the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
The decay of the refocused Hahn echo in double electron–electron resonance (DEER) experiments
Thorsten Bahrenberg
Samuel M. Jahn
Akiva Feintuch
Daniella Goldfarb
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- Final revised paper (published on 16 Apr 2021)
- Supplement to the final revised paper
- Preprint (discussion started on 26 Jan 2021)
Interactive discussion
Status: closed
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CC1: 'Comment on mr-2021-10', Janne Soetbeer, 03 Feb 2021
The authors of the manuscript “The decay of the refocused Hahn echo in DEER experiments” under discussion at Magnetic Resonance experimentally test optimal DEER observer sequence settings for two refocusing pulses (i.e. optimizing the 4- or 5-pulse DEER scheme) for a nitroxide, a trityl radical and a gadolinium(III) ion in frozen protonated and deuterated water-glycerol glass. CCE simulations for the nitroxide in a water-glycerol mixture rationalize the observed decoherence behavior for cases where proton-driven nuclear spin diffusion induces electron spin decoherence. Overall, the Results and Discussion section on the experimental data would benefit from a more careful and consistent discussion on contributing dephasing mechanisms. In this context, I would like to draw the authors’ attention to our own article called “Dynamical decoupling in water-glycerol glasses: a comparison of nitroxides, trityl radicals and gadolinium complexes” under review at another journal since January 6th 2021. We made this manuscript available as a preprint under https://doi.org/10.26434/chemrxiv.13678447.v1 (hereinafter called DD-watergly2021) to facilitate the discussion here.
Comments regarding the discussion on dephasing mechanisms:
- Fig. 3/157-159: “While there is little difference between the refocused echo decay and the two-pulse echo decay for small τ2 values.” I agree with this observation, though the authors could strengthen the interpretation of their results by also noting the progressive change of the maxima along τ1 for increasing τ2 in Fig. 3c. The maximum at τ2 = 1 µs is particularly sharp and broadens for τ2 > 1 µs. This effect and the described deviation originate from the “fast” decoherence process driven by nitroxide methyl nuclei at low temperatures first demonstrated in glassy o-terphenyl (Soetbeer et al., 2018) which also contributes in water-glycerol glass (see DD-watergly2021: Fig. 4b) at the short time scale investigated here. Whereas our work stays in the DD condition e.g. of Carr-Purcell (CP) n = 2, the authors’ choice of τ2 values in Fig. 3c acts as a filter to probe the two dephasing contributions arising either from nitroxide or solvent nuclei. Though this short time window is less relevant for DEER application work, understanding of this type of decoherence contributions are of fundamental interest. The authors should mention this contribution to also provide a more coherent discussion, as in the context of OX063 and Gd(III) data, dephasing mechanisms arising from the paramagnetic species itself are discussed (see next point).
- Line 212-214: “This indicates that NSD, induced by the trityl OX063 protons themselves is still a contributing mechanism …”. I note that our own work also identifies the OX063 protons as a source for NSD and we compare its decay under DD to the partially deuterated trityl radical OX071, demonstrating the DD is more efficient for short interpulse delays (DD-watergly2021: Section 3.3.3 in the main text, and Fig. Sa20 b/d in the SI part A) compared to partial trityl deuteration. Hence, we have experimental evidence for what is a speculation here.
- Line 218-219: “In protonated solvent, the shape of the 2D decay is similar to the ones observed for 3-maleimido-proxyl and trityl OX063”. I note that the echo maximum in Fig. 7a does not follow the τ1 = τ2 line even at short delay times, whereas it does follow this line at early times for nitroxide/trityl in Fig. 3a/6a. Therefore, the behavior should not be called “similar”. It likely originates from a ZFS-driven dephasing contribution (see next point).
- Line 220-222: “…, indicating that a second dephasing mechanism in addition to NSD is contributing, such as the transient zero field splitting mechanism. (Raitsimring et al., 2014)”
Line 223-225: “in deuterated solvents, … nuclear spin diffusion plays a role [for Gd(III)] dephasing that is lower than in trityl OX063 but higher than in 3-maleimido-proxyl”
This discussion is inconsistent and requires further elaboration regarding the transient zero field splitting (tZFS) mechanism/Raitsimring et al., 2014 for the following reasons. First, the cited work introduces the tZFS for |mS| > ½ transitions. Specifically, the Abstract of the article states “tZFS induced phase relaxation mechanism becomes dominant (or at least significant) when all other well-known phase relaxation mechanisms, such as spectral diffusion caused by nuclear spin diffusion, instantaneous and electron spin spectral diffusion, are significantly suppressed by matrix deuteration and low concentration”, and the cited article furthermore argues that the |mS| = ½ transition behaves analogous to a S = ½ system, meaning that the dephasing at this field position is NSD-driven. Based on this citation alone, it is astonishing that the authors consider the tZFS mechanism in case of the protonated solvent but do not discuss its contribution in the deuterated case. Moreover, as the refocused Hahn echo decay was recorded at the maximum of the EPR spectrum, thus probing the |mS| = ½ transition, the authors need to comment on this finding as it is in conflict with the statement in Raitsimring et al., 2014. In fact, our own DD study relies on three Gd(III) complexes with varying ZFS to demonstrate that in protonated water-glycerol glass a ZFS-driven dephasing mechanism contributes at the central Gd(III) field position (DD-watergly2021: Fig. 7a, Section 3.4.2). Second, the authors’ spin concentration choice of 100 µM is highly likely to lead to ID contribution in deuterated water-glycerol glass. For this reason, the observed decoherence behavior (Line 223-225) cannot be interpreted as deuteron-driven NSD exclusively. On the one hand, because tZFS dominates the dephasing for Gd(III) (as our own DD data proves, DD-watergly2021: Fig. 7c). On the other hand, because at the same spin concentration and pulse excitation bandwidth, ID provides a more significant dephasing pathway for trityl radicals compared to nitroxides. We discuss this aspect in our own work (DD-watergly2021: section 3.3.1), stating that nitroxides are spectrally more diluted. To assess differences in deuteron-driven NSD, the authors would need to choose a lower spin concentration and demonstrate experimentally that ID is negligible.
Comments regarding the data analysis/CCE simulations:
- Fig. 3a/b seem to display a small asymmetry with respect to fixed τ2, variable τ1 compared to fixed τ1, variable τ2.The same appears in Fig. 6a for OX063. The authors should comment whether this is an artefact arising from the data analysis or reflects a true asymmetry.
- Figure 5a/b: The location of the maxima along τ1/τ2 (red lines) display many irregularities in particular for small interpulse delays. The authors should comment on their origin. Potentially, these stem from 2H ESEEM, if this is the case, the authors should specify in the Methods section how these modulations are treated during the normalization.
- Line 260: The presented CCE simulations are performed in a water-glycerol mixture, though previous published CCE results were obtained in pure water (Canarie et al., 2020), reasoning that “since MD simulations in pure water are well calibrated, whereas water-glycerol mixtures are significantly less tested against experiment, particularly in the solid phase.” How did the authors ensure that the calibration of the water-glycerol glass is appropriate?
- Line 275: “Remarkably, [the simulated refocused-echo decay] matches the experimental result both in shape and time scale…”
The reader would benefit from adding the experimental data trace of CP n = 2 in Fig. 9c so that the time scale and shape as well as CCE convergence can be judged more easily (e.g. as done in Canarie et al., 2020). This display is likely to reveal a mismatch for short τ1/τ2 as evident from comparing the normalized slices (red lines) in Fig. 3a-b with the ones in Fig. 9 a-b. I also expect this from my own experimental results (DD-watergly2021: SI, Fig. Sa12 CP n = 2 for protonated nitroxide in protonated water-glycerol at 40 K – according to Fig. Sa5 comparable to decay behavior at 20-30 K used in the article under discussion). This contribution originates from the methyl protons of the nitroxide. - Line 281-282: “Including two-nucleus clusters in the simulation yields an echo decay that has the correct shape and an almost correct time scale. Adding three-nucleus clusters improves the time scale slightly…” Considering Fig. 9c 2-CCE is ~ 1 µs off from 3-CCE decayed at 4 µs. This deviation is relatively large and convergence appears to be reached for 3-CCE so that the authors should reconsider their somewhat misleading wording here.
Comment regarding the sample choice:
The article presents the refocused echo decay as a function of τ1 and τ2 for a nitroxide, a trityl radical and GdCl3 in protonated and deuterated water-glycerol glass as specified in the Introduction (Line 78-79). The authors should justify the additional sample choice/discussion of the Gd-C2-labeled MdfA protein solubilized in detergent (DDM) micelle without providing the full data with τ1 and τ2 variation. First, because this sample varies many experimental parameters at once, namely
- Gd-C2-complex instead of Gd(III) ion, altering the ZFS
- additional HF field arising from the protein’s protons (which appears to be the variable of interest and thus should be the only varied parameter)
- micelle environment instead of aqueous water-glycerol mixture
- two labeling sites which may be exposed to different local environments
Second, compared to frozen water-glycerol solvents the micelle environment is known to accelerate the electron spin dephasing strongly (e.g. see Dastvan et al., 2010). For both reasons, it is not clear to me how the reader benefits from this somewhat unconnected “application example”.
For a stronger discussion, the authors should consider to compare a single-labeled water-soluble protein with the chosen spin label in the same solvent environment e.g. at best in a deuterated water-glycerol mixture to be sensitive to the protein’s protons. Our own DD study in water-glycerol took exactly this approach for Gd-DOTA-M (DD-watergly2021: Fig. 7c-d and section 3.4.2), demonstrating the decoupling effect for proton-driven NSD arising from the protein’s backbone.
General comments:- Line 250: “range of 3-4 µs” (blue trace)? This should refer to the yellow and purple trace.
- Due to the eight-step phase cycle your experiments do not correspond to a CPMG but instead to a CP sequence.
Comments regarding citations:- Line 45/Eq 1: Zecevic et al., 1998 uses the stretched exponential model, but the cited equation cannot be found in this work.
- Line 50: In Jeschke and Polyhach, 2007 the approximation reads τ = τ2 if τ2 >> τ1 and in this limit the Hahn decay approximates the refocused echo decay well (as visible in Fig. 3c, Fig. 4c, Fig. 6c). If the statement in Line 72-75 “In the context of DEER, it is usually assumed that the refocused echo decays monotonically as a function of the overall pulse sequence length 2(τ1 + τ2), similar to the two-pulse echo.” refers to the above approximation, it should be rephrased.
- Line 132-133: Technically, Harbridge et al., 2003 determined the CPMG time constant, which corresponds to the decay of the n refocused echoes between n refocusing pulses. The work under discussion observes the decay of the refocused Hahn echo, more closely related to our dynamical decoupling (DD) study in OTP (Soetbeer et al., 2018) as well as our recent DD study in water-glycerol glass (DD-watergly2021). Both works systematically address the effect of DD for nuclear spin diffusion (NSD) for organic radicals (and gadolinium complexes) “dilute frozen solutions at cryogenic temperature” (Line 131-132) for both protonated and deuterated matrices, the authors should cite.
- Line 177-179: “It is apparent that NSD is suppressed here and DD is ineffective. The decay is dominated by other dephasing mechanisms such as instantaneous diffusion (ID) …” We demonstrated this effect for 20 compared to 100 µM protonated nitroxide in deuterated OTP (Soetbeer et al., 2018, Fig. 8d-f). The latter matches the used concentration choice in the present work, so that a citation would be appropriate.
References
DD-watergly2021 https://doi.org/10.26434/chemrxiv.13678447.v1
Canarie et al., 2020 https://doi.org/10.1021/acs.jpclett.0c00768
Soetbeer et al., 2018 https://doi.org/10.1039/C7CP07074H
Raitsimring et al., 2014 https://doi.org/10.1016/j.jmr.2014.09.012
Dastvan et al., 2010 https://doi.org/10.1021/jp1060039- AC1: 'Reply on CC1', Daniella Goldfarb, 28 Feb 2021
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RC1: 'Comment on mr-2021-10', Mike Bowman, 03 Feb 2021
The manuscript "The decay of the refocused Hahn echo in DEER experiments" is a significant advance toward understanding nuclear spin diffusion and its role in limiting most types of pulse EPR spectroscopic experiments. Nuclear spin diffusion and other mechanisms contributing to spectral diffusion and decay of signals limit sensitivity and the length of time for which a signal can be measured. Efforts to model it have been made since the 1960's, but required oversimplification of the model to such an extent that in many cases echo decay would be impossible or results were qualitative.
However, this paper uses computational power and modeling techniques that are now available to treat the spin system and spin-spin interactions without oversimplification and to construct realistic molecular models of the distribution of nuclei in the sample. The result is an impressive quantitative agreement with experimental measurements in threee different systems relevant to many DEER experiments. This provides some insights and guidance on how to optimize samples and measurements. However the model applied here also has some relevance to other pulse EPR measurements such as: ESEEM, ENDOR (both Mims and Davies), and HYSCORE, to name a few. This paper has relevance and impact for other forms of pulse EPR.
The experimental part of the paper and the choice of samples are a good compromise between freedom from other sources of echo decay and relevance to typical DEER mesurements. So results at the longest times and for the highest deuteration may be limited by appearance of instantaneous diffusion, local modes, molecular motion, and methyl group rotation. But within those boundaries, the calculations and experiments seem in good agreement.
Measurements were also made of a Gd-labelled protein. There are many grounds for criticizing the use of this particular sample. It certainly cannot be used to validate the modeling and calculations. However, it provides an important indication that the results, that are validated in better defined model systems, do have relevance to 'real' samples.
Although it is not really mentioned in the paper, one of the important aspects of the experimental measurements is that they are made at W-band. This almost completely supresses any ESEEM from protons and deuterons both because of its tiny amplitude at high magnetic field and because of the difficulty in exciting it with microwave pulses broader than the nuclear Zeeman period. Labs operating at lower microwave frequencies will be affected by ESEEM but the computations as described here also would include ESEEM. The point is that ESEEM becomes relevant at lower frequencies and may modify the results obtained here for W-band, but that point lies beyond the scope of this paper in establishing the modeling and calculations.
However, the paper does not disclose some very important and relevant experimental details needed for readers to evaluate the experimental results. What are the approximate pulse widths and turning angles of the microwave pulses in the measurements? Does the strength of the perpendicular part of the microwave magnetic field vary across or along the samples? Were any checks made for instantaneous diffusion at the longest times? What was measured--peak point of echo, integral of echo, window between half height points of echo,...?
Although it is possible to find many things that could have been added to this paper, they do not seem to reach the importance of two major results: 1) a framework for quantitatively modeling the effect of nuclear spin diffusion on pulse EPR measurements; 2) confirming the importance of pairs and triples of nuclei in nuclear spin diffusion-driven electron spin echo decay.
I did find a couple of typos that need correcting: line 279 - "couplings IS neglected"; and line 351 - "socalled".The chapter by Ian Brown should be supplemented by the chapter (W. B. Mims, in Electron Paramagnetic Resonance, ed. S. Geschwind, Plenum, New York, 1972, pp. 263-352.) and by the book on spin echoes by Salikhov, Semenov and Tsvetkov (or perhaps the chapter by Salikhov and Tsvetkov in Kevan and Schwartz, I think it covers nuclear spin diffusion).
- AC2: 'Reply on RC1', Daniella Goldfarb, 28 Feb 2021
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CC2: 'Comment on mr-2021-10: Code availability?', Nino Wili, 04 Feb 2021
Dear authors,
Once again, it is amazing to see that numerical simulations can be made efficient enough to treat realistic spin systems. I am glad you deposited the experimental and simulated traces on zenodo, but I was wondering where and how you will make the code and the MD coordinates available? This would help the community (or - more honestly - at least me) to apply the same simulations to other problems. For example, I would like to look at the electron coherence decay under continuous microwave irradiation.
I understand that your standards are very high, but this code would be valuable even if it is not fool-proof and documented as rigorously as "EasySpin".
Thank you and best wishes,
Nino Wili
- AC3: 'Reply on CC2', Daniella Goldfarb, 28 Feb 2021
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RC2: 'Comment on mr-2021-10', Thomas Prisner, 09 Feb 2021
The authors describe in this manuscript the optimization of pulse settings (the original Hahn echo time) of a 4-pulse DEER experiment. Experiments are shown for nitroxide, trityl and Gd paramagnetic centers at W-band frequencies for deuterated and protonated water solvent. They demonstrate that the time interval t1 optimally is optimally set as t2 for short times of t2 and somewhat shorter for long t2 values. These experimental findings could be quantitatively reproduced by computer simulation of the interaction between the radical with 2-5 nuclear spins - similar to an earlier publications where such calculations have been demonstrated for experiments at more common Q- and X-band frequencies. Overall this work demonstrates very impressively that quantitative simulation of the experimental data can be achieved with couled spin clusters (of at least 3).
I have some questions and remarks which might be helpful also for other readers in the final version of the paper:
1) The data are all recorded at W-band. This has of course the advantage that the classical ESEEM effects are reduced. On the other side the authors describe the decoherence of the EPR signal as a nuclear-spin-cluster electron spin decoherence arising from the interference of nuclear coherences arising from the different hyperfine coupling of two nuclear spins. This is an interesting model but would probably also imply a field dependence. It would be interesting to give a statement in this direction. Also, the term SzAzxIx is omitted in this calculations (different from the earlier publication for data at Q-band and X-band). It would be good to also explain this in more detail. The experiments are performed at the maximum of the EPR spectra. Tm for nitroxides at high field is known to be orientation dependent. Again the authors should comment on this aspect.
2) The authors demonstrate that for samples with 25% 50% 75% and 100% protonation this dephasing is efficient but claim that this is not the case for fully deuterated samples. In the cited work by Soetbeer et al. it is shown that dynamic decoupling is also effective for 100% deuterated samples. It would be nice to discuss this point more carefully. Also in the above mentioned work Tm was analysed by two different components with streched exponential with a 50/50 ratio. It would again be important to discuss this differences to the treatment here which is relying only on one mechanism.
3) The red maxima shown in the 2D datasets should also be presented in 4 6b and 7b for consistancy.
- AC4: 'Reply on RC2', Daniella Goldfarb, 28 Feb 2021
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RC3: 'Comment on mr-2021-10', Anonymous Referee #3, 10 Feb 2021
This is a very interesting study by the Goldfarb and Stoll labs demonstrating that the common assumption of short tau1 values leading to larger signals in DEER might not always be met. Tau2 will determine the distance range that can be retrieved from the DEER data and tau1 is commonly chosen short to minimize time for echo dephasing. The authors very clearly demonstrate that extending tau1 for a given tau2 can lead to increased sensitivity. This appears to be most relevant for samples with limited possibilities for deuterium exchange. Nevertheless, this is an important finding to report especially as optimizing tau1 for a given tau2 will likely be a very quick experiment in contrast to DEER averaging times that will often average for may hours if sensitivity is limiting. The authors further make an excellent effort to rationalize their findings in in terms of numeric simulations and conceptualization.
From the practitioner’s point of view this has sparked a number of questions that might be worth commenting on in the final version of the manuscript. I am aware that some of the simulations or experiments that would be required to exhaust these questions will be beyond the scope of this work but I believe at least commenting on them will be of interest to the reader.
- All experiments and simulations are performed at W-band. Considering that most reported DEER experiments have been measured at X- and Q-band how do these effects translate at lower fields. I suppose the non-zero transition amplitudes of the formally forbidden transitions will increase while the nuclear Larmor frequency will decrease. Is the overall effect field-independent? This should be straightforward to simulate. The title of the manuscript suggests a general treatment.
- Would softer pulses be expected to lead to decreased dephasing. This has been shown in the context of instantaneous diffusion (Jeschke and Polyhach, 2007) but in terms of forbidden transitions this might be relevant here as well.
- When deuterating the solution of 3-maleimido-proxyl the data are interpreted as nuclear spin diffusion being suppressed and dipolar decoupling becoming ineffective as other dephasing mechanisms become dominating. Has this been explored using lower concentration or softer pulses? At sufficiently low concentration would dynamic decoupling become effective again in deuterated samples. Could deuterium nuclei be simulated using the same approach but potentially fewer nuclei?
- Different scenarios of residual proton content will likely lead to different outcomes. 25% of protons already have a significant effect but there are no experimental points up to full deuteration. Is it feasible to thin out the protons in the simulation until the dephasing effect will vanish when proton clusters with sizeable nuclear couplings become improbable
- For non-homogeneous distributions of protons that will be most relevant practically (El Mkami et al., 2014) it will be very interesting to see the influence of the proximity of protons. The full effect was recovered with protons in 1.2 nm. This suggests the dephasing of a spin label well solvated in deuterated solution away from the protein will be substantially slower than when buried in the fold of a protonated protein or membrane. Will the simulation approach be applicable to inhomogeneous distributions of protons?
- The MdfA double mutant V44C/V307C doubly labelled with Gd-C2 is measured in detergent micelles. Without further knowledge of structure and labelling positions the effect of non-exchangeable protons is hard to predict. An earlier report by Dastvan et al. (https://doi.org/10.1021/jp1060039) suggests the increased proton density in lipids in comparison to aqueous solution leads to increased dephasing. This might also be relevant for detergent. In this light, this might not be the most relevant protein system to demonstrate these results from homogeneous solutions of free spin labels.
- Without having done the simulations, is my extrapolation that a larger number of proton clusters and larger couplings between protons expected for media with increased proton density will lead to faster dephasing consistent with the findings here?
Further points
The introduction of the 3 and 4 pulse DEER sequences seems to suggest they were initially reported in 1984 and 2000, respectively. I suggest changing the wording or adding the original references.
(Jeschke and Polyhach, 2007) set the S/N ~ exp(-2tmax/T2) and this still holds in the approximation that even with an optimized tau1 the refocused echo will decay exponentially with tau2.
The discussion of dephasing by electron-electron dipolar interaction is confusing. An increased concentration will lead to larger signal and faster dephasing. As shown in (Jeschke and Polyhach, 2007) there will be an optimal concentration depending on the required trace length. If dilution lead to longer averaging times dilution it was overdone.
In line 74 it is said short tau1 values minimize phase relaxation” but considering instantaneous diffusion I suggest “minimize dephasing”.
- AC5: 'Reply on RC3', Daniella Goldfarb, 28 Feb 2021
Peer review completion

