Nanomolar Pulse Dipolar EPR Spectroscopy in Proteins; the CuII- CuII and Nitroxide-Nitroxide Cases

The study of ever more complex biomolecular assemblies implicated in human health and disease is facilitated by a suite of complementary biophysical methods. Pulse Dipolar electron paramagnetic resonance Spectroscopy (PDS) is a powerful tool that provides highly precise geometric constraints in frozen solution, however the drive towards PDS at physiologically relevant sub-μM concentrations is limited by the currently achievable concentration sensitivity. Recently, PDS using a combination of nitroxide and CuII based spin labels allowed measuring 500 nM concentration of a model protein. Using commercial instrumentation and spin labels we demonstrate CuII-CuII and nitroxide-nitroxide PDS measurements at protein concentrations below previous examples reaching 500 and 100 nM, respectively. These results demonstrate the general feasibility of sub-μM PDS measurements at short to intermediate distances (~1.5 - 3.5 nm), and are of particular relevance for applications where the achievable concentration is limiting.


Temperature-dependent relaxation behavior
Relaxation measurements performed at different temperatures from 10 K to 50 K informed about the temperature with optimum sensitivity for the NO-NO PELDOR and the Cu II -Cu II RIDME experiments, respectively. Figure S1: Sensitivity profiles for nitroxide-nitroxide PELDOR (left, mono-exponential approximation of T1) and Cu II -Cu II RIDME (right, mono-and bi-exponential approximation of T1 in red and blue, respectively). Profiles were calculated using equations given in Wort et al., 1 and measurement temperatures of 50 K and 30 K (for the mono-exponential approximation of T1) show > 90% of maximal sensitivity under experiment conditions. SNR = signal-to-noise ratio.
The longitudinal relaxation times (T1) estimated under the mono-and bi-exponential approximations, 1/e times, and 1/2e 2 times for Cu II -chelate and R1 nitroxide are given in tables S1-2, respectively. Note that at all temperatures, the 1/2e 2 times are within 20% of the 1/e times, indicating that the relaxation behavior is well met by the mono-exponential approximation. The phase memory times (Tm) estimated under the stretched exponential approximation for Cu II -chelate and R1 nitroxide are given in tables S3-4, respectively.

Temperature Monoexponential T1
Bi-exponential T1      Figure S2: Comparison of RIDME data obtained at different concentrations and processing conditions. Top: 500 nM, measurement with 34 ms mixing time, all other rows: 500 mM protein, mixing times in ms are indicated (35 or 65 ms, or deconvoluted, corresponding to the ratios 35/5 or 65/5, respectively). Left: raw RIDME traces (black) with background function (grey), the vertical line indicates where traces were cut; middle: background-corrected data (black) with fit (grey); right: corresponding distance distributions given as 95% confidence intervals (± 2) with 50% noise added for error estimation during statistical analysis. Color bars represent reliability ranges (green: shape reliable; yellow: mean and width reliable; orange: mean reliable: red: no quantification possible).

S5
Additional RIDME measurements were performed at high protein concentration to assess the unexpected ~3 nm peak observed in the 500 nM sample of the tetra-histidine construct. This peak is not present at the higher concentration sample measured using different mixing times for deconvolution and recorded with approximately two-fold longer evolution time at high SNR. This results in a more accurate estimation of the background function and allows the data to be cut, which subsequently improves fitting. This is not feasible at the lower concentration; however, we can demonstrate that the peak at the expected distance of ~2.4 nm is stable while the additional peaks are fully uncertain after statistical analysis (i.e., are dependent on the choice of background start time, zero-time artefact, etc.). The figure below shows the 500 nM sample of the tetra-histidine construct with different choices of background start time, demonstrating the effect on the additional peaks while the 'true' distance peak is unaffected.   Figure S3: Comparison of RIDME data obtained at 500 nM protein concentration. The same experimental data as shown in Figure S2 top row was processed with either a background start time of 30 ns (top) or 50 ns (bottom). Left: raw RIDME traces (black) with background function (grey); middle: background-corrected data (black) with fit (grey); right: corresponding distance distributions. At the earliest background start time the ~3 nm peak is mostly suppressed, while already at 50 ns start time it is clearly visible as a distinct peak.  Left: raw PELDOR trace (black) with background function (grey); middle: background-corrected data (black) with fit (grey); right: corresponding distance distributions given as 95% confidence intervals (± 2) with 50% noise added for error estimation during statistical analysis. Color bars represent reliability ranges (green: shape reliable; yellow: mean and width reliable; orange: mean reliable: red: no quantification possible). Regularization parameters varied depending on concentration: 100 for 100 nM, 1 for 500 nM, and 0.1 for 25 mM protein.

Additional
At 25 mM protein concentration of the I6R1/K28R1 construct the trace can be recorded over a longer evolution time, thus improving reliability for longer distances in the corresponding distribution. These data indicate that the bimodal shape of the distribution peak at 2.5 nm is indeed true. This suggests that down to concentrations as low as 500 nM one can reliably retain the true distance information. At even lower concentration (100 nM) the mean distance can still be retrieved; however, the resolution of the bimodality is lost due to i) low SNR and ii) necessity of a larger regularization parameter.
To confirm this observation, data for the 500 nM were processed with a regularization parameter of 10 and 100, and vice versa, the 100 nM data were processed with smaller regularization parameters, as shown below.   Figure S6: Comparison of PELDOR data obtained at 100 nM concentration using smaller regularization parameters a. Top: a = 10; bottom: a = 1. Left: background-corrected data (black) with fit (grey); right: corresponding distance distributions given as 95% confidence intervals (± 2) with 50% noise added for error estimation during statistical analysis. Color bars represent reliability ranges (green: shape reliable; yellow: mean and width reliable; orange: mean reliable: red: no quantification possible). With the smaller a some probability for bimodality is observed, however the SNR is too poor to be certain.
Deep neural network processing was performed using DEERNet 2 within the Spinach 3 spin dynamics software (version 2.5.5459, Nov 2020). Input data were the same as used for the DeerAnalysis processing, but the time axis was supplied from 0 to tmax as required (i.e., the negative points of the time trace were removed). DEERNet results of PELDOR data confirm DeerAnalysis results in that the second conformation is clearly distinguishable at 500 nM GB1 concentration, while at 100 nM the 95% confidence band would allow rejecting a second conformation (i.e., it is possible to draw a line without a second conformation present without leaving the confidence band). DEERNet results for the RIDME data show that the additional distance ~3 nm observed after DeerAnalysis processing is fully uncertain (and thus, potentially not real), confirming the RIDME data obtained for the 500 mM sample. Figure S8: DEERNet results for 500 nM GB1 I6H/N8H/K28H/Q32H (1.6 mM Cu II -NTA) RIDME data.

S9
Wavelet denoising was performed using WavPDS (db6 wavelet). 4 Input data were the same as used for the DeerAnalysis processing, but the RIDME data were provided background-corrected (.fit file) to avoid background issues. After denoising, data were subjected to Tikhonov regularization within DeerAnalysis without further background correction.
As observed for the original PELDOR data, in our hands the bimodal distribution was not recovered at 100 nM protein concentration after denoising. As observed with the original RIDME data, in our hands an artefact peak at ~3 nm is preserved after denoising.  Figure S10: WavPDS results for 500 nM GB1 I6H/N8H/K28H/Q32H (1.6 mM Cu II -NTA) RIDME data.

Instantaneous diffusion
The effect of instantaneous diffusion (ID;) on signal decay was determined as described previously varying the flip-angle of the second pulse of Hahn echo from  to /5. 5 All measurements were recorded at the magnetic field where the signal maximum was found in the field swept EPR spectrum. No ID was observable at 500 nM protein concentration, so experiments were repeated at 25 mM protein concentration, however there was still no observable ID. This suggests that the effect of two spin labels in the same molecule is negligible in terms of dipolar dephasing in the system under study.

Sensitivity considerations
Our aim is to better understand why different experiments require different concentrations to achieve similar sensitivities. The relative performance of Cu II -Cu II PELDOR, Cu II -Cu II RIDME, and Cu II -nitroxide RIDME has been quantified previously. 1 Here, we investigate how nitroxide-nitroxide PELDOR ranks in comparison. All sensitivity calculations were performed as outlined in previous reports. 1,5 "Dummy" PELDOR and RIDME experiments Dummy PELDOR and RIDME traces were recorded for the I6R1/K28R1 construct at 500 nM and 25 mM protein concentration. The total number of echoes per point for each trace was kept constant (four shots per point in a 2-step phase cycle for PELDOR and one shot per point in an 8-step phase cycle for RIDME) and calculated noise levels (RMSD, root mean square deviation, estimated from the second and third quartile of the imaginary part of the phase-corrected trace) for each trace are compared. At 500 nM protein concentration, results show the lowest noise for HQ (high Q, critically coupled resonator) RIDME while noise is approximately a factor 2.6 higher for LQ (low Q, over-coupled resonator) RIDME and a factor ~3.9 higher for PELDOR.
Results suggest critical coupling gains a factor of ~2.6 in the single frequency experiment whereas offresonance detection only loses a factor of ~1.5 (4-pulse DEER versus 5-pulse RIDME sequences overcoupled). This does not consider effects of modulation depth and signal averaging (shot repetition time) on sensitivities.
At 25 mM protein concentration, this is less clear-cut. Very low RMSD values ranging from 0.14 % to 0.38 % in a single scan lead to baseline imperfections contributing to the RMSD, which therefore does not reflect pure thermal noise anymore. The above factors change to 1.4 and 1.9, respectively, reproducing the same qualitative trend.

S13
Below, results are shown for comparison of nitroxide-nitroxide PELDOR at 100 nM and 500 nM protein concentration (GB1 I6R1/K28R1 construct) and Cu II -Cu II RIDME at 500 nM protein concentration (GB1 I6H/N8H/K28H/Q32H construct).  Regarding the PELDOR measurements, one would expect the relative St of the 100 nM nitroxide-nitroxide PELDOR to be approximately 20, i.e., a factor 5 lower than at 500 nM. However, observed St at low concentration is another factor ~3 worse, which can be attributed to difficulties in optimization (pulses, phase, field position etc.) due to the very low signal; a slight shift in field position away from the maximum of the field swept spectrum would also explain the reduced modulation depth. This can therefore be considered a 'penalty' on achievable sensitivity at very low concentrations.

Experiment
Regarding the Cu II -Cu II RIDME, the affinity of the Cu II -NTA for the double-histidine site is currently limiting sensitivity, as indicated by a modulation depth of ~5% instead of ~25%. One solution would be either to covalently bind copper ions or to replace one double-histidine site with a nitroxide for Cu II -nitroxide RIDME. In the latter case, a saturation of the double-histidine site is possible with similar sensitivity St compared to Cu II -Cu II RIDME. Thus, calculating with a modulation depth of 25%, the relative St would go up by a factor 5 from 10 to 50 at 500 nM, and thus would be ~10 at 100 nM compared to 7 for the corresponding nitroxide-nitroxide PELDOR. We therefore postulate that Cu II -nitroxide RIDME measurements should be possible at protein concentrations of 100 nM (or less).

Simulated modulation depth profile for the tetra-histidine construct
The observed modulation depth of ~5.5% for the Cu II -Cu II RIDME measurement is consistent with prediction, based on the simulated sensitivity profile shown below. 6 The maximum of the profile is 0.22, which for a maximum theoretical modulation depth of 25.7% yields an expected modulation depth of 5.7%. Since the labelling efficiency is limited by the presence of the β-sheet double-histidine motif, simulation of a sensitivity profile for a tetra-histidine construct containing two α-helical double-histidine motifs was performed. The predicted maximum of the profile is ~0.50, which for a maximum theoretical modulation depth of 25.7% yields an expected modulation depth of >12%.

Literature search
Nitroxide-nitroxide PELDOR PubMed was searched on 30 November 2020 for the search terms "PELDOR" or "DEER" and "EPR". The time range was 2017 to 2020. The search resulted in 124 publications, including 9 reviews, which were not further investigated. 61 out of the remaining 115 publications showing nitroxide-nitroxide PELDOR data on biomolecules (protein, DNA, or RNA) were used for statistical analysis. 5, All these 61 publications provided details regarding biomolecule and spin concentration, and we had excluded any spin concentrations above 400 micromolar to not artificially inflate the average. We found an average (mean) spin concentration of 116 mM, a minimum of 5 mM in one case, and as stated above the maximum was set by us to 400 mM. The standard deviation was 90 mM, showing the large spread across values, with the median being at 100 mM spin concentration.
Metal-metal RIDME On 22 January 2021, the Milikisyants paper 67 introducing the 5-pulse RIDME sequence had 91 citations. Out of these citations, 13 papers described metal-metal RIDME data and provided details regarding biomolecule or chemical compound and spin concentration and were used for statistical analysis. 1,[68][69][70][71][72][73][74][75][76][77][78][79] We found an average (mean) spin concentration of 253 mM, a minimum of 25 mM in one case, and a maximum of 1000 mM. The standard deviation was 259 mM, showing the large spread across values, with the median being at 100 mM spin concentration.