Spin relaxation measurements of electrostatic bias in intermolecular exploration

We utilize the paramagnetic contribution to proton spin-lattice relaxation rate constants induced by freely diffusing charged paramagnetic centers to investigate the effect of charge on the intermolecular exploration of a protein by the small molecule. The proton NMR spectrum provided 255 resolved resonances that report how the explorer molecule local concentration varies with position on the surface. The measurements integrate over local dielectric constant variations, and, in principle, provide an experimental characterization of the surface free energy sampling biases introduced by the charge distribution on the protein. The experimental results for ribonuclease A obtained using positive, neutral, and negatively charged small nitroxide radicals are qualitatively similar to those expected from electrostatic calculations. However, while systematic electrostatic trends are apparent, the three different combinations of the data sets do not yield internally consistent values for the electrostatic contribution to the intermolecular free energy. We attribute this failure to the weakness of the electrostatic sampling bias for charged nitroxides in water and local variations in effective translational diffusion constant at the water-protein interface, which enters the nuclear spin relaxation equations for the nitroxide-proton dipolar coupling.     

Comparing continuous wave progressive saturation EPR and time domain saturation recovery EPR over the entire motional range of nitroxide spin labels

The measurement of spin-lattice relaxation rates from spin labels, such as nitroxides, in the presence and absence of spin relaxants provides information that is useful for determining biomolecular properties such as nucleic acid dynamics and the interaction of proteins with membranes. We compare X-band continuous wave (CW) and pulsed or time domain (TD) EPR methods for obtaining spin-lattice relaxation rates of spin labels across the entire range of rotational motion to which relaxation rates are sensitive. Model nitroxides and spin-labeled biological species are used to illustrate the potential complications that arise in extracting relaxation data under conditions typical to biological experiments. The effect of super hyperfine (SHF) structure is investigated for both CW and TD spectra. First and second harmonic absorption and dispersion CW spectra of the nitroxide spin label, TEMPOL, are all fit simultaneously to a model of SHF structure over a range of microwave amplitudes. The CW spectra are novel because all harmonics and microwave phases were acquired simultaneously using our homebuilt CW/TD spectrometer. The effect of the SHF structure on the pulsed free induction decay (FID) and pulsed saturation recovery spectrum is shown for both protonated and deuterated TEMPOL. We present novel pulsed saturation recovery measurements on biological molecules, including spin-lattice relaxation rates of spin-labeled proteins and spin-labeled double-stranded DNA. The impact of structure and dynamics on relaxation rates are discussed in the context of each of these examples. Collisional relaxation rates with oxygen and transition metal paramagnetic relaxants are extracted using both continuous wave and time domain methods. The extent of the errors inherent in the CW method and the advantages of pulsed methods for unambiguously measuring collisional relaxation rates are discussed. Spin-lattice relaxation rates, determined by both CW and pulsed methods, are used to determine the electrostatic potential on the surface of a protein.     

Bi-exponential proton transverse relaxation rate (R2) image analysis using RF field intensity-weighted spin density projection: potential for R2 measurement of iron-loaded liver

A bi-exponential proton transverse relaxation rate (R(2)) image analysis technique has been developed that enables the discrimination of dual compartment transverse relaxation behavior in systems with rapid transverse relaxation enhancement. The technique is particularly well suited to single spin-echo imaging studies where a limited number of images are available for analysis. The bi-exponential R(2) image analysis is facilitated by estimation of the initial proton spin density signal within the region of interest weighted by the RF field intensities. The RF field intensity-weighted spin density map is computed by solving a boundary value problem presented by a high spin density, long T(2) material encompassing the region for analysis. The accuracy of the bi-exponential R(2) image analysis technique is demonstrated on a simulated dual compartment manganese chloride phantom system with relaxation rates and relative population densities between the two compartments similar to the bi-exponential transverse relaxation behavior expected of iron loaded liver. Results from analysis of the phantoms illustrate the potential of bi-exponential R(2) image analysis with RF field intensity-weighted spin density projection for quantifying transverse relaxation enhancement as it occurs in liver iron overload.     

Spin-Label EPR for Determining Polarity and Proticity in Biomolecular Assemblies: Transmembrane Profiles

Hyperfine couplings and g-values of nitroxyl spin labels are sensitive to polarity and hydrogen bonding in the environment probed. The dependences of these electronic paramagnetic resonance (EPR) properties on environmental dielectric permittivity and proticity are reviewed. Calibrations are given, in terms of the Block–Walker reaction field and local proton donor concentration, for the nitroxides that are commonly used in spin labeling of lipids and proteins. Applications to studies of the transverse polarity profiles in lipid bilayers, which constitute the permeability barrier of biological membranes, are reviewed. Emphasis is given to parallels with the permeation profiles of oxygen and nitric oxide that are determined from spin-label relaxation enhancements by using nonlinear continuous-wave EPR and saturation recovery EPR, and with permeation profiles of D₂O that are determined by using ²H electron spin echo envelope modulation spectroscopy.     

Enhancing the relaxivity of paramagnetic coordination complexes through the optimization of the molecular electrostatic potential

The low relaxivity of paramagnetic coordination complexes limits their use as contrast agents in magnetic resonance imaging (MRI). To address this problem, we study the relationship between the molecular structure of these complexes and their relaxivity. While others have investigated the vibrational modes as molecular determinants of the electronic spin relaxation time, we focus on the analysis of the molecular electrostatic potential (MEP) of the paramagnetic coordination complex. Electrostatic forces dominate the interaction between the coordination complex and water. Hence, in addition to steric forces, the molecular electrostatic potential should be a determinant of the lifetime of the water-metal link (t_m), the internuclear distance between the water hydrogens and the metal (R), and the number of water molecules attached to the metal in the inner and outer spheres of coordination. We compute the molecular electrostatic potential for a series of model metalloporphyrins because their physical and biologic properties are well known, and they are putative magnetic resonance imaging contrast agents with affinity to neoplastic tissue. Replacing the sulfonato groups in MnTPPS4 with carboxylate groups in the ortho position of the phenyl rings attached to the meso carbons results in an electrostatic focusing field that should reduce R and increase t_m. Similar substitutions involving polar groups, including one modeled after a well-known picket-fence porphyrin, are not strong enough to generate a focusing field. Instead, these polar groups should modulate the water-metal interactions through steric interactions. Molecular dynamic simulations show a large outer sphere of coordination around the paramagnet that extends almost three times the distance of the inner sphere of coordination.     

Modulation of the distance dependence of paramagnetic relaxation enhancements by CSA × DSA cross-correlation

Paramagnetic metal ions with fast-relaxing electronic spin and anisotropic susceptibility tensor provide a rich source of structural information that can be derived from pseudo-contact shifts, residual dipolar couplings, dipole-dipole Curie spin cross-correlation, and paramagnetic relaxation enhancements. The present study draws attention to a cross-correlation effect between nuclear relaxation due to anisotropic chemical shielding (CSA) and due to the anisotropic dipolar shielding (DSA) caused by the electronic Curie spin. This CSA x DSA cross-correlation contribution seems to have been overlooked in previous interpretations of paramagnetic relaxation enhancements. It is shown to be sufficiently large to compromise the 1/r6 distance dependence usually assumed. The effect cannot experimentally be separated from auto-correlated DSA relaxation. It can increase or decrease the observed paramagnetic relaxation enhancement. Under certain conditions, the effect can dominate the entire paramagnetic relaxation, resulting in nuclear resonances narrower than in the absence of the paramagnetic center. CSAxDSA cross-correlation becomes important when paramagnetic relaxation is predominantly due to the Curie rather than the Solomon mechanism. Therefore the effect is most pronounced for relaxation by metal ions with large magnetic susceptibility and fast-relaxing electron spin. It most strongly affects paramagnetic enhancements of transverse relaxation in macromolecules and of longitudinal relaxation in small molecules.     

Distance between a native cofactor and a spin label in the reaction centre of Rhodobacter sphaeroides by a two-frequency pulsed electron paramagnetic resonance method and molecular dynamics simulations

The distance between the paramagnetic state of a native cofactor and a spin label is measured in the photosynthetic reaction centre from the bacterium Rhodobacter sphaeroides R26. A two-frequency pulsed electron paramagnetic resonance method [double-electron-electron spin resonance (DEER)] is used. A distance of 3.05 nm between the semiquinone anion state of the primary acceptor (Q(A)) and the spin label at the native cysteine at position 156 in the H-subunit is found. Molecular-dynamics (MD) simulations are performed to interpret the distance. A 6 ns run comprising the entire RC protein yields a distance distribution that is close to the experimental one. The average distance found by the MD simulation is smaller than the distance obtained by DEER by at least 0.2 nm. To better represent the experiments performed at low temperature (60K), a MD method to mimic the freezing-in of the room-temperature conformations is introduced. Both MD methods yield similar distances, but the second method has a trend towards a wider distance distribution.     

Electric field influence on spin polarization vector behaviour of the negative muon in silicon

When a negatively charged muon is captured by a silicon atom, the atom is transformed into a solitary acceptor center similar to an Al atom. An external electric field influences the formation process of the neutral acceptor center (A.C.). It is shown in this article that the behaviour of the muon polarization vector changes appreciably in electric fields with intensities E\,\gtrsim\,10 V/cm. We estimate the muon spin relaxation rate \varLambda_μ in the so‐called “dirty limit”; for example, interaction between an internal electric field from charged impurities and a nonzero dipole moment of the A.C. is taken into account. A phonon mechanism is proposed to explain the temperature dependence of \varLambda_μ. We also estimate the value of the paramagnetic shift of the muon spin precession frequency \delta\omega/\omega₀ which is also temperature dependent. This revised version was published online in August 2006 with corrections to the Cover Date.     

Cross-correlation effects involving curie spin relaxation in methyl groups

Cross-correlation effects arising in methyl protons due to the simultaneous presence of dipole-dipole, chemical shift anisotropy, and Curie spin relaxation mechanisms in paramagnetic systems are analyzed. We assess the potential of obtaining structural constraints from the cross-correlation of Curie spin relaxation with dipolar relaxation mechanisms among methyl proton spins. By theoretical analysis and numerical simulations we characterize the transfer functions describing the interconversion processes of different ranks of multispin order. The time dependence of these processes contains a new type of structural information, the orientation of the methyl C(3)-axis with respect to the electron center. Experimental confirmation is found for selected methyl groups in low spin Fe(3+) sperm whale myoglobin.     

Exchange and dipolar spin-spin interaction and rotational diffusion in saturation transfer EPR spectroscopy

Saturation transfer EPR spectroscopy (STEPR) provides a means for investigating weak spin-spin interaction between spin-labelled molecules because the spectral intensity is proportional to the effective spin-lattice relaxation time,T ₁ ^eff. Rate equations for the spin population defferences yield equivalent results for the dependence ofT ₁ ^eff on the physical (or chemical) and Heisenberg spin exchange rates and show thatT ₁ ^eff depends on the extent of redistribution of saturation throughout the anisotropic spin label powder lineshape. This approach yields a particularly simple formulation for the dependence of the STEPR lineshape on slow rotational diffusion. The effects of spin exchange are readily distinguished from those of slow rotational diffusion because of the insensitivity of the STEPR lineshape in the former case. The characteristic dependence of the STEPR spectral intensity on spin concentration allows determination of the exchange rate and can be used for studying slow translational diffusion, e.g. of spin-labelled proteins. Dipolar relaxation induced by paramagnetic ions gives a linear dependence of the reciprocal spin label STEPR intensity on metal ion concentration. STEPR measurements with spin-labelled lipid molecules in gel phase membranes in the presence of Ni²⁺ ions yield reliable distance information and provide calibrations for use with other systems.     

Determination of the electron relaxation rates in paramagnetic metal complexes: applicability of available NMR methods

Four different approaches for determining the electron relaxation rates in paramagnetic metallo-proteins are investigated, using a paramagnetic Ni2+ complex of a protein as an example. All four approaches rely on the determination of the longitudinal paramagnetic relaxation enhancements, R1p, of the 1H nuclei and the backbone 15N nuclei. Three of the methods utilize the field dependence of the R1p rates. It is found that the applicability of each of these methods depends on whether the fast-motion condition, omegaS2tau2<1, applies to the electron relaxation, omegaS being the Larmor frequency of the electron spin S and tau the correlation time of the electron relaxation. If the fast-motion condition is fulfilled, the electron relaxation rate can be obtained from the ratio of the R1p rates of one or more protons at two magnetic field strengths (method A). On the other hand, if the fast-motion condition does not apply, more elaborate methods must be used that, in general, require a determination of the R1p rates over a larger range of magnetic field strengths (method C). However, in the case of paramagnetic metal ions with relatively slow electron relaxation rates only two magnetic field strengths suffice, if the R1p rates of a hetero nucleus are included in the analysis (method B). In the fourth method (method D), the electron relaxation is estimated as a parameter in a structure calculation, using distance constraints derived from proton R1p rates at only one magnetic field strength. In general, only methods B and C give unambiguous electron relaxation rates.     

Structural determination of spin label immobilization and orientation: a Monte Carlo minimization approach

Electron paramagnetic resonance (EPR) is often used in the study of the orientation and dynamics of proteins. However, there are two major obstacles in the interpretation of EPR signals: (a) most spin labels are not fully immobilized by the protein, hence it is difficult to distinguish the mobility of the label with respect to the protein from the reorientation of the protein itself; (b) even in cases where the label is fully immobilized its orientation with respect to the protein is not known, which prevents interpretation of probe reorientation in terms of protein reorientation. We have developed a computational strategy for determining whether or not a spin label is immobilized and, if immobilized, predicting its conformation within the protein. The method uses a Monte Carlo minimization algorithm to search the conformational space of labels within known atomic level structures of proteins. To validate the method a series of spin labels of varying size and geometry were docked to sites on the myosin head catalytic and regulatory domains. The predicted immobilization and conformation compared well with the experimentally determined mobility and orientation of the label. Thus, probes can now be targeted to report on various modes of molecular dynamics: immobilized probes to report on protein backbone and domain dynamics or floppy probes to report on the extent of steric restriction experienced by the side chain.     

The reverse shift of the EPR line of paramagnetic centers coupled to species with a fast paramagnetic relaxation

The EPR spectrum of the spin 1/2 paramagnetic centers with a relatively slow relaxation is considered in the case when they are coupled via the Heisenberg exchange interaction to partners which have short times of the longitudinal and transverse paramagnetic relaxation. Under these conditions only the EPR line of paramagnetic centers with a relatively slow relaxation is detectable in experiment. The shape of this line is analyzed by solving numerically kinetic equations for the spin density matrix for simple model systems. Depending on a ratio between the exchange integral and the paramagnetic relaxation rates of partner spins, the EPR line shifts in opposite directions. For moderate relaxation rates, as the relaxation rates decrease, the EPR line shifts toward the gravity center of the total EPR spectrum. In the case of extremely fast relaxation, as the relaxation rates decrease, the reverse shift of the EPR line is expected, the line shifts away from the gravity center of the total EPR spectrum. This type of the non-monotonous line shift was experimentally observed for the monocrystal of [CuNd₂(C₄O₄)₄(H₂O)₁₆] · 2H₂O when relaxation rates were changed by temperature variation.     

Chromium(III) complexes as intermolecular probes

Metal ion complexes provide flexible paramagnetic centers that may be used to define intermolecular contacts in a variety of solution phase environments because both the charge and electronic relaxation properties of the complex may be varied. For most complex ions, there are several proton equilibria that may change the effective charge on the complex as a function of pH which in turn affects the efficacy of application for defining the electrostatic surfaces of co-solute molecules. We report here spectrophotometric and nuclear spin relaxation studies on aqueous solutions of chromium(III) complexes of EDTA, DTPA, and bis-amides of both. The effective charges available from these paramagnetic centers range from -3 to +1 and we report the pH ranges over which the effective charge is defined with confidence for application in magnetic relaxation experiments.     

Fast and accurate characterization of biological membranes by EPR spectral simulations of nitroxides

A method by which it is possible to characterize the membranes of biological samples on the basis of the EPR spectral lineshape simulation of membrane-dissolved nitroxide spin probes is described. The presented simulation procedure allows the determination of the heterogeneous structure of biological membranes and fluidity characteristics of individual membrane domains. The method can deal with isotropic and anisotropic orientations of nitroxides introduced into the biological samples described by restricted fast motion with a correlation time between 0.01 and 10 ns. The linewidths of the Lorentzian lineshapes are calculated in a restricted fast-motion approximation. In the special case of samples with high concentrations of nitroxides or in the presence of paramagnetic ions, the lineshapes are calculated directly from the exchange-coupled Bloch equations. The parameters describing ordering, relaxation, polarity, and the portions of the individual spectral components are extracted by optimizing the simulated spectra to the experimental spectrum with either a Simplex or a Monte Carlo algorithm. To improve the algorithm's efficiency, a new way of characterizing the goodness of fits is introduced. The new criterion is based on the standard least-squares function, but with special weighting of the partial sums. Its benefits are confirmed with membrane spectral simulation. Two classes of examples-simulation and optimizations of synthetic spectra to evaluate the accuracy of the optimization algorithms and simulation and optimization of EPR spectra of nitroxides in liposome suspensions in the presence of a broadening agent and in human leukocytes are shown.     

Evaluation of spin labels for in-cell EPR by analysis of nitroxide reduction in cell extract of Xenopus laevis oocytes

Spin-label electron paramagnetic resonance (SL-EPR) spectroscopy has become a powerful and useful tool for studying structure and dynamics of biomacromolecules. However, utilizing these methods at physiological temperatures for in-cell studies is hampered by reduction of the nitroxide spin labels and thus short half-lives in the cellular environment. Consequently, reduction kinetics of two structurally different nitroxides was investigated in cell extracts of Xenopus laevis oocytes using rapid-scan cw-experiments at X-band. The five member heterocyclic ring nitroxide PCA (3-carboxy-2,2,5,5-tetramethylpyrrolidinyl-1-oxy) under investigation features much higher stability against intracellular reduction than the six member ring analog TOAC (2,2,6,6-tetramethylpiperidine-N-oxyl-4-amino-4-carboxilic acid) and is therefore a suitable spin label type for in-cell EPR. The kinetic data can be described according to the Michaelis–Menten model and thus suggest an enzymatic or enzyme-mediated reduction process.     

Electron paramagnetic resonance study of the nuclear spin dynamics in an AlAs quantum well

The nuclear spin dynamics in an asymmetrically doped 16-nm AlAs quantum well grown along the [001] direction has been studied experimentally using the time decay of the Overhauser shift of paramagnetic resonance of conduction electrons. The nonzero spin polarization of nuclei causing the initial observed Overhauser shift is due the relaxation of the nonequilibrium spin polarization of electrons into the nuclear subsystem near electron paramagnetic resonance owing to the hyperfine interaction. The measured relaxation time of nuclear spins near the unity filling factor is (530 ± 30) min at the temperature T = 0.5 K. This value exceeds the characteristic spin relaxation times of nuclei in GaAs/AlGaAs heterostructures by more than an order of magnitude. This fact indicates the decrease in the strength of the hyperfine interaction in the AlAs quantum well in comparison with GaAs/AlGaAs heterostructures.     

Rotational resonance NMR: separation of dipolar coupling and zero quantum relaxation

The solid state NMR technique of rotational resonance (R2) has been used extensively to measure distances approaching 5-6 A between 13C nuclei in a variety of compounds including amyloidogenic peptides and membrane proteins. The accuracy of the distance information extracted from the time-dependent spin dynamics at R2 is often limited by the accuracy with which the relevant zero-quantum lineshape parameters are estimated. Here we demonstrate that measurement of spinning frequency dependent magnetization exchange dynamics provides data from which both distance and zero-quantum relaxation parameters can be extracted independently. In addition to providing more accurate distance information, this technique allows examination of the zero-quantum lineshape, which can indicate the presence of correlated relaxation or chemical shift distributions between dipolar-coupled sites. With this approach we have separated the contribution of dipolar couplings and zero quantum relaxation to R2 exchange curves. Thus, we have significantly improved the accuracy of the measurement of the intramolecular, internuclear distances between a pair of 13C's in two model compounds (N-acetyl-D,L-valine and glycylglycine.HCl) that lie in the distance range 4.6-4.7 A.     

Modulation of the distance dependence of paramagnetic relaxation enhancements by CSA x DSA cross-correlation

Paramagnetic metal ions with fast-relaxing electronic spin and anisotropic susceptibility tensor provide a rich source of structural information that can be derived from pseudo-contact shifts, residual dipolar couplings, dipole-dipole Curie spin cross-correlation, and paramagnetic relaxation enhancements. The present study draws attention to a cross-correlation effect between nuclear relaxation due to anisotropic chemical shielding (CSA) and due to the anisotropic dipolar shielding (DSA) caused by the electronic Curie spin. This CSA x DSA cross-correlation contribution seems to have been overlooked in previous interpretations of paramagnetic relaxation enhancements. It is shown to be sufficiently large to compromise the 1/r6 distance dependence usually assumed. The effect cannot experimentally be separated from auto-correlated DSA relaxation. It can increase or decrease the observed paramagnetic relaxation enhancement. Under certain conditions, the effect can dominate the entire paramagnetic relaxation, resulting in nuclear resonances narrower than in the absence of the paramagnetic center. CSAxDSA cross-correlation becomes important when paramagnetic relaxation is predominantly due to the Curie rather than the Solomon mechanism. Therefore the effect is most pronounced for relaxation by metal ions with large magnetic susceptibility and fast-relaxing electron spin. It most strongly affects paramagnetic enhancements of transverse relaxation in macromolecules and of longitudinal relaxation in small molecules.