Two‐dimensional electron–electron double resonance and electron spin–echo study of solute dynamics in smectics

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

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.

2D-ELDOR using full S(c-) fitting and absorption lineshapes

Recent progress in developing 2D-ELDOR (2D electron-electron double resonance) techniques to better capture molecular dynamics in complex fluids, particularly in model and biological membranes, is reported. The new "full S(c-) method", which corrects the spectral analysis for the phase distortion effects present in the experiments, is demonstrated to enhance the sensitivity of 2D-ELDOR in reporting on molecular dynamics in complex membrane environments. That is, instead of performing spectral fitting in the magnitude mode, our new method enables simultaneous fitting of both the real and imaginary components of the S(c-) signal. The full S(c-) fitting not only corrects the phase distortions in the experimental data but also more accurately determines instrumental dead times. The phase corrections applied to the S(c-) spectrum enable the extraction of the pure absorption-mode spectrum, which is characterized by much better resolution than the magnitude-mode spectrum. In the absorption mode, the variation of homogeneous broadening, which reports on the dynamics of the spin probe, can even be observed by visual inspection. This new method is illustrated with results from model membranes of dipalmitoyl-sn-glycero-phosphatidylcholine (DPPC)-cholesterol binary mixtures, as well as with results from plasma membrane vesicles of mast cells. In addition to the dynamic parameters, which provide quantitative descriptions for membranes at the molecular level, the high-resolution absorption spectra themselves may be used as a "fingerprint" to characterize membrane phases and distinguish coexisting components in biomembranes. Thus we find that 2D-ELDOR is greatly improved with the new "full S(c-) method" especially for exploring the complexity of model and biological membranes.

Effects of finite pulse width on two-dimensional Fourier transform electron spin resonance

Two-dimensional (2D) Fourier transform ESR techniques, such as 2D-ELDOR, have considerably improved the resolution of ESR in studies of molecular dynamics in complex fluids such as liquid crystals and membrane vesicles and in spin labeled polymers and peptides. A well-developed theory based on the stochastic Liouville equation (SLE) has been successfully employed to analyze these experiments. However, one fundamental assumption has been utilized to simplify the complex analysis, viz. the pulses have been treated as ideal non-selective ones, which therefore provide uniform irradiation of the whole spectrum. In actual experiments, the pulses are of finite width causing deviations from the theoretical predictions, a problem that is exacerbated by experiments performed at higher frequencies. In the present paper we provide a method to deal with the full SLE including the explicit role of the molecular dynamics, the spin Hamiltonian and the radiation field during the pulse. The computations are rendered more manageable by utilizing the Trotter formula, which is adapted to handle this SLE in what we call a "Split Super-Operator" method. Examples are given for different motional regimes, which show how 2D-ELDOR spectra are affected by the finite pulse widths. The theory shows good agreement with 2D-ELDOR experiments performed as a function of pulse width.

New technologies in electron spin resonance

New electron spin resonance (ESR) technologies have been developed, which have led to new and improved applications. (a) The development of two-dimensional Fourier transform (FT) ESR required spectrometers providing intense pi/2 microwave pulses of very short (3-5 ns) duration, wide bandwidths, and very short dead times. It has enabled studies that resolve sophisticated details of molecular dynamics in complex fluids. (b) Methods that produce multiple quantum coherences by pulsed ESR now enable accurate measurements of large distances (>12A). (c) One of the most important advances has been the extension of ESR to high magnetic fields and high frequencies. This has benefited from the utilization of quasi-optical methods, especially above 150 GHz. The greatly improved orientational resolution and the faster "snapshot" of motions that are provided by ESR at high frequencies enhance studies of molecular dynamics. The use of both high and lower frequencies enables one to unravel faster and slower modes from the complex dynamics of fluids and macromolecules. (d) The development of FT-ESR imaging required substantial pulsed field gradients lasting only 50-100 ns. ESR imaging is effective in studying diffusion in fluids. Areas for further development are also described.

Multifrequency two-dimensional Fourier transform ESR: an X/Ku-band spectrometer

A two-dimensional Fourier Transform ESR (2D FT ESR) spectrometer operating at 9.25 and 17.35 GHz is described. The Ku-band bridge uses an efficient heterodyne technique wherein 9.25 GHz is the intermediate frequency. At Ku-band the sensitivity is increased by almost an order of magnitude. One may routinely collect a full 2D ELDOR spectrum in less than 20 min for a sample containing 0.5-5 nmol of nitroxide spin-probe in the slow-motional regime. Broad spectral coverage at Ku-band is obtained by use of a bridged loop-gap resonator (BLGR) and of a dielectric ring resonator (DR). It is shown that an even more uniform spectral excitation is obtained by using shorter microwave pulses of about 3 ns duration. The dead-time at Ku-band is just 30-40 ns, yielding an improved SNR in 2D ELDOR spectra of nitroxide spin-probes with T2 as short as 20-30 ns. A comparison of 2D ELDOR spectra obtained at 9.25 and 17. 35 GHz for spin-labeled phospholipid probes (16PC) in 1,2-dimyristoyl-sn-glycero-3-phosphoglycerol (DMPG) membrane vesicles showed that both spectra could be satisfactorily simulated using the same set of model parameters even though they are markedly different in appearance. The improved sensitivity and shorter dead-time at Ku-band made it possible to obtain orientation-dependent 2D ELDOR spectra of the Cholestane (CSL) spin-probe in macroscopically aligned lipid bilayers of egg yolk PC using samples containing only 1 mg of lipid and just 5 nmol of spin-probe.

Selective placement of electron spin resonance spin labels: new structural methods for peptides and proteins

Electron spin resonance (ESR) is more powerful than ever as a technique for solving biochemical and biophysical problems. Part of the great utility of ESR arises from the use of modern biochemical methods to place spin labels at important positions along the primary sequence of a peptide or protein.