Dipolar pathways in multi-spin and multi-dimensional dipolar EPR spectroscopy

Dipolar electron paramagnetic resonance (EPR) experiments, such as double electron–electron resonance (DEER), measure distributions of nanometer-scale distances between unpaired electrons, which provide valuable information for structural characterization of proteins and other macromolecular systems. We present an extension to our previously published general model based on dipolar pathways valid for multi-dimensional dipolar EPR experiments with more than two spin-1/2 labels. We examine the 4-pulse DEER and TRIER experiments in terms of dipolar pathways and show experimental results confirming the theoretical predictions. This extension to the dipolar pathways model allows the analysis of previously challenging datasets and the extraction of multivariate distance distributions.

Files and data II.
Materials and methods III.
Results of the analysis: Parameter tables IV.
Results of the analysis: Full traces V. Two-spin model analyses

I. Files and data
This SI.zip package contains the following files and folders: • SI.pdf This file.
• data/* Folder containing all experimental datasets presented in the publication.
• HSC_simulations/* Folder containing the Harmonic Segmented Chain (HSC) simulation script, as well as the data corresponding to the simulations presented in the publication.
• MMMx_simulations/* Folder containing the MMMx simulation script, as well as the data corresponding to the simulations presented in the publication.
• multispin_dipolar_pathway_calculator.ipynb Jupyter notebook with the function for calculating all possible theoretical dipolar pathways for arbitrary pulse sequences and multi-spin systems.
• multispin_analysis_module.py Python module containing the collection of custom functions required to run the analysis scripts • analysis_multispin_DEER.ipynb/.py/.html Jupyter notebook containing the analysis of the DEER data including scripts, figures, and fits with confidence intervals. A Python script copy is provided for executing the contents of the Jupyter notebook if Jupyter is not installed. An HTML copy is provided for reading the contents of the Jupyter notebook if Python and Jupyter are not installed.
• analysis_multispin_TRIER.ipynb/.py/.html Jupyter notebook containing the analysis of the TRIER data including scripts, figures, and fits with confidence intervals. A Python script copy is provided for executing the contents of the Jupyter notebook if Jupyter is not installed. An HTML copy is provided for reading the contents of the Jupyter notebook if Python and Jupyter are not installed.
• analysis_twospin_DEER.ipynb/.py/.html Jupyter notebook containing the local and global analysis of the 4-pulse DEER data using two-spin models with non-parametric distance distributions. including scripts, figures, and fits with confidence intervals. A Python script copy is provided for executing the contents of the Jupyter notebook if Jupyter is not installed. An HTML copy is provided for reading the contents of the Jupyter notebook if Python and Jupyter are not installed.
• LICENSE License disclaimer pertaining all code provided here.
The following software were used to run the scripts provided in this SI: • Windows10 • Python 3.8 (specific packages are listed in the scripts) • DeerLab v0.14.3 • Matlab 2019b • MMMx 1.0

Sample preparation
The oligoPPE substances T011 and T111 were synthesized in the group of Prof. Adelheidt Godt, Bielefeld University, Germany [Jeschke2009]. The samples with total nitroxide concentrations of 100 − 300 μmol/L were produced by dissolving 0.1 mg of the pure sample substance in perdeuterated o-terphenyl, synthesized by Herbert Zimmermann, MPI for Medical Research Heidelberg, heated slightly above the melting point of 60 • C. The crystallized samples were powdered and filled into EPR quartz tubes with maximum diameters of 3 mm (for DEER measurements) or 1.6 mm (for TRIER measurements). To avoid crystallization of the solvent and thus intermolecular aggregation, immediately before introducing the sample tube into the pre-cooled EPR probehead (50 K), the samples were melted again in the hot air stream of a heat gun and shock-frozen in liquid nitrogen. The samples were stored at 4 • C. The solvents of all model compounds were deuterated, as this extends the accessible upper distance limit and improves the resolution of the DEER and TRIER experiments. Detailed descriptions of the syntheses, the spin labeling procedure and further characteristics of those samples can be found in the main text and in the Supporting Information of [Jeschke2009, Jeschke2010, Sajid2009].
The tetraradical Q5 was synthesized by Olav Schiemann and published by Bode et al. in [Bode2007].

Measurements
Four-pulse DEER experiments were measured with the standard pulse sequence shown in Figure 6.1 on either a Bruker Elexsys II E580 or a Bruker Elexsys E680 pulse EPR spectrometer (Bruker Biospin, Karlsruhe, Germany), both operating at at X-band frequencies (9.3 GHz), equipped with a Bruker Flexline 3 mm split-ring resonator overcoupled to Q ≈ 100. A temperature of 50 K was used with a shot repetition time of 4 ms. For the Elexsys E580, the second microwave frequency (ELDOR frequency channel pump) was provided by an E8257D PSG Analog Signal Generator (Agilent, Santa Clara, CA) limited to a power setting of 17 dBm and fed into one of the mw pulse forming units of the spectrometer. For the Elexsys II E580 and the E680 spectrometers, the built-in second frequency source was used. The DEER experiments were performed with the pump frequency pump at the maximum of the nitroxide spectrum. The maximum was determined for each substance individually with a field-swept electron spin echo (FSESE) experiment. The frequency of the observer pulse was increased by 65 MHz relative to the frequency of the pump channel. Observer pulse lengths were 32 ns for the π/2 and π pulses. In all experiments, receiver offset was cancelled by a [(+x)-(-x)] phase cycle applied to the first excitation pulse. Variation of the inversion efficiency of the DEER experiment was achieved by variation of the pump pulse power and subsequent phase readjustment of the observer pulses.
TRIER experiments were performed on a home-built high-power ultra-wideband Q-Band spectrometer [Doll2014], that is equipped with a 8 GSa/s arbitrary waveform generator and a 200 W traveling wavetube amplifier. Essential for TRIER experiments is the used home-built ultra-broad-band pent loop-gap resonator with a loaded quality factor around 120 that accepts capillaries with an outer diameter of 1.6 nm. Both TRIER experiments were performed at 50 K and with a shot repetition time of 2 ms. The center of the nitroxide spectrum was placed in the center of the broad-band resonator and the TRIER observer frequency was set 45-50 MHz lower than the spectral maximum. Pump pulses were placed symmetrically around the observer pulses at an offset of +-90 MHz with respect to the center of the observer pulses. For compound T011, a gaussian-shaped observer sequence and asymmetric hyperbolic secant pump pulses were employed. TRIER experiments on T111 were performed using chirped observer pulses and asymmetric hyperbolic secant pump pulses. In both cases, the amplitudes of the observer pulses were optimized for maximal TRIER echo amplitude, while pump pulse amplitudes were adjusted as a compromise between maximal inversion efficiency and a clean inversion profile without significant side-bands. To ensure a constant adiabaticity over the entire pulse excitation range, resonator compensation was applied for all frequency-swept pulses [Doll2017]. Further details on the used pulses can be found in tables 1 and 2. For T011, TRIER inter-pulse delays were set as follows: τ1 = 400 ns, τ2 = 4600 ns, τ3 = 500 ns. For T111 τ1 = 400 ns, τ2 = 2800 ns and τ3 = 500 ns were used. To record the TRIER data, both pump pulses were incremented independently in steps of 40 ns. With 70 points per dimension this resulted in a TRIER signal with a total length of 2800 ns per dimension for T011. For T111, 116 points were recorded along each dimension, resulting in a total sequence length of 4640 ns along both dimensions. Phase cycling was applied as described in [Pribitzer2017].  The heat-stable complex of subunits Rpo4 and Rpo7 (also known as F and E, respectively) of the archeal RNA polymerase of M. jannaschii were purified according to established protocols. [Klose2012, Werner2002]. For more details, see also the supporting information of [Pribitzer2018]. The labelling sites for the Rpo4/7 complex (Rpo4: C36, G63C; Rpo7: V49C) were selected from a larger set of sites reported in [Klose2012], where all pairwise distances from DEER experiments have been measured. The two subunits, Rpo4 and Rpo7, of the Rpo4/7 complex were individually over-expressed in Escherichia coli following the established protocols. Protein concentrations were determined with a NanoDrop Spectrophotometer ND-1000 (Witec AG) using the calculated extinction coefficients [Gasteiger2003] of = 29.34 L mmol −1 cm −1 for Rpo4/7. The individual subunits or the complex of Rpo4/7 were spin labelled with tenfold molar excess of MTSL ((1-oxyl-2,2,5,5tetramethylpyrroline-3methyl)methanethiosulfonate, Toronto Research Chemicals) over cysteine concentration at a protein concentration of 10 μM. Unreacted spin label was washed out by repeated concentration and re-dilution in a 10 kDa MWCO centrifugal concentrator (Vivaspin-500, 10 kDa MWCO, Sigma-Aldrich). Removal of the free nitroxide label and spin label attachment was checked by CW EPR spectroscopy. The final protein samples were lyophilised and resuspended in a D2O/d8glycerol mixture (1:1 by volume) and transferred into the 3 mm (outer diameter) sample tube.

Measurements
Four-pulse DEER experiments were measured with the standard pulse sequence shown in Figure 6.1 on a home-built Qband spectrometer. The detection frequency was 34.5-34.8 GHz. The pump/detection frequency offsets were: Δ = − = 0.1 GHz. Pumping was always performed at the maximum of the nitroxide spectrum. The DEER measurements were performed at 50 K with a shot repetition time of 4 ms. Pulse powers were optimized using nutation experiments. All pulses had a length of 12 ns. The value of the first refocusing delay was 400 ns. A phase cycle [+(+x)-(-x)] was applied to the π/2 observer pulse to cancel receiver offset. Variation of the inversion efficiency of the DEER experiment was again achieved by variation of the pump pulse power and subsequent phase readjustment of the observer pulses.
TRIER experiments were measured with a home-built Q-band AWG spectrometer. All details on the pulse sequence and pulse shape parameters can be found in [Pribitzer2018].

III. Results of the analysis: Full traces
Figures S1-S3 show the full traces for the oligoPPE 4-pulse DEER datasets (in the main text, only the first three microseconds of the trace are shown for clarity).

IV. Results of the analysis: Parameter tables
Tables S3-S9 collect the DeerLab summaries for each of the global models used to analyze the 4pulse DEER and TRIER datasets. The tables contain information on the goodness-of-fit statistics and fitted values (with 95%-confidence intervals) for each model parameter fitted to the data.

V. Two-spin model analyses
Analysis of the 4-pulse DEER datasets using two-spin models with non-parametric distance distributions with DeerLab. Figures S4-S7 show the results of a global analysis over all database with a global distance distribution. Figures S8-S11 show the results of the local analyses of the individual datasets.
The results show the effects of the incorrect modelling of multi-spin systems as two-spin systems.
Analysis script: analysis_twospin_DEER.ipynb Figure S4: Global analysis with DeerLab of the T111 triradical oligoPPE 4-pulse DEER data acquired at different power attenuation levels (indicated next to each dataset) using a two-spin model with a non-parametric distance distribution. The left panel shows the experimental data as grey dots and the fitted model as a blue line. The right panel shows the global non-parametric distance distribution as a blue line with its 95%-confidence intervals shown as a blue shaded area. 7dB 5dB 4dB 3dB 2dB 0dB Figure S5: Global analysis with DeerLab of the T011 triradical oligoPPE 4-pulse DEER data acquired at different power attenuation levels (indicated next to each dataset) using a two-spin model with a non-parametric distance distribution. The left panel shows the experimental data as grey dots and the fitted model as a blue line. The right panel shows the global non-parametric distance distribution as a blue line with its 95%-confidence intervals shown as a blue shaded area. 0dB 3dB 5dB 7dB 8dB 9dB 11dB Figure S6: Global analysis with DeerLab of the tetraradical oligoPPE 4-pulse DEER data acquired at different power attenuation levels (indicated next to each dataset) using a two-spin model with a non-parametric distance distribution. The left panel shows the experimental data as grey dots and the fitted model as a blue line. The right panel shows the global non-parametric distance distribution as a blue line with its 95%-confidence intervals shown as a blue shaded area. 0dB 2dB 4dB 6dB Figure S7: Global analysis with DeerLab of the Rpo47 triradical protein complex 4-pulse DEER data acquired at different power attenuation levels (indicated next to each dataset) using a two-spin model with a non-parametric distance distribution. The left panel shows the experimental data as grey dots and the fitted model as a blue line. The right panel shows the global non-parametric distance distribution as a blue line with its 95%-confidence intervals shown as a blue shaded area. 0dB 6dB 9dB Figure S8: Local analysis with DeerLab of the T111 triradical oligoPPE 4-pulse DEER data using a two-spin model with a non-parametric distance distribution. For each dataset, the left panels show the experimental data as grey dots and the fitted model as a blue line. The right panels show the corresponding non-parametric distance distributions as a blue line with their 95%-confidence intervals shown as a blue shaded area.

Figure S9
: Local analysis with DeerLab of the T011 triradical oligoPPE 4-pulse DEER data using a two-spin model with a non-parametric distance distribution. For each dataset, the left panels show the experimental data as grey dots and the fitted model as a blue line. The right panels show the corresponding non-parametric distance distributions as a blue line with their 95%-confidence intervals shown as a blue shaded area.
Figure S10: Local analysis with DeerLab of the tetraradical oligoPPE 4-pulse DEER data using a two-spin model with a non-parametric distance distribution. For each dataset, the left panels show the experimental data as grey dots and the fitted model as a blue line. The right panels show the corresponding non-parametric distance distributions as a blue line with their 95%-confidence intervals shown as a blue shaded area.
Figure S11: Local analysis with DeerLab of the Rpo47 protein complex 4-pulse DEER data using a two-spin model with a non-parametric distance distribution. For each dataset, the left panels show the experimental data as grey dots and the fitted model as a blue line. The right panels show the corresponding non-parametric distance distributions as a blue line with their 95%-confidence intervals shown as a blue shaded area.