Skip to main content
SpringerLink
Log in

Multiple sequence comparison and n-dimensional image reconstruction

  • Conference paper
  • First Online:
Combinatorial Pattern Matching (CPM 1993)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 684))

Included in the following conference series:

Abstract

Calculation of dot-matrices is a widespread tool in pairwise sequence comparison. In recent studies the usefulness of dot-matrices for multiple sequence alignment has been proved. Viewing dot-matrices as projections of unknown n-dimensional points, we consider the multiple alignment problem (for n sequences) as an n-dimensional image reconstruction problem with noise. From this perspective we introduce and develop the filtering method due to Vingron and Argos (J. Mol. Biol. (1991), 218, pp. 33–43). We discuss a conjecture of theirs regarding the number of iterations their algorithm requires and demonstrate that this number may be large. An improved version of the original algorithm is introduced that avoids costly dot-matrix multiplications and runs in O(n 3·L3) time (L is the length of the longest sequence). This is equivalent to only one iteration of the original algorithm. We also discuss applications to DNA/protein sequence comparisons.

This research was supported by grants from the National Science Foundation (DMS 90-05833, DMS 90-05833) and the National Institute of Health (GM-36230). This paper was written when P.A.P. was at the Department of Mathematics, University of Southern California, Los Angeles.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aho, A.V., Hopcroft, J.E. and Ullman: The Design and Analysis of Computer Algorithms. Addison-Wesley, 1974.

    Google Scholar 

  2. Altschul, S.F and Lipman, D.J. (1989) Trees, stars, and multiple biological sequence alignment. SIAM J. Appl. Math., 49, 179–209.

    Google Scholar 

  3. Argos, P. (1987) A Sensitive Procedure to Compare Amino Acid Sequences. J. Mol. Biol., 193, 385–396.

    Google Scholar 

  4. Bern, M. and Eppstein, D. (1992) Mesh Generation and Optimal Triangulation. In: Computing in Euclidean Geometry, F.K. Hwang and D.-Z. Du, editors, World Scientific, 1992, 23–90.

    Google Scholar 

  5. Carillo, H. and Lipman, D. (1988) The multiple sequence alignment problem in biology. SIAM J. Appl. Math., 48, 1073–1082.

    Google Scholar 

  6. Chan, S.C., Wong, A.K.C. and Chiu, D.K.Y. (1992) A survey of multiple sequence comparison methods. Bull. Math. Biol., 54, 563–598.

    Google Scholar 

  7. Gotoh, O. (1986) Alignment of Three Biological Sequences with an Efficient Trace-back Procedure. J. Theor. Biol., 121, 327–337.

    Google Scholar 

  8. Gotoh, O. (1990) Consistency of Optimal Sequence Alignments. Bull. Math. Biol., 52, 509–525.

    Google Scholar 

  9. Karlin,S., Morris,M., Ghandour,G. and Leung,M.-Y. (1988) Efficient algorithms for molecular sequence analysis. Proc. Nat. Acad. Sci. U.S.A., 85, 841–845.

    Google Scholar 

  10. Maizel, J.V. and Lenk R.P. (1981) Enhanced graphic matrix analysis of nucleic acid and protein sequences. Proc. Nat. Acad. Sci. USA, 78, 7665–7669.

    Google Scholar 

  11. McMorris, F.R. and Meacham, C.F. (1983) Partition intersection graphs. Ars Combin., 16-B, 133–138.

    Google Scholar 

  12. Miller, W. (1993) Building multiple alignments from pairwise alignments. Comp. Appl. Biosci., to appear.

    Google Scholar 

  13. Murata, M., Richardson, J.S. and Sussman, J.L. (1985) Simultaneous comparison of three protein sequences. Proc. Nat. Acad. Sci. U.S.A., 82, 3073–3077.

    Google Scholar 

  14. Pevzner P.A. Multiple alignment, communication cost, and graph matchings. SIAM J. Appl. Math., 52, 1992, 1763–1779.

    Google Scholar 

  15. Roytberg, M.A. (1992) A search for common patterns in many sequences. Comp. Appl. Biosci., 8, 57–64.

    Google Scholar 

  16. Schuler, G.D., Altschul S.F. and Lipman, D.J. (1991) A Workbench for Multiple Sequence Alignment Construction and Analysis. PROTEINS: Structure, Function and Genetics, 9, 180–190.

    Google Scholar 

  17. Sobel, E. and Martinez, H. (1986) A multiple sequence alignment program. Nucleic Acids Res., 14, 363–374.

    Google Scholar 

  18. Vihinen, M. (1988) An algorithm for simultaneous comparison of several sequences. Comp. Appl. Biosci., 4, 89–92.

    Google Scholar 

  19. Vingron, M. and Argos, P. (1989) A fast and sensitive multiple sequence alignment algorithm. Comp. Appl. Biosci., 5, 115–121.

    Google Scholar 

  20. Vingron and Argos (1991) Motif recognition and alignment for many sequences by comparison of dot-matrices J. Mol. Biol. 218, pp. 33–43.

    Google Scholar 

  21. Waterman, M.S. (1984) General methods of sequence comparison. Bull. Math. Biol., 46, 473–500.

    Google Scholar 

  22. Waterman, M.S., Arratia, R. and Galas, D.J. (1984) Pattern recognition in several sequences: Consensus and Alignment. Bull. Math. Biol., 46, 515–527.

    Google Scholar 

  23. Waterman, M.S. and Eggert, M. (1987) A new algorithm for best subsequence alignments with application to tRNA-rRNA comparisons. J. Mol. Biol., 197, 723–725.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Southern California, 90089-1113, Los Angeles, CA

    Martin Vingron

  2. Computer Science Department, The Pennsylvania State University 333 Whitmore Laboratory, 16802, University Park, PA

    Pavel A. Pevzner

Authors
  1. Martin Vingron
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Pavel A. Pevzner
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Alberto Apostolico Maxime Crochemore Zvi Galil Udi Manber

Rights and permissions

Reprints and permissions

Copyright information

© 1993 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Vingron, M., Pevzner, P.A. (1993). Multiple sequence comparison and n-dimensional image reconstruction. In: Apostolico, A., Crochemore, M., Galil, Z., Manber, U. (eds) Combinatorial Pattern Matching. CPM 1993. Lecture Notes in Computer Science, vol 684. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0029809

Download citation

  • DOI: https://doi.org/10.1007/BFb0029809

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-56764-6

  • Online ISBN: 978-3-540-47732-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation