Model-free model elimination: A new step in the model-free dynamic analysis of NMR relaxation data

Article

Abstract

Model-free analysis is a technique commonly used within the field of NMR spectroscopy to extract atomic resolution, interpretable dynamic information on multiple timescales from the R1, R2, and steady state NOE. Model-free approaches employ two disparate areas of data analysis, the discipline of mathematical optimisation, specifically the minimisation of a χ2 function, and the statistical field of model selection. By searching through a large number of model-free minimisations, which were setup using synthetic relaxation data whereby the true underlying dynamics is known, certain model-free models have been identified to, at times, fail. This has been characterised as either the internal correlation times, τe, τf, or τs, or the global correlation time parameter, local τm, heading towards infinity, the result being that the final parameter values are far from the true values. In a number of cases the minimised χ2 value of the failed model is significantly lower than that of all other models and, hence, will be the model which is chosen by model selection techniques. If these models are not removed prior to model selection the final model-free results could be far from the truth. By implementing a series of empirical rules involving inequalities these models can be specifically isolated and removed. Model-free analysis should therefore consist of three distinct steps: model-free minimisation, model-free model elimination, and finally model-free model selection. Failure has also been identified to affect the individual Monte Carlo simulations used within error analysis. Each simulation involves an independent randomised relaxation data set and model-free minimisation, thus simulations suffer from exactly the same types of failure as model-free models. Therefore, to prevent these outliers from causing a significant overestimation of the errors the failed Monte Carlo simulations need to be culled prior to calculating the parameter standard deviations.

Keywords

data analysis error analysis mathematical modelling model-free analysis model elimination model selection model validation NMR relaxation 

Abbreviations

AIC

Akaike’s Information Criteria

χ2

chi-squared function

ck

constraint value

CSA

Chemical Shift Anisotropy

DMG

Double Motion Grid

εi

elimination value

NOE

nuclear Overhauser effect

r

bond length

R1

spin-lattice relaxation rate

R2

spin-spin relaxation rate

Rex

chemical exchange relaxation rate

RG

Rex Grid

S2, Sf2, and Ss2

model-free generalised order parameters

τe, τf, and τs

model-free effective internal correlation times

τm

global rotational correlation time.

References

  1. Andrec M., Montelione G.T., Levy R.M. (1999). J. Magn. Reson. 139: 408–421CrossRefADSGoogle Scholar
  2. Bellomo N., Preziosi L. (1994) Modelling Mathematical Methods and Scientific Computation, CRC Mathematical Modelling Series. CRC Press, Boca Raton, FLGoogle Scholar
  3. Chen J., Brooks C.L., Wright P.E. (2004). J. Biomol. NMR 29: 243–257CrossRefGoogle Scholar
  4. Clore G.M., Szabo A., Bax A., Kay L.E., Driscoll P.C., Gronenborn A.M. (1990). J. Am. Chem. Soc. 112: 4989–4991CrossRefGoogle Scholar
  5. d’Auvergne E.J., Gooley P.R. (2003). J. Biomol. NMR 25: 25–39CrossRefGoogle Scholar
  6. Fushman D., Cahill S., Cowburn D. (1997). J. Mol. Biol. 266: 173–194CrossRefGoogle Scholar
  7. Korzhnev D.M., Billeter M., Arseniev A.S., Orehkov V.Yu. (2001). Prog. NMR Spectrosc. 38: 197–266CrossRefGoogle Scholar
  8. Lipari G., Szabo A. (1982a). J. Am. Chem. Soc. 104: 4546–4559CrossRefGoogle Scholar
  9. Lipari G., Szabo A. (1982b). J. Am. Chem. Soc. 104: 4559–4570CrossRefGoogle Scholar
  10. Mandel A.M., Akke M., Palmer A.G. (1995). J. Mol. Biol. 246: 144–163CrossRefGoogle Scholar
  11. Orekhov V.Yu., Korzhnev D.M., Diercks T., Kessler H., Arseniev A.S. (1999). J. Biomol. NMR 14: 345–356CrossRefGoogle Scholar
  12. Orekhov V.Yu., Nolde D.E, Golovanov A.P., Korzhnev D.M., Arseniev A.S. (1995). Appl. Magn. Reson. 9: 581–588CrossRefGoogle Scholar
  13. Palmer A.G., Rance M., Wright P.E. (1991). J. Am. Chem. Soc. 113: 4371–4380CrossRefGoogle Scholar
  14. Zhuravleva A.V., Korzhnev D.M., Kupce E., Arseniev A.S., Billeter M., Orekhov V.Yu. (2004). J. Mol. Biol. 342: 1599–1611CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  1. 1.Department of Biochemistry and Molecular Biology, Bio21 Institute of Biotechnology and Molecular ScienceUniversity of MelbourneParkvilleAustralia

Personalised recommendations