Journal of Biomolecular NMR

, Volume 64, Issue 2, pp 165–173 | Cite as

Non-uniform sampling of NMR relaxation data

  • Troels E. Linnet
  • Kaare TeilumEmail author


The use of non-uniform sampling of NMR spectra may give significant reductions in the data acquisition time. For quantitative experiments such as the measurement of spin relaxation rates, non-uniform sampling is however not widely used as inaccuracies in peak intensities may lead to errors in the extracted dynamic parameters. By systematic reducing the coverage of the Nyquist grid of 15N Carr-Purcell-Meiboom-Gill (CPMG) relaxation dispersion datasets for four different proteins and performing a full data analysis of the resulting non-uniform sampled datasets, we have compared the performance of the multi-dimensional decomposition and iterative re-weighted least-squares algorithms in reconstructing spectra with accurate peak intensities. As long as a single fully sampled spectrum is included in a series of otherwise non-uniform sampled two-dimensional spectra, multi-dimensional decomposition reconstructs the non-uniform sampled spectra with high accuracy. For two of the four analyzed datasets, a coverage of only 20 % results in essentially the same results as the fully sampled data. As exemplified by other data, such a low coverage is in general not enough to produce reliable results. We find that a coverage level not compromising the final results can be estimated by recording a single full two-dimensional spectrum and reducing the spectrum quality in silico.


Relaxation dispersion Non-uniform sampling Protein NMR Multi-dimensional decomposition 



We thank Edward d’Auvergne for the valuable discussions and Daniel Malmodin and Lau Dalby Nielsen for reading the manuscript. This research was supported by the Danish Council for Independent Research (11-106683).

Supplementary material

10858_2016_20_MOESM1_ESM.pdf (570 kb)
Supplementary material 1 (PDF 570 kb)


  1. Aoto PC, Fenwick RB, Kroon GJA, Wright PE (2014) Accurate scoring of non-uniform sampling schemes for quantitative NMR. J Magn Reson 246:31–35. doi: 10.1016/j.jmr.2014.06.020 CrossRefADSGoogle Scholar
  2. Ban D, Mazur A, Carneiro MG et al (2013) Enhanced accuracy of kinetic information from CT-CPMG experiments by transverse rotating-frame spectroscopy. J Biomol NMR 57:73–82. doi: 10.1007/s10858-013-9769-z CrossRefGoogle Scholar
  3. Carver JP, Richards RE (1972) A general two-site solution for the chemical exchange produced dependence of T2 upon the carr-Purcell pulse separation. J Magn Reson 6:89–105. doi: 10.1016/0022-2364(72)90090-X ADSGoogle Scholar
  4. Delaglio F, Grzesiek S, Vuister GW et al (1995) NMRPipe: a multidimensional spectral processing system based on UNIX pipes. J Biomol NMR 6:277–293. doi: 10.1007/BF00197809 CrossRefGoogle Scholar
  5. Farrow NA, Muhandiram R, Singer AU et al (1994) Backbone dynamics of a free and phosphopeptide-complexed Src homology 2 domain studied by 15N NMR relaxation. Biochemistry 33:5984–6003. doi: 10.1021/bi00185a040 CrossRefGoogle Scholar
  6. Helmus JJ, Jaroniec CP (2013) Nmrglue: an open source Python package for the analysis of multidimensional NMR data. J Biomol NMR 55:355–367. doi: 10.1007/s10858-013-9718-x CrossRefGoogle Scholar
  7. Hiller S, Ibraghimov I, Wagner G, Orekhov VY (2009) Coupled decomposition of four-dimensional NOESY spectra. J Am Chem Soc 131:12970–12978. doi: 10.1021/ja902012x CrossRefGoogle Scholar
  8. Hoch JC, Maciejewski MW, Mobli M et al (2014) Nonuniform sampling and maximum entropy reconstruction in multidimensional NMR. Acc Chem Res 47:708–717. doi: 10.1021/ar400244v CrossRefGoogle Scholar
  9. Holland DJ, Bostock MJ, Gladden LF, Nietlispach D (2011) Fast multidimensional NMR spectroscopy using compressed sensing. Angew Chem Int Ed 50:6548–6551. doi: 10.1002/anie.201100440 CrossRefGoogle Scholar
  10. Hyberts SG, Heffron GJ, Tarragona NG et al (2007) Ultrahigh-resolution (1)H-(13)C HSQC spectra of metabolite mixtures using nonlinear sampling and forward maximum entropy reconstruction. J Am Chem Soc 129:5108–5116. doi: 10.1021/ja068541x CrossRefGoogle Scholar
  11. Hyberts SG, Milbradt AG, Wagner AB et al (2012) Application of iterative soft thresholding for fast reconstruction of NMR data non-uniformly sampled with multidimensional Poisson Gap scheduling. J Biomol NMR 52:315–327. doi: 10.1007/s10858-012-9611-z CrossRefGoogle Scholar
  12. Hyberts SG, Robson SA, Wagner G (2013) Exploring signal-to-noise ratio and sensitivity in non-uniformly sampled multi-dimensional NMR spectra. J Biomol NMR 55:167–178. doi: 10.1007/s10858-012-9698-2 CrossRefGoogle Scholar
  13. Jaravine VA, Zhuravleva AV, Permi P et al (2008) Hyperdimensional NMR spectroscopy with nonlinear sampling. J Am Chem Soc 130:3927–3936. doi: 10.1021/ja077282o CrossRefGoogle Scholar
  14. Jones JA, Hodgkinson P, Barker AL, Hore PJ (1996) Optimal sampling strategies for the measurement of spin-spin relaxation times. J Magn Reson B 113:25–34. doi: 10.1006/jmrb.1996.0151 CrossRefGoogle Scholar
  15. Kazimierczuk K, Orekhov VY (2011) Accelerated NMR spectroscopy by using compressed sensing. Angew Chem Int Ed 50:5556–5559. doi: 10.1002/anie.201100370 CrossRefGoogle Scholar
  16. Korzhnev DM, Ibraghimov IV, Billeter M, Orekhov VY (2001) MUNIN: application of three-way decomposition to the analysis of heteronuclear NMR relaxation data. J Biomol NMR 21:263–268. doi: 10.1023/A:1012982830367 CrossRefGoogle Scholar
  17. 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 CrossRefADSGoogle Scholar
  18. Long D, Delaglio F, Sekhar A, Kay LE (2015) Probing invisible, excited protein states by non-uniformly sampled pseudo-4D CEST spectroscopy. Angew Chem Int Ed. doi: 10.1002/anie.201504070 Google Scholar
  19. 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. doi: 10.1021/ja983961a CrossRefGoogle Scholar
  20. Matsuki Y, Eddy MT, Herzfeld J (2009) Spectroscopy by integration of frequency and time domain information for fast acquisition of high-resolution dark spectra. J Am Chem Soc 131:4648–4656. doi: 10.1021/ja807893k CrossRefGoogle Scholar
  21. 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. doi: 10.1021/jp2081116 CrossRefGoogle Scholar
  22. Mayzel M, Rosenlöw J, Isaksson L, Orekhov VY (2014) Time-resolved multidimensional NMR with non-uniform sampling. J Biomol NMR 58:129–139. doi: 10.1007/s10858-013-9811-1 CrossRefGoogle Scholar
  23. Mobli M, Hoch JC (2008) Maximum entropy spectral reconstruction of non-uniformly sampled data. Concepts Magn Reson Part A Bridg Educ Res 32A:436–448. doi: 10.1002/cmr.a.20126 CrossRefGoogle Scholar
  24. Morin S, Linnet TE, Lescanne M et al (2014) Relax: the analysis of biomolecular kinetics and thermodynamics using NMR relaxation dispersion data. Bioinformatics 30:2219–2220. doi: 10.1093/bioinformatics/btu166 CrossRefGoogle Scholar
  25. Mulder FA, Skrynnikov NR, Hon B et al (2001) Measurement of slow (micros-ms) time scale dynamics in protein side chains by (15)N 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
  26. Orekhov VY, Jaravine VA (2011) Analysis of non-uniformly sampled spectra with multi-dimensional decomposition. Prog Nucl Magn Reson Spectrosc 59:271–292. doi: 10.1016/j.pnmrs.2011.02.002 CrossRefGoogle Scholar
  27. Palmer AG, Rance M, Wright PE (1991) Intramolecular motions of a zinc finger DNA-binding domain from Xfin characterized by proton-detected natural abundance carbon-13 heteronuclear NMR spectroscopy. J Am Chem Soc 113:4371–4380. doi: 10.1021/ja00012a001 CrossRefGoogle Scholar
  28. Palmer MR, Suiter CL, Henry GE et al (2015) Sensitivity of nonuniform sampling NMR. J Phys Chem B 119:6502–6515. doi: 10.1021/jp5126415 CrossRefGoogle Scholar
  29. Paramasivam S, Suiter CL, Hou G et al (2012) Enhanced sensitivity by nonuniform sampling enables multidimensional MAS NMR spectroscopy of protein assemblies. J Phys Chem B 116:7416–7427. doi: 10.1021/jp3032786 CrossRefGoogle Scholar
  30. Qu X, Mayzel M, Cai J-F et al (2014) Accelerated NMR spectroscopy with low-rank reconstruction. Angew Chem Int Ed n/a–n/a. doi:  10.1002/anie.201409291
  31. Rovnyak D, Sarcone M, Jiang Z (2011) Sensitivity enhancement for maximally resolved two-dimensional NMR by nonuniform sampling. Magn Reson Chem MRC 49:483–491. doi: 10.1002/mrc.2775 CrossRefGoogle Scholar
  32. Schmieder P, Stern AS, Wagner G, Hoch JC (1997) Quantification of maximum-entropy spectrum reconstructions. J Magn Reson 125:332–339. doi: 10.1006/jmre.1997.1117 CrossRefADSGoogle Scholar
  33. 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 CrossRefADSGoogle Scholar
  34. Stern AS, Donoho DL, Hoch JC (2007) NMR data processing using iterative thresholding and minimum l(1)-norm reconstruction. J Magn Reson 188:295–300. doi: 10.1016/j.jmr.2007.07.008 CrossRefADSGoogle Scholar
  35. Teilum K, Poulsen FM, Akke M (2006) The inverted chevron plot measured by NMR relaxation reveals a native-like unfolding intermediate in acyl-CoA binding protein. Proc Natl Acad Sci USA 103:6877–6882. doi: 10.1073/pnas.0509100103 CrossRefADSGoogle Scholar
  36. Teilum K, Smith MH, Schulz E et al (2009) Transient structural distortion of metal-free Cu/Zn superoxide dismutase triggers aberrant oligomerization. Proc Natl Acad Sci USA 106:18273–18278. doi: 10.1073/pnas.0907387106 CrossRefADSGoogle Scholar
  37. Tollinger M, Skrynnikov N, Mulder FAA et al (2001) Slow dynamics in folded and unfolded states of an SH3 domain. J Am Chem Soc 123:11341–11352. doi: 10.1021/ja011300z CrossRefGoogle Scholar
  38. Webb H, Farrell D, Søndergaard CR et al (2011) Remeasuring HEWL pK(a) values by NMR spectroscopy: methods, analysis, accuracy, and implications for theoretical pK(a) calculations. Proteins 79:685–702. doi: 10.1002/prot.22886 CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.SBiNLab and the Linderstrøm-Lang Centre for Protein Science, Department of BiologyUniversity of CopenhagenCopenhagen NDenmark

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