Journal of Biomolecular NMR

, Volume 65, Issue 3–4, pp 143–156 | Cite as

Evaluating the influence of initial magnetization conditions on extracted exchange parameters in NMR relaxation experiments: applications to CPMG and CEST



Transient excursions of native protein states to functionally relevant higher energy conformations often occur on the μs–ms timescale. NMR spectroscopy has emerged as an important tool to probe such processes using techniques such as Carr–Purcell–Meiboom–Gill (CPMG) relaxation dispersion and Chemical Exchange Saturation Transfer (CEST). The extraction of kinetic and structural parameters from these measurements is predicated upon mathematical modeling of the resulting relaxation profiles, which in turn relies on knowledge of the initial magnetization conditions at the start of the CPMG/CEST relaxation elements in these experiments. Most fitting programs simply assume initial magnetization conditions that are given by equilibrium populations, which may be incorrect in certain implementations of experiments. In this study we have quantified the systematic errors in extracted parameters that are generated from analyses of CPMG and CEST experiments using incorrect initial boundary conditions. We find that the errors in exchange rates (kex) and populations (pE) are typically small (<10 %) and thus can be safely ignored in most cases. However, errors become larger and cannot be fully neglected (20–40 %) as kex falls near the lower limit of each method or when short CPMG/CEST relaxation elements are used in these experiments. The source of the errors can be rationalized and their magnitude given by a simple functional form. Despite the fact that errors tend to be small, it is recommended that the correct boundary conditions be implemented in fitting programs so as to obtain as robust estimates of exchange parameters as possible.


Conformational exchange CPMG CEST Spin relaxation Boundary conditions 



We thank Enrico Rennella for helpful discussions and Rina Rosenzweig, Alaji Bah and Jacob Brady for providing protein samples. This project is supported by grants from the Canadian Institutes of Health Research and the Natural Sciences and Engineering Research Council of Canada. L.E.K. holds a Canada Research Chair in Biochemistry.

Supplementary material

10858_2016_45_MOESM1_ESM.pdf (380 kb)
Supplementary material 1 (PDF 380 kb)


  1. Bah A et al (2015) Folding of an intrinsically disordered protein by phosphorylation as a regulatory switch. Nature 519:106-U240. doi:10.1038/nature13999 Google Scholar
  2. Bai YW, Milne JS, Mayne L, Englander SW (1993) Primary structure effects on peptide group hydrogen exchange. Proteins 17:75–86. doi:10.1002/prot.340170110 CrossRefGoogle Scholar
  3. Baldwin AJ, Kay LE (2009) NMR spectroscopy brings invisible protein states into focus. Nat Chem Biol 5:808–814. doi:10.1038/nchembio.238 CrossRefGoogle Scholar
  4. Baldwin AJ, Kay LE (2013) An R expression for a spin in chemical exchange between two sites with unequal transverse relaxation rates. J Biomol NMR 55:211–218. doi:10.1007/s10858-012-9694-6 CrossRefGoogle Scholar
  5. Boehr DD, McElheny D, Dyson HJ, Wright PE (2006) The dynamic energy landscape of dihydrofolate reductase catalysis. Science 313:1638–1642. doi:10.1126/science.1130258 ADSCrossRefGoogle Scholar
  6. Bouvignies G, Vallurupalli P, Kay LE (2014) Visualizing side chains of invisible protein conformers by solution NMR. J Mol Biol 426:763–774. doi:10.1016/j.jmb.2013.10.041 CrossRefGoogle Scholar
  7. Farrow NA, Zhang OW, Forman-Kay JD, Kay LE (1994) A heteronuclear correlation experiment for simultaneous determination of 15N longitudinal decay and chemical exchange rates of systems in slow equilibrium. J Biomol NMR 4:727–734. doi:10.1007/Bf00404280 CrossRefGoogle Scholar
  8. Fawzi NL, Ying JF, Ghirlando R, Torchia DA, Clore GM (2011) Atomic-resolution dynamics on the surface of amyloid-beta protofibrils probed by solution NMR. Nature 480:268-U161. doi:10.1038/nature10577 CrossRefGoogle Scholar
  9. Grzesiek S, Bax A (1993) The importance of not saturating H2O in protein NMR. Application to sensitivity enhancement and NOE measurements. J Am Chem Soc 115:12593–12594. doi:10.1021/ja00079a052 CrossRefGoogle Scholar
  10. Hansen DF, Led JJ (2003) Implications of using approximate Bloch–McConnell equations in NMR analyses of chemically exchanging systems: application to the electron self-exchange of plastocyanin. J Magn Reson 163:215–227. doi:10.1016/S1090-7807(03)00062-4 ADSCrossRefGoogle Scholar
  11. Hansen DF, Vallurupalli P, Lundstrom P, Neudecker P, Kay LE (2008) Probing chemical shifts of invisible states of proteins with relaxation dispersion NMR spectroscopy: how well can we do? J Am Chem Soc 130:2667–2675. doi:10.1021/ja078337p CrossRefGoogle Scholar
  12. Hansen AL, Lundstrom P, Velyvis A, Kay LE (2012) Quantifying millisecond exchange dynamics in proteins by CPMG relaxation dispersion NMR using side-chain 1H probes. J Am Chem Soc 134:3178–3189. doi:10.1021/ja210711v CrossRefGoogle Scholar
  13. Henzler-Wildman KA et al (2007) Intrinsic motions along an enzymatic reaction trajectory. Nature 450:838-U813. doi:10.1038/nature06410 Google Scholar
  14. Ishima R, Torchia DA (2003) Extending the range of amide proton relaxation dispersion experiments in proteins using a constant-time relaxation-compensated CPMG approach. J Biomol NMR 25:243–248. doi:10.1023/A:1022851228405 CrossRefGoogle Scholar
  15. 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. doi:10.1007/s10858-005-3593-z CrossRefGoogle Scholar
  16. Ishima R, Torchia DA (2006) Accuracy of optimized chemical-exchange parameters derived by fitting CPMG R2 dispersion profiles when R20a ≠ R20b. J Biomol NMR 34:209–219. doi:10.1007/s10858-005-6226-7 CrossRefGoogle Scholar
  17. Ishima R, Wingfield PT, Stahl SJ, Kaufman JD, Torchia DA (1998) Using amide 1H and 15N transverse relaxation to detect millisecond time-scale motions in perdeuterated proteins: application to HIV-1 protease. J Am Chem Soc 120:10534–10542. doi:10.1021/ja981546c CrossRefGoogle Scholar
  18. Ishima R, Louis JM, Torchia DA (1999) Transverse 1H cross relaxation in 1H–15N correlated 1H CPMG experiments. J Magn Reson 137:289–292. doi:10.1006/jmre.1998.1672 ADSCrossRefGoogle Scholar
  19. Ishima R, Louis JM, Torchia DA (2001) Characterization of two hydrophobic methyl clusters in HIV-1 protease by NMR spin relaxation in solution. J Mol Biol 305:515–521. doi:10.1006/jmbi.2000.4321 CrossRefGoogle Scholar
  20. Karplus M, Kuriyan J (2005) Molecular dynamics and protein function. Proc Natl Acad Sci USA 102:6679–6685. doi:10.1073/pnas.0408930102 ADSCrossRefGoogle Scholar
  21. Kay LE, Keifer P, Saarinen T (1992) Pure absorption gradient enhanced heteronuclear single quantum correlation spectroscopy with improved sensitivity. J Am Chem Soc 114:10663–10665. doi:10.1021/ja00052a088 CrossRefGoogle Scholar
  22. Korzhnev DM, Salvatella X, Vendruscolo M, Di Nardo AA, Davidson AR, Dobson CM, Kay LE (2004) Low-populated folding intermediates of Fyn SH3 characterized by relaxation dispersion NMR. Nature 430:586–590. doi:10.1038/nature02655 ADSCrossRefGoogle Scholar
  23. Korzhnev DM, Bezsonova I, Lee S, Chalikian TV, Kay LE (2009) Alternate binding modes for a ubiquitin-SH3 domain interaction studied by NMR spectroscopy. J Mol Biol 386:391–405. doi:10.1016/j.jmb.2008.11.055 CrossRefGoogle Scholar
  24. Korzhnev DM, Religa TL, Banachewicz W, Fersht AR, Kay LE (2010) A transient and low-populated protein-folding intermediate at atomic resolution. Science 329:1312–1316. doi:10.1126/science.1191723 ADSCrossRefGoogle Scholar
  25. Korzhnev DM, Vernon RM, Religa TL, Hansen AL, Baker D, Fersht AR, Kay LE (2011) Nonnative interactions in the FF domain folding pathway from an atomic resolution structure of a sparsely populated intermediate: an NMR relaxation dispersion study. J Am Chem Soc 133:10974–10982. doi:10.1021/ja203686t CrossRefGoogle Scholar
  26. Kovrigin EL, Kempf JG, Grey MJ, Loria JP (2006) Faithful estimation of dynamics parameters from CPMG relaxation dispersion measurements. J Magn Reson 180:93–104. doi:10.1016/j.jmr.2006.01.010 ADSCrossRefGoogle Scholar
  27. Lukhele S, Bah A, Lin H, Sonenberg N, Forman-Kay JD (2013) Interaction of the eukaryotic initiation factor 4E with 4E-BP2 at a dynamic bipartite interface. Structure 21:2186–2196. doi:10.1016/j.str.2013.08.030 CrossRefGoogle Scholar
  28. Mangia S, Traaseth NJ, Veglia G, Garwood M, Michaeli S (2010) Probing slow protein dynamics by adiabatic R and R NMR experiments. J Am Chem Soc 132:9979–9981. doi:10.1021/ja1038787 CrossRefGoogle Scholar
  29. McConnell HM (1958) Reaction rates by nuclear magnetic resonance. J Chem Phys 28:430–431. doi:10.1063/1.1744152 ADSCrossRefGoogle Scholar
  30. Mittermaier AK, Kay LE (2006) New tools provide new insights in NMR studies of protein dynamics. Science 312:224–228. doi:10.1126/science.1124964 ADSCrossRefGoogle Scholar
  31. Mittermaier AK, Kay LE (2009) Observing biological dynamics at atomic resolution using NMR. Trends Biochem Sci 34:601–611. doi:10.1016/j.tibs.2009.07.004 CrossRefGoogle Scholar
  32. Montelione GT, Wagner G (1989) 2D chemical exchange NMR spectroscopy by proton-detected heteronuclear correlation. J Am Chem Soc 111:3096–3098. doi:10.1021/ja00190a072 CrossRefGoogle Scholar
  33. Mulder FAA, Skrynnikov NR, Hon B, Dahlquist FW, Kay LE (2001) Measurement of slow (μs–ms) time scale dynamics in protein side chains by 15N relaxation dispersion NMR spectroscopy: application to Asn and Gln residues in a cavity mutant of T4 lysozyme. J Am Chem Soc 123:967–975. doi:10.1021/ja003447g CrossRefGoogle Scholar
  34. Neudecker P et al (2012) Structure of an intermediate state in protein folding and aggregation. Science 336:362–366. doi:10.1126/science.1214203 ADSCrossRefGoogle Scholar
  35. Noggle JH, Schirmer RE (1971) The nuclear Overhauser effect. Academic Press, LondonGoogle Scholar
  36. Palmer AG (2014) Chemical exchange in biomacromolecules: past, present, and future. J Magn Reson 241:3–17. doi:10.1016/j.jmr.2014.01.008 ADSCrossRefGoogle Scholar
  37. Palmer AG (2015) Enzyme dynamics from NMR spectroscopy. Acc Chem Res 48:457–465. doi:10.1021/ar500340a CrossRefGoogle Scholar
  38. Palmer AG, Massi F (2006) Characterization of the dynamics of biomacromolecules using rotating-frame spin relaxation NMR spectroscopy. Chem Rev 106:1700–1719. doi:10.1021/cr0404287 CrossRefGoogle Scholar
  39. Palmer AG, Cavanagh J, Wright PE, Rance M (1991) Sensitivity improvement in proton-detected two-dimensional heteronuclear correlation NMR spectroscopy. J Magn Reson 93:151–170. doi:10.1016/0022-2364(91)90036-S ADSGoogle Scholar
  40. Palmer AG, Kroenke CD, Loria JP (2001) Nuclear magnetic resonance methods for quantifying microsecond-to-millisecond motions in biological macromolecules. Methods Enzymol 339:204–238. doi:10.1016/S0076-6879(01)39315-1 CrossRefGoogle Scholar
  41. Press WH, Teukolsky SA, Vetterling WT, Flannery BP (1998) Numerical recipes in C, 2nd edn. Cambridge University Press, CambridgeMATHGoogle Scholar
  42. Rivalta I, Sultan MM, Lee NS, Manley GA, Loria JP, Batista VS (2012) Allosteric pathways in imidazole glycerol phosphate synthase. Proc Natl Acad Sci USA 109:E1428–E1436. doi:10.1073/pnas.1120536109 ADSCrossRefGoogle Scholar
  43. Schleucher J, Sattler M, Griesinger C (1993) Coherence selection by gradients without signal attenuation: application to the three-dimensional HNCO experiment. Angew Chem Int Ed 32:1489–1491. doi:10.1002/anie.199314891 CrossRefGoogle Scholar
  44. Sekhar A, Kay LE (2013) NMR paves the way for atomic level descriptions of sparsely populated, transiently formed biomolecular conformers. Proc Natl Acad Sci USA 110:12867–12874. doi:10.1073/pnas.1305688110 ADSCrossRefGoogle Scholar
  45. Sekhar A, Rosenzweig R, Bouvignies G, Kay LE (2015) Mapping the conformation of a client protein through the Hsp70 functional cycle. Proc Natl Acad Sci USA 112:10395–10400. doi:10.1073/pnas.1508504112 ADSCrossRefGoogle Scholar
  46. Sklenar V, Torchia D, Bax A (1987) Measurement of 13C longitudinal relaxation using 1H detection. J Magn Reson 73:375–379. doi:10.1016/0022-2364(87)90214-9 ADSGoogle Scholar
  47. Sugase K, Dyson HJ, Wright PE (2007) Mechanism of coupled folding and binding of an intrinsically disordered protein. Nature 447:1021-U1011. doi:10.1038/nature05858 CrossRefGoogle Scholar
  48. Traaseth NJ et al (2012) Heteronuclear Adiabatic Relaxation Dispersion (HARD) for quantitative analysis of conformational dynamics in proteins. J Magn Reson 219:75–82. doi:10.1016/j.jmr.2012.03.024 ADSCrossRefGoogle Scholar
  49. Vallurupalli P, Hansen DF, Stollar E, Meirovitch E, Kay LE (2007) Measurement of bond vector orientations in invisible excited states of proteins. Proc Natl Acad Sci USA 104:18473–18477. doi:10.1073/pnas.0708296104 ADSCrossRefGoogle Scholar
  50. Vallurupalli P, Bouvignies G, Kay LE (2012) Studying “invisible” excited protein states in slow exchange with a major state conformation. J Am Chem Soc 134:8148–8161. doi:10.1021/ja3001419 CrossRefGoogle Scholar
  51. Wang CY, Rance M, Palmer AG (2003) Mapping chemical exchange in proteins with MW > 50 kD. J Am Chem Soc 125:8968–8969. doi:10.1021/ja035139z CrossRefGoogle Scholar
  52. Yuwen T, Skrynnikov NR (2014) CP-HISQC: a better version of HSQC experiment for intrinsically disordered proteins under physiological conditions. J Biomol NMR 58:175–192. doi:10.1007/s10858-014-9815-5 CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Departments of Molecular Genetics, Biochemistry and ChemistryThe University of TorontoTorontoCanada
  2. 2.Program in Molecular Structure and FunctionHospital for Sick ChildrenTorontoCanada

Personalised recommendations