When comparing two biological sequences, it is often desirable for a gap to be assigned a cost not directly proportional to its length. If affine gap costs are employed, in other words if opening a gap costsv and each null in the gap costsu, the algorithm of Gotoh (1982,J. molec. Biol. 162, 705) finds the minimum cost of aligning two sequences in orderMN steps. Gotoh's algorithm attempts to find only one from among possibly many optimal (minimum-cost) alignments, but does not always succeed. This paper provides an example for which this part of Gotoh's algorithm fails and describes an algorithm that finds all and only the optimal alignments. This modification of Gotoh's algorithm still requires orderMN steps. A more precise form of path graph than previously used is needed to represent accurately all optimal alignments for affine gap costs.
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Altschul, S. F. and B. W. Erickson. 1986. “A Nonlinear Measure of Subalignment Similarity and its Significance Levels.”Bull. math. Biol. 48, 617–632.
Erickson, B. W. and P. H. Sellers. 1983. “Recognition of Patterns in Genetic Sequences.” InTime Warps, String Edits, and Macromolecules: The Theory and Practice of Sequence Comparison, D. Sankoff and J. B. Kruskal (Eds), pp. 55–91. Reading, MA: Addison-Wesley.
Fitch, W. M. and T. F. Smith. 1983. “Optimal Sequence Alignments.”Proc. natn. Acad. Sci. U.S.A. 80, 1382–1386.
Gotoh, O. 1982. “An Improved Algorithm for Matching Biological Sequences.”J. molec. Biol. 162, 705–708.
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. molec. Biol. 48, 443–453.
Schwartz, R. M. and M. O. Dayhoff. 1978. “Matrices for Detecting Distant Relationships.” InAtlas of Protein Sequence and Structure, Vol. 5, Suppl. 3, M. O. Dayhoff (Ed.), pp. 345–358. Washington, DC: National Biomedical Research Foundation.
Sellers, P. H. 1974. “On the Theory and Computation of Evolutionary Distances.”SIAM J. appl. Math. 26, 787–793.
Smith, T. F., M. S. Waterman and W. M. Fitch. 1981. “Comparative Biosequence Metrics.”J. molec. Evol. 18, 38–46.
Taniguchi, T. H. Matsui, T. Fujita, C. Takaoka, N. Kashima, R. Yoshimoto and J. Hamuro. 1983. “Structure and Expression of a Cloned cDNA for Human Interleukin-2.”Nature 302, 305–310.
Taylor, P. 1984. “A Fast Homology Program for Aligning Biological Sequences.”Nucl. Acids Res. 12, 447–455.
Waterman, M. S. 1984. “Efficient Sequence Alignment Algorithms.”J. theor. Biol. 108, 333–337.
—, T. F. Smith and W. A. Beyer. 1976. “Some Biological Sequence Metrics.”Adv. Math. 20, 367–387.
Ukkonen, E. 1983. “On Approximate String Matching.”Proc. Int. Conference on the Foundations of Computer Theory, Lecture Notes in Computer Science, Vol. 158, pp. 487–496. Berlin: Springer-Verlag.
Yokota, T., N. Arai, F. Lee, D. Rennick, T. Mosmann and K. Arai. 1985. “Use of a cDNA Expression Vector for Isolation of Mouse Interleukin 2 cDNA Clones: Expression of T-Cell Growth Factor Activity After Transfection of Monkey Cells.”Proc. natn. Acad. Sci. U.S.A. 82, 68–72.
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Altschul, S.F., Erickson, B.W. Optimal sequence alignment using affine gap costs. Bltn Mathcal Biology 48, 603–616 (1986). https://doi.org/10.1007/BF02462326
- Optimal Path
- Vertical Edge
- Optimal Alignment
- Horizontal Edge
- Cost Assignment