A Low ‐ Spin Co II /Nitroxide Complex for Distance Measurements at Q ‐ Band Frequencies

: Pulse dipolar electron paramagnetic resonance spectroscopy (PDS) is continuously fur ‐ thering the understanding of chemical and biological assemblies through distance measurements in the nanometer range. New paramagnets and pulse sequences can provide structural insights not accessible through other techniques. In the pursuit of alternative spin centers for PDS, we synthe ‐ sized a low ‐ spin Co II complex bearing a nitroxide (NO) moiety, where both the Co II and NO have an electron spin S of 1/2. We measured Co II ‐ NO distances with the well ‐ established double electron– electron resonance (DEER aka PELDOR) experiment, as well as with the five ‐ and six ‐ pulse relaxa ‐ tion ‐ induced dipolar modulation enhancement (RIDME) spectroscopies at Q ‐ band frequencies (34 GHz). We first identified challenges related to the stability of the complex in solution via DEER and X ‐ ray crystallography and showed that even in cases where complex disproportionation is unavoid ‐ able, Co II ‐ NO PDS measurements are feasible and give good signal ‐ to ‐ noise (SNR) ratios. Specifi ‐ cally, DEER and five ‐ pulse RIDME exhibited an SNR of ~100, and while the six ‐ pulse RIDME ex ‐ hibited compromised SNR, it helped us minimize unwanted signals from the RIDME traces. Last, we demonstrated RIDME at a 10 μ M sample concentration. Our results demonstrate paramagnetic Co II to be a feasible spin center in medium magnetic fields with opportunities for PDS studies in ‐ volving Co II ions.


Introduction
Pulse dipolar electron paramagnetic resonance (EPR) spectroscopy (PDS) allows measuring the distance between two or more electron spins in the nanometer range by exploiting their magnetic dipole moment [1][2][3]. Typically, PDS measures the dipolar coupling, , between two spins, which has an inverse cube root dependence on their distance ( ), according to equation [4]: where is the permeability of the vacuum, is the Bohr magneton, , are the factors of the two electron spins, ħ is the reduced Planck constant, and is the angle between the vector connecting the two spin centers and the external magnetic field. In this work, we focus on two PDS techniques, the double electron-electron resonance [2,[5][6][7] (DEER/PELDOR) and relaxation-induced dipolar modulation enhancement [8] (RIDME) experiments (pulse sequences in Figure 1), to measure the distance between two different spin centers: that of paramagnetic Co II and a nitroxide (NO) radical placed on a chemical model system. In DEER and RIDME, the dipolar coupling is measured with pulses applied at two or one microwave (mw) frequencies, respectively. In DEER, one set of spins is monitored on the observe frequency (νobs), while another set of spins is flipped on the pump frequency (νpump) (Figure 1a). If the distance to be measured involves two different types of spin centers, e.g., one paramagnetic metal ion (Cu II , Gd III , Mn II with electron spin S = 1/2, 7/2, 5/2, respectively) and one organic radical (nitroxide or trityl radical, S = 1/2) the pulses are placed to observe one type of spin, while flipping the other type of spin. In order to obtain high effective sensitivity, one typically pumps the NO or trityl spin that exhibits narrow EPR spectrum, while observing the paramagnetic metal ion (see a comparison of their EPR linewidths in Table S1, Supplementary Materials). In RIDME, one type of spin is observed in the frequency νobs, while the other type of spin is let to flip spontaneously by its longitudinal relaxation during the time interval Tmix [9] (Figure 1b,c). Therefore, RIDME performs well in systems involving a slow and a fast relaxing spin, such as a fast relaxing paramagnetic metal ion and a slower relaxing organic radical [10][11][12][13][14][15][16][17][18], but it has also been expanded to two paramagnetic metal centers [16,[19][20][21][22][23][24][25][26][27], as well as between organic radicals [28][29][30]. The increased sensitivity of RIDME in such mixed systems stems from the inherent increased modulation depth (Δ) of the experiment as a result of a large amount of spontaneously flipped spins, in contrast to the limited excitation bandwidth by mw pulses in DEER [31]. Additionally, during RIDME, one can exploit working under close to critically coupling conditions as only one frequency needs to be accommodated in the resonator profile, in contrast to DEER, where an over-coupled resonator is required in order to accommodate two frequencies. Another advantage of RIDME is that it is free of orientation selection (OS) effects with respect to the flipped spin, assuming a homogeneous longitudinal relaxation of the paramagnetic metal center along the EPR spectrum, simply because spins from the entire EPR spectrum are flipped during Tmix. It should be also noted that in contrast to high-spin Gd III [23,25,26] and Mn II [15,24] ions, where RIDME affords overtone frequencies due to the excitation of EPR transitions between multiple spin manifolds, this is not the case for 1/2 spin metal ions, such as of Co II studied here. Low-spin Co II , like Cu II , exhibits only one spin transition (−1/2→+1/2); therefore, the analysis and interpretation of data is straightforward and similar to DEER. The major limitation of RIDME is the steep background signal decay that is particularly relevant for protonated samples [11,32] and, to a lesser extent, some systematic signals (artifacts) [16,30] appearing in the RIDME traces. While the first are related to sample concentration and the matrix used, the latter are related primarily to experimental parameters. Recently, Abdullin et al. introduced the six-pulse RIDME sequence (Figure 1c), which was shown to significantly minimize these unwanted signals [30].
In the present work, we report on the use of DEER and RIDME with a pair of Co II /NO spins engineered into a chemical model system. Low-spin Co II is a less explored metal ion than Cu II , Gd III or Mn II , even though its favorable spectroscopic properties (S = 1/2 and not very fast relaxation [46]) make it suitable for PDS. Surprisingly, even though there have been developed ligands that bind to Cu II [47][48][49], Gd III [37] or Mn II [50,51] ions serving as spin labels, no such ligand has been developed for Co II for PDS. One challenge of Co II is its broad EPR spectrum of ~75 mT at the X-band, though it is comparable to that of Cu II (see Table S1, Supplementary Materials), whereas the synthesis of ligands that afford lowspin Co II is probably the most challenging part. Additionally, Co II with terpyridine ligands is known to behave as a spin crossover system above temperatures of 30 K [52,53]. So far, PDS studies on Co II are sparse and involve methodological developments. The first report on Co II demonstrated, for the first time, the use of broadband (wideband uniform rate smooth truncation, WURST) pulses to improve the signal-to-noise ratio (SNR) of Co II -NO DEER at the X-band by increasing the number of pumped Co II spins [54]. In another report, three spin effects were deliberately manifested in a NO-spacer-Co II -spacer-NO chemical model using WURST pulses that excited the entire NO EPR spectrum at X-band DEER measurements [46]. Additionally, OS effects in a Co II /NO system were studied with W-band DEER and RIDME, where the g-anisotropy of NO was resolved and only the low g component of Co II could be observed due to bandwidth limitations [10]. On the other hand, Co II has been taken up by paramagnetic nuclear magnetic resonance (NMR) studies involving high-spin Co II (S = 3/2) bound to a protein via a thio-reactive EDTA ligand [55,56], via the doubleHis motif [57], via a ligand that binds with click chemistry to RNA [58] or by replacing their diamagnetic counterparts in metal-dependent proteins [59,60].
Here, we expand the methodology to Co II -NO PDS at Q-band frequencies on a wellcharacterized Co II /NO chemical model. Specifically, we employ and discuss the performance of the standard five-pulse RIDME, as well as its six-pulse variant, and of DEER. We show that five-pulse RIDME and DEER have comparable SNR, whereas the SNR of six-pulse RIDME is somewhat compromised. We further show that the artifacts of the five-pulse RIDME are minimized in the six-pulse experiment also for the Co II /NO pair. Last, we show Co II -NO RIDME measurements to be feasible on a 10 μM sample.

Synthesis of the Chemical Model
The aim was to synthesize a chemical model system that bears a low-spin Co II and a NO with the distance between NO and Co II in the accessible distance range for PDS, minimizing through bond communication between the two spins, i.e., the spacer between the NO and Co II should not feature extended conjugation. Low-spin Co II is afforded by an octahedral geometry around the metal center with strong-field ligands, such as terpyridine. Thus, we coordinated the metal with two terpyridine-based ligands, one of which is functionalized with an NO at its end. To do so, we first synthesized a precursor, (terpyridine)Co II Cl2, from terpyridine and dichlorobis(triphenylphosphine)Co II (1a, see reaction in Scheme 1 and Figure S1, Supplementary Materials), in which Co II has a mononuclear pseudo-square pyramidal geometry found previously from X-ray structure determination [61]. Then, 1a was reacted with a previously characterized NO-labeled terpyridine ligand L [62] to form the target complex 1, which was isolated as a solid after precipitation with PF6 − counter ions and characterized by mass spectrometry and elemental analysis (see Section 4 and Figure S2, Supplementary Materials). The ester bond in L is expected to disrupt the conjugation between NO and Co II spins, as it was shown previously that the introduction of an ester bond afforded negligible conjugation between NO and Cu II spins [63]. Additionally, in L2Co II complex, DEER [46] and RIDME [10] did not show through-bond communication between the spins. Scheme 1. Synthetic procedure of precursor 1a and of target complex 1.

PDS on 1
Initial attempts to perform PDS distance measurements on 1 in various organic solvents or their mixtures failed due to poor solubility of the complex in organic media as well as 'bad glass' formation upon sample freezing and, subsequently, fast relaxation properties of the paramagnetic species [64]. Generally, we found that dissolving the complex in a small percentage of coordinating solvent and then adding the non-polar organic solvent improved solubility and helped the formation of 'good glass' upon sample freezing. The solvents that worked well here were DMF-d7/C7D8 (1/9) for RIDME and DMF/2-MeTHF (1/9) for DEER samples. Deuteration in RIDME is necessary, as protons can significantly affect the background decay of the experiment, complicating data analysis [32]. Additionally, we found that weakly coordinating anions further improve the relaxation properties of the Co II . Therefore, we proceeded to in situ exchanging the PF6 − ions with the more weakly coordinating anion BPh4 − [65] by adding excess of NaBPh4 salt before addition of the solvents (see Section 4).
We performed Co II -NO DEER at 15 K at Q-band frequencies in 1 mM solution of 1 ( Figure 2). Slowing down the Co II relaxation is crucial, as a fast transverse relaxation of Co II would disfavor DEER when observing Co II (see Figures S4-S6, Supplementary Materials for X-and Q-band relaxation data on 1). We initially performed the DEER by pumping NO and observing Co II with the setup shown in Figure 2a, where the blue and red lines indicate the observe and pump positions, respectively, and Δν is the pump-probe frequency offset of 150 MHz (5.3 mT). The experiment exhibited a steep background decay due to pumping NO spins, which are in high concentrations, affording a modulation depth, Δ, of ~26% and a Co II -NO distance of ~2.6 nm when using the DeerAnalysis [66] software. The distance is in agreement with the X-ray structure of L [62] and previous distance measurements on similar compounds [10,11,46], and Δ is close to the value on bis-nitroxide-labeled protein samples [67] under our spectrometer and experimental conditions, indicating that the majority of chemical species in the solution are complex 1. The sensitivity (often synonymous with the SNR) was calculated (see Section 4 and Supplementary Materials, Table S4) to be 103. Throughout the text we refer to the SNR as the modulation-to-noise ratio, whereas the sensitivity corrected for different numbers of accumulated echoes and repetition rates is referred to as St (sensitivity per unit time, given in the Supplementary Materials, Table S4). We additionally performed a DEER measurement by pumping Co II and observing NO spins using the same setup as in Figure 2a, with the pump-probe positions exchanged. In this case, the pump pulse excited only a small fraction of the broad Co II EPR spectrum, affording a less pronounced background decay and a Δ of ~0.6%. Using this setup, the SNR was 11, i.e., 10 times lower than when pumping NO, as expected. Nonetheless, the measurement afforded again a ~2.6 nm Co II -NO distance with high reliability. It should be mentioned that while Co II -NO DEER is feasible at the Q-band, the corresponding Cu II -NO measurements are challenging due to the large spectral separation of Cu II and NO spins of ~20 mT exceeding the bandwidth of most setups [46]. Here, we also tested directly whether the ligands exchange in solution by performing NO-NO DEER ( Figure S7, SI). If ligand exchange occurs, the species expected to form in solution are L2Co II , (terpyridine)2Co II and 1 (in 1:1:2 ratio) and we should recover a NO-NO DEER oscillation, originating from L2Co II complexes. The NO-NO DEER was performed by observing and pumping NO with Δν = 80 MHz (2.9 mT) at 20 K under conditions optimized for the NO, i.e., with a repetition time of 20 ms. NO-NO DEER is known to perform optimally at 40-60 K [68,69]; however, here, a lower measurement temperature was necessary due to the paramagnetic relaxation enhancement of the NO spins by Co II . Previously, we found that a temperature of 10-20 K is optimal for measuring NO-NO DEER in the presence of Co II [46], in agreement with the X-band NO relaxation data (Supplementary Materials, Figure S5). The NO-NO DEER trace featured again a steep background decay due to the high concentration of NO spins and a Δ of ~17%. The NO-NO distance was found to be 5.2 nm, which is double the Co II -NO distance originating from L2Co II complexes, suggesting that partial ligand mixing occurred before freezing the sample. Moreover, ligand mixing was also observed on a similar Co II complex that does not bear a NO group using X-ray structure determination (see details in Supplementary Materials). Both NO-NO DEER and the X-ray demonstrate the kinetic lability of terpyridine ligands with Co II ions that might affect the performance of PDS on 1.
We then proceeded to perform Co II -NO RIDME measurements on 1 mM solution of 1 at 15 K. The experiment was performed by observing at the maximum of the NO EPR spectrum (indicated with the green line on Figure 2a) to minimize OS effects and to obtain maximum sensitivity, whereas the Co II spin flip was achieved spontaneously during the Tmix. We performed both the five-pulse and the newly introduced six-pulse sequence. The most commonly used five-pulse RIDME is known to exhibit artifacts that alter the background and might affect the shape of the distance distribution [16,30]. These artifacts were found to appear at times t = τ1 and t = τ2 − τ1 [30], and the six-pulse RIDME was shown to significantly minimize them. On the downside, six-pulse RIDME can feature artifacts at t = τ2 − 2τ1, which, however, can be truncated during data analysis. As we worked at Qband and the sample was dissolved in a deuterated matrix, each RIDME experiment was recorded as a unique measurement with τ-averaging over one period of the inverse deuterium Larmor frequency proving sufficient to remove unwanted electron spin echo envelope modulation (ESEEM), without the need to perform a reference measurement. The estimation of the Tmix was performed by the inversion recovery profile of Co II spins, as well as from our previous data on a similar Co II complex [10]. The primary RIDME data were analyzed by fitting a fifth-order polynomial background function due to the pronounced background decay of RIDME. Δ was found to be ~36% and ~32% and the SNR to be 114 and 73 for the five-and six-pulse sequences, respectively. The modulation depth was less than the 45% expected for quantitative metal-NO pairs [11,16,44], indicating again partial ligand mixing in agreement with the Co II -NO and NO-NO DEER data. The SNR of the five-pulse RIDME was similar to that of the DEER pumping NO (see Table S4, Supplementary Materials), whereas the six-pulse RIDME measurement exhibited lower SNR. The five-pulse sequence exhibited an artifact at 1.4-1.6 μs, which we assign to the τ2 − τ1 artifact observed by Abdullin et al. [30]. This artifact was significantly smaller in the six-pulse RIDME measurement. The Co II -NO distance distribution was again found to be centered at ~2.6 nm, in agreement with the DEER experiments and similar metal complexes [10,15,39,46].
Lastly, we proceeded to test the performance of Co II -NO RIDME on a sample two orders of magnitude lower in concentration, i.e., on a 10 μM sample of 1 (Figure 3). Again, the five-and six-pulse RIDME sequences were performed on the maximum of the NO spectrum (green line on Figure 2a). As the sample concentration was significantly lower, we found the longitudinal relaxation (T1) and other T1-related relaxation effects to be significantly slower, and we performed RIDME at 30 K, as we also did not see significant modulation at 15 K. In this sample, the RIDME experiment exhibited a reduced Δ of ~18% and ~13%, with SNR values of 29 and 1 for the five-and six-pulse sequences, respectively. The lower Δ of the 10 μM sample might be due to the coordination of DMF-d7 on the Co II ion upon sample dilution or due to a suboptimal Tmix. The SNR of five-pulse RIDME on the 10 μM sample was approximately four times lower than the 1 mM sample. Partially, the lower SNR can be attributed to the lower Δ of the 10 μM sample. The rest of the loss in SNR comes from the lower sample concentration itself. Again, the five-pulse RIDME exhibited an artifact at short times (300 ns), as well as at ~1.1-1.5 μs, which we tentatively assign to those observed by Abdullin et al. [30], as both were reduced in the six-pulse experiment. Overall, we could measure Co II -NO RIDME on a 10 μM sample of 1, the SNR of which was compromised by the sample properties, nonetheless not affecting the reliable determination of the distance distribution, which is in agreement with the PDS data on the higher concentration sample.

Conclusions
In this work, we reported the synthesis of a new Co II /nitroxide complex for DEER and RIDME measurements at Q-band frequencies. The tailor-made complex geometry afforded a low-spin Co II with favorable spectroscopic properties for DEER and RIDME. Particularly, Co II -NO RIDME was employed on a 10 μM sample and the application of the six-pulse sequence helped us eliminate unwanted signals from the time traces. The overall SNR of five-pulse RIDME and DEER measurements were similar; however, Co II -NO RIDME did not reach the potential of the Cu II -NO pair, where applications down to 500 nM have been reported [22,44]. One limitation of the SNR comes from the sample properties. We have shown using X-ray crystallography on a similar Co II complex, as well as with NO-NO DEER on 1, that a fraction of the complex disproportionates in coordinating solvents. The issue of complex disproportionation becomes resolved in a scenario where water-soluble ligands would be designed that bind Co II tighter than terpyridine. This would, in turn, allow improved RIDME performance. As reports on Co II ions in PDS are sparse, measurements at Q-band frequencies, becoming widely adopted by most EPR laboratories, allow further establishing Co II for PDS. We further revealed some of the challenges that have to be met before this metal ion becomes a promising candidate for applications in biomolecular samples.

General Synthesis Conditions
All commercially available reagents were used as purchased: dichlorobis(triphenylphosphine)Co II (Sigma Aldrich, St. Louis, MO, USA), terpyridine (Alfa Aesar, Haverhill, MA, USA) and NH4PF6 (Acros Organics, Geel, Belgium), while the synthesis of ligand L has been reported previously [62]. Solvents were of laboratory-grade purity, reactions were performed in open air and rt refers to room temperature (20-25 °C). Infrared (IR) spectra were acquired on a Shimadzu Fourier transform IR Affinity-1 Infrared spectrometer. Nuclear magnetic resonance (NMR) spectra were acquired on a 500 MHz Bruker Ascend spectrometer in the deuterated solvent stated. Chemical shifts are quoted in parts per million (ppm) and referenced to the residual solvent peak(s). Mass spectrometric data were acquired via atmospheric pressure chemical ionization (APCI) and matrix-assisted laser desorption/ionization (MALDI) at the EPSRC National Facility for Mass Spectrometry, Swansea. Elemental analysis was performed in London Metropolitan University, where the solid samples were weighed using a Mettler Toledo high-precision scale and analyzed using ThermoFlash 2000.

X-ray Crystallography
X-ray diffraction data for compound 2ʹ (see structure in Supplementary Materials) were collected at 173 K using a Rigaku MM-007HF High Brilliance RA generator/confocal optics with XtaLAB P100 diffractometer (Cu Kα radiation (λ = 1.54187 Å)). Intensity data were collected using both ω and φ steps, accumulating area detector images spanning at least a hemisphere of a reciprocal space. Data were collected and processed (including correction for Lorentz, polarization and absorption) using CrystalClear [72]. The structure was solved using charge-flipping methods (Superflip [73]) and refined using full-matrix least-squares against F 2 (SHELXL-201/3 [74]). Non-hydrogen atoms were refined anisotropically, and hydrogen atoms were refined using a riding model. The thin, platy crystals diffracted weakly at higher angles, even with long exposures. This weaker high-resolution data lead to elevated values of Rint, poor observed-to-unique data ratios and minor discrepancies in some bond lengths. The structure could nevertheless be unambiguously determined. All calculations were performed using the CrystalStructure

EPR Sample Preparation
10 equivalents of NaBPh4 were added to solid 1, the solids were taken up in DMF (or DMF-d7) and mixed thoroughly via pipetting until everything was dissolved, forming a transparent brown solution. Then, C7D8 or 2-MeTHF was added, the mixture was again mixed thoroughly, transferred to the EPR tube (3 mm outer diameter, OD) and frozen in liquid nitrogen. The final sample volume was 75 μL. The 10 μM sample was prepared by thawing the 1 mM sample and diluting it with a pre-mixed solution of DMF-d7/C7D8 (1/9).

EPR Spectroscopy
All EPR data were recorded on a Bruker ELEXSYS E580 pulsed X-band (9.7 GHz) or Q-band (34.0 GHz) spectrometer including the second frequency option (E580-400U). Pulses were amplified by travelling wave tube (TWT) amplifiers (1 kW at X-band and 150 W at Q-band) from Applied Systems Engineering. An MD5 dielectric ring resonator (Xband) and a 3 mm cylindrical resonator ER 5106QT-2w in TE012 mode (Q-band) and standard flex line probe heads were used. The temperature was stabilized using a continuous flow via a variable temperature helium flow cryostat from Oxford Instruments (Xband) or a cryogen-free variable temperature cryostat from Cryogenic Ltd. (Q-band).

Echo-Detected EPR Spectrum
The echo-detected EPR (ED-EPR) spectrum was recorded at 15 K and optimized for the Co II spin using the ( /2 − − − -echo) sequence monitoring the echo intensity while sweeping the magnetic field. Here, /2, pulses were set to 12, 24 ns, to 400 μs and repetition rate to 407 μs.

Inversion Recovery Data
Inversion recovery (I.R.) data were collected using the ( − T − /2 − − − -echo) sequence monitoring the echo intensity as a function of the interval T. Co II and NO X-band I.R. data were recorded in the temperature range 5-50 K at 340.0 mT and 345.3 mT, respectively, using /2, pulses of 20, 40 ns, inversion pulse of 20 ns and of 200 μs; the time increment and repetition time varied with the temperature. Co II Q-band I.R. was recorded at 1160 mT at 30 K using /2, pulses of 12, 24 ns, respec-tively, 24 ns inversion pulse and of 800 μs, repetition time 1 ms and time increment 250 ns (see Figures S4-S6, Supplementary Materials).

Phase Memory Time Data
Phase memory time data were collected using a Hahn echo ( /2 − − − -echo) sequence monitoring the echo intensity as a function of the interval . Co II and NO X-band phase memory time data were recorded in the temperature range 5-50 K at 340.0 mT and 345.3 mT, respectively using /2, pulses of 16, 32 ns, a starting of 120 μs and time increment of 12 ns; the repetition time varied with the temperature. Co II phase memory time data exhibited strong Co II ESEEM due to interaction of the un-paired electron with the nuclear spin of Co II (I=7/2), whereas NO data exhibited 1 H ESEEM. NO and Co II Qband phase memory times were recorded at 1213 and 1196 mT at 15 K using /2, pulses of 12, 14 ns (NO), 16, 32 ns (Co II ), a starting of 380 μs and time increment of 20 ns and repetition time 5 ms (see Figures S4-S6, Supplementary Materials).

Data Analysis
The primary DEER and RIDME data were transformed into distance distributions using the DeerAnalysis2018 [66] software and Tikhonov regularization with the L-curve [76] criterion. The background contributions to the primary DEER data were removed by fitting a background homogeneous to three dimensions for the DEER and fifth order polynomial function for the RIDME data using the default background start value giving the Δ values reported herein. An exception is the 5-pulse RIDME of 1 mM sample, where the background start was set manually to 100 ns, as default background start was unrealistic. In general, the RIDME data on 1 mM sample could also be fitted by fitting the dimensionality of the background or with different order polynomial functions, but as the 10 μM data could only be fitted with fifth order polynomial function, we analyzed all RIDME data similarly. The regularization parameter was 10 for the RIDME and 1 and for the DEER data, respectively. The contributions of the background signal were evaluated within the validation tool of the DeerAnalysis2018 program. The validation was performed from 5% to 80% of the time traces for DEER and from 5% to 15% for RIDME, respectively, in 16 trials, and a white noise of level 1.5 in 10 trials was added. In the NO-NO DEER measurements, no noise was added during validation. For all validation procedures, only datasets within 15% of the best root-mean-square deviation were retained (i.e., default prune level 1.15), affording the confidence intervals (gray shadowed areas) of the plotted distance distributions. The color bars below the distance distributions denote the reliability of the distance as follows: green = shape reliable; yellow = mean and width reliable; orange = mean reliable; red = non-reliable. The data were also analyzed with two user-unbiased methods; first, DEERNet, which utilizes neuronal networks to predict the distance distribution [77] within Spinach [78] software in MATLAB R2020b. Second, with simultaneous comparative treatment employing neuronal network analysis and Tikhonov regularization (ComparativeDeerAnalyzer, CDA), which computes the distance distribution and its uncertainty using DeerAnalysis2021b in MATLAB R2020b. The DEERNet and CDA analysis results are given in Supplementary Materials, Figures S8-S20, respectively. CDA could not run for the 5-pulse RIDME measurement on the 10 μM sample. The modulation depth values as calculated automatically from DEERNet and CDA are reported in Table S4, Supplementary Materials. All data are available in reference [79].

Calculation of Sensitivity
The sensitivity was calculated similarly to what was described previously [44]. Briefly, it was first calculated as modulation-to-noise ratio, i.e., Δ/noise level, where Δ was calculated automatically in CDA and the noise level was estimated using the imaginary part of phase-corrected and normalized time domain data, again calculated in CDA or, where mentioned, with a self-written MATLAB script. Then, this value was divided by the square root (sqrt) of (number of scans × shots-per-point × τ-averaging × phase cycle) to give the modulation-to-noise ratio normalized for the number of echoes, Se. To account for different repetition rates, Se was multiplied with the sqrt of the inverse repetition rate to yield the sensitivity per unit time (St). The sensitivity values are mentioned throughout the texts and are summarized in Supplementary Materials, Table S4.

Informed Consent Statement: Not applicable.
Data Availability Statement: Digital data underpinning the results presented in this manuscript.