Journal of Computer-Aided Molecular Design

, Volume 17, Issue 7, pp 435–461 | Cite as

A Bayesian molecular interaction library

  • Ville-Veikko Rantanen
  • Mats Gyllenberg
  • Timo Koski
  • Mark S. Johnson


We describe a library of molecular fragments designed to model and predict non-bonded interactions between atoms. We apply the Bayesian approach, whereby prior knowledge and uncertainty of the mathematical model are incorporated into the estimated model and its parameters. The molecular interaction data are strengthened by narrowing the atom classification to 14 atom types, focusing on independent molecular contacts that lie within a short cutoff distance, and symmetrizing the interaction data for the molecular fragments. Furthermore, the location of atoms in contact with a molecular fragment are modeled by Gaussian mixture densities whose maximum a posteriori estimates are obtained by applying a version of the expectation-maximization algorithm that incorporates hyperparameters for the components of the Gaussian mixtures. A routine is introduced providing the hyperparameters and the initial values of the parameters of the Gaussian mixture densities. A model selection criterion, based on the concept of a `minimum message length' is used to automatically select the optimal complexity of a mixture model and the most suitable orientation of a reference frame for a fragment in a coordinate system. The type of atom interacting with a molecular fragment is predicted by values of the posterior probability function and the accuracy of these predictions is evaluated by comparing the predicted atom type with the actual atom type seen in crystal structures. The fact that an atom will simultaneously interact with several molecular fragments forming a cohesive network of interactions is exploited by introducing two strategies that combine the predictions of atom types given by multiple fragments. The accuracy of these combined predictions is compared with those based on an individual fragment. Exhaustive validation analyses and qualitative examples (e.g., the ligand-binding domain of glutamate receptors) demonstrate that these improvements lead to effective modeling and prediction of molecular interactions.

combining posterior probabilities expectation-maximization algorithm maximum a posteriori estimates mixture model protein-ligand recognition 


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  1. 1.
    Goodford, P.J., J. Med. Chem., 28 (1985) 849.Google Scholar
  2. 2.
    Wade, R.C., Clark, K.J. and Goodford, P.J., J.Med. Chem., 36 (1993) 140.Google Scholar
  3. 3.
    Wade, R.C. and Goodford, P.J., J.Med. Chem., 36 (1993) 148.Google Scholar
  4. 4.
    Kellogg, G.E., Semus, S.F. and Abraham, D.J., J. Comput.-Aided Mol. Des., 5 (1991) 545.Google Scholar
  5. 5.
    Danziger, D.J. and Dean, P.M., P. Roy. Soc. Lond. B Biol., 236 (1989) 101.Google Scholar
  6. 6.
    Danziger, D.J. and Dean, P.M., P. Roy. Soc. Lond. B Biol., 236 (1989) 115.Google Scholar
  7. 7.
    Laskowski, R.A., Thornton, J.M., Humblet, C. and Singh, J., J. Mol. Biol., 259 (1996) 175.Google Scholar
  8. 8.
    Pitt, W.R. and Goodfellow, J.M., Protein Eng., 4 (1991) 531.Google Scholar
  9. 9.
    Böhm, H.J., J. Comput.-Aided Mol. Des., 6 (1992) 61. 461Google Scholar
  10. 10.
    Böhm, H.J., J. Comput.-Aided Mol. Des., 6 (1992) 593.Google Scholar
  11. 11.
    Böhm, H.J., J. Comput.-Aided Mol. Des., 8 (1994) 623.Google Scholar
  12. 12.
    Bruno, I.J., Cole, J.C., Lommerse, J.P., Rowland, R.S., Taylor, R. and Verdonk, M.L., J. Comput.-Aided Mol. Des., 11 (1997) 525.Google Scholar
  13. 13.
    Verdonk, M.L., Cole, J.C. and Taylor R., J. Mol. Biol., 289 (1999) 1093.Google Scholar
  14. 14.
    Nissink, J.W.M., Verdonk, M.L. and Klebe, G., J. Comput.-Aided Mol. Des., 14 (2000) 787.Google Scholar
  15. 15.
    Verdonk, M.L., Cole, J.C., Watson, P., Gillet, V. and Willett, P., J. Mol. Biol., 307 (2001) 841.Google Scholar
  16. 16.
    Boer, D.R., Kroon J., Cole, J.C., Smith, B. and Verdonk, M.L., J. Mol. Biol., 312 (2001) 275.Google Scholar
  17. 17.
    Klebe, G., J. Mol. Biol., 237 (1994) 212.Google Scholar
  18. 18.
    Verkhivker, G., Appelt, K., Freer, S.T. and Villafranca, J.E., Protein Eng., 8 (1995) 677.Google Scholar
  19. 19.
    Mitchell, J.B.O., Laskowki, R.A., Alex, A. and Thornton, J.M., J. Comput. Chem., 20 (1999) 1165.Google Scholar
  20. 20.
    Mitchell, J.B.O., Laskowki, R.A., Alex, A., Forster, M.J. and Thornton, J.M., J. Comput. Chem., 20 (1999) 1177.Google Scholar
  21. 21.
    Muegge, I. and Martin, Y.C., J. Med. Chem., 42 (1999) 791.Google Scholar
  22. 22.
    Gohlke, H., Hendlich, M. and Klebe, G., J. Mol. Biol., 295 (2000) 337.Google Scholar
  23. 23.
    Hendlich, M., Acta Crystallogr. D, 54 (1998) 1178.Google Scholar
  24. 24.
    Berman, H.M., Westbrook, J., Feng, Z., Gilliland, G., Bhat, T.N., Weissig, H., Shindyalov, I.N. and Bourne, P.E., Nucleic Acids Res., 28 (2000) 235.Google Scholar
  25. 25.
    Rantanen, V.-V., Denessiouk, K.A., Gyllenberg, M., Koski, T. and Johnson, M.S., J. Mol. Biol., 313 (2001) 197.Google Scholar
  26. 26.
    Bernardo, J.M. and Smith, A.F.M., Bayesian Theory, John Wiley and Sons, Chichester, UK, 1994.Google Scholar
  27. 27.
    McLachlan, G.J. and Krishnan, T., The EM Algorithm and Extensions, John Wiley and Sons, New York, 1997.Google Scholar
  28. 28.
    McLachlan, G.J. and Peel, T., Finite Mixture Models, John Wiley and Sons, New York, 2000.Google Scholar
  29. 29.
    Durbin, R., Eddy, S.R., Krogh, A. and Mitchison, G.J., Biological Sequence Analysis: Probabilistic Models for Proteins and Nucleic Acids, Cambridge University Press, Cambridge, 1998.Google Scholar
  30. 30.
    Lanterman, A.D., Int. Stat. Rev., 69 (2001) 185.Google Scholar
  31. 31.
    Li, A.-J. and Nussinov, R., Proteins, 32 (1998) 111.Google Scholar
  32. 32.
    Rantanen, V.-V., Gyllenberg, M., Koski, T. and Johnson, M.S., Bioinformatics, 18 (2002) 1257.Google Scholar
  33. 33.
    Bondi, A., J. Phys. Chem., 68 (1964) 441.Google Scholar
  34. 34.
    Böhning, D., Schlattman, P. and Lindsay, B.G., Biometrics, 48 (1992) 283.Google Scholar
  35. 35.
    Ewens, W.J. and Grant, G.R., Statistical Methods of Bioinformatics, Springer Verlag, New York, 2001.Google Scholar
  36. 36.
    Geiger, D. and Heckerman, D., Ann. Stat., 25 (1997) 1344.Google Scholar
  37. 37.
    Gyllenberg, M. and Koski, T., Math. Biosci., 177&178 (2002) 161.Google Scholar
  38. 38.
    Geiger, D. and Heckerman, D., Ann. Stat., 30 (2002) 1412.Google Scholar
  39. 39.
    Gauvain, J.-L. and Lee, C.-H., IEEE T. Speech Audi. P., 2 (1994) 291.Google Scholar
  40. 40.
    Hastie, T. and Tibshirani, R., J. Roy. Stat. Soc. B Met., 58 (1996) 158.Google Scholar
  41. 41.
    Rissanen, J., IEEE T. Inform. Theory, 42 (1996) 40.Google Scholar
  42. 42.
    Rissanen, J., J. Comput. Syst. Sci., 55 (1997) 89.Google Scholar
  43. 43.
    Figueiredo, M. and Jain, A.K., IEEE T. Pattern Anal., 24 (2002) 381.Google Scholar
  44. 44.
    Wallace, C.S. and Freeman, P.R., J. Roy. Stat. Soc. B Met., 49 (1987) 241.Google Scholar
  45. 45.
    Wallace, C.S. and Freeman, P.R., J. Roy. Stat. Soc. B Met., 54 (1992) 195.Google Scholar
  46. 46.
    Samudrala, R. and Moult, J., J. Mol. Biol., 275 (1998) 895.Google Scholar
  47. 47.
    Chou, P.Y. and Fasman, G.D., Biochemistry, 13 (1974) 211.Google Scholar
  48. 48.
    Kittler, J., Hatef, M., Duin, R.P.W. and Matas, J., IEEE T. Pattern Anal., 20 (1998) 226.Google Scholar
  49. 49.
    Tax, D.M.J., van Breukelen, M., Duin, R.P.W. and Kittler, J., Pattern Recogn., 33 (2000) 1475.Google Scholar
  50. 50.
    Kuusinen, A., Arvola, M. and Keinänen, K., EMBO J., 14 (1995) 6327.Google Scholar
  51. 51.
    Armstrong, N., Sun, Y., Chen, G.Q. and Gouaux, E., Nature, 395 (1998) 913.Google Scholar
  52. 52.
    Armstrong, N. and Gouaux, E., Neuron, 28 (2000) 165.Google Scholar
  53. 53.
    Kraulis, P.J., J. Appl. Crystallogr., 24 (1991) 946.Google Scholar
  54. 54.
    Merritt, E.A. and Bacon, D.J., Methods Enzymol., 277 (1997) 505.Google Scholar

Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • Ville-Veikko Rantanen
    • 1
    • 2
  • Mats Gyllenberg
    • 1
  • Timo Koski
    • 3
  • Mark S. Johnson
    • 2
  1. 1.Department of MathematicsUniversity of TurkuTurkuFinland
  2. 2.Department of Biochemistry and PharmacyÅbo Akademi UniversityTurkuFinland
  3. 3.Department of MathematicsLinköping UniversityLinköpingSweden

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