Journal of Biomolecular NMR

, Volume 25, Issue 1, pp 25–39 | Cite as

The use of model selection in the model-free analysis of protein dynamics

  • Edward J. d'AuvergneEmail author
  • Paul R. Gooley


Model-free analysis of NMR relaxation data, which is widely used for the study of protein dynamics, consists of the separation of the global rotational diffusion from internal motions relative to the diffusion frame and the description of these internal motions by amplitude and timescale. Five model-free models exist, each of which describes a different type of motion. Model-free analysis requires the selection of the model which best describes the dynamics of the NH bond. It will be demonstrated that the model selection technique currently used has two significant flaws, under-fitting, and not selecting a model when one ought to be selected. Under-fitting breaks the principle of parsimony causing bias in the final model-free results, visible as an overestimation of S2 and an underestimation of τe and Rex. As a consequence the protein falsely appears to be more rigid than it actually is. Model selection has been extensively developed in other fields. The techniques known as Akaike's Information Criteria (AIC), small sample size corrected AIC (AICc), Bayesian Information Criteria (BIC), bootstrap methods, and cross-validation will be compared to the currently used technique. To analyse the variety of techniques, synthetic noisy data covering all model-free motions was created. The data consists of two types of three-dimensional grid, the Rex grids covering single motions with chemical exchange {S2e,Rex}, and the Double Motion grids covering two internal motions {Sf2,Ss2s}. The conclusion of the comparison is that for accurate model-free results, AIC model selection is essential. As the method neither under, nor over-fits, AIC is the best tool for applying Occam's razor and has the additional benefits of simplifying and speeding up model-free analysis.

AIC model-free analysis model selection NMR relaxation protein dynamics 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Supplementary material

supp1.pdf (4.2 mb)
Supplementary material 1 (4,2 MB)
supp2.pdf (4.3 mb)
Supplementary material 2 (4,2 MB)
supp3.pdf (4 mb)
Supplementary material 3 (4,0 MB)
supp4.pdf (4.4 mb)
Supplementary material 4 (4,4 MB)
supp5.pdf (2.1 mb)
Supplementary material 5 (2,0 MB)


  1. Abragham, A. (1961) The Principles of Nuclear Magnetism, Clarendon Press, Oxford.Google Scholar
  2. Akaike, H. (1973) In Information Theory and an Extension of the Maximum Likelihood Principle, Petrov, B.N. and Csaki, F. (Eds.), Proceedings of the 2nd International Symposium on Information Theory, Budapest, Academiai Kiado, pp. 267-281.Google Scholar
  3. Andrec, M., Inman, K.G., Weber, D.J., Levy, R.M. and Montelione, G.T. (2000) J. Magn. Reson., 146, 66-80.CrossRefADSGoogle Scholar
  4. Andrec, M., Montelione, G.T. and Levy, R.M. (1999) J. Magn. Reson., 139, 408-421.CrossRefADSGoogle Scholar
  5. Burnham, K.P. and Anderson, D.R. (1998) Model Selection and Inference: A Practical Information-Theoretic Approach, Springer-Verlag, New York.Google Scholar
  6. Clore, G.M., Szabo, A., Bax, A., Kay, L.E., Driscoll, P.C. and Gronenborn, A.M. (1990) J. Am. Chem. Soc., 112, 4989-4991.CrossRefGoogle Scholar
  7. Edwards, A.W.F. (1972) Likelihood, Cambridge University Press, London.Google Scholar
  8. Farrow, N.A., Muhandiram, R., Singer, A.N., Pascal, S.M., Kay, C.M., Gish, G., Shoelson, S.E., Pawson, T., Forman-Kay, J.D. and Kay, L.E. (1994) Biochemistry, 33, 5984-6003.CrossRefGoogle Scholar
  9. Hurvich, C.M. and Tsai, C-L. (1989) Biometrika, 76, 297-307.MathSciNetCrossRefGoogle Scholar
  10. Jin, D., Andrec, M., Montelione, G.T. and Levy, R.M. (1998) J. Biomol. NMR, 12, 471-492.CrossRefGoogle Scholar
  11. Korzhnev, D.M., Orekhov, V.Y. and Arseniev, A.S. (1997) J. Magn. Reson., 127, 184-191.CrossRefGoogle Scholar
  12. Kullback, S. and Leibler, R.A. (1951) Ann. Math. Stat., 22, 79-86.MathSciNetGoogle Scholar
  13. Linhart, H. and Zucchini, W. (1986) Model Selection, John Wiley and Sons, New York.Google Scholar
  14. Lipari, G. and Szabo, A. (1982a) J. Am. Chem. Soc., 104, 4546-4559.CrossRefGoogle Scholar
  15. Lipari, G. and Szabo, A. (1982b) J. Am. Chem. Soc., 104, 4559-4570.CrossRefGoogle Scholar
  16. Mandel, A.M., Akke, M. and Palmer, A.G. (1995) J. Mol. Biol., 246, 144-163.CrossRefGoogle Scholar
  17. Millet, O., Loria, J.P, Kroenke, C.D., Pons, M. and Palmer, A.G. (2000) J. Am. Chem. Soc., 122, 2867-2877.CrossRefGoogle Scholar
  18. Osborne, M.J. and Wright, P.E (2001) J. Biomol. NMR, 19, 209-230.CrossRefGoogle Scholar
  19. Palmer, A.G., Rance, M. and Wright, P.E. (1991) J. Am. Chem. Soc., 113, 4371-4380.CrossRefGoogle Scholar
  20. Pawley, N.H., Wang, C., Koide, S. and Nicholson, L.K. (2001) J. Biomol. NMR, 20, 149-165.CrossRefGoogle Scholar
  21. Schwarz, G. (1978) Ann. Stat., 6, 461-464.zbMATHGoogle Scholar
  22. Tugarinov, V., Liang, Z., Shapiro, Y.E., Freed, J.H. and Meirovitch, E. (2001) J. Am. Chem. Soc., 123, 3055-3063.CrossRefGoogle Scholar
  23. Zucchini, W. (2000) J. Math. Psychol., 44, 41-61.zbMATHCrossRefGoogle Scholar

Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  1. 1.Department of Biochemistry and Molecular BiologyUniversity of MelbourneMelbourneAustralia

Personalised recommendations