A New Variational Framework for Rigid-Body Alignment

  • Tsuyoshi Kato
  • Koji Tsuda
  • Kentaro Tomii
  • Kiyoshi Asai
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3138)

Abstract

We present a novel algorithm for estimating the rigid-body transformation of a sequence of coordinates, aiming at the application to protein structures. Basically the sequence is modeled as a hidden Markov model where each state outputs an ellipsoidal Gaussian. Since maximum likelihood estimation requires to solve a complicated optimization problem, we introduce a variational estimation technique, which performs singular value decomposition in each step. Our probabilistic algorithm allows to superimpose a number of sequences which are rotated and translated in arbitrary ways.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Bashford, D., Lesk, A.M., Chothia, C.: Determinants of a protein fold: unique features of the globin amino acid sequences. J. Mol. Biol. 196, 199–216 (1987)CrossRefGoogle Scholar
  2. 2.
    Challis, J.H.: A procedure for determining rigid body transformation parameters. J. Biomechanics 28, 733–737 (1995)CrossRefGoogle Scholar
  3. 3.
    Weng, Z., Szustakowski, J.D.: Protein structure alignment using a genetic algorithm. Proteins: structure, function, and genetics 38(4), 428–440 (2000)CrossRefGoogle Scholar
  4. 4.
    Jaakkola, T., Haussler, D.: Exploiting generative models in discriminative classifiers. In: NIPS, vol. 11, pp. 487–493. MIT Press, Cambridge (1999)Google Scholar
  5. 5.
    Jordan, M.I., Ghahramani, Z., Jaakkola, T., Saul, L.: An introduction to variational methods for graphical methods. In: Jordan, M.I. (ed.) Learning in Graphical Models, pp. 105–161. MIT Press, Cambridge (1998)Google Scholar
  6. 6.
    Mount, D.W.: Bioinformatics: Sequence and Genome Analysis. Cold Spring Harbor Laboratory Press (March 2001)Google Scholar
  7. 7.
    Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, New York (1999)MATHCrossRefGoogle Scholar
  8. 8.
    Rabiner, L.R.: A tutorial on hidden Markov models and selected applications in speech recognition. Proc. IEEE 77, 257–286 (1989)CrossRefGoogle Scholar
  9. 9.
    Revow, M.D., Williams, C.K.I., Hinton, G.E.: Using generative models for handwritten digit recognition. IEEE T. PAMI 18(6), 592–606 (1996)Google Scholar
  10. 10.
    Seeger, M.: Learning with labeled and unlabeled data. Technical report, Institute for Adaptive and Neural Computation, University of Edinburgh (2001)Google Scholar
  11. 11.
    Shindyalov, I.N., Bourne, P.E.: Protein structure alignment by incremental combinatorial extension (CE) of the optimal path. Protein Engineering 11, 739–747 (1998)CrossRefGoogle Scholar
  12. 12.
    Smyth, P.: Clustering sequences with hidden markov models. In: NIPS, vol. 9, pp. 648–654. The MIT Press, Cambridge (1997)Google Scholar
  13. 13.
    Tsuda, K., Kin, T., Asai, K.: Marginalized kernels for biological sequences. Bioinformatics 18 (Suppl. 1), S268–S275 (2002)Google Scholar
  14. 14.
    Wu, T.D., Hastie, T., Schmidler, S.C., Brutlag, D.L.: Regression analysis of multiple protein structures. J. Comput. Biol. 5(3), 585–595 (1998)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Tsuyoshi Kato
    • 1
  • Koji Tsuda
    • 1
    • 2
  • Kentaro Tomii
    • 1
  • Kiyoshi Asai
    • 1
    • 3
  1. 1.AIST Computational Biology Research CenterTokyoJapan
  2. 2.Max Planck Institute of Biological CyberneticsTübingenGermany
  3. 3.Graduate School of Frontier SciencesThe University of TokyoKashiwaJapan

Personalised recommendations