Abstract
We have previously reported on the measurement of exact NOEs (eNOEs), which yield a wealth of additional information in comparison to conventional NOEs. We have used these eNOEs in a variety of applications, including calculating high-resolution structures of proteins and RNA molecules. The collection of eNOEs is challenging, however, due to the need to measure a NOESY buildup series consisting of typically four NOESY spectra with varying mixing times in a single measurement session. While the 2D version can be completed in a few days, a fully sampled 3D-NOESY buildup series can take 10 days or more to acquire. This can be both expensive as well as problematic in the case of samples that are not stable over such a long period of time. One potential method to significantly decrease the required measurement time of eNOEs is to use non-uniform sampling (NUS) to decrease the number of points measured in the indirect dimensions. The effect of NUS on the extremely tight distance restraints extracted from eNOEs may be very pronounced. Therefore, we investigated the fidelity of eNOEs measured from three test cases at decreasing NUS densities: the 18.4 kDa protein human Pin1, the 4.1 kDa WW domain of Pin1 (both in 3D), and a 4.6 kDa 14mer RNA UUCG tetraloop (2D). Our results show that NUS imparted negligible error on the eNOE distances derived from good quality data down to 10% sampling for all three cases, but there is a noticeable decrease in the eNOE yield that is dependent upon the underlying sparsity, and thus complexity, of the sample. For Pin1, this transition occurred at roughly 40% while for the WW domain and the UUCG tetraloop it occurred at lower NUS densities of 20% and 10%, respectively. We rationalized these numbers through reconstruction simulations under various conditions. The extent of this loss depends upon the number of scans taken as well as the number of peaks to be reconstructed. Based on these findings, we have created guidelines for choosing an optimal NUS density depending on the number of peaks needed to be reconstructed in the densest region of a 2D or 3D NOESY spectrum.
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References
Aoto PC, Fenwick RB, Kroon GJA, Wright PE (2014) Accurate scoring of non-uniform sampling schemes for quantitative NMR. J Magn Reson. https://doi.org/10.1016/j.jmr.2014.06.020
Barna JC, Laue E, Mayger M, Skilling J, Worrall SJ (1987) Exponential sampling, an alternative method for sampling in two-dimensional NMR experiments. J Magn Reson. https://doi.org/10.1016/0022-2364(87)90225-3
Boelens R, Koning TMG, Kaptein R (1988) Determination of biomolecular structures from proton-proton NOE’s using a relaxation matrix approach. J Mol Struct. https://doi.org/10.1016/0022-2860(88)80062-0
Boelens R, Koning TMG, van der Marel GA, van Boom JH, Kaptein R (1989) Iterative procedure for structure determination from proton-proton NOEs using a full relaxation matrix approach. Application to a DNA octamer. J Magn Reson 82:290–308
Born A et al (2018a) Backbone and side-chain chemical shift assignments of full-length, apo, human Pin1, a phosphoprotein regulator with interdomain allostery. Biomol NMR Assign 13:85
Born A et al (2018b) Efficient stereospecific Hβ2/3 NMR assignment strategy for mid-size proteins. Magnetochemistry 4:25
Bostock MJ, Holland DJ, Nietlispach D (2012) Compressed sensing reconstruction of undersampled 3D NOESY spectra: application to large membrane proteins. J Biomol NMR. https://doi.org/10.1007/s10858-012-9643-4
Brüschweiler R et al (1992) Influence of rapid intramolecular motion on NMR cross-relaxation rates. A molecular dynamics study of antamanide in solution. J Am Chem Soc. https://doi.org/10.1021/ja00033a002
Bürgi R, Pitera J, van Gunsteren WF (2001) Assessing the effect of conformational averaging on the measured values of observables. J Biomol NMR. https://doi.org/10.1023/A:1011295422203
Chi CN et al (2015a) A structural ensemble for the enzyme cyclophilin reveals an orchestrated mode of action at atomic resolution. Angew Chemie Int Ed 54:11657–11661
Chi CN, Strotz D, Riek R, Vögeli B (2015b) Extending the eNOE data set of large proteins by evaluation of NOEs with unresolved diagonals. J Biomol NMR 62:63–69
Chi CN, Strotz D, Riek R, Vögeli B (2018) NOE-derived methyl distances from a 360 kDa proteasome complex. Chem A Eur J 24:2270–2276
Delaglio F et al (1995) NMRPipe: a multidimensional spectral processing system based on UNIX pipes. J Biomol NMR 6:277–293
Güntert P, Buchner L (2015) Combined automated NOE assignment and structure calculation with CYANA. J Biomol NMR 62:453–471
Güntert P, Mumenthaler C, Wüthrich K (1997) Torsion angle dynamics for NMR structure calculation with the new program Dyana. J Mol Biol 273:283–298
Hansen DF (2019) Using deep neural networks to reconstruct non-uniformly sampled NMR spectra. J Biomol NMR. https://doi.org/10.1007/s10858-019-00265-1
Hiller S, Ibraghimov I, Wagner G, Orekhov VY (2009) Coupled decomposition of four-dimensional NOESY spectra. J Am Chem Soc. https://doi.org/10.1021/ja902012x
Hoch JC (1989) Modern spectrum analysis in nuclear magnetic resonance: alternatives to the Fourier transform. Methods Enzymol. https://doi.org/10.1016/0076-6879(89)76014-6
Holland DJ, Bostock MJ, Gladden LF, Nietlispach D (2011) Fast multidimensional NMR spectroscopy using compressed sensing. Angew Chemie Int Ed. https://doi.org/10.1002/anie.201100440
Hyberts SG, Frueh DP, Arthanari H, Wagner G (2009) FM reconstruction of non-uniformly sampled protein NMR data at higher dimensions and optimization by distillation. J Biomol NMR. https://doi.org/10.1007/s10858-009-9368-1
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. https://doi.org/10.1021/ja908004w
Hyberts SG, Milbradt AG, Wagner AB, Arthanari H, Wagner G (2012a) Application of iterative soft thresholding for fast reconstruction of NMR data non-uniformly sampled with multidimensional Poisson Gap scheduling. J Biomol NMR. https://doi.org/10.1007/s10858-012-9611-z
Hyberts SG, Arthanari H, Wagner G (2012b) Applications of non-uniform sampling and processing. Top Curr Chem. https://doi.org/10.1007/128_2011_187
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. https://doi.org/10.1007/s10858-012-9698-2
Hyberts SG, Arthanari H, Robson SA, Wagner G (2014) Perspectives in magnetic resonance: NMR in the post-FFT era. J Magn Reson. https://doi.org/10.1016/j.jmr.2013.11.014
Hyberts SG, Robson SA, Wagner G (2017) Interpolating and extrapolating with hmsIST: seeking a t max for optimal sensitivity, resolution and frequency accuracy. J Biomol NMR 68:139–154
Jaravine VA, Zhuravleva AV, Permi P, Ibraghimov I, Orekhov VY (2008) Hyperdimensional NMR spectroscopy with nonlinear sampling. J Am Chem Soc. https://doi.org/10.1021/ja077282o
Kalk A, Berendsen HJC (1976) Proton magnetic relaxation and spin diffusion in proteins. J Magn Reson. https://doi.org/10.1016/0022-2364(76)90115-3
Keepers JW, James TL (1984) A theoretical study of distance determinations from NMR. Two-dimensional nuclear overhauser effect spectra. J Magn Reson 57:404–426
Koradi R, Billeter M, Wüthrich K (1996) MOLMOL: a program for display and analysis of macromolecular structures. J Mol Graph 14:51–55
Kumar A, Wagner G, Ernst RR, Wuethrich K (1981) Buildup rates of the nuclear Overhauser effect measured by two-dimensional proton magnetic resonance spectroscopy: implications for studies of protein conformation. J Am Chem Soc 103:3654–3658
Lu KP, Hanes SD, Hunter T (1996) A human peptidyl-prolyl isomerase essential for regulation of mitosis. Nature. https://doi.org/10.1038/380544a0
Monajemi H (2016) Phase transitions in deterministic compressed sensing, with applications to magnetic resonance spectroscopy. Stanford University. https://doi.org/10.13140/RG.2.2.21686.80960
Monajemi H, Donoho DL (2018) Sparsity/undersampling tradeoffs in anisotropic undersampling, with applications in MR imaging/spectroscopy. Inf Inference A J IMA 00:1–46
Neuhaus D, Williamson M (2000) The nuclear overhauser effect in structural and conformational analysis. New York: Cambridge
Nichols P et al (2017) The exact nuclear overhauser enhancement: recent advances. Molecules 22:1176
Nichols PJ et al (2018a) Extending the applicability of exact nuclear overhauser enhancements to large proteins and RNA. ChemBioChem. https://doi.org/10.1002/cbic.201800237
Nichols PJ et al (2018b) High-resolution small RNA structures from exact nuclear overhauser enhancement measurements without additional restraints. Nat Commun Biol. https://doi.org/10.1038/s42003-018-0067-x
Nozinovic S, Fürtig B, Jonker HRA, Richter C, Schwalbe H (2009) High-resolution NMR structure of an RNA model system: the 14-mer cUUCGg tetraloop hairpin RNA. Nucleic Acids Res 38:683–694
Orekhov VY, Ibraghimov I, Billeter M (2003) Optimizing resolution in multidimensional NMR by three-way decomposition. J Biomol NMR. https://doi.org/10.1023/A:1024944720653
Orts J, Vögeli B, Riek R (2012) Relaxation matrix analysis of spin diffusion for the NMR structure calculation with eNOEs. J Chem Theory Comput 8:3483–3492
Orts J, Vögeli B, Riek R, Güntert P (2013) Stereospecific assignments in proteins using exact NOEs. J Biomol NMR. https://doi.org/10.1007/s10858-013-9780-4
Palmer MR et al (2015) Sensitivity of nonuniform sampling NMR. J Phys Chem B. https://doi.org/10.1021/jp5126415
Post CB (1992) Internal motional averaging and three-dimensional structure determination by nuclear magnetic resonance. J Mol Biol. https://doi.org/10.1016/0022-2836(92)90471-U
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. https://doi.org/10.1007/BF00156615
Solomon I (1955) Relaxation processes in a system of two spins. Phys Rev 99:559–565
Stern AS, Hoch JC (2015) A new approach to compressed sensing for NMR. Magn Reson Chem 53:908–912
Stern AS, Li KB, Hoch JC (2002) Modern spectrum analysis in multidimensional NMR spectroscopy: comparison of linear-prediction extrapolation and maximum-entropy reconstruction. J Am Chem Soc. https://doi.org/10.1021/ja011669o
Stern AS, Donoho DL, Hoch JC (2007) NMR data processing using iterative thresholding and minimum l1-norm reconstruction. J Magn Reson 188:295–300
Strotz D, Orts J, Minges M, Vögeli B (2015) The experimental accuracy of the uni-directional exact NOE. J Magn Reson 259:32–46
Strotz D, Orts J, Chi CN, Riek R, Vögeli B (2017) ENORA2 exact NOE analysis program. J Chem Theory Comput 13:4336–4346
Strotz D, Orts J, Kadavath H, Friedmann M, Ghosh D, Olsson S, Chi C, Pokharna A, Güntert P, Vögeli B, Riek R (2020) Protein allostery at atomic resolution. Angew Chem Int Engl Ed. https://doi.org/10.1002/anie.202008734
Vögeli B (2014a) The nuclear Overhauser effect from a quantitative perspective. Prog Nucl Magn Reson Spectrosc 78:1–46
Vögeli B et al (2009) Exact distances and internal dynamics of perdeuterated ubiquitin from NOE buildups. J Am Chem Soc 131:17215–17225
Vögeli B, Friedmann M, Leitz D, Sobol A, Riek R (2010) Quantitative determination of NOE rates in perdeuterated and protonated proteins: practical and theoretical aspects. J Magn Reson 204:290–302
Vögeli B, Güntert P, Riek R (2013) Multiple-state ensemble structure determination from eNOE spectroscopy. Mol Phys 111:437–454
Vögeli B et al (2014b) Towards a true protein movie: a perspective on the potential impact of the ensemble-based structure determination using exact NOEs dedicated to Prof Dr Christian Griesinger. J Magn Reson 241:53–59
Vögeli B, Olsson S, Güntert P, Riek R (2016) The Exact NOE as an alternative in ensemble structure determination. Biophys J 110:113–126
von Schlippenbach T, Oefner PJ, Gronwald W (2018) Systematic evaluation of non-uniform sampling parameters in the targeted analysis of urine metabolites by 1H,1H 2D NMR spectroscopy. Sci Rep. https://doi.org/10.1038/s41598-018-22541-0
Vranken WF et al (2005) The CCPN data model for NMR spectroscopy: development of a software pipeline. Proteins Struct Funct Genet 59:687–696
Wüthrich, K. NMR of Proteins and Nucleic Acids. 32, (Wiley, 1986).
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. https://doi.org/10.1007/s10858-016-0072-7
Zinovjev K, Liepinsh E (2013) Validation of the CHARMM27 force field for nucleic acids using 2D nuclear overhauser effect spectroscopy. J Biophys Chem 04:58–65
Acknowledgements
This research is funded by NSF Grant 1917254 for Infrastructure Innovation for Biological Research and a start-up package from the University of Colorado to B.V.
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Nichols, P.J., Born, A., Henen, M.A. et al. Reducing the measurement time of exact NOEs by non-uniform sampling. J Biomol NMR 74, 717–739 (2020). https://doi.org/10.1007/s10858-020-00344-8
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DOI: https://doi.org/10.1007/s10858-020-00344-8