Bulletin of Mathematical Biology

, Volume 48, Issue 5–6, pp 603–616 | Cite as

Optimal sequence alignment using affine gap costs

  • Stephen F. Altschul
  • Bruce W. Erickson


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.


Optimal Path Vertical Edge Optimal Alignment Horizontal Edge Cost Assignment 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. Altschul, S. F. and B. W. Erickson. 1986. “A Nonlinear Measure of Subalignment Similarity and its Significance Levels.”Bull. math. Biol. 48, 617–632.zbMATHMathSciNetCrossRefGoogle Scholar
  2. 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.Google Scholar
  3. Fitch, W. M. and T. F. Smith. 1983. “Optimal Sequence Alignments.”Proc. natn. Acad. Sci. U.S.A. 80, 1382–1386.CrossRefGoogle Scholar
  4. Gotoh, O. 1982. “An Improved Algorithm for Matching Biological Sequences.”J. molec. Biol. 162, 705–708.CrossRefGoogle Scholar
  5. 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.CrossRefGoogle Scholar
  6. 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.Google Scholar
  7. Sellers, P. H. 1974. “On the Theory and Computation of Evolutionary Distances.”SIAM J. appl. Math. 26, 787–793.zbMATHMathSciNetCrossRefGoogle Scholar
  8. Smith, T. F., M. S. Waterman and W. M. Fitch. 1981. “Comparative Biosequence Metrics.”J. molec. Evol. 18, 38–46.CrossRefGoogle Scholar
  9. 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.CrossRefGoogle Scholar
  10. Taylor, P. 1984. “A Fast Homology Program for Aligning Biological Sequences.”Nucl. Acids Res. 12, 447–455.Google Scholar
  11. Waterman, M. S. 1984. “Efficient Sequence Alignment Algorithms.”J. theor. Biol. 108, 333–337.MathSciNetGoogle Scholar
  12. —, T. F. Smith and W. A. Beyer. 1976. “Some Biological Sequence Metrics.”Adv. Math. 20, 367–387.zbMATHMathSciNetCrossRefGoogle Scholar
  13. 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.Google Scholar
  14. 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.CrossRefGoogle Scholar

Copyright information

© Society for Mathematical Biology 1986

Authors and Affiliations

  • Stephen F. Altschul
    • 1
    • 2
  • Bruce W. Erickson
    • 1
  1. 1.The Rockefeller UniversityNew YorkU.S.A.
  2. 2.Department of Applied MathematicsMassachusetts Institute of TechnologyCambridgeU.S.A.

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