the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 21 Feb 2024
Dynamic averaging of anisotropic interactions and its dependence on motional time scales in MAS solid-state NMR
Abstract. Dynamic processes in molecules can occur on a large range of time scales, and it is important to understand which time scales of motion contribute to different parameters used in dynamics measurements. For spin relaxation, this can easily be understood from the sampling of the spectral-density function by different relaxation-rate constants. In addition to data from relaxation measurements, determining dynamically-averaged anisotropic interactions in magic-angle spinning (MAS) solid-state NMR allows better quantification of the amplitude of molecular motion. For partially averaged anisotropic interactions, the relevant time scales of motion are not so clearly defined and whether the averaging depends on the experimental methods (e.g., pulse sequences) or conditions (e.g., MAS frequency, magnitude of anisotropic interaction, rf-field amplitudes) is not fully understood. To investigate these questions, we performed numerical simulations of dynamic systems based on the stochastic Liouville equation using several experiments for recoupling the dipolar-coupling, CSA or quadrupolar coupling. The transition between slow motion, where parameters characterizing the anisotropic interaction are not averaged, and fast motion, where the tensors are averaged leading to a scaled anisotropic quantity, occurs over a window of motional rate constants that depends mainly on the strength of the interaction. This transition region can span two orders of magnitude in exchange-rate constants (typically in the μs range) but depends only marginally on the employed recoupling scheme or sample spinning frequency. Residual couplings in off-magic-angle experiments, however, average over longer time scales of motion. While in principle one may gain information on the time scales of motion from the transition area, extracting such information is hampered by low signal-to-noise ratio in experimental spectra due to fast relaxation that occurs in the same region.
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RC1: 'Comment on mr-2024-4', Kay Saalwächter, 05 Mar 2024
In this work, the effect of motions on the intermediate (spectral) timescale on results of MAS NMR experiments (with a focus on CP and recoupling) is studied by dynamic spin dynamics simulations. Of central interest is the rate constant-dependent apparent interaction strength obtained by fitting the data (intensity vs. pulse sequence time). Salient results are that the transition between the slow and fast exchange regimes is nearly independent of the MAS rate and mostly dependent on the interaction strength. Some interesting observations on off-MAS 1D experiments are reported, suggesting that the slow to fast transition is located in a different dynamic window, enabling the extraction of fast-limit tensor parameters more easily (but some open questions arise, see below).My main critique is that this work does not report sufficiently new results. Rather, its abstract and introduction, and the scientific background presented, are too much focused on the authors' background in relaxation time studies. The actually relevant and abundant literature on the well-known effects of intermediate motions on MAS experiments is ignored completely. The paper thus cannot claim the required level of novelty. I attempt a literature summary below, with some bias towards work from my group, and describe how this links up to the given paper. The authors will thus see that most of the observed effects are already known and/or can even be predicted with published and partly rather simple theories. Moreover, and rather seriously, the rather relevant effect of signal loss during the pulse sequence is ignored, i.e. T2 (and the less serious T1rho in CP). Its importance arises from (i) the possibility to extract motional timescales from actual T2 or signal loss data (most published works focus on this) and (ii) its potential to pose severe experimental limitations.I think the mere fitting of apparent tensor widths does not have much of a virtue, considering that the analyzed time-domain signals do not actually encode an effective tensorial width, but are the result of a complex interplay of tensorial dephasing and random frequency jumps due to motions (where only the slow and fast tensor limits matter), resulting in fits that necessarily deviate from the data. The result that the fitted apparent tensorial width transitions from the slow to the fast regime within roughly 1-2 decades of rate constants is not surprising - rather it is known and in my view only of limited use. The T2 minimum is much more diagnostic (see below).In the manuscript, the T2 effect (signal loss) in REDOR is normalized away by division through S0. In CP the T1rho effect is weak (it seems too weak, see below). In the wPARS, the T2 effect contributes and affects the fitted tensor width in a different way as in REDOR, as wPARS is implemented via a dephasing rather than an intensity build-up protocol (additional T2 losses are largest close to the transition but are obscured as they add onto the coherent dephasing). This requires closer scrutiny, using a suitable no-coherent-dephasing T2-only reference experiment, which could simply contain an actual or a virtual pi pulse (= phase inversion) in the sequence center on the I spin (proton) channel. Thus, in all experiments, the T2-related signal loss during the sequence is of central concern, and not just the effect of T2 during the detection period as stated on p.11 (the latter being predicted by the simplest model of Suwelack et al. in 1980). My main point is that considering this in the fits in addition to the apparent tensor width (using reference experiments) will give a much clearer and more complete picture.Thus, I suggest a rejection and a new submission once the focus has been changed (working out new insights better, e.g. by clarifying T1rho and T2 effects being different in the different experimental approaches; working out the off-MAS results).relevant literature not considered:Suwelack et al. 1980, JCP 73, 2559Waugh et al. have early on clarified the effect of motions on MAS centerband width (T2 minimum predicted, which depends on MAS rate)A. Schmidt et al. 1986, JCP 85, 4248; A. Schmidt and S. Vega, JCP 1987, 87, 6895Vega/Griffin have used Floquet theory to predict MAS sideband spectra across the intermediate regime; effective tensor widths can be fitted to these predictions. This relates to the 2H part of the manuscript.L. Frydman and B.Frydman 1990, Magn. Reson. Chem. 28, 355Simplified theory approach for MAS sideband patterns with intermed. motions.J.H. Christensen et al. 1992, J. Magn. Reson. 100, 437Simple time-slicing approach to predict MAS sideband patterns with intermed. motions, 2H MAS NMR covered.Z. Luz et al. 1993, J. Chem. Phys. 99, 7544Application of the Vega theory and equivalent simpler theory for MAS sidebands to clarify motions in a special application.=> Appreciating the state of the art up to here, it is seen that the 2H NMR analyses in Figs. 7 and 8 fall far short of it. The high tensor widths in Fig.8 are a strange fitting artifact; better apparent widths can likely be obtained by fitting the initial part of on-resonance MAS time domain signals (first half rotor period). Alternatively or in addition, the T2 contribution to signal loss beyond tensorial dephasing can be normalized away by the T2 decay taken from a fit of the long-time rotor-echo decay (this constitutes the reference experiment in this case). I suspect that the results for the apparent tensor widths obtained considering such a separate quantification of the broadening will be very similar to the results discussed for the pulse sequences.J.R. Long et al. 1994, JACS 116, 11950Griffin and co. calculate dynamics effects on MAS spectra and discuss interference effects with decoupling pulse sequences, focusing on the important line broadening (signal loss).I. Fischbach and K. Saalwächter 2002, J. Magn. Reson. 157, 17Probably the first account of effects of intermediate motions in recoupling experiments, focusing on both apparent tensor width as well as on effective T2 in REDOR-based CSA (using the CODEX pulse sequence). An admittedly special case; this work is not as systematic with regards to MAS rate and tensor variations (indeed leaving room for a broader account). But the virtual equivalence of heteronuclear dipolar and CSA recoupling is merely trivial and all reported trends from the present manuscript are already apparent from this earlier paper: Its Fig.2 shows that the T2 effect related to recoupled tensorial dephasing ("recoupled echo") shows essential MAS independence, as opposed to the "no recoupling" reference echo (that reflects the T2 calculated by Suwelack 1980). Fig.7 shows the apparent tensor width transition as well as the T2-related signal loss, both as a function of jump rate, very similar to many plots of the manuscript.E.R. deAzevedo et al. 2008, JCP 128, 104505Effect of intermediate motions on DIPSHIFT experiments, showing (importantly) that the effective IS-dipolar MAS time-domain signals can be theoretically described by Anderson-Weiss theory. See the cited ref. 18-20, in particularJ. Hirschinger 2006, Concepts Magn. Reson. A 28a, 307.The latter paper gives guidelines of how to possibly predict all effects observed in the present manuscript in a similar way by just considering the relevant effective interaction (scaled appropriately considering the pulse sequence) and a suitable "model-free" ansatz for the correlation function of motion (treating the fast-limit averaging in terms of an order parameter), including MAS rotation in the correlation function. Relations between specific motional geometries (e.g. jumps or diffusion on a cone with a given opening angle) and the order parameter are well documented in the literature, which is more general than just specifying jump angles. Moreover, multi-mode dynamics (section 3.4 of the manuscript) are also best described in terms of a correlation function featuring a two-step correlation loss.[Later works along this line (Cobo et al., JMR 2012 and 2014) focus on REDOR-recoupled DIPSHIFT experiments, where again AW theory works amazingly well.]M.F. Cobo et al. 2009, PCCP 11, 7036.Intermediate motions in CP experiments. Again, Hirschinger has highlighted how to extend AW theory to CP:J. Hirschinger 2008, SSNMR 34, 210.Of course, AW predictions do not reproduce the T1rho decay and also no coherent oscillations (neither for CP nor for REDOR), due to the Gaussian assumption (see Fig.8 of Cobo 2009). But tensor widths encoded in the initial rise/decay in the form of a second moment are always right; Hartmann-Hahn matching profiles are predicted nearly quantitatively!Here, I wonder why in the present manuscript the T1rho effects are so much weaker (only seen in Fig.S1, but not in Fig.2a) than the ones measured and simulated by Cobo et al. The authors may want to check their code, simulating with the spin system parameters of Cobo et al., just to make sure.With all these earlier works considered, I hope that the authors agree that rather many statements and claims in their paper should be carefully reconsidered and possibly rephrased, and that the paper requires significant additions to reach a sufficient level of novelty.Finally, let me comment on the rather interesting off-MAS observations, which are well worth being worked out in more detail. The possibility to see the tensorial averaging in a much slower regime before the onset of deleterious line broadening is an asset! But the result is obscured by the fitting artifacts related to the negative tensorial width. Fig. S9 shows that the sign of the tensor is rather ill-defined; the chi^2 surfaces are almost symmetric for the most part. This goes along well with the common notion that the sign of a dipolar tensor alone is not encoded in a simple 1D spectrum (as splittings or sidebands are symmetric). The only very slight asymmetry arises from the additivity of the J coupling in the formula for the evolution phase (see eq. 1), breaking the symmetry. A more systematic study is recommended, and possibly a case with dynamics not showing a negative order parameter.l.439: 1 s^3 must be a typoCitation: https://doi.org/
10.5194/mr-2024-4-RC1 -
AC1: 'Reply on RC1', Matthias Ernst, 06 Mar 2024
Dear Kay,
thank you for your detailed and insightful report on our manuscript.
It seems to us that we were not successful in conveying the main question that we wanted to address with this paper very well. The question we wanted to address was indeed motivated by "the authors' background in relaxation time studies". We were interested which dynamic time scales contribute to partially averaged anisotropic interactions measured in MAS NMR that are most often used in combination with relaxation data to get a better characterization of the amplitude and time scales of motions. When performing such a joint analysis, it is of utmost importance to know which motional time scales are actually sensed by the dipolar order parameters. In published literature on such combined analysis, this question is often somewhat circumvented, and it is assumed that the dipolar coupling covers all time scales (e.g. references (1, 2); this assumption is not correct), or that the slow motions have an amplitude that is so small that it would go undetected in experimentally measured order parameters (e.g. (3)), which may be correct in come cases, but not generally. In the “detectors” approach (4, 5), it is also (and incorrectly) assumed that the dipolar order parameter covers all time scales. In our view, such a joint analyses of relaxation data and dipolar order parameters, thus, lack a solid basis with respect to the time scale covered by the latter, and one should take into account which motional time scales are detected by these residual couplings.
The relevant questions to us are whether different recoupling methods cover different ranges, whether scaling of the couplings extends the range and what parameters influence the range of time scales covered by the scaled anisotropic interactions. We are not aware of publications in the literature that look at these questions in terms of MAS frequency, recoupling experiments and parameters. However, we believe that these are important questions if one wants to use such order parameters in combination with relaxation data. A detailed description of the recoupling behavior in the transition region was in no way our goal and is, for our purpose, only important to define the time scales that contribute to the partially averaged anisotropic quantities.
We are aware that there is a large literature that covers this intermediate range and in hindsight we should have mentioned this in the introduction and should have included references to some of the methods. Since it was not our intention to characterize the detailed line shape in the transition area, we do not think that a more complex data evaluation in that range of motional time scales adds any additional value to the paper. Our simplistic approach was motivated by the typical data evaluation done when residual dipolar couplings are evaluated experimentally. We are aware of the additional relaxation from the intermediate motion during recoupling (T2/T1rho) as well as during the data acquisition in real experiments.
As a way forward, we propose the following changes to the manuscript.
(i) We will change the title to “Evaluating the motional time scales contributing to averaged anistotropic interactions in MAS NMR" to make the topic of the paper clearer. In our opinion, the abstract conveys the intention of the paper quite well.
(ii) We will rewrite the introduction to include a more detailed discussion of the intermediate time-scale regime and to make the aim of the paper hopefully clearer. This will include references to different approaches for a better description of intermediate time-scale motions. We will stress that we are mainly interested in characterization of the three motional regimes (fast, intermediate, slow) in order to determine which time scales contribute to the partially averaged anisotropic interactions.
(iii) In the methods section we will again stress that determining the order parameter in the transition region is not meant as a complete characterization of the motional processes in this region but a way to determine the three main areas of motional processes: fast, transition area, slow. We will mention that there are more complex ways to analyze dynamics data in the intermediate regime and motivate why we used such a simple approach.
(iv) In the results and discussion section we will emphasize that we are mostly interested in the fast motion regime and try to reduce the discussion of the intermediate regime to focus the paper on the topic.
(v) We will also try to emphasize in the conclusions what the important results are.
Some detailed answers to specific questions:
"Here, I wonder why in the present manuscript the T1rho effects are so much weaker (only seen in Fig.S1, but not in Fig.2a) than the ones measured and simulated by Cobo et al. The authors may want to check their code, simulating with the spin system parameters of Cobo et al., just to make sure."
The T1rho decay strongly depends on the rate constant, and the magnitude of the dipolar coupling used in the simulations as can be seen from Fig. S1. The parameters selected in Fig. 2a corresponds to the k=1e3s-1 and \delta/2\pi=5kHz plot in Fig. S1. The simulations of Kobo assume a much stronger one-bond CH coupling with a \delta/2\pi=46kHz.
We hope that these changes address the main points of your review report.
- J. D. Haller, P. Schanda, 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 (2013).
- V. Chevelkov, U. Fink, B. Reif, Quantitative analysis of backbone motion in proteins using MAS solid-state NMR spectroscopy. J. Biomol. NMR. 45, 197–206 (2009).
- T. Zinkevich, V. Chevelkov, B. Reif, K. Saalwächter, A. Krushelnitsky, Internal protein dynamics on ps to μs timescales as studied by multi-frequency 15N solid-state NMR relaxation.J. Biomol. NMR. 57, 219–235 (2013).
- K. Zumpfe, A. A. Smith, Model-Free or Not ? Front. Mol. Biosci. 8, 727553 (2021).
- A. A. Smith, M. Ernst, B. H. Meier, Optimized “detectors” for dynamics analysis in solid-state NMR. J. Chem. Phys. 148, 045104 (2018).
Citation: https://doi.org/10.5194/mr-2024-4-AC1 -
RC2: 'Reply on AC1', Kay Saalwächter, 08 Mar 2024
Dear Matthias,
thank you for your detailed reply. With your explanations, I can now better appreciate the purpose and motivation of the work. We also seem to agree that, besides backing up and serving the motivation, the work should be based on an account of relevant previous work in the field that helps in addressing the problem.
I do acknowledge that your work does not intend to provide strategies to extract slow motional timescales. But I do not agree with the implication to not make changes in the material to be presented. I should also take the chance to make clearer why changes are in my view necessary, in particular an account of T2 phenomena: A sole interest in the fast-motion regime and reducing the discussion of the intermediate regime (to quote your reply) will hardly serve the goal. If the goal is to aid protein NMR relaxometry studies by enabling the reliable measurement of effective tensor widths (relevant to pre-define order parameters), then it is of utmost importance to know if the data is subject to intermediate-regime effects!
As is obvious from most of the fitted data, the shape of the curves is not immediately diagnostic of the dynamic regime. One should therefore use any possible (and in the given case even simple) option to be sure about the measurement of a fast-limit average. And this involves T2 effects as a second, much clearer source of information. Temperature variation is always limited in protein NMR since one is interested in physiological conditions; one may mainly cool to freeze out a potential slow-motional process interfering with the tensor quantification once it is identified, so as to arrive at the correct order parameter for the fast motions probed by relaxation analyses. The best basis of this extra experimental effort is to check the T2 losses as a direct indicator.Therefore, in order to confirm a reliable fast-limit averaged order parameter, a qualitative pinning down of the intermediate regime also in terms of T2 effects is relevant, if not the only reliable way. I will thus endorse publication only if these are included in the presentation and discussion.For each of the methods considered, this means:CP: this seems uncritical, as the intensity build-up encoding the tensor width occurs on a ca. 10 times faster timescale that the T1rho decay. But this also means that a CP build-up alone will not serve the goal to identify problems with the correct tensor width.REDOR: the DeltaS/S0 curve (being T2-compensated) has in principle the same problem, although with somewhat more pronounced effects of reduced oscillations indicating the intermediate regime. But here, the separate analysis of S0 (which is available!) will clearly bring out the potentially strong T2 effect that can help to identify incomplete/partial averaging and thus an ill-defined S value.wPARS: here, the experiment is run in a dephasing mode, which is dangerous to start with. This means that the imperfection compensation inherent to REDOR is skipped. And again, a reference experiment will show the potentially strong T2 effect relevant to identify partial averaging. The reference experiment would in this case be the same pulse sequence but with a virtual pi pulse, i.e. a simple phase inversion, at the center of the wPARS sequence. This should not pose any significant challenges.CSA recoupling: same as wPARS. Here, the T2 effect seems directly visible in the form of a decay of the 50% intensity plateau. Yet again, a reference experiment could easily be devised.off-MAS: the reply does not address my concerns with the fitting instability related to the limited sensitivity to the sign of the tensor. This should be taken up. Removing the sign information by just reporting the modulus (and moving details concerning the sign to the SI) seems advised.2H MAS sidebands: here, again, the reference experiment is part of the data, it is merely the decay of the rotor echoes, for which theory is well-developed (Suwelack et al.). This should be taken up.Best regards,KayCitation: https://doi.org/10.5194/mr-2024-4-RC2 -
AC4: 'Reply on RC2', Matthias Ernst, 14 Mar 2024
Dear Kay,
while we agree that motions in this intermediate time scale are very important and interesting (and difficult) to characterize, we disagree that they are very important in the context of measuring order parameters from scaled anisotropic interactions. If the amplitude of motion in the intermediate regime is small, it will not affect the measurements of the order parameters much and fits of static tensors will work with small distortions. If the amplitude of motion in the intermediate regime is large, the fits will break down. But we must remember that such measurements for site-specific order parameters require typically a 2D or 3D spectrum with at least two polarization-transfer steps and two evolution periods. Larger amplitude intermediate motion will make the polarization transfer inefficient for either INEPT or CP and at the same time the lines will be broadened in t1 and t2. Therefore, we expect that parts of the molecule with larger amplitude intermediate motions will have a low S/N ratio and a high-quality data analysis will be impossible.
We will discuss this problem in the revised manuscript and add a plot of the typical (real) T2 dependence as a function of MAS and correlation time. We agree that determining T2 (or better T1rho since real T2 are difficult/impossible to measure in solids) is always a good idea to spot such areas of the molecule, but experience shows that often those resonances are missing in the spectra.
We will discuss the aspects of T2/T1rho for the various sequences. However, developing new T2 compensated experiments by implementing reference experiments is, in our opinion, beyond the scope of the manuscript.
The offMAS measurements are currently part of our research. We are trying to implement a better way of doing such offMAS experiments and in this context, we will look at the detailed behavior of the recoupling in that region. Again this is beyond the scope of the current manuscript where we have included offMAS mainly because there are experimental data acquired with it in the literature.
Citation: https://doi.org/10.5194/mr-2024-4-AC4
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AC4: 'Reply on RC2', Matthias Ernst, 14 Mar 2024
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AC1: 'Reply on RC1', Matthias Ernst, 06 Mar 2024
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RC3: 'Comment on mr-2024-4', Anonymous Referee #2, 09 Mar 2024
In their manuscript, Aebischer et al. describe the motional time scale dependence of averaging of anisotropic interactions in MAS solid-state NMR experiments. In particular, the authors investigate the CP, REDOR and wPARS pulse scheme for slow, fast and intermediate exchange. Furthermore, CSA recoupling, quadrupolar coupling experiments, and off magic angle experiments are considered. Simulations were carried out using GAMMA. Subsequently, the obtained results were fit using reference simulations that were carried out for rigid systems.
The paper is written very nicely. The graphics work is well done, and the text is comprehensive. I have very little to complain about the manuscript. There are only a few minor points.1) simulation input files should be made available as part of the supporting information.2) a link to the GAMMA source code should be included in the revised manuscript.I disagree with reviewer #1 that the paper has to discuss all the existing literature that has been published on the topic of intermediate exchange. I agree, however, that the readers should be made aware that relaxation based experiments such as R2 have to be performed to yield complementary information on the underlying motional regime.In agreement with the corresponding author, I see this work in the framework of an analysis of order parameters in case dipolar interactions are only partially averaged.For users interested in applying order parameter experiments to characterize their systems, the influence of intermediate motion on the order parameter is of high interest. At the same time, users have to be made aware of effects that occur in an intermediate motional regime.I therefore recommend to accept the manuscript after the changes suggested by the corresponding author are incorporated into the manuscript.Citation: https://doi.org/10.5194/mr-2024-4-RC3 -
AC2: 'Reply on RC3', Matthias Ernst, 12 Mar 2024
Thank you for the positive feedback to our manuscript.
We will make all simulation input files, the GAMMA code, and MATLAB and python processing files available through the ETH Research Collection (https://www.research-collection.ethz.ch/) where it will be long-term accessible with a DOI. We will not put up all the simulated data files there since it is an immense body of data that can be reproduced quite easily based on the scripts and GAMMA simulation code.
As already pointed out in the response to Reviewer 1, we will update the manuscript as outlined there and expand the description of the behavior in the intermediate regime.
Citation: https://doi.org/10.5194/mr-2024-4-AC2
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AC2: 'Reply on RC3', Matthias Ernst, 12 Mar 2024
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RC4: 'Comment on mr-2024-4', Anonymous Referee #3, 13 Mar 2024
The manuscript by Ernst and coworkers attempts to further our understanding of how different pulse sequences techniques respond to changes in the timescale of motion and whether there are any advantages/disadvantages to a particular sequence while estimating dynamics via a single order parameter. The sequences considered are REDOR, CP and wPARS. They also consider CSA recoupling, quadrupolar patterns, and off-MAS experiment for this treatment as well.It is definitely a relief to see Fig. 3 where all the sequences respond in a similar manner, showing a smooth transition between the slow and fast motion regimes, and that a minimal dependence on MAS is observed. I do find Fig 4 a bit surprising. I wonder if the minimal effect on the wPARS sequence upon changing the window duration is because the addition of a window does not really change the effective Hamiltonian description (except for the scaling factor), while this is not true for the epsilon-REDOR and the tilted-angle CP experiment. If this is true, can one then expect that as one spins faster, the deviations that one sees in CP and REDOR will progressively get smaller?
I find the results presented in this manuscript quite valuable as making the choice between different recoupling sequence, especially at fast MAS frequencies is non-trivial even from a technical standpoint. Results presented here seem to suggest that at least as far as motional regimes are concerned, all the methods are pretty much equal and other considerations (rf requirements, robustness, etc) can take precedence.
Hence, although I appreciate the detailed review from Reviewer #1, I think that the scope of this manuscript is narrower while still filling in an important missing gap. I will recommend that this manuscript be accepted with the changes that the authors have previously suggested.
Citation: https://doi.org/10.5194/mr-2024-4-RC4 -
AC3: 'Reply on RC4', Matthias Ernst, 14 Mar 2024
Thank you for the positive report.
We believe that the "minimal effect on the wPARS sequence upon changing the window duration" is due to the relatively small scaling factor of the window as shown in Fig. S8. In REDOR and CP the changes in the effective coupling are much larger which most likely explains the larger changes in the fitted values especially in the transition region. We do not understand the behavior of the REDOR sequence that seems to behave differently in the transition area.
Our main result is indeed that the dynamic time scales measured by the order parameter of the residual dipolar coupling is indeed mainly dependent on the magnitude of the interaction and only to a much lower extent on the methods or parameter used for the recoupling. We must admit that this was somewhat unexpected for us but maybe other people have a better intuition and would have expected this result.
Citation: https://doi.org/10.5194/mr-2024-4-AC3
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AC3: 'Reply on RC4', Matthias Ernst, 14 Mar 2024
Status: closed
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RC1: 'Comment on mr-2024-4', Kay Saalwächter, 05 Mar 2024
In this work, the effect of motions on the intermediate (spectral) timescale on results of MAS NMR experiments (with a focus on CP and recoupling) is studied by dynamic spin dynamics simulations. Of central interest is the rate constant-dependent apparent interaction strength obtained by fitting the data (intensity vs. pulse sequence time). Salient results are that the transition between the slow and fast exchange regimes is nearly independent of the MAS rate and mostly dependent on the interaction strength. Some interesting observations on off-MAS 1D experiments are reported, suggesting that the slow to fast transition is located in a different dynamic window, enabling the extraction of fast-limit tensor parameters more easily (but some open questions arise, see below).My main critique is that this work does not report sufficiently new results. Rather, its abstract and introduction, and the scientific background presented, are too much focused on the authors' background in relaxation time studies. The actually relevant and abundant literature on the well-known effects of intermediate motions on MAS experiments is ignored completely. The paper thus cannot claim the required level of novelty. I attempt a literature summary below, with some bias towards work from my group, and describe how this links up to the given paper. The authors will thus see that most of the observed effects are already known and/or can even be predicted with published and partly rather simple theories. Moreover, and rather seriously, the rather relevant effect of signal loss during the pulse sequence is ignored, i.e. T2 (and the less serious T1rho in CP). Its importance arises from (i) the possibility to extract motional timescales from actual T2 or signal loss data (most published works focus on this) and (ii) its potential to pose severe experimental limitations.I think the mere fitting of apparent tensor widths does not have much of a virtue, considering that the analyzed time-domain signals do not actually encode an effective tensorial width, but are the result of a complex interplay of tensorial dephasing and random frequency jumps due to motions (where only the slow and fast tensor limits matter), resulting in fits that necessarily deviate from the data. The result that the fitted apparent tensorial width transitions from the slow to the fast regime within roughly 1-2 decades of rate constants is not surprising - rather it is known and in my view only of limited use. The T2 minimum is much more diagnostic (see below).In the manuscript, the T2 effect (signal loss) in REDOR is normalized away by division through S0. In CP the T1rho effect is weak (it seems too weak, see below). In the wPARS, the T2 effect contributes and affects the fitted tensor width in a different way as in REDOR, as wPARS is implemented via a dephasing rather than an intensity build-up protocol (additional T2 losses are largest close to the transition but are obscured as they add onto the coherent dephasing). This requires closer scrutiny, using a suitable no-coherent-dephasing T2-only reference experiment, which could simply contain an actual or a virtual pi pulse (= phase inversion) in the sequence center on the I spin (proton) channel. Thus, in all experiments, the T2-related signal loss during the sequence is of central concern, and not just the effect of T2 during the detection period as stated on p.11 (the latter being predicted by the simplest model of Suwelack et al. in 1980). My main point is that considering this in the fits in addition to the apparent tensor width (using reference experiments) will give a much clearer and more complete picture.Thus, I suggest a rejection and a new submission once the focus has been changed (working out new insights better, e.g. by clarifying T1rho and T2 effects being different in the different experimental approaches; working out the off-MAS results).relevant literature not considered:Suwelack et al. 1980, JCP 73, 2559Waugh et al. have early on clarified the effect of motions on MAS centerband width (T2 minimum predicted, which depends on MAS rate)A. Schmidt et al. 1986, JCP 85, 4248; A. Schmidt and S. Vega, JCP 1987, 87, 6895Vega/Griffin have used Floquet theory to predict MAS sideband spectra across the intermediate regime; effective tensor widths can be fitted to these predictions. This relates to the 2H part of the manuscript.L. Frydman and B.Frydman 1990, Magn. Reson. Chem. 28, 355Simplified theory approach for MAS sideband patterns with intermed. motions.J.H. Christensen et al. 1992, J. Magn. Reson. 100, 437Simple time-slicing approach to predict MAS sideband patterns with intermed. motions, 2H MAS NMR covered.Z. Luz et al. 1993, J. Chem. Phys. 99, 7544Application of the Vega theory and equivalent simpler theory for MAS sidebands to clarify motions in a special application.=> Appreciating the state of the art up to here, it is seen that the 2H NMR analyses in Figs. 7 and 8 fall far short of it. The high tensor widths in Fig.8 are a strange fitting artifact; better apparent widths can likely be obtained by fitting the initial part of on-resonance MAS time domain signals (first half rotor period). Alternatively or in addition, the T2 contribution to signal loss beyond tensorial dephasing can be normalized away by the T2 decay taken from a fit of the long-time rotor-echo decay (this constitutes the reference experiment in this case). I suspect that the results for the apparent tensor widths obtained considering such a separate quantification of the broadening will be very similar to the results discussed for the pulse sequences.J.R. Long et al. 1994, JACS 116, 11950Griffin and co. calculate dynamics effects on MAS spectra and discuss interference effects with decoupling pulse sequences, focusing on the important line broadening (signal loss).I. Fischbach and K. Saalwächter 2002, J. Magn. Reson. 157, 17Probably the first account of effects of intermediate motions in recoupling experiments, focusing on both apparent tensor width as well as on effective T2 in REDOR-based CSA (using the CODEX pulse sequence). An admittedly special case; this work is not as systematic with regards to MAS rate and tensor variations (indeed leaving room for a broader account). But the virtual equivalence of heteronuclear dipolar and CSA recoupling is merely trivial and all reported trends from the present manuscript are already apparent from this earlier paper: Its Fig.2 shows that the T2 effect related to recoupled tensorial dephasing ("recoupled echo") shows essential MAS independence, as opposed to the "no recoupling" reference echo (that reflects the T2 calculated by Suwelack 1980). Fig.7 shows the apparent tensor width transition as well as the T2-related signal loss, both as a function of jump rate, very similar to many plots of the manuscript.E.R. deAzevedo et al. 2008, JCP 128, 104505Effect of intermediate motions on DIPSHIFT experiments, showing (importantly) that the effective IS-dipolar MAS time-domain signals can be theoretically described by Anderson-Weiss theory. See the cited ref. 18-20, in particularJ. Hirschinger 2006, Concepts Magn. Reson. A 28a, 307.The latter paper gives guidelines of how to possibly predict all effects observed in the present manuscript in a similar way by just considering the relevant effective interaction (scaled appropriately considering the pulse sequence) and a suitable "model-free" ansatz for the correlation function of motion (treating the fast-limit averaging in terms of an order parameter), including MAS rotation in the correlation function. Relations between specific motional geometries (e.g. jumps or diffusion on a cone with a given opening angle) and the order parameter are well documented in the literature, which is more general than just specifying jump angles. Moreover, multi-mode dynamics (section 3.4 of the manuscript) are also best described in terms of a correlation function featuring a two-step correlation loss.[Later works along this line (Cobo et al., JMR 2012 and 2014) focus on REDOR-recoupled DIPSHIFT experiments, where again AW theory works amazingly well.]M.F. Cobo et al. 2009, PCCP 11, 7036.Intermediate motions in CP experiments. Again, Hirschinger has highlighted how to extend AW theory to CP:J. Hirschinger 2008, SSNMR 34, 210.Of course, AW predictions do not reproduce the T1rho decay and also no coherent oscillations (neither for CP nor for REDOR), due to the Gaussian assumption (see Fig.8 of Cobo 2009). But tensor widths encoded in the initial rise/decay in the form of a second moment are always right; Hartmann-Hahn matching profiles are predicted nearly quantitatively!Here, I wonder why in the present manuscript the T1rho effects are so much weaker (only seen in Fig.S1, but not in Fig.2a) than the ones measured and simulated by Cobo et al. The authors may want to check their code, simulating with the spin system parameters of Cobo et al., just to make sure.With all these earlier works considered, I hope that the authors agree that rather many statements and claims in their paper should be carefully reconsidered and possibly rephrased, and that the paper requires significant additions to reach a sufficient level of novelty.Finally, let me comment on the rather interesting off-MAS observations, which are well worth being worked out in more detail. The possibility to see the tensorial averaging in a much slower regime before the onset of deleterious line broadening is an asset! But the result is obscured by the fitting artifacts related to the negative tensorial width. Fig. S9 shows that the sign of the tensor is rather ill-defined; the chi^2 surfaces are almost symmetric for the most part. This goes along well with the common notion that the sign of a dipolar tensor alone is not encoded in a simple 1D spectrum (as splittings or sidebands are symmetric). The only very slight asymmetry arises from the additivity of the J coupling in the formula for the evolution phase (see eq. 1), breaking the symmetry. A more systematic study is recommended, and possibly a case with dynamics not showing a negative order parameter.l.439: 1 s^3 must be a typoCitation: https://doi.org/
10.5194/mr-2024-4-RC1 -
AC1: 'Reply on RC1', Matthias Ernst, 06 Mar 2024
Dear Kay,
thank you for your detailed and insightful report on our manuscript.
It seems to us that we were not successful in conveying the main question that we wanted to address with this paper very well. The question we wanted to address was indeed motivated by "the authors' background in relaxation time studies". We were interested which dynamic time scales contribute to partially averaged anisotropic interactions measured in MAS NMR that are most often used in combination with relaxation data to get a better characterization of the amplitude and time scales of motions. When performing such a joint analysis, it is of utmost importance to know which motional time scales are actually sensed by the dipolar order parameters. In published literature on such combined analysis, this question is often somewhat circumvented, and it is assumed that the dipolar coupling covers all time scales (e.g. references (1, 2); this assumption is not correct), or that the slow motions have an amplitude that is so small that it would go undetected in experimentally measured order parameters (e.g. (3)), which may be correct in come cases, but not generally. In the “detectors” approach (4, 5), it is also (and incorrectly) assumed that the dipolar order parameter covers all time scales. In our view, such a joint analyses of relaxation data and dipolar order parameters, thus, lack a solid basis with respect to the time scale covered by the latter, and one should take into account which motional time scales are detected by these residual couplings.
The relevant questions to us are whether different recoupling methods cover different ranges, whether scaling of the couplings extends the range and what parameters influence the range of time scales covered by the scaled anisotropic interactions. We are not aware of publications in the literature that look at these questions in terms of MAS frequency, recoupling experiments and parameters. However, we believe that these are important questions if one wants to use such order parameters in combination with relaxation data. A detailed description of the recoupling behavior in the transition region was in no way our goal and is, for our purpose, only important to define the time scales that contribute to the partially averaged anisotropic quantities.
We are aware that there is a large literature that covers this intermediate range and in hindsight we should have mentioned this in the introduction and should have included references to some of the methods. Since it was not our intention to characterize the detailed line shape in the transition area, we do not think that a more complex data evaluation in that range of motional time scales adds any additional value to the paper. Our simplistic approach was motivated by the typical data evaluation done when residual dipolar couplings are evaluated experimentally. We are aware of the additional relaxation from the intermediate motion during recoupling (T2/T1rho) as well as during the data acquisition in real experiments.
As a way forward, we propose the following changes to the manuscript.
(i) We will change the title to “Evaluating the motional time scales contributing to averaged anistotropic interactions in MAS NMR" to make the topic of the paper clearer. In our opinion, the abstract conveys the intention of the paper quite well.
(ii) We will rewrite the introduction to include a more detailed discussion of the intermediate time-scale regime and to make the aim of the paper hopefully clearer. This will include references to different approaches for a better description of intermediate time-scale motions. We will stress that we are mainly interested in characterization of the three motional regimes (fast, intermediate, slow) in order to determine which time scales contribute to the partially averaged anisotropic interactions.
(iii) In the methods section we will again stress that determining the order parameter in the transition region is not meant as a complete characterization of the motional processes in this region but a way to determine the three main areas of motional processes: fast, transition area, slow. We will mention that there are more complex ways to analyze dynamics data in the intermediate regime and motivate why we used such a simple approach.
(iv) In the results and discussion section we will emphasize that we are mostly interested in the fast motion regime and try to reduce the discussion of the intermediate regime to focus the paper on the topic.
(v) We will also try to emphasize in the conclusions what the important results are.
Some detailed answers to specific questions:
"Here, I wonder why in the present manuscript the T1rho effects are so much weaker (only seen in Fig.S1, but not in Fig.2a) than the ones measured and simulated by Cobo et al. The authors may want to check their code, simulating with the spin system parameters of Cobo et al., just to make sure."
The T1rho decay strongly depends on the rate constant, and the magnitude of the dipolar coupling used in the simulations as can be seen from Fig. S1. The parameters selected in Fig. 2a corresponds to the k=1e3s-1 and \delta/2\pi=5kHz plot in Fig. S1. The simulations of Kobo assume a much stronger one-bond CH coupling with a \delta/2\pi=46kHz.
We hope that these changes address the main points of your review report.
- J. D. Haller, P. Schanda, 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 (2013).
- V. Chevelkov, U. Fink, B. Reif, Quantitative analysis of backbone motion in proteins using MAS solid-state NMR spectroscopy. J. Biomol. NMR. 45, 197–206 (2009).
- T. Zinkevich, V. Chevelkov, B. Reif, K. Saalwächter, A. Krushelnitsky, Internal protein dynamics on ps to μs timescales as studied by multi-frequency 15N solid-state NMR relaxation.J. Biomol. NMR. 57, 219–235 (2013).
- K. Zumpfe, A. A. Smith, Model-Free or Not ? Front. Mol. Biosci. 8, 727553 (2021).
- A. A. Smith, M. Ernst, B. H. Meier, Optimized “detectors” for dynamics analysis in solid-state NMR. J. Chem. Phys. 148, 045104 (2018).
Citation: https://doi.org/10.5194/mr-2024-4-AC1 -
RC2: 'Reply on AC1', Kay Saalwächter, 08 Mar 2024
Dear Matthias,
thank you for your detailed reply. With your explanations, I can now better appreciate the purpose and motivation of the work. We also seem to agree that, besides backing up and serving the motivation, the work should be based on an account of relevant previous work in the field that helps in addressing the problem.
I do acknowledge that your work does not intend to provide strategies to extract slow motional timescales. But I do not agree with the implication to not make changes in the material to be presented. I should also take the chance to make clearer why changes are in my view necessary, in particular an account of T2 phenomena: A sole interest in the fast-motion regime and reducing the discussion of the intermediate regime (to quote your reply) will hardly serve the goal. If the goal is to aid protein NMR relaxometry studies by enabling the reliable measurement of effective tensor widths (relevant to pre-define order parameters), then it is of utmost importance to know if the data is subject to intermediate-regime effects!
As is obvious from most of the fitted data, the shape of the curves is not immediately diagnostic of the dynamic regime. One should therefore use any possible (and in the given case even simple) option to be sure about the measurement of a fast-limit average. And this involves T2 effects as a second, much clearer source of information. Temperature variation is always limited in protein NMR since one is interested in physiological conditions; one may mainly cool to freeze out a potential slow-motional process interfering with the tensor quantification once it is identified, so as to arrive at the correct order parameter for the fast motions probed by relaxation analyses. The best basis of this extra experimental effort is to check the T2 losses as a direct indicator.Therefore, in order to confirm a reliable fast-limit averaged order parameter, a qualitative pinning down of the intermediate regime also in terms of T2 effects is relevant, if not the only reliable way. I will thus endorse publication only if these are included in the presentation and discussion.For each of the methods considered, this means:CP: this seems uncritical, as the intensity build-up encoding the tensor width occurs on a ca. 10 times faster timescale that the T1rho decay. But this also means that a CP build-up alone will not serve the goal to identify problems with the correct tensor width.REDOR: the DeltaS/S0 curve (being T2-compensated) has in principle the same problem, although with somewhat more pronounced effects of reduced oscillations indicating the intermediate regime. But here, the separate analysis of S0 (which is available!) will clearly bring out the potentially strong T2 effect that can help to identify incomplete/partial averaging and thus an ill-defined S value.wPARS: here, the experiment is run in a dephasing mode, which is dangerous to start with. This means that the imperfection compensation inherent to REDOR is skipped. And again, a reference experiment will show the potentially strong T2 effect relevant to identify partial averaging. The reference experiment would in this case be the same pulse sequence but with a virtual pi pulse, i.e. a simple phase inversion, at the center of the wPARS sequence. This should not pose any significant challenges.CSA recoupling: same as wPARS. Here, the T2 effect seems directly visible in the form of a decay of the 50% intensity plateau. Yet again, a reference experiment could easily be devised.off-MAS: the reply does not address my concerns with the fitting instability related to the limited sensitivity to the sign of the tensor. This should be taken up. Removing the sign information by just reporting the modulus (and moving details concerning the sign to the SI) seems advised.2H MAS sidebands: here, again, the reference experiment is part of the data, it is merely the decay of the rotor echoes, for which theory is well-developed (Suwelack et al.). This should be taken up.Best regards,KayCitation: https://doi.org/10.5194/mr-2024-4-RC2 -
AC4: 'Reply on RC2', Matthias Ernst, 14 Mar 2024
Dear Kay,
while we agree that motions in this intermediate time scale are very important and interesting (and difficult) to characterize, we disagree that they are very important in the context of measuring order parameters from scaled anisotropic interactions. If the amplitude of motion in the intermediate regime is small, it will not affect the measurements of the order parameters much and fits of static tensors will work with small distortions. If the amplitude of motion in the intermediate regime is large, the fits will break down. But we must remember that such measurements for site-specific order parameters require typically a 2D or 3D spectrum with at least two polarization-transfer steps and two evolution periods. Larger amplitude intermediate motion will make the polarization transfer inefficient for either INEPT or CP and at the same time the lines will be broadened in t1 and t2. Therefore, we expect that parts of the molecule with larger amplitude intermediate motions will have a low S/N ratio and a high-quality data analysis will be impossible.
We will discuss this problem in the revised manuscript and add a plot of the typical (real) T2 dependence as a function of MAS and correlation time. We agree that determining T2 (or better T1rho since real T2 are difficult/impossible to measure in solids) is always a good idea to spot such areas of the molecule, but experience shows that often those resonances are missing in the spectra.
We will discuss the aspects of T2/T1rho for the various sequences. However, developing new T2 compensated experiments by implementing reference experiments is, in our opinion, beyond the scope of the manuscript.
The offMAS measurements are currently part of our research. We are trying to implement a better way of doing such offMAS experiments and in this context, we will look at the detailed behavior of the recoupling in that region. Again this is beyond the scope of the current manuscript where we have included offMAS mainly because there are experimental data acquired with it in the literature.
Citation: https://doi.org/10.5194/mr-2024-4-AC4
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AC4: 'Reply on RC2', Matthias Ernst, 14 Mar 2024
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AC1: 'Reply on RC1', Matthias Ernst, 06 Mar 2024
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RC3: 'Comment on mr-2024-4', Anonymous Referee #2, 09 Mar 2024
In their manuscript, Aebischer et al. describe the motional time scale dependence of averaging of anisotropic interactions in MAS solid-state NMR experiments. In particular, the authors investigate the CP, REDOR and wPARS pulse scheme for slow, fast and intermediate exchange. Furthermore, CSA recoupling, quadrupolar coupling experiments, and off magic angle experiments are considered. Simulations were carried out using GAMMA. Subsequently, the obtained results were fit using reference simulations that were carried out for rigid systems.
The paper is written very nicely. The graphics work is well done, and the text is comprehensive. I have very little to complain about the manuscript. There are only a few minor points.1) simulation input files should be made available as part of the supporting information.2) a link to the GAMMA source code should be included in the revised manuscript.I disagree with reviewer #1 that the paper has to discuss all the existing literature that has been published on the topic of intermediate exchange. I agree, however, that the readers should be made aware that relaxation based experiments such as R2 have to be performed to yield complementary information on the underlying motional regime.In agreement with the corresponding author, I see this work in the framework of an analysis of order parameters in case dipolar interactions are only partially averaged.For users interested in applying order parameter experiments to characterize their systems, the influence of intermediate motion on the order parameter is of high interest. At the same time, users have to be made aware of effects that occur in an intermediate motional regime.I therefore recommend to accept the manuscript after the changes suggested by the corresponding author are incorporated into the manuscript.Citation: https://doi.org/10.5194/mr-2024-4-RC3 -
AC2: 'Reply on RC3', Matthias Ernst, 12 Mar 2024
Thank you for the positive feedback to our manuscript.
We will make all simulation input files, the GAMMA code, and MATLAB and python processing files available through the ETH Research Collection (https://www.research-collection.ethz.ch/) where it will be long-term accessible with a DOI. We will not put up all the simulated data files there since it is an immense body of data that can be reproduced quite easily based on the scripts and GAMMA simulation code.
As already pointed out in the response to Reviewer 1, we will update the manuscript as outlined there and expand the description of the behavior in the intermediate regime.
Citation: https://doi.org/10.5194/mr-2024-4-AC2
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AC2: 'Reply on RC3', Matthias Ernst, 12 Mar 2024
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RC4: 'Comment on mr-2024-4', Anonymous Referee #3, 13 Mar 2024
The manuscript by Ernst and coworkers attempts to further our understanding of how different pulse sequences techniques respond to changes in the timescale of motion and whether there are any advantages/disadvantages to a particular sequence while estimating dynamics via a single order parameter. The sequences considered are REDOR, CP and wPARS. They also consider CSA recoupling, quadrupolar patterns, and off-MAS experiment for this treatment as well.It is definitely a relief to see Fig. 3 where all the sequences respond in a similar manner, showing a smooth transition between the slow and fast motion regimes, and that a minimal dependence on MAS is observed. I do find Fig 4 a bit surprising. I wonder if the minimal effect on the wPARS sequence upon changing the window duration is because the addition of a window does not really change the effective Hamiltonian description (except for the scaling factor), while this is not true for the epsilon-REDOR and the tilted-angle CP experiment. If this is true, can one then expect that as one spins faster, the deviations that one sees in CP and REDOR will progressively get smaller?
I find the results presented in this manuscript quite valuable as making the choice between different recoupling sequence, especially at fast MAS frequencies is non-trivial even from a technical standpoint. Results presented here seem to suggest that at least as far as motional regimes are concerned, all the methods are pretty much equal and other considerations (rf requirements, robustness, etc) can take precedence.
Hence, although I appreciate the detailed review from Reviewer #1, I think that the scope of this manuscript is narrower while still filling in an important missing gap. I will recommend that this manuscript be accepted with the changes that the authors have previously suggested.
Citation: https://doi.org/10.5194/mr-2024-4-RC4 -
AC3: 'Reply on RC4', Matthias Ernst, 14 Mar 2024
Thank you for the positive report.
We believe that the "minimal effect on the wPARS sequence upon changing the window duration" is due to the relatively small scaling factor of the window as shown in Fig. S8. In REDOR and CP the changes in the effective coupling are much larger which most likely explains the larger changes in the fitted values especially in the transition region. We do not understand the behavior of the REDOR sequence that seems to behave differently in the transition area.
Our main result is indeed that the dynamic time scales measured by the order parameter of the residual dipolar coupling is indeed mainly dependent on the magnitude of the interaction and only to a much lower extent on the methods or parameter used for the recoupling. We must admit that this was somewhat unexpected for us but maybe other people have a better intuition and would have expected this result.
Citation: https://doi.org/10.5194/mr-2024-4-AC3
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AC3: 'Reply on RC4', Matthias Ernst, 14 Mar 2024
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