Two-dimensional ESR Research Articles

Microsecond dynamics in proteins by two-dimensional ESR. II. Addressing computational challenges

Two-dimensional electron-electron double resonance (2D-ELDOR) provides extensive insight into molecular motions. Recent developments permitting experiments at higher frequencies (95 GHz) provide molecular orientational resolution, enabling a clearer description of the nature of the motions. In previous work, we provided simulations for the case of domain motions within proteins that are themselves slowly tumbling in a solution. In order to perform these simulations, it was found that the standard approach of solving the relevant stochastic Liouville equation using the efficient Lanczos algorithm for this case breaks down, so algorithms were employed that rely on the Arnoldi iteration. While they lead to accurate simulations, they are very time-consuming. In this work, we focus on a variant known as the rational Arnoldi algorithm. We show that this can achieve a significant reduction in computation time. The stochastic Liouville matrix, which is of very large dimension, N, is first reduced to a much smaller dimension, m, e.g., from N ∼ O(104) to m ∼ 60, that spans the relevant Krylov subspace from which the spectrum is predicted. This requires the selection of the m frequency shifts to be utilized. A method of adaptive shift choice is introduced to optimize this selection. We also find that these procedures help in optimizing the pruning procedure that greatly reduces the dimension of the initial N dimensional stochastic Liouville matrix in such subsequent computations.

Microsecond Exchange Processes Studied by Two-Dimensional ESR at 95 GHz.

Exchange processes which include conformational change, protonation/deprotonation, and binding equilibria are routinely studied by 2D exchange NMR techniques, where information about the exchange of nuclei between environments with different NMR shifts is obtained from the development of cross-peaks. Whereas 2D NMR enables the real time study of millisecond and slower exchange processes, 2D ESR in the form of 2D-ELDOR (two-dimensional electron-electron double resonance) has the potential for such studies over the nanosecond to microsecond real time scales. Cross-peak development due to chemical exchange has been seen previously for semiquinones in ESR, but this is not possible for most common ESR probes, such as nitroxides, studied at typical ESR frequencies because, unlike NMR, the exchanging states yield ESR signals that are not resolved from each other within their respective line widths. But at 95 GHz, it becomes possible to resolve them in many cases because of the increased g-factor resolution. The 95 GHz instrumental developments occurring at ACERT now enable such studies. We demonstrate these new capabilities in two studies: (A) the protonation/deprotonation process for a pH-sensitive imidazoline spin label in aqueous solution where the exchange rate and the population ratio of the exchanging states are controlled by the concentration and pH of the buffer solution, respectively, and (B) a nitroxide radical partitioning between polar (aqueous) and nonpolar (phospholipid) environments in multilamellar lipid vesicles, where the cross-peak development arises from the exchange of the nitroxide between the two phases. This work represents the first example of the observation and analysis of cross-peaks arising from chemical exchange processes involving nitroxide spin labels.

Microsecond dynamics in proteins by two-dimensional ESR: Predictions.

Two-dimensional electron-electron double resonance (2D-ELDOR) provides extensive insight into molecular motions. Recent developments permitting experiments at higher frequencies (95 GHz) provide molecular orientational resolution, enabling a clearer description of the nature of the motions. In this work, simulations are provided for the example of domain motions within proteins that are themselves slowly tumbling in solution. These show the nature of the exchange cross-peaks that are predicted to develop in real time from such domain motions. However, we find that the existing theoretical methods for computing 2D-ELDOR experiments over a wide motional range begin to fail seriously when applied to very slow motions characteristic of proteins in solution. One reason is the failure to obtain accurate eigenvectors and eigenvalues of the complex symmetric stochastic Liouville matrices describing the experiment when computed by the efficient Lanczos algorithm in the range of very slow motion. Another, perhaps more serious, issue is that these matrices are "non-normal," such that for the very slow motional range even rigorous diagonalization algorithms do not yield the correct eigenvalues and eigenvectors. We have employed algorithms that overcome both these issues and lead to valid 2D-ELDOR predictions even for motions approaching the rigid limit. They are utilized to describe the development of cross-peaks in 2D-ELDOR at 95 GHz for a particular case of domain motion.

Effect of fluorine position on the coordinating ability of fluorosalicylic acids — An experimental study complemented with computations

The complexation of 3-, 4-, and 6-fluorosalicylic acids (HL) with copper(II) was investigated in aqueous solution by pH-potentiometry combined with UV–visible spectrophotometry, and in 50v/v % water–methanol mixture by the two-dimensional ESR simulation method. Both methods showed the formation of [CuLH−1] and [CuL2H−2]2− of high stabilities, and, at low excess of ligand, the ESR-silent mixed hydroxido complex [Cu2L2H−3]−. Further species were also identified by the two-dimensional ESR simulation method: [CuL]+ in the acidic region, the minor dimer [Cu2L2H−2], and the cis and the trans isomers for [CuL2H−2]2−. The position of the fluorine atom in the aromatic ring had significant effect on the coordination abilities of the ligands, in good correlation with their reported biological activities. It was 3-fluorosalicylic acid, which formed the most stable complexes [CuLH−1] and [CuL2H−2]2−, while the mononuclear complexes with 6-fluorosalicylic acid were found to be the least stable. For the other ligands (including 5-fluorosalicylic acid studied recently), complexes of medium stabilities were formed. For the interpretation of these findings, ab initio and semi-empirical quantum chemical calculations were carried out for the ligand molecules, isolated and surrounded by water molecules, respectively.

Equilibria of 3-Pyridylmethanol with Copper(II). A Comparative Electron Spin Resonance Study by the Decomposition of Spectra in Liquid and Frozen Solutions

The copper(II)-3-pyridylmethanol (L) system was investigated in aqueous solution by two-dimensional ESR evaluation at 298 K, and computer simulation of the individual anisotropic spectra at 77 K. The data revealed that the paramagnetic copper(II) complexes [CuL] (2+), [CuL 2] (2+), [CuL 3] (2+), and [CuL 4] (2+) are formed up to pH approximately 7 at a moderate or high excess of ligand. As compared with chelating ligands, two differences were observed for the complexation of 3-pyridylmethanol with copper(II): (1) In contrast with the well-resolved spectra in frozen solution, considerable line-broadening and distortion of the spectral shapes were seen at 298 K, which was interpreted in terms of isomeric equilibria and the medium-rate interconversion of various complexes on the ESR time-scale. (2) At low temperature, there were dramatic changes in the concentration distribution, the minor complexes with higher numbers of coordinating ligands ([CuL 3] (2+) and in particular [CuL 4] (2+)) becoming strongly favored. This phenomenon is explained by the significant differences in the formation enthalpy values of various species, shifting the equilibria according to the van't Hoff equation, and a significant undercooling in the course of fast freezing of the solution, which enhances the changes of the concentration distribution.

Complexation of 5-fluorosalicylic acid with copper(II): A pH-potentiometric, UV–vis spectroscopic, and electron spin resonance study by the two-dimensional simulation of spectra

The copper(II)–5-fluorosalicylic acid system was investigated in water and 50 v/v% water–methanol mixture by pH potentiometry combined with UV–vis spectrophotometry, and by the two-dimensional ESR simulation method, respectively. The data revealed that the stable paramagnetic mono- and bis(salicylato) copper(II) complexes [CuLH −1] and [CuL 2H −2] 2− are formed, and at low excess of ligand, the ESR-silent mixed hydroxo complex [Cu 2L 2H −3] − is also a major species. By the two-dimensional ESR simulation method, the species [CuL] + in the acidic region, and the minor dimer [Cu 2L 2H −2] were also identified, and the cis and trans isomers of [CuL 2H −2] 2− were characterized. In frozen solutions, the ESR analysis revealed a slight rhombic distortion of coordination polyhedra for the latter three species.

Assessment of ESR-CT imaging by comparison with autoradiography for the distribution of a blood-brain-barrier permeable spin probe, MC-PROXYL, to rodent brain

Blood-brain-barrier (BBB)-permeable, 3-methoxycarbonyl-2,2,5,5-tetramethylpyrrolidine-1-yloxy (MC-PROXYL) and BBB-impermeable carbamoyl-PROXYL were used to assess the ESR imaging technique by comparing with autoradiography. For this purpose, spin probes, 14C-labeled at their five-membered ring, [14C]MC-PROXYL and [14C]carbamoyl-PROXYL, were newly synthesized. These probes were i.p. or i.v. injected into rats and autoradiograms were recorded. The autoradiograms of rat head showed that [14C]MC-PROXYL distributed well in the brain compared to [14C]carbamoyl-PROXYL. In vivo ESR spectra and two-dimensional ESR images of isolated rat brain treated with MC- or carbamoyl-PROXYL also indicated the extensive distribution of MC-PROXYL but not carbamoyl-PROXYL in the rat brain. The three-dimensional ESR images of the head of rats and mice were consistent with the fact that MC-PROXYL but not carbamoyl-PROXYL is incorporated into the brain. The ESR-CT images were better for mice than rats. However, the quality of the ESR-CT images was still not satisfactory. Although the resolution and sensitivity of the ESR-CT images were worse than those of the autoradiographic images, the former technique has unique features and advantages; e.g., functional, noninvasive and three-dimensional detection.

Microspeciation in the copper(II)-L-histidylglycine system. An ESR study by the two-dimensional computer simulation method.

Twelve ESR-active (and one inactive) copper(II) complexes of L-histidylglycine (HL) were characterized via their formation (micro)constants and ESR parameters obtained by two-dimensional ESR spectroscopic evaluation in aqueous solution. In strongly acidic media, the ligand is coordinated through its N-terminal donor groups: the complex [CuLH(2)](3+) involves monodentate imidazole binding, whereas [CuLH](2+) involves bidentate ligation through the amino and imidazole N atoms. This histamine-like bonding mode also predominates in the isomers of [CuL(2)], formed at ligand excess near pH 7: in the major 4N isomer, both ligands occupy two equatorial sites, while in the 3N isomer, the second dipeptide is coordinated equatorially by the amino and axially by the imidazole groups. At above pH 3-4, deprotonation of the peptide group also starts: in approximately 60% of the molecules of [CuL](+), the peptide group is deprotonated, while in the minor isomer histamine-like coordination occurs. At higher pH, the active dimer [Cu(2)L(2)H(-2)], the mixed hydroxo complexes (the inactive [Cu(2)L(2)H(-3)](-) and the active [CuLH(-2)](-)), and the bis complexes [CuL(2)H](+) and [CuL(2)H(-1)](-) all involve tridentate equatorial ligation of the backbone by the amino and deprotonated peptide N and the carboxylate O atoms. In the active dimer, the neutral imidazole groups form bridges between CuLH(-1) units. In [CuL(2)H](+), the second ligand is bound equatorially via its imidazole group; in [CuL(2)H(-1)](-), the L ligand occupies the fourth equatorial site and an axial site through its amino and imidazole N atoms, respectively.

Application of lanthanide ion doped alkaline metal sulfates to ESR imaging

Imperfections and defects are well known to form in the alkaline metal sulfates after X-ray irradiation. The paramagnetic radicals (SO3− and SO4−) were produced by the irradiation of X-ray in the Gd ion doped K3Na(SO4)2. The ESR signal of SO3− radical in the Gd ion doped K3Na(SO4)2 was isotropic and thermally stable. The ESR signal intensity depended on an absorbed dose range of X-ray from 10−5 to 102 Gy. We planned to apply lanthanide (Ln) ion doped K3Na(SO4)2 rods to ESR imaging. Two-dimensional ESR image shows clearly a distribution of SO3− radical formed in the Gd ion doped K3Na(SO4)2 rod by the irradiation of X-ray. The results obtained in this study suggest that the Gd ion doped K3Na(SO4)2 rod is available to two-dimensional ESR dosimetry.

Right-angle sample spinning electron spin resonance

Right-angle sample spinning electron spin resonance (RAS-ESR) is introduced. In this new pulse ESR technique the sample is rotated along an axis perpendicular to the direction of the static magnetic field B0. RAS-ESR can be applied to improve sensitivity and spectral resolution of ESR, electron spin echo envelope modulation, and electron nuclear double resonance spectra of orientationally disordered systems. A detailed qualitative description of two-dimensional (2D) anisotropy-resolved ESR (AR-ESR), a technique that is based on RAS is given. It is demonstrated that the anisotropy of a spin system can be used to disentangle a field-swept powder ESR spectrum into a second dimension. This new dimension is obtained by Fourier transformation of the stimulated echo modulations caused by incrementing the spinning frequency. Details of the probe assembly for sample spinning at temperatures T⩾10 K with spinning frequencies between 0 and 500 Hz, frequency increments of minimum 0.2 Hz, a long-time frequency stability better than 1 Hz, and the possibility of sample exchange at these temperatures are given. The performance of the RAS-ESR spectrometer is demonstrated by a stimulated echo 2D AR-ESR experiment on a transition metal complex in a polycrystalline host material.

Molecular Dynamics of a Liquid Crystalline Polymer Studied by Two-Dimensional Fourier Transform and CW ESR

Two-dimensional Fourier transform (2D-FT) and CW-ESR experiments at X-band frequencies were performed over a broad range of temperatures covering the solid and melt states of a liquid crystalline (LC) polymer. The CW-ESR experiments were analyzed by conventional motional models. The nematic phase was macroscopically aligned in the dc magnetic field, whereas the solid state showed microscopic order but macroscopic disorder (MOMD). An end-label on the polymer showed smaller ordering and larger reorientational rates than that of the cholestane (CSL) spin probe dissolved in the same polymer, since the former can reorient by local internal chain modes. It was demonstrated that the 2D-FT-ESR experiments provide greatly enhanced resolution to the ordering and dynamics of the end-label, especially when performed as 2D-ELDOR (electron−electron double resonance) experiments as a function of mixing time. The conventional model of Brownian reorientation in an orienting potential was unsuccessful in interpreting these...

Measurements of Diffusion Processes in HEMA-DEGMA Hydrogels by ESR Imaging

The diffusion coefficients of small paramagnetic tracers (nitroxide spin probes) and spin-labeled poly(ethylene oxide) in hydrogels were measured at 300 K, using two-dimensional spatial-spectral ESR imaging (ESRI). The gels were prepared by copolymerization of 2-hydroxyethyl methacrylate (HEMA) and 2-(2-hydroxyethoxy)ethyl methacrylate (DEGMA), in the presence of a fixed molar concentration of glycol dimethacrylate as the cross-linker and 4,4'-azobis(4-cyanopentanoic acid) as the initiator. Variation of the amount of water in equilibrium with the gel was achieved by polymerizing different molar ratios of the monomers. Experimental concentration profiles of the diffusant were measured as a function of time, and each profile was obtained by image reconstruction, from a complete set of projections. The diffusion coefficients were determined by simulating all experimental profiles, using the Fick model of diffusion for an initially confined tracer diffusing into a finite system. The diffusion coefficients depend on the amount of water in the gels. The variation of the diffusion coefficients D with the weight fraction of the copolymer in the gel is consistent with the free volume model. The variation ofD with the molecular mass M of the diffusant scales as M -0.8 in gels containing ≥67 wt % water and as M -1.4 for the gel containing 55 wt % water. The advantages and present limitations of 2D spatial-spectral ESRI for measuring transport properties in polymers are discussed.

Two-dimensional Fourier-transform electron spin resonance in complex fluids

Two-dimensional Fourier-transform ESR spectra from a complex fluid characterized by very short free induction decay times are reported. They provide enhanced resolution to dynamic molecular structure compared to conventional cw-ESR spectra which are inhomogeneously broadened by the macroscopic disorder. A general theoretical analysis based on the stochastic Liouville equation permits us to accurately determine the microscopic ordering and motional dynamic rates by non-linear least-squares fitting to experiment.

Theory of two-dimensional ESR with nuclear modulation

A formalism for computing 2D ESR lineshapes with nuclear modulation is developed in a form which is useful for planning phase cycles for particular purposes. A simple method of processing spectra, utilizing quadrature detection, is shown to enhance the selectivity of the phase cycling techniques. Computed ESR-COSY, ESR-SECSY, and 2D ELDOR lineshapes are presented for several kinds of polycrystalline and single-crystal samples which exhibit nuclear modulation, due to one or several nuclei. The two-dimensional methods are found to give more detailed structural information than the corresponding ESEEM spectra. New phase cycles are found to eliminate completely all transverse and axial peaks in 2D ELDOR and in ESR-COSY, and at the same time eliminate all artifacts arising from incomplete image rejection. Other phase cycles are presented for selecting in those experiments only axial peaks, for measuring T1. It is also shown how selective phase cycles may help to distinguish between coherent and exchange cross peaks. In the special case of nitroxides in typical Zeeman fields, there are no significant nuclear modulation effects from the 14N nuclear spin interaction, but those from the protons (or deuterons) will, in general, be significant.

Ａ，Ｘ，Ｙ型ゼオライトにおけるスピンプローブ拡散のＥＳＲイメージングによる研究

Spectral-spatial two-dimensional ESR imaging was applied to studies on the behavior of di-t-butyl nitroxide (DTBN) adsorbed on A-, X-, and Y-type zeolites. The variation of spin distribution and total spin concentration was observed under annealing treatments. In X- and Y-type zeolites DTBN was adsorbed preferentially at the gas-introduced side of the sample. In consrast DTBN was adsorbed over the whole sample uniformly in A-type zeolite. A difference in the spatial distribution was noted also by desorption.

Hyperfine sublevel correlation (hyscore) spectroscopy: a 2D ESR investigation of the squaric acid radical

We propose a two-dimensional pulsed ESR experiment and demonstrate its capabilities in correlating hyperfine sublevels belonging to the same electron spin.

Two-dimensional Fourier transform ESR spectroscopy

New Fourier transform ESR techniques, which permit rapid data acquisition of ESR spectra, now allow one to perform a variety of two-dimensional ESR experiments. Two prototype experiments on a fast motional nitroxide spectrum are described. The first is based upon detection of the Han echo and may be used for discriminating the homogeneous broadening of an inhomogeneous spectrum (and/or the echo envelope modulation). The second is based upon detection of the FID after the three-pulse Jeener–Ernst sequence, and it leads to cross peaks due to Heisenberg spin exhange among the hyperfine lines.