The very well written and well-illustrated manuscript by Robertson et al. from the Bax group entitled “Four-dimensional NOE-NOE spectroscopy of SARS-CoV-2 Main Protease to facilitateresonance assignment and structural analysis”describes two 4D [1H,1H]-NOESY NMR experiments and their application to a large protein system of 2×306 residues.  The detailed precise description allows not only to reproduce the pulse sequences straight-forwardly, but also highlights the importance that are in the details such as the absence of phase distortion of the spectrum relevant for the application of NUS obtained by the introduction of two composite 1H 180° pulses, and the optimization of the phase cycle to 4 and the excitation of resonances only to the “amide side” of the water frequency to enable high resolution acquisition. Of high interest is the NOESY-NOESY-TROSY experiment reminiscent of the first 3D experiments (by the Kaptein group) because of its information content for assignment and distance restraint collection along with its inherent high signal to noise because it comprises a relaxation-based magnetisation transfer. This is well illustrated for the large system under study.

In short, the presented manuscript is recommended for publication. The only small suggestions perhaps are

(i) highlight the two composite pulses in the pulse sequence

(ii) indicate, that the 4D NOESY-NOESY-TROSY does not comprise NOEs from amide protons that are upfield of the water resonance.

The manuscript presents the setup and combined use of two 4D NOESY experiments for resonance assignment and and structural studies of larger proteins by NMR. The combination of 4D TROSY-NOESY-TROSY and selective 4D NOESY-NOESY-TROSY turns out to be essential to simplify the complex 1H-1H dipolar relaxation network of the 712 res. homodimeric main protease of SARS-CoV-2. The authors indicate that the presented experiments were invaluable to validate the resonance assignments and subsequent structural analysis of this medically highly relevant protein, an exciting result, the detailed results of which will be presented elsewhere. This manuscript focusses in particular on the recording of the two types of 4D NOE-based spectra and presents several examples.

To make the 4D recording feasible, the spectra were recorded using NUS sampling, with a sampling sparsity of 0.54% for the 4D TROSY-NOESY-TROSY and 1.69% for the 4D NOESY-NOESY-TROSY. The resulting spectral quality is excellent. I have to compliment the authors as well that they show and describe the pulse sequences in recommendable detail and provide the scripts and details for processing.

The description of the NUS usage and detailed description of its results makes this paper very valuable and opens practical implementation and realistic acquisition times of these 4D acquisition methods. However, I suggest to provide more detail for the NUS sampling in the supplement, to be able to reproduce the NUS time series, also for different or future instruments.

The 4D NOESY-NOESY-TROSY experiment, a concatenation of 3D NOESY-NOESY and 2D TROSY (or 2D NOESY and 3D NOESY-TROSY…) has not been demonstrated before, is new, as well as the combination of both 4D’s for detailed analysis, which presents a major step forward for studying large proteins by NMR.

However, the 4D TROSY-NOESY-TROSY is not really new. It is rather an improved version of similar experiments, not only the 4D HMQC-NOESY-TROSY by the authors (Barnes et al, 2019) and 4D HMQC-NOESY-HMQC (Grzesiek et al, 1995), both referred to. There is also similarity to the 4D TROSY-NOESY-TROSY by Xia et al (2000, JBNMR 18, 261), which could be cited. Would there also have been an advantage of recording a diagonal-free version of this (Diercks et al 2010, JACS 132, 2138)?

I suggest to additionally deposit the pulse sequences, parameters and processing scripts of the supplement electronically. This would also allow to add the file bits.jfy.

Some detailed remarks:

p.4 l.103/104     Writing it this way “data matrix consists of 1536* x 90* x 91* x 90* complex points“ can be confusing. It reads as if 90*90*91*8 fids were recorded, which with ns=4 would be a 1.5 yr experiment. In fact, the experiment recorded only 31896 fids and thus the full ‘data’ matrix (if created at all) is largely empty (How does Bruker store the sparse NUS data? Is the large sparse data matrix indeed filled with zeros? Even for archiving storage?).

p.4 l.104   91* (1H) t2 increments is bit counterintuitive number, which may occur when t2 was the last incremented time and the measurement halted, though not unusual when planning subsequent measurements. Since it could also be a stalling measurement related to an instrument hardware/software issue, into which others may also run when using this sequence and parameter setup. Was it coincidence, planned, or is a warning footnote in the supplement at place?

p.4 l.109   Recording time 88 h? (2 + 0.2 + 0.12 + 0.03) x4 x31896 = 83 h. Where did the extra 5h for the two 4D’s go into? Or did I miss a delay? There appears a hidden delay. Is this internal handling of NUS or I/O by Bruker?  If there is a hidden delay, is it constant or could it be interfering with steady-state? Or was there a typing error?

p.6 l.171   idem. Recording time 110 h, (1.7 + 0.3 + 0.05) x4 x43856 = 100 h. Where is the extra 10 h?

The spectra Fig.2b and Fig.3 (diagonal signals) show double Lorentzian lineshapes. This may be cause of some overlap in Fig.2b and obscure signals close to the diagonal in Fig.3. The related 4D HMQC-NOESY-TROSY in Barnes et al. (2019) in fact showed more Gaussian lineshapes. Or, would the current data processing be optimal for S/N for this sample?

p.4 l.105   Since Bruker and TopSpin 3.1 is not the only and/or forever configuration for NMR acquisition, the NUS release version and the method to generate the random numbers, distribution function, parameters and seeds could be provided (or the generated array of delays), and certainly when deposited.

p.5. l.117  Caption Fig. 1. I suggest to write ‘selective EBURP2’, to be consistent with description on p.10 l.277. Only on p.10 it became clear that the f1,f2 time-evolution periods in the 4D cover only the spectral region downfield from the water line. Maybe this can already be mentioned on p.6 in the Methods, also to fully appreciate the f1,f2 sampling in that section. To be complete, it could be indicated in the description of the experiment of Fig.1b, that it is a selective 4D NOESY-NOESY-TROSY, and that it thus focusses on the amideproton NOE networks which fully makes sense for a perdeuterated protein.

p.6 l.161   Add the ref. (Ying et al) for SMILE already here, since it appears now only later on p.10

p.8 l.208   Labelling error: …are highlighted in the regular 2D 1H-  15N TROSY-HSQC spectrum of Figure 2a.  This is 2b in the Figure and caption. Idem,… a-helix (Fig. 2b,c), b-sheet (Fig. 2d,e), and a loop region (Fig. 2f,g). Description in text and Figure do not correspond.

Fig. 2b. (and discussion p.8. l.224 etc)       Diagonal intensities can vary, due to differences in longitudinal relaxation. However, the ‘diagonal’ cross-peak of L232 in Fig. 2b appears almost the same intensity as the sequential cross-peak to V233. Idem M235 and A234. Is this true, illusion, or due to contour levels chosen? If true, that diagonal and cross-peak have equal intensity, the NOE mixing time would be far beyond an optimum NOE cross-peak intensity, or not? (at least in 2-spin approximation, cf. Fig.3, Jeener et al 1979, J Chem Phys 71, 4546). Would 50 ms as in the f1,f2 planes of Fig.3 for this large 712 res. protein have been more appropriate, in hindsight?

p.12 l.338 Such weak direct NOEs are well possible in perdeuterated proteins (Koharudin et al. 2003 JMR 163, 228), but of course here they could also correspond to a relay via a -OH.

p.13 l.342-343  Depending on the deuteration level the 4D NOESY-NOESY-TROSY may also show NOE cross-peaks to aromatic protons. How complete was the deuteration of the SARS-CoV-2 main protease? From the description of the protein production on p.4, the description of the isotope labelling for this protein is missing. When available, the isotope levels could then be indicated in Section 2.1 as well.

The reviewed manuscript  submitted by Ad Bax and collaborators describes a four dimensional NOE experiments strategy applied for amide signal assignment of large dimeric SARS-1 CoV-2 protease.

The paper is well and clearly written and the detailed description of experiments is provided in Supporting Information. The presented experimental results are of high quality and are reported convincingly. The presented approach is interesting and scientifically sound, and there is a novelty in this work. Additionally, the very important nowadays subject of study and presented methods  make this article certainly interesting for Journal readership. Therefore, undoubtedly I am recommending the paper for publication.

Minor points:

- would be very informative to present a full 2D Trosy-hsqc spectrum of studied protein. The spectrum presented on Fig. 2b seems to be a fragment.

- how many amide peaks could be observed on 2D correlation spectrum?

- Authors informed that assignment will be published elsewhere, however  would be good to provide information regarding how many not-proline amide diagonal peaks were detected in 4D experiments out of almost 300 possible? How, mentioned at p.3 isomerization of P184 influenced the assignment process? Is it possible to assign both isomers?

General comments

This article by Bax and colleagues describes new 4D-TROSY-NOESY-TROSY and 4D-NOESY-NOESY-TROSY experiments applied to the perdeuterated 68-kDa dimer of the SARS-CoV-2 M^pro protease expressed in a D₂O E. coli culture. The 4D-TROSY-NOESY-TROSY is an improved version of earlier 4D ¹⁵N/¹⁵N-edited NOESYs, whereas the 4D-NOESY-NOESY-TROSY is a new combination of the 3D NOESY/NOESY pioneered by the Kaptein group with a TROSY detection. The 4Ds were acquired with extended acquisition times in all indirect dimensions using NU sampling within about 4 days experimental time. The spectral resolution and sensitivity are excellent and a number of very clear and extensive ¹H^N NOE networks in alpha helices and beta sheets are observed. The 4D-NOESY-NOESY-TROSY in particular is well suited for larger proteins since magnetization losses are minimal during the two NOE transfer steps. As the authors indicate, the NOESYs will be very helpful for obtaining assignments of such larger proteins by combining their information with that of the less-sensitive conventional triple-resonance assignment experiments and/or that of existing structures. The manuscript is very well written. The experiments are well documented by the printout of the pulse sequences and processing scripts in the supplementary information, which should make it easy for others to use the sequences.

As such this article should be very interesting and helpful for the readership of ‘Magnetic Resonance’.

Specific Comments

1. Figure 2b shows a large region of a ¹H-¹⁵N correlation spectrum. The figure legend is missing a description of subpanel b. Is this a 2D TROSY? A proper description in the legend as well as experimental details should be provided.
2. The number of resonances of the ¹H-¹⁵N 2D in Figure 2b is rather small for a 306-residue protein. I counted about one hundred resonances. Is this due to missing ¹H back exchange? The authors should discuss this point and indicate which percentage of the amides did exchange.
3. In this respect what would be the prospects for using similar sequences for protonated large proteins?
4. The authors use a rather high concentration of 0.9 mM dimer/1.8 mM monomer. Do they observe any aggregation? What are the prospects for applying the sequences to lower concentrations?
5. Could the authors please also indicate ¹H^N and possibly ¹⁵N T₂ relaxation times?
6. What is the reason for having 0.3 mM DSS in the buffer?
7. It would be helpful to not only provide the pulse programs and processing scripts as PDFs but also as plain text files.

Technical corrections

page 3, line 74: kD should be kDa