Orientation selection in distance measurements between nitroxide spin labels at 94 GHz EPR with variable dual frequency irradiation †

Pulsed electron–electron double resonance (PELDOR, also known as DEER) has become a method of choice to measure distances in biomolecules. In this work we show how the performance of the method can be improved at high EPR frequencies (94 GHz) using variable dual frequency irradiation in a dual mode cavity in order to obtain enhanced resolution toward orientation selection. Dipolar evolution traces of a representative RNA duplex and an a-helical peptide were analysed in terms of possible bi-radical structures by considering the inherent ambiguity of symmetry-related solutions.

Orientation selection in distance measurements between nitroxide spin labels at 94 GHz EPR with variable dual frequency irradiation † Igor Tkach, a Soraya Pornsuwan, a Claudia Ho ¨bartner, b Falk Wachowius, b Snorri Th.Sigurdsson, c Tatiana Y. Baranova, d Ulf Diederichsen, d Giuseppe Sicoli a and Marina Bennati* ad Pulsed electron-electron double resonance (PELDOR, also known as DEER) has become a method of choice to measure distances in biomolecules.In this work we show how the performance of the method can be improved at high EPR frequencies (94 GHz) using variable dual frequency irradiation in a dual mode cavity in order to obtain enhanced resolution toward orientation selection.Dipolar evolution traces of a representative RNA duplex and an a-helical peptide were analysed in terms of possible bi-radical structures by considering the inherent ambiguity of symmetry-related solutions.
Measurements of inter-spin distances on the nanometer scale by pulsed electron paramagnetic resonance (EPR) spectroscopy have become a frequently used spectroscopic tool to gain structural information about proteins or nucleic acids.The experiment [1][2][3][4] requires either endogenous paramagnetic centers or the insertion of spin labels by site specific modifications of the investigated biomacromolecule. 5This technique can also provide information on the relative orientation of the spin probes, 6 if they are oriented in the biomolecule under study, as in the case of endogenous amino acid radicals and co-factors 7,10 or nitroxide radicals in nucleic acids. 8Nevertheless, general applicability of the orientation measurements using nitroxide spin labels in diamagnetic proteins, in spite of their extensive application as distance markers, is still representing a challenge.7][18][19] Particularly, recent analysis of orientation selection at low frequencies revealed that the problem of reconstructing bi-radical structures based on triples of Euler angles is non-trivial due to ambiguities in the solutions. 18n the present work, we demonstrate the performance of 94 GHz PELDOR/DEER by employing a novel dual-mode resonator 20 in the millimeter-wave range that covers all possible frequency separations in the EPR spectrum of spin labels and is adapted to a commercial spectrometer.The results permit us to explore the feasibility of data analysis for two representative cases of biological systems, a RNA duplex and an a-helical peptide.2][23] The chemical structure of the spin labels as well as their insertion position in the respective sequences is displayed in Fig. 1.Synthesis and characterization of the samples were described in previous papers. 22,23he experiments were based on the 4-pulse DEER (doubleelectron electron resonance) or PELDOR (pulsed-electron double resonance) sequence to measure inter-spin distances that requires two microwave frequencies to pump and detect each electron spin of the target bi-radical, respectively.The distance information is encoded in the observed dipolar oscillation and can be best determined in experiments at low EPR frequencies (9 GHz/0.34T).The time evolution of the echo intensity for an isolated spin pair AB is given by: 1,2 where V 0 is the echo intensity at the time t = 0, y dd is the angle between the dipolar vector and the external magnetic field, l is the modulation depth or the fraction of spin pairs excited by pump and detection pulses.The dipolar frequency o d of an isolated spin pair AB is related to the inter-spin distance r AB by: g A and g B being the g values of the two spins.If the modulation depth does not depend on the molecular orientation, V(t) results from the sum of contributions of all possible orientations y dd .When the experiment is performed at so-called high field and frequency, i.e. o e Z 94 GHz, the EPR line of nitroxides is dominated by the anisotropy of the electron Zeeman interaction (g anisotropy).In this case, if orientation correlation between the labels exists, the DEER/PELDOR traces V(t) become a function of the mutual radical orientation.First, the distribution of the dipolar frequencies in the traces depends on the fraction of detected molecular orientations.7][8][9] The Fourier Transformation (FT) of the traces results in distorted dipolar Pake patterns (i.e.incomplete distribution of dipolar frequencies in a powder sample) with characteristic line intensities given by the afore-mentioned probability function.
In Fig. 2 we display a series of 94 GHz DEER/PELDOR experiments of the RNA duplex and the a-helical peptide.A commercial W-band resonator (Bruker TeraFlex) was used that allows for a maximal separation of pump and detection frequencies of 56 MHz at 400 mW of available microwave power (Bruker Power Upgrade 2). 12For the RNA duplex (Fig. 2b, left), the orientation selection at 94 GHz shows clear deformations of the Pake patterns, with the parallel component of the dipolar tensor (D J ) appearing at resonances close to g z in the EPR spectrum and maximal modulation depth observed between g x and g y .This is qualitatively consistent with a distance vector interconnecting the labels that is almost parallel to the duplex stacking axis (Fig. 1).We note that the observation of such a pronounced orientation effect in the RNA sample is made possible by the well-defined orientation of the label, as found by a comparative experiment with a more flexible TEMPO-derived label; 24 in the latter experiment we were not able to observe any orientation selectivity in the 94 GHz traces.Restricted mobility of the RNA label (Fig. 1) is consistent with a recent crystal structure of an A-form DNA duplex containing this probe 25 and corresponding PELDOR experiments on DNA. 8,13n contrast, for the a-helical peptide the parallel frequency component of the dipolar tensor is not visible (Fig. 2b, right) but we detect a pronounced field dependence of the peak intensities resulting from a variation in modulation depth in the time traces.We also note that comparative experiments at X-band (9 GHz) display orientation selection in the RNA sample, as previously reported also in DNA sequences, 8,13 but the absence of any orientation effect in the peptide sample (Fig. S1 and S2, ESI †).
In order to better detect orientational selectivity, we performed a second series of experiments by using the dual-mode resonator 20 that permits a frequency separation up to 800 MHz (Fig. 3a).The separation Dn of pump and detection frequencies was tuned over the entire range of the nitroxide spectrum, i.e. up to about 400 MHz (Fig. 3).This procedure is mandatory if the two labels in the bi-radical are non-collinear and their resonances cannot be pumped and detected simultaneously by a small Dn.The experiment with the RNA duplex (Fig. 3b) shows similar results as in Fig. 2b, i.e. both frequency components of the dipolar tensor are detectable by changing the detection position in the EPR line.Thus, the data with the two different setups were consistent.In Fig. 3c the dipolar spectra of the a-helical peptide are displayed for various frequency separations across the EPR line.Here, the changes in the Pake patterns become more subtle because of a complex probability response function reflected in the traces.Moreover, the two canonical frequencies of the Pake (D J and D > )  cannot be separated at any resonance position, suggesting a non-collinear mutual orientation of the g tensor axes in the bi-radical.More traces at variable frequency separation for both samples are displayed in Fig. 4.
The time traces at 94 GHz with either fixed or variable frequency separations were analyzed independently using homewritten fitting routines 7 in MATLAB adapted for nitroxide radicals (ESI †) and the solutions were subsequently compared.The bi-radical structure was defined as the orientation of the spin labels with respect to the common interconnecting dipolar vector.This results in two consecutive Euler rotations, first between the g frame of spin 2 (either A or B in eqn ( 2)) into the principal axis of the dipolar tensor D (R(a 2 , b 2 , g 2 )) and then from the latter into the g frame of spin 1 (R(a 1 , b 1 , g 1 )). 7Due to the axial symmetry of the D tensor only five Euler angles are required, therefore the Euler angle g 2 was set to zero.We point out that both consecutive rotations are required to reconstruct a 3-dimensional bi-radical structure and not only the frame transformation between the g tensors, which is the product of those.Conformational distribution was neglected for the RNA sample due to the rigid fusion of the nitroxidecontaining isoindoline ring to the cytidine nucleobase (Fig. 1) and projecting into the major groove of the RNA duplex. 23For the TOPP label in the peptide, the nitroxide bond is located at a defined position in space as an elongation of the C a -C b axis (Fig. 1), however it possesses one axis of rotation (C a -C b ) that is almost collinear with the N-O direction. 22A second rotation is possible around the C-N bond interconnecting the rings, which coincides with the C a -C b axis.The combined effect of these two rotations was considered in the analysis through a libration around the N-O (g x ) axis by an angle c.The transformations used are illustrated in Scheme 1.
All principal values of the g, D and hyperfine A tensors were determined independently from simulations of 94 GHz EPR spectra (Table 1, caption) and distance measurements at 9 GHz (ESI †).To optimize computational time, the parameter c for the TOPP label was first set to zero and the obtained best solutions were examined subsequently as a function of c.Thus, the parameter space for the fit reduced to five Euler angles defining the bi-radical structure.We tested arbitrary starting sets of Euler angles and the solution mostly converged to the same quintuplet within a distribution of values up to about AE101.However, from some starting points we found that other combinations of the five Euler angles delivered  similar fit qualities.A closer inspection of these solutions revealed that they were symmetry-related, as discussed below.In Table 1 we report the solutions from the fits together with derived symmetryrelated solutions compatible with the biomolecule structure.The parameters x and b 0 are introduced to describe the angles between the N-O axes of the labels and the nitroxide planes, respectively (Fig. 4c).The libration angle c was found to deteriorate the rmsd for values above AE201 but not to improve it (Fig. S4, ESI †).Consideration of small distributions of the Euler angles would likely improve the analysis but is neglected for simplicity.Time traces superimposed to the obtained fits are displayed in Fig. 4.
Comparison of the entries in Table 1 indicates that in the RNA case the solution from variable Dn leads to comparable rmsd and x, b 0 angles as the solution for fixed Dn.This is consistent with the fact that the experiment with a small and fixed Dn is suited for detecting bi-radicals with almost collinear orientations of the labels, as expected in the RNA duplex.On the other hand, the results for the a-helical peptide clearly indicated that the data with variable frequency separation lead to a better quality of fits.This is even more evident when screening the rmsd over the variation of each angle around the solution (Fig. 4d and Fig. S5, ESI †).The rmsd from the data with fixed frequency separation is similar over a wide range of Euler angles, in contrast to well-pronounced minimum observed from the data at variable Dn.This behavior reflects the different capability of the data to pose constraints for the fit.
The result that very different quintuplets of Euler angles delivered very similar rmsd raised the question as to which solution represents the bi-radical structure of the bio-molecule.Ambiguities in the solution were pointed out also in previous works 6,18,27 and are inherent to the symmetry of the spin Hamiltonian involved.Therefore, we examined whether the dipolar traces are sensitive to a change in the directions of the g-tensor principal axes from positive to negative, or, in other words, to a 1801 rotation of the spin label around one of the g principal axes.Such operations change the quintuplet of Euler angles describing the bi-radical structure and, if applied for instance to label 2, will change the location of label 1 in the 3D space.Thus, we applied all these possible operations (1801 rotations around the g axes) to the first and second label and also to their combination and arrived at 16 symmetry-related solutions that are listed in the ESI † (Table S6, ESI †).Explicit computation of the traces for all these solutions gave identical fits (rmsd) of the PELDOR traces.Since the labels employed in this study are not distinguishable, the solutions might represent a transformation from label 1 to 2 or vice versa.
The 16 symmetry-related solutions for both data sets and samples were examined one-by-one by modeling one label into the Pymol structures, used as simple reference, and the position of the second label was reconstructed from the coordinates of the first label according to each solution. 26The operation was carried out for both possible positions of the label in the Scheme 1 Frame transformations in a bi-radical structure.g and D denote the frames of the g-and the dipolar tensor, respectively.For the TOPP label the angle c accounts for a distribution of orientations around the g x axis up to a value AE c with the angles c 1 and c 2 taken as one single parameter.sequence (S6, ESI †).Interestingly, we found that most solutions can be in principle discarded because they are not compatible with the expected structures.Four solutions were left for the RNA duplex and two for the peptide, which are reported in Table 1 and illustrated in Fig. 4. A more detailed evaluation of these solutions in terms of bio-molecular structure would require more sophisticated molecular modeling, which is beyond the scope of this work.

Conclusions
This work reports the performance of a more general experimental set up, based on variable dual frequency irradiation, to perform DEER/PELDOR at high frequencies without limitations by the difference in resonance frequency of two spin labels.Although individual aspects of the work (rigid labels, high frequency PEL-DOR/DEER, wideband excitation, analysis and symmetries) were discussed in the past, we demonstrate here the combination of all these features.The results show that experiments at variable frequency separation in combination with spin labels of restricted mobility supply high quality data amenable to analysis of the orientation selection in terms of bi-radical structures.Experiments at fixed frequency separation provide sufficient constraints only for bi-radicals with g axes in almost collinear arrangement.The feasibility of data analysis permitted us to recognize several symmetry-related solutions.Evaluation of these solutions is possible if information on the global molecular structure is available or additional experimental constraints are introduced.

Fig. 1
Fig.1Schematic structures (PyMol, DeLano Scientific LLC) of the investigated biomolecules, i.e. an a-helical peptide (left) and a RNA duplex (right) containing nitroxide spin-labels with restricted mobility.The orientation of the magnetic g-tensor in the nitroxide radicals is illustrated.Inter-spin distances of 3.1 AE 0.3 and 2.8 AE 0.2 nm were determined at 9 GHz (Fig.S1 and S2, ESI †).Previous studies indicated that insertion of the spin labels does not affect the standard A-form of the RNA duplex as well as the a-helical peptide structure.22,23

Fig. 2
Fig. 2 94 GHz DEER/PELDOR at a fixed frequency separation of 56 MHz.(a) 94 GHz ESE spectrum of the RNA sample showing the pulse excitation width and the band width limitation of a single mode cavity (left).(b) FT-dipolar spectra for the RNA (left) and the a-helical peptide (right) as a function of the observation field.Maximum l was 5% for the RNA and 4.5% for the peptide.Intensities are scaled with respect to l max .The number of traces was selected based on the field steps with size on the order of the excitation band width (B10 G).Exp.parameters: [C] = 60 mM (RNA) and 50 mM (peptide), p/2 = 16 ns, p = 32 ns, p ELDOR = 56 ns, Dn (fixed) = 56 MHz, shots per point (SPP) = 20, shot repetition time (SRT) = 10 ms, 2-step phase cycling, 36-196 scans (1.3-7 h).T = 50 K.

Fig. 4
Fig. 4 Left: Comparison of the experimental PELDOR/DEER traces (blue lines) with calculated traces (best fits, red lines) for the experiments at variable and fixed frequency separation of the RNA duplex (a) and for the helical peptide (b), respectively.Center/right: bi-radical structures representing the symmetryrelated solutions in Table 1.For the RNA, both data sets deliver similar solutions.For the peptide, only solutions from variable Dn are considered.(c) Angles between the nitroxide planes, b 0 , and between the nitroxide N-O bonds, x.(d) A representative plot of the rmsd as a function of the variation of the Euler angles a 1 , b 1 , g 1 for the peptide.

Table 1
Summary of the Euler angles a describing the label orientations in the RNA duplex and the a-helical peptide a Euler angles are defined using the right-handed coordinate system for counter-clockwise rotations around z, y 0 , z 00 .The primes denote the new coordinate systems generated after each rotation.b Definition given in the text.The following tensor principal axis values (x,y,z) were used to simulate the EPR lines: (a) RNA label: g xyz = [2.0083,2.0061, 2.0023]; A xyz = [4.6,5.0, 37] G; (b) TOPP label: g xyz = [2.0101,2.0065, 2.0023]; A xyz = [6.3,6.3, 34] G.The rmsd values were calculated over all traces of one data set.The trace with largest modulation depth was normalized to unity.c Symmetry-related solutions #6 and #9 from S6b (ESI) and #1 and #2 from S6d (ESI).d Symmetry-related solutions #11 and #14 from S6c (ESI).