Skip to main content
SpringerLink
Log in

Exploring signal-to-noise ratio and sensitivity in non-uniformly sampled multi-dimensional NMR spectra

  • Article
  • Published:
Journal of Biomolecular NMR Aims and scope Submit manuscript

Abstract

It is well established that non-uniform sampling (NUS) allows acquisition of multi-dimensional NMR spectra at a resolution that cannot be obtained with traditional uniform acquisition through the indirect dimensions. However, the impact of NUS on the signal-to-noise ratio (SNR) and sensitivity are less well documented. SNR and sensitivity are essential aspects of NMR experiments as they define the quality and extent of data that can be obtained. This is particularly important for spectroscopy with low concentration samples of biological macromolecules. There are different ways of defining the SNR depending on how to measure the noise, and the distinction between SNR and sensitivity is often not clear. While there are defined procedures for measuring sensitivity with high concentration NMR standards, such as sucrose, there is no clear or generally accepted definition of sensitivity when comparing different acquisition and processing methods for spectra of biological macromolecules with many weak signals close to the level of noise. Here we propose tools for estimating the SNR and sensitivity of NUS spectra with respect to sampling schedule and reconstruction method. We compare uniformly acquired spectra with NUS spectra obtained in the same total measuring time. The time saving obtained when only 1/k of the Nyquist grid points are sampled is used to measure k-fold more scans per increment. We show that judiciously chosen NUS schedules together with suitable reconstruction methods can yield a significant increase of the SNR within the same total measurement time. Furthermore, we propose to define the sensitivity as the probability to detect weak peaks and show that time-equivalent NUS can considerably increase this detection sensitivity. The sensitivity gain increases with the number of NUS indirect dimensions. Thus, well-chosen NUS schedules and reconstruction methods can significantly increase the information content of multidimensional NMR spectra of challenging biological macromolecules.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

Abbreviations

NMR:

Nuclear magnetic resonance

hmsIST:

Harvard Medical School implementation of the iterative soft thresholding approach

FFT:

Fast Fourier transformation

References

  • 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 73:69–77

    Google Scholar 

  • Bostock MJ, Holland DJ, Nietlispach D (2012) Compressed sensing reconstruction of undersampled 3D NOESY spectra: application to large membrane proteins. J Biomol NMR 54(1):15–32. doi:10.1007/s10858-012-9643-4

    Article  Google Scholar 

  • Candes EJ, Wakin MB, Boyd SP (2008) Enhancing sparsity by reweighted l1 minimization. Fourier Anal Appl 14:877–905

    Article  MathSciNet  MATH  Google Scholar 

  • Coggins BE, Zhou P (2008) High resolution 4-D spectroscopy with sparse concentric shell sampling and FFT-CLEAN. J Biomol NMR 42(4):225–239. doi:10.1007/s10858-008-9275-x

    Article  Google Scholar 

  • Coggins BE, Werner-Allen JW, Yan AK, Zhou P (2012) Rapid protein global fold determination using ultrasparse sampling, high-dynamic range artifact suppression, and time-shared NOESY. J Am Chem Soc. doi:10.1021/ja307445y

    Google Scholar 

  • Denk W, Baumann R, Wagner G (1986) Quantitative evaluation of cross peak intensities by projection of two-dimensional NOE spectra on a linear space spanned by a set of reference resonance lines. J Magn Reson 67:386–390

    Google Scholar 

  • Drori I (2007) Fast l1 minimization by iterative thresholding for multidimensional NMR spectroscopy. Eurasip J Adv Signal Process 2007:1–10

    Article  MathSciNet  Google Scholar 

  • Gronenborn AM, Filpula DR, Essig NZ, Achari A, Whitlow M, Wingfield PT, Clore GM (1991) A novel, highly stable fold of the immunoglobulin binding domain of streptococcal protein G. Science 253(5020):657–661

    Article  ADS  Google Scholar 

  • Hiller S, Ibraghimov I, Wagner G, Orekhov VY (2009) Coupled decomposition of four-dimensional NOESY spectra. J Am Chem Soc 131(36):12970–12978. doi:10.1021/ja902012x

    Article  Google Scholar 

  • Hoch JC (1989) Modern spectrum analysis in nuclear magnetic resonance: alternatives to the Fourier transform. Methods Enzymol 176:216–241

    Article  Google Scholar 

  • Hoch JC, Stern AS (1996) NMR data processing. Wiley-Liss, New York

    Google Scholar 

  • Hoch JC, Stern AS (2001) Maximum entropy reconstruction, spectrum analysis and deconvolution in multidimensional nuclear magnetic resonance. Methods Enzymol 338:159–178

    Article  Google Scholar 

  • Högbom JA (1974) Aperture synthesis with a non-regular distribution of interferometer baselines. Astron Astrophys Suppl 15:417–426

    ADS  Google Scholar 

  • Holland DJ, Bostock MJ, Gladden LF, Nietlispach D (2011) Fast multidimensional NMR spectroscopy using compressed sensing. Angew Chem 50(29):6548–6551. doi:10.1002/anie.201100440

    Article  Google Scholar 

  • 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(16):5108–5116

    Article  Google Scholar 

  • 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(3):283–294. doi:10.1007/s10858-009-9368-1

    Article  Google Scholar 

  • 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(7):2145–2147. doi:10.1021/ja908004w

    Article  Google Scholar 

  • Hyberts SG, Arthanari H, Wagner G (2011) Applications of non-uniform sampling and processing. Top Curr Chem. doi:10.1007/128_2011_187

    Google Scholar 

  • Hyberts SG, Arthanari H, Wagner G (2012a) Applications of non-uniform sampling and processing. Top Curr Chem 316:125–148. doi:10.1007/128_2011_187

    Article  Google Scholar 

  • Hyberts SG, Milbradt AG, Wagner AB, Arthanari H, Wagner G (2012b) Application of iterative soft thresholding for fast reconstruction of NMR data non-uniformly sampled with multidimensional Poisson Gap scheduling. J Biomol NMR 52(4):315–327. doi:10.1007/s10858-012-9611-z

    Article  Google Scholar 

  • Jaravine V, Ibraghimov I, Orekhov VY (2006) Removal of a time barrier for high-resolution multidimensional NMR spectroscopy. Nat Methods 3(8):605–607. doi:10.1038/nmeth900

    Article  Google Scholar 

  • Kazimierczuk K, Orekhov VY (2011) Accelerated NMR spectroscopy by using compressed sensing. Angew Chem 50(24):5556–5559. doi:10.1002/anie.201100370

    Article  Google Scholar 

  • Kazimierczuk K, Zawadzka A, Kozminski W, Zhukov I (2007) Lineshapes and artifacts in multidimensional Fourier transform of arbitrary sampled NMR data sets. J Magn Reson 188(2):344–356. doi:10.1016/j.jmr.2007.08.005

    Article  ADS  Google Scholar 

  • Kazimierczuk K, Zawadzka A, Kozminski W (2008) Optimization of random time domain sampling in multidimensional NMR. J Magn Reson 192(1):123–130. doi:10.1016/j.jmr.2008.02.003

    Article  ADS  Google Scholar 

  • Kupce E, Freeman R (2003) Projection-reconstruction of three-dimensional NMR spectra. J Am Chem Soc 125(46):13958–13959

    Article  Google Scholar 

  • Kupce E, Freeman R (2005) Fast multidimensional NMR: radial sampling of evolution space. J Magn Reson 173(2):317–321. doi:10.1016/j.jmr.2004.12.004

    Article  ADS  Google Scholar 

  • 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(13):4648–4656. doi:10.1021/ja807893k

    Article  Google Scholar 

  • Mobli M, Stern AS, Hoch JC (2006) Spectral reconstruction methods in fast NMR: reduced dimensionality, random sampling and maximum entropy. J Magn Reson 182(1):96–105. doi:10.1016/j.jmr.2006.06.007

    Article  ADS  Google Scholar 

  • Rovnyak D, Frueh DP, Sastry M, Sun ZY, Stern AS, Hoch JC, Wagner G (2004a) Accelerated acquisition of high resolution triple-resonance spectra using non-uniform sampling and maximum entropy reconstruction. J Magn Reson 170(1):15–21

    Article  ADS  Google Scholar 

  • Rovnyak D, Hoch JC, Stern AS, Wagner G (2004b) Resolution and sensitivity of high field nuclear magnetic resonance spectroscopy. J Biomol NMR 30(1):1–10

    Article  Google Scholar 

  • Stanek J, Kozminski W (2010) Iterative algorithm of discrete Fourier transform for processing randomly sampled NMR data sets. J Biomol NMR 47(1):65–77. doi:10.1007/s10858-010-9411-2

    Article  Google Scholar 

  • Stanek J, Augustyniak R, Kozminski W (2011) Suppression of sampling artefacts in high-resolution four-dimensional NMR spectra using signal separation algorithm. J Magn Reson. doi:10.1016/j.jmr.2011.10.009

    Google Scholar 

  • Stern AS, Donoho DL, Hoch JC (2007) NMR data processing using iterative thresholding and minimum l(1)-norm reconstruction. J Magn Reson 188(2):295–300. doi:10.1016/j.jmr.2007.07.008

    Article  ADS  Google Scholar 

  • Tugarinov V, Kay LE, Ibraghimov I, Orekhov VY (2005) High-resolution four-dimensional 1H–13C NOE spectroscopy using methyl-TROSY, sparse data acquisition, and multidimensional decomposition. J Am Chem Soc 127(8):2767–2775

    Article  Google Scholar 

  • Wen J, Wu J, Zhou P (2011) Sparsely sampled high-resolution 4-D experiments for efficient backbone resonance assignment of disordered proteins. J Magn Reson 209(1):94–100. doi:10.1016/j.jmr.2010.12.012

    Article  ADS  Google Scholar 

  • Zhou P, Lugovskoy AA, Wagner G (2001) A solubility-enhancement tag (SET) for NMR studies of poorly behaving proteins. J Biomol NMR 20(1):11–14

    Article  Google Scholar 

Download references

Acknowledgments

This research was supported by the National Institutes of Health (Grants GM047467, GM094608 and EB002026), and the Agilent Foundation.

Author information

Authors and Affiliations

  1. Department of Biological Chemistry and Molecular Pharmacology, Harvard Medical School, 240 Longwood Avenue, Boston, MA, 02115, USA

    Sven G. Hyberts, Scott A. Robson & Gerhard Wagner

Authors
  1. Sven G. Hyberts
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Scott A. Robson
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Gerhard Wagner
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Gerhard Wagner.

Additional information

The programs for generating Poisson Gap Sampling schedule and for reconstruction of NUS spectra are available upon request.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary material 1 (PDF 1,187 kb)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hyberts, S.G., Robson, S.A. & Wagner, G. Exploring signal-to-noise ratio and sensitivity in non-uniformly sampled multi-dimensional NMR spectra. J Biomol NMR 55, 167–178 (2013). https://doi.org/10.1007/s10858-012-9698-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10858-012-9698-2

Keywords

Search

Navigation