Focus: Two-dimensional electron-electron double resonance and molecular motions: The challenge of higher frequencies

Abstract

The development, applications, and current challenges of the pulsed ESR technique of two-dimensional Electron-Electron Double Resonance (2D ELDOR) are described. This is a three-pulse technique akin to 2D Exchange Nuclear Magnetic Resonance, but involving electron spins, usually in the form of spin-probes or spin-labels. As a result, it required the extension to much higher frequencies, i.e., microwaves, and much faster time scales, with π/2 pulses in the 2-3 ns range. It has proven very useful for studying molecular dynamics in complex fluids, and spectral results can be explained by fitting theoretical models (also described) that provide a detailed analysis of the molecular dynamics and structure. We discuss concepts that also appear in other forms of 2D spectroscopy but emphasize the unique advantages and difficulties that are intrinsic to ESR. Advantages include the ability to tune the resonance frequency, in order to probe different motional ranges, while challenges include the high ratio of the detection dead time vs. the relaxation times. We review several important 2D ELDOR studies of molecular dynamics. (1) The results from a spin probe dissolved in a liquid crystal are followed throughout the isotropic → nematic → liquid-like smectic → solid-like smectic → crystalline phases as the temperature is reduced and are interpreted in terms of the slowly relaxing local structure model. Here, the labeled molecule is undergoing overall motion in the macroscopically aligned sample, as well as responding to local site fluctuations. (2) Several examples involving model phospholipid membranes are provided, including the dynamic structural characterization of the boundary lipid that coats a transmembrane peptide dimer. Additionally, subtle differences can be elicited for the phospholipid membrane phases: liquid disordered, liquid ordered, and gel, and the subtle effects upon the membrane, of antigen cross-linking of receptors on the surface of plasma membrane, vesicles can be observed. These 2D ELDOR experiments are performed as a function of mixing time, Tm, i.e., the time between the second and third π/2 pulses, which provides a third dimension. In fact, a fourth dimension may be added by varying the ESR frequency/magnetic field combination. Therefore, (3) it is shown how continuous-wave multifrequency ESR studies enable the decomposition of complex dynamics of, e.g., proteins by virtue of their respective time scales. These studies motivate our current efforts that are directed to extend 2D ELDOR to higher frequencies, 95 GHz in particular (from 9 and 17 GHz), in order to enable multi-frequency 2D ELDOR. This required the development of quasi-optical methods for performing the mm-wave experiments, which are summarized. We demonstrate state-of-the-art 95 GHz 2D ELDOR spectroscopy through its ability to resolve the two signals from a spin probe dissolved in both the lipid phase and the coexisting aqueous phase. As current 95 GHz experiments are restricted by limited spectral coverage of the π/2 pulse, as well as the very short T2 relaxation times of the electron spins, we discuss how these limitations are being addressed.

FIG. 1.

The pulse sequences for (a) the standard 2D ELDOR experiment and (b) SECSY format of 2D ELDOR experiments. The two coherence pathways for this experiment are also shown.

FIG. 2.

2D ELDOR signals at 17.3 GHz versus mixing time, T_m, of 16-PC in liquid-crystalline phase from pure lipid vesicles (left column) compared with 16 PC in liquid-ordered phase (right column) from 1:1 ratio lipid to cholesterol at 51 °C. Modified with permission from J. H. Freed, Annu. Rev. Phys. Chem. 51, 655 (2000). Copyright 2000 by Annual Reviews.

FIG. 3.

Reference frames that define the orientation of a sample to study its structural and dynamic properties. (i) Lab frame (LF) is defined with respect to the external magnetic field, whose direction is used as its z-axis; (ii) director frame (DF) is defined by the local director, $\hat{n}$, tilted relative to the magnetic field by the angle ψ and obtained by the transformation by the set of Euler angles Ψ_L→D from LF to DF; (iii) molecular frame (MF) is fixed within the molecule and obtained by the transformation by the set of Euler angles Ω_D→M; (iv) g-tensor frame (GF), the principal-axes frame of the g-tensor of the unpaired electron is obtained using the transformation Φ_M→G from MF to GF; (v) A-tensor frame (AF), defined by the principal-axes of the A-tensor, is obtained using Ω_A from GF to AF.

FIG. 4.

(a) Rotational diffusion coefficients for the probe: $R_{\parallel }^0$ (open circles) and $R_{\perp }^0$ (open triangles), as well as the cage (plus signs), plotted as a function of temperature. (b) Mean field (macroscopic) orienting potential parameters: $a_0^2$ (open circles) and $a_2^2$ (open triangles) as a function of temperature. (c) Cage potential parameters: $c_0^2$ (open circles) and $c_2^2$ (open triangles) as a function of temperature (fits to SRLS model; adapted with permission from V. S. S. Sastry et al., J. Chem. Phys. 105, 5753 (1996); copyright 1996 by AIP Publishing LLC).

FIG. 5.

Contour plots of the 3 lipid phases: approximate absorption 2D ELDOR spectra in the SECSY format (cf. Fig. 1), acquired from samples of 16-PC in DPPC-cholesterol vesicles, in the normalized contour presentation, which displays the homogeneous linewidths in the f₁ direction. The upper, middle, and lower contours represent L_d, L_o, and gel phases, respectively. Reprinted with permission from Fig. 5 of Y. W. Chiang et al., Appl. Magn. Reson. 31, 375 (2007). Copyright 2007 by Springer International Publishing AG.

FIG. 6.

(Top) Phase diagram of binary mixtures of DPPC-cholesterol containing 16-PC determined according to 2D ELDOR analysis. Triangles and filled circles indicate the compositions studied. (Bottom) 2D ELDOR spectra, from compositions as marked, show distinctive patterns and line shape variations for one to characterize the membrane phases. (Standard magnitude mode shown for convenience; reprinted with permission from Fig. 6 of Y. W. Chiang et al., Appl. Magn. Reson. 31, 375 (2007). Copyright 2007 by Springer International Publishing AG.⁵⁶)

FIG. 7.

The two 2D ELDOR pure absorption spectral components (in the SECSY mode) representing the coexisting L_o and L_d regions in the PMV. They were obtained from the best theoretical fit to the experimental spectrum for the un-cross-linked PMV at 30 °C for T_m = 50 ns. Reprinted with permission from Y.-W. Chiang et al., J. Phys. Chem. B 115, 10462 (2011). Copyright 2011 by American Chemical Society.

FIG. 8.

The population of the L_o component, coexisting with the L_d, in the uncross-linked versus cross-linked PMV samples with respect to temperature. Reprinted with permission from Y.-W. Chiang et al., J. Phys. Chem. B 115, 10462 (2011). Copyright 2011 by American Chemical Society.

FIG. 9.

ESR spectra of PDT/toluene at 250 GHz in various motional regimes: motional narrowing (−40 °C, −60 °C), slow motion (−81 °C, −100 °C), and rigid limit (−119 °C, −129 °C). Reproduced with permission from Fig. 11.1 of S. K. Misra and J. H. Freed, “Molecular motions,” in Multifrequency Electron Paramagnetic Resonance (Wiley-VCH Verlag GmbH & Co. KGaA, 2011), pp. 497–544 (cf. Ref. 58). Copyright 2011 by Wiley-VCH Verlag GmbH & Co. KGaA.

FIG. 10.

Simulated first-derivative multifrequency ESR spectra for a nitroxide, reorienting with a rotational diffusion constant R = 10⁸ s⁻¹ (corresponding to rotational correlation time τ_R = 1.67 ns) in the range 15–2000 GHz. From this, it is clear that a motional process that appears fast at lower frequencies will appear slow at higher frequencies. Modified with permission from J. H. Freed, Annu. Rev. Phys. Chem. 51, 655 (2000). Copyright 2000 by Annual Reviews.

FIG. 11.

An example of how multifrequency ESR distinguishes motion at different temperatures, as exhibited by the ESR spectra of T4 lysozyme spin-labeled at mutant site 72 at 9, 95, 170, and 240 GHz at 2, 12, 22, and 32 °C. (Left panel of figure adapted with permission from Z. Zhang et al., J. Phys. Chem. B 114, 5503 (2010). Copyright 2010 by American Chemical Society. Right panel of figure generated from PDB 1YLD, structure rendered by PyMOL, Schrödinger, LLC.)

FIG. 12.

Schematic diagram of a typical quasioptical bridge: A quasioptical beam is launched from the transmitter (Tx) at the bottom right of the figure, reflected off the wire-grid polarizer, and directed into the corrugated waveguide. The reflected signal that has orthogonal polarization to the transmitted pulse passes through the first wire-grid polarizer, where it is focused by the mirror onto the receiver (Rx). The second wire-grid polarizer and the associated Faraday rotator (at the top of the figure) provide additional isolation between the signal and the transmitted pulses. Adapted with permission from Fig. 8 of Earle et al., Magn. Reson. Chem. 43, S256 (2005). Copyright 2005 by John Wiley & Sons, Ltd.

FIG. 13.

The ESR probehead: differential screw drives attached to the various components allow simultaneous adjustment of the resonant frequency (via the mirror adjustment) characteristic impedance (via the semitransparent mirror/mesh adjustment) and sample positioning. Adapted with permission from Fig. 8 of K. A. Earle et al., Magn. Reson. Chem. 43, S256 (2005). Copyright 2005 by John Wiley & Sons, Ltd.

FIG. 14.

Reprinted with permission from W. Hofbauer et al., Rev. Sci. Instrum. 75, 1194 (2004). Copyright 2004 by AIP Publishing LLC. Spectrometer block diagram. The low-power (90 mW) transmitter-receiver is augmented with a 1 kW mm-wave amplifier (EIK). Transmit and receive signal paths are duplexed in a quasioptical setup, as shown in Fig. 12.

FIG. 15.

For an isotropically tumbling nitroxide, the T₂ decay time will exhibit a minimum as the system transitions from the rigid limit (very slow tumbling) to the rapidly tumbling limit. As the ESR frequency increases, this minimum T₂ time shifts to faster tumbling rates and smaller absolute values. At 95 GHz, it is 10⁸ s⁻¹ and 4 ns, respectively. The rectangular box shows the range of motional rates—spanning approximately 2 orders of magnitude—that are inaccessible with the current dead times. The experimental spectra shown underneath are examples of data acquired outside this range. (Black inset simulation of T₂ vs. correlation time from Ref. ; adapted with permission from Fig. 9 of K. A. Earle et al., Magn. Reson. Chem. 43, S256 (2005). Copyright 2005 by John Wiley & Sons, Ltd.)

FIG. 16.

A spin-echo experiment, acquired with 7 min of signal averaging from a sample of 1.5 mM TEMPO dissolved in dibutyl pthalate at 17 °C, measures the T₂ decay (along t_echo) of the signal amplitude across all frequency components, f, of the spectrum. Note how the spectral component with ∼20 ns is close to the detection threshold. This component has approximately half the signal to noise of the ∼34 ns component.

FIG. 17.

Signal from a sample of 1 mM TEMPO partitioned between water and 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC). In contrast to a typical 9.4 GHz cw spectrum (top left panel), the spectrum at 95 GHz (bottom left pane) demonstrates the benefits of the increased g-anisotropy, permitting a better distinction between nitroxides in the lipid vs water phase, leading to noticeable changes in the spectra at different temperatures. The extra dimension of 2D ELDOR allows separation of the peaks arising from the nitroxide partitioning in the two different phases. Note that at 17 °C, we begin to see the limitations of the current state-of-the-art—the signal with shorter T₂ from the TEMPO in the lipid phase decays during the spectrometer dead time before detection of the 2D ELDOR signal begins, leaving only signal from the component that resides in the water.