Graphs and Combinatorics

, Volume 6, Issue 2, pp 133–146 | Cite as

On the number of alignments ofk sequences

  • J. R. Griggs
  • P. Hanlon
  • A. M. Odlyzko
  • M. S. Waterman
Original Papers


Numerous studies by molecular biologists concern the relationships between several long DNA sequences, which are listed in rows with some gaps inserted and with similar positions aligned vertically. This motivates our interest in estimating the number of possible arrangements of such sequences. We say that ak sequence alignment of sizen is obtained by inserting some (or no) 0's intok sequences ofn 1's so that every sequence has the same length and so that there is no position which is 0 in allk sequences. We show by a combinatorial argument that for any fixedk≥1, the numberf(k, n) ofk alignments of lengthn grows like (c k ) n as n → ∞, wherec k = (21/k − 1) -k . A multi-dimensional saddle-point method is used to give a more precise estimate forf(k, n).


Sequence Alignment Precise Estimate Similar Position Molecular Biologist Combinatorial Argument 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Griggs, J.R., Hanlon, P., Waterman, M.S.: Sequence alignments with matched sections. SIAM J. Alg. Disc. Meth.7, No. 4, 604–608 (1986)Google Scholar
  2. 2.
    Laquer, H.T.: Asymptotic limits for a two-dimensional recursion. Stud. Appl. Math.64, 271–277 (1981)Google Scholar
  3. 3.
    Stanton, R.G., Cowan, D.D.: Note on a square functional equation. SIAM Rev.12, 277–279 (1970)Google Scholar
  4. 4.
    Ullrich, A., Bell, J.R., Chen, E.Y., Herrera, R., Petruzzelli, L.M., Dull, T.J., Gray, A., Coussens, L., Liao, Y.C., Tsubokawa, M., Mason, A., Seeburg, P.H., Grunfeld, C., Rosen O.M., Ramachandran, J.: Human insulin receptor and its relationship to the tyrosine kinase family of oncogenes. Nature313, 756–761 (1985)Google Scholar
  5. 5.
    Waterman, M.S.: General methods of sequence comparison. Bulletin of Math. Bio.46, 473–500 (1984)Google Scholar

Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • J. R. Griggs
    • 1
  • P. Hanlon
    • 2
  • A. M. Odlyzko
    • 3
  • M. S. Waterman
    • 4
  1. 1.Department of MathematicsUniversity of South CarolinaColumbiaUSA
  2. 2.Department of MathematicsCaltechPasadenaUSA
  3. 3.AT&T Bell LaboratoriesMurray HillUSA
  4. 4.Departments of Mathematics and Molecular BiologyUniversity of Southern CaliforniaLos AngelesUSA

Personalised recommendations