Articles | Volume 5, issue 1
https://doi.org/10.5194/mr-5-69-2024
© Author(s) 2024. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/mr-5-69-2024
© Author(s) 2024. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Evaluating the motional timescales contributing to averaged anisotropic interactions in MAS solid-state NMR
Kathrin Aebischer
Department of Chemistry and Applied Biosciences, ETH Zürich, Vladimir-Prelog-Weg 2, 8093 Zurich, Switzerland
Lea Marie Becker
Institute of Science and Technology Austria (ISTA), Am Campus 1, 3400 Klosterneuburg, Austria
Paul Schanda
Institute of Science and Technology Austria (ISTA), Am Campus 1, 3400 Klosterneuburg, Austria
Department of Chemistry and Applied Biosciences, ETH Zürich, Vladimir-Prelog-Weg 2, 8093 Zurich, Switzerland
Related authors
Kathrin Aebischer, Zdeněk Tošner, and Matthias Ernst
Magn. Reson., 2, 523–543, https://doi.org/10.5194/mr-2-523-2021, https://doi.org/10.5194/mr-2-523-2021, 2021
Short summary
Short summary
The radio-frequency (rf) field amplitude in solid-state NMR probes changes over the sample volume, i.e. different parts of the sample will experience different nutation frequencies. If the sample is rotated inside the coil as it is typical for magic angle spinning in solid-state NMR, such a position-dependent inhomogeneity leads to an additional time dependence of the rf field amplitude. We show that such time-dependent modulations do not play an important role in many experiments.
Kathrin Aebischer, Nino Wili, Zdeněk Tošner, and Matthias Ernst
Magn. Reson., 1, 187–195, https://doi.org/10.5194/mr-1-187-2020, https://doi.org/10.5194/mr-1-187-2020, 2020
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Resonant pulses in a spin-lock frame are used to select parts of the rf-field distribution in NMR experiments. Such pulses can be implemented in a straightforward way and arbitrarily shaped pulses can be used. We show an application of such pulses in homonuclear decoupling where restricting the amplitude distribution of the rf field leads to improved performance.
Luzian Thomas and Matthias Ernst
Magn. Reson., 5, 153–166, https://doi.org/10.5194/mr-5-153-2024, https://doi.org/10.5194/mr-5-153-2024, 2024
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The paper investigates the suitability of an existing solution-state NMR spin decoupling sequence for use as a low-power solid-state NMR decoupling sequence under sample spinning. Complications arise from resonance conditions between the spin modulations by the pulse sequence and the sample rotation. We show that the timing of the pulse sequence is the most important criterion needed to achieve good decoupling. The paper gives recommendations for optimum parameters.
Federico Napoli, Jia-Ying Guan, Charles-Adrien Arnaud, Pavel Macek, Hugo Fraga, Cécile Breyton, and Paul Schanda
Magn. Reson., 5, 33–49, https://doi.org/10.5194/mr-5-33-2024, https://doi.org/10.5194/mr-5-33-2024, 2024
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Protons (1H) are useful reporters of protein structure and dynamics in solid-state NMR. However, 1H abundance is detrimental to the resolution of NMR spectra. Substituting 1H by deuterons has been an efficient strategy to improve spectral quality, but when the crucial backbone amide sites are not protonated, much information is loss. We propose a method to completely protonate the amide sites, while maintaining high-resolution information, which partially also extends to backbone alpha-1H.
Aaron Himmler, Mohammed M. Albannay, Gevin von Witte, Sebastian Kozerke, and Matthias Ernst
Magn. Reson., 3, 203–209, https://doi.org/10.5194/mr-3-203-2022, https://doi.org/10.5194/mr-3-203-2022, 2022
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Dynamic nuclear polarization requires a waveguide that connects the cold (1–10 K) sample space to the outside. To reduce the heating of the sample, a waveguide is produced from steel which has low thermal conductivity but attenuates the microwaves. Therefore, the inside of the waveguide should be plated with silver to reduce electrical losses. We show a new simple way to electroplate such waveguides with a thin silver layer and show that this improves the experimental performance.
Václav Římal, Morgane Callon, Alexander A. Malär, Riccardo Cadalbert, Anahit Torosyan, Thomas Wiegand, Matthias Ernst, Anja Böckmann, and Beat H. Meier
Magn. Reson., 3, 15–26, https://doi.org/10.5194/mr-3-15-2022, https://doi.org/10.5194/mr-3-15-2022, 2022
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Through the advent of fast magic-angle spinning and high magnetic fields, the spectral resolution of solid-state NMR spectra has recently been greatly improved. To take full advantage of this gain, the magnetic field must be stable over the experiment time of hours or even days. We thus monitor the field by simultaneous acquisition of a frequency reference (SAFR) and use this information to correct multidimensional spectra improving resolution and availability of productive magnet time.
Kathrin Aebischer, Zdeněk Tošner, and Matthias Ernst
Magn. Reson., 2, 523–543, https://doi.org/10.5194/mr-2-523-2021, https://doi.org/10.5194/mr-2-523-2021, 2021
Short summary
Short summary
The radio-frequency (rf) field amplitude in solid-state NMR probes changes over the sample volume, i.e. different parts of the sample will experience different nutation frequencies. If the sample is rotated inside the coil as it is typical for magic angle spinning in solid-state NMR, such a position-dependent inhomogeneity leads to an additional time dependence of the rf field amplitude. We show that such time-dependent modulations do not play an important role in many experiments.
Matías Chávez, Thomas Wiegand, Alexander A. Malär, Beat H. Meier, and Matthias Ernst
Magn. Reson., 2, 499–509, https://doi.org/10.5194/mr-2-499-2021, https://doi.org/10.5194/mr-2-499-2021, 2021
Short summary
Short summary
Sample rotation around the magic angle averages out the dipolar couplings in homonuclear spin systems in a first-order approximation. However, in higher orders, residual coupling terms remain and lead to a broadening of the spectral lines. We investigate the source of this broadening and the effects on the powder line shape in small spin systems with and without chemical shifts. We show that one can expect different scaling behavior as a function of the spinning frequency for the two cases.
Alicia Vallet, Adrien Favier, Bernhard Brutscher, and Paul Schanda
Magn. Reson., 1, 331–345, https://doi.org/10.5194/mr-1-331-2020, https://doi.org/10.5194/mr-1-331-2020, 2020
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We introduce ssNMRlib, a library of pulse sequences and jython scripts for user-friendly setup and acquisition of solids-state NMR experiments. ssNMRlib facilitates all steps of data acquisition, including calibration of various pulse-sequence parameters and semi-automatic setup of even complex high-dimensional experiments, using an intuitive graphical user interface, launched directly within Bruker's Topspin acquisition program.
Kathrin Aebischer, Nino Wili, Zdeněk Tošner, and Matthias Ernst
Magn. Reson., 1, 187–195, https://doi.org/10.5194/mr-1-187-2020, https://doi.org/10.5194/mr-1-187-2020, 2020
Short summary
Short summary
Resonant pulses in a spin-lock frame are used to select parts of the rf-field distribution in NMR experiments. Such pulses can be implemented in a straightforward way and arbitrarily shaped pulses can be used. We show an application of such pulses in homonuclear decoupling where restricting the amplitude distribution of the rf field leads to improved performance.
Johannes Hellwagner, Liam Grunwald, Manuel Ochsner, Daniel Zindel, Beat H. Meier, and Matthias Ernst
Magn. Reson., 1, 13–25, https://doi.org/10.5194/mr-1-13-2020, https://doi.org/10.5194/mr-1-13-2020, 2020
Short summary
Short summary
This paper analyzes a commonly used line-narrowing mechanism (homonuclear decoupling) in solid-state NMR and discusses what limits the achievable line width. Based on theoretical considerations, the contribution of different effects to the line width is discussed and a new contributing term is identified. This research allows us to evaluate new ways to improve the line width in such homonuclear decoupled spectra.
Related subject area
Field: Solid-state NMR | Topic: Applications – biological macromolecules
Characterization of nucleosome sediments for protein interaction studies by solid-state NMR spectroscopy
Relaxation-induced dipolar exchange with recoupling (RIDER) distortions in CODEX experiments
Ulric B. le Paige, ShengQi Xiang, Marco M. R. M. Hendrix, Yi Zhang, Gert E. Folkers, Markus Weingarth, Alexandre M. J. J. Bonvin, Tatiana G. Kutateladze, Ilja K. Voets, Marc Baldus, and Hugo van Ingen
Magn. Reson., 2, 187–202, https://doi.org/10.5194/mr-2-187-2021, https://doi.org/10.5194/mr-2-187-2021, 2021
Short summary
Short summary
NMR studies can be of great help in understanding the molecular mechanisms of nucleosome functions. For solid-state NMR, nucleosomes need to be tightly packed together. We show that centrifugation of nucleosomes results in formation of gels with very high packing ratios yet without pronounced order in the packing and without formation of specific or stable inter-nucleosome contacts. This makes the approach suitable also for the study of proteins that bind weakly to the nucleosome.
Alexey Krushelnitsky and Kay Saalwächter
Magn. Reson., 1, 247–259, https://doi.org/10.5194/mr-1-247-2020, https://doi.org/10.5194/mr-1-247-2020, 2020
Short summary
Short summary
This work presents systematic methodological study of one of the types of the nuclear magnetic resonance experiments that enables study of molecular dynamics on a millisecond timescale. A modification of a standard experiment was suggested that excludes possible artefacts and distortions. It has been demonstrated that the standard experiment reveals slow overall motion of proteins in a rigid crystal lattice, whereas the artefact-free experimental setup demonstrates that the proteins are rigid.
Cited articles
Abergel, D. and Palmer, A. G.: On the use of the stochastic Liouville equation in nuclear magnetic resonance: Application to R1ρ relaxation in the presence of exchange, Concepts Magn. Reso. A, 19A, 134–148, https://doi.org/10.1002/cmr.a.10091, 2003. a, b
Aebischer, K.: Evaluating the motional time scales contributing to averaged anisotropic interactions in MAS solid-state NMR, ETH Zurich [data set and code], https://doi.org/10.3929/ethz-b-000666765, 2024. a
Aebischer, K. and Ernst, M.: INEPT and CP transfer efficiencies of dynamic systems in MAS solid-state NMR, J. Magn. Reson., 359, 107617, https://doi.org/10.1016/j.jmr.2024.107617, 2024. a, b
Akbey, Ü.: Site-specific protein methyl deuterium quadrupolar patterns by proton-detected 3D 2H–13C–1H MAS NMR spectroscopy, J. Biomol. NMR, 76, 23–28, https://doi.org/10.1007/s10858-021-00388-4, 2022. a, b
Akbey, Ü.: Site-specific protein backbone deuterium 2Hα quadrupolar patterns by proton-detected quadruple-resonance 3D 2HαCαNH MAS NMR spectroscopy, Solid State Nucl. Mag., 125, 101861, https://doi.org/10.1016/j.ssnmr.2023.101861, 2023. a, b, c, d
Asami, S. and Reif, B.: Comparative Study of REDOR and CPPI Derived Order Parameters by 1H-Detected MAS NMR and MD Simulations, J. Phys. Chem. B, 121, 8719–8730, https://doi.org/10.1021/acs.jpcb.7b06812, 2017. a
Asami, S. and Reif, B.: Accessing Methyl Groups in Proteins via 1H-detected MAS Solid-state NMR Spectroscopy Employing Random Protonation, Sci. Rep., 9, 15903, https://doi.org/10.1038/s41598-019-52383-3, 2019. a
Blackledge, M.: Recent progress in the study of biomolecular structure and dynamics in solution from residual dipolar couplings, Prog. Nucl. Mag. Res. Sp., 46, 23–61, https://doi.org/10.1016/j.pnmrs.2004.11.002, 2005. a
Blümich, B. and Hagemeyer, A.: Two-dimensional 13C exchange spectroscopy with off-magic angle spinning, Chem. Phys. Lett., 161, 55–59, https://doi.org/10.1016/S0009-2614(89)87031-9, 1989. a
Brüschweiler, R.: Dipolar averaging in NMR spectroscopy: From polarization transfer to cross relaxation, Prog. Nucl. Mag. Res. Sp., 32, 1–19, https://doi.org/10.1016/S0079-6565(97)00010-1, 1998. a
Callon, M., Malär, A. A., Lecoq, L., Dujardin, M., Fogeron, M., Wang, S., Schledorn, M., Bauer, T., Nassal, M., Böckmann, A., and Meier, B. H.: Fast Magic‐Angle‐Spinning NMR Reveals the Evasive Hepatitis B Virus Capsid C‐Terminal Domain, Angew. Chem. Int. Ed., 134, e202201083, https://doi.org/10.1002/ange.202201083, 2022. a, b
Chen, L., Wang, Q., Hu, B., Lafon, O., Trébosc, J., Deng, F., and Amoureux, J.-P.: Measurement of hetero-nuclear distances using a symmetry-based pulse sequence in solid-state NMR, Phys. Chem. Chem. Phys., 12, 9395, https://doi.org/10.1039/b926546e, 2010. a, b
Cheng, V. B., Suzukawa, H. H., and Wolfsberg, M.: Investigations of a nonrandom numerical method for multidimensional integration, J. Chem. Phys., 59, 3992–3999, https://doi.org/10.1063/1.1680590, 1973. a
Chevelkov, V., Fink, U., and Reif, B.: Accurate Determination of Order Parameters from 1H, 15N Dipolar Couplings in MAS Solid-State NMR Experiments, J. Am. Chem. Soc., 131, 14018–14022, https://doi.org/10.1021/ja902649u, 2009. a
Chevelkov, V., Lange, S., Sawczyc, H., and Lange, A.: Accurate Determination of Motional Amplitudes in Biomolecules by Solid-State NMR, ACS Phys. Chem. Au., 3, 199–206, https://doi.org/10.1021/acsphyschemau.2c00053, 2023. a, b
Cobo, M. F., Maliňáková, K., Reichert, D., Saalwächter, K., and Ribeiro deAzevedo, E.: Intermediate motions and dipolar couplings as studied by Lee–Goldburg cross-polarization NMR: Hartmann–Hahn matching profiles, Phys. Chem. Chem. Phys., 11, 7036–7047, https://doi.org/10.1039/B907674C, 2009. a
Concistrè, M., Carignani, E., Borsacchi, S., Johannessen, O. G., Mennucci, B., Yang, Y., Geppi, M., and Levitt, M. H.: Freezing of Molecular Motions Probed by Cryogenic Magic Angle Spinning NMR, J. Phys. Chem. Lett., 5, 512–516, https://doi.org/10.1021/jz4026276, pMID: 26276602, 2014. a
deAzevedo, E. R., Saalwächter, K., Pascui, O., de Souza, A. A., Bonagamba, T. J., and Reichert, D.: Intermediate motions as studied by solid-state separated local field NMR experiments, J. Chem. Phys., 128, 104505, https://doi.org/10.1063/1.2831798, 2008. a
Gauto, D. F., Macek, P., Barducci, A., Fraga, H., Hessel, A., Terauchi, T., Gajan, D., Miyanoiri, Y., Boisbouvier, J., Lichtenecker, R., Kainosho, M., and Schanda, P.: Aromatic Ring Dynamics, Thermal Activation, and Transient Conformations of a 468 kDa Enzyme by Specific 1H–13C Labeling and Fast Magic-Angle Spinning NMR, J. Am. Chem. Soc., 141, 11183–11195, https://doi.org/10.1021/jacs.9b04219, 2019. a
Gullion, T.: Introduction to rotational‐echo, double‐resonance NMR, Concepts Magn. Reso., 10, 277–289, https://doi.org/10.1002/(SICI)1099-0534(1998)10:5<277::AID-CMR1>3.0.CO;2-U, 1998. a, b, c
Gullion, T. and Schaefer, J.: Rotational-echo double-resonance NMR, J. Magn. Reson., 81, 196–200, https://doi.org/10.1016/0022-2364(89)90280-1, 1989. a, b, c
Haller, J. D. and Schanda, P.: Amplitudes and time scales of picosecond-to-microsecond motion in proteins studied by solid-state NMR: a critical evaluation of experimental approaches and application to crystalline ubiquitin, J. Biomol. NMR, 57, 263–280, https://doi.org/10.1007/s10858-013-9787-x, 2013. a
Harris, C. R., Millman, K. J., der Walt, S. J., Gommers, R., Virtanen, P., Cournapeau, D., Wieser, E., Taylor, J., Berg, S., Smith, N. J., Kern, R., Picus, M., Hoyer, S., van Kerkwijk, M. H., Brett, M., Haldane, A., del Río, J. F., Wiebe, M., Peterson, P., Gérard-Marchant, P., Sheppard, K., Reddy, T., Weckesser, W., Abbasi, H., Gohlke, C., and Oliphant, T. E.: Array programming with NumPy, Nature, 585, 357–362, https://doi.org/10.1038/s41586-020-2649-2, 2020. a
Hartmann, S. R. and Hahn, E. L.: Nuclear double resonance in the rotating frame, Phys. Rev., 128, 2042, https://doi.org/10.1103/PhysRev.128.2042, 1962. a
Hirschinger, J.: A simple analytical model to describe dynamic magic-angle spinning experiments, Concepts Magn. Reso. A, 28A, 307–320, https://doi.org/10.1002/cmr.a.20064, 2006. a, b
Hirschinger, J.: Analytical solutions to several magic-angle spinning NMR experiments, Solid State Nucl. Mag., 34, 210–223, https://doi.org/10.1016/j.ssnmr.2008.10.001, 2008. a, b
Hologne, M., Chen, Z., and Reif, B.: Characterization of dynamic processes using deuterium in uniformly 2H, 13C, 15N enriched peptides by MAS solid-state NMR, J. Magn. Reson., 179, 20–28, https://doi.org/10.1016/j.jmr.2005.10.014, 2006. a
Hong, M.: Structure, Topology, and Dynamics of Membrane Peptides and Proteins from Solid-State NMR Spectroscopy, J. Phys. Chem. B, 111, 10340–10351, https://doi.org/10.1021/jp073652j, 2007. a
Hong, M., Yao, X., Jakes, K., and Huster, D.: Investigation of Molecular Motions by Lee-Goldburg Cross-Polarization NMR Spectroscopy, J. Phys. Chem. B, 106, 7355–7364, https://doi.org/10.1021/jp0156064, 2002. a
Hou, G., Byeon, I.-J. L., Ahn, J., Gronenborn, A. M., and Polenova, T.: 1H–13C 1H–15N Heteronuclear Dipolar Recoupling by R-Symmetry Sequences Under Fast Magic Angle Spinning for Dynamics Analysis of Biological and Organic Solids, J. Am. Chem. Soc., 133, 18646–18655, https://doi.org/10.1021/ja203771a, 2011. a
Hou, G., Byeon, I.-J. L., Ahn, J., Gronenborn, A. M., and Polenova, T.: Recoupling of chemical shift anisotropy by R-symmetry sequences in magic angle spinning NMR spectroscopy, J. Chem. Phys., 137, 134201, https://doi.org/10.1063/1.4754149, 2012. a, b
Hou, G., Lu, X., Vega, A. J., and Polenova, T.: Accurate measurement of heteronuclear dipolar couplings by phase-alternating R-symmetry (PARS) sequences in magic angle spinning NMR spectroscopy, J. Chem. Phys., 141, 104202, https://doi.org/10.1063/1.4894226, 2014. a
Hunter, J. D.: Matplotlib: A 2D graphics environment, Comput. Sci. Eng., 9, 90–95, https://doi.org/10.1109/MCSE.2007.55, 2007. a
Jain, M. G., Mote, K. R., Hellwagner, J., Rajalakshmi, G., Ernst, M., Madhu, P. K., and Agarwal, V.: Measuring strong one-bond dipolar couplings using REDOR in magic-angle spinning solid-state NMR, J. Chem. Phys., 150, 134201, https://doi.org/10.1063/1.5088100, 2019a. a, b
Jain, M. G., Rajalakshmi, G., Agarwal, V., Madhu, P., and Mote, K. R.: On the direct relation between REDOR and DIPSHIFT experiments in solid-state NMR, J. Magn. Reson., 308, 106563, https://doi.org/10.1016/j.jmr.2019.07.050, 2019b. a
Kristensen, J. H., Bildsøe, H., Jakobsen, H. J., and Nielsen, N. C.: Theory and simulations of molecular dynamics in 2H MAS NMR, J. Magn. Reson., 100, 437–443, https://doi.org/10.1016/0022-2364(92)90279-G, 1992. a
Krushelnitsky, A., Reichert, D., and Saalwächter, K.: Solid-state NMR approaches to internal dynamics of proteins: From picoseconds to microseconds and seconds, Acc. Chem. Res., 46, 2028–2036, https://doi.org/10.1021/ar300292p, 2013. a
Kubo, R.: Stochastic Liouville Equations, J. Math. Phys., 4, 174–183, https://doi.org/10.1063/1.1703941, 1963. a, b
Kustanovich, I., Vega, S., and Zaborowski, E.: Dynamic off-magic-angle sample spinning NMR of deuterium, J. Magn. Reson., 93, 441–446, https://doi.org/10.1016/0022-2364(91)90023-M, 1991. a
Lamley, J. M. and Lewandowski, J. R.: Relaxation-based magic-angle spinning NMR approaches for studying protein dynamics, eMagRes, 5, 1423–1434, https://doi.org/10.1002/9780470034590.emrstm1417, 2016. a
Lamley, J. M., Lougher, M. J., Sass, H.-J., Rogowski, M., Grzesiek, S., and Lewandowski, J. R.: Unraveling the complexity of protein backbone dynamics with combined 13C and 15N solid-state NMR relaxation measurements, Phys. Chem. Chem. Phys., 17, 21997–22008, https://doi.org/10.1039/C5CP03484A, 2015. a
Levitt, M. H.: Symmetry-Based Pulse Sequences in Magic-Angle Spinning Solid-State NMR, John Wiley & Sons, Ltd, ISBN 9780470034590, https://doi.org/10.1002/9780470034590.emrstm0551, 2007. a, b, c
Lewandowski, J. R.: Advances in Solid-State Relaxation Methodology for Probing Site-Specific Protein Dynamics, Acc. Chem. Res., 46, 2018–2027, https://doi.org/10.1021/ar300334g, 2013. a
Long, J. R., Sun, B. Q., Bowen, A., and Griffin, R. G.: Molecular Dynamics and Magic Angle Spinning NMR, J. Am. Chem. Soc., 116, 11950–11956, https://doi.org/10.1021/ja00105a039, 1994. a, b
Lorieau, J. L. and McDermott, A. E.: Conformational Flexibility of a Microcrystalline Globular Protein: Order Parameters by Solid-State NMR Spectroscopy, J. Am. Chem. Soc., 128, 11505–11512, https://doi.org/10.1021/ja062443u, 2006. a
Lu, X., Zhang, H., Lu, M., Vega, A. J., Hou, G., and Polenova, T.: Improving dipolar recoupling for site-specific structural and dynamics studies in biosolids NMR: windowed RN-symmetry sequences, Phys. Chem. Chem. Phys., 18, 4035–4044, https://doi.org/10.1039/C5CP07818K, 2016. a, b
Martin, R. W., Kelly, J. E., and Collier, K. A.: Spatial reorientation experiments for NMR of solids and partially oriented liquids, Prog. Nucl. Mag. Res. Sp., 90, 92–122, https://doi.org/10.1016/j.pnmrs.2015.10.001, 2015. a
Moro, G. J. and Freed, J. H.: Efficient computation of magnetic resonance spectra and related correlation functions from stochastic Liouville equations, J. Phys. Chem., 84, 2837–2840, https://doi.org/10.1021/j100459a001, 1980. a, b
Munowitz, M. G., Griffin, R. G., Bodenhausen, G., and Huang, T. H.: Two-dimensional rotational spin-echo nuclear magnetic resonance in solids: correlation of chemical shift and dipolar interactions, J. Am. Chem. Soc., 103, 2529–2533, https://doi.org/10.1021/ja00400a007, 1981. a
Nielsen, N. C., Strassø, L. A., and Nielsen, A. B.: Dipolar recoupling, Top. Curr. Chem., 306, 1–45, https://doi.org/10.1007/128_2011_129, 2012. a, b
Nishiyama, Y., Malon, M., Potrzebowski, M. J., Paluch, P., and Amoureux, J.-P.: Accurate NMR determination of C–H or N–H distances for unlabeled molecules, Solid State Nucl. Mag., 73, 15–21, https://doi.org/10.1016/j.ssnmr.2015.06.005, 2016. a
Nowacka, A., Bongartz, N., Ollila, O., Nylander, T., and Topgaard, D.: Signal intensities in 1H–13C CP and INEPT MAS NMR of liquid crystals, J. Magn. Reson., 230, 165–175, https://doi.org/10.1016/j.jmr.2013.02.016, 2013. a, b
Paluch, P., Pawlak, T., Amoureux, J.-P., and Potrzebowski, M. J.: Simple and accurate determination of X-H distances under ultra-fast MAS NMR, J. Magn. Reson., 233, 56–63, https://doi.org/10.1016/j.jmr.2013.05.005, 2013. a
Paluch, P., Trébosc, J., Nishiyama, Y., Potrzebowski, M. J., Malon, M., and Amoureux, J.-P.: Theoretical study of CP-VC: A simple, robust and accurate MAS NMR method for analysis of dipolar C-H interactions under rotation speeds faster than ca. 60 kHz, J. Magn. Reson., 252, 67–77, https://doi.org/10.1016/j.jmr.2015.01.002, 2015. a
Pileio, G., Guo, Y., Pham, T. N., Griffin, J. M., Levitt, M. H., and Brown, S. P.: Residual Dipolar Couplings by Off-Magic-Angle Spinning in Solid-State Nuclear Magnetic Resonance Spectroscopy, J. Am. Chem. Soc., 129, 10972–10973, https://doi.org/10.1021/ja0721115, 2007. a, b
Pines, A., Gibby, M. G., and Waugh, J. S.: Proton‐Enhanced Nuclear Induction Spectroscopy, A Method for High Resolution NMR of Dilute Spins in Solids, J. Chem. Phys., 56, 1776–1777, https://doi.org/10.1063/1.1677439, 1972. a
Saalwächter, K. and Fischbach, I: The Application of MAS Recoupling Methods in the Intermediate Motional Regime, J. Magn. Reson., 157, 17–30, https://doi.org/10.1006/jmre.2002.2552, 2002. a, b
Schanda, P., Meier, B. H., and Ernst, M.: Quantitative Analysis of Protein Backbone Dynamics in Microcrystalline Ubiquitin by Solid-State NMR Spectroscopy, J. Am. Chem. Soc., 132, 15957–15967, https://doi.org/10.1021/ja100726a, 2010. a
Schanda, P., Huber, M., Boisbouvier, J., Meier, B. H., and Ernst, M.: Solid-State NMR Measurements of Asymmetric Dipolar Couplings Provide Insight into Protein Side-Chain Motion, Angew. Chem. Int. Ed., 50, 11005–11009, https://doi.org/10.1002/anie.201103944, 2011a. a, b
Schanda, P., Meier, B. H., and Ernst, M.: Accurate measurement of one-bond H-X heteronuclear dipolar couplings in MAS solid-state NMR, J. Magn. Reson., 210, 246–259, https://doi.org/10.1016/j.jmr.2011.03.015, 2011b. a
Schmidt, A. and Vega, S.: NMR line shape analysis for two‐site exchange in rotating solids, J. Chem. Phys., 87, 6895–6907, https://doi.org/10.1063/1.453384, 1987. a, b
Schmidt, A. and Vega, S.: Dynamic off-magic-angle sample spinning NMR spectroscopy, Chem. Phys. Lett., 157, 539–542, https://doi.org/10.1016/S0009-2614(89)87407-X, 1989. a
Schmidt, A., Smith, S. O., Raleigh, D. P., Roberts, J. E., Griffin, R. G., and Vega, S.: Chemical exchange effects in the NMR spectra of rotating solids, J. Chem. Phys., 85, 4248–4253, https://doi.org/10.1063/1.451796, 1986. a, b
Shi, X. and Rienstra, C. M.: Site-Specific Internal Motions in GB1 Protein Microcrystals Revealed by 3D 2H–13C–13C Solid-State NMR Spectroscopy, J. Am. Chem. Soc., 138, 4105–4119, https://doi.org/10.1021/jacs.5b12974, 2016. a, b, c, d
Smith, A. A., Ernst, M., and Meier, B. H.: Optimized “detectors” for dynamics analysis in solid-state NMR, J. Chem. Phys., 148, 045104, https://doi.org/10.1063/1.5013316, 2018. a
Smith, S. A., Levante, T. O., Meier, B. H., and Ernst, R. R.: Computer simulations in magnetic resonance. An object-oriented programming approach, J. Magn. Reson., 106, 75–105, https://doi.org/10.1006/jmra.1994.1008, 1994. a
Stejskal, E. O., Schaefer, J., and Waugh, J. S.: Magic-angle spinning and polarization transfer in proton-enhanced NMR, J. Magn. Reson., 28, 105–112, https://doi.org/10.1016/0022-2364(77)90260-8, 1977. a
Suwelack, D., Rothwell, W. P., and Waugh, J. S.: Slow molecular motion detected in the NMR spectra of rotating solids, J. Chem. Phys., 73, 2559–2569, https://doi.org/10.1063/1.440491, 1980. a, b
van Rossum, B.-J., de Groot, C. P., Ladizhansky, V., Vega, S., and de Groot, H. J. M.: A Method for Measuring Heteronuclear (1H−13C) Distances in High Speed MAS NMR, J. Am. Chem. Soc., 122, 3465–3472, https://doi.org/10.1021/ja992714j, 2000. a
Vega, A. J. and Fiat, D.: Relaxation theory and the stochastic Liouville equation, J. Magn. Reson., 19, 21–30, https://doi.org/10.1016/0022-2364(75)90024-4, 1975. a, b
Vugmeyster, L. and Ostrovsky, D.: Static solid-state 2H NMR methods in studies of protein side-chain dynamics, Prog. Nucl. Mag. Res. Sp., 101, 1–17, https://doi.org/10.1016/j.pnmrs.2017.02.001, 2017. a
Watt, E. D. and Rienstra, C. M.: Recent advances in solid-state nuclear magnetic resonance techniques to quantify biomolecular dynamics, Anal. Chem., 86, 58–64, https://doi.org/10.1021/ac403956k, 2014. a
Xue, K., Mamone, S., Koch, B., Sarkar, R., and Reif, B.: Determination of methyl order parameters using solid state NMR under off magic angle spinning, J. Biomol. NMR, 73, 471–475, https://doi.org/10.1007/s10858-019-00253-5, 2019a. a
Xue, K., Mühlbauer, M., Mamone, S., Sarkar, R., and Reif, B.: Accurate Determination of 1H-15N Dipolar Couplings Using Inaccurate Settings of the Magic Angle in Solid-State NMR Spectroscopy, Angew. Chem. Int. Ed., 58, 4286–4290, https://doi.org/10.1002/anie.201814314, 2019b. a
Yan, S., Suiter, C. L., Hou, G., Zhang, H., and Polenova, T.: Probing structure and dynamics of protein assemblies by magic angle spinning NMR spectroscopy, Acc. Chem. Res., 46, 2047–58, https://doi.org/10.1021/ar300309s, 2013. a
Zhao, X., Eden, M., and Levitt, M. H.: Recoupling of heteronuclear dipolar interactions in solid-state NMR using symmetry-based pulse sequences, Chem. Phys. Lett., 342, 353–361, https://doi.org/10.1016/S0009-2614(01)00593-0, 2001. a, b
Zumpfe, K. and Smith, A. A.: Model-Free or Not?, Front. Mol. Biosci., 8, 727553, https://doi.org/10.3389/fmolb.2021.727553, 2021. a, b
Short summary
To characterize the amplitude of dynamic processes in molecules, anisotropic parameters can be measured using solid-state NMR. However, the timescales of motion that lead to such a scaling of the anisotropic interactions are not clear. Using numerical simulations in small spin systems, we could show that mostly the magnitude of the anisotropic interaction determines the range of timescales detected by the scaled anisotropic interaction, and experimental parameters play a very minor role.
To characterize the amplitude of dynamic processes in molecules, anisotropic parameters can be...