Abstract
Recently algorithms for parametric alignment (Watermanet al., 1992,Natl Acad. Sci. USA 89, 6090–6093; Gusfieldet al., 1992,Proceedings of the Third Annual ACM-SIAM Discrete Algorithms) find optimal scores for all penalty parameters, both for global and local sequence alignment. This paper reviews those techniques. Then in the main part of this paper dynamic programming methods are used to compute ensemble alignment, finding all alignment scores for all parameters. Both global and local ensemble alignments are studied, and parametric alignment is used to compute near optimal ensemble alignments.
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Literature
Byers, T. H. and M. S. Waterman. 1984. Determining all optimal and near-optimal solutions when solving shortest path porblems by dynamic programming.Oper. Res. 32, 1381.
Fernandez-Baca, D. and S. Srinivasan. 1991. Constructing the minimization diagram of a two-parameter problem.Oper. Res. Lett. 10, 87–93.
Finkelstein, A. V. and M. A. Roytberg. 1993. Computation of biopolymers: a general approach to different problems.BioSystems 30, 1–19.
Gusfield, D., K. Balasubramian and D. Naor. 1992. InProceedings of the Third Annual ACM-SIAM Discrete Algorithms, 432–439.
Howell, J. A., T. F. Smith and M. S. Waterman. 1980. Computation of generating functions for biological molecules.SIAM J. Appl Math. 39, 119–133.
McCaskill, J. S. 1990. The equilibrium partition function and base pair binding probabilities for RNA secondary structure.Biopolymers 29, 1105–1119.
Naor, D. and D. Brutlag. 1993. On Suboptimal alignments of biological sequences.Proc. of the Fourth International Symposium on Combinatorial Pattern Matching, Padova, Italy, June 1993. Lecture Notes in Computer Science.
Needleman, S. B. and C. D. Wunsch. 1970. A general method applicable to the search for similarities in the amino acid sequences of two proteins.J. mol. Biol. 48, 443–453.
Tavaré, S. 1986. Some mathematical questions in biology—DNA sequence analysis. InLectures on Mathematics in the Life Sciences,17, 29–56. The American Mathematical Society, Providence, Rhode Island.
Thorne, J. L., H. Kishino and J. Felsenstein. 1991. An evolutionary model for maximum likelihood alignment of DNA sequences.J. mol. Evol. 33, 114–124.
Thorne, J. L., H. Kishino and J. Felsenstein. 1992. Inching toward reality: an improved likelihood model of sequence evolution.J. mol. Evol. 34, 3–16.
Vingron, M. and P. Argos. 1990. Determination of reliable regions in protein sequence alignments.Prot. Engng 3, 565–569.
Vingron, M. and M. S. Waterman. 1993. Rapid and accurate estimates of statistical significance for sequence database searches.J. mol. Biol. (in press).
Waterman, M. S. 1983. Sequence alignment in the neighbourhood of the optimum with general applications to dynamic programming.Natl. Acad. Sci. USA 80, 3123.
Waterman, M. S. 1984. General methods of sequence comparison.Bull. Math. Biol. 46, 473–500.
Waterman, M. S. 1989. Sequence alignments. In:Mathematical Methods for DNA Sequences, M. S. Waterman (Ed.). CRC Press.
Waterman, M. S., M. Eggert and E. Lander. 1992. Parametric sequence comparisons. InNatl. Acad. Sci. USA,89, 6090–6093.
Zhang, M. Q. and T. G. Marr. 1993. Alignment of molecular sequences by random path analysis. Manuscript.
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Waterman, M.S. Parametric and ensemble sequence alignment algorithms. Bltn Mathcal Biology 56, 743–767 (1994). https://doi.org/10.1007/BF02460719
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DOI: https://doi.org/10.1007/BF02460719