Abstract
Relaxation dispersion spectroscopy is one of the most widely used techniques for the analysis of protein dynamics. To obtain a detailed understanding of the protein function from the view point of dynamics, it is essential to fit relaxation dispersion data accurately. The grid search method is commonly used for relaxation dispersion curve fits, but it does not always find the global minimum that provides the best-fit parameter set. Also, the fitting quality does not always improve with increase of the grid size although the computational time becomes longer. This is because relaxation dispersion curve fitting suffers from a local minimum problem, which is a general problem in non-linear least squares curve fitting. Therefore, in order to fit relaxation dispersion data rapidly and accurately, we developed a new fitting program called GLOVE that minimizes global and local parameters alternately, and incorporates a Monte-Carlo minimization method that enables fitting parameters to pass through local minima with low computational cost. GLOVE also implements a random search method, which sets up initial parameter values randomly within user-defined ranges. We demonstrate here that the combined use of the three methods can find the global minimum more rapidly and more accurately than grid search alone.
Similar content being viewed by others
References
Bhabha G, Lee J, Ekiert DC, Gam J, Wilson IA, Dyson HJ, Benkovic SJ, Wright PE (2011) A dynamic knockout reveals that conformational fluctuations influence the chemical step of enzyme catalysis. Science 332:234–238
Bieri M, Gooley PR (2011) Automated NMR relaxation dispersion data analysis using NESSY. BMC Bioinformatics 12:421
Boehr DD, McElheny D, Dyson HJ, Wright PE (2006) The dynamic energy landscape of dihydrofolate reductase catalysis. Science 313:1638–1642
Bouvignies G, Vallurupalli P, Hansen DF, Correia BE, Lange O, Bah A, Vernon RM, Dahlquist FW, Baker D, Kay LE (2011) Solution structure of a minor and transiently formed state of a T4 lysozyme mutant. Nature 477:111–114
Carver JP, Richards RE (1972) A general two-site solution for the chemical exchange produced dependence of T2 upon the Carr-Pursell pulse separation. J Magn Reson 6:89–105
Henzler-Wildman KA, Thai V, Lei M, Ott M, Wolf-Watz M, Fenn T, Pozharski E, Wilson MA, Petsko GA, Karplus M, Hübner CG, Kern D (2007) Intrinsic motions along an enzymatic reaction trajectory. Nature 450:838–844
Hwang TL, van Zijl PC, Mori S (1998) Accurate quantitation of water-amide proton exchange rates using the phase-modulated CLEAN chemical EXchange (CLEANEX-PM) approach with a Fast-HSQC (FHSQC) detection scheme. J Biomol NMR 11:221–226
Ishima R, Torchia DA (2005) Error estimation and global fitting in transverse-relaxation dispersion experiments to determine chemical-exchange parameters. J Biomol NMR 32:41–54
Karplus M (2010) Dynamical aspects of molecular recognition. J Mol Recognit 23:102–104
Kirkpatrick S, Gelatt CD, Vecchi MP (1983) Optimization by simulated annealing. Science 220:671–680
Kleckner IR, Foster MP (2011) GUARDD: user-friendly MATLAB software for rigorous analysis of CPMG RD NMR data. J Biomol NMR 52:11–22
Li Z, Scheraga HA (1987) Monte Carlo-minimization approach to the multiple-minima problem in protein folding. Proc Natl Acad Sci USA 84:6611–6615
Loria JP, Rance M, Palmer AG (1999) A relaxation-compensated Carr–Purcell–Meiboom–Gill sequence for characterizing chemical exchange by NMR spectroscopy. J Am Chem Soc 121:2331–2332
Matsuki Y, Konuma T, Fujiwara T, Sugase K (2011) Boosting protein dynamics studies using quantitative nonuniform sampling NMR spectroscopy. J Phys Chem B 115:13740–13745
Meinhold DW, Wright PE (2011) Measurement of protein unfolding/refolding kinetics and structural characterization of hidden intermediates by NMR relaxation dispersion. Proc Natl Acad Sci USA 108:9078–9083
Metropolis N, Rosenbluth AW, Rosenbluth MN, Teller M, Teller E (1953) Equation of state calculations by very fast computing machines. J Chem Phys 21:1087–1092
Mosteller F, Tukey J (1968) Data analysis, including statistics. In: Lindzey G, Aronson E (eds) Handbook of social psychology, vol 2. Addison-Wesley, Reading, pp 80–203
Neudecker P, Robustelli P, Cavalli A, Walsh P, Lundström P, Zarrine-Afsar A, Sharpe S, Vendruscolo M, Kay LE (2012) Structure of an intermediate state in protein folding and aggregation. Science 336:362–366
Press WH, Teukolsky SA, Vetterling WT, Flannery BP (2007) Numerical recipes 3rd edition: the art of scientific computing. Cambridge University Press, Cambridge
Schanda P, Brutscher B, Konrat R, Tollinger M (2008) Folding of the KIX domain: characterization of the equilibrium analog of a folding intermediate using 15N/13C relaxation dispersion and fast 1H/2H amide exchange NMR spectroscopy. J Mol Biol 380:726–741
Sugase K, Dyson HJ, Wright PE (2007a) Mechanism of coupled folding and binding of an intrinsically disordered protein. Nature 447:1021–1025
Sugase K, Lansing JC, Dyson HJ, Wright PE (2007b) Tailoring relaxation dispersion experiments for fast-associating protein complexes. J Am Chem Soc 129:13406–13407
Tollinger M, Skrynnikov NR, Mulder FA, Forman-Kay JD, Kay LE (2001) Slow dynamics in folded and unfolded states of an SH3 domain. J Am Chem Soc 123:11341–11352
Vallurupalli P, Hansen DF, Kay LE (2008) Structures of invisible, excited protein states by relaxation dispersion NMR spectroscopy. Proc Natl Acad Sci USA 105:11766–11771
Yanagi K, Sakurai K, Yoshimura Y, Konuma T, Lee YH, Sugase K, Ikegami T, Naiki H, Goto Y (2012) The monomer-seed interaction mechanism in the formation of the β2-microglobulin amyloid fibril clarified by solution NMR techniques. J Mol Biol 422:390–402
Acknowledgments
This work was supported by a Grant-in-Aid for Scientific Research on Innovative Areas (to K.S.) from the MEXT of Japan and by grant GM075995 (to P.E.W.) from the National Institutes of Health. J.L. was supported by postdoctoral fellowship grant PF-05-056-01 from the American Cancer Society. GLOVE is available upon request to the authors.
Author information
Authors and Affiliations
Corresponding author
Electronic supplementary material
Below is the link to the electronic supplementary material.
Rights and permissions
About this article
Cite this article
Sugase, K., Konuma, T., Lansing, J.C. et al. Fast and accurate fitting of relaxation dispersion data using the flexible software package GLOVE. J Biomol NMR 56, 275–283 (2013). https://doi.org/10.1007/s10858-013-9747-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10858-013-9747-5