Alignment of Optical Maps

  • Anton Valouev
  • Lei Li
  • Yu-Chi Liu
  • David C. Schwartz
  • Yi Yang
  • Yu Zhang
  • Michael S. Waterman
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3500)


We introduce a new scoring method for calculation of alignments of optical maps. Missing cuts, false cuts and sizing errors present in optical maps are addressed by our alignment score through calculation of corresponding likelihood ratios. The Sizing error model is derived through the application of CLT and validated by residual plots collected from real data. Missing cuts and false cuts are modeled as Bernoulli and Poisson events respectively. This probabilistic framework is used to derive an alignment score through calculation of likelihood ratio. Consequently, this allows to achieve maximal descriminative power for alignment calculation. The proposed scoring method is naturally embedded within a well known DP framework for finding optimal alignments.


Alignment Score Optimal Alignment Matching Region Digestion Rate Optimal Score 
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.
    Bateman, H., Erdelyi, A.: Higher Transcendental Functions, vol. 82. Mc Graw-Hill Book Company, New York (1953)Google Scholar
  2. 2.
    Abramowitz, M., Stegun, I.A.: Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing, p. 374. Dover, New York (1972)Google Scholar
  3. 3.
    Waterman, M.S.: Introduction to Computational Biology, pp. 201–202. Chapman & Hall, Boca Raton (1995)zbMATHGoogle Scholar
  4. 4.
    Ananthraman, T., Mishra, B., Schwartz, D.C.: Genomics via Optical Mapping II: Ordered Restriction Maps. Journal of Computational Biology 4(2), 91–118 (1997)CrossRefGoogle Scholar
  5. 5.
    Grimmett, G., Stirzaker, D.: Probability and Random Processes. Oxford University Press, Oxford (1982)zbMATHGoogle Scholar
  6. 6.
    Myers, E.W.: Whole Genome DNA Sequencing Computing in Science and Engineering, pp. 33–43 (1999)Google Scholar
  7. 7.
    Huang, X., Waterman, M.S.: Dynamic Programming Algorithms for Restriction Map Comparison. CABIOS 8(5), 511–520 (1992)Google Scholar
  8. 8.
    Antoniotti, M., Ananthraman, T., Paxia, S., Mishra, B.: Genomics via Optical Mapping IV: Sequence Validation via Optical Map Matching. NYU-TR2000-811 (2001)Google Scholar
  9. 9.
    Ananthraman, T., Mishra, B.: A Probabilistic Analysis of False Positives in Optical Map Alignment and Validation. In: Algorithms in Bioinformatics, First International Workshop, WABI 2001 Proceedings (2001)Google Scholar
  10. 10.
    Ananthraman, T., Schwartz, D.C., Mishra, B.: Genomics via Optical Mapping III: Contiging Genomic DNA and Variations. In: Proceedings 1th Intl Cnf. on Intelligent Systems for Molecular Biology (1999)Google Scholar
  11. 11.
    Waterman, M.S., Smith, T.F., Katcher, H.: Algorithms for Restriction Map Comparisons. Nucleic Acids Research 12, 237–242 (1984)CrossRefGoogle Scholar
  12. 12.
    Lim, A., Dimalanta, E.T., Potamousis, K.D., Yen, G., Apodoca, J., Tao, C., Lin, J., Qi, R., Skiadas, J., Ramanathan, A., Perna, N.T., Plunkett III, G., Burland, V., Mau, B., Hackett, J., Blattner, F.R., Ananthraman, T.S., Mishra, B., Schwartz, D.C.: Hotgun optical maps of the whole Escherichia coli O157:H7 genome. Genome Res. 11(9), 1584–1593 (2001)CrossRefGoogle Scholar
  13. 13.
    Schwartz, D.C., Li, X., Hernandez, L.I., Ramnarain, S., Huff, E.J., Wang, Y.K.: Ordered restriction maps of Saccharomyces cerevisiae chromosomes constructed by optical mapping. Science 262(5130), 110–114 (1993)CrossRefGoogle Scholar
  14. 14.
    Myers, E.W., Huang, X.: An O (N 2 log N) restriction map comparison and search algorithm. Bull. Math. Biol. 54(4), 599–618 (1992)zbMATHGoogle Scholar
  15. 15.
    Huang, X., Madan, A.: CAP3: A DNA Sequence Assembly Program 9(9), 868–877 (1999)Google Scholar
  16. 16.
    Huang, X., Miller, W.: A time-efficient, linear-space local similarity algorithm 12, 337–357 (1991)Google Scholar
  17. 17.
    Dimalanta, E.T., Lim, A., Runnheim, R., Lamers, C., Churas, C., Forrest, D.K., de Pablo, J.J., Graham, M.D., Coppersmith, S.N., Schwartz, D.C.: A microfluidic system for large DNA molecule arrays. Anal. Chem. 7, 5293–5301 (2004)CrossRefGoogle Scholar
  18. 18.
    Zhou, S., Kile, A., Bechner, M., Place, M., Kvikstad, E., Deng, W., Wei, J., Severin, J., Runnheim, R., Churas, C., Forrest, D., Dimalanta, E., Lamers, C., Burland, V., Blattner, F., Schwartz, D.: A single molecule approach to bacterial genomic comparisons via Optical Mapping. J. Bacteriol (2004) (in press)Google Scholar
  19. 19.
    Smith, T.F., Waterman, M.S.: Comparison of biosequences. Adv. Appl. Math. 2, 482–489 (1981)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Anton Valouev
    • 1
  • Lei Li
    • 1
  • Yu-Chi Liu
    • 2
  • David C. Schwartz
    • 4
  • Yi Yang
    • 1
  • Yu Zhang
    • 3
  • Michael S. Waterman
    • 1
  1. 1.Department of MathematicsUniversity of Southern CaliforniaLos AngelesUSA
  2. 2.Molecular and Computational Biology Program, Department of Biological SciencesUniversity of Southern CaliforniaLos AngelesUSA
  3. 3.Department of StatisticsHarvard UniversityCambridgeUSA
  4. 4.Laboratory for Molecular and Computational Genomics, Departments of Genetics and ChemistryUniversity of Wisconsin-MadisonMadisonUSA

Personalised recommendations