Journal of Biomolecular NMR

, Volume 47, Issue 1, pp 65–77 | Cite as

Iterative algorithm of discrete Fourier transform for processing randomly sampled NMR data sets

  • Jan Stanek
  • Wiktor Koźmiński


Spectra obtained by application of multidimensional Fourier Transformation (MFT) to sparsely sampled nD NMR signals are usually corrupted due to missing data. In the present paper this phenomenon is investigated on simulations and experiments. An effective iterative algorithm for artifact suppression for sparse on-grid NMR data sets is discussed in detail. It includes automated peak recognition based on statistical methods. The results enable one to study NMR spectra of high dynamic range of peak intensities preserving benefits of random sampling, namely the superior resolution in indirectly measured dimensions. Experimental examples include 3D 15N- and 13C-edited NOESY-HSQC spectra of human ubiquitin.


Multidimensional NMR spectroscopy Fourier transformation Sparse sampling Random sampling NOESY Proteins Ubiquitin 



Special thanks are addressed at Maxim Mayzel from Swedish NMR Centre for his help in using MDD package, and at prof. J.C. Hoch from University of Connecticut Health Center for providing access to Rowland NMR Toolkit v.3. This work was supported by grant number: N301 07131/2159, founded by Ministry of Science and Higher Education in years 2006-2009. Research cofinanced by the European Social Fund and State funds under the Integrated Regional Operational Programme, Measure 2.6 “Regional Innovation Strategies and transfer of knowledge”, Mazovian Voivodship project “Mazovian Ph.D. Scholarship”.


  1. Armstrong GS, Mandelshtam VA, Shaka AJ, Bendiak B (2005) Rapid high-resolution four-dimensional NMR spectroscopy using the filter diagonalization method and its advantages for detailed structural elucidation of oligosaccharides. J Magn Reson 173:160–168CrossRefADSGoogle Scholar
  2. Barna JCJ, Tan SM, Laue ED (1988) Use of CLEAN in conjunction with selective data sampling for 2D NMR experiments. J Magn Reson 78:327–332Google Scholar
  3. Blackford LS, Demmel J, Dongarra J, Duff I, Hammarling S, Henry G, Heroux M, Kaufman L, Lumsdaine A, Petitet A, Pozo R, Remington K, Whaley RC (2002) An updated set of basic linear algebra subprograms (BLAS). ACM Trans Math Soft 28:135–151CrossRefGoogle Scholar
  4. Bodenhausen G, Ernst RR (1981) The accordion experiment, a simple approach to three-dimensional NMR spectroscopy. J Magn Reson 45:367–373Google Scholar
  5. Bracewell RN (2000) The Fourier transform and its applications. McGraw-Hill Higher Education, New YorkGoogle Scholar
  6. Coggins BE, Zhou P (2007) Sampling of the NMR time domain along concentric rings. J Magn Reson 184:207–221CrossRefADSGoogle Scholar
  7. Coggins BE, Zhou P (2008) High resolution 4-D spectroscopy with sparse concentric shell sampling and FFT-CLEAN. J Biomol NMR 42:225–239CrossRefGoogle Scholar
  8. Ding K, Gronenborn AM (2002) Novel 2D triple-resonance NMR experiments for sequential resonance assignments of proteins. J Magn Reson 156:262–268CrossRefADSGoogle Scholar
  9. 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
  10. Frigo M, Johnson SG (2005) The design and implementation of FFTW3. Proc IEEE 93:216–231CrossRefGoogle Scholar
  11. Frydman L, Scherf T, Lupulescu A (2002) The acquisition of multidimensional NMR spectra within a single scan. Proc Natl Acad Sci 99:15662–15858CrossRefGoogle Scholar
  12. Goddart TD, Kneller DG (1989–2008) SPARKY 3. University of California, San FranciscoGoogle Scholar
  13. Hiller S, Fiorito F, Wüthrich, Wider G (2005) Automated projection spectroscopy (APSY). P Natl Acad Sci USA 102:10876–10881CrossRefADSGoogle Scholar
  14. Hoch JC, Stern AS (1996) NMR data processing. Wiley, New YorkGoogle Scholar
  15. Högbom J (1974) Aperture synthesis with a non-regular distribution of interferometer baselines. Astron Astrophys Suppl 15:417–426ADSGoogle Scholar
  16. Hyberts SG, Frueh DP, Arthanari H, Wagner G (2009) FM reconstruction of non-uniformly sampled protein NMR data at higher dimensions and optimization by distillation. J Biomol NMR 45:283–294CrossRefGoogle Scholar
  17. Kazimierczuk K, Zawadzka A, Koźmiński W, Zhukov I (2006) Random sampling of evolution time space and Fourier transform processing. J Biomol NMR 36:157–168CrossRefGoogle Scholar
  18. Kazimierczuk K, Zawadzka A, Koźmiński W, Zhukov I (2007) Lineshapes and artifacts in multidimensional Fourier transform of arbitrary sampled NMR data sets. J Magn Reson 188:344–356CrossRefADSGoogle Scholar
  19. Kazimierczuk K, Zawadzka A, Koźmiński W (2008a) Optimization of random time domain sampling in multidimensional NMR. J Magn Reson 192:123–130CrossRefADSGoogle Scholar
  20. Kazimierczuk K, Zawadzka A, Koźmiński W, Zhukov I (2008b) Determination of spin-spin couplings from ultrahigh resolution 3D NMR spectra obtained by optimized random sampling and multidimensional Fourier transformation. J Am Chem Soc 130:5404–5405CrossRefGoogle Scholar
  21. Kazimierczuk K, Zawadzka A, Koźmiński W (2009) Narrow peaks and high dimensionalities: exploiting the advantages of random sampling. J Magn Reson 197:219–228CrossRefADSGoogle Scholar
  22. 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
  23. Koźmiński W, Zhukov I (2003) Multiple quadrature detection in reduced dimensionality experiments. J Biomol NMR 26:157–166CrossRefGoogle Scholar
  24. Kupče E, Freeman R (2003a) Projection-reconstruction of three-dimensional NMR spectra. J Am Chem Soc 125:13958–13959CrossRefGoogle Scholar
  25. Kupče E, Freeman R (2003b) Reconstruction of the three-dimensional NMR spectrum of a protein from a set of plane projection. J Biomol NMR 27:383–387CrossRefGoogle Scholar
  26. Kupče E, Freeman R (2005) Fast multidimensional NMR: radial sampling of evolution space. J Magn Reson 173:317–321CrossRefADSGoogle Scholar
  27. Luan T, Jaravine V, Yee A, Arrowsmith CH, Orekhov VY (2005) Optimization of resolution and sensitivity of 4D NOESY using multidimensional decomposition. J Biomol NMR 33:1–14CrossRefGoogle Scholar
  28. Malmodin D, Billeter M (2005a) Multiway decomposition of NMR spectra with coupled evolution periods. J Am Chem Soc 127:13486–13487CrossRefGoogle Scholar
  29. Malmodin D, Billeter M (2005b) Signal identification in NMR spectra with coupled evolution periods. J Magn Reson 176:47–53CrossRefADSGoogle Scholar
  30. Mandelshtam VA, Taylor HS, Shaka AJ (1998) Application of the filter diagonalization method to one- and two-dimensional NMR spectra. J Magn Reson 133:304–312CrossRefADSGoogle Scholar
  31. Marion D (2005) Fast acquisition of NMR spectra using fourier transform of non-equispaced data. J Biomol NMR 32:141–150CrossRefGoogle Scholar
  32. Marion D (2006) Processing of ND NMR spectra sampled in polar coordinates: a simple fourier transform instead of reconstruction. J Biomol NMR 36:45–54CrossRefGoogle Scholar
  33. 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 131:4648–4656CrossRefGoogle Scholar
  34. Mobli M, Stern A, Hoch JC (2006) Spectral reconstruction methods in fast NMR: reduced dimensionality, random sampling and maximum entropy. J Magn Reson 182:96–105CrossRefADSGoogle Scholar
  35. Mobli M, Maciejewski MW, Gryk MR, Hoch JC (2007) Automatic maximum entropy spectral reconstruction in NMR. J Biomol NMR 39:133–139CrossRefGoogle Scholar
  36. Orekhov VY, Ibraghimov I, Billeter M (2003) Optimizing resolution in multidimensional NMR by three-way decomposition. J Biomol NMR 27:165–173CrossRefGoogle Scholar
  37. Press WH, Flannery BP, Teukolsky SA, Vetterling WT (2007) Numerical recipes in C, 3rd edn. Cambridge University Press, CambridgeGoogle Scholar
  38. Rovnyak D, Frueh DP, Sastry M, Sun ZYJ, Stern AS, Hoch JC, Wagner G (2004) Accelerated acquisition of high resolution triple-resonance spectra using non-uniform sampling and maximum entropy reconstruction. J Magn Reson 170:15–21CrossRefADSGoogle Scholar
  39. Schanda P, Melckebeke HV, Brutscher B (2006) Speeding up three-dimensional protein NMR experiments to a few minutes. J Am Chem Soc 128:9042–9043CrossRefGoogle Scholar
  40. Szyperski T, Yeh DC, Sukumaran DK, Moseley HNB, Montelione GT (2002) Reduced-dimensionality NMR spectroscopy for high-throughput protein resonance assignment. P Natl Acad Sci USA 99:8009–8014CrossRefADSGoogle Scholar
  41. Tugarinov V, Kay LE, Ibraghimov I, Orekhov VY (2005) Highresolution four-dimensional H-1-C-13 NOE spectroscopy using methyl-TROSY, sparse data acquisition, and multidimensional decomposition. J Am Chem Soc 127:2767–2775CrossRefGoogle Scholar
  42. Zawadzka-Kazimierczuk A, Kazimierczuk K, Koźmiński W (2010) A set of 4D NMR experiments of enhanced resolution for easy resonance assignment in proteins. J Magn Reson 202:109–116CrossRefADSGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Faculty of ChemistryUniversity of WarsawWarsawPoland

Personalised recommendations