A Better Method for Length Distribution Modeling in HMMs and Its Application to Gene Finding

  • Broňa Brejová
  • Tomáš Vinař
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2373)


Hidden Markov models (HMMs) have proved to be a useful abstraction in modeling biological sequences. In some situations it is necessary to use generalized HMMs in order to model the length distributions of some sequence elements because basic HMMs force geometric-like distributions. In this paper we suggest the use of an arbitrary length distributions with geometric tails to model lengths of elements in biological sequences. We give an algorithm for annotation of a biological sequence in O(ndm 2 Δ) time using such length distributions coupled with a suitable generalization of the HMM; here n is the length of the sequence, m is the number of states in the model, d is a parameter of the length distribution, and Δ is a small constant dependent on model topology (compared to previously proposed algorithms with O(n 3 m 2) time [10]). Our techniques can be incorporated into current software tools based on HMMs.

To validate our approach, we demonstrate that many length distributions in gene finding can be accurately modeled with geometric-tail length distribution, keeping parameter d small.


computational biology hidden Markov models gene finding length distribution 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    C. Burge and S. Karlin. Prediction of complete gene structures in human genomic DNA. Journal of Molecular Biology, 268(1):78–94, 1997.CrossRefGoogle Scholar
  2. 2.
    C. B. Burge. Identification of Genes in Human Genomic DNA. PhD thesis, Department of Mathematics, Stanford University, March 1997.Google Scholar
  3. 3.
    M. Burset and R. Guigó. Evaluation of gene structure prediction programs. Genomics, 34(3):353–357, 1996.CrossRefGoogle Scholar
  4. 4.
    I. Dunham et al. The DNA sequence of human chromosome 22. Nature, 402(6761):489–495, 1999.CrossRefGoogle Scholar
  5. 5.
    R. Durbin, S. Eddy, A. Krogh, and G. Mitchison. Biological sequence analysis: Probabilistic models of proteins and nucleic acids. Cambridge University Press, 1998.Google Scholar
  6. 6.
    A. Krogh. Two methods for improving performance of an HMM and their application for gene finding. In Proceedings of the 5th International Conference on Intelligent Systems for Molecular Biology (ISMB), pages 179–186, 1997.Google Scholar
  7. 7.
    D. Kulp, D. Haussler, M. G. Reese, and F. H. Eeckman. A generalized hidden Markov model for the recognition of human genes in DNA. In Proceedings of the 4th International Conference on Intelligent Systems for Molecular Biology (ISMB), pages 134–142, 1996.Google Scholar
  8. 8.
    L. P. Lim and C. B. Burge. A computational analysis of sequence features involved in recognition of short introns. Proceedings of the National Academy of Sciences USA, 98(20):11193–11198, 2001.CrossRefGoogle Scholar
  9. 9.
    R. B. Lyngsø and C. N. S. Pedersen. Complexity of comparing hidden Markov models. Technical Report ALCOMFT-TR-01-144, Algorithms and Complexity-Future Technologies Project (ALCOM-FT), June 2001.Google Scholar
  10. 10.
    L. R. Rabiner. A tutorial on Hidden Markov models and selected applications in speech recognition. Proceedings of the IEEE, 77(2):257–285, 1989.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Broňa Brejová
    • 1
  • Tomáš Vinař
    • 1
  1. 1.School of Computer ScienceUniversity of WaterlooCanada

Personalised recommendations