Letter pubs.acs.org/JPCL
RIDME Spectroscopy with Gd(III) Centers Sahand Razzaghi,† Mian Qi,‡ Anna I. Nalepa,§ Adelheid Godt,‡ Gunnar Jeschke,† Anton Savitsky,§ and Maxim Yulikov*,† †
Laboratory of Physical Chemistry, Department of Chemistry and Applied Biosciences, ETH Zurich, Vladimir-Prelog-Weg 2, 8093 Zurich, Switzerland ‡ Faculty of Chemistry and Center for Molecular Materials, Bielefeld University, Universitätsstraße 25, 33615 Bielefeld, Germany § Max-Planck-Institut für Chemische Energiekonversion, Stiftstrasse 34-36, D-45470 Mülheim an der Ruhr, Germany S Supporting Information *
ABSTRACT: The relaxation induced dipolar modulation enhancement (RIDME) technique is applied at W-band microwave frequencies around 94 GHz to a pair of Gd(III) complexes that are connected by a rodlike spacer, and the extraction of the interspin distance distribution is discussed. A dipolar pattern derived from RIDME experimental data is a superposition of Pake-like dipolar patterns corresponding to the fundamental dipolar interaction and higher harmonics thereof. Intriguingly, the relative weights of the stretched patterns do not depend significantly on mixing time. As much larger modulation depths can be achieved than in double electron−electron resonance distance measurements at the same frequency, Gd(III)−Gd(III) RIDME may become attractive for structural characterization of biomacromolecules and biomolecular complexes.
SECTION: Biophysical Chemistry and Biomolecules
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incompletely spin-labeled samples or for studying weakly bound protein complexes. The modulation depth in the DEER experiment with observer spins A is determined by the fraction of spins B that can be inverted by the pump microwave pulse (Figure 1c) and thus by the ratio of pump pulse excitation bandwidth to total spectral width. In contrast, modulation depth in the RIDME experiment22,23 depends on stochastic changes of the magnetic quantum number m of the B spins by spontaneous relaxation events and is thus independent of excitation bandwidth and total spectral width. In the dead-time free version of RIDME pulse sequence (Figure 1d), the pump pulse of the analogous DEER sequence is replaced by a (π/2)−Tmix−(π/2) mixing block that restores up to half of the transverse magnetization of the A spins, while longitudinal relaxation events change the magnetic quantum number of fractions fΔm of the B spins by Δm, leading to a shift of the A spin resonance frequency by Δm ωdd, where ωdd is the dipolar frequency that encodes the distance information. For nitroxides with electron spin S = 1/2, |Δm| is bounded by 1 and the time constant of the relaxation events is the longitudinal relaxation time T1. Hence, both fΔm and the loss of A spin echo amplitude during the mixing time are on the order of exp(−Tmix/T1), and a mixing time Tmix comparable to T1 maximizes the product of echo amplitude and
uring the past two decades, distance measurements in spin-labeled macromolecules have become a very important application of pulse electron paramagnetic resonance (EPR) spectroscopy.1−7 An overwhelming majority of the reported studies utilize the double electron−electron resonance (DEER) pulse sequence8,9 for directly measuring magnetic electron−electron dipolar interactions between the paramagnetic centers from which distance distributions in the range of ∼15−80 Å can be derived by first principles. Commonly nitroxide-based spin labels are employed because of their small size, which is comparable to native amino acid side groups in proteins,10−12 and wide availability. Their main disadvantages are loss of the unpaired spin under reducing conditions, for instance, in living cells, instability at very low or very high pH, and complications of data analysis by orientation selection13 at high fields and frequencies.14,15 Over the past decade, Gd(III) complexes have been developed as alternative spin labels for high-field/high-frequency DEER measurements, which are attractive because they require much less sample volume.16−21 The Gd(III)-based spin labels do not exhibit significant orientation selection and are chemically more stable. Furthermore, their much faster longitudinal relaxation allows for DEER measurements at lower temperatures, where thermal polarization of the electron spins is higher. The sensitivity advantage arising from this higher polarization is, however, offset by an almost one order of magnitude lower depth of dipolar oscillations with respect to the total spin echo intensity than for nitroxides, which is particularly problematic for © XXXX American Chemical Society
Received: October 8, 2014 Accepted: October 30, 2014
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in modulation depth is only moderate. Another complication in RIDME measurements may arise from artifacts caused by the longitudinal nuclear spin relaxation27 or by the modulation of hyperfine couplings due to slow intramolecular motion, as was previously reported for slow methyl group reorientation in nitroxides.28 For these reasons, RIDME remained a niche technique to date, although some interesting applications were reported for organic radicals and for combining organic radicals with transition-metal centers in model compounds and proteins.29−35 Crucially, the advantage of increased modulation depth is expected to be larger for Gd(III) than for nitroxides. At cryogenic temperatures, the commonly used Gd(III) complexes in water/glycerol frozen solutions have a T2/T1 ratio in the range between 0.01 and 0.1,36 by orders of magnitude larger than the one of nitroxides. This ratio can be further increased by using deuterated solvents, which increase the transverse relaxation time T2 of Gd(III) ions by reducing hyperfine spectral diffusion, but do not significantly influence T1. (See the Supporting Information for the longitudinal relaxation data.) At Q-band frequencies (∼34 GHz), such matrix deuteration causes rather strong nuclear electron spin echo envelope modulations that complicate the analysis of RIDME data because they introduce an artifact at deuterium Larmor frequency (∼7.8 MHz at 1.2 T) that translates to distances around 1.9 nm (data not shown). However, at W-band frequencies around 94 GHz that are of greater interest, nuclear modulation depth is reduced by almost a factor of 8, and furthermore the artifact (∼22 MHz at 3.4 T) translates to a less critical distance range around 1.3 nm. Dynamic hyperfine modulation is less critical for Gd(III) complexes than for nitroxides because spin density transfer from lanthanide ions to their ligands is small and typical ligands do not have methyl groups close to the lanthanide ion that would retain mobility down to very low temperatures. These considerations suggest that Gd(III)−Gd(III) RIDME at the W band might provide higher sensitivity than W-band Gd(III)−Gd(III) DEER. However, complications arise from the Gd(III) ion having a high total electron spin of S = 7/2 (eight energy levels) as compared with only two energy levels (S = 1/2) for nitroxide radicals, which makes relaxation behavior much more complex. If we stick, for the moment, to the notion of a single longitudinal relaxation time T1, for mixing times Tmix ≫ T1, the fraction of Gd(III)−Gd(III) pairs with Δm ≠ 0, which is the sum of all fΔm except for f 0 and corresponds to the total modulation depth P(Δm ≠ 0), will attain a steady-state value that does no longer depend on Tmix. By analogy to the considerations for nitroxides,37 in the hightemperature limit, where all levels are almost equally populated, the steady-state modulation depth is P(Δm ≠ 0) = 1−1/(2S + 1). On the one hand, modulation depth converges to a larger value for Gd(III)−Gd(III) pairs (0.875) as compared with the nitroxide−nitroxide pairs (0.5), which is an advantage. On the other hand, Δm can assume any integer value between −2S and 2S, which for Gd(III) introduces higher harmonics of ωdd into the dipolar modulations that are weighted with f |Δm| = f−Δm + fΔm. The unknown weighting factors f |Δm| and, in particular, their expected dependence on experimental settings might severely complicate data analysis and lead to ambiguities. In the following, we demonstrate that this problem is far less serious than anticipated. To study dependence of Gd(III)−Gd(III) RIDME data on Tmix and compare them to DEER data, we dissolved the model
Figure 1. (a) Structural formula of the studied compound and (b) its W-band two-pulse echo-detected EPR spectrum: the arrows mark the spectral position of pump and observation pulses in DEER and the detection position in RIDME. (c) Pulse sequence of the dead-time free four-pulse DEER experiment. (d) Pulse sequence of the dead-time free five-pulse RIDME experiment.23 Note the replacement of the pump pulse in DEER by the mixing block (π/2)−Tmix−(π/2) in the RIDME experiment.
modulation depth, that is, total sensitivity. More detailed considerations show that T2-related mechanisms, such as spectral diffusion, also contribute to the loss of A spin echo amplitude, which suggests that a high T2/T1 ratio may improve RIDME sensitivity. A measurement temperature is chosen where T2 attains its low-temperature maximum to optimize sensitivity for the other building blocks of the sequence.7 For the nitroxide−nitroxide pairs, to which RIDME was first applied,22−25 the T2/T1 ratio is very small under such conditions. Although this ratio could be improved by adding relaxation enhancers,26 the technique cannot usually compete with DEER on nitroxides because in this case the improvement 3971
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Figure 2. Model-free analysis of RIDME time traces: (a) primary time traces (solid lines) and the background fits (red dashed lines); (b) form factor RIDME time traces (solid lines) and their best model-free fits by DeerAnalysis (red dashed lines); (c) comparison of the shapes of all four RIDME form factor traces with the corresponding Gd(III)−Gd(III) DEER form factor time trace; and (d) comparison of the distance distributions obtained from the model-free analysis of RIDME (green) and DEER (black) data. In panel c, all form factor time traces are rescaled for the same modulation depth for better visualization. RIDME data shown: Tmix = 4 μs (violet), Tmix = 8 μs (light blue), Tmix = 16 μs (navy blue), and Tmix = 24 μs (green). Pulse settings: first interpulse delay d1 = 400 ns; initial second delay d2 = 280 ns; initial last interpulse delay d3 = 3 μs; (π/2) = 12 ns; (π) = 24 ns. Concentration: 500 μM.
For comparison, the 1/e decay time for the longitudinal magnetization of Gd(III) centers in the studied model compound, which is a proxy for a universal longitudinal relaxation time T1, is in the range between 13 and 15 μs. (See the Supporting Information.) In contrast with RIDME, the reference Gd(III)−Gd(III) DEER experiment yields a small modulation depth of only ∼0.05. (See the Supporting Information.) As a prerequisite to distance distribution analysis, intermolecular background was removed from the experimental RIDME time traces with the DeerAnalysis software.39 Stretched exponential background functions were empirically chosen, the primary time traces were divided by these functions (form factors shown in Figure 2b), and the constant contribution f 0 was removed before further processing. If the renormalized dipolar evolution functions are naively processed by the same Tikhonov regularization that is used for the DEER data, an apparent distance distribution results that differs from the correct distribution measured with the DEER experiment (Figure 2d). In this difference, the main artifact peak near 2.8 nm arises from the |Δm| = 2 contribution, whereas |Δm| > 2 contributions appear to be minor. Surprisingly and significantly, the shape of the RIDME form factors does not depend significantly on mixing time Tmix (Figure 2b): after renormalization, the dipolar evolution functions superimpose almost perfectly (Figure 2c). In other words, while f 0 decreases and P(Δm ≠ 0) increases with
compound (Figure 1a) that contains two Gd(III) complexes connected by a rodlike spacer (the multistep synthesis of the model compound will be published separately) to a concentration of 500 μM in D2O with 50% (v/v) glycerol-d8. The solution was filled into a quartz sample tube (i.d. 0.6 mm, o.d. 0.84 mm) and subsequently shock-frozen by immersion into liquid nitrogen. The pulsed EPR experiments were performed on a modified commercial W-band EPR spectrometer (Bruker Elexsys E680) operating at ∼94 GHz.38 All experiments were carried out using a home-built W-band ENDOR cavity with a microwave frequency bandwidth of 130 MHz.38 The sample temperature was stabilized with a helium flow cryostat. RIDME measurements were done using the following pulse sequence: (π/2)−d1−(π)−d2−(π/2)−Tmix− (π/2)−d3−(π)−d4−echo (with d4 = d2 + d3 − d1) (Figure 1d).23 RIDME pulse settings were: first interpulse delay d1 = 400 ns; initial second delay d2 = 280 ns; initial last interpulse delay d3 = 3 μs; (π/2) = 12 ns; (π) = 24 ns. Pulse settings for the reference DEER measurements were: (π/2)det = 16 ns; (π)det = 32 ns; (π)pump = 16 ns. We recorded a series of RIDME time traces with mixing times Tmix= 4, 8, 16, and 24 μs at temperature T = 20 K (Figure 2). The eight-step phase-cycling protocol was used, and the RIDME signal was detected on the refocused virtual echo, as has been described previously.23 As expected, we observed buildup of dipolar oscillations at much shorter mixing times than for nitroxide-nitroxide pairs, and a modulation depth of ∼0.55 was reached at the longest tested mixing time of 24 μs. 3972
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Figure 3. Model-based analysis of RIDME time traces: (a) distance distribution from the model-free fit of DEER data (black) and the approximation of the main peak by a Gaussian function (blue); (b) FT form factor (dipolar pattern) resulting from the Gaussian approximation of the DEER data (Δm = 1, myrtle green) along with its stretched modifications by stretching factor of Δm = 2 (red), Δm = 3 (blue), Δm = 4 (green), Δm = 5 (orange), Δm = 6 (bordeaux), and Δm = 7 (purple); and (c) RIDME form factor time trace (black) and its best fit (blue) as a linear combination of the first three stretched dipolar patterns from (b) Δm = 1, 2, 3 with weights f1 = f 2 = 0.44 and f 3 = 0.12. The inset in panel c shows the comparison of the corresponding experimental and simulated FT form factors, color code as for the time domain data. Gaussian fit parameters: ⟨r⟩ = 3.5 nm; σr = 0.15 nm.
increasing mixing time, ratios between f |Δm| with different |Δm| ≠ 0 are constants of motion within our experimental precision. Fitting of the RIDME form factor by a distance distribution is most easily understood on the basis of the dipolar spectrum, which is the Fourier-transform (FT) of the form factor (Figure 3). In DEER to a good approximation the pump pulse only inverts single-quantum transitions, so that the resonance frequency of A spins can only change by the basic dipolar frequency ωdd. For a fixed distance, the dipolar spectrum is then a Pake pattern. In contrast, in the RIDME experiment, an arbitrary number of relaxation events between states with different magnetic quantum number m can happen during the mixing period. In addition, even a single relaxation event can, in principle, change m by any nonzero integer between -S − m and S − m. Thus, modulation contributions by higher harmonics of the dipolar frequency of up to 7ωdd are expected for Gd(III). Because modulation is described by the even function cos(Δm ωdd t), only the absolute value |Δm| is of concern. The corresponding dipolar patterns for the higher order relaxation events can be described by stretching the primary first-order dipolar pattern by |Δm|. After approximating the DEER-based distance distribution with a Gaussian function (Figure 3a), we calculated the corresponding time-domain and FT form factors by Gaussian convolution in distance domain and simulated the experimental RIDME FT form factors by a linear combination of the stretched FT form factors (Figure 3b) with coefficients f |Δm| (Figure 3c). Including the contributions with |Δm| ≥ 4 did not significantly influence the output, and they were thus discarded in the analysis. We found that the combination of equal fractions f1 = f 2 = 0.44 of the basic and the second harmonic dipolar pattern and a fraction f 3 = 0.12 of the third harmonic pattern reproduces the experimental data quite well (Figure 3c). The remaining deviations may be caused by the oversimplified model of a Gaussian distance distribution. This proportion is valid for all four detected RIDME traces because the shape of the form factor traces does not depend on mixing time. In fact, we had expected a dependence of the form factor on mixing time because the probability of multiple spin flips and thus the contribution of higher harmonics should increase with increasing mixing time. Only at very long mixing times a steady state should be reached; however, such times are clearly not
attained in our experiments, where modulation depth increases throughout the whole range of mixing times and the values Tmix are comparable to the longitudinal relaxation time of the Gd(III) centers. (See the Supporting Information.) To understand the unexpected behavior, we now turn to a simplified kinetic analysis. For this, we denote those spin pairs, for which no relaxation events of the B spins have happened during the mixing time, as species B0 and those with |Δm| = 1, 2, 3... as B1, B2, B3... and assume that the system can be described by a set of linear differential equations, determining the evolution of populations for species B0, B1, B2, B3... If only single-quantum relaxation (|Δm| = 1) is possible as an individual relaxation event, then higher harmonics can arise only from a series of relaxation events B0 → B1 → B2 → B3... Because before the mixing time only species B0 is present, for Tmix ≪ T1 species B1 would be populated approximately linear with time, species B2 would build up with t2, and so on. In such a case, the relative ratios B1/ B2 and B1/B3 would decrease with time, which is not what we observe. In contrast, if individual relaxation events can change m by two (double-quantum relaxation) and three (triplequantum relaxation) and if the contribution of trajectories with only a single event dominates, we deal with kinetics as in parallel first-order reactions for which the relative fractions of the “product” species B1, B2, and B3 are indeed a constant of motion. When relaxing the simplifying assumptions, we find that rate constants k1 = 19800 s−1, k2 = 25100 s−1, and k3 = 5820 s−1 are consistent with our observations within experimental precision (Supporting Information Figure S3). Note that this kinetic analysis is preliminary. The presence of a direct process with |Δm| = 3 is quite unusual, and Figures 2 and 3 indicate that the presence of such direct process can be suggested with less certainty than for the |Δm| = 2. A potential possibility of the relaxation events with |Δm| = 3 might be rationalized by considering a relaxation event, which is of a second order on the ZFS. The jj coupling between f electrons in the Gd(III) multiplet contains terms of a form S1S2 and might thus induce change of |Δm| ≤ 2. The relaxation event, consisting of an excitation to an upper fine structure multiplet with a consequent relaxation back to the ground multiplet might, accordingly, induce transitions with |Δm| ≤ 4. A detailed 3973
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band16,19), the W-band RIDME experiments have modulation depths up to ten times higher, comparable to the ones in the benchmark nitroxide−nitroxide DEER measurements at Xband and Q-band frequencies. Although ultrawideband pump pulses40,41 may improve Gd(III)−Gd(III) DEER modulation depths, our preliminary experiments show that they would remain much smaller than with RIDME. Considering the smaller sample volume required for W-band experiments in combination with large dipolar modulation depths, Gd(III)− Gd(III) RIDME may lead to a combination of very high absolute and concentration sensitivities that surpass the performance of W-band Gd(III)−Gd(III) DEER. Whether this potential can be realized will depend on better understanding of relaxation kinetics of Gd(III) centers and of RIDME background decay functions. Further experiments along these lines are currently in progress in our laboratories.
analysis of the longitudinal relaxation kinetics requires additional RIDME experiments at different temperatures for Gd(III)−Gd(III) pairs with other distances and for other ligand structures. Such studies are also expected to provide new insights into the relaxation processes in Gd(III) centers. Our preliminary measurements indicate that at 10 K and at 30 K the relative weights of the dipolar harmonics are also approximately constant at different mixing times Tmix, whereas these weights are temperature-dependent. If this independence of the Gd(III)−Gd(III) RIDME form factor traces on mixing time turns out to be a general feature, data can be analyzed in terms of distance distributions in a similar way as DEER data. Analysis of RIDME data would just require modification of the Tikhonov kernel that should be constructed by linear combination of the fundamental, second, and third harmonic dipolar evolution functions with known fixed weights. Further development also needs to address the background functions, which are for now purely empirical. Theoretical understanding of these functions and experimental validation of the background model may be required to minimize background correction artifacts for broader distance distributions. Here we note that for nitroxides and organic radicals, in general, the main contribution to the background decay comes from the interaction of paramagnetic centers with the surrounding magnetic nuclei.23 The RIDME background decay is thus determined by nuclear spin diffusion, which has a nearly constant rate at temperatures around 10−30 K, where RIDME experiments on Gd(III)−Gd(III) pairs seem to be feasible. If Gd(III) complexes behave in the same way, the background function will depend on mixing time, but for sufficiently dilute samples not on sample concentration or spin labeling efficiency. We further note that for long mixing times the RIDME time traces decay faster than the DEER trace, as expected under the assumption of an additional, nuclear modulation-related decay mechanism. Such faster decay leads to reduced signal-to-noise ratio in the form factor at long times because the primary data are divided by the background decay function. This would also shorten the maximum detectable length of the time trace, which is directly connected to the longest measurable distance. Note, however, that background decay rate and modulation depth are coupled in both DEER and RIDME. A quantitative estimate of the influence of differences in background decay on signal-tonoise ratio requires scaling to the same modulation depth, which is nontrivial, because spectral information in DEER and RIDME traces is not the same. Also note that detection of a full oscillation at the second harmonic requires only half the dipolar evolution time as detection of one period of the fundamental frequency. Hence, a shorter RIDME trace, which has better signal-to-noise ratio, may contain the same (or comparable) distance distribution information as contained in a longer DEER trace. Further work is thus required to find out whether RIDME or DEER provides access to longer Gd(III)−Gd(III) distances. To conclude, our results indicate that for Gd(III)−Gd(III) pairs at W-band frequencies relative performance of RIDME compared with DEER distance measurements is much better than for nitroxide−nitroxide pairs at X band. Furthermore, RIDME data analysis for this system of paired S = 7/2 spins appears to be simpler and more robust than expected. Unlike Gd(III)−Gd(III) DEER experiments at the W band, in which maximum modulation depth of ∼0.05 can be observed16,18,20 (similar or yet lower modulation depths are observed at Q
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ASSOCIATED CONTENT
S Supporting Information *
Author contributions, echo-detected EPR spectrum and fieldresolved longitudinal relaxation data, details of DEER measurements, and details of kinetic model to simulate the RIDME data. This material is available free of charge via the Internet at http://pubs.acs.org.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS We acknowledge financial support by the Max-PlanckGesellschaft (A.N. and A.S.), SNSF (S.R., M.Y., and G.J., grant 200020_14441), and DFG (M.Q., and A.G., SPP1601). M.Y. is thankful to Prof. Leonid Kulik (Novosibisk Institute of Chemical Kinetics and Combustion) for discussions on the RIDME technique.
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REFERENCES
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