Skip to main content
SpringerLink
Log in

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

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

Abstract

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.

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
Fig. 5

Similar content being viewed by others

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.

References

  • Asakura T, Ashida J, Yamane T, Kameda T, Nakazawa Y, Ohgo K, Komatsu K (2001) A repeated \(\beta\)-turn structure in poly(Ala-Gly) as a model for silk I of Bombyx mori silk fibroin studied with two-dimensional spin-diffusion NMR under off magic angle spinning and rotational echo double resonance. J Mol Biol 306(2):291

    Article  Google Scholar 

  • Becker S, Bobin J, Candès EJ (2011) NESTA: a fast and accurate first-order method for sparse recovery. SIAM J Imaging Sci 4(1):1

    Article  MathSciNet  MATH  Google Scholar 

  • Chang MC, Kimia BB (2011) Measuring 3D shape similarity by graph-based matching of the medial scaffolds. Comput Vis Image Underst 115(5):707

    Article  Google Scholar 

  • Chevelkov V, Rehbein K, Diehl A, Reif B (2006) Ultrahigh resolution in proton solid-state NMR spectroscopy at high levels of deuteration. Angew Chem Int Ed 45(23):3878

    Article  Google Scholar 

  • Colvin MT, Silvers R, Ni QZ, Can TV, Sergeyev I, Rosay M, Donovan KJ, Michael B, Wall J, Linse S, Griffin RG (2016) Atomic resolution structure of monomorphic \(\beta\)42 amyloid fibrils. J Am Chem Soc 138(30):9663

    Article  Google Scholar 

  • 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(3):277

    Article  Google Scholar 

  • Delaglio F, Walker GS, Farley KA, Sharma R, Hoch JC, Arbogast LW, Brinson RG, Marino JP (2017) Non-uniform sampling for all: more NMR spectral quality, less measurement time. Am Pharm Rev 20(4):339–681

    Google Scholar 

  • Drori I (2007) Fast minimization by iterative thresholding for multidimensional NMR spectroscopy. EURASIP J Adv Signal Process 2007(1):020248

    Article  MathSciNet  MATH  Google Scholar 

  • Fraga H, Arnaud CA, Gauto DF, Audin M, Kurauskas V, Macek P, Krichel C, Guan JY, Boisbouvier J, Sprangers R, Breyton C, Schanda P (2017) Solid-Sate NMR H–N–(C)–H and H–N–C–C 3D/4D correlation experiments for resonance assignment of large proteins. ChemPhysChem 18(19):2697

    Article  Google Scholar 

  • Ghosh U, Yau WM, Tycko R (2018) Coexisting order and disorder within a common 40-residue amyloid-\(\beta\) fibril structure in Alzheimer’s disease brain tissue. Chem Commun 54:5070

    Article  Google Scholar 

  • Helmus JJ, Jaroniec CP (2013) Nmrglue: an open source Python package for the analysis of multidimensional NMR data. J Biomol NMR 55(4):355

    Article  Google Scholar 

  • Hoch JC, Maciejewski MW, Mobli M, Schuyler AD, Stern AS (2014) Nonuniform sampling and maximum entropy reconstruction in multidimensional NMR. Acc Chem Res 47(2):708

    Article  Google Scholar 

  • Hoop CL, Lin HK, Kar K, Magyarfalvi G, Lamley JM, Boatz JC, Mandal A, Lewandowski JR, Wetzel R, van der Wel PCA (2016) Huntingtin exon 1 fibrils feature an interdigitated \(\beta\)-hairpin-based polyglutamine core. Proc Nat Acad Sci USA 113(6):1546

    Article  ADS  Google Scholar 

  • Huber M, Böckmann A, Hiller S, Meier BH (2012) 4D solid-state NMR for protein structure determination. Phys Chem Chem Phys 14:5239

    Article  Google Scholar 

  • Hunter JD (2007) Matplotlib: a 2D graphics environment. Comput Sci Eng 9(3):90

    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

    Article  Google Scholar 

  • Hyberts SG, Milbradt AG, Wagner AB, Arthanari H, Wagner G (2012) 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

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Jaudzems K, Polenova T, Pintacuda G, Oschkinat H, Lesage A (2018) DNP NMR of biomolecular assemblies. J Struct Biol 206:90–98

    Article  Google Scholar 

  • Kazimierczuk K, Zawadzka A, Koźmiński W, Zhukov I (2006) Random sampling of evolution time space and Fourier transform processing. J Biomol NMR 36(3):157

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

  • Kazimierczuk K, Stanek J, Zawadzka-Kazimierczuk A, Koźmiński W (2010) Random sampling in multidimensional NMR spectroscopy. Prog Nucl Magn Reson Spectrosc 57(4):420

    Article  Google Scholar 

  • Leigh KE, Sharma M, Mansueto MS, Boeszoermenyi A, Filman DJ, Hogle JM, Wagner G, Coen DM, Arthanari H (2015) Structure of a herpesvirus nuclear egress complex subunit reveals an interaction groove that is essential for viral replication. Proc Nat Acad Sci USA 112(29):9010

    Article  ADS  Google Scholar 

  • Linden AH, Franks WT, Akbey Ü, Lange S, van Rossum BJ, Oschkinat H (2011) Cryogenic temperature effects and resolution upon slow cooling of protein preparations in solid state NMR. J Biomol NMR 51(3):283

    Article  Google Scholar 

  • Linser R, Sarkar R, Krushelnitzky A, Mainz A, Reif B (2014) Dynamics in the solid state: perspectives for the investigation of amyloid aggregates, membrane proteins, and soluble protein complexes. J Biomol NMR 59:1

    Article  Google Scholar 

  • Linser R, Bardiaux B, Andreas LB, Hyberts SG, Morris VK, Pintacuda G, Sunde M, Kwan AH, Wagner G (2014) Solid-state NMR structure determination from diagonal-compensated, sparsely nonuniform-sampled 4D proton–proton restraints. J Am Chem Soc 136(31):11002

    Article  Google Scholar 

  • Lopez del Amo JM, Schmidt M, Fink U, Dasari M, Fändrich M, Reif B (2012) An asymmetric dimer as the basic subunit in Alzheimer’s disease amyloid \(\beta\)-fibrils. Angew Chem 124(25):6240

    Article  Google Scholar 

  • Loquet A, Sgourakis NG, Gupta R, Giller K, Riedel D, Goosmann C, Griesinger C, Kolbe M, Baker D, Becker S, Lange A (2012) Atomic model of the type III secretion system needle. Nature 486:276

    Article  ADS  Google Scholar 

  • Lu JX, Qiang W, Yau WM, Schwieters C, Meredith S, Tycko R (2013) Molecular structure of \(\beta\)-amyloid fibrils in Alzheimer’s disease brain tissue. Cell 154(6):1257

    Article  Google Scholar 

  • Marcotte I, van Beek J, Meier B (2007) Molecular disorder and structure of spider dragline silk investigated by two-dimensional solid-state NMR spectroscopy. Macromolecules 40:1995

    Article  ADS  Google Scholar 

  • McKinney W (2010) In: van der Walt S, Millman J (eds) Proceedings of the 9th python in science conference, pp 51–56

  • Millman KJ, Aivazis M (2011) Python for scientists and engineers. Comput Sci Eng 13(2):9

    Article  Google Scholar 

  • Morris VK, Linser R, Wilde KL, Duff AP, Sunde M, Kwan AH (2012) Solid-state NMR spectroscopy of functional amyloid from a fungal hydrophobin: a well-ordered beta-sheet core amidst structural heterogeneity. Angew Chem Int Ed 51(50):12621

    Article  Google Scholar 

  • Palmer MR, Suiter CL, Henry GE, Rovnyak J, Hoch JC, Polenova T, Rovnyak D (2015) Sensitivity of nonuniform sampling NMR. J Phys Chem B 119(22):6502

    Article  Google Scholar 

  • Pérez F, Granger BE (2007) IPython: a system for interactive scientific computing. Comput Sci Eng 9(3):21

    Article  Google Scholar 

  • Petkova AT, Ishii Y, Balbach JJ, Antzutkin ON, Leapman RD, Delaglio F, Tycko R (2002) A structural model for Alzheimer’s \(\beta\)-amyloid fibrils based on experimental constraints from solid state NMR. Proc Nat Acad Sci USA 99(26):16742

    Article  ADS  Google Scholar 

  • Qiang W, Yau WM, Lu JX, Collinge J, Tycko R (2017) Structural variation in amyloid-\(\beta\) fibrils from Alzheimer’s disease clinical subtypes. Nature 541:217

    Article  ADS  Google Scholar 

  • Rovnyak D, Filip C, Itin B, Stern AS, Wagner G, Griffin RG, Hoch JC (2003) Multiple-quantum magic-angle spinning spectroscopy using nonlinear sampling. J Magn Reson 161(1):43. https://doi.org/10.1016/S1090-7807(02)00189-1

    Article  ADS  Google Scholar 

  • Sekiyama N, Arthanari H, Papadopoulos E, Rodriguez-Mias RA, Wagner G, Léger-Abraham M (2015) Molecular mechanism of the dual activity of 4EGI-1: Dissociating eIF4G from eIF4E but stabilizing the binding of unphosphorylated 4E-BP1. Proc Nat Acad Sci USA 112(30):E4036

    Article  ADS  Google Scholar 

  • Stanek J, Koźmiński W (2010) Iterative algorithm of discrete Fourier transform for processing randomly sampled NMR data sets. J Biomol NMR 447:65–77

    Article  Google Scholar 

  • Stern AS, Donoho DL, Hoch JC (2007) NMR data processing using iterative thresholding and minimum l1-norm reconstruction. J Magn Reson 188(2):295

    Article  ADS  Google Scholar 

  • Struppe J, Quinn CM, Lu M, Wang M, Hou G, Lu X, Kraus J, Andreas LB, Stanek J, Lalli D, Lesage A, Pintacuda G, Maas W, Gronenborn AM, Polenova T (2017) Expanding the horizons for structural analysis of fully protonated protein assemblies by NMR spectroscopy at MAS frequencies above 100 kHz. Solid State Nucl Magn Reson 87(July):117

    Article  Google Scholar 

  • Sun S, Yan S, Guo C, Li M, Hoch JC, Williams JC, Polenova T (2012) A time-saving strategy for MAS NMR spectroscopy by combining nonuniform sampling and paramagnetic relaxation assisted condensed data collection. J Phys Chem B 116(46):13585

    Article  Google Scholar 

  • Travis OE (2006) A guide to NumPy. Trelgol Publishing, New York

    Google Scholar 

  • Tycko R (2014) Physical and structural basis for polymorphism in amyloid fibrils. Protein Sci 23(11):1528

    Article  Google Scholar 

  • Uluca B, Viennet T, Petrović D, Shaykhalishahi H, Weirich F, Gönülalan A, Strodel B, Etzkorn M, Hoyer W, Heise H (2018) DNP-enhanced MAS NMR: a tool to snapshot conformational ensembles of \(\alpha\)-Synuclein in different states. Biophys J 114(7):1614. https://doi.org/10.1016/j.bpj.2018.02.011

    Article  Google Scholar 

  • Urbanczyk M, Bernin D, Kozminski W, Kazimierczuk K (2013) Iterative thresholding algorithm for multiexponential decay applied to PGSE NMR data. Anal Chem 85(3):1828

    Article  Google Scholar 

  • van Beek JD, Beaulieu L, Schäfer H, Demura M, Asakura T, Meier BH (2000) Solid-state NMR determination of the secondary structure of Samia cynthia ricini silk. Nature 405:1077

    Article  ADS  Google Scholar 

  • Vasa SK, Singh H, Rovó P, Linser R (2018) Dynamics and interactions of a 29 kDa human enzyme studied by solid-state NMR. J Phys Chem Lett 9(6):1307

    Article  Google Scholar 

  • Xiang S, Biernat J, Mandelkow E, Becker S, Linser R (2014) Backbone assignment for minimal protein amounts of low structural homogeneity in the absence of deuteration. J Biomol NMR 59:1

    Article  Google Scholar 

  • Xiang S, Chevelkov V, Becker S, Lange A (2014) Towards automatic protein backbone assignment using proton-detected 4D solid-state NMR data. J Biomol NMR 60(2):85

    Article  Google Scholar 

  • Xiang S, Biernat J, Mandelkow E, Becker S, Linser R (2016) Backbone assignment for minimal protein amounts of low structural homogeneity in the absence of deuteration. Chem Commun 52:4002

    Article  Google Scholar 

  • Xiang S, Kulminskaya N, Habenstein B, Biernat J, Tepper K, Paulat M, Griesinger C, Becker S, Lange A, Mandelkow E, Linser R (2017) A two-component adhesive: tau fibrils arise from a combination of a well-defined motif and conformationally flexible interactions. J Am Chem Soc 139(7):2639

    Article  Google Scholar 

  • Ying J, Delaglio F, Torchia DA, Bax A (2017) Sparse multidimensional iterative lineshape-enhanced (SMILE) reconstruction of both non-uniformly sampled and conventional NMR data. J Biomol NMR 68(2):101

    Article  Google Scholar 

  • Zhou DH, Shea JJ, Nieuwkoop AJ, Franks WT, Wylie BJ, Mullen C, Sandoz D, Rienstra CM (2007) Solid-state protein-structure determination with proton-detected triple-resonance 3D magic-angle-spinning NMR spectroscopy. Angew Chem Int Ed 46(44):8380

    Article  Google Scholar 

  • Zinke M, Fricke P, Samson C, Hwang S, Wall JS, Lange S, Zinn-Justin S, Lange A (2017) Bacteriophage tail-tube assembly studied by proton-detected 4D solid-state NMR. Angew Chem Int Ed 56(32):9497

    Article  Google Scholar 

Download references

Acknowledgements

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.)

Author information

Authors and Affiliations

  1. Faculty for Chemistry and Pharmacy, Ludwig-Maximilians-University Munich, Butenandtstr. 5-13, 81377, Munich, Germany

    Ekaterina Burakova, Suresh K. Vasa, Alexander Klein & Rasmus Linser

  2. Faculty of Chemistry and Chemical Biology, Technical University Dortmund, Otto-Hahn-Straße 4a, 44227, Dortmund, Germany

    Ekaterina Burakova, Suresh K. Vasa, Alexander Klein & Rasmus Linser

Authors
  1. Ekaterina Burakova
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Suresh K. Vasa
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Alexander Klein
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Rasmus Linser
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Rasmus Linser.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Electronic supplementary material 1 (PDF 1903 kb)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

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

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10858-019-00291-z

Keywords

Search

Navigation