Data Sampling in Multidimensional NMR: Fundamentals and Strategies

  • Mark W. Maciejewski
  • Mehdi Mobli
  • Adam D. Schuyler
  • Alan S. Stern
  • Jeffrey C. HochEmail author
Part of the Topics in Current Chemistry book series (TOPCURRCHEM, volume 316)


Beginning with the introduction of Fourier Transform NMR by Ernst and Anderson in 1966, time domain measurement of the impulse response (free induction decay) consisted of sampling the signal at a series of discrete intervals. For compatibility with the discrete Fourier transform, the intervals are kept uniform, and the Nyquist theorem dictates the largest value of the interval sufficient to avoid aliasing. With the proposal by Jeener of parametric sampling along an indirect time dimension, extension to multidimensional experiments employed the same sampling techniques used in one dimension, similarly subject to the Nyquist condition and suitable for processing via the discrete Fourier transform. The challenges of obtaining high-resolution spectral estimates from short data records were already well understood, and despite techniques such as linear prediction extrapolation, the achievable resolution in the indirect dimensions is limited by practical constraints on measuring time. The advent of methods of spectrum analysis capable of processing nonuniformly sampled data has led to an explosion in the development of novel sampling strategies that avoid the limits on resolution and measurement time imposed by uniform sampling. In this chapter we review the fundamentals of uniform and nonuniform sampling methods in one- and multidimensional NMR.


Nonuniform sampling Spectrum analysis 



We thank Gerhard Wagner for providing a pre-publication manuscript for the contribution by Hyberts and Wagner in this volume. We thank Sven Hyberts for providing the Poisson gap sampling schedules used in Fig. 8, and for helpful discussions. JCH gratefully acknowledges support from the US National Institutes of Health (grants GM047467 and RR020125).


  1. 1.
    Ernst RR, Anderson WA (1966) Application of Fourier transform spectroscopy to magnetic resonance. Rev Sci Instrum 37:93–102CrossRefGoogle Scholar
  2. 2.
    Hoch JC, Stern AS (1996) NMR data processing. Wiley-Liss, New YorkGoogle Scholar
  3. 3.
    Beckman RA, Zuiderweg ERP (1995) Guidelines for the use of oversampling in protein NMR. J Magn Reson A113:223–231Google Scholar
  4. 4.
    Delsuc MA, Lallemand JY (1986) Improvement of dynamic range in NMR by oversampling. J Magn Reson 69:504–507Google Scholar
  5. 5.
    Rovnyak D, Hoch JC, Stern AS, Wagner G (2004) Resolution and sensitivity of high field nuclear magnetic resonance spectroscopy. J Biomol NMR 30:1–10CrossRefGoogle Scholar
  6. 6.
    Jeener J (1971) Oral presentation, Ampere International Summer School, YugoslaviaGoogle Scholar
  7. 7.
    States DJ, Haberkorn RA, Ruben DJ (1982) A two-dimensional nuclear Overhauser experiment with pure absorption phase in four quadrants. J Magn Reson 48:286–292Google Scholar
  8. 8.
    Stern AS, Li K-B, Hoch JC (2002) Modern spectrum analysis in multidimensional NMR spectroscopy: comparison of linear-prediction extrapolation and maximum-entropy reconstruction. J Am Chem Soc 124:1982–1993CrossRefGoogle Scholar
  9. 9.
    Wernecke SJ, D’ Addario LR (1977) Maximum entropy image reconstruction. IEEE Trans Comput 26:351–364CrossRefGoogle Scholar
  10. 10.
    Skilling J, Bryan R (1984) Maximum entropy image reconstruction: general algorithm. Mon Not R Astron Soc 211:111–124Google Scholar
  11. 11.
    Stern AS, Donoho DL, Hoch JC (2007) NMR data processing using iterative thresholding and minimum l(1)-norm reconstruction. J Magn Reson 188:295–300CrossRefGoogle Scholar
  12. 12.
    Hyberts SG, Heffron GJ, Tarragona NG, Solanky K, Edmonds KA, Luithardt H, Fejzo J, Chorev M, Aktas H, Colson K, Falchuk KH, Halperin JA, Wagner G (2007) Ultrahigh-resolution (1)H-(13)C HSQC spectra of metabolite mixtures using nonlinear sampling and forward maximum entropy reconstruction. J Am Chem Soc 129:5108–5116CrossRefGoogle Scholar
  13. 13.
    Bretthorst GL (1990) Bayesian Analysis I. Parameter estimation using quadrature NMR models. J Magn Reson 88:533–551Google Scholar
  14. 14.
    Chylla RA, Markley JL (1993) Improved frequency resolution in multidimensional constant-time experiments by multidimensional Bayesian analysis. J Biomol NMR 3:515–533CrossRefGoogle Scholar
  15. 15.
    Chylla RA, Markley JL (1995) Theory and application of the maximum likelihood principle to NMR parameter estimation of multidimensional NMR data. J Biomol NMR 5:245–258CrossRefGoogle Scholar
  16. 16.
    Jaravine V, Ibraghimov I, Orekhov VY (2006) Removal of a time barrier for high-resolution multidimensional NMR spectroscopy. Nat Methods 3:605–607CrossRefGoogle Scholar
  17. 17.
    Bro R (1997) PARAFAC. Tutorial and applications. Chemometr Intell Lab Syst 38:149–171CrossRefGoogle Scholar
  18. 18.
    Kazimierczuk K, Kozminski W, Zhukov I (2006) Two-dimensional Fourier transform of arbitrarily sampled NMR data sets. J Magn Reson 179:323–328CrossRefGoogle Scholar
  19. 19.
    Press WH, Flannery BP, Teukolsky SA, Vetterling WT (1992) Numerical recipes in Fortran. Cambridge University Press, CambridgeGoogle Scholar
  20. 20.
    Pannetier N, Houben K, Blanchard L, Marion D (2007) Optimized 3D-NMR sampling for resonance assignment of partially unfolded proteins. J Magn Reson 186:142–149CrossRefGoogle Scholar
  21. 21.
    Bodenhausen G, Ernst RR (1969) The accordion experiment, a simple approach to three-dimensional NMR spectroscopy. J Magn Reson 45(1981):367–373Google Scholar
  22. 22.
    Barna JCJ, Laue ED, Mayger MR, Skilling J, Worrall SJP (1987) Exponential sampling: an alternative method for sampling in two dimensional NMR experiments. J Magn Reson 73:69Google Scholar
  23. 23.
    Carr PA, Fearing DA, Palmer AG (1998) 3D accordion spectroscopy for measuring15N and13CO relaxation rates in poorly resolved NMR spectra. J Magn Reson 132:25–33CrossRefGoogle Scholar
  24. 24.
    Chen K, Tjandra N (2009) Direct measurements of protein backbone 15 N spin relaxation rates from peak line-width using a fully-relaxed Accordion 3D HNCO experiment. J Magn Reson 197:71–76CrossRefGoogle Scholar
  25. 25.
    Szyperski T, Wider G, Bushweller JH, Wüthrich K (1993) Reduced dimensionality in triple resonance NMR experiments. J Am Chem Soc 115:9307–9308CrossRefGoogle Scholar
  26. 26.
    Szyperski T, Wider G, Bushweller JH, Wüthrich K (1993) 3D 13 C-15 N-heteronuclear two-spin coherence spectroscopy for polypeptide backbone assignments in 13 C-15 N-double-labeled proteins. J Biomol NMR 3:127–132Google Scholar
  27. 27.
    Kim S, Szyperski T (2003) GFT NMR, a new approach to rapidly obtain precise high-dimensional NMR spectral information. J Am Chem Soc 125:1385–1393CrossRefGoogle Scholar
  28. 28.
    Coggins BE, Zhou P (2006) Polar Fourier transforms of radially sampled NMR data. J Magn Reson 182:84–95CrossRefGoogle Scholar
  29. 29.
    Coggins BE, Zhou P (2007) Sampling of the NMR time domain along concentric rings. J Magn Reson 184:207–221CrossRefGoogle Scholar
  30. 30.
    Bretthorst GL (2001) Nonuniform sampling: bandwidth and aliasing. In: Rychert J, Erickson G, Smith CR (eds) Maximum entropy and Bayesian methods in science and engineering. Springer, New York, pp 1–28Google Scholar
  31. 31.
    Bretthorst GL (2008) Nonuniform sampling: bandwidth and aliasing. Concepts Magn Reson 32A:417–435CrossRefGoogle Scholar
  32. 32.
    Schmieder P, Stern AS, Wagner G, Hoch JC (1993) Application of nonlinear sampling schemes to COSY-type spectra. J Biomol NMR 3:569–576CrossRefGoogle Scholar
  33. 33.
    Schmieder P, Stern AS, Wagner G, Hoch JC (1994) Improved resolution in triple-resonance spectra by nonlinear sampling in the constant-time domain. J Biomol NMR 4:483–490CrossRefGoogle Scholar
  34. 34.
    Aggarwal K, Delsuc MA (1997) Triangular sampling of multidimensional NMR data sets. Magn Reson Chem 35:593–596CrossRefGoogle Scholar
  35. 35.
    Eghbalnia HR, Bahrami A, Tonelli M, Hallenga K, Markley JL (2005) High-resolution iterative frequency identification for NMR as a general strategy for multidimensional data collection. J Am Chem Soc 127:12528–12536CrossRefGoogle Scholar
  36. 36.
    Hiller S, Fiorito F, Wüthrich K (2005) Automated projection spectroscopy (APSY). Proc Natl Acad Sci USA 102:10876–10888CrossRefGoogle Scholar
  37. 37.
    Bartels C, Xia T-H, Billeter M, Güntert P, Wüthrich K (1995) The program XEASY for computer-supported NMR spectral analysis of biological macromolecules. J Biomol NMR 5:1–10CrossRefGoogle Scholar
  38. 38.
    Delaglio F, Grzesiek S, Vuister GW, Zhu G, Pfeifer J, Bax A (1995) NMRPipe: a multidimensional spectral processing system based on UNIX pipes. J Biomol NMR 6:277–293CrossRefGoogle Scholar
  39. 39.
    Johnson BA (2004) Using NMR view to visualize and analyze the NMR spectra of macromolecules. Methods Mol Biol 278:313–352Google Scholar
  40. 40.
    Goddard TD, Kneller DG (2006) SPARKY 3, University of California, San FranciscoGoogle Scholar
  41. 41.
    Hyberts SG, Takeuchi K, Wagner G (2010) Poisson-gap sampling and forward maximum entropy reconstruction for enhancing the resolution and sensitivity of protein NMR data. J Am Chem Soc 132:2145–2147CrossRefGoogle Scholar
  42. 42.
    Maciejewski MW, Qui HZ, Rujan I, Mobli M, Hoch JC (2009) Nonuniform sampling and spectral aliasing. J Magn Reson 199:88–93CrossRefGoogle Scholar
  43. 43.
    Kumar A, Brown SC, Donlan ME, Meier BU, Jeffs PW (1991) Optimization of two-dimensional NMR by matched accumulation. J Magn Reson 95:1–9Google Scholar
  44. 44.
    Mehdi M, Alan SS, Jeffrey CH (2006) Spectral Reconstruction Methods in Fast NMR: Reduced Dimensionality, Random Sampling, and Maximum Entropy Reconstruction. J Magn Reson 192:96–105Google Scholar
  45. 45.
    Mehdi M, Alan SS, Wolfgang B, Glenn FK, Jeffrey CH, (2010) A non-uniformly sampled 4D HCC(CO)NH-TOCSY experiment processed using maximum entropy for rapid protein sidechain assignment. J Magn Reson 204:160–164Google Scholar
  46. 46.
    Hoch JC, Maciejewski MW, Filipovic B (2008) Randomization improves sparse sampling in multidimensional NMR. J Magn Reson 193:317–20Google Scholar
  47. 47.
    Mark WM, Harry Z, Qui IR, Mehdi M, Jeffrey CH (2009) Nonuniform sampling and spectral aliasing. J Magn Reson 199:88–93Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Mark W. Maciejewski
    • 1
  • Mehdi Mobli
    • 2
  • Adam D. Schuyler
    • 1
  • Alan S. Stern
    • 3
  • Jeffrey C. Hoch
    • 1
    Email author
  1. 1.Department of Molecular, Microbial, and Structural BiologyUniversity of Connecticut Health CenterFarmingtonUSA
  2. 2.Division of Chemistry and Structural Biology, Institute for Molecular BioscienceThe University of QueenslandBrisbaneAustralia
  3. 3.Rowland Institute at HarvardCambridgeUSA

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