Pulsed EPR Dipolar Spectroscopy on Spin Pairs with one Highly Anisotropic Spin Center: The Low‐Spin FeIII Case

Abstract Pulsed electron paramagnetic resonance (EPR) dipolar spectroscopy (PDS) offers several methods for measuring dipolar coupling constants and thus the distance between electron spin centers. Up to now, PDS measurements have been mostly applied to spin centers whose g‐anisotropies are moderate and therefore have a negligible effect on the dipolar coupling constants. In contrast, spin centers with large g‐anisotropy yield dipolar coupling constants that depend on the g‐values. In this case, the usual methods of extracting distances from the raw PDS data cannot be applied. Here, the effect of the g‐anisotropy on PDS data is studied in detail on the example of the low‐spin Fe3+ ion. First, this effect is described theoretically, using the work of Bedilo and Maryasov (Appl. Magn. Reson. 2006, 30, 683–702) as a basis. Then, two known Fe3+/nitroxide compounds and one new Fe3+/trityl compound were synthesized and PDS measurements were carried out on them using a method called relaxation induced dipolar modulation enhancement (RIDME). Based on the theoretical results, a RIDME data analysis procedure was developed, which facilitated the extraction of the inter‐spin distance and the orientation of the inter‐spin vector relative to the Fe3+ g‐tensor frame from the RIDME data. The accuracy of the determined distances and orientations was confirmed by comparison with MD simulations. This method can thus be applied to the highly relevant class of metalloproteins with, for example, low‐spin Fe3+ ions.


Introduction
Pulsed EPR dipolar spectroscopy (PDS), which includes techniques such as pulsed electron-electron double resonance (PELDOR or DEER), [1,2] double quantum coherence EPR (DQC), [3] single-frequency technique for refocusing dipolar couplings (SIFTER), [4] and relaxation induced dipolar modulation enhancement (RIDME), [5,6] is av aluable method for determining biomolecular structuresa nd their conformationalc hanges during function. [7] The method is based on the measurement of the dipolar coupling between electron spin centers and provides information about the inter-spin distances and, in favorable cases, the relative orientation of these centers. As the majority of biomolecules are naturally diamagnetic, PDS on such systems typically requires site directed labeling of the biomolecule with spin labels. [8][9][10][11][12] The most common spin labels are nitroxides, [9][10][11][12] althoughanumber of alternatives based on Gd 3 + , [13,14] Cu 2 + , [15,16] trityl [17][18][19][20] and photoexcited porphyrins [21] have been reported. In addition to the spin labels, there is a keen interest of using naturally occurring paramagneticc ofactors, such as Cu 2 + , [22][23][24][25][26][27][28] low-spin (LS) Fe 3 + , [6,[29][30][31][32] high-spin( HS) Fe 3 + , [33] HS Mn 2 + , [34][35][36][37][38] Mo 5 + , [30] Co 2 + , [39,40] iron-sulfur clusters, [27,41,42] manganese clusters, [43] tyrosins, [44,45] semiquinones [46] or flavins, [29,47,48] forP DS measurements. The obvious advantage of using intrinsic spin centers is that the number of spin labels required for PDS and, consequently,t he number of structuralp erturbations to the native biomolecular structure can be reduced. Moreover,i ntrinsic spin centers often have a well-defined, fixed position within the fold of the biomolecule and, thus, can provide more accurate distance constraints as compared to flexible spin labels. In addition, PDS-based distance measurements between an intrinsic spin centera nd spin labels at different sites of ab iomoleculeenable the localization of the intrinsics pin centers within the biomolecular fold through trilateration [49] or the docking of different parts of protein complexes using paramagnetic metal ions as anchor points. [50] Low-spin Fe 3 + ions occur widely in metalloproteins, [51][52][53] for example in hemoglobin,m yoglobin, or cytochromes, and constitute as such an important spin probe for PDS. As compared to organic radicals and other low-spinm etal centers like Cu 2 + , LS Fe 3 + ions have al arge g-tensor anisotropya nd shorter relaxation times, which impose significant challenges on PDS measurements and the corresponding data analysis.D ue to the significant g-anisotropy,t he spectral width of LS Fe 3 + ions largely exceeds the bandwidth of typical microwave pulses at usual microwave frequencies. Consequently,w hen the PDS signal is acquired on the LS Fe 3 + centers, only as mall fraction of these centers contributes to the signal. This, together with the short T m relaxation rate of the LS Fe 3 + ions, led to al ow signal-to-noise ratio (SNR) of the X-and Q-band PELDOR time traces acquired on the LS Fe 3 + /nitroxide spin pair in neuroglobin. [54] Later,t he value of SNR was improved by af actor of 30 using composite pulses at W-band. [32] However,e ven though a reasonable SNR could be achieved, an accurate conversion of the PELDOR time traces into the distance distributions can be obstructed by orientation selectivitye ffects,d ue to selective excitation of certain orientations of the LS Fe 3 + spin. The commonw ay to account for the orientations electivity is to measure several PELDOR time traces for different orientations of an anisotropic spin and then to analyze all time traces together. [55][56][57][58][59] However,t his procedure is not applicable to the spin pair LS Fe 3 + /nitroxide, because the differencei nr esonance frequencies between LS Fe 3 + ions and nitroxides exceeds the bandwidthso fE PR resonators and microwave amplifiers.
The difficulties of PELDOR experiments involving LS Fe 3 + /organic radical spin pairs can be circumvented by using another PDS technique called RIDME. The keyd ifferenceo ft his technique to PELDOR is that one of the dipolar-coupled spins is flipped not by as electivem icrowavep ulse, called pump pulse, but by non-selective spontaneousr elaxation events. Since the T 1 relaxation times of organic radicals is typically much longer than the T 1 relaxation times of LS Fe 3 + ions, the RIDME signal is usuallya cquired on the organic radicals, whereas the Fe 3 + spins are flipped by spontaneous relaxation. The experiment done this way has several advantages.F irst, the detection of the RIDME signal on the organic radical, which has as mall ganisotropy and al ong T m relaxation time, results in ag ood SNR of the RIDME time trace. Second,a ni nfinite effective bandwidth of the stochastic Fe 3 + spin flips can provide RIDME modulation depthsofu pt o50% and ensures the absence of orientation selectivityf rom LS Fe 3 + .T hese advantages were confirmed in previous RIDME studies on LS Fe 3 + /flavin, [29] LS Fe 3 + /nitroxide [6,31] and LS Fe 3 + /trityl [20] spin pairs. Although acquiring RIDME time traces on LS Fe 3 + /organic radicals pin pairs is fairly straightforward, the conversion of these time traces into the distance distributions is challenging. As was pointed out by Milikisyants et al. [6] and later by Astashkin et al., [29] the deviation of the three principal g-values of LS Fe 3 + ions from the g-factor of the free electron (g e % 2.0023) is large enough that it cannot be neglectedi nR IDME dataa nalysis. This meanst hat the common methods of PDS data analysis, whicha ssumesb oth spinst ob ea lmost isotropic, cannot be applied in the presentc ase. Instead, the theory of Bedilo and Maryasov [60] for the dipolarc oupling betweena nisotropic spins centers has to be used in this case. The first application of this theory for the analysis of RIDME data wasr eported by Astashkin et al. [29] There, the RIDME spectrumo ft he LS Fe 3 + /flavin spin pair was simulated using am odified equation for the dipolar coupling constant, which provided estimates of the inter-spind istance and two angles that determine the relative orientation of the Fe 3 + g-tensor with respectt ot he distance vector. However, this analysis was done only in as emi-quantitative way,b ecause usage of the four-pulse RIDME sequence lead to time traces with significant dead time and the SNR was ratherl ow.
The aim of the study here is therefore to explore the effect of g-anisotropy on the RIDME data of LS Fe 3 + /organic radical systemsa nd to establish aq uantitative analysis for such data. First, the theoryo ft he dipole-dipole interaction between aL S Fe 3 + ion and an organic radicali sg iven and then the predictions are derived for the shape of the corresponding dipolar spectra. To confirmt he predictions experimentally,t wo known Fe 3 + /nitroxide compounds, 1 and 2, [61] ando ne new Fe 3 + /trityl compound, 1T,w ere synthesized( Figure1)a nd RIDME data was acquired on them. The obtained RIDMEt ime traces were analyzed using the program DipFit,w hich was originally developed for the high-spin Fe 3 + /nitroxide pairs [33] but was extended here to the case of LS Fe 3 + .A tl ast, the DipFit-based distance and angular distributions were comparedt ot he results of molecular dynamics( MD) simulations and to the distance distributions obtained for the same RIDME data by meanso f the program DeerAnalysis. [62]

Theory
The theory of dipole-dipole interaction between two anisotropic spin-1 = 2 centers was developed by Bedilo and Maryasov [60] and was later extended to the case of ad ipole-dipole interaction between one anisotropic spin-1 = 2 center ando ne isotropic spin-1 = 2 center. [29,33] The latter case appliesf or the spin pairs LS Fe 3 + /organic radical, because the g-anisotropy of organic radicalh as usually little effect on dipolar spectraa nd thus can be neglected. Therefore, and as shown previously by us, [33] the dipolar coupling frequency n dd of such spin pairs can be described by Equation (1): in which m 0 is the vacuum permeability, h is the Planck constant, b g and g eff are the g-tensor and the effective g-factor of the LS Fe 3 + ion, respectively, r is the inter-spin vector with the length r and the unit vector n,a nd B 0 is the vector of applied magnetic field with the length B 0 .Note that the product (B 0 /B 0 , n)isusually denoted as cos(q), in which q is the angle between the inter-spin distance vector and the applied magnetic field. Comparing Equation (1) with the equation for the dipolar coupling between two isotropic spin-1/2 centers [Eq. (2)]: reveals that both equations differ by the factor g 1eff /g e and the angulart erm in the square brackets.Inthe case of two isotropic spins, the latter term depends only on the angle q,w hereas when one of the spins is anisotropic, it also dependso nt he orientation of the distance vector with respect to the g-tensor of the anisotropic spin center. Such orientation can be described by two spherical angles,the polar (x)a nd azimuthal (f) angles( Figure 2). Thus, the dipolar coupling frequencies dependn ot only on r and q,b ut also on the g-values of the anisotropic spin centera nd the angles x and f. To get ad eeper insight into how the g-anisotropy of LS Fe 3 + centers influences the dipolar spectra,s pectrals imulations were performed on the basis of Equation (1), using g 1xx = 1.56, g 1yy = 2.28, g 1zz = 2.91 for the principal g-values of the low-spin Fe 3 + center (they correspond to the experimental g-values discussedb elow).T he g-value of the organic radical was set to g e = 2.0023 and the inter-spin distance to 2.50 nm. The angles x and f were varied in the range [08,9 0 8]w ith steps of 108 and 308,r espectively.A veraging of the dipolar coupling frequencyo ver all possible orientations of the spin pair with respect to B 0 was done by the Monte-Carlo methodu sing 10 6 random samples. The obtained powder-averaged spectra are showni nF igure 3. The abscissa of the depicted spectra is given in units derived from Equation (3): which corresponds to the dipolar coupling constanto fa ni sotropic spin pair with the same inter-spin distance as used   Figure 3r eveals ap rominentdeviation of the calculated spectra from the well-known Pake doublet.W hereas the Pake doublet has two characteristic singularities, often referred to as perpendicular (q = 908)a nd parallel( q = 08)c omponents,a ll calculated spectra here displayt hree singularities instead. In analogy to the Pake doublet, theses ingularitiesc an be subdivided into two perpendicular components, which correspond to q = 908,a nd one parallel component, which corresponds to q = 08.M oreover,t he frequencies,a tw hich the singularities appear in Figure 3, do not have af ixed ratio, as in the case of the Pake doublet, but depend on the principal g-values of the LS Fe 3 + centera nd the angles x and f. This dependencec an be readily explained on example of four spectra corresponding to the angular combinations (x, f) = (08,0 8), (08,9 0 8), (908,0 8) and (908,9 0 8). For the angular combination (08,0 8), r is collinear to the g 1zz -axis of the LS Fe 3 + g-tensor.C onsequently,t he parallel component of the spectrumi ss caled by g 1zz ,y ieldinga singularity at 2(g 1zz /g e )n 0 % 2.91 n 0 . Then, the other two components of the LS Fe 3 + g-tensor give rise to two perpendicular components, which appear at (g 1xx /g e )n 0 % 0.78 n 0 and (g 1yy /g e )n 0 % 1.14 n 0 . The same assignment of singularities also holds for the spin pair geometry with (x, f) = (08,9 0 8), because the shape of the dipolar spectrum does not depend on the f angle as soon as the x angle equals 08.F or the angular combination (908,0 8), r is aligned along the g 1xx -axis of the LS Fe 3 + g-tensor.T hus, the parallelc omponent of the spectrum is scaled by g 1xx and appears at 2(g 1xx /g e )n 0 % 1.56 n 0 ,w hereas two perpendicular components are scaled by g 1yy and g 1zz and appear at (g 1yy /g e )n 0 % 1.14 n 0 and (g 1zz /g e )n 0 % 1.45 n 0 ,r espectively.F inally,t he angularc ombination (908,9 0 8)c orresponds to the case where r is collinear to the g 1yy -axis of the LS Fe 3 + g-tensor.I nt his case, the parallel component of the spectrum is determinedb yt he value of g 1yy ,w hich yields the singularity at 2(g 1yy /g e )n 0 % 2.28 n 0 ,w hereas the perpendicular components of the spectrum are scaled by g 1xx and g 1zz and appear at (g 1xx /g e )n 0 % 0.78 n 0 and( g 1zz /g e )n 0 % 1.45 n 0 . Note that the dipolar spectra in Figure 3w ere simulated for certain valueso fr, x and f. If the molecule, which hosts the spin pair,h as some flexibility,t he geometric parameters r, x and f will have some distributions. Obviously,t he distributions P(r), P(x)and P(f)w ill affect the shape and the width the corresponding dipolars pectra.T his effect will lead to the averaging the dipolar frequency given by Equation (1) over these distributions. Moreover,apossible correlation between the values of r, x and f might affect the dipolar spectra.T hus,t he determinationo fP(r), P(x)a nd P(f)f rom the dipolar spectra is a complex, ill-posed problem.N evertheless, ap ossible algorithm to extract these distributions from the dipolar spectra using severals implifying assumptions is proposed in the Experimental section.

EPR measurements
Details of the experimental setups are described in Chapter 2o f the Supporting Information. The RIDME experiments on the model compounds were performed using the five-pulse sequence p/2Àt 1 ÀpÀ(t 1 + t)-p/2ÀT mix Àp/2À(t 2 Àt)ÀpÀt 2 -echo. [6] The frequency of the microwave pulses was set in resonance with either the maximum of the nitroxide spectrum, for 1·Im 2 and 2·Im 2 ,o r with the maximum of the trityl spectrum for 1T·Im 2 .T he lengths of the p/2 and p pulses were 12 and 24 ns, respectively. t 1 and t 2 intervals were set to 300 ns and 3 ms, respectively.T he optimal values of T mix and the temperature of RIDME experiments T were determined based on the temperature-dependent inversion recovery measurements on the LS Fe 3 + center (Chapter 7i nt he Supporting Information). This yielded T mix = 100 msa nd T = 10 Kf or all three model compounds. During the RIDME experiment, t was linearly incremented from À50 ns to 2880 ns in increments of 8ns, yielding 360 data points in total. The shot repetition time was set to 10 ms. To avoid overlap with unwanted echoes with the detected refocused virtual echo, 16-step phase cycling was employed (Chapter 7i nt he Supporting Information). In order to suppress deuterium ESEEM (Chapter 7i nt he Supporting Information), the initial values of t 1 and t 2 were incremented stepwise and independently from each other with an increment of 8nsa nd 16 steps per inter-pulse interval, [64] resulting in additional 256 averaging cycles. As ar esult, the duration of as ingle RIDME experiment was about 4hours.

RIDME data analysis
The first step of the RIDME data analysis was the usual removal of the non-oscillating background from the original RIDME time traces. According to the recent publication by Keller et al., [65] the shape of the RIDME background is described by an exponential function with an argument having al inear and aq uadratic terms with respect to t. In practice, it is often approximated by as tretched exponential function or athird-order polynomial function. [31,65,66] Here, the background was fitted here by at hird order polynomial function using the program DeerAnalysis. [62] The same program was used to divide the original RIDME time traces by the background function and then to perform fast Fourier transformation (FFT) of the background corrected time traces. This procedure yielded the so-called RIDME spectra. In the next step, the RIDME time traces were fitted by means of the program DipFit [33] (free available at https://github.com/dinarabdullin). In this program, the distributions P(r), P(x)a nd P(f)w ere approximated by Gaussians and the corresponding mean values hri, hxi, hfi and standard deviations Dr, Dx, Df were used as fitting parameters. All six fitting parameters were optimized until the simulated time trace or the simulated spectrum provided the best root-mean-square deviation (RMSD) to the experimental time trace or the experimental spectrum, respectively.T he simulation of the dipolar spectrum for certain values of hri, hxi, hfi, Dr, Dx,a nd Df was done by averaging Equation (1) over the corresponding distributions P(r), P(x)a nd P(f)a nd, additionally,o ver the angle q (powder averaging). The averaging was performed via the Monte-Carlo method with 10 6 random samples. The values of r, x and f were assumed to have no correlation with each other.T he g-tensor of the LS Fe 3 + center was set to the experimental values described below.F or simplicity,t he nitroxide's and trityl's principal g-values were set to g e . In order to simulate the RIDME time trace, the 10 6 values of the dipolar frequency were used to compute the sum in Equation (4): [67] Vt ðÞ V 0 in which, N is the number of Monte-Carlo samples, and l is the modulation depth parameter,w hich was determined from the experimental RIDME time traces.

Molecular modeling
The structure optimization and MD simulations for model compounds 1·Im 2 , 2·Im 2 and 1T·Im 2 were done using the stand-alone program xtb. [68] Evaluation of the MD trajectories was performed with the program TRAVIS. [69] Owing to the bi-radical electronic structure and the large molecular size of the model compounds, the semi-empirical tight-binding method GFN2-xTB/GBSA [70] was applied (for details see Chapter 11 in Supporting Information).
To enable the comparison of the MD results with the structural information from RIDME, the distributions P(r), P(x)a nd P(f)w ere calculated based on the MD trajectories. The values of r were determined as the distance between the Fe atom and the center of the NÀOb ond of the nitroxide radical or the central Ca tom of the trityl radical. To determine the angular parameters x and f,t he orientation of the LS Fe 3 + g-tensor relative to tetraphenylporphyrin (TPP) had to be defined. Here, this orientation was set to the one reported for Fe(TPP)(4-MeIm) 2 + . [71] Thus, the g zz -axis of LS Fe 3 + was orthogonal to the TPP plane and aligned with the Fe-N(imidazole) bond. The corresponding g xx -a nd g yy -axes were aligned with two orthogonal Fe-N(porphyrin) bonds within the TPP plane. Based on this definition of the g-axes, x was determined as the angle between the g zz -axis of LS Fe 3 + and the inter-spin vector r. The angle between the g xx -axis and the projection of r on the TPP plane yielded the value of f. The resulting MD distributions of r, x and f are summarized in Figure S10.

Results and Discussion
Preparation of the modelcompounds The HS-precursors 1·Cl, 2·Cl and 1T·Cl were synthesized as described in the Experimental part. Adding 10 4 equivalents of imidazole to the three compounds lead to the formation of the bis-imidazole adducts 1·Im 2 , 2·Im 2 and 1T·Im 2 and conversion of the Fe 3 + from the HS-to the LS-state. In order to confirm the LS-state of the Fe 3 + ions in 1·Im 2 , 2·Im 2 and 1T·Im 2 ,Xband cw-EPR spectra of these compounds were measured at 15 K ( Figures 4a nd S2). The obtained spectra do show the characteristic signal of the LS Fe 3 + ion, whichi so verlaid with the sharp saturated signal of the nitroxide or trityl radicals. No HS Fe 3 + signal, as found for 1·Cl and 2·Cl, [61] was observed in the region of g % 6. Thus, cw-EPR proofs complete conversion of the HS Fe 3 + ion into its LS-state, which is in agreement with previouss tudies. [72,73] The principal g-values of the LS Fe 3 + ion were found to be identical for all three compounds, g zz = 2.91 AE 0.01, g yy = 2.28 AE 0.01 and g xx = 1.56 AE 0.04. All three gvaluesa re in agreement with those reported for the LS Fe 3 + ion in Fe(TPP)(Im) 2 + [73] and Fe(TPP)(4-MeIm) 2 + . [71] The spectrum of 1T·Im 2 + contains an additional weaks ignal at g % 4.3, which is assigned to free Fe 3 + ions that drop out of the porphyrin ring. [74]

RIDME measurements
The RIDME time traces recorded on 1·Im 2 , 2·Im 2 and 1T·Im 2 are shown in Figure 5a and the correspondingb ackground-corrected time traces are depicted in Figure5b. All RIDME time traces have av ery good SNR (see Chapter 8i nt he Supporting Information) and display several clear oscillation periods. The obtained modulation depthse qual 30 %, 40 %a nd 42 %f or 1·Im 2 , 2·Im 2 and 1T·Im 2 ,r espectively.T he difference between the modulation depths, as well as the deviation of these depthsf rom the expected value of 50 %, is likely due to partial m 2 -oxo-dimerization of the Fe 3 + porphyrins, which wasa lready observede arlier for the given model compounds. [61] The dipolar spectra corresponding to each of the RIDME time traces are depicted in Figure 5c.I naddition to the dipolar spectra,w hicha ppear within AE 10 MHz for all three model compounds, the RIDME spectra of 1·Im 2 and 2·Im 2 display a weak peak at about 12 MHz. This peak can be assigned to nitroxide ESEEM (FigureS4) and results from incomplete 14 NESEEM suppression by the modulation averaging Scheme. Since the amplitude of the unsuppressed ESEEM peak is weak, no furthera ttempts were taken to removei t. Note also that this detrimental ESEEM peak is absenti nt he RIDME spectrum of the trityl-based model compound 1T·Im 2 .

RIDMEd ata analysis
After the successful acquisition of RIDME data on the model compounds, the next step is the extraction of the distributions P(r), P(x)a nd P(f)f rom this data. This was done by means of the program DipFit,w hich approximatesa ll three distributions by Gaussiansa nd performs the fitting of the RIDME time traces using the mean values and standard deviations of r, x and f as fitting parameters. Figure 5b shows that good fits to the RIDMEt ime traces were obtained for all three model compounds. The parameters of the distributions P(r), P(x)a nd P(f), which led to these fits, are listed in Table 1. In order to estimate how defined these parameters are, the six-dimensional parameter space needs to be explored, which is avery time expensive procedure. Instead, the lower bound for parameters' uncertainty was determined here by recording the dependence of the goodness of fit on different pairs of fitting parameters, while setting the four other parameters to their optimized values. As am easuref or the goodness of fit, the RMSD be-  Figure S6. Parameter ranges,i nw hich 110% of the minimal RMSD are reached, were used to determine the approximate confidence intervals for the optimized parameters ( Table 1). Note that such error-estimationc riterioni sa lso used in the program PeldorFit, where it was shown to yield reasonable error estimates of fitting parameters. [75] As follows from Table 1, the confidence intervals of the mean inter-spin distance hri and the corresponding standard deviation Dr are well below 1 for all three model compounds.S uch ap recision of the obtained inter-spin distances reveals high sensitivity of the RIDME experiment towards these two parameters. The confidence intervalso ft he angularp arameters hxi and Dx are also similarf or all three compounds.
They are in the order of AE 208 for both hxi and Dx. The confidence intervals for the angular parameters hfi and Df are in average similar to the ones of hxi and Dx butd isplay al arger distribution of their values between differentm odel compounds. The precision of the mean value hfi varies between AE 78 (1T·Im 2 )a nd AE 308 (2·Im 2 ), and the precisiono ft he width Df takes values between AE 98 (1T·Im 2 )a nd AE 208 (1·Im 2 ). Such difference in the confidence intervals of hfi and Df correlates with the differencei nt he best RMSD values obtained for each of the model compounds. Figure 6r eveals that the lowest RMSD value amongt he three model compounds was obtained for 1T·Im 2 ,w hereas the larger RMSD valuesw ere obtained for 1·Im 2 and 2·Im 2 .
In addition, the optimized distributions P(r), P(x)a nd P(f) were used to simulate the dipolar spectra in Figure5c. As can be seen, the simulated spectra provide an overall agreement with the experimentally obtained spectra.Aslight deviation betweent he experimental and simulated spectra around the zero frequency for 1·Im 2 and 2·Im 2 can be due to the imperfection introduced by the background correction. This deviation could not be avoided neither by using variousd ifferent background fitting functions, such as stretched exponentialorp olynomial, nor by varying the starting point for the background fitting. Recently,R itsch et al. have reported on as imilare ffect observed for aC u 2 + /nitroxide spin system and assigned this distortion of the RIDME spectrum to the backgrounda rtifact that appears at the beginning of RIDME time traces. [75] The ongoing work on the description of the RIDME background might help to explain this empirical observation in the future. Another reason for the observedd eviation might be as light orientation selectivity,w hich is due to the partial excitation of the nitroxides pectrum in the RIDME experiment.

Comparison to MD simulations
In order to relate the obtainedd istributions P(r), P(x)a nd P(f) to the structure and dynamics of the model compounds, MD simulations were carried out for each of them. Based on these simulations, qualitative estimates of all three distributions were derived (FigureS10) and, to allow direct comparison to the RIDME results, the meanv alues andt heir standardd eviation were calculated for each distribution. The calculated parameters are listed in Ta ble 1a nd are depicted in Figure6by circles.
Ta ble 1r eveals an excellent agreementb etween the RIDME and MD distance parameters hri and Dr fora ll three model compounds. Both methods predict that 1·Im 2 and 2·Im 2 have similar mean Fe 3 + -nitroxide distances of~2.50 nm and 2.47 nm, respectively,w hereas the mean Fe 3 + -trityl distance in 1T·Im 2 is~0.15 nm longert han the Fe 3 + -nitroxide distance in the structurally similarcompound 1·Im 2 .The latter difference is due to the larger size of the trityl radicala sc ompared to the nitroxide radical. The widths of the inter-spin distance distributions Dr are below 0.1 nm and differ between the model compounds by less than 0.02 nm, which reflects as imilarf lexibility of the linker/nitroxide motifs of 1·Im 2 and 2·Im 2 andt he linker/ trityl motif of 1T·Im 2 . Table 1. RIDME-and MD-based parameterso fd istributions P(r), P(x)a nd P(f)i n1·Im 2 , 2·Im 2 and 1T·Im 2 .  Ag ood agreement between RIDME andM Dw as achieved not only for the distance parameters but also for the angular parameters hxi and Dx. For all three model compounds, MD simulations yielded hxi and Dx valueso f~908 and~158,r espectively.B oth values are within the confidence intervals of the corresponding parameters determined by RIDME (see Ta ble 1a nd Figure 6). Note that hxi = 908 describes the case where the inter-spin vector is perpendicular to the g zz -axis of the Fe 3 + ion. As g zz is orthogonalt ot he TPP plane, [71] the interspin vectorh as to be in plane with the TPP ring (Figure 7a). In terms of structure, this means that the linker/nitroxide and linker/trityl motifs are in plane with the TPP ring. The distribution of the x angles around 908 with as tandard deviation Dx 158 can be attributed to bending dynamics of the linkers, which leads to as light inclination of the linker/nitroxide and linker/trityl motifs relative to theTPP plane (Figure 7a). This dynamics fits to the observed dynamics of other compounds with similar linker groups. [25,26,57] The MD derived value of hfi is for all three model compounds 458.T his value is within the confidence intervals of the RIDME derived values of hfi for 1·Im 2 and 2·Im 2 and deviates by 58 from the RIDMEd erived value of hfi for 1T·Im 2 .S imilarly, the differenceb etween the RIDME and MD estimateso fDf dependso nt he model compound. In the case of 1·Im 2 and 2·Im 2 ,t he RIDMEv alues of Df have large confidence intervals (see Figure 6), which include the MD prediction.I nt he case of 1T·Im 2 ,t he RIDME value of Df is well-defined and deviates by at least 78 from the corresponding MD prediction.Apossible explanation for this difference can be based on the following: The angle f is determined by the orientationso ft he g xx -a nd g yy -axes of the Fe 3 + ion and the orientationo ft he inter-spin vector. In the MD simulations, the orientations of the g xx -a nd g yy -axes were fixed along two orthogonal FeÀNb onds of the TPP ring. Thus, the MD values of Df are determined only by the dynamics of the linker/nitroxide or linker/trityl motifs, which changesi nt he orientation of the inter-spin vectorr elative to the fixed g-axes. In addition, the distribution of g xx -a nd g yy -orientations within the TPP plane might also contribute to Df. According to previousw orks, such distribution can be caused by rotationo ft he axial ligands relative to the TPP plane. [71,76] If one takes this distribution into account,t he RIDMEw idth Df can be represented as as uperposition of a width Df r ,w hich is due to the dynamics of thel inker/radical motifs, and aw idth Df g ,w hich stems from the distribution of g xx -a nd g yy -orientations within the TPP plane and which is causedb yt he rotationo ft he axial ligands ( Figure 7b). If both contributions are approximated by Gaussians with standard deviations Df r and Df g ,t he total width is given by Df 2 = Df r 2 + Df g 2 .A ssuming that Df and Df r can be associated with the RIDME-andM D-based widths,r espectively, Df g = 268 can be determinedf or 1T·Im 2 .N ote that as imilard istribution of the g xx -a nd g yy -orientations aroundt he porphyrin's FeÀN bondsw as reported for Fe(TPP)(4-MeIm) 2 + ; AE 258 based on proton HYSCORE experiments. [71] Comparison with 2·Cl As the molecular skeleton of 2·Cl is the same as for 2·Im 2 ,b oth compounds differ only with respectt ot heir spin states, HS for the former and LS for the latter.I ti st hus of interestt oc ompare the geometric parameters obtained from their RIDME data. The RIDMEm easurements on HS 2·Cl were reported in our previous paper. [33] There, it was not possible to determine the P(f)d istribution, because the g-tensor of the HS Fe 3 + ion had axial symmetry.I na nalogyt ot he RIDME-based distributions here, the distributions P(r)a nd P(x)o ft he HS compound were described by the mean values, hri = 2.52 AE 0.03 nm and hxi = 898 AE 48,a nd the standard deviations, Dr = 0.06 AE 0.05 nm and Dx = 68 AE 38,r espectively.T hese values revealagood overall agreement with the corresponding values for 2·Im 2 (see Ta ble 1). Thus, theser esultss how the consistency between the distances and angles x determined for the LS Fe 3 + /nitroxide and the HS Fe 3 + /nitroxide.

Comparison to DeerAnalysis
To reveal the effect of the g-anisotropy on the RIDME data analysis,t he RIDME time traces of 1·Im 2 , 2·Im 2 and 1T·Im 2 were additionally analyzed by means of the program DeerAnalysis, [62] which neglects the anisotropy of the LS Fe 3 + spin centers. Figure 8d epicts the distance distributions obtained by Deer-Analysis for all three model systems. For the sake of comparison, these distributionsa re overlaid with the corresponding Figure 7. Schematic representation of the geometric parameters hxi and hfi and their distributions widths Dx and Df for the model compounds 1·Im 2 , 2·Im 2 and 1T·Im 2 .The Fe 3 + andnitroxide (or trityl) spin centersa re depicted as black spheres. The inter-spin vector is shown by blue vector.The g-axes of the Fe 3 + ions are depicted as red vectors. a) The view is setparallel to the TPP plane. The TPP core is drawn as ab lack bar.b)The view is set perpendicular to the TPPplane. Df r denotes the contributiont oDf which is due to the dynamics of the linker/radicalm otifs, and Df g denotest he contribution to Df which stems from the distribution of g xx -and g yy -orientations within the TPPplane. DipFit and MD distance distributions. As can be seen from Figure 8, the DeerAnalysis distributionsh ave ac lear difference to the DipFit and MD distributions.T his differencec oncerns the most probable distances,w hich are smaller by~0.25 nm for the DeerAnalysis distributionst han for the DipFita nd MD distributions, as well as the shape of the distance distributions, which are sharp and unimodal in the case of DipFit and MD but are broad and have several prominent shoulders in the case of DeerAnalysis. To interpret the obtained deviation of the DeerAnalysis distance distributions from the corresponding DipFit and MD distributions, it is sufficientt oc onsider Equations (1) and (2). Neglecting their angular parts and putting these two equations equal to each other,t han each distance r in Equation (1) will correspond to the distance r' = r·(g e /g 1eff ) 1/3 in Equation (2). This result shows that each actual distance r corresponds to an umber of artificial distances r' in the Deer-Analysis distribution. Colored barsi nF igure 8d epict the positions of these artificial distances calculated for the DipFit parameter hri (Table 1) and the three principal g-values of the LS Fe 3 + ion (g xx , g yy ,a nd g zz in Figure 4). Since g zz (= 2.91) and g yy (= 2.28) are larger than g e ,the corresponding artificial distances are smaller than the actual distances. In contrast, g xx (= 1.56) is smaller than g e and the corresponding artificial distance is larger than the actual distance. Thus, the g-anisotropy of Fe 3 + leads to as hift of the DeerAnalysis distances relative to the actual distances, and the differentp rincipal g-values of Fe 3 + give rise to severals houldersi nt he DeerAnalysis distributions. In order to predict the exact values of the artificial distances and their relative probabilities,t he angular terms of Equations (1) and (2) have to be taken into account as well. This will lead to an additional dependence of the artificial distances on angles x and f,w hich are included in the angular term of Equation (1). The dependence of the DeerAnalysis distributions on x and f is responsible for the fact that the shoulders in the DeerAnalysis distributions appeara tn ot exactly the calculated artificial distances and that these shoulders have different relative probabilities(see Figure 8).
Thus, the g-anisotropy of the LS Fe 3 + ion has as ignificant effect on the RIDME data analysis. Because of this, we revisited the analysis of the RIDME data, reported earlier for the cyto-chromeP 450cam mutant C58R1 [31] (see Chapter 10 in the Sup-porting Information). Although the g-anisotropy of the LS Fe 3 + centeri ss maller for cytochrome P450cam (g xx = 1.91, g yy = 2.25, g zz = 2.42) [31] then for the model compounds here, ac leard ifferenceb etween the DipFit and DeerAnalysis distance distributions waso btained( Figure 9). This difference concerns mostly the most probabled istance, which is smaller by 0.15 nm for the DeerAnalysis distribution as compared to DipFit distribution. The width of the DeerAnalysis distribution is only slightly larger than the width of the DipFit distribution,w hich is in agreement with the reduced g-anisotropy mentioned above. The DipFit derived distance distribution agrees less wellw ith the MtssWizard [77,78] prediction than the DeerAnalysis one. However, the difference is close the average error of Mtss-Wizard( 0.3 nm) and, thus, can be assigned to the uncertainty of in silico prediction.

Conclusions
The effect of the g-anisotropy of LS Fe 3 + ions on the RIDME data was described in detail and confirmed experimentally for LS Fe 3 + /nitroxide and LS Fe 3 + /trilyl spin pairs. The dipolar spectra of such spin pairs were shown to depend not only on the inter-spin distances but also on the principal g-values of LS Fe 3 + andt he relative orientationo ft he inter-spin vector rela- Figure 8. Comparison of DipFit (blackl ines)and DeerAnalysis (red lines)based inter-spin distancedistributions for 1·Im 2 + , 2·Im 2 + and 1T·Im 2 + .Asareference, the MD predictions of the distance distributions are depicted as gray shades.C olored bars depictt he positionso fa rtificial distances that are obtained for the actual distance hri and three principal g-values of the LS Fe 3 + center whenthe g-anisotropy of the Fe 3 + centeri sn eglected in the RIDME data analysis. tive to the g-frame of Fe 3 + .T he latter orientation was described by two angular parameters, ap olar angle x and an azimuthal angle f. The distance distribution P(r)a nd the angular distributions P(x)a nd P(f)c ould be extracted from the experi-mentalR IDME data with the fitting program DipFit.I nc ontrast, the analysis of the same RIDME data using the program Deer-Analysis, which neglects g-anisotropy,l ed to an error of 0.25 nm in the meani nter-spin distances, compared to 0.01 nm in the case of DipFit, and errors in the distribution width and shape. In addition, to the distance parameters, DipFit yieldedt he mean values and standard deviations of angular parameters x and f with an average uncertainty of 208. The comparison of the RIDME-derived distributions P(r), P(x) and P(f)w ith the their MD-based predictions revealed very good consistency for all three model systems considered. This result provest hat not only P(r)b ut also P(x)a nd P(f)c an be reliably determined from the RIDME data. Thus, this work provides an important guideline for further applications of PDS to the highly relevant class of LS Fe 3 + containing proteins and extends the arsenal of available programs for the analysiso fP DS data from anisotropic spin centers.