Slow-motion Regime Research Articles

Lipid mobility and order in bovine rod outer segment disk membranes. A spin-label study of lipid-protein interactions.

Lipid-protein interactions in bovine rod outer segment disk membranes have been studied by using a series of eight stearic acid spin-label probes which were labeled at different carbon atom positions in the chain. In randomly oriented membrane dispersions, the electron spin resonance (ESR) spectra of the C-8, C-9, C-10, C-11, C-12, C-13, and C-14 atom positional isomers all apparently consist of two components. One of the components corresponds closely to the spectra obtained from dispersions of the extracted membrane lipids, and the other, which is characterized by a considerably greater degree of motional restriction of the lipid chains, is induced by the presence of the protein. Digital subtraction has been used to separate the two components. The proportion of the motionally restricted lipid component is approximately constant, independent of the position of the spin-label group, and corresponds to 30-40% of the total spin-label spectral intensity. The hyperfine splitting of the outer maxima in the difference spectra of the motionally restricted component decreases, and concomitantly, the line widths increase with increasing temperature but change relatively little with increasing distance of the spin-label group from the polar head-group region. This indicates that the corresponding chain motions of the protein-interacting lipids lie in the slow-motion regime of spin-label ESR spectroscopy (tau R approximately 10(-8) S) and that the mobility of these lipids increases with increasing temperature but does not vary greatly along the length of the chain. The data from the hyperfine splittings also suggest the existence of a polarity gradient immediately adjacent to the protein surface, as observed in the fluid lipid regions of the membrane. The more fluid lipid component is only slightly perturbed relative to the lipids alone (for label positions 5-14, inclusive), indicating the presence of chain motions on the nanosecond time scale, and the spectra also reveal a similar polarity profile in both lipid and membrane environments. ESR spectra have also been obtained as a function of magnetic field orientation with oriented membrane samples. For the C-14 atom positional isomer, the motionally restricted component is observed to have a large hyperfine splitting, with the magnetic field oriented both parallel and perpendicular to the membrane normal. This indicates that the motionally restricted lipid chains have a broad distribution of orientations at this label position.(ABSTRACT TRUNCATED AT 400 WORDS)

Spin-lattice relaxation of ligand nuclei in slowly reorienting paramagnetic complexes in the electronic doublet spin state ( [formula omitted]). A theoretical approach for strongly coupled two-spin systems

In this paper a general theory for treating the spin-lattice relaxation of a ligand nucleus (denoted by I) is derived for a metal complex in a doublet electron spin state ( S = 1 2 ). The dipole-dipole SI interaction is treated for the case where the electron spin is also strongly coupled to the metal nucleus K. The SK interaction considered here is the hyperfine coupling, both scalar (SC) and dipolar (DD). The present theory is valid for slowly reorienting complexes in solution and can, furthermore, incorporate relaxation effects of the electron spin S, and the metal nucleus K due to processes which are faster than, and independent of, reorientation, i.e., for processes that fulfil the strong narrowing conditions. The effects of chemical exchange of the ligands and of anisotropic reorientation of the complex are also studied. Together with our previous studies of paramagnetic complexes with electron spin S ≧ 1, that have been recently reviewed by J. Kowalewski, L. Nordenskiöld, N. Benetis, and P. O. Westlund, ( Prog. NMR Spectrosc. 17, 141 (1985)), the present work completes the elementary relaxation features of ligand nuclei of metal complexes in the slow motional regime. The present theory is shown to be more general than the theory of Bertini and co-workers ( J. Magn. Reson. 59 , 213 (1984)), which can be obtained as a limit of the present approach by decoupling the reorientation from the motions of the S-K two spin system. The treatment of a strongly coupled two-spin system is emphasized since it provides a necessary step to the treatment of the relaxation of paramagnetic doublets.

Nuclear spin relaxation in paramagnetic systems ( S = 1) in the slow-motion regime for the electron spin. IV. Motional anisotropy and noncoinciding dipole-dipole and zero-field splitting tensors

In this work, a paramagnetic complex in which the interacting electron ( S) and nuclear ( I) spins are connected by a vector not coinciding with the principal coordinate system of the zero-field-splitting (ZFS) tensor of the electron spin is considered as a model system. It is shown that the behavior of the dipole-dipole (DD) nuclear spin relaxation in such a system changes drastically when the electron spin enters the slow-motion regime. The effect of the slow motion is shown to be strongly dependent on the angle between the DD vector and the z axis of the principal coordinate system of the ZFS tensor. The present theory is valid for all possible values of the experimental variables and gives the Solomon equations as a limit of lowest order. The relation of the new theory to the modified Solomon-Bloembergen (MSB) equations is also discussed. If the anisotropic reorientation is incoporated (coinciding ZFS and diffusion tensors), the present theory, to the lowest order, yields the same results for the DD interaction of two interacting spins as obtained by Woessner ( J. Chem. Phys. 37, 647 (1962) . The internal diffusion can also be easily incorporated. The differences between the traditional theory and the slow-motion results, as well as the effects on relaxation in some interesting experimental situations are demonstrated by appropriate diagrams.

Electron spin resonance study of phospholipid membranes employing a comprehensive line-shape model.

The electron spin resonance spectra of the 1-myristoyl-2-[6-(4,4-dimethyloxazolidine-N-oxyl)myristoyl]-sn-glycero- 3-phosphocholine spin-label in highly oriented, fully hydrated bilayers of 1,2-dimyristoyl-sn-glycero-3-phosphocholine have been studied as a function of temperature and magnetic field orientation. The oriented spectra show clear indications of slow motional components (rotational correlation times greater than 3 ns) even in the fluid phase (T greater than 23 degrees C), indicating that motional narrowing theory is not applicable to the spectral analysis. The spectra have been simulated by a comprehensive line-shape model that incorporates trans-gauche isomerization in addition to restricted anisotropic motion of the lipid long molecular axis and that is valid in all motional regimes. In the gel (L beta') phase the spin-label chains are found to be tilted at 28 degrees with respect to the normal of the orienting plane. In the intermediate (P beta') phase there is a continuous distribution of tilt angles between 0 degrees and 25 degrees. In fluid (L alpha) phase there is no net tilt of the lipid chains. The chains rotate at an intermediate rate about their long axis in the fluid phase (tau R,parallel = 1.4-6.6 ns for T = 50-25 degrees C), but the reorientation of the chain axis is much slower (tau R, perpendicular= 13-61 ns for T = 50-25 degrees C), whereas trans-gauche isomerization (at the C-6 position) is rapid (tau J less than or equal to 0.2 ns). Below the chain melting transition both chain reorientation and chain rotation are at the ESR rigid limit (tau R greater than or equal to 100 ns), and trans-gauche isomerization is in the slow-motion regime (tau J = 3.7-9.5 ns for T = 22-2 degrees C). The chain order parameter increases continuously with decreasing temperature in the fluid phase (SZZ = 0.47-0.61 for T = 50-25 degrees C), increases abruptly on going below the chain melting transition, and then increases continuously in the intermediate phase (SZZ = 0.79-0.85 for T = 22-14 degrees C) to an approximately constant value in the gel phase (SZZ congruent to 0.86 for T = 10-2 degrees C).(ABSTRACT TRUNCATED AT 400 WORDS)

Discussion on the EPR sensitivity in the slow-motion regime.

Discussion on the EPR sensitivity in the slow-motion regime.

Copper complex E.P.R. lineshape simulation in the slow motion regime

Copper complexes are present in many biological systems dissolved in an isotropic or ordered fluid matrix. For such systems E.P.R. lineshape studies in the slow motion region are often incomplete due to both the slowness of simulation programs and inherent approximations in the fitting routines. The aim of this paper is to describe a fast computational procedure for simulating E.P.R. lineshapes of such magnetic species. We take into account, in a very simple way, the angular dependence of the transition probability. Furthermore we criticize carefully the assumption of deleting, in the slow motion regime, the pseudosecular terms.

Nuclear spin-lattice and spin-spin relaxation in paramagnetic systems in the slow-motion regime for the electron spin. III. Dipole-dipole and scalar spin-spin interaction for [formula omitted] and [formula omitted

The theory for nuclear spin relaxation in paramagnetic complexes, where the electron spin relaxation is allowed to be in the slow-motion regime, [ Mol. Phys. 48, 329 (1983)] is generalized to spin states of multiplicity higher than triplet. Numerical calculations of nuclear spin-spin and nuclear spin-lattice relaxation rates are reported for electron spin systems ( S = 3 2 , S = 5 2 ), coupled to the nuclear spin system via dipole-dipole and scalar spin-spin interaction. Analogous to the S = 1 case, in the region when the zero-field splitting interaction is larger than the electron Zeeman interaction, the spectral densities show qualitatively different behavior than that described by the Solomon-Bloembergen (SB) theory. Furthermore, the spectral densities show an additional structure, a “soft plateau,” compared to the S = 1 case. This extra structure is a characteristic feature for half-integer electron spin systems ( S ⩾ 3 2 ). It is shown that this structure is mainly due to the lifting of the Kramers degeneracy of the |S ± 1 2 〉 level. The results show that the interference spectral density at zero frequency K 0,0 DD-SC(0), i.e., the contribution to the nuclear spin-spin relaxation due to the interference term when both dipole-dipole and scalar coupling are present, does not vanish in the Redfield region for the electron spin system.

Q-band electron spin resonance studies of slow motions in bilayers with high order

Q-band electron spin resonance (ESR) experiments on macroscopically oriented multilayers of dimyristoyl lecithin/cholesterol (2:1 molar ratio)/cholestane spin label, order parameter S ≈ 1, have been carried out in the temperature range −32°C to +20°C. The spectra were simulated by a numerical soultion of the stochastic Liouville equation using Padé approximants. The simulations show that the rates of reorientation of the spin label molecules their long axes fall within the slow-motion regime. At low temperatures the molecular motion is best described in terms of a small step diffusion model, while at the higher temperatures a random jump model or an intermediate jump model provides a better description.

Nuclear spin relaxation in paramagnetic systems ( S = 1) in the slow-motion regime for the electron spin. II. The dipolar T2 and the role of scalar interaction

The previously presented theory ( Mol. Phys. 48, 329 (1983)) for the dipolar contribution to the spin-lattice relaxation in paramagnetic systems is extended. The theory, which allows the electron spin relaxation to be in the slow motion regime, is generalized to cover both the longitudinal and the transverse relaxation and to include both the dipole-dipole (DD) and the scalar interaction in the Hamiltonian coupling the nuclear spin to the lattice. The lattice is described in terms of the electron Zeeman interaction, a zero-field splitting (ZFS) of cylindrical symmetry and the isotropic rotational diffusion. It is shown that the spectral densities at the nuclear Larmor frequency and at zero frequency consist of three terms. Besides the usual DD and scalar components, a cross-term is shown to contribute to nuclear spin relaxation rates for certain parameter ranges. In the absence of exchange, the numerical calculations for S = 1 show that the DD and cross term spectral densities at zero frequency are independent of the magnetic field and the ZFS parameter. This is traced to the cross correlation between the DD and ZFS interactions. A formal way to include chemical exchange in the model is sketched. The effect of including exchange is that the DD-ZFS cross correlation is reduced.

Nuclear spin relaxation in a paramagnetic nickel(II) complex. An experimental test of new theoretical models

Paramagnetic relaxation enhancement data are reported for 15N and 1H in aniline in the presence of bis(2,2,6,6-tetramethylheptanedionato)nickel(II). For 15N, the spin-lattice as well as spin-spin relaxation rates are reported at two magnetic fields (2.35 and 5.875 T) and over a temperature range of 244 to 356 K. For 1H we report T 1 data at two fields (5.875 and 9.4 T) over a temperature range of 263 to 333 K. The experimental data are fitted to a new theoretical model, not invoking the concept of electron spin relaxation times, which is valid in the slow motion regime for the electron spin. The parameters obtained form a consistent set and have reasonable values, but the 15N results could not be fitted using the conventional model based on the modified Solomon-Bloembergen equations.

Spin echoes in the slow-motion regime

Utilisation de l'approche de mouvement lent au probleme de l'allure de raie, pour obtenir des expressions analytiques des amplitudes d'echo de spin et de leurs allures de raie resultantes, pour des systemes modules par diffusion de rotation

Fast-computational approach to the evaluation of slow-motion EPR spectra in terms of a generalized Langevin equation

A Mori-type generalized Langevin equation is shown to be the only theoretical tool necessary for setting up a fast-computational method of evaluating EPR spectra. The advantages of this algorithm, concerning memory storage and time consumption, are clearly illustrated by explicitly evaluating the line shape of a nitroxide spin probe both in an isotropic liquid solution and in a liquid-crystal mesophase. This method makes theoretical EPR spectra of an orientated system in the slow-motion regime readily available. It is shown that the presence of an orientating potential renders the EPR spectrum much more sensitive to the details of molecular dynamics, thereby making this a potentially powerful tool for monitoring rotational dynamics in liquid mesophases.

Nuclear spin relaxation in paramagnetic systems

A theory of nuclear spin relaxation in paramagnetic systems, allowing for the electron spin relaxation to be in the slow motion regime, is presented. The formulation is general and can, for example, be used to derive formally the modified Solomon-Bloembergen equations. The theory is applied to the specific problem of nuclear spin lattice relaxation caused by the dipole-dipole interaction between the nuclear spin and an electron spin (S = 1). The lattice is described in terms of the electron Zeeman interaction, a zero field splitting of cylindrical symmetry and isotropic rotational diffusion. The resulting equations are solved numerically for a range of parameter values of practical interest and limiting cases are discussed. In the slow motion regime for the electron spin relaxation (that is, where the zero field splitting is larger than the rotational diffusion constant), the behaviour of the nuclear spin-lattice relaxation rate predicted using the present formalism differs qualitatively from the predicti...

Adiabatic and pendulum approximations to the retarded Josephson equation

The retarded Josephson equation, which is a second-order differential-integral equation, can be approximated by differential equations in different ways. There are the well-known adiabatic approximations which are justifiable for small ac-voltage amplitudes and in the slow-motion regime. Another type of approximation makes use of the pendulum analogy, where the arguments of the functions entering in the adiabatic current phase relation are replaced by time averages. Several modifications of this average pendulum approximation will be discussed. In particular, the characteristics of these different approximations are compared with the exact result in a limit where the agreement should be rather good. In the same limit the solutions are also investigated by asymptotic expansions under very general conditions.

Low-lying vibrational modes and the theory of local and transport properties at ferroelectric and other structural phase transitions

Abstract The temperature dependence of the critical contributions to the exponent of the Debye—Waller factor (DWF), which corresponds to that of the linewidth of the electron paramagnetic resonance (EPR) in the “slow-motion regime”, is calculated as well as the temperature dependence of the critical contributions to the electrical resistivity of ferroelectrics and other structural phase transitions (e.g., anti-ferroelectrics, A-15 structure compounds, etc.). Special attention is paid to the derivation of additional predictions for the critical behaviour of uniaxial ferroelectrics employing the Larkin-Khmelnitskii theory and to the experimental observability of the predicted logarithmic correction terms. The interrelationship between low-lying vibrational modes and the critical behaviour of the investigated quantities is exhibited.

Equation of state, Debye-Waller factor, and electrical resistivity of ferroelectrics near their critical point

The Larkin-Khmelnitskii theory of uniaxial ferroelectrics is used to derive further predictions for the critical behavior of ferroelectrics, including "local properties" and transport properties. Special attention is paid to the experimental observability of the predicted logarithmic correction terms. In particular, in the expansion of the electric field E in powers of the dielectric polarization $P$, i.e., $E=P\ensuremath{\Sigma}{i}^{}{f}_{2i}(T){P}^{2i}$, the temperature dependence of the coefficients ${f}_{2}\ensuremath{\propto}{|\mathrm{ln}(\frac{T}{{T}_{c}\ensuremath{-}1})|}^{\ensuremath{-}1}$ and ${f}_{4}\ensuremath{\propto}{(\frac{T}{{T}_{c}\ensuremath{-}1})}^{\ensuremath{-}1}{|\mathrm{ln}(\frac{T}{{T}_{c}\ensuremath{-}1})|}^{\ensuremath{-}\frac{4}{3}}$ is obtained, deviating significantly from ${f}_{2}=\mathrm{const}$ and ${f}_{4}=\mathrm{const}$ of the simple Landau theory. We argue that the nonanalytic behavior of ${f}_{2}$ could be measured more easily than either the logarithmic correction in ${f}_{0}\ensuremath{\propto}(\frac{T}{{T}_{c}\ensuremath{-}1}){|\mathrm{ln}(\frac{T}{{T}_{c}\ensuremath{-}1})|}^{\ensuremath{-}\frac{1}{3}}$ or the specific-heat singularity $C\ensuremath{\propto}{|\mathrm{ln}(\frac{T}{{T}_{c}\ensuremath{-}1})|}^{\frac{1}{3}}$. We show that recent experiments on tri-glycine sulfate by Ehses and M\"user are in good agreement with our predictions. Moreover, we calculate the temperature dependence of the critical contribution to the Debye-Waller-factor exponent $W$ which corresponds to that of the electron-paramagnetic-resonance linewidth in the "slow-motion regime." We find ${W}_{\mathrm{crit}}\ensuremath{\propto}(\frac{T}{{T}_{c}\ensuremath{-}1})\ifmmode\times\else\texttimes\fi{}{|\mathrm{ln}(\frac{T}{{T}_{c}\ensuremath{-}1})|}^{\frac{1}{3}}$ above ${T}_{c}$ and ${W}_{\mathrm{crit}}\ensuremath{\propto}(\frac{1\ensuremath{-}T}{{T}_{c}}){|\mathrm{ln}(\frac{T}{{T}_{c}\ensuremath{-}1})|}^{\frac{2}{3}}$ below ${T}_{c}$. A reinterpretation of available experiments is suggested. Finally, we obtain the temperature dependence of the critical contributions to the $\mathrm{dc}$ electrical resistivity $\ensuremath{\rho}$ both for ferroelectrics and other structural phase transitions. While $\frac{d\ensuremath{\rho}}{\mathrm{dT}}$ is shown to have the same singularity as the specific heat in ferroelectrics both below ${T}_{c}$ and above ${T}_{c}$ we obtain in the other cases $\frac{d\ensuremath{\rho}}{\mathrm{dT}}\ensuremath{\propto}{(\frac{1\ensuremath{-}T}{{T}_{c}})}^{2\ensuremath{\beta}\ensuremath{-}1}$ for $T<{T}_{c}$, and $\frac{d\ensuremath{\rho}}{\mathrm{dT}}\ensuremath{\propto}C\ensuremath{\propto}{(\frac{T}{{T}_{c}\ensuremath{-}1})}^{\ensuremath{-}\ensuremath{\alpha}}$ for $T>{T}_{c}$, where $\ensuremath{\beta}$ is the orderparameter exponent. A discussion of a recent experiment in SnTe is given, and our results for the electrical resistivity of semiconducting ferroelectrics are compared with those for ferromagnets and antiferromagnets.