitivity and selectivity of the Smith–Waterman and FASTA algorithms publication-title: Genomics – year: 1995 ident: bib018 article-title: A Course in Probability and Statistics – volume: 64 start-page: 100 year: 1985 end-page: 118 ident: bib019 article-title: Algorithms for approximate string matching publication-title: Inform. 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Math. doi: 10.1137/0152101 – volume: 8 start-page: 481 year: 1992 ident: 10.1016/j.jcss.2007.03.012_bib003 article-title: Aligning two sequences within a specified diagonal band publication-title: CABIOS – ident: 10.1016/j.jcss.2007.03.012_bib009 doi: 10.1145/301250.301376 – volume: 43 start-page: 425 year: 1991 ident: 10.1016/j.jcss.2007.03.012_bib011 article-title: Optimization, approximation, and complexity classes publication-title: J. Comput. System Sci. doi: 10.1016/0022-0000(91)90023-X – ident: 10.1016/j.jcss.2007.03.012_bib008 – ident: 10.1016/j.jcss.2007.03.012_bib024 – volume: 7 start-page: 1 year: 1991 ident: 10.1016/j.jcss.2007.03.012_bib017 article-title: Fast optimal alignment publication-title: CABIOS – volume: 64 start-page: 100 year: 1985 ident: 10.1016/j.jcss.2007.03.012_bib019 article-title: Algorithms for approximate string matching publication-title: Inform. Control doi: 10.1016/S0019-9958(85)80046-2 – ident: 10.1016/j.jcss.2007.03.012_bib007 – year: 1995 ident: 10.1016/j.jcss.2007.03.012_bib023 – volume: 30 start-page: 141 year: 1993 ident: 10.1016/j.jcss.2007.03.012_bib004 article-title: Efficient methods for multiple sequence alignment with guaranteed error bounds publication-title: Bull. Math. Biol. doi: 10.1007/BF02460299 – volume: 1 start-page: 337 year: 1994 ident: 10.1016/j.jcss.2007.03.012_bib020 article-title: On the complexity of multiple sequence alignment publication-title: J. Comput. Biol. doi: 10.1089/cmb.1994.1.337 |
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