Phase transition in vector spin glasses

We first give an experimental and theoretical introduction to spin glasses, and then discuss the nature of the phase transition in spin glasses with vector spins. Results of Monte Carlo simulations of the Heisenberg spin glass model in three dimensions are presented. A finite size scaling analysis of the correlation length of the spins and chiralities shows that there is a single, finite-temperature transition at which both spins and chiralities order.     

The diffusion-concentration product of oxygen in lipid bilayers using the spin-label T1 method

A method is described to measure the oxygen diffusion-concentration product, DO[O2], at any locus that can be probed or labeled using nitroxide radicals. The method is based on the dependence of the spin-lattice relaxation time T1 of the spin label on the bimolecular collision rate with oxygen. Strong Heisenberg exchange between spin label and oxygen contributes directly to T1 of the spin label, while dipolar interactions are negligible. Both time-domain and continuous wave saturation methods for studying T1 are considered. The method has been applied to phospholipid liposomes using fatty acid spin labels. A discontinuity in DO[O2] at the main phase transition was observed.     

Diffusion of oxygen in water and hydrocarbons using an electron spin resonance spin-label technique.

The Smoluchowski equation for the bimolecular collision rate of dissolved oxygen molecules with spin labels yielded values for the diffusion constant of oxygen in water that are in agreement with the Stokes-Einstein equation (D infinity T/eta, where eta is the macroscopic viscosity) and with published values obtained by conventional methods. Heisenberg exchange at an interaction distance of 4.5 A occurs with a probability close to one for each encounter. In mixed hydrocarbons (olive oil, paraffin oils) and sec-butyl benzene, D infinity (T/eta)rho, where rho lies between 0.5 and 1. Oxygen diffuses in the hydrocarbons between 10 and 100 times more rapidly than predicted from the macroscopic viscosity. Similar results would be expected for diffusion of oxygen in model and biological membranes. Parallel measurements of rotational diffusion of the spin labels show little correlation with measurements of translational diffusion of oxygen. Dipolar interactions between spin labels and oxygen appear negligible except in the limit of highest viscosities.     

Enzymatic sequence-specific spin labeling of a DNA fragment containing the recognition sequence of EcoRI endonuclease

Deoxyuridine analogs spin labeled in position 5 have been enzymatically incorporated sequence specifically into an oligodeoxyribonucleotide to form a spin-labeled 26-mer. The 26-mer contains the EcoRI-binding site and two labels which are located symmetrically close to the binding site. The labels are separated from one another far beyond the Heisenberg spin-exchange distance. The local base motion as determined by ESR spectroscopy is of the order of 4 ns in the oligonucleotide duplex. This is the same value as reported earlier for local T motions in polynucleotide duplexes, thereby providing direct experimental evidence that the ESR line shape of spin levels covalently attached to nucleic acids depends primarily on the local dynamics of the nucleic acid building blocks.     

Protein conformation from electron spin relaxation data.

Electron spin relaxation data from five ferric proteins are analyzed in terms of the fractal model of protein structures. Details of this model are presented. The results lead to a characterization of protein structures by a single parameter, the fractal dimension, d. This structural parameter is shown to determine the temperature dependence of the Raman electron spin relaxation rate, which varies as T3 + 2d. Computations of d are made using x-ray data for 17 proteins. The results range from d = 1.76 for lysozyme to d = 1.34 for ferredoxin. These values are compared with values of d obtained from the present electron spin relaxation data on five ferric proteins. Typical results are d = 1.34 +/- 0.06 from relaxation data and 1.34 +/- 0.05 from x-ray data for ferredoxin; d = 1.67 +/- 0.03 from relaxation data and 1.66 +/- 0.05 from x-ray data for ferricytochrome c. The data thus support the theoretical model. Applications of this spin resonance technique to the study of changes in protein conformation are discussed.     

Magnetic properties of a cobalt(II) dimer of pseudo tetrahedral geometry [Co2{(CO)9Co3C---COO}5, C14H19N2H]

The crystalline ion pair [Co₂{OOC---CCo₃(CO)₉}₅, C₁₀H₆(N(CH₃)₂)₂H] (1) presents unusual magnetic properties. The X-band EPR spectrum of 1 at room temperature presents two unresolved bands at g=1.98 and 4.55. At a low temperature (20 K), the cluster of clusters 1 presents a complicated spectrum with an intense signal at 1700 G. The magnetic susceptibility of 1 was fit to a two spin S₁=S₂=3/2 Heisenberg model, with J=11.2 cm⁻¹ and a g value of 2.3. There is no field dependence of the magnetization, which suggests intramolecular coupling between the two tetrahedral centers of the cluster. Molecular orbital modeling indicates a sigma path of exchange between two topologically non-equivalent cobalt(II) centers.     

The Effect of Oxygen at Physiological Levels on the Detection of free Radical Intermediates by Electron Paramagnetic Resonance

It is well known that oxygen enhances Che relaxation of free radical EPR probes through spin lattice and Heisenberg spin-spin interactions with consequent effect on the line height and width. The two relaxation processes have opposing effects on the signal heights and depend on the concentration of oxygen, the incident microwave power, and the presence of other paramagnetic species. During EPR studies of chemical, biochemical, and cellular processes involving free radicals, molecular oxygen has significant magnetic influence on the EPR signal intensity of the free radical species under investigation in addition to affecting the rates of production of the primary species and the stability of the spin adduct nitroxides. These effects are often overlooked and can cause artifacts and lead to erroneous interpretation. In the present study, the effects of oxygen and ferricyanide on the EPR signal height of stable and persistent spin adduct nitroxides at commonly employed microwave powers were examined. The results show that under commonly adopted EPR spectrometer instrumental conditions, artifactual changes in the EPR signal of spin adducts occur and the best way to avoid them is by keeping the oxygen level constant using a gas-permeable cell.     

Oxygen permeation profile in lipid membranes: comparison with transmembrane polarity profile

Permeation of oxygen into membranes is relevant not only to physiological function, but also to depth determinations in membranes by site-directed spin labeling. Spin-lattice (T(1)) relaxation enhancements by air or molecular oxygen were determined for phosphatidylcholines spin labeled at positions (n = 4-14, 16) of the sn-2 chain in fluid membranes of dimyristoyl phosphatidylcholine, by using nonlinear continuous-wave electron paramagnetic resonance (EPR). Both progressive saturation and out-of-phase continuous-wave EPR measurements yield similar oxygen permeation profiles. With pure oxygen, the T(2)-relaxation enhancements determined from homogeneous linewidths of the linear EPR spectra are equal to the T(1)-relaxation enhancements determined by nonlinear EPR. This confirms that both relaxation enhancements occur by Heisenberg exchange, which requires direct contact between oxygen and spin label. Oxygen concentrates in the hydrophobic interior of phospholipid bilayer membranes with a sigmoidal permeation profile that is the inverse of the polarity profile established earlier for these spin-labeled lipids. The shape of the oxygen permeation profile in fluid lipid membranes is controlled partly by the penetration of water, via the transmembrane polarity profile. At the protein interface of the KcsA ion channel, the oxygen profile is more diffuse than that in fluid lipid bilayers.     

Conformation of spin-labeled melittin at membrane surfaces investigated by pulse saturation recovery and continuous wave power saturation electron paramagnetic resonance.

Melittin spin-labeled specifically with a nitroxide at positions 7, 21, 23, or the amino terminus was bound to phospholipid membranes, and the exposure of the spin label to the aqueous phase was investigated by measurement of Heisenberg exchange with chromium oxalate in the solution. The exchange frequency was determined by saturation recovery electron paramagnetic resonance (EPR) using a loop-gap resonator. This method allows use of very low concentrations (less than 1 mM) of chromium oxalate compared with conventional measurements of EPR line broadening (typically 50 mM), thus avoiding problems associated with high metal ion concentration. Differences in exchange frequency between the various positions were also estimated by continuous wave power saturation methods. In either approach, the spin label at lysine 7 was found to be the most exposed to chromium oxalate whereas that at lysine 23 was found to be the least exposed. This is consistent with a model for the membrane bound peptide in which an amphiphilic helix lies with its axis parallel to the bilayer surface and the hydrophobic moment points toward the bilayer interior.     

Watson–Crick pairing,the Heisenberg group and Milnor invariants

We study the secondary structure of RNA determined by Watson–Crick pairing without pseudo-knots using Milnor invariants of links. We focus on the first non-trivial invariant, which we call the Heisenberg invariant. The Heisenberg invariant, which is an integer, can be interpreted in terms of the Heisenberg group as well as in terms of lattice paths. We show that the Heisenberg invariant gives a lower bound on the number of unpaired bases in an RNA secondary structure. We also show that the Heisenberg invariant can predict allosteric structures for RNA. Namely, if the Heisenberg invariant is large, then there are widely separated local maxima (i.e., allosteric structures) for the number of Watson–Crick pairs found. Partially supported by DST (under grant DSTO773) and UGC (under SAP-DSA Phase IV).     

Solution of the nitroxide spin-label spectral overlap problem using pulse electron spin resonance.

Short-pulse saturation-recovery (SR) electron spin resonance (ESR) methods have been used to measure the lateral diffusion of a nitroxide-labeled cholesterol analogue (3-spiro-[2'-(N-oxyl-4',4'-dimethyloxazoladine)]-cholestane, CSL) in multilamellar liposomal dispersions. SR experiments were performed on samples containing 14NCSL:15NCSL pairs, and recovery signals were analyzed for initial conditions and multiexponential time constants by computer simulation. Rate equations describing the system were written and solved. The time constants contain combinations of electron spin lattice relaxation times Tle for both isotopes and the Heisenberg exchange rate constant Kx. We have investigated the complication that occurs from overlap of ESR spectral fragments from 14N and 15N moieties. The time constants of the multiexponential signals are independent of ESR line shape and position. From Kx, lateral diffusion constants of CSL in dimyristoylphosphatidylcholine (DMPC) were calculated (D = 1.7 x 10(-8) at 27 degrees C and 2.7 x 10(-8) cm2/s at 37 degrees C). It is shown that short-pulse saturation-recovery methods are able to overcome the ESR spectral overlap problem that is encountered in conventional ESR and continuous wave electron-electron double resonance (CW ELDOR) studies of spin-spin interactions. The present method can be extended to more complex situations involving spin labels in different environments with physical and chemical exchange.     

Two dimensional diffusion of small molecules on protein surfaces: an EPR study of the restricted translational diffusion of protein-bound spin labels

Heisenberg spin exchange rates and dipole-dipole spin lattice relaxation rates for deuterated ¹⁴N- and ¹⁵N-spin labels bound selectively to the histidine His15 and to the lysines Lys13, 96, 97 of the lysozyme molecule have been determined with the aid of electron spin resonance spectroscopy. The results can be interpreted in terms of a two dimensional translational diffusion of the nitroxide tips of the spin labels along the protein surface within restricted surface areas. The spin labels are regarded as models for long amino acid side chains and as probes for the dynamics of protein and water in the vicinity of the protein surface. The translational diffusion coefficient DP_II is reduced by a factor of between six and thirty compared to the value of D found for the spin labels in bulk water, its value for T = 295 K is given by (1.3±0.6)·10^–10m²s^–1 D (2.4±0.3) 10^–11 m²s^–1. Offprint requests to: H.-J. Steinhoff     

Accessibility of nitroxide side chains: absolute Heisenberg exchange rates from power saturation EPR

In site-directed spin labeling, the relative solvent accessibility of spin-labeled side chains is taken to be proportional to the Heisenberg exchange rate (W(ex)) of the nitroxide with a paramagnetic reagent in solution. In turn, relative values of W(ex) are determined by continuous wave power saturation methods and expressed as a proportional and dimensionless parameter Pi. In the experiments presented here, NiEDDA is characterized as a paramagnetic reagent for solvent accessibility studies, and it is shown that absolute values of W(ex) can be determined from Pi, and that the proportionality constant relating them is independent of the paramagnetic reagent and mobility of the nitroxide. Based on absolute exchange rates, an accessibility factor is defined (0 < rho < 1) that serves as a quantitative measure of side-chain solvent accessibility. The accessibility factors for a nitroxide side chain at 14 different sites in T4 lysozyme are shown to correlate with a structure-based accessibility parameter derived from the crystal structure of the protein. These results provide a useful means for relating crystallographic and site-directed spin labeling data, and hence comparing crystal and solution structures.     

A novel steroidal spin label for membrane structure studies: synthesis and applications

2,2,6,6-Tetramethyl piperidine-N-oxyl nitroxyls are known to partition between aqueous and lipid phases, thus serving as probes to study membrane dynamics. The synthesis of a novel steroidal spin label, 3alpha-hydroxycholan-24-yl-(2",2",6",6"-tetramethyl-N-oxyl)p iperidyl butan-1',4'-dioate, containing 2,2,6,6-tetramethylpiperidine-N-oxyl moiety covalently bonded to the side chain in 3,24-caprostan-diol has been described. The localization of this spin label in model biomembranes has been studied by using electron spin resonance, differential scanning calorimetry, and 1H and 31P NMR spectroscopic techniques. Its applicability in studying the phase transition properties of model membrane L-alpha-dipalmitoyl phosphatidyl choline in the presence and absence of drugs has been described by using electron spin resonance. The label has also been used to study the permeability of epinephrine into membrane. The results have shown the applicability of the spin label as a potential spin probe in the study of biomembranes.     

Single-ion anisotropy effects on the energy spectra of spin S = 1 Heisenberg ring

The energy spectra of the quantum spin S = 1 ring in the presence and absence of magnetic field are calculated. The numerical exact diagonalization technique exploiting the point-group symmetry is applied to the Heisenberg spin Hamiltonian with single-ion anisotropy modelling approximately the dodecanuclear nickel cluster Ni₁₂(O₂CMe)₁₂(chp)₁₂(H₂O)₆(THF)₆. The energy-level dependence of the anisotropy parameter D is analyzed and the field-dependent level-crossing is presented.     

The physical chemistry of Hemes II. Electron paramagnetic resonance study of the interaction of some iron(III)-porphyrins with fluoride ion in dimethylformamide

The interaction of F⁻ with high and low spin ferric deuteroporphyrin IX dimethyl ester and a low spin model compound, bis(histidine methyl ester) deuterohemin IX has been studied in dimethylformamide solution by low-temperature EPR. The reaction of F⁻ with these complexes leads to high spin compounds. The structure of the EPR line at g = 2 is due to superhyperfine interactions with axial fluoride ligands. It allows their identification as mono- or difluoride complexes. Their optical absorption spectra are reported. In the particular cases of bis(imidazole) deuterohemin IX dimethyl ester and of the model compound, the variations of the EPR spectra as functions of concentration of ionic ligand are reported. Three new low spin complexes are thus obtained. They are characterized by a specific interaction of F⁻ with the NH group of the imidazole ring. This is proved following a second independent study in which we report the changes in g tensor principal values of low spin ferric porphyrins with the basicity (pK_a) of various nitrogenous bases.     

Study of molecular mobility in biological membranes by 2-mm band ESR spectroscopy

Temperature relationship was measured of ESR spectra of spin probes--derivatives of fatty acids whose nitroxyl fragments are incorporated into surface and inner layers of phosphatidylcholine liposomes (T = 180-260 K), as well as of the probe in model ethanol solution (T = 110-220 K). Data on the nature and rotation frequency of probe nitroxyl fragments were obtained from the analysis of the spectra. It was shown that the frequency of the probes movement in the systems under study corresponds to the slow movement region, i.e. it is not above 10(7) s-1.     

Rotational diffusion and intermolecular collisions of a spin labeled alpha-helical peptide determined by electron spin echo spectroscopy.

Short peptides that are composed mainly of alanine have recently been shown to form alpha-helices in aqueous solution at low temperature (Marqusee, S., and R. L. Baldwin. 1987. Proc. Natl. Acad. Sci. 84:8898-8902; Marqusee, S., V. H. Robbins, and R. L. Baldwin. 1989. Proc. Natl. Acad. Sci. USA. 86:5286-5290). These peptides are excellent models for probing structure and dynamics in isolated helical domains. In previous work we have designed and synthesized spin labeled analogs of these helix-forming peptides and we have shown that these analogs retain the folding characteristics of the parent peptide (Todd, A. P., and G. L. Millhauser. 1991. Biochemistry. 30:5515-5523). Using conventional continuous wave electron spin resonance (CW ESR) we have further shown that local motion is more pronounced near the helix amino terminus than in the central region as the peptide is thermally unfolded (Miick, S. M., A. P. Todd, and G. L. Millhauser. 1991. Biochemistry. 30:9498-9503). In this present work we use electron spin echo (ESE) spectroscopy to further refine our understanding of the solution dynamics of the 3K-8 peptide, which is a 16-mer with a nitroxide spin label attached at position 8. We find that the spin echo decays are well described by a single exponential function and that the determined correlation times are close to those previously derived from CW experiments. Variable concentration ESE experiments have directly revealed Heisenberg spin exchange (HSE) interactions and we find that the interpeptide collision rate is near to that expected for a free species in solution.(ABSTRACT TRUNCATED AT 250 WORDS)     

Spin transition of camphor-bound cytochrome P-450. 1. local paH and electrostatic interactions.

Variations of the spin state in camphor-bound cytochrome P-450 are interpreted in the light of the polyelectrolyte theory and its implications on the microenvironment of the heme. The ratio of high-spin to low-spin iron can serve as a tool to determine the local paH in the microenvironment of a group (pK0, app approximately 5.4) which governs the spin state. The local paH depends on the electrostatic potential created by negatively charged groups (pKa = 5.6), modulated in turn by paH and by the screening effect of ionic strength. A model is given for the proton-coupled spin state change.