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.

1. 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).
2. 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).
3. 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).
4. K. Zumpfe, A. A. Smith, Model-Free or Not ? Front. Mol. Biosci. 8, 727553 (2021).
5. A. A. Smith, M. Ernst, B. H. Meier, Optimized “detectors” for dynamics analysis in solid-state NMR. J. Chem. Phys. 148, 045104 (2018).

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.

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.