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Non-uniform sampling in quantitative assessment of heterogeneous solid-state NMR line shapes


Non-uniform sampling has been successfully used for solution and solid-state NMR of homogeneous samples. In the solid state, protein samples are often dominated by inhomogeneous contributions to the homogeneous line widths. In spite of different technical strategies for peak reconstruction by different methods, we validate that NUS can generally be used also for such situations where spectra are made up of complex peak shapes rather than Lorentian lines. Using the RMSD between subsampled and reconstructed data and those spectra obtained with uniform sampling for a sample comprising a wide conformational distribution, we quantitatively evaluate the identity of inhomogeneous peak patterns. The evaluation comprises Iterative Soft Thresholding (hmsIST implementation) as a method explicitly not assuming Lorentian lineshapes, as well as Sparse Multidimensional Iterative Lineshape Enhanced (SMILE) algorithm and Signal Separation Algorithm (SSA) reconstruction, which do work on the basis of Lorentian lineshape models, with different sampling densities. Even though individual peculiarities are apparent, all methods turn out principally viable to reconstruct the heterogeneously broadened peak shapes.

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Data availability

The IPython notebooks, scripts for NMRPipe for data processing (including setup for hmsIST and SMILE reconstruction), sample SSA cleaning and reconstruction logs are available from the authors upon request/on the lab webpage.


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We are grateful for SSA scripts by Jan Stanek, Wiktor Koźmiński, and Michał J. Górka, as well as constructive discussion with Sven G. Hyberts. Financial support is acknowleged from the Deutsche Forschungsgemeinschaft (SFB 749, TP A13, SFB 1309, TP 03, and the Emmy Noether program), the Verband der Chemischen Industrie (VCI, Liebig program), the Excellence Clusters CiPS-M and RESOLV, and the Center for NanoScience (CeNS). A.K. and Romeo Dubini are acknowledged for daily providing E.B. with some good coffee. (Gefördert durch die Deutsche Forschungsgemeinschaft (DFG) im Rahmen der Exzellenzstrategie des Bundes und der Länder – EXC 2033 – Projektnummer 390677874. Gefördert durch die Deutsche Forschungsgemeinschaft (DFG) – SFB 1309 – 325871075.)

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Burakova, E., Vasa, S.K., Klein, A. et al. Non-uniform sampling in quantitative assessment of heterogeneous solid-state NMR line shapes. J Biomol NMR 74, 71–82 (2020). https://doi.org/10.1007/s10858-019-00291-z

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  • Non-uniform sampling
  • hmsIST
  • Sparse sampling
  • SSA
  • Heterogeneous samples