In the manuscript, Waudby and Christodoulou present a novel NMR strategy to probe chemical exchange processes on the order of microsecond to millisecond by analyzing the static magnetic field-dependence of the relaxation rates of a set of multiple-quantum (MQ) coherence of side-chain ¹H-¹³C methyl groups. The proposed experimental strategy is based on the previously reported approaches analyzing double quantum (DQ) and zero quantum (ZQ) coherences of methyl ¹H-¹³C correlations, as developed by Toyama et al. (Nat. Commun. 2017) and Gill et al (JBNMR 2011, JBNMR 2019). In this paper, the authors extend their methods by including the magnetic field-dependence of four-spin double quantum (DQ’) and quadruple quantum (QQ) coherences to break the symmetry of the ¹H and ¹³C chemical shift contributions to the DQ and ZQ coherences, which enables to determine the values for the relative amplitudes of ¹H and ¹³C chemical shift differences between two exchanging conformers. The authors also show that the joint analyses of magnetic-field dependence of these MQ coherences and ¹³C-¹H MQ/¹H SQ CPMG relaxation dispersion experiments enable the extraction of robust thermodynamic and kinetic parameters. The established methodology is successfully applied to 108-residue FLN5, the fifth immunoglobulin domain from the Dictyostelium discoideum filamin protein, and two distinct conformational exchange processes with the k_ex of ~870 s^-1 and ~6,900 s^-1 are identified.

The paper is very well and clearly written and most of the details, including the theoretical backgrounds and pulse programs/processing scripts, are provided. The approach presented here would be extremely useful for characterizing fast exchange processes, such as microsecond-order conformational dynamics and weak ligand-binding processes, and thus would greatly accelerate investigations of various biologically and chemically important systems. The idea of observing quadruple coherence is really fascinating and would attract great interest from the broad NMR community. Therefore, I strongly recommend publication in Magnetic Resonance.

I have a few suggestions for further improvement as follows.

(1) Throughout the paper, the authors assume that the conformational exchange processes affecting ¹³C and ¹H chemical shifts are always completely correlated (i.e. they can be described with the same k_ex and p_B). This should be clearly mentioned somewhere in the main text (though this is implied in lines 81-88 and line 100). I agree that this assumption is very reasonable in most cases, however, the ¹³C chemical shift is sensitive to the side-chain rotameric changes and ¹H chemical shift is more sensitive to ring-current effects from the proximal aromatic rings, and these two processes can be attributed to two distinct conformational fluctuations with different thermodynamic and kinetic parameters. This was also suggested in the analyses of T4 lysozyme in the previous work by Toyama et al.

(2) Line 103 “While it is possible to determine the relative sign of 𝜉C and 𝜉H from the sign of Δ𝑅_MQ,ex,  additional approaches are also required to determine their absolute signs.”

Here, the authors pointed out that absolute signs of ¹³C and ¹H chemical shift differences cannot be unambiguously determined by the previous approaches, however, the Hahn-echo analyses of ZQ, DQ’, and QQ coherences presented in this paper also cannot provide the absolute signs in principle (as can be seen in two symmetric optimal values in Fig 5C and D). In that sense, this sentence may be a bit misleading.

(3) Line 126. It may be helpful to mention that the relaxation induced by the external deuterons is not considered here.

(4) Line 173. “We observe no fixed ordering of the various relaxation rates, and indeed in some cases four spin relaxation rates are slower than ZQ or DQ rates (e.g. for QQ relaxation in L701CD1, Fig. 2B, right hand panel).”

The QQ relaxation is the fastest in L701, I guess this should be written as L664CG2.

(5) Line 186. Here, the authors propose the F1-decoupled HSQC to obtain ¹³C CSA values. I wonder how effective this approach would be when considering the applications to more complex systems. such as high molecular proteins. In large proteins, the outer components of the quartet decay very rapidly and these outer lines are almost invisible, which might affect the accuracy of the 2D line-shape analyses as there is less information available. Furthermore, in large systems, the signal overlap can be much more severe. In such a case, the pseudo-4D type experiment as originally proposed by Toyama et al may be a preferable.

(6) Line 221 and Fig 4. Is the IP and AP scheme inverted in the pulse scheme in figure 4? Also, after the purge element, the phase of phi2 should be on y to purge the fast-relaxing outer components as these outer components evolve with J and become orthogonal with respect to the slowly-relaxing central component.

(7) Line 280. Please label I743 and L701 on the structure.

(8) Line 285. Regarding the best-fit parameters displayed in Figs 6 C and D, how did the authors determine the absolute sign of the ¹³C and ¹H chemical shift differences? The absolute sign of the ¹³C and ¹H chemical shift differences cannot be determined from the analyses of Hahn-echo relaxation measurements and ¹³C-¹H MQ/¹H-SQ CPMG dispersion experiments also do not provide the information of the sign of ¹³C and ¹H chemical shift differences.

(9) Line 380. Please indicate the exact labeling pattern of “[²H, ¹³CH₃ -ILV]-labeled” sample. I imagine the CH₃/CD₃ labeling for Leu/Val would be important to reduce the effects of spin flips by the external protons.

(10) Regarding Fig S3, it would be worthwhile to mention that the slope is not exactly 1 and the offset has a non-zero value. It would be useful to comment on the potential sources of these deviations.

This paper describes an important development of a novel Hahn echo experiment for methyl quadruple quantum coherences. The theory shows that the Hahn echo relaxation rate constant is very sensitive to exchange and breaks the problem of symmetry that prevents absolute sign determination of chemical shift differences in other Hahn echo experiments. Pulse sequence for the experiment is well-described and validated (and shows excellent sensitivity). The experimental work is very thorough and includes careful assessment of the contributions of  chemical shift anisotropy to the field-dependent relaxation rates. Finally, the paper shows how joint analysis of the Hahn echo and CPMG measurements leads to more complete characterization of the exchange process. I expect this new experiment to be widely adopted in the set of powerful NMR experiments using the unique properties of methyl groups to characterize dynamics processes.

It may be that the authors are already at work on extensions to this work, but it seems feasible to modify the sequence for dispersion type measurements, using for example the heteronuclear double resonance relaxation approaches of Bodenhausen and coworkers, because dephasing of longitudinal 1H operators is not an issue (as in DQ/ZQ TROSY approaches). 

Minor:

Should table 1 include contributions for relaxation from dipole interactions with remote deuterons? The dipole interaction is weaker, but in a deuterated background, there are many deuterons.

In the joint analysis (Fig. 6 for example), were individual CSA values used for each spin or average values for residue type? Does it matter within the experimental uncertainties shown? Do other users need to remeasure the CSA's for each protein or are average values enough?

In Fig. 6C and 6D, should the x-axis be magnetic field-squared?

The authors have done an excellent job of referencing a now extensive literature on chemical exchange in biological molecules. A couple of other references might be of interest:

Multiple quantum relaxation outside the fast-exchange limit:

C. Wang and A. G. Palmer, Differential multiple quantum relaxation caused by chemical exchange outside the fast exchange limit, J. Biomol. NMR 24, 263-268 (2002)

Joint Hahn echo/CPMG analysis of 13C relaxation:

N. E. O’Connell, et al., Partially folded equilibrium intermediate of the villin headpiece HP67 defined by 13C relaxation dispersion, J. Biomol. NMR 45, 85-98 (2009).