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Application of iterative soft thresholding for fast reconstruction of NMR data non-uniformly sampled with multidimensional Poisson Gap scheduling

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Abstract

The fast Fourier transformation has been the gold standard for transforming data from time to frequency domain in many spectroscopic methods, including NMR. While reliable, it has as a drawback that it requires a grid of uniformly sampled data points. This needs very long measuring times for sampling in multidimensional experiments in all indirect dimensions uniformly and even does not allow reaching optimal evolution times that would match the resolution power of modern high-field instruments. Thus, many alternative sampling and transformation schemes have been proposed. Their common challenges are the suppression of the artifacts due to the non-uniformity of the sampling schedules, the preservation of the relative signal amplitudes, and the computing time needed for spectra reconstruction. Here we present a fast implementation of the Iterative Soft Thresholding approach (istHMS) that can reconstruct high-resolution non-uniformly sampled NMR data up to four dimensions within a few hours and make routine reconstruction of high-resolution NUS 3D and 4D spectra convenient. We include a graphical user interface for generating sampling schedules with the Poisson-Gap method and an estimation of optimal evolution times based on molecular properties. The performance of the approach is demonstrated with the reconstruction of non-uniformly sampled medium and high-resolution 3D and 4D protein spectra acquired with sampling densities as low as 0.8%. The method presented here facilitates acquisition, reconstruction and use of multidimensional NMR spectra at otherwise unreachable spectral resolution in indirect dimensions.

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Abbreviations

NMR:

Nuclear magnetic resonance

IST:

Iterative soft thresholding

istHMS:

Implementation of IST at Harvard Medical School

FM reconstruction:

Forward maximum entropy reconstruction

MDD:

Multi-dimensional decomposition

FDM:

Filter diagonalization method

FFT:

Fast Fourier transformation

DFT:

Discrete Fourier transformation

NOE:

Nuclear Overhauser enhancement

NOESY:

NOE spectroscopy

GUI:

Graphical user interface

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Acknowledgment

This research was supported by the National Institutes of Health (Grants GM047467, CA127990, GM094608 and EB002026). We thank Dr. Koh Takeuchi for providing the data used in Fig. 7B.

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Authors and Affiliations

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

    Sven G. Hyberts, Alexander G. Milbradt, Andreas B. Wagner, Haribabu Arthanari & Gerhard Wagner

  2. Wentworth Institute of Technology, 550 Huntington Avenue, Boston, MA, 02115, USA

    Andreas B. Wagner

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  1. Sven G. Hyberts
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  2. Alexander G. Milbradt
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  3. Andreas B. Wagner
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  4. Haribabu Arthanari
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  5. Gerhard Wagner
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Correspondence to Gerhard Wagner.

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Contribution from Harvard Medical School, Boston, MA 02115, USA.

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Hyberts, S.G., Milbradt, A.G., Wagner, A.B. et al. 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 (2012). https://doi.org/10.1007/s10858-012-9611-z

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