Advertisement

Journal of Biomolecular NMR

, Volume 73, Issue 10–11, pp 545–560 | Cite as

Reaching the sparse-sampling limit for reconstructing a single peak in a 2D NMR spectrum using iterated maps

  • Robert L. Blum
  • Jared Rovny
  • J. Patrick Loria
  • Sean E. BarrettEmail author
Article
  • 202 Downloads

Abstract

Many of the ubiquitous experiments of biomolecular NMR, including \(R_2\), \(R_{1\rho }\), and CEST, involve acquiring repeated 2D spectra under slightly different conditions. Such experiments are amenable to acceleration using non-uniform sampling spectral reconstruction methods that take advantage of prior information. We previously developed one such technique, an iterated maps method (DiffMap) that we successfully applied to 2D NMR spectra, including \(R_2\) relaxation dispersion data. In that prior work, we took a top-down approach to reconstructing the 2D spectrum with a minimal number of sparse samples, reaching an undersampling fraction that appeared to leave some room for improvement. In this study, we develop an in-depth understanding of the action of the DiffMap algorithm, identifying the factors that cause reconstruction errors for different undersampling fractions. This improved understanding allows us to formulate a bottom-up approach to finding the lowest number of sparse samples required to accurately reconstruct individual spectral features with DiffMap. We also discuss the difficulty of extending this method to reconstructing many peaks at once, and suggest a way forward.

Keywords

Difference map DiffMap Sparse sampling Reconstruction Nonuniform sampling 

Notes

Acknowledgements

We thank G. Manley for acquiring the IGPS data set. We thank D. Cui, G. Manley, and S. Elrington for helpful discussions. J.P. Loria acknowledges the support of the NSF through Grant No. MCB-1615415, and the NIH through Grant No. GM112781. R. Blum, J. Rovny, and S. Barrett acknowledge the support of the NSF through Grant No. DMR-1610313 and Grant No. DMR-1310274. R. Blum is an NSF fellow and this material is based upon work supported by the NSF GRFP under Grant No. DGE-1122492.

Supplementary material

10858_2019_262_MOESM1_ESM.pdf (1.7 mb)
Electronic supplementary material 1 (PDF 1779 kb)

References

  1. Billeter M (2017) Non-uniform sampling in biomolecular NMR. J Biomol NMR 68(2):65–66.  https://doi.org/10.1007/s10858-017-0116-7 CrossRefGoogle Scholar
  2. Bostock M, Nietlispach D (2018) Compressed sensing: reconstruction of non-uniformly sampled multidimensional NMR data. Concepts Magn Reson Part A 46A(2):e21438.  https://doi.org/10.1002/cmr.a.21438 CrossRefGoogle Scholar
  3. Elser V (2003) Phase retrieval by iterated projections. J Opt Soc Am A 20(1):40–55.  https://doi.org/10.1364/JOSAA.20.000040 ADSCrossRefGoogle Scholar
  4. Elser V, Rankenburg I, Thibault P (2007) Searching with iterated maps. Proc Natl Acad Sci USA 104(2):418–423.  https://doi.org/10.1073/pnas.0606359104 ADSMathSciNetCrossRefzbMATHGoogle Scholar
  5. Fienup JR (1982) Phase retrieval algorithms: a comparison. Appl Opt 21(15):2758–2769.  https://doi.org/10.1364/AO.21.002758 ADSCrossRefGoogle Scholar
  6. Foucart S, Rauhut H (2013) A mathematical introduction to compressive sensing. Springer, New YorkCrossRefGoogle Scholar
  7. Frey MA, Sethna ZM, Manley GA, Sengupta S, Zilm KW, Loria JP, Barrett SE (2013) Accelerating multidimensional NMR and MRI experiments using iterated maps. J Magn Reson 237:100–109.  https://doi.org/10.1016/j.jmr.2013.09.005 ADSCrossRefGoogle Scholar
  8. Haacke E, Lindskogj E, Lin W (1991) A fast, iterative, partial-Fourier technique capable of local phase recovery. J Magn Reson 92(1):126–145.  https://doi.org/10.1016/0022-2364(91)90253-P ADSCrossRefGoogle Scholar
  9. Hoch J, Stern A (1996) NMR data processing, 1st edn. Wiley-Liss, New YorkGoogle Scholar
  10. 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.  https://doi.org/10.1021/ja908004w pMID: 20121194CrossRefGoogle Scholar
  11. Hyberts SG, Arthanari H, Robson SA, Wagner G (2014) Perspectives in magnetic resonance: NMR in the post-FFT era. J Magn Reson 241:60–73.  https://doi.org/10.1016/j.jmr.2013.11.014 ADSCrossRefGoogle Scholar
  12. Hyberts SG, Robson SA, Wagner G (2017) Interpolating and extrapolating with hmsist: seeking a tmax for optimal sensitivity, resolution and frequency accuracy. J Biomol NMR 68(2):139–154.  https://doi.org/10.1007/s10858-017-0103-z CrossRefGoogle Scholar
  13. Kazimierczuk K, Orekhov VY (2011) Accelerated NMR spectroscopy by using compressed sensing. Angew Chem 123(24):5670–5673.  https://doi.org/10.1002/ange.201100370 CrossRefGoogle Scholar
  14. Kazimierczuk K, Orekhov VY (2012) A comparison of convex and non-convex compressed sensing applied to multidimensional NMR. J Magn Reson 223:1–10.  https://doi.org/10.1016/j.jmr.2012.08.001 ADSCrossRefGoogle Scholar
  15. Korzhnev DM, Kloiber K, Kay LE (2004) Multiple-quantum relaxation dispersion NMR spectroscopy probing millisecond time-scale dynamics in proteins: theory and application. J Am Chem Soc 126(23):7320–7329.  https://doi.org/10.1021/ja049968b pMID: 15186169CrossRefGoogle Scholar
  16. Linnet TE, Teilum K (2016) Non-uniform sampling of NMR relaxation data. J Biomol NMR 64(2):165–173.  https://doi.org/10.1007/s10858-016-0020-6 CrossRefGoogle Scholar
  17. Lipchock JM, Loria JP (2010) Nanometer propagation of millisecond motions in V-type allostery. Structure 18(12):1596–1607.  https://doi.org/10.1016/j.str.2010.09.020 CrossRefGoogle Scholar
  18. Lisi GP, Currier AA, Loria JP (2018) Glutamine hydrolysis by imidazole glycerol phosphate synthase displays temperature dependent allosteric activation. Front Mol Biosci 5:4.  https://doi.org/10.3389/fmolb.2018.00004 CrossRefGoogle Scholar
  19. Loria JP, Rance M, Palmer AG (1999) A relaxation-compensated Carr-Purcell-Meiboom-Gill sequence for characterizing chemical exchange by NMR spectroscopy. J Am Chem Soc 121(10):2331–2332.  https://doi.org/10.1021/ja983961a CrossRefGoogle Scholar
  20. Maciejewski MW, Qui HZ, Rujan I, Mobli M, Hoch JC (2009) Nonuniform sampling and spectral aliasing. J Magn Reson 199(1):88–93.  https://doi.org/10.1016/j.jmr.2009.04.006 ADSCrossRefGoogle Scholar
  21. Maciejewski MW, Schuyler AD, Gryk MR, Moraru II, Romero PR, Ulrich EL, Eghbalnia HR, Livny M, Delaglio F, Hoch JC (2017) NMRbox: a resource for biomolecular NMR computation. Biophys J 112(8):1529–1534.  https://doi.org/10.1016/j.bpj.2017.03.011 CrossRefGoogle Scholar
  22. 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.  https://doi.org/10.1021/ja807893k CrossRefGoogle Scholar
  23. Matsuki Y, Eddy MT, Griffin RG, Herzfeld J (2010) Rapid three-dimensional MAS NMR spectroscopy at critical sensitivity. Angew Chem Int Ed 49(48):9215–9218.  https://doi.org/10.1002/anie.201003329 CrossRefGoogle Scholar
  24. Matsuki Y, Konuma T, Fujiwara T, Sugase K (2011) Boosting protein dynamics studies using quantitative nonuniform sampling NMR spectroscopy. J Phys Chem B 115(46):13740–13745.  https://doi.org/10.1021/jp2081116 pMID: 21992609CrossRefGoogle Scholar
  25. Mayzel M, Kazimierczuk K, Orekhov VY (2014) The causality principle in the reconstruction of sparse NMR spectra. Chem Commun 50:8947–8950.  https://doi.org/10.1039/C4CC03047H CrossRefGoogle Scholar
  26. Mobli M, Hoch JC (2008) Maximum entropy spectral reconstruction of nonuniformly sampled data. Concepts Magn Reson Part A 32A(6):436–448.  https://doi.org/10.1002/cmr.a.20126 CrossRefGoogle Scholar
  27. Neudecker P, Lundström P, Kay LE (2009) Relaxation dispersion NMR spectroscopy as a tool for detailed studies of protein folding. Biophys J 96(6):2045–2054.  https://doi.org/10.1016/j.bpj.2008.12.3907 CrossRefGoogle Scholar
  28. Orekhov VY, Jaravine VA (2011) Analysis of non-uniformly sampled spectra with multi-dimensional decomposition. Prog Nucl Magn Reson Spectrosc 59(3):271–292.  https://doi.org/10.1016/j.pnmrs.2011.02.002 CrossRefGoogle Scholar
  29. Palmer AG, Kroenke CD, Loria JP (2001) Nuclear magnetic resonance methods for quantifying microsecond-to-millisecond motions in biological macromolecules. In: James TL, Dötsch V, Schmitz U (eds) Nuclear magnetic resonance of biological macromolecules—Part B, methods in enzymology, vol 339, Academic Press, New York, Chap 10, pp 204 – 238,  https://doi.org/10.1016/S0076-6879(01)39315-1 Google Scholar
  30. Palmer AG, Massi F (2006) Characterization of the dynamics of biomacromolecules using rotating-frame spin relaxation NMR spectroscopy. Chem Rev 106(5):1700–1719.  https://doi.org/10.1021/cr0404287 pMID: 16683750CrossRefGoogle Scholar
  31. Paramasivam S, Suiter CL, Hou G, Sun S, Palmer M, Hoch JC, Rovnyak D, Polenova T (2012) Enhanced sensitivity by nonuniform sampling enables multidimensional MAS NMR spectroscopy of protein assemblies. J Phys Chem B 116(25):7416–7427.  https://doi.org/10.1021/jp3032786 pMID: 22667827CrossRefGoogle Scholar
  32. Rovnyak D, Schuyler AD (2018) Advances in alternative sampling and processing. Concepts Magn Reson Part A 46A(2):e21458.  https://doi.org/10.1002/cmr.a.21458 CrossRefGoogle Scholar
  33. Rovny J, Blum RL, Loria JP, Barrett SE (2019) Accelerating 2D NMR relaxation dispersion experiments using iterated maps. J Biomol NMR.  https://doi.org/10.1007/s10858-019-00263-3 CrossRefGoogle Scholar
  34. Schlossmacher EJ (1973) An iterative technique for absolute deviations curve fitting. J Am Stat Assoc 68(344):857–859.  https://doi.org/10.1080/01621459.1973.10481436 CrossRefzbMATHGoogle Scholar
  35. Shchukina A, Kasprzak P, Dass R, Nowakowski M, Kazimierczuk K (2017) Pitfalls in compressed sensing reconstruction and how to avoid them. J Biomol NMR 68(2):79–98.  https://doi.org/10.1007/s10858-016-0068-3 CrossRefGoogle Scholar
  36. Stanek J, Koźmiński W (2010) Iterative algorithm of discrete Fourier transform for processing randomly sampled NMR data sets. J Biomol NMR 47(1):65–77.  https://doi.org/10.1007/s10858-010-9411-2 CrossRefGoogle Scholar
  37. States D, Haberkorn R, Ruben D (1982) A two-dimensional nuclear overhauser experiment with pure absorption phase in four quadrants. J Magn Reson 48(2):286–292.  https://doi.org/10.1016/0022-2364(82)90279-7 ADSCrossRefGoogle Scholar
  38. 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.  https://doi.org/10.1016/j.jmr.2007.07.008 ADSCrossRefGoogle Scholar
  39. van Zijl PCM, Yadav NN (2011) Chemical exchange saturation transfer (CEST): what is in a name and what isn’t? Magn Reson Med 65(4):927–948.  https://doi.org/10.1002/mrm.22761 CrossRefGoogle Scholar
  40. Walinda E, Morimoto D, Sugase K (2018) Resolving biomolecular motion and interactions by \({R}_2\) and \({R}_{1\rho }\) relaxation dispersion NMR. Methods 148:28–38.  https://doi.org/10.1016/j.ymeth.2018.04.026 CrossRefGoogle Scholar
  41. 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):101–118.  https://doi.org/10.1007/s10858-016-0072-7 CrossRefGoogle Scholar
  42. Zhu G, Bax A (1990) Improved linear prediction for truncated signals of known phase. J Magn Reson 90(2):405–410.  https://doi.org/10.1016/0022-2364(90)90150-8 ADSCrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of PhysicsYale UniversityNew HavenUSA
  2. 2.Department of ChemistryYale UniversityNew HavenUSA
  3. 3.Department of Molecular Biophysics and BiochemistryYale UniversityNew HavenUSA

Personalised recommendations