Abstract
Central to structural studies of biomolecules are multidimensional experiments. These are lengthy to record due to the requirement to sample the full Nyquist grid. Time savings can be achieved through undersampling the indirectly-detected dimensions combined with non-Fourier Transform (FT) processing, provided the experimental signal-to-noise ratio is sufficient. Alternatively, resolution and signal-to-noise can be improved within a given experiment time. However, non-FT based reconstruction of undersampled spectra that encompass a wide signal dynamic range is strongly impeded by the non-linear behaviour of many methods, which further compromises the detection of weak peaks. Here we show, through an application to a larger α-helical membrane protein under crowded spectral conditions, the potential use of compressed sensing (CS) l 1-norm minimization to reconstruct undersampled 3D NOESY spectra. Substantial signal overlap and low sensitivity make this a demanding application, which strongly benefits from the improvements in signal-to-noise and resolution per unit time achieved through the undersampling approach. The quality of the reconstructions is assessed under varying conditions. We show that the CS approach is robust to noise and, despite significant spectral overlap, is able to reconstruct high quality spectra from data sets recorded in far less than half the amount of time required for regular sampling.
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References
Atreya HS, Szyperski T (2004) G-matrix Fourier transform NMR spectroscopy for complete protein resonance assignment. Proc Natl Acad Sci USA 101:9642–9647. doi:10.1073/pnas.0403529101
Barna JCJ, Laue ED, Mayger MR et al (1987) Exponential sampling, an alternative method for sampling in two-dimensional NMR experiments. J Magn Reson 73:69–77
Beck A, Teboulle M (2009) A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM J Imag Sci 2:183–202. doi:10.1137/080716542
Bredies K, Lorenz DA (2008) Iterated hard shrinkage for minimization problems with sparsity constraints. SIAM J Sci Comput 30:657–683. doi:10.1137/060663556
Candes EJ, Romberg J, Tao T (2006) Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information. IEEE Trans Inf Theory 52:489–509. doi:10.1109/TIT.2005.862083
Chylla RA, Markley JL (1995) Theory and application of the maximum likelihood principle to NMR parameter estimation of multidimensional NMR data. J Biomol NMR 5:245–258. doi:10.1007/BF00211752
Coggins BE, Zhou P (2008) High resolution 4-D spectroscopy with sparse concentric shell sampling and FFT-CLEAN. J Biomol NMR 42:225–239. doi:10.1007/s10858-008-9275-x
Daubechies I, Defrise M, De Mol C (2004) An iterative thresholding algorithm for linear inverse problems with a sparsity constraint. Commun Pure Appl Math 57:1413–1457. doi:10.1002/cpa.20042
Donoho DL (2006) Compressed sensing. IEEE Trans Inf Theory 52:1289–1306. doi:10.1109/TIT.2006.871582
Drori I (2007) Fast l 1 minimization by iterative thresholding for multidimensional NMR Spectroscopy. EURASIP J Adv Sig Pr 2007:1–11. doi:10.1155/2007/20248
Eddy MT, Ruben D, Griffin RG, Herzfeld J (2012) Deterministic schedules for robust and reproducible non-uniform sampling in multidimensional NMR. J Magn Reson 214:296–301
Fiaux J, Bertelsen EB, Horwich AL, Wüthrich K (2002) NMR analysis of a 900 K GroEL-GroES complex. Nature 418:207–211. doi:10.1038/nature00860
Freeman R, Kupče E (2003) New methods for fast multidimensional NMR. J Biomol NMR 27:101–114. doi:10.1023/A:1024960302926
Frydman L, Scherf T, Lupulescu A (2002) The acquisition of multidimensional NMR spectra within a single scan. Proc Natl Acad Sci USA 99:15858–15862. doi:10.1073/pnas.252644399
Gautier A, Mott HR, Bostock MJ et al (2010) Structure determination of the seven-helix transmembrane receptor sensory rhodopsin II by solution NMR spectroscopy. Nat Struct Mol Biol 17:768–774. doi:10.1038/nsmb.1807
Hiller S, Garces RG, Malia TJ et al (2008) Solution structure of the integral human membrane protein VDAC-1 in detergent micelles. Science 321:1206–1210. doi:10.1126/science.1161302
Hoch JC, Stern AS, Donoho DL, Johnstone IM (1990) Maximum entropy reconstruction of complex (phase-sensitive) spectra. J Magn Reson 86:236–246. doi:10.1016/j.jmr.2007.07.008
Hoch JC, Maciejewski MW, Filipovic B (2008) Randomization improves sparse sampling in multidimensional NMR. J Magn Reson 193:317–320. doi:10.1016/j.jmr.2008.05.011
Holland DJ, Malioutov DM, Blake A et al (2010) Reducing data acquisition times in phase-encoded velocity imaging using compressed sensing. J Magn Reson 203:236–246. doi:10.1016/j.jmr.2010.01.001
Holland DJ, Bostock MJ, Gladden LF, Nietlispach D (2011) Fast multidimensional NMR spectroscopy using compressed sensing. Angew Chem Int Ed 50:6548–6551. doi:10.1002/anie.201100440
Hu S, Lustig M, Chen AP et al (2008) Compressed sensing for resolution enhancement of hyperpolarized 13C flyback 3D-MRSI. J Magn Reson 192:258–264. doi:10.1016/j.jmr.2008.03.003
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 132:2145–2147. doi:10.1021/ja908004w
Hyberts SG, Arthanari H, Wagner G (2011) Applications of non-uniform sampling and processing. Top Curr Chem. doi:10.1007/128
Hyberts SG, Milbradt AG, Wagner AB et al (2012) 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. doi:10.1007/s10858-012-9611-z
Kazimierczuk K, Orekhov VY (2011) Accelerated NMR spectroscopy by using compressed sensing. Angew Chem Int Ed 50:5556–5559. doi:10.1002/anie.201100370
Kazimierczuk K, Koźmiński W, Zhukov I (2006) Two-dimensional Fourier transform of arbitrarily sampled NMR data sets. J Magn Reson 179:323–328. doi:10.1016/j.jmr.2006.02.001
Kazimierczuk K, Zawadzka A, Koźmiński W (2008) Optimization of random time domain sampling in multidimensional NMR. J Magn Reson 192:123–130. doi:10.1016/j.jmr.2008.02.003
Kazimierczuk K, Stanek J, Zawadzka-Kazimierczuk A, Koźmiński W (2010) Random sampling in multidimensional NMR spectroscopy. Prog Nucl Magn Reson Spectrosc 57:420–434. doi:10.1016/j.pnmrs.2010.07.002
Kim HJ, Howell SC, Van Horn WD et al (2009) Recent advances in the application of solution NMR spectroscopy to multi-span integral membrane proteins. Prog Nucl Magn Reson Spectrosc 55:335–360. doi:10.1016/j.pnmrs.2009.07.002
Kupce E, Freeman R (2003) Projection-reconstruction of three-dimensional NMR spectra. J Am Chem Soc 125:13958–13959. doi:10.1021/ja038297z
Kupce E, Freeman R (2004) Projection-reconstruction technique for speeding up multidimensional NMR spectroscopy. J Am Chem Soc 126:6429–6440. doi:10.1021/ja049432q
Kupce E, Nishida T, Freeman R (2003) Hadamard NMR spectroscopy. Prog Nucl Magn Reson Spectrosc 42:95–122. doi:10.1016/S0079-6565(03)00022-0
Logan BF (1965) Properties of high-pass signals. Ph.D. Thesis, Columbia University, New York
Lustig M, Donoho DL, Pauly JM (2007) Sparse MRI: the application of compressed sensing for rapid MR imaging. Magn Reson Med 58:1182–1195. doi:10.1002/mrm.21391
Mandelshtam VA (2000) The multidimensional filter diagonalization method: I. Theory and numerical implementation. J Magn Reson 144:343–356. doi:10.1006/jmre.2000.2023
Marion D (2005) Fast acquisition of NMR spectra using Fourier transform of non-equispaced data. J Biomol NMR 32:141–150. doi:10.1007/s10858-005-5977-5
Marion D (2006) Processing of ND NMR spectra sampled in polar coordinates: a simple Fourier transform instead of a reconstruction. J Biomol NMR 36:45–54. doi:10.1007/s10858-006-9066-1
Marion D, Ikura M, Tschudin R, Bax A (1989) Rapid recording of 2D NMR spectra without phase cycling. Application to the study of hydrogen exchange in proteins. J Magn Reson 85:393–399
Mobli M, Stern AS, Hoch JC (2006) Spectral reconstruction methods in fast NMR: reduced dimensionality, random sampling and maximum entropy. J Magn Reson 182:96–105. doi:10.1016/j.jmr.2006.06.007
Natarajan BK (1995) Sparse approximate solutions to linear systems. SIAM J Comput 24:227–234. doi:10.1137/S0097539792240406
Nietlispach D, Gautier A (2011) Solution NMR studies of polytopic α-helical membrane proteins. Curr Opin Struct Biol 21:497–508. doi:10.1016/j.sbi.2011.06.009
Orekhov VY, Ibraghimov IV, Billeter M (2001) MUNIN: a new approach to multi-dimensional NMR spectra interpretation. J Biomol NMR 20:49–60. doi:10.1023/A:1011234126930
Otazo R, Kim D, Axel L, Sodickson DK (2010) Combination of compressed sensing and parallel imaging for highly accelerated first-pass cardiac perfusion MRI. Magn Reson Med 64:767–776. doi:10.1002/mrm.22463
Pervushin K, Riek R, Wider G, Wüthrich K (1997) Attenuated T-2 relaxation by mutual cancellation of dipole–dipole coupling and chemical shift anisotropy indicates an avenue to NMR structures of very large biological macromolecules in solution. Proc Natl Acad Sci USA 94:12366–12371
Piotto M, Saudek V, Sklenář V (1992) Gradient-tailored excitation for single-quantum NMR spectroscopy of aqueous solutions. J Biomol NMR 2:661–665. doi:10.1007/BF02192855
Rovnyak D, Frueh DP, Sastry M et al (2004) Accelerated acquisition of high resolution triple-resonance spectra using non-uniform sampling and maximum entropy reconstruction. J Magn Reson 170:15–21. doi:10.1016/j.jmr.2004.05.016
Rovnyak D, Sarcone M, Jiang Z (2011) Sensitivity enhancement for maximally resolved two-dimensional NMR by nonuniform sampling. Magn Reson Chem 49:483–491. doi:10.1002/mrc.2775
Schmieder P, Stern A, Wagner G, Hoch J (1993) Application of nonlinear sampling schemes to COSY-type spectra. J Biomol NMR 3:569–576. doi:10.1007/BF00174610
Schmieder P, Stern AS, Wagner G, Hoch JC (1994) Improved resolution in triple-resonance spectra by nonlinear sampling in the constant-time domain. J Biomol NMR 4:483–490. doi:10.1007/BF00156615
Sprangers R, Velyvis A, Kay LE (2007) Solution NMR of supramolecular complexes: providing new insights into function. Nat Methods 4:697–703. doi:10.1038/nmeth1080
Stern AS, Donoho DL, Hoch JC (2007) NMR data processing using iterative thresholding and minimum l 1 -norm reconstruction. J Magn Reson 188:295–300. doi:10.1016/j.jmr.2007.07.008
Tugarinov V, Kay LE, Ibraghimov IV, Orekhov VY (2005) High-resolution four-dimensional 1H–13C NOE spectroscopy using methyl-TROSY, sparse data acquisition, and multidimensional decomposition. J Am Chem Soc 127:2767–2775. doi:10.1021/ja044032o
Vranken WF, Boucher W, Stevens TJ et al (2005) The CCPN data model for NMR spectroscopy: development of a software pipeline. Proteins 59:687–696. doi:10.1002/prot.20449
Yang J, Zhang Y (2011) Alternating direction algorithms for l 1 -problems in compressive sensing. SIAM J Sci Comput 33:250–278. doi:10.1137/090777761
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Bostock, M.J., Holland, D.J. & Nietlispach, D. Compressed sensing reconstruction of undersampled 3D NOESY spectra: application to large membrane proteins. J Biomol NMR 54, 15–32 (2012). https://doi.org/10.1007/s10858-012-9643-4
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DOI: https://doi.org/10.1007/s10858-012-9643-4