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

Paramagnetic NMR in solution and the solid state

The field of paramagnetic NMR has expanded considerably in recent years. This review addresses both the theoretical description of paramagnetic NMR, and the way in which it is currently practised. We provide a review of the theory of the NMR parameters of systems in both solution and the solid state. Here we unify the different languages used by the NMR, EPR, quantum chemistry/DFT, and magnetism communities to provide a comprehensive and coherent theoretical description. We cover the theory of the paramagnetic shift and shift anisotropy in solution both in the traditional formalism in terms of the magnetic susceptibility tensor, and using a more modern formalism employing the relevant EPR parameters, such as are used in first-principles calculations. In addition we examine the theory first in the simple non-relativistic picture, and then in the presence of spin-orbit coupling. These ideas are then extended to a description of the paramagnetic shift in periodic solids, where it is necessary to include the bulk magnetic properties, such as magnetic ordering at low temperatures. The description of the paramagnetic shift is completed by describing the current understanding of such shifts due to lanthanide and actinide ions. We then examine the paramagnetic relaxation enhancement, using a simple model employing a phenomenological picture of the electronic relaxation, and again using a more complex state-of-the-art theory which incorporates electronic relaxation explicitly. An additional important consideration in the solid state is the impact of bulk magnetic susceptibility effects on the form of the spectrum, where we include some ideas from the field of classical electrodynamics. We then continue by describing in detail the solution and solid-state NMR methods that have been deployed in the study of paramagnetic systems in chemistry, biology, and the materials sciences. Finally we describe a number of case studies in paramagnetic NMR that have been specifically chosen to highlight how the theory in part one, and the methods in part two, can be used in practice. The systems chosen include small organometallic complexes in solution, solid battery electrode materials, metalloproteins in both solution and the solid state, systems containing lanthanide ions, and multi-component materials used in pharmaceutical controlled-release formulations that have been doped with paramagnetic species to measure the component domain sizes.

Multiscale nuclear magnetic relaxation dispersion of complex liquids in bulk and confinement

The nuclear magnetic relaxation dispersion (NMRD) technique consists of measurement of the magnetic-field dependence of the longitudinal nuclear-spin-lattice relaxation rate 1/T₁. Usually, the acquisition of the NMRD profiles is made using a fast field cycling (FFC) NMR technique that varies the magnetic field and explores a very large range of Larmor frequencies (10 kHz < ω₀/(2π) <40 MHz). This allows extensive explorations of the fluctuations to which nuclear spin relaxation is sensitive. The FFC technique thus offers opportunities on multiple scales of both time and distance for characterizing the molecular dynamics and transport properties of complex liquids in bulk or embedded in confined environments. This review presents the principles, theories and applications of NMRD for characterizing fundamental properties such as surface correlation times, diffusion coefficients and dynamical surface affinity (NMR wettability) for various confined liquids. The basic longitudinal and transverse relaxation equations are outlined for bulk liquids. The nuclear relaxation of a liquid confined in pores is considered in detail in order to find the biphasic fast exchange relations for a liquid at proximity of a solid surface. The physical-chemistry of liquids at solid surfaces induces striking differences between NMRD profiles of aprotic and protic (water) liquids embedded in calibrated porous disordered materials. A particular emphasis of this review concerns the extension of FFC NMR relaxation to industrial applications. For instance, it is shown that the FFC technique is sufficiently rapid for following the progressive setting of cement-based materials (plasters, cement pastes, concretes). The technique also allows studies of the dynamics of hydrocarbons in proximity of asphaltene nano-aggregates and macro-aggregates in heavy crude oils as a function of the concentration of asphaltenes. It also gives new information on the wettability of petroleum fluids (brine and oil) embedded in shale oil rocks. It is useful for understanding the relations and correlations between NMR relaxation times T₁ and T₂, diffusion coefficients D, and viscosity η of heavy crude oils. This is of particular importance for interpreting T₁, T₂, 2D T₁-T₂ and D-T₂ correlation spectra that could be obtained down-hole, thus giving a valuable tool for investigating in situ the molecular dynamics of petroleum fluids. Another domain of interest concerns biological applications. This is of particular importance for studying the complex dynamical spectrum of a folded polymeric structure that may span many decades in frequency or time. A direct NMRD characterization of water diffusional dynamics is presented at the protein interface. NMR experiments using a shuttle technique give results well above the frequency range accessible via the FFC technique; examples of this show protein dynamics over a range from fast and localized motions to slow and delocalized collective motions involving the whole protein. This review ends by an interpretation of the origin of the proton magnetic field dependence of T₁ for different biological tissues of animals; this includes a proposal for interpreting in vivo MRI data from human brain at variable magnetic fields, where the FFC relaxation analysis suggests that brain white-matter is distinct from grey-matter, in agreement with diffusion-weighted MRI imaging.

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.

Imaging agents based on lanthanide doped nanoparticles

This review summarizes the recent progress of single and multimodal imaging agents based on lanthanide doped nanoparticles.

Rational design for multifunctional non-liposomal lipid-based nanocarriers for cancer management: theory to practice

Nanomedicines have gained more and more attention in cancer therapy thanks to their ability to enhance the tumour accumulation and the intracellular uptake of drugs while reducing their inactivation and toxicity. In parallel, nanocarriers have been successfully employed as diagnostic tools increasing imaging resolution holding great promises both in preclinical research and in clinical settings. Lipid-based nanocarriers are a class of biocompatible and biodegradable vehicles that provide advanced delivery of therapeutic and imaging agents, improving pharmacokinetic profile and safety. One of most promising engineering challenges is the design of innovative and versatile multifunctional targeted nanotechnologies for cancer treatment and diagnosis. This review aims to highlight rational approaches to design multifunctional non liposomal lipid-based nanocarriers providing an update of literature in this field.

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.

Nuclear quadrupole resonance lineshape analysis for different motional models: stochastic Liouville approach

A general theory of lineshapes in nuclear quadrupole resonance (NQR), based on the stochastic Liouville equation, is presented. The description is valid for arbitrary motional conditions (particularly beyond the valid range of perturbation approaches) and interaction strengths. It can be applied to the computation of NQR spectra for any spin quantum number and for any applied magnetic field. The treatment presented here is an adaptation of the "Swedish slow motion theory," [T. Nilsson and J. Kowalewski, J. Magn. Reson. 146, 345 (2000)] originally formulated for paramagnetic systems, to NQR spectral analysis. The description is formulated for simple (Brownian) diffusion, free diffusion, and jump diffusion models. The two latter models account for molecular cooperativity effects in dense systems (such as liquids of high viscosity or molecular glasses). The sensitivity of NQR slow motion spectra to the mechanism of the motional processes modulating the nuclear quadrupole interaction is discussed.

Quadrupole relaxation enhancement--application to molecular crystals

A general theory of field dependent spin-lattice relaxation for nuclei of the spin quantum number 1/2 (1H, 19F, 13C) caused by dipole-dipole interactions with neighboring quadrupolar nuclei (nuclei possessing a quadrupolar moment) is presented. The theory is valid for arbitrary motional conditions and should be treated as a quadrupolar counterpart of the paramagnetic relaxation enhancement theory. When the energy level splitting of the dipolar spin (I=1/2) matches one of the transition frequencies of the quadrupolar nuclei one can observe a local enhancement of the dipolar spin relaxation (referred to as "quadrupolar peaks"). To see such effects the dynamics modulating the spin interactions has to be relatively slow. This brings the system beyond the validity range of perturbation approaches and requires the stochastic Liouville equation to be applied. The presented theory describes the quadrupolar relaxation enhancement (QRE) for an arbitrary spin quantum number of the quadrupolar nuclei and includes the asymmetry of the quadrupolar coupling. It has been applied to interpret the shape of magnetization curves (amplitude of 1H magnetization versus magnetic field) for the molecular crystal [C3N2H5]6[Bi4Br18] ([C3N2H5]-imidazolium). The magnetization curves show several dips (local minima) attributed to 1H-14N quadrupolar relaxation enhancement effects. In addition, as a limiting case a perturbation approach to QRE has been presented and its validity conditions have been discussed.

High-relaxivity magnetic resonance imaging contrast agents. Part 2. Optimization of inner- and second-sphere relaxivity

RATIONALE AND OBJECTIVES

The observed relaxivity of gadolinium-based contrast agents has contributions from the water molecule(s) that bind directly to the gadolinium ion (inner-sphere water), long-lived water molecules and exchangeable protons that make up the second-sphere of coordination, and water molecules that diffuse near the contrast agent (outer-sphere). Inner- and second-sphere relaxivity can both be increased by optimization of the lifetimes of the water molecules and protons in these coordination spheres, the rotational motion of the complex, and the electronic relaxation of the gadolinium ion. We sought to identify new high-relaxivity contrast agents by systematically varying the donor atoms that bind directly to gadolinium to increase inner-sphere relaxivity and concurrently including substituents that influence the second-sphere relaxivity.

METHODS

Twenty gadolinium-1,4,7,10-tetraazacyclo-dodecane-N,N',N″,N'″-tetraacetato derivatives were prepared and their relaxivity determined in presence and absence of human serum albumin as a function of temperature and magnetic field. Data was analyzed to extract the underlying molecular parameters influencing relaxivity. Each compound had a common albumin-binding group and an inner-sphere donor set comprising the 4 tertiary amine N atoms from cyclen, an α-substituted acetate oxygen atom, 2 amide oxygen atoms, an inner-sphere water oxygen atom, and a variable donor group. Each amide nitrogen was substituted with different groups to promote hydrogen bonding with second-sphere water molecules.

RESULTS

Relativities at 0.47 and 1.4 T, 37°C, in serum albumin ranged from 16.0 to 58.1 mM(-1)s(-1) and from 12.3 to 34.8 mM(-1)s(-1), respectively. The reduction of inner-sphere water exchange typical of amide donor groups could be offset by incorporating a phosphonate or phenolate oxygen atom donor in the first coordination sphere, resulting in higher relaxivity. Amide nitrogen substitution with pendant phosphonate or carboxylate groups increased relaxivity by as much as 88% compared with the N-methyl amide analog. Second-sphere relaxivity contributed as much as 24 and 14 mM(-1)s(-1) at 0.47 and 1.4 T, respectively.

CONCLUSIONS

Water/proton exchange dynamics in the inner- and second-coordination sphere can be predictably tuned by choice of donor atoms and second-sphere substituents, resulting in high-relaxivity agents.

High relaxivity magnetic resonance imaging contrast agents. Part 1. Impact of single donor atom substitution on relaxivity of serum albumin-bound gadolinium complexes

RATIONALE AND OBJECTIVES

The donor atoms that bind to gadolinium in contrast agents influence inner-sphere water exchange and electronic relaxation, both of which determine observed relaxivity. The effect of these molecular parameters on relaxivity is greatest when the contrast agent is protein bound. We sought to determine an optimal donor atom set to yield high relaxivity compounds.

METHODS

A total of 38 gadolinium-1,4,7,10-tetraazacyclo-dodecane-N,N',N'',N'''-tetraacetato derivatives were prepared and relaxivity was determined in the presence and absence of human serum albumin as a function of temperature and magnetic field. Each compound had a common albumin-binding group and differed only by substitution of different donor groups at one of the macrocycle nitrogens. Oxygen-17 isotope relaxometry at 7.05 T was performed to estimate water exchange rates.

RESULTS

Changing a single donor atom resulted in changes in water exchange rates ranging across 3 orders of magnitude. Donor groups increased water exchange rate in the order: phosphonate ∼ phenolate > α-substituted acetate > acetate > hydroxamate ∼ sulfonamide > amide ∼ pyridyl ∼ imidazole. Relaxivites at 0.47 and 1.4 T, 37°C, ranged from 12.3 to 55.6 mM(-1)s(-1) and from 8.3 to 32.6 mM(-1)s(-1) respectively. Optimal relaxivities were observed when the donor group was an α-substituted acetate. Electronic relaxation was slowest for the acetate derivatives as well.

CONCLUSIONS

Water exchange dynamics and relaxivity can be predictably tuned by choice of donor atoms.

Fluorine dynamics in BaF2 crystal lattice as an example of complex motion in a simple system

Fluorine relaxation profiles for a BaF(2) single crystal collected at several temperatures have been analyzed in terms of essentially different motional models: free rotational and free translational diffusion. The analysis has been performed to critically review the sensitivity of field dependent relaxation studies to mechanisms of molecular motions. The tested motional models do not realistically describe the fluorine dynamics within the crystal lattice. They have been chosen to attempt to answer quite fundamental questions regarding the feasibility of the field dependent nuclear spin relaxation studies to provide unique information on dynamic processes: 1. Is it possible to get information about the motional mechanisms by analyzing relaxation profiles collected in a broad frequency range? 2. To what extent is it possible to reasonably reproduce relaxation profiles in terms of unrealistic motional models? It has been concluded from the analysis that the rotational model leading to a single exponential correlation function explains the experimental data much better than the translational one. Validity regimes of the second order perturbation theory have been discussed in the context of the investigated system and the applied models.

Field cycling methods as a tool for dynamics investigations in solid state systems: recent theoretical progress

In this paper physical mechanisms and theoretical treatments of polarization transfer and field-dependent relaxation in solid state systems, containing mutually coupled spins of spin quantum numbers I=12 (spins 12) and S1 (quadrupolar spins), are presented. First, theoretical descriptions of these effects are given in detail for an illustrative, simple system. Next, it is shown how to generalize the theories to much more complex spin systems. The polarization transfer and relaxation effects are illustrated by several examples. Typical misunderstandings regarding their physical origins are clarified. This paper reviews recent theoretical descriptions of the polarization transfer and relaxation phenomena. Its goal is to popularize the proper theoretical treatments with the intention to establish them as standard tools for analyzing field cycling data.

A gadolinium triacetic monoamide DOTA derivative with a methanethiosulfonate anchor group. Relaxivity properties and conjugation with albumin and thiolated particles

The gadolinium(III) complex with a new DOTA-based ligand bearing a methanethiosulfonate group (MTS) was synthesized and its relaxivity properties were investigated. MTS-ADO3A is a triacid DOTA derivative with an amide arm substituted by an ethylmethanethiosulfonate function. This ligand was obtained in two steps: tri-tert-butyl 2,2',2''-(1,4,7,10-tetraazacyclododecane-1,4,7-triyl)triacetate was reacted with S-(2-aminoethyl)methanesulfonothioate and the tert-butyl groups were removed with trifluoroacetic acid. The Gd(III) MTS-ADO3A complex readily formed disulfide bonds with albumin (BSA) in its native and reduced forms and with thiolated silica particles. Four- to five-fold relaxivity increases at 20 MHz were measured on the isolated adducts. The EuMTS-ADO3A chelate was found to be monohydrated by fluorescence and the relaxivity parameters of the Gd(III) complex were obtained by (17)O NMR and by measuring the nuclear magnetic relaxation dispersion between 0.01 and 80 MHz. The water exchange time tau(m) is increased upon forming disulfide bonds with macromolecules and particles and the relaxivity gains of all the complexes are limited by the tau(m) factor. Forming covalent or hydrophobic/electrostatic bonds with BSA seems to bring about similar relaxivity changes but the covalent BSA adducts can be isolated and their properties can be directly studied. The addition of dithiothreitol or glutathione leads to the removal of the metal chelates from the macromolecules, as indicated by the relaxation times reverting to their values before binding. It is thus expected that the chelate will stay in the body long enough for imaging but will still be excreted through the kidneys.

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.

Field-dependent nuclear relaxation of spins 1/2 induced by dipole-dipole couplings to quadrupole spins: LaF3 crystals as an example

A general theory of spin-lattice nuclear relaxation of spins I=1/2 caused by dipole-dipole couplings to quadrupole spins S1, characterized by a non-zero averaged (static) quadrupole coupling, is presented. In multispin systems containing quadrupolar and dipolar nuclei, transitions of spins 1/2 leading to their relaxation are associated through dipole-dipole couplings with certain transitions of quadrupole spins. The averaged quadrupole coupling attributes to the energy level structure of the quadrupole spin and influences in this manner relaxation processes of the spin 1/2. Typically, quadrupole spins exhibit also a complex multiexponential relaxation sensed by the dipolar spin as an additional modulation of the mutual dipole-dipole coupling. The proposed model includes both effects and is valid for an arbitrary magnetic field and an arbitrary quadrupole spin quantum number. The theory is applied to interpret fluorine relaxation profiles in LaF3 ionic crystals. The obtained results are compared with predictions of the 'classical' Solomon relaxation theory.

Evolution of solid state systems containing mutually coupled dipolar and quadrupole spins: perturbation treatment

Perturbation approach to time evolution of multi-spin systems containing quadrupole and dipolar spins has been presented and discussed. The treatment comprises polarization transfer effects, field-dependent relaxation processes of dipolar as well as quadrupole spins and combined results of both of them. Complete theories dealing with various aspects of the spin dynamic processes have been proposed. Because of an educational character of this paper, relevant assumptions, limitations and even particular steps of the proposed treatments have been discussed in detail. Special emphasis is put on understanding of validity regimes of the perturbation treatment, depending on relative strengths of spin interactions and timescales of relevant motional processes affecting them. Motional regimes required for spins to be involved in essentially different evolution pathways like polarization transfers or relaxation have been illustrated by experimental examples.

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.

Nuclear spin relaxation study of aqueous raffinose solution in the presence of a gadolinium contrast agent

Paramagnetic enhancement of nuclear spin-lattice relaxation rates (PREs) was measured in aqueous solution of the trisaccharide raffinose in the presence of a gadolinium(III) complex, GdDTPA-BMA, used as a magnetic resonance imaging contrast agent. The relaxation enhancement of aqueous protons was measured over a broad range of magnetic fields, using field-cycling apparatus in addition to conventional spectrometers. The nuclear magnetic relaxation dispersion profile thus obtained was interpreted with a recently developed model, allowing for both inner- and outer-sphere relaxation. The relaxation enhancement for the carbon-13 nuclei in raffinose was studied under high-resolution conditions at three magnetic fields, whereas the sugar proton PRE was measured at two fields. The PRE of the sugar nuclei could be interpreted in a consistent way, assuming that it was caused by the outer-sphere mechanism. The electron spin relaxation was found to be a less important source of modulation of the electron-nuclear dipole-dipole interaction than the mutual translational diffusion.

On the philosophy of optimizing contrast agents. An analysis of 1H NMRD profiles and ESR lineshapes of the Gd(III)complex MS-325+HSA

A generalization of the modified SBM theory is developed in closed analytical form. The theory is applied to describe the paramagnetically enhanced water proton spin-lattice relaxation rates of the aqueous-systems containing a gadolinium(S=7/2) complex(MS-325) in the presence or absence of human serum albumin (HSA). MS-325 binds to HSA: in the absence of the protein the reorientational time, tauR, is short, but when HSA is added tauR becomes much longer. In this way, the effect of reorientational motion, static (Delta s), and transient (Delta t) zero-field splitting (ZFS) interactions on both the water proton relaxivity and the Gd ESR lineshapes are investigated. Two dynamic models of electron spin relaxation are presented, characterized by transient and static ZFS-interactions. X-, Q-, and W-bands ESR spectra of MS-325+HSA are analyzed in order to describe the effect on the electron spin system upon binding to a macromolecule. A computer program based on this theory is developed which calculates solvent water proton T1 NMRD profiles and the corresponding X-, Q-, U-, and W-bands ESR lineshapes.