General treatment of paramagnetic relaxation enhancement associated with translational diffusion

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.

Solvent paramagnetic relaxation enhancement as a versatile method for studying structure and dynamics of biomolecular systems

Solvent paramagnetic relaxation enhancement (sPRE) is a versatile nuclear magnetic resonance (NMR)-based method that allows characterization of the structure and dynamics of biomolecular systems through providing quantitative experimental information on solvent accessibility of NMR-active nuclei. Addition of soluble paramagnetic probes to the solution of a biomolecule leads to paramagnetic relaxation enhancement in a concentration-dependent manner. Here we review recent progress in the sPRE-based characterization of structural and dynamic properties of biomolecules and their complexes, and aim to deliver a comprehensive illustration of a growing number of applications of the method to various biological systems. We discuss the physical principles of sPRE measurements and provide an overview of available co-solute paramagnetic probes. We then explore how sPRE, in combination with complementary biophysical techniques, can further advance biomolecular structure determination, identification of interaction surfaces within protein complexes, and probing of conformational changes and low-population transient states, as well as deliver insights into weak, nonspecific, and transient interactions between proteins and co-solutes. In addition, we present examples of how the incorporation of solvent paramagnetic probes can improve the sensitivity of NMR experiments and discuss the prospects of applying sPRE to NMR metabolomics, drug discovery, and the study of intrinsically disordered proteins.

NMR Relaxivities of Paramagnetic, Ultra-High Spin Heterometallic Clusters within Polyoxometalate Matrix as a Function of Solvent and Metal Ion

Selectivity and image contrast are always challenging in magnetic resonance imaging (MRI), which are - inter alia - addressed by contrast agents. These compounds still need to be improved, and their relaxation properties, i. e., their paramagnetic relaxation enhancement (PRE), needs to be understood. The main goal is to improve specificity and relaxivities, especially at the high magnetic fields currently exploited not only in material science but also in the medical environment. Longitudinal and transverse relaxivities, r₁ and r₂ , which correspond to the longitudinal and transverse relaxation rates R₁ and R_2, normalized to the concentration of the paramagnetic moieties, need to be considered because both contribute to the image contrast. ¹ H-relaxivities r₁ and r₂ of high-spin heterometallic clusters were studied containing lanthanide and transition-metal ions within a polyoxometalate matrix. A wide range of magnetic fields from 0.5 T/20 MHz to 33 T/1.4 GHz was applied. The questions addressed here concern the rotational and diffusion correlation times which determine the relaxivities and are affected by the solvent's viscosity. Moreover, the variation of the lanthanide and transition-metal ions of the clusters provided insights into the sensitivity of PRE with respect to the electron spin properties of the paramagnetic centers as well as cooperative effects between lanthanides and transition metal ions.

Field-dependent paramagnetic relaxation enhancement in solutions of Ni(II): What happens above the NMR proton frequency of 1 GHz?

An extended set of paramagnetic relaxation enhancement (PRE) data, up to the field of 32.9 Tesla, is reported for protons in an acidified aqueous solution of a Ni(II) salt in the presence and in the absence of added glycerol. For the 55% w/w glycerol sample, a distinct maximum in the PRE vs magnetic field curve is observed for the first time. The data are analysed using the Swedish slow-motion theory, including both the intramolecular (inner-sphere) and intermolecular (outer-sphere) contributions. The results indicate that estimating the outer-sphere part in the presence of the more efficient inner-sphere term is a difficult task.

Dynamics of Dimethylbutanols in Plastic Crystalline Phases by Field Cycling 1H NMR Relaxometry

2,2-Dimethylbutan-1-ol (2,2-DM-1-B), 3,3-dimethylbutan-1-ol (3,3-DM-1-B), and 3,3-dimethylbutan-2-ol (3,3-DM-2-B) show a rich solid-state polymorphism, which includes one or more plastic crystalline phases (also referred to as orientationally disordered crystalline (ODIC) phases) and glass of the liquid or ODIC phases. In this work, the dynamics of the three isomeric alcohols was investigated in the liquid and plastic crystalline phases by fast field cycling ¹H NMR relaxometry in the temperature range between 213 and 303 K. The analysis of the nuclear magnetic relaxation dispersion curves (i.e., longitudinal relaxation rate R₁ vs ¹H Larmor frequency) acquired for the different alcohols at different temperatures gave quantitative information on internal motions, overall molecular reorientations, and molecular self-diffusion. Self-diffusion coefficients were also determined in the liquid phase and in some ODIC phases of the samples from the trends of ¹H R₁ as a function of the frequency square root at low frequencies. Remarkable changes in the temperature trends of correlation times and self-diffusion coefficients were found at the transition between the liquid and the ODIC phase for 2,2-DM-1-B and 3,3-DM-1-B, and between ODIC phases for 3,3-DM-2-B, the latter sample showing a markedly different dynamic and phase behavior.

Model - free approach to quadrupole spin relaxation in solid 209Bi-aryl compounds

Nuclear Quadrupole Resonance (NQR) experiments were performed for deuterated and non-deuterated triphenylbismuth (BiPh3) to inquire into 209Bi relaxation mechanisms. The studies are motivated by the idea of exploiting Quadrupole Relaxation Enhancement (QRE) as a novel contrast mechanism for Magnetic Resonance Imaging. From this perspective relaxation features of nuclei possessing quadrupole moment (quadrupole nuclei) are of primary importance for the contrast effect. Spin-spin relaxation rates associated with the NQR lines were described in terms of the Redfield relaxation theory assuming that the relaxation is caused by fluctuations of the electric field gradient tensor at the position of the quadrupole nucleus that are described by an exponential correlation function. The description referred to as a model-free approach is an analogy of the description used for paramagnetic contrast agents. It was demonstrated that for the deuterated compound this approach captures the essential features of 209Bi relaxation, but it should not be applied for non-deuterated compounds as dipolar interactions between neighbouring protons and the quadrupole nucleus considerably contribute to the relaxation of the last one. Thus, the relaxation scenario for species containing quadrupole nuclei is fundamentally different than for paramagnetic contrast agents and this fact has to be taken into account when predicting contrast effects based on QRE.

209Bi quadrupole relaxation enhancement in solids as a step towards new contrast mechanisms in magnetic resonance imaging

²⁰⁹Bi containing species have the potential to become novel contrast agents for MRI.

Self-diffusion studies by intra- and inter-molecular spin-lattice relaxometry using field-cycling: Liquids, plastic crystals, porous media, and polymer segments

Field-cycling NMR relaxometry is a well-established technique for probing molecular dynamics in a frequency range from typically a few kHz up to several tens of MHz. For the interpretation of relaxometry data, it is quite often assumed that the spin-lattice relaxation process is of an intra-molecular nature so that rotational fluctuations dominate. However, dipolar interactions as the main type of couplings between protons and other dipolar species without quadrupole moments can imply appreciable inter-molecular contributions. These fluctuate due to translational displacements and to a lesser degree also by rotational reorientations in the short-range limit. The analysis of the inter-molecular proton spin-lattice relaxation rate thus permits one to evaluate self-diffusion variables such as the diffusion coefficient or the mean square displacement on a time scale from nanoseconds to several hundreds of microseconds. Numerous applications to solvents, plastic crystals and polymers will be reviewed. The technique is of particular interest for polymer dynamics since inter-molecular spin-lattice relaxation diffusometry bridges the time scales of quasi-elastic neutron scattering and field-gradient NMR diffusometry. This is just the range where model-specific intra-coil mechanisms are assumed to occur. They are expected to reveal themselves by characteristic power laws for the time-dependence of the mean-square segment displacement. These can be favorably tested on this basis. Results reported in the literature will be compared with theoretical predictions. On the other hand, there is a second way for translational diffusion phenomena to affect the spin-lattice relaxation dispersion. If rotational diffusion of molecules is restricted, translational diffusion properties can be deduced even from molecular reorientation dynamics detected by intra-molecular spin-lattice relaxation. This sort of scenario will be relevant for adsorbates on surfaces or polymer segments under entanglement and chain connectivity constraints. Under such conditions, reorientations will be correlated with translational displacements leading to the so-called RMTD relaxation process (reorientation mediated by translational displacements). Applications to porous glasses, protein solutions, lipid bilayers, and clays will be discussed. Finally, we will address the intriguing fact that the various time limits of the segment mean-square displacement of polymers in some cases perfectly reproduce predictions of the tube/reptation model whereas the reorientation dynamics suggests strongly deviating power laws.

Relaxivity and toxicological properties of manganese oxide nanoparticles for MRI applications

Manganese oxide nanoparticles (MONs) have received growing attention as alternative T ₁ MRI contrast agents due to the association of commercial gadolinium-based contrast agents with nephrogenic systemic fibrosis. Since the seminal publication first describing the use of MONs as positive T ₁ contrast agents, there is an ongoing impetus to develop MONs of higher T ₁ signal intensity for better diagnostic efficacy. Indeed, various MON-based nanoprobe designs have been proposed, such as the employment of a mesoporous nanomaterial with MONs evenly dispersed within, or the traditional coating of a biocompatible layer onto the surface of MONs to form a core-shell configuration. Recent advances in this field also propose stimuli-responsive MONs that capitalize on an acidic dissolution or in situ reduction to release Mn²⁺ ions for a multi-fold increase in MRI contrast. However, the potential nanotoxicity of MONs remains a key obstacle to the clinical translation of MON-based T ₁ contrast agents. Due to the wide variety of functionalities and physicochemical properties of MONs, there is also a lack of consensus on the toxicological properties of MONs. In addition, the r ₁ relaxivity of MRI contrast agents typically decreases at higher field strength. Hence, it highlights the need to develop MON-based contrast agents with higher relaxivities. In this regard, this article aims to present a thorough review of MONs for MRI applications, with particular emphasis on their relaxivity and toxicological properties. In order to systematically review the current state-of-the-art for the development of MONs for MRI applications, the MON-based T ₁ contrast agents are categorized based on the structure of the nanomaterial system. Key parameters that influence the nanotoxicity of MONs are also examined while the absorption, distribution, metabolism and excretion of MON in vivo are evaluated to discern how long the nanoparticles will be present within the body, as well as to predict the organs or tissues in which they distribute.

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.

ESR lineshape and 1H spin-lattice relaxation dispersion in propylene glycol solutions of nitroxide radicals--joint analysis

Electron Spin Resonance (ESR) spectroscopy and Nuclear Magnetic Relaxation Dispersion (NMRD) experiments are reported for propylene glycol solutions of the nitroxide radical: 4-oxo-TEMPO-d16 containing (15)N and (14)N isotopes. The NMRD experiments refer to (1)H spin-lattice relaxation measurements in a broad frequency range (10 kHz-20 MHz). A joint analysis of the ESR and NMRD data is performed. The ESR lineshapes give access to the nitrogen hyperfine tensor components and the rotational correlation time of the paramagnetic molecule. The NMRD data are interpreted in terms of the theory of paramagnetic relaxation enhancement in solutions of nitroxide radicals, recently presented by Kruk et al. [J. Chem. Phys. 138, 124506 (2013)]. The theory includes the effect of the electron spin relaxation on the (1)H relaxation of the solvent. The (1)H relaxation is caused by dipole-dipole interactions between the electron spin of the radical and the proton spins of the solvent molecules. These interactions are modulated by three dynamic processes: relative translational dynamics of the involved molecules, molecular rotation, and electron spin relaxation. The sensitivity to rotation originates from the non-central positions of the interacting spin in the molecules. The electronic relaxation is assumed to stem from the electron spin-nitrogen spin hyperfine coupling, modulated by rotation of the radical molecule. For the interpretation of the NMRD data, we use the nitrogen hyperfine coupling tensor obtained from ESR and fit the other relevant parameters. The consistency of the unified analysis of ESR and NMRD, evaluated by the agreement between the rotational correlation times obtained from ESR and NMRD, respectively, and the agreement of the translation diffusion coefficients with literature values obtained for pure propylene glycol, is demonstrated to be satisfactory.

Quantitative cw Overhauser effect dynamic nuclear polarization for the analysis of local water dynamics

Liquid state Overhauser effect Dynamic Nuclear Polarization (ODNP) has experienced a recent resurgence of interest. The ODNP technique described here relies on the double resonance of electron spin resonance (ESR) at the most common, i.e. X-band (∼10GHz), frequency and ¹H nuclear magnetic resonance (NMR) at ∼15 MHz. It requires only a standard continuous wave (cw) ESR spectrometer with an NMR probe inserted or built into an X-band cavity. We focus on reviewing a new and powerful manifestation of ODNP as a high frequency NMR relaxometry tool that probes dipolar cross relaxation between the electron spins and the ¹H nuclear spins at X-band frequencies. This technique selectively measures the translational mobility of water within a volume extending 0.5-1.5 nm outward from a nitroxide radical spin probe that is attached to a targeted site of a macromolecule. It allows one to study the dynamics of water that hydrates or permeates the surface or interior of proteins, polymers, and lipid membrane vesicles. We begin by reviewing the recent advances that have helped develop ODNP into a tool for mapping the dynamic landscape of hydration water with sub-nanometer locality. In order to bind this work coherently together and to place it in the context of the extensive body of research in the field of NMR relaxometry, we then rephrase the analytical model and extend the description of the ODNP-derived NMR signal enhancements. This extended model highlights several aspects of ODNP data analysis, including the importance of considering all possible effects of microwave sample heating, the need to consider the error associated with various relaxation rates, and the unique ability of ODNP to probe the electron-¹H cross-relaxation process, which is uniquely sensitive to fast (tens of ps) dynamical processes. By implementing the relevant corrections in a stepwise fashion, this paper draws a consensus result from previous ODNP procedures and then shows how such data can be further corrected to yield clear and reproducible saturation of the NMR hyperpolarization process. Finally, drawing on these results, we broadly survey the previous ODNP dynamics literature. We find that the vast number of published, empirical hydration dynamics data can be reproducibly classified into regimes of surface, interfacial, vs. buried water dynamics.

Translational diffusion in paramagnetic liquids by 1H NMR relaxometry: nitroxide radicals in solution

For nitroxide radicals in solution one can identify three frequency regimes in which (1)H spin-lattice relaxation rate of solvent molecules depend linearly on square root of the (1)H resonance frequency. Combining a recently developed theory of nuclear (proton) spin-lattice relaxation in solutions of nitroxide radicals [D. Kruk et al., J. Chem. Phys. 137, 044512 (2012)] with properties of the spectral density function associated with translational dynamics, relationships between the corresponding linear changes of the relaxation rate (for (14)N spin probes) and relative translational diffusion coefficient of the solvent and solute molecules have been derived (in analogy to (15)N spin probes [E. Belorizky et al., J. Phys. Chem. A 102, 3674 (1998)]). This method allows a simple and straightforward determination of diffusion coefficients in spin-labeled systems, by means of (1)H nuclear magnetic resonance (NMR) relaxometry. The approach has thoroughly been tested by applying to a large set of experimental data-(1)H spin-lattice relaxation dispersion results for solutions of different viscosity (decalin, glycerol, propylene glycol) of (14)N and (15)N spin probes. The experiments have been performed versus temperature (to cover a broad range of translational diffusion coefficients) using field cycling spectrometer which covers three decades in (1)H resonance frequency, 10 kHz-20 MHz. The limitations of NMR relaxometry caused by the time scale of the translational dynamics as well as electron spin relaxation have been discussed. It has been shown that for spin-labeled systems NMR relaxometry gives access to considerably faster diffusion processes than for diamagnetic systems.

Sensitivity of 2H NMR spectroscopy to motional models: proteins and highly viscous liquids as examples

In order to study to what extent mechanisms of molecular motion can be unambiguously revealed by (2)H NMR spectroscopy, (2)H spectra for proteins (chicken villin protein headpiece HP36, selectively methyl-deuterated at leucine-69, C(δ) D(3)) and binary systems of high viscosity (benzene-d(6) in tricresyl phosphate) have been carefully analyzed as illustrative examples (the spectra are taken from the literature). In the first case, a model of restricted diffusion mediated by jumps between rotameric orientations has been tested against jump- and free diffusion models which describe rotational motion combined with jump dynamics. It has been found that the set of (2)H spectra of methyl-deuterated at leucine-69 chicken villin protein headpiece HP36 can be consistently explained by different motional models as well as by a gaussian distribution of correlation times assuming isotropic rotation (simple brownian diffusion model). The last finding shows that when the possible distribution of correlation times is not very broad one might not be able to distinguish between heterogeneous and homogenous (but more complex) dynamics by analyzing (2)H lineshapes. For benzene-d(6) in tricresyl phosphate, the dynamics is heterogeneous and it has been demonstrated that a gaussian distribution of correlation times reproduces well the experimental lineshapes, while for a Cole-Davidson distribution the agreement is somewhat worse. For inquires into the sensitivity of quadrupolar NMR spectral analysis (by "quadrupolar NMR spectroscopy we understand NMR spectroscopy of nuclei possessing quadrupole moment), the recently presented theoretical approach [Kruk et al., J. Chem. Phys. 135, 224511 (2011)] has been used as it allows simulating quadrupolar spectra for arbitrary motional conditions by employing the stochastic Liouville equation.

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.

Diffusional mechanisms augment the fluorine MR relaxation in paramagnetic perfluorocarbon nanoparticles that provides a "relaxation switch" for detecting cellular endosomal activation

PURPOSE

To develop a physical model for the (19)F relaxation enhancement in paramagnetic perfluorocarbon nanoparticles (PFC NP) and demonstrate its application in monitoring cellular endosomal functionality through a "(19)F relaxation switch" phenomenon.

MATERIALS AND METHODS

An explicit expression for (19)F longitudinal relaxation enhancement was derived analytically. Monte-Carlo simulation was performed to confirm the gadolinium-induced magnetic field inhomogeneity inside the PFC NP. Field-dependent T(1) measurements for three types of paramagnetic PFC NPs were carried out to validate the theoretical prediction. Based on the physical model, (19)F and (1)H relaxation properties of macrophage internalized paramagnetic PFC NPs were measured to evaluate the intracellular process of NPs by macrophages in vitro.

RESULTS

The theoretical description was confirmed experimentally by field-dependent T(1) measurements. The shortening of (19)F T(1) was found to be attributed to the Brownian motion of PFC molecules inside the NP in conjunction with their ability to permeate into the lipid surfactant coating. A dramatic change of (19)F T(1) was observed upon endocytosis, revealing the transition from intact bound PFC NP to processed constituents.

CONCLUSION

The proposed first-principle analysis of (19)F spins in paramagnetic PFC NP relates their structural parameters to the special MR relaxation features. The demonstrated "(19)F relaxation switch" phenomenon is potentially useful for monitoring cellular endosomal functionality.

Joint analysis of ESR lineshapes and 1H NMRD profiles of DOTA-Gd derivatives by means of the slow motion theory

The "Swedish slow motion theory" [Nilsson and Kowalewski, J. Magn. Reson. 146, 345 (2000)] applied so far to Nuclear Magnetic Relaxation Dispersion (NMRD) profiles for solutions of transition metal ion complexes has been extended to ESR spectral analysis, including in addition g-tensor anisotropy effects. The extended theory has been applied to interpret in a consistent way (within one set of parameters) NMRD profiles and ESR spectra at 95 and 237 GHz for two Gd(III) complexes denoted as P760 and P792 (hydrophilic derivatives of DOTA-Gd, with molecular masses of 5.6 and 6.5 kDa, respectively). The goal is to verify the applicability of the commonly used pseudorotational model of the transient zero field splitting (ZFS). According to this model the transient ZFS is described by a tensor of a constant amplitude, defined in its own principal axes system, which changes its orientation with respect to the laboratory frame according to the isotropic diffusion equation with a characteristic time constant (correlation time) reflecting the time scale of the distortional motion. This unified interpretation of the ESR and NMRD leads to reasonable agreement with the experimental data, indicating that the pseudorotational model indeed captures the essential features of the electron spin dynamics.

Geometrical confinement of gadolinium-based contrast agents in nanoporous particles enhances T1 contrast

Magnetic resonance imaging contrast agents are currently designed by modifying their structural and physiochemical properties to improve relaxivity and to enhance image contrast. Here, we show a general method for increasing relaxivity by confining contrast agents inside the nanoporous structure of silicon particles. Magnevist, gadofullerenes and gadonanotubes were loaded inside the pores of quasi-hemispherical and discoidal particles. For all combinations of nanoconstructs, a boost in longitudinal proton relaxivity r(1) was observed: Magnevist, r(1) ≈ 14 mM(-1) s(-1)/Gd(3+) ion (∼ 8.15 × 10(+7) mM(-1) s(-1)/construct); gadofullerenes, r(1) ≈ 200 mM(-1) s(-1)/Gd(3+) ion (∼ 7 × 10(+9) mM(-1) s(-1)/construct); gadonanotubes, r(1) ≈ 150 mM(-1) s(-1)/Gd(3+) ion (∼ 2 × 10(+9) mM(-1) s(-1)/construct). These relaxivity values are about 4 to 50 times larger than those of clinically available gadolinium-based agents (∼ 4 mM(-1) s(-1)/Gd(3+) ion). The enhancement in contrast is attributed to the geometrical confinement of the agents, which influences the paramagnetic behaviour of the Gd(3+) ions. Thus, nanoscale confinement offers a new and general strategy for enhancing the contrast of gadolinium-based contrast agents.