Pulse dipolar EPR for determining nanomolar binding affinities

Protein interaction studies often require very low concentrations and highly sensitive biophysical methods. Here, we demonstrate that pulse dipolar electron paramagnetic resonance spectroscopy allows measuring dissociation constants in the nanomolar range. This approach is appealing for concentration-limited biomolecular systems and medium-to-high-affinity binding studies, demonstrated here at 50 nanomolar protein concentration.


A. EPR Sample Preparation
A construct of the immunoglobulin-binding B1 domain of group G streptococcal protein G (GB1) with one double-histidine motif and one cysteine residue (I6C/K28H/Q32H) was used in this study. Expression, purification, and spin labelling with MTSL and Cu II -NTA for this construct has been described previously. 1 For PDS experiments, samples with a final volume of 65 L were prepared with varying protein and Cu II -NTA concentrations in deuterated phosphate buffer (42.4 mM Na2HPO4, 7.6 mM KH2PO4, 150 mM NaCl, pH 7.4) and 50% (v/v) deuterated ethylene glycol (Deutero) for cryoprotection as described. 1 Samples were transferred to 3 mm quartz EPR tubes and immediately immersed in liquid nitrogen.
In total, three pseudo-titration series were prepared of five discrete samples each, one at 100 nM and two at 50 nM final protein concentration, respectively. Cu II -NTA concentrations ranged from 0.1 to 8.1 M. In addition, a control sample was prepared at 25 M protein and 30 M Cu II -NTA concentration for dummy experiments (see below).

B. Pulse dipolar EPR Spectroscopy
Pulse Dipolar EPR Spectroscopy (PDS) was performed at 34 GHz (Q-band) frequency, operating on a Bruker ELEXSYS E580 spectrometer with second frequency option (E580-400U) and 3 mm cylindrical resonator (ER 5106QT2-2w in TE012 mode). A pulse travelling wave tube (TWT) amplifier (Applied Systems Engineering) with nominal output of 150 W was used for pulse amplification. Temperature was controlled using a cryogen-free variable temperature cryostat (Cryogenic Ltd) operating in the 3.5 K to 300 K temperature range. 5-pulse RIDME experiments 2 for the 50 and 100 nM pseudo-titration series were recorded with the pulse sequence (π/2 -τ1 -π -(τ1 + t) -π/2 -Tmix -π/2 -(τ2 -t) -π -τ2 -echo) at the field position corresponding to the maximum of the Cu II -NTA field-swept spectrum with 8-step phase cycling, a 1 of 400 ns, a 2 of 1500 ns, a shot repetition time (SRT) of 30 ms, and a critically coupled resonator (high Q). Measurements were recorded for ~60 hours on average at 30 K and with a short (reference) and a long mixing time (5 and 200 s, respectively) to allow deconvolution of the traces as described previously. 1 "Dummy" PELDOR and RIDME measurements (1 scan each) were recorded at 25 M protein concentration (construct GB1 I6R1/K28H/Q32H) for sensitivity estimates as described previously. 1 In these experiments, all delays are set to be constant, shifting the entire sequence by the dipolar increment. The corresponding trace is thus only varied by thermal noise on the acquired echo. Dummy RIDME experiments were recorded at 30 K, SRT 30 ms, and both, with a critically coupled and an over-coupled resonator to determine the effect of high versus low Q on sensitivity. Dummy PELDOR experiments were performed based on the 4-pulse DEER 3-5 pulse sequence (π/2(A) -τ1 -π(A) -(τ1 + t) -π(B) -(τ2 -t) -π(A) -τ2 -echo) at 50 K as described previously, 6 with a frequency offset (pump -detection frequency) of +80 MHz (~3 mT) and SRT 5 ms; 1 of 400 ns, 2 of 1300 ns, and pulse lengths of 16 and 32 ns for /2 and  detection, respectively.
C. PDS Data Processing and Analysis RIDME experiments were analyzed using DeerAnalysis2015 7 as previously described. 8 Briefly, data were subjected to Tikhonov regularization using a homogeneous 6-dimensional background function followed by statistical analysis (validation tool) varying background start from 5 to 30% of the trace length in 8 trials and varying the background dimension from 3 to 6 in 7 trials. Resulting best-fit background start time and dimension were subsequently used as starting points for a second round of Tikhonov regularization followed by a second round of S4 statistical analysis, this time also including the addition of 50% random noise in 16 trials; one of the two 50 nM series required a modification: only 10% random noise was added in the second validation round (Fig. S3). Second round validation trials were pruned with a prune level of 1.15, where trials exceeding the root mean square deviation of the best fit by at least 15% are discarded. In all cases the regularization parameter  was chosen according to the L-curve criterion 9 and the goodness-of-fit. Additionally, RIDME data were analysed with deep neural network processing employing DEERNet 10 (Spinach Rev 5662) with specified RIDME background 11,12 within DeerAnalysis2022 (downloaded 2 February 2022) and with the standalone ComparativeDeerAnalyzer (Spinach Rev 5501) without specific RIDME background for comparison.

D. Modelling
Predicted distance distribution was modelled based on the GB1 crystal structure PDB 4WH4. 13 An R1 moiety was introduced at residue 6 and Cu II -NTA at residues 28 and 32. All modelling was done using MMM 2021.2, 14,15 assuming ambient temperature (298 K). The corresponding cartoon representation and predicted distance distribution are shown in Figure 1 of the main text. S5

S8
DEERNet analysis with RIDME background within DeerAnalysis2022 afforded results for all samples from the 100 nM pseudo-titration series, however for the lowest Cu II -NTA concentration only the modulation depth was retrievable, not a distance distribution. For the two 50 nM pseudo-titration series, 6 out of 10 DEERNet analyses failed; we therefore refrain from using the remaining data sets here.  Fig. S4: DEERNet RIDME data obtained for 100 nM GB1 I6R1/K28H/Q32H pseudo-titration series. Left: stacked raw RIDME traces with background function (grey); middle: background-corrected data with fit (grey); right: corresponding distance distributions with error estimate. Colour bars represent reliability ranges (green: shape reliable; yellow: mean and width reliable; orange: mean reliable: red: no quantification possible). RIDME data analysed with the standalone ComparativeDeerAnalyzer (Spinach Rev 5501) yielded reports for all but the lowest Cu II -NTA concentration for the 100 nM pseudo-titration; for the two 50 nM series 6 out of 10 possible reports were obtained, and we therefore refrain from using the remaining data sets here. Full reports for the 100 nM series are available at the end of the ESI.

B. Modulation Depths and Sensitivities
RIDME modulation depths were obtained either during processing in DeerAnalysis from the second round of Tikhonov regularisation (i.e., using optimised background start time and background dimension, see section "PDS Data Processing and Analysis" for details), as well as from processing in DEERNet and CDA (100 nM only). Calculated noise levels (root mean square deviation, RMSD, as estimated from the second and third quartile of the imaginary part of the phase-corrected RIDME trace) are used for sensitivity calculations as described previously 8 and detailed below. Dummy PELDOR and RIDME traces were recorded for the GB1 I6R1/K28H/Q32H construct at 25 M protein concentration (Table S1)   Results suggest that critical coupling gains a factor of ~1.8 in the single frequency (RIDME) experiment, whereas off-resonance detection loses a factor of ~1.9 (PELDOR vs RIDME LQ), not considering actual sensitivities which are further depending on modulation depths and signal averaging (see below). Results reproduce the same qualitative trend as obtained previously for the GB1 I6R1/K28R1 construct. 8 S9 Sensitivities (S) were determined as the ratio of modulation depth (), obtained from Tikhonov regularisation, to noise (RMSD). S values were further divided by the square root of total echoes per point and multiplied with the square root of the averaging rate, yielding the sensitivity per unit time (St). 8 For the three independent titration series performed in this study, a summary of obtained modulation depths from different processing approaches (see section 1.C for details) and sensitivities S and St is given in Table S2 below. Differences in modulation depths obtained from the CDA versus DEERNet can be attributed to the different background models (see section 1C). The average St for the 100 nM series is expected to be two times larger than the average St over the two 50 nM series. This is confirmed by experimental values for St (0.51 vs. 0.22, respectively) within error, suggesting some additional 'penalty' for reducing concentration to the point where optimising the experiment becomes negatively affected by the low signal, as observed previously. 8 However, this penalty is lower for RIDME (this study) than for PELDOR, 8 likely owing to the more straightforward process of setting up RIDME experiments. The average sensitivity S (modulation-depth-to-noise ratio), a common parameter to assess PDS data quality, for the 100 nM pseudo-titration series was 16.0, while the average S for the two 50 nM series combined was 6.6. These findings are in line with recent recommendations that sensitivities substantially below 10 should not be used to analyse distance distributions. 16

S11
C. Binding Studies Binding affinities for the pseudo-titration series based on experimental RIDME modulation depths () were determined as described previously. 1 Estimates for spin-lattice relaxation times (T1) were determined previously for the Cu II -NTA concentrations used here, assuming a monoexponential relaxation behaviour (Table S4); in addition, data were fitted assuming a uniform T1 of 50 s for comparison of the relative stability of the determined dissociation constants (KD). The mixing time Tmix and T1 dependent modulation depth (Tmix) was calculated as described. 1 The ratio / Tmix is given as 'percentage loading' in the main text ( Figure 3). The 68% confidence interval (CI) bounds are taken as the binding isotherms simulated with the fitted KD value ± , except for the 50 nM (I) series assuming uniform T1, where this would result in a negative and thus, unphysical KD. Therefore, in this case a tighter binding was assumed, with the affinity upper bound simulated as 6.3 × 10 -11 and the affinity lower bound simulated as 1.38 × 10 -7 . Here,  is calculated as the standard deviation of the fitted Gaussian to the onedimensional error surfaces (shown in figure S8). Error contour plots for the 100 nM and one of the 50 nM pseudo-titration series illustrate the high reproducibility of the results albeit the larger error at lower concentration, demonstrating the validity of the approach to use PDS for low-concentration protein interaction studies:

5) CDA Reports
In the following the full CDA reports obtained for the 100 nM series are attached.