Nuclear Spin Relaxation in Paramagnetic Systems: Electron Spin Relaxation Effects under Near-Redfield Limit Conditions and Beyond

1H Spin-Lattice Relaxation Processes in Solutions of H2N-Fe3O4 Nanoparticles: Insights from NMR Relaxometry

1H spin-lattice relaxation experiments have been performed for water and glycerol/water solutions of H2N-Fe3O4 superparamagnetic nanoparticles (NPs) of about 7 nm diameter. The experiments encompass a broad frequency range covering 3 orders of magnitude, from 10 kHz to 10 MHz (referring to 1H resonance frequency), and have been performed in the temperature range from 298 to 313 K, varying the concentration of the superparamagnetic species. This extensive dataset has been used for twofold purposes. The first one is to serve as a challenge for thorough tests of theoretical models describing nuclear relaxation in solutions of superparamagnetic NPs, depending on their magnetic properties and dynamics of the solvent molecules. The challenge is posed by the wish to reproduce the data in a broad range of magnetic fields (not only at high fields) and by the need to explain the differences in the relaxation scenarios for water and glycerol/water solutions by varying only the solvent parameters. The second purpose is to get insights into the magnetic properties (electronic relaxation properties) of the nanoparticles due to their high applicational potential.

Large Protein Assemblies for High-Relaxivity Contrast Agents: The Case of Gadolinium-Labeled Asparaginase

Biologics are emerging as the most important class of drugs and are used to treat a large variety of pathologies. Most of biologics are proteins administered in large amounts, either by intramuscular injection or by intravenous infusion. Asparaginase is a large tetrameric protein assembly, currently used against acute lymphoblastic leukemia. Here, a gadolinium(III)-DOTA derivative has been conjugated to asparaginase, and its relaxation properties have been investigated to assess its efficiency as a possible theranostic agent. The field-dependent ¹H longitudinal relaxation measurements of water solutions of gadolinium(III)-labeled asparaginase indicate a very large increase in the relaxivity of this paramagnetic protein complex with respect to small gadolinium chelates, opening up the possibility of its use as an MRI contrast agent.

Nanosized T1 MRI Contrast Agent Based on a Polyamidoamine as Multidentate Gd Ligand

A linear polyamidoamine (PAA) named BAC-EDDS, containing metal chelating repeat units composed of two tert-amines and four carboxylic groups, has been prepared by the aza-Michael polyaddition of ethylendiaminodisuccinic (EDDS) with 2,2-bis(acrylamido)acetic acid (BAC). It was characterized by size exclusion chromatography (SEC), FTIR, UV–Vis and NMR spectroscopies. The pK_a values of the ionizable groups of the repeat unit were estimated by potentiometric titration, using a purposely synthesized molecular ligand (Agly-EDDS) mimicking the structure of the BAC-EDDS repeat unit. Dynamic light scattering (DLS) and ζ-potential analyses revealed the propensity of BAC-EDDS to form stable nanoaggregates with a diameter of approximately 150 nm at pH 5 and a net negative charge at physiological pH, in line with an isoelectric point <2. BAC-EDDS stably chelated Gd (III) ions with a molar ratio of 0.5:1 Gd (III)/repeat unit. The stability constant of the molecular model Gd-Agly-EDDS (log K = 17.43) was determined as well, by simulating the potentiometric titration through the use of Hyperquad software. In order to comprehend the efficiency of Gd-BAC-EDDS in contrasting magnetic resonance images, the nuclear longitudinal (r₁) and transverse (r₂) relaxivities as a function of the externally applied static magnetic field were investigated and compared to the ones of commercial contrast agents. Furthermore, a model derived from the Solomon–Bloembergen–Morgan theory for the field dependence of the NMR relaxivity curves was applied and allowed us to evaluate the rotational correlation time of the complex (τ = 0.66 ns). This relatively high value is due to the dimensions of Gd-BAC-EDDS, and the associated rotational motion causes a peak in the longitudinal relaxivity at ca. 75 MHz, which is close to the frequencies used in clinics. The good performances of Gd-BAC-EDDS as a contrast agent were also confirmed through in vitro magnetic resonance imaging experiments with a 0.2 T magnetic field.

Longitudinal and transverse NMR relaxivities of Ln(III)-DOTA complexes: A comprehensive investigation

Longitudinal and transverse ¹H nuclear magnetic resonance relaxivities of Ln(III)-DOTA complexes (with Ln = Gd, Tb, Dy, Er; DOTA = 1,4,7,10-tetraazacyclododecane-N,N',N^″,N‴-tetraacetic acid) and Mn(II) aqueous solutions were measured in a wide range of frequencies, 10 kHz to 700 MHz. The experimental data were interpreted by means of models derived from the Solomon-Bloembergen-Morgan theory. The data analysis was performed assuming the orbital angular momentum L = 0 for Gd-DOTA and the aqua ion [Mn(H₂O)₆]²⁺ and L ≠ 0 for Dy-, Tb-, and Er-DOTA. A refined estimation of the zero-field-splitting barrier Δ and of the modulation correlation time τ_v was obtained for [Mn(H₂O)₆]²⁺ by extending the fitting of nuclear magnetic relaxation dispersion profiles to the low-field regime. The Gd-DOTA fitting parameters resulted in good agreement with the literature, and the fit of transverse relaxivity data confirmed the negligibility of the scalar interaction in the nuclear relaxation mechanism. Larger transverse relaxivities of Dy-DOTA and Tb-DOTA (∼10 mM^-1 s^-1) with respect to Er-DOTA (∼1 mM^-1 s^-1) were observed at 16 T. Such higher values are suggested to be due to a shorter residence time τ_m that is possibly linked to the fluctuations of the hyperfine interaction and the different shape of the magnetic anisotropy. The possible employment of Dy-DOTA, Tb-DOTA, and Er-DOTA as negative magnetic resonance imaging contrast agents for high-field applications was envisaged by collecting spin-echo images at 7 T. Particularly in Dy- and Tb-derivatives, the transverse relaxivity at 16 T is of the order of the Gd-one at 1.5 T.

Unveiling protein dynamics in solution with field-cycling NMR relaxometry

Field-cycling NMR relaxometry is a well-established technique that can give information on molecular structure and dynamics of biological systems. It provides the nuclear relaxation rates as a function of the applied magnetic field, starting from fields as low as ~ 10^-4 T up to about 1-3 T. The profiles so collected, called nuclear magnetic relaxation dispersion (NMRD) profiles, can be extended to include the relaxation rates at the largest fields achievable with high resolution NMR spectrometers. By exploiting this wide range of frequencies, the NMRD profiles can provide information on motions occurring on time scales from 10^-6 to 10^-9 s. ¹H NMRD measurements have proved very useful also for the characterization of paramagnetic proteins, because they can help characterise a number of parameters including the number, distance and residence time of water molecules coordinated to the paramagnetic center, the reorientation correlation times and the electron spin relaxation time, and the electronic structure at the metal site.

Magnetic susceptibility and paramagnetism-based NMR

The magnetic interactions between the nuclear magnetic moment and the magnetic moment of unpaired electron(s) depend on the structure and dynamics of the molecules where the paramagnetic center is located and of their partners. The long-range nature of the magnetic interactions is thus a reporter of invaluable information for structural biology studies, when other techniques often do not provide enough data for the atomic-level characterization of the system. This precious information explains the flourishing of paramagnetism-assisted NMR studies in recent years. Many paramagnetic effects are related to the magnetic susceptibility of the paramagnetic metal. Although these effects have been known for more than half a century, different theoretical models and new approaches have been proposed in the last decade. In this review, we have summarized the consequences for NMR spectroscopy of magnetic interactions between nuclear and electron magnetic moments, and thus of the presence of a magnetic susceptibility due to metals, and we do so using a unified notation.

Chemistry of MRI Contrast Agents: Current Challenges and New Frontiers

Tens of millions of contrast-enhanced magnetic resonance imaging (MRI) exams are performed annually around the world. The contrast agents, which improve diagnostic accuracy, are almost exclusively small, hydrophilic gadolinium(III) based chelates. In recent years concerns have arisen surrounding the long-term safety of these compounds, and this has spurred research into alternatives. There has also been a push to develop new molecularly targeted contrast agents or agents that can sense pathological changes in the local environment. This comprehensive review describes the state of the art of clinically approved contrast agents, their mechanism of action, and factors influencing their safety. From there we describe different mechanisms of generating MR image contrast such as relaxation, chemical exchange saturation transfer, and direct detection and the types of molecules that are effective for these purposes. Next we describe efforts to make safer contrast agents either by increasing relaxivity, increasing resistance to metal ion release, or by moving to gadolinium(III)-free alternatives. Finally we survey approaches to make contrast agents more specific for pathology either by direct biochemical targeting or by the design of responsive or activatable contrast agents.

Lanthanide-induced relaxation anisotropy

Lanthanide ions accelerate nuclear spin relaxation by two primary mechanisms: dipolar and Curie. Both are commonly assumed to depend on the length of the lanthanide-nucleus vector, but not on its direction. Here we show experimentally that this is wrong - careful proton relaxation data analysis in a series of isostructural lanthanide complexes (Ln = Tb, Dy, Ho, Er, Tm, Yb) reveals angular dependence in both Curie and dipolar relaxation. The reasons are: (a) that magnetic susceptibility anisotropy can be of the same order of magnitude as the isotropic part (contradicting the unstated assumption in Guéron's theory of the Curie relaxation process), and (b) that zero-field splitting can be much stronger than the electron Zeeman interaction (Bloembergen's original theory of the lanthanide-induced dipolar relaxation process makes the opposite assumption). These factors go beyond the well researched cross-correlation effects; they alter the relaxation theory treatment and make strong angular dependencies appear in the nuclear spin relaxation rates. Those dependencies are impossible to ignore - this is now demonstrated both theoretically and experimentally, and suggests that a major revision is needed of the way lanthanide-induced relaxation data are used in structural biology.

Interaction of Spin-Labeled Lipid Membranes with Transition Metal Ions

The large values of spin relaxation enhancement (RE) for PC spin-labels in the phospholipid membrane induced by paramagnetic metal salts dissolved in the aqueous phase can be explained by Heisenberg spin exchange due to conformational fluctuations of the nitroxide group as a result of membrane fluidity, flexibility of lipid chains, and, possibly, amphiphilic nature of the nitroxide label. Whether the magnetic interaction occurs predominantly via Heisenberg spin exchange (Ni) or by the dipole–dipole (Gd) mechanism, it is essential for the paramagnetic ion to get into close proximity to the nitroxide moiety for efficient RE. For different salts of Ni the RE in phosphatidylcholine membranes follows the anionic Hofmeister series and reflects anion adsorption followed by anion-driven attraction of paramagnetic cations on the choline groups. This adsorption is higher for chaotropic ions, e.g., perchlorate. (A chaotropic agent is a molecule in water solution that can disrupt the hydrogen bonding network between water molecules.) However, there is no anionic dependence of RE for model membranes made from negatively charged lipids devoid of choline groups. We used Ni-induced RE to study the thermodynamics and electrostatics of ion/membrane interactions. We also studied the effect of membrane composition and the phase state on the RE values. In membranes with cholesterol a significant difference is observed between PC labels with nitroxide tethers long enough vs not long enough to reach deep into the membrane hydrophobic core behind the area of fused cholesterol rings. This study indicates one must be cautious in interpreting data obtained by PC labels in fluid membranes in terms of probing membrane properties at different immersion depths when it can be affected by paramagnetic species at the membrane surface.

High relaxivity Gd(III)-DNA gold nanostars: investigation of shape effects on proton relaxation

Gadolinium(III) nanoconjugate contrast agents (CAs) have distinct advantages over their small-molecule counterparts in magnetic resonance imaging. In addition to increased Gd(III) payload, a significant improvement in proton relaxation efficiency, or relaxivity (r1), is often observed. In this work, we describe the synthesis and characterization of a nanoconjugate CA created by covalent attachment of Gd(III) to thiolated DNA (Gd(III)-DNA), followed by surface conjugation onto gold nanostars (DNA-Gd@stars). These conjugates exhibit remarkable r1 with values up to 98 mM(-1) s(-1). Additionally, DNA-Gd@stars show efficient Gd(III) delivery and biocompatibility in vitro and generate significant contrast enhancement when imaged at 7 T. Using nuclear magnetic relaxation dispersion analysis, we attribute the high performance of the DNA-Gd@stars to an increased contribution of second-sphere relaxivity compared to that of spherical CA equivalents (DNA-Gd@spheres). Importantly, the surface of the gold nanostar contains Gd(III)-DNA in regions of positive, negative, and neutral curvature. We hypothesize that the proton relaxation enhancement observed results from the presence of a unique hydrophilic environment produced by Gd(III)-DNA in these regions, which allows second-sphere water molecules to remain adjacent to Gd(III) ions for up to 10 times longer than diffusion. These results establish that particle shape and second-sphere relaxivity are important considerations in the design of Gd(III) nanoconjugate CAs.

Nuclear magnetic resonance relaxivities: investigations of ultrahigh-spin lanthanide clusters from 10 MHz to 1.4 GHz

Paramagnetic relaxation enhancement is often explored in magnetic resonance imaging in terms of contrast agents and in biomolecular nuclear magnetic resonance (NMR) spectroscopy for structure determination. New ultrahigh-spin clusters are investigated with respect to their NMR relaxation properties. As their molecular size and therefore motional correlation times as well as their electronic properties differ significantly from those of conventional contrast agents, questions about a comprehensive characterization arise. The relaxivity was studied by field-dependent longitudinal and transverse NMR relaxometry of aqueous solutions containing Fe(III)(10)Dy(III)(10) ultrahigh-spin clusters (spin ground state 100/2). The high-field limit was extended to 32.9 T by using a 24 MW resistive magnet and an ultrahigh-frequency NMR setup. Interesting relaxation dispersions were observed; the relaxivities increase up to the highest available fields, which indicates a complex interplay of electronic and molecular correlation times.

Gd(III)-labeled peptide nanofibers for reporting on biomaterial localization in vivo

Bioactive supramolecular nanostructures are of great importance in regenerative medicine and the development of novel targeted therapies. In order to use supramolecular chemistry to design such nanostructures, it is extremely important to track their fate in vivo through the use of molecular imaging strategies. Peptide amphiphiles (PAs) are known to generate a wide array of supramolecular nanostructures, and there is extensive literature on their use in areas such as tissue regeneration and therapies for disease. We report here on a series of PA molecules based on the well-established β-sheet amino acid sequence V3A3 conjugated to macrocyclic Gd(III) labels for magnetic resonance imaging (MRI). These conjugates were shown to form cylindrical supramolecular assemblies using cryogenic transmission electron microscopy and small-angle X-ray scattering. Using nuclear magnetic relaxation dispersion analysis, we observed that thermal annealing of the nanostructures led to a decrease in water exchange lifetime (τm) of hundreds of nanoseconds only for molecules that self-assemble into nanofibers of high aspect ratio. We interpret this decrease to indicate more solvent exposure to the paramagnetic moiety on annealing, resulting in faster water exchange within angstroms of the macrocycle. We hypothesize that faster water exchange in the nanofiber-forming PAs arises from the dehydration and increase in packing density on annealing. Two of the self-assembling conjugates were selected for imaging PAs after intramuscular injections of the PA C16V3A3E3-NH2 in the tibialis anterior muscle of a murine model. Needle tracts were clearly discernible with MRI at 4 days postinjection. This work establishes Gd(III) macrocycle-conjugated peptide amphiphiles as effective tracking agents for peptide amphiphile materials in vivo over the timescale of days.

Curie-type paramagnetic NMR relaxation in the aqueous solution of Ni(ii)

The magnetic field of the Curie spin manifests itself as both the pNMR shielding tensor and Curie relaxation, in analogy with CSA relaxation theory.

Experimental determination of microsecond reorientation correlation times in protein solutions

Reorientation correlation times in protein solutions are key determinants for feasibility and quality of NMR experiments. Yet, their accurate estimate is not easy, especially in the case of very large proteins. We show that nuclear magnetic relaxation dispersion (NMRD) can accurately determine reorientation times up to the microsecond range. A theoretical description for the analysis of the NMRD profiles is provided, and the protein reorientation time is shown to be provided by the longest correlation time among those needed to reproduce the experimental profile. Measurements are performed using samples of the archaeal proteasome double ring α7α7 and of αB-Crystallin in glycerol solutions.

Jahn-Teller dynamics in a series of high-symmetry Co(II) chelates determine paramagnetic relaxation enhancements

NMR paramagnetic relaxation enhancements (PREs) of a series of structurally characterized, trigonal bis-trispyrazolylborate (Tp) chelates of high-spin Co(II), spanning 100-850 MHz in field, are reported. Prior knowledge of the metal-nucleus distances allows numerical extraction of position-dependent electron spin relaxation rates (τ(c)(-1)) from direct measurement of the individual PREs of the four symmetry distinct protons in Co(Tp)(2), using available closed-form expressions. The data for this electronically complex system where spin-orbit coupling defines the ground state electronic structure are analyzed in terms of the Solomon-Bloembergen-Morgan (SBM) relations, as well as available zero-field splitting limit theories. A simple angular correction is shown to be sufficient to reconcile the individual τ(c)(T) data for the four classes of protons. The data identify a previously unrecognized dynamic Jahn-Teller effect in these historically important complexes, with a barrier of ~230 cm(-1), pointing to a level of dynamics in trispyrazolylborate chemistry that has not been described before, and further show that it is the Jahn-Teller that is responsible for the PREs in fluid solution. A field-dependent component is also identified for the two protons nearest g(//), which is suggested to arise due to Zeeman mixing of excited state character into the ground level.

A modular system for the synthesis of multiplexed magnetic resonance probes

We have developed a modular architecture for preparing high-relaxivity multiplexed probes utilizing click chemistry. Our system incorporates azide bearing Gd(III) chelates and a trialkyne scaffold with a functional group for subsequent modification. In optimizing the relaxivity of this new complex, we undertook a study of the linker length between a chelate and the scaffold to determine its effect on relaxivity. The results show a strong dependence on flexibility between the individual chelates and the scaffold with decreasing linker length leading to significant increases in relaxivity. Nuclear magnetic resonance dispersion (NMRD) spectra were obtained to confirm a 10-fold increase in the rotational correlation time from 0.049 to 0.60 ns at 310 K. We have additionally obtained a crystal structure demonstrating that modification with an azide does not impact the coordination of the lanthanide. The resulting multinuclear center has a 500% increase in per Gd (or ionic) relaxivity at 1.41 T versus small molecule contrast agents and a 170% increase in relaxivity at 9.4 T.

Albumin binding, relaxivity, and water exchange kinetics of the diastereoisomers of MS-325, a gadolinium(III)-based magnetic resonance angiography contrast agent

The amphiphilic gadolinium complex MS-325 ((trisodium-{(2-(R)-[(4,4-diphenylcyclohexyl) phosphonooxymethyl] diethylenetriaminepentaacetato) (aquo)gadolinium(III)}) is a contrast agent for magnetic resonance angiography (MRA). MS-325 consists of two slowly interconverting diastereoisomers, A and B (65:35 ratio), which can be isolated at pH > 8.5 (TyeklAr, Z.; Dunham, S. U.; Midelfort, K.; Scott, D. M.; Sajiki, H.; Ong, K.; Lauffer, R. B.; Caravan, P.; McMurry, T. J. Inorg. Chem. 2007, 46, 6621-6631). MS-325 binds to human serum albumin (HSA) in plasma resulting in an extended plasma half-life, retention of the agent within the blood compartment, and an increased relaxation rate of water protons in plasma. Under physiological conditions (37 degrees C, pH 7.4, phosphate buffered saline (PBS), 4.5% HSA, 0.05 mM complex), there is no statistical difference in HSA affinity or relaxivity between the two isomers (A 88.6 +/- 0.6% bound, r1 = 42.0 +/- 1.0 mM(-1) s(-1) at 20 MHz; B 90.2 +/- 0.6% bound, r1 = 38.3 +/- 1.0 mM(-1) s(-1) at 20 MHz; errors represent 1 standard deviation). At lower temperatures, isomer A has a higher relaxivity than isomer B. The water exchange rates in the absence of HSA at 298 K, kA298 = 5.9 +/- 2.8 x 10(6) s(-1), kB298 = 3.2 +/- 1.8 x 10(6) s(-1), and heats of activation, DeltaHA = 56 +/- 8 kJ/mol, DeltaHB = 59 +/- 11 kJ/mol, were determined by variable-temperature 17O NMR at 7.05 T. Proton nuclear magnetic relaxation dispersion (NMRD) profiles were recorded over the frequency range of 0.01-50 MHz at 5, 15, 25, and 35 degrees C in a 4.5% HSA in PBS solution for each isomer (0.1 mM). Differences in the relaxivity in HSA between the two isomers could be attributed to the differing water exchange rates.

Paramagnetic relaxation of protons in rotationally immobilized proteins

The proton magnetic relaxation dispersion profiles are reported over the proton Larmor frequency range from 0.01 to 30 MHz for cross-linked gels and for the dry lyophilized bovine serum albumin covalently labeled at lysine with diethylenetriaminepentaacetic acid chelates of either Gd(III) or Mn(II) ions. The proton spin-lattice relaxation dispersion for the cross-linked paramagnetic protein gel is accurately represented as a sum of two major relaxation contributions. The diamagnetic term is a power law from the magnetic field dependence of the protein protons. The paramagnetic term is approximately described by the Solomon-Bloembergen-Morgan class of models. However, the paramagnetic relaxation mechanism in the dry lyophilized protein is fundamentally different and we develop a new quantitative description of the dispersion profile. In the dry case, no peak in the proton relaxation dispersion profile is detected from the field dependence of the electron spin relaxation times. The high-field paramagnetic relaxation dispersion is a power law in the Larmor frequency with an exponent of -0.8, which results from modulation of the electron-nuclear coupling by the intramolecular dynamics of the protein which primarily propagates along the primary structure of the protein. The low-field plateau is caused by the interruption of the electron-nuclear spin correlation by electron spin relaxation. This new quantitative description provides a simple approach to the measurement of electron spin-lattice relaxation times in paramagnetic protein systems at room temperature based on the magnetic field dependence of the proton spin-lattice relaxation rate constant.

NMR Spectroscopy of Paramagnetic Metalloproteins

This article deals with the solution structure determination of paramagnetic metalloproteins by NMR spectroscopy. These proteins were believed not to be suitable for NMR investigations for structure determination until a decade ago, but eventually novel experiments and software protocols were developed, with the aim of making the approach suitable for the goal and as user-friendly and safe as possible. In the article, we also give hints for the optimization of experiments with respect to each particular metal ion, with the aim of also providing a handy tool for nonspecialists. Finally, a section is dedicated to the significant progress made on 13C direct detection, which reduces the negative effects of paramagnetism and may constitute a new chapter in the whole field of NMR spectroscopy.

NMR paramagnetic relaxation due to the S=5∕2 complex, Fe(III)-(tetra-p-sulfonatophenyl)porphyrin: Central role of the tetragonal fourth-order zero-field splitting interaction

The metalloporphyrins, Me-TSPP [Me=Cr(III), Mn(III), Mn(II), Fe(III), and TSPP=meso-(tetra-p-sulfonatophenyl)porphyrin], which possess electron spins S=3/2, 2, 5/2, and 5/2, respectively, comprise an important series of model systems for mechanistic studies of NMR paramagnetic relaxation enhancement (NMR-PRE). For these S>1/2 spin systems, the NMR-PRE depends critically on the detailed form of the zero-field splitting (zfs) tensor. We report the results of experimental and theoretical studies of the NMR relaxation mechanism associated with Fe(III)-TSPP, a spin 5/2 complex for which the overall zfs is relatively large (D approximately = 10 cm(-1)). A comparison of experimental data with spin dynamics simulations shows that the primary determinant of the shape of the magnetic relaxation dispersion profile of the water proton R1 is the tetragonal fourth-order component of the zfs tensor. The relaxation mechanism, which has not previously been described, is a consequence of zfs-induced mixing of the spin eigenfunctions of adjacent Kramers doublets. We have also investigated the magnetic-field dependence of electron-spin relaxation for S=5/2 in the presence of a large zfs, such as occurs in Fe(III)-TSPP. Calculations show that field dependence of this kind is suppressed in the vicinity of the zfs limit, in agreement with observation.

Electron spin relaxation due to reorientation of a permanent zero field splitting tensor

Electron spin relaxation of transition metal ions with spin S> or =1 results primarily from thermal modulation of the zero field splitting (zfs) tensor. This occurs both by distortion of the zfs tensor due to intermolecular collisions and, for complexes with less than cubic symmetry, by reorientational modulation of the permanent zfs tensor. The reorientational mechanism is much less well characterized in previous work than the distortional mechanism although it is an important determinant of nuclear magnetic resonance (NMR) paramagnetic relaxation enhancement phenomena (i.e., the enhancement of NMR relaxation rates produced by paramagnetic ions in solution or NMR-PRE). The classical density matrix theory of spin relaxation does not provide an appropriate description of the reorientational mechanism at low Zeeman field strengths because the zero-order spin wave functions are stochastic functions of time. Using spin dynamics simulation techniques, the time correlation functions of the spin operators have been computed and used to determine decay times for the reorientational relaxation mechanism for S=1. In the zfs limit of laboratory field strengths (H(Zeem)<<H(zfs) (composite function)), when the zfs tensor is cylindrical, the spin decay is exponential, the spin relaxation time, tau(S) (composite function) approximately 0.53tau(R)((1)), where tau(R)((1)) is the reorientational correlation time of a molecule-fixed vector. The value of tau(S) (composite function) is independent of the magnitude of the cylindrical zfs parameter (D), but it depends strongly on low symmetry zfs terms (the E/D ratio). Other spin dynamics (SD) simulations examined spin decay in the intermediate regime of field strengths where H(Zeem) approximately H(zfs) (composite function), and in the vicinity of the Zeeman limit. The results demonstrate that the reorientational electron spin relaxation mechanism is often significant when H(zfs) (composite function)> or =H(Zeem), and that its neglect can lead to serious errors in the interpretation of NMR-PRE data.

Nuclear spin relaxation in paramagnetic systems (S>/=1) under fast rotation conditions

A new theoretical model for nuclear spin relaxation in paramagnetic systems in solution has been developed. Fast rotational motion is included in the model, both as a source of modulation of the static zero-field splitting, which provides a mechanism for electron spin relaxation, and as an origin of the stochastic variation of the electron spin-nuclear spin dipole-dipole interaction leading to nuclear spin relaxation. At the limit of low magnetic field, the model is essentially identical to the earlier formulations from our laboratory, but new closed-form expressions are given for the inner- and outer-sphere relaxation at the high-field limit. Numerical comparisons with a general theory are reported for the inner-sphere case. In addition, some nuclear magnetic relaxation dispersion (NMRD) profiles from the literature are considered for systems where experiments have been done with both low-molecular weight paramagnetic complexes and their adducts with proteins. Previously developed theories are used to interpret data for the slowly rotating protein adducts, and good fits of the fast-rotating counterparts are obtained by further adjustment of one or two additional parameters.