Pulse Dipolar Electron Paramagnetic Resonance Spectroscopy Distance Measurements at Low Nanomolar Concentrations: The CuII-Trityl Case

Recent sensitivity enhancements in pulse dipolar electron paramagnetic resonance spectroscopy (PDS) have afforded distance measurements at submicromolar spin concentrations. This development opens the path for new science as more biomolecular systems can be investigated at their respective physiological concentrations. Here, we demonstrate that the combination of orthogonal spin-labeling using CuII ions and trityl yields a >3-fold increase in sensitivity compared to that of the established CuII-nitroxide labeling strategy. Application of the recently developed variable-time relaxation-induced dipolar modulation enhancement (RIDME) method yields a further ∼2.5-fold increase compared to the commonly used constant-time RIDME. This overall increase in sensitivity of almost an order of magnitude makes distance measurements in the range of 3 nm with protein concentrations as low as 10 nM feasible, >2 times lower than the previously reported concentration. We expect that experiments at single-digit nanomolar concentrations are imminent, which have the potential to transform biological PDS applications.

1. Three of the four authors are also authors of a recent community paper that defined standards for measuring and analyzing PELDOR/DEER data on nitroxides (Ref.4).I see with great dismay that the current manuscript does not live up to the standards set in the community paper.The community agreed that signal-to-noise ratio (SNR, defined as modulation-to-noise ratio) should exceed 20.The authors should not claim a concentration sensitivity that refers to data with lower SNR than that.
2. The same community paper discourages the use of the two-step data analysis whose results the authors show in the main text.Instead, it recommends the use of automated workflows.The community paper specifically requests that parameter choices in data analysis have no element of user discretion and that uncertainty bands are reported as 95% confidence intervals.The uncertainty bands reported in the main text were derived by an outdated approach and are statistically not well defined.Two different criteria were used for selecting the regularization parameter (L curve and GCV).It is unclear which data set was processed with which criterion and why.For the 5 nM sample, less noise was added than for the other samples.The authors did analyze their data with state-of-the-art software, too, but they do not base their conclusions on the results of such analysis.This must be fixed.
3. Reporting concentration sensitivity for pulsed dipolar spectroscopy only makes sense together with reporting of the measured distance.This is because concentration sensitivity depends very strongly on distance.The Abstract and the Conclusion must state the measured distance of 3 nm together with the concentration sensitivity.
4. I object to the sentence "It is conceivable that these are often concentration-limited, either due to poor solubility or low expression yield".Conceivable it may be, but I have never heard of it or experienced it in my own research.Nitroxide-nitroxide PELDOR/DEER with a state-of-the-art highpower Q-band spectrometer is feasible with any expression yield at which a protein can still be handled in a wetlab.If the authors know a case, where more sensitive experiments, such as smFRET, were feasible and nitroxide-nitroxide PELDOR was not, they should provide a reference.The same applies to solubility.Some proteins undergo liquid-liquid phase separation already at concentrations where nitroxide-nitroxide PELDOR is not applicable.Measuring the dispersed state of such proteins is a case where the approach of the authors would be required.
5. If the authors want to argue with in-cell EPR, they should discuss whether a Cu(II)-dHis-NTAlabelled protein is stable in cell for the time required to prepare a sample.I doubt that.The authors could convince me and the readers by a reference.
6.The authors selectively discuss advantages of their approach and do not mention disadvantages.For instance, SLIM is (much) larger than a nitroxide label.Thus, SLIM is more prone to disturbing native structure.The Cu(II) labelling with the dHis motif puts more stringent requirements to the labelling site than approaches based on a single cysteine residue.Cu(II) labelling may also be problematic for proteins that bind Cu(II) unspecifically.Such limitations need to be mentioned.

Minor:
7. The authors argue that the SLIM label improves sensitivity because rectangular pulses cannot excite the whole nitroxide spectrum.What about Cu(II)-nitroxide RIDME with a chirp observer sequence?8. Table S4, report should report the raw S values (modulation-to-noise ratios).The sensitivity per unit time can be reported as well.In this case, the unit must be given.9.The abbreviation "ctvtRIDME" in the SI is undefined.To me it is also unclear what the "ct" means here.

Reviewer: 2
Comments to the Author With recent development of DEER measurements, the key issues including the stability and quality of spin labels in structural biology still remain.The manuscript presents an way to improve the sensitivity of DEER measurement with trityl-Cu(II) couple following the published NO-Cu(II) pair.Overall, the experiments were well designed and the results are sound.However, the reviewer has several serious reservations that I wish the authors address correctly. Major:

1)
In the introduction, the reference 2 in line 49 is wrong.It is not the in-cell NO measurements.The authors have to cite correct references.In addition, there are too many selfcitations and I suggest the authors cite the references probably in this field.

2)
The authors argue the improvement of trityl-Cu(III) DEER signal to noise, which I certainly agree, but the reliability of low-concentration data has to be addressed clearly.For example, in Figure 2c (25 nm and 10 nm) the varied distance distributions in the low-concentration data compared with the high-concentration ones.The additional distance in the sample of 25 nm, which is in great contrast to the others.Similarly, in Figure 3c.
These inconsistences have to be explained and convince the users the shortened measurement time does not sacrifice the signal to noise and reliability.

3)
One serious comment: the author use the two His in a protein and one additional NTA to chelate the copper ion, the stability of this trinary complex has to be discussed in very low concentration of protein samples, and preparations of the samples rather than direct dilutions from concentrated ones.Otherwise, this gain is not convincing for the EPR users.
Minor: It would be nice to comment on the in-cell applications of this method.

Reviewer: 3
Comments to the Author Referee report Manuscript title: "Enhanced sensitivity for pulse dipolar EPR spectroscopy using variable time RIDME" Authors: Joshua L. Wort et al.

Submitted to JPC Letters
The manuscript describes approaches to improved sensitivity of distance determination by RIDME, a pulsed EPR technique widely used.A combination of using a trityl spin label instead of the commonly used nitroxides and the application of a procedure to optimize RIDME parameters lead to an improvement in sensitivity that promises reaching the 10 nanomolar range of protein concentrations.
The study clearly is a large step ahead in the sensitivity of distance determination by pulsed dipolar spectroscopy and merits speedy publication in the form of a letter.
Several points need the attention of the authors: 1.In Fig. 3, the data are shown for the 50 nanomolar and 25 nanomolar concentrations, and in contrast to Fig. 2, conventional RIDME, the accumulation times are the same.The concentration changes by a factor of two, yet the noise in the raw data (Fig. 3a) seems disproportionally higher for 25 nanomolar, compared to 50 nanomolar.Also, the uncertainty range (Fig. 3c) for the former sample is significantly worse.Perhaps the latter point is owing to the overly conservative error estimate.Perhaps the authors could comment on this point in the SI.
2. Overall the manuscript is well written and clear, Yet, on p. 8, lines 9 and 10, "lower concentrations led to significantly increased confidence bands" can lead to confusion: increased confidence, means less confidence in this case, so rephrasing would be good.
3. On p. 7, line 34," Thus, compared to the CuNTA-nitroxide RIDME measured at 30 K, 52 here the unfavourable change in the Boltzmann distribution res…" This description is clear to magnetic resonance audiences, yet for the readers of JPC letters this seems too specialized.The authors could consider rephrasing or referring to the SI for details. 4. As rightly pointed out, the protein is a well-chosen model system with a stable fold and a relative short distance between the label positions.Consequently, relatively short evolution times and clear modulation facilitate the experiment.Could the authors sketch how, in their view, less optimal situations would affect the concentration limit?Once these points are taken care of, this is a fine manuscript that is relevant for protein molecular structure investigations and will be of interest for a large range of the readership of JCPLett.The urgency of this publication derives from the fact that the nanomolar sensitivity approached here represents one of the bottlenecks for using the pulsed dipolar EPR spectroscopy methods to real, biochemically relevant questions.We would like to thank the reviewers for their efforts in carefully assessing the manuscript.The reviewer and editorial comments and our point-by-point reply can be found overleaf.We believe the reviewers' suggestions have improved manuscript and supplementary information.
Therefore, we hope the current manuscript is acceptable for publication in The Journal of Physical Chemistry Letters.
The manuscript has been published as an author preprint on chemRxiv Three of the four authors are also authors of a recent community paper that defined standards for measuring and analyzing PELDOR/DEER data on nitroxides (Ref.4).I see with great dismay that the current manuscript does not live up to the standards set in the community paper.The community agreed that signal-to-noise ra�o (SNR, defined as modula�on-to-noise ra�o) should exceed 20.The authors should not claim a concentra�on sensi�vity that refers to data with lower SNR than that.While this may sound pedan�c, all four authors of the current manuscript are also authors of reference 4. Reference 4 describes guidelines for authors and reviewers of scien�fic outputs involving PELDOR/DEER data.While we agree that some considera�ons are equally valid for RIDME experiments, we must refer the referee to footnote b of table 3 in reference 4 that explicitly states: "If an SNR of 20 cannot be achieved at the required trace length, data with an SNR down to 10 can s�ll provide useful restraints."We have added the following statement to make this clear to the reader: "While this is below the recent recommenda�on of a modula�on-to-noise ra�o of at least 20, this data is s�ll of sufficient quality to provide useful structural restraints. 4" 2.
The same community paper discourages the use of the two-step data analysis whose results the authors show in the main text.Instead, it recommends the use of automated workflows.The community paper specifically requests that parameter choices in data analysis have no element of user discre�on and that uncertainty bands are reported as 95% confidence intervals.The uncertainty bands reported in the main text were derived by an outdated approach and are sta�s�cally not well defined.Two different criteria were used for selec�ng the regulariza�on parameter (L curve and GCV).It is unclear which data set was processed with which criterion and why.For the 5 nM sample, less noise was added than for the other samples.The authors did analyze their data with state-of-the-art so�ware, too, but they do not base their conclusions on the results of such analysis.This must be fixed.The community white paper does not state that the two-step approach is wrong and must not be used.Instead, it points to the issue and calls for reliable and tested single step approaches.The paper does also not call for all legacy data to be reanalysed.We choose here to use both, the two-and single-step approaches.This is exactly the approach taken in reference 4, where all laboratories par�cipa�ng in the ring-test did use the two-step analysis and the comparison to newer approaches was done in the supplement.In addi�on, it is also not so clear which of the analyses is supposedly incorrect, and the reviewer does not specify this.Along these lines, the Consensus DEER Analyzer so�ware fails to process certain data despite the modula�on-to-noise ra�o being above 10 and no other obvious problem with the data.We are confident that single-step and automated approaches will be widely adopted once their general applicability and robustness has been established and their documenta�on and usability meet user demand.
We have clarified the choice of the regularisa�on parameter in the SI (chapter 8, page S9).Furthermore, the data will become openly accessible, and anyone concerned can retrace the analysis and draw their own conclusions.Adding lower amounts of noise to the 5 nM sample was done to demonstrate that the failed distance analysis is not caused by the noise added in valida�on.Please note that we specifically point out that in this case, even though only 10% noise was added, we do not deem the resul�ng distance distribu�on reliable.

3.
Repor�ng concentra�on sensi�vity for pulsed dipolar spectroscopy only makes sense together with repor�ng of the measured distance.This is because concentra�on sensi�vity depends very strongly on distance.The Abstract and the Conclusion must state the measured distance of 3 nm together with the concentra�on sensi�vity.We have added the requested clarifica�on to abstract and conclusion.

4.
I object to the sentence "It is conceivable that these are o�en concentra�on-limited, either due to poor solubility or low expression yield".Conceivable it may be, but I have never heard of it or experienced it in my own research.Nitroxide-nitroxide PELDOR/DEER with a state-of-the-art highpower Q-band spectrometer is feasible with any expression yield at which a protein can s�ll be handled in a wetlab.If the authors know a case, where more sensi�ve experiments, such as smFRET, were feasible and nitroxide-nitroxide PELDOR was not, they should provide a reference.The same applies to solubility.Some proteins undergo liquid-liquid phase separa�on already at concentra�ons where nitroxide-nitroxide PELDOR is not applicable.Measuring the dispersed state of such proteins is a case where the approach of the authors would be required.We rephrased this sentence by removing "o�en".We also added a statement and referenced liquidliquid phase separa�on.Providing references where smFRET worked but PELDOR did not is difficult to do because failed experiments are rarely reported in the literature.However, examples from the lab of OS are sea urchin and human SAC I and TRIM71 (Kolanus, collaborator of OS).We would love to be able to express these in large enough amounts for PELDOR studies but are currently only able to reach sample amounts that would sa�sfy smFRET.

5.
If the authors want to argue with in-cell EPR, they should discuss whether a Cu(II)-dHis-NTAlabelled protein is stable in cell for the �me required to prepare a sample.I doubt that.The authors could convince me and the readers by a reference.We have added the relevant paper from the Ruthstein lab: "Despite its vulnerability to reduc�on CuNTA has been used for in-cell PDS. 52"

6.
The authors selec�vely discuss advantages of their approach and do not men�on disadvantages.For instance, SLIM is (much) larger than a nitroxide label.Thus, SLIM is more prone to disturbing na�ve structure.The Cu(II) labelling with the dHis mo�f puts more stringent requirements to the labelling site than approaches based on a single cysteine residue.Cu(II) labelling may also be problema�c for proteins that bind Cu(II) unspecifically.Such limita�ons need to be men�oned.8][49][50] " We also added a sentence to the introduc�on: "Addi�onally, different spin labels may lead to different degrees of perturba�on of na�ve structure due to their size and interac�ons with protein residues, e.g.trityl labels." We also have added a sentence clarifying that CuNTA labelling is not prone to unspecific binding as labelling with Cu without chelator is: "CuNTA increases specificity to dHis sites compared to free Cu II in solu�on, which has higher propensity to unspecific binding. 42,47,51" The authors argue that the SLIM label improves sensi�vity because rectangular pulses cannot excite the whole nitroxide spectrum.What about Cu(II)-nitroxide RIDME with a chirp observer sequence?We did not try this, but literature suggests no improvement htps://doi.org/10.1016/j.jmr.2019.07.047.

8.
Table S4, report should report the raw S values (modula�on-to-noise ra�os).The sensi�vity per unit �me can be reported as well.In this case, the unit must be given.We added the raw S (modula�onto-noise ra�o) values.

9.
The abbrevia�on "ctvtRIDME" in the SI is undefined.To me it is also unclear what the "ct" means here.
We have added the defini�on to the SI: ctvtRIDME (constant and variable �me RIDME in a single combined pulse program).

Reviewer: 2
With recent development of DEER measurements, the key issues including the stability and quality of spin labels in structural biology s�ll remain.The manuscript presents an way to improve the sensi�vity of DEER measurement with trityl-Cu(II) couple following the published NO-Cu(II) pair.Overall, the experiments were well designed and the results are sound.However, the reviewer has several serious reserva�ons that I wish the authors address correctly.We thank the reviewer for considering our experiments "well designed" and the results "sound".However, we would like to emphasise that the manuscript deals with RIDME and not DEER experiments.This confusion of PDS methods raises some concern regarding the suitability of this reviewer.

1)
In the introduc�on, the reference 2 in line 49 is wrong.It is not the in-cell NO measurements.The authors have to cite correct references.In addi�on, there are too many self-cita�ons and I suggest the authors cite the references probably in this field.The paragraph in ques�on discusses Pulsed Dipolar EPR Spectroscopy (and not just PELDOR), the need for paramagne�c centres, and their use in in vitro and in cellulo experiments.This is not limited to nitroxides.Reference 2 from the Bordignon lab describes in vitro measurements on nitroxide labels and in cellulo measurements on Gd III labels.All of this is within scope of the text, and we cannot follow where this is supposed to be erroneous.The reviewer seems to be misled that this is a PELDOR/DEER manuscript.We report and discuss RIDME applica�ons and the use of CuNTA and trityl.Given that our labs have made significant contribu�ons to the development and applica�ons of RIDME (including the vtRIDME experiment), CuNTA and SLIM labelling (including the development of SLIM) the references reflect this.The other reviewers are not concerned by our reference list.

2)
The authors argue the improvement of trityl-Cu(III) DEER signal to noise, which I certainly agree, but the reliability of low-concentra�on data has to be addressed clearly.For example, in Figure 2c (25 nm and 10 nm) the varied distance distribu�ons in the low-concentra�on data compared with the highconcentra�on ones.The addi�onal distance in the sample of 25 nm, which is in great contrast to the others.Similarly, in Figure 3c.These inconsistences have to be explained and convince the users the shortened measurement �me does not sacrifice the signal to noise and reliability.We cannot follow the reviewer's concern.There are no addi�onal distances outside the confidence es�mates.While there is distance probability appearing, it is within uncertainty.Thus, the analysis shows exactly what is expected.Larger noise gives larger uncertainty, but no new distance artefacts as suggested by reviewer 2.

3)
One serious comment: the author use the two His in a protein and one addi�onal NTA to chelate the copper ion, the stability of this trinary complex has to be discussed in very low concentra�on of protein samples, and prepara�ons of the samples rather than direct dilu�ons from concentrated ones.Otherwise, this gain is not convincing for the EPR users.All samples were prepared from mixing diluted protein stocks with diluted CuNTA stocks not dilu�ng the final complex as suggested by the reviewer (this is described in detail in the reference given -ref.55 in the main text, ref. 1 in the SI).Thus, complex stability is not a problem.As for mul�dentate ligands, CuNTA is orders of magnitude more stable than the complex formed with the dHis mo�f.Dissocia�on constants assumed for labelling are cited and the CuNTA excess is calculated to lead to 90% labelling.
Minor: It would be nice to comment on the in-cell applica�ons of this method.There have not yet been any in cell applica�ons of this method.But we cite a paper from the Ruthstein lab on the use of dHisCuNTA in in cellulo experiments (see response to reviewer 1).

Reviewer: 3
Manuscript �tle: "Enhanced sensi�vity for pulse dipolar EPR spectroscopy using variable �me RIDME" Although this is not the manuscript �tle the comments clearly refer to the manuscript in ques�on.
Authors: Joshua L. Wort et al.Dr Wort is not an author on the current manuscript.

1.
In Fig. 3, the data are shown for the 50 nanomolar and 25 nanomolar concentra�ons, and in contrast to Fig. 2, conven�onal RIDME, the accumula�on �mes are the same.The concentra�on changes by a factor of two, yet the noise in the raw data (Fig. 3a) seems dispropor�onally higher for 25 nanomolar, compared to 50 nanomolar.Also, the uncertainty range (Fig. 3c) for the former sample is significantly worse.Perhaps the later point is owing to the overly conserva�ve error es�mate.Perhaps the authors could comment on this point in the SI.We have added a sentence to the SI to discuss this: "The 25 nM sample is worse than extrapola�on would suggest.As we cannot measure the final concentra�ons but just the stocks and then dilute this may be an error or just varia�on.However, we believe it would be unethical to remove a data point for no objec�ve reason."

2.
Overall the manuscript is well writen and clear, Yet, on p. 8, lines 9 and 10, "lower concentra�ons led to significantly increased confidence bands" can lead to confusion: increased confidence, means less confidence in this case, so rephrasing would be good.We rephrased to: "lower concentra�ons led to significantly increased uncertain�es including broader confidence bands and such data should only be interpreted with great care."

3.
On p. 7, line 34," Thus, compared to the CuNTA-nitroxide RIDME measured at 30 K, 52 here the unfavourable change in the Boltzmann distribu�on res…" This descrip�on is clear to magne�c resonance audiences, yet for the readers of JPC leters this seems too specialized.The authors could consider rephrasing or referring to the SI for details.We rephrased to: "… here the unfavourable change in thermal polarisa�on resul�ng from a 10 K increase in temperature was outweighed by faster repe��on rate with higher temperature."

4.
As rightly pointed out, the protein is a well-chosen model system with a stable fold and a rela�ve short distance between the label posi�ons.Consequently, rela�vely short evolu�on �mes and clear modula�on facilitate the experiment.Could the authors sketch how, in their view, less op�mal situa�ons would affect the concentra�on limit?
We have added to the conclusion paragraph: "It is expected that longer distances and broader or more complex distribu�ons will require longer dipolar evolu�on �mes or beter modula�on-to-noise ra�o.This would likely demand higher concentra�ons than achieved here."
Please submit your publica�on files without any markups.Any copies that contain highlights, colored text, or tracked changes should be submited as "Suppor�ng Informa�on for Review Only.We will submit manuscript and SI files without markup and add files with changes highlighted in yellow as review only material.

2.
Title: Using acronyms in �tle is discouraged.Please spell out all acronyms in the �tle of the manuscript and Suppor�ng Informa�on.We have changed the �tle to "Pulse Dipolar Electron Paramagne�c Resonance Spectroscopy Distance Measurements at Low Nanomolar Concentra�ons: the Cu II -Trityl Case".

3.
References: In both the main file and the suppor�ng informa�on, fix the style of all references to use JPCL forma�ng (check all references carefully).***JPC Leters reference forma�ng requires that journal references should contain: () around numbers, author names, ar�cle �tle (�tles en�rely in �tle case or en�rely in lower case), abbreviated journal �tle (italicized), year (bolded), volume (italicized), and pages (first-last).Book references should contain author names, book �tle (in the same patern), publisher, city, and year.Websites must include date of access.
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4.
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5.
Suppor�ng Informa�on: Please number SI pages in the following format: "S1, S2…" Page numbering has been changed as requested.The revised version addressed partially the pointes raised by the reviewer.The reviewer admits fact of the mis-typed DEER and RIDME in previously submitted comments, but understands the meaning of DEER, RIDME and DQC.All the distance measurement relies on key: the memory time of the spin label during the dipolar evolution time, which restricts the distance limits for determination.The reviewer would not argue the theory of this work since there is no development in this direction in this work.However, the review would ask the author to address carefully the concentration of samples for distance measurements since reliable distance is essential in these experiments.

1)
Reference 2 is an excellent work on the stability assay of NO spin labels for in cell measurements.It is the stability of NO spin label itself for in cell distance measurement but not the concentration of protein samples.This has to be stated clearly in the manuscript and it has to be for the EPR users.

2)
Again, the signal to noise in the measured data for low concentrations.The reviewer pointed out the inconsistency is the reliability of the data for very low concentration.

3)
The reviewer understands the high stability of NTA-Cu.However, the binding affinity of NTA-Cu for two additional HIS is certainly variable and it is also geometry and buffer (potentially binding ligands or pH) dependent.The reviewer's concern is the author has to state the case objectively, because the author used only one case of GB1 K28H/Q32H for such small and rock protein.If they would claim their proposed measurement more convincing, they have to measure a number of two His mutants of different proteins.One case is just not convincing.I wish the authors to state the comments clearly.
The points of 2 and 3 were already pointed by reviewer 1 in different ways.The measurements of the samples with concentrations of 50 and 25 nanomolar in Fig. 3 are the only ones where the data are presented in such a way that a direct comparison of S/N can be made.For the other concentrations, measurement conditions differ, making such a comparison impossible.The authors argue that the 25 nanomolar sample is 'an outlier', yet fail to show that for the remaining concentrations the S/N indeed follows the 'extrapolated trend' of S/N vs. concentrations.Otherwise, the suggestion that the 25 nanomolar sample is an outlier, together with the rather vague statement that the concentrations themselves may be flawed, because based on dilutions only, is weak.Perhaps the authors should give confidence levels for the concentrations, particularly for the 5 nanomolar concentration.We would like to thank the reviewers for their efforts in carefully assessing the manuscript.
The reviewer comments and our point-by-point reply can be found overleaf.We believe we have fully addressed all remaining and newly raised concerns.Therefore, we hope the current manuscript is acceptable for publication in The Journal of Physical Chemistry Letters.
The manuscript has been published as an author preprint on chemRxiv

Responses to reviewer comments
We thank all reviewers 2 and 3 for carefully reading the manuscript and providing additional detailed suggestions for improvement.In the following we provide the reviewers' comments in black text, with point-by-point responses in blue text.We have carefully addressed all their comments, and believe the clarity of manuscript and supplementary information have been further improved.
Therefore, we hope the current manuscript is acceptable for publication in The Journal of Physical Chemistry Letters.

Reviewer: 2
Recommendation: This paper may be publishable, but major revision is needed; I would like to be invited to review any future revision.

Comments:
The revised version addressed partially the pointes raised by the reviewer.The reviewer admits fact of the mis-typed DEER and RIDME in previously submitted comments, but understands the meaning of DEER, RIDME and DQC.All the distance measurement relies on key: the memory time of the spin label during the dipolar evolution time, which restricts the distance limits for determination.The reviewer would not argue the theory of this work since there is no development in this direction in this work.It is unclear what the reviewer is trying to express by mentioning the phase memory time of the spin label -yes, it does affect the maximum achievable dipolar evolution time, which determines the distance limits.As the reviewer will be aware the phase memory time will become concentration independent at low concentrations as e.g., instantaneous diffusion contributions will be negligible.We have refrained from discussing concentration and deuteration effects as they are well-reported.However, to make practitioners new to the field aware we have now cited two manuscripts detailing the effects of local concentration and deuteration on the phase memory time and achievable distances: "At sufficiently low temperature and spin concentration the electron spin dephasing time becomes concentration independent, 56 and the achievable distance range is largely limited by deuteration levels of the sample. 4, 57" However, the review would ask the author to address carefully the concentration of samples for distance measurements since reliable distance is essential in these experiments.We understand that the reviewer considers our previous wording too nuanced and encourages us to be very explicit regarding concentration of samples limiting sensitivity, which in turn limits reliability of distance measurements.We have now stated more clearly in the manuscript text that even though the used label combination affords measurements at lower concentrations than previously reported, not all data shown is desirable for interpretation of distance distributions but used to show the trend in sensitivity and allow analysis: "Thus, concentrations below 50 nM remain a challenge for ctRIDME even when using CuNTA-SLIM label pairs, and higher-quality data with lower uncertainties than seen for 10 and 25 nM will be required to e.g., determine whether multiple distance populations are present, as observed previously."

1)
Reference 2 is an excellent work on the stability assay of NO spin labels for in cell measurements.It is the stability of NO spin label itself for in cell distance measurement but not the concentration of protein samples.This has to be stated clearly in the manuscript and it has to be for the EPR users.
We have clarified that the paper by Kucher et al. describes similar (~100 nM) protein concentrations for PELDOR measurements in vitro using nitroxide spin labels and in-cell using gadolinium labels.

2)
Again, the signal to noise in the measured data for low concentrations.The reviewer pointed out the inconsistency is the reliability of the data for very low concentration.As stated above, we now understand that the reviewer feels we were not clear enough that Figures 2 and 3 do contain data that, while displaying the trends in improved sensitivity we aim to demonstrate, should not actually be used for obtaining high-quality structural restraints.We have emphasised and clarified this in the revised manuscript: "we would refrain from using data obtained at lower [than 50 nM] concentrations using ctRIDME due to the poor modulation-to-noise ratios achieved" and "While for the 50 nM vtRIDME a modulation-to-noise ratio > 20 was achieved with 8 h averaging time, the 25 nM and 10 nM samples yielded ratios < 10 with 8 h and 18 h averaging time, respectively; data of this quality should not be used to interpret distance distributions."We are further clarifying that the 25 nM sample is an outlier, see also reviewer #3. 3) The reviewer understands the high stability of NTA-Cu.However, the binding affinity of NTA-Cu for two additional HIS is certainly variable and it is also geometry and buffer (potentially binding ligands or pH) dependent.The reviewer's concern is the author has to state the case objectively, because the author used only one case of GB1 K28H/Q32H for such small and rock protein.If they would claim their proposed measurement more convincing, they have to measure a number of two His mutants of different proteins.One case is just not convincing.I wish the authors to state the comments clearly.We have extended the relevant part of the introduction as follows: "Depending on the secondary structural elements (-helix or -sheet), dissociation constants (Kd) were determined to be in the order of 10 -5 to 10 -7 under EPR conditions. 49,52 n advantage of using spectroscopically orthogonal labels is that binding sites can be saturated by an excess of CuNTA without overlap with the detected signal. 52Furthermore, the dHis-CuNTA labelling has been shown to be robust against competing ligands and retaining its high affinity binding over a wide pH range, thus demonstrating biologically relevant compatibility. 50While the majority of the benchmarking studies on dHis-CuNTA have been performed on different constructs of a model protein (GB1, vide infra), this labelling approach has also been applied to a variety of more complex biological systems. 30,45,53 "Thus, all points of concern of the reviewer -applicability to different proteins and robustness to geometry, pH, competitors -have been investigated and we have now explicitly pointed to the relevant references.
The points of 2 and 3 were already pointed by reviewer 1 in different ways.Reviewer 1 seemed satisfied with our revised manuscript.We believe we have fully addressed all concerns about data quality and general applicability of our findings.
Dipolar Electron Paramagnetic Resonance Spectroscopy Distance Measurements at Low Nanomolar Concentrations: the Cu II -Trityl Case" St Andrews, 24 th December 2023 Dear Editors, We are submitting the revised manuscript "Pulse Dipolar Electron Paramagnetic Resonance Spectroscopy Distance Measurements at Low Nanomolar Concentrations: the Cu II -Trityl Case" authored by Dr Katrin Ackermann, Mr Caspar Heubach, Prof. Olav Schiemann, and Dr Bela E. Bode for your kind consideration for publication as a Letter in The Journal of Physical Chemistry Letters.

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DOI:10.26434/chemrxiv-2023-j6mvr).To meet institutional and research funder open access requirements, any accepted manuscript arising shall be open access under a Creative Commons Attribution (CC BY) reuse licence with zero embargo.
In all cases of reused or adapted images, even those from papers published open access or in ACS publica�ons, you must cite the source with a credit line in the figure legend.Please use the following format: "Reproduced/adapted from [REFERENCE #].Copyright [YEAR] [Publisher/Copyright holder]." jz-2023-03311t.R2 Name: Peer Review Information for "Pulse Dipolar Electron Paramagnetic Resonance Spectroscopy Distance Measurements at Low Nanomolar Concentrations: the Cu<sup>II</sup>-Trityl Case" : "Pulse Dipolar Electron Paramagnetic Resonance Spectroscopy Distance Measurements at Low Nanomolar Concentrations: the CuII -Trityl Case" Authors: Ackermann et al.Submitted to JPC Letters My points are largely answered by the revision.I am a bit confused about the answer to my question 1.: Author's Response to Peer Review Comments: Dr Bela Bode Biomolecular Sciences Research Complex Centre of Magnetic Resonance Purdie Building, North Haugh, St Andrews, Fife, Scotland, United Kingdom, KY16 9ST T: +44 (0)1334 463869 F: +44 (0)1334 463808 E: beb2@st-andrews.ac.ukThe University of St Andrews is a charity registered in Scotland, No: SC013532 Manuscript: "Pulse Dipolar Electron Paramagnetic Resonance Spectroscopy Distance Measurements at Low Nanomolar Concentrations: the Cu II -Trityl Case" St Andrews, 10 th January 2024 Dear Editors, We are submitting the revised manuscript "Pulse Dipolar Electron Paramagnetic Resonance Spectroscopy Distance Measurements at Low Nanomolar Concentrations: the Cu II -Trityl Case" authored by Dr Katrin Ackermann, Mr Caspar Heubach, Prof. Olav Schiemann, and Dr Bela E. Bode for your kind consideration for publication as a Letter in The Journal of Physical Chemistry Letters.

(
DOI:10.26434/chemrxiv-2023-j6mvr).To meet institutional and research funder open access requirements, any accepted manuscript arising shall be open access under a Creative Commons Attribution (CC BY) reuse licence with zero embargo.