Theory of spin relaxation by translational diffusion in two‐dimensional systems

Water Dynamics in Fish Collagen Gels-Insight from NMR Relaxometry

1H spin-lattice relaxation experiments have been performed for gels based on fish collagen in order to analyze water dynamics. The covered frequency range ranges from 10 kHz to 10 MHz; in some cases, the temperature has varied as well. The relaxation data have been reproduced in terms of two models of water motion-a model including two relaxation contributions associated with the diffusion of water molecules on the macromolecular surfaces and a second model being just a phenomenological power law. The concept of surface diffusion has led to a very good agreement with the experimental data and a consistent set of parameters, with the diffusion coefficients being about five orders of magnitude slower compared to bulk water for one of the pools and considerably faster for the second one (smaller by factors between 2 and 20 compared to bulk water). In some cases, the attempt to reproduce the data in terms of a power law has led to a good agreement with the experimental data (the power law factor varying between 0.41 and 0.57); however, in other cases, the discrepancies are significant. This outcome favors the concept of surface diffusion.

Dynamic water profile in various type of cheese analysed by means of Nuclear Magnetic Resonance relaxometry

The aim of the study was to enquire to which extend 1H spin-lattice Nuclear Magnetic Resonance relaxometry data collected over a broad range of resonance frequencies (from 10kHz to 10MHz) have the potential to be used for assessing quality and authenticity of different categories of cheese. The following cheeses were selected mozzarella (M), processed cheese (C), pizza cheese (P) and pizza cheese with modified fat phase (PC), low-fat cheese (LF) and long ripened cheese (R). The cheeses from different production plants (1,2,3) and various cheese production batches (a, b, c) were used in the study. The samples from each group were subjected to instrumental composition analysis (FoodScan analyzer type 78810, FOSS, Hillerod, Denmark), water activity assessment (AQUA LAB 4TEV analyzer, type S40001855, USA) and determination of the NMRD profiles (SMARtracer FFC relaxometer, Stelar S.r.l, Italy, 2017). The state and dynamics of water present in products as free and bound water largely determines the properties of food products, including cheeses. NMR relaxometry studies of cheese enable to reveal relaxation features characteristic of specific categories of cheese. Consequently, the studies can be treated as a step toward exploiting NMR relaxometry for accessing quality and authenticity of cheese. It was shown that at low resonance frequencies, the lower the moisture, the larger the relaxation rate. The durability and quality of cheeses depend on the presence and condition of water, so it is necessary to find a relationship between the presence, condition and mobility of water in cheeses, to increase and improve the quality and extend the shelf life.

Dynamical properties of solid and hydrated collagen: Insight from nuclear magnetic resonance relaxometry

1H spin-lattice Nuclear Magnetic Resonance relaxometry experiments have been performed for collagen and collagen-based artificial tissues in the frequency range of 10 kHz-20 MHz. The studies were performed for non-hydrated and hydrated materials. The relaxation data have been interpreted as including relaxation contributions originating from 1H-1H and 1H-14N dipole-dipole interactions, the latter leading to Quadrupole Relaxation Enhancement effects. The 1H-1H relaxation contributions have been decomposed into terms associated with dynamical processes on different time scales. A comparison of the parameters for the non-hydrated and hydrated systems has shown that hydration leads to a decrease in the dipolar relaxation constants without significantly affecting the dynamical processes. In the next step, the relaxation data for the hydrated systems were interpreted in terms of a model assuming two-dimensional translational diffusion of water molecules in the vicinity of the macromolecular surfaces and a sub-diffusive motion leading to a power law of the frequency dependencies of the relaxation rates. It was found that the water diffusion process is slowed down by at least two orders of magnitude compared to bulk water diffusion. The frequency dependencies of the relaxation rates in hydrated tissues and hydrated collagen are characterized by different power laws (ωH-β, where ωH denotes the 1H resonance frequency): the first of about 0.4 and the second close to unity.

1H spin-lattice NMR relaxation in the presence of residual dipolar interactions - Dipolar relaxation enhancement

A model of spin-lattice relaxation for spin-1/2 nuclei in the presence of a residual dipole-dipole coupling has been presented. For slow dynamics the model predicts a bi-exponential relaxation at low frequencies, when the residual dipole-dipole interaction dominates the Zeeman coupling. Moreover, according to the model a frequency-specific relaxation enhancement, referred to as Dipolar Relaxation Enhancement (DRE) in analogy to the Quadrupole Relaxation Enhancement (QRE) is expected. The frequency position of the relaxation maximum is determined by the amplitude of the residual dipole-dipole interaction. Experimental examples of relaxation properties that might be attributed to the DRE are presented. The DRE effect has the potential to be exploited, in analogy to QRE, as a unique source of information about molecular dynamics and structure.

Mechanism of Water Dynamics in Hyaluronic Dermal Fillers Revealed by Nuclear Magnetic Resonance Relaxometry

1 H spin-lattice nuclear magnetic resonance relaxation experiments were performed for five kinds of dermal fillers based on hyaluronic acid. The relaxation data were collected over a broad frequency range between 4 kHz and 40 MHz, at body temperature. Thanks to the frequency range encompassing four orders of magnitude, the dynamics of water confined in the polymeric matrix was revealed. It is demonstrated that translation diffusion of the confined water molecules exhibits a two-dimensional character and the diffusion process is slower than diffusion in bulk water by 3-4 orders of magnitude. As far as rotational dynamics of the confined water is concerned, it is shown that in all cases there is a water pool characterized by a rotational correlation time of about 4×10-9  s. In some of the dermal fillers a fraction of the confined water (about 10 %) forms a pool that exhibits considerably slower (by an order of magnitude) rotational dynamics. In addition, the water binding capacity of the dermal fillers was quantitatively compared.

Dynamics of Solid Proteins by Means of Nuclear Magnetic Resonance Relaxometry

1H Nuclear magnetic resonance (NMR) relaxometry was exploited to investigate the dynamics of solid proteins. The relaxation experiments were performed at 37 °C over a broad frequency range, from approximately 10 kHz to 40 MHz. Two relaxation contributions to the overall 1H spin-lattice relaxation were revealed; they were associated with 1H-1H and 1H-14N magnetic dipole-dipole interactions, respectively. The 1H-1H relaxation contribution was interpreted in terms of three dynamical processes occurring on timescales of 10-6 s, 10-7 s, and 10-8 s, respectively. The 1H-14N relaxation contribution shows quadrupole relaxation enhancement effects. A thorough analysis of the data was performed revealing similarities in the protein dynamics, despite their different structures. Among several parameters characterizing the protein dynamics and structure (e.g., electric field gradient tensor at the position of 14N nuclei), the orientation of the 1H-14N dipole-dipole axis, with respect to the principal axis system of the electric field gradient, was determined, showing that, for lysozyme, it was considerably different than for the other proteins. Moreover, the validity range of a closed form expression describing the 1H-14N relaxation contribution was determined by a comparison with a general approach based on the stochastic Liouville equation.

Anisotropy of the electron spin-lattice relaxation. PO32- radical in glycinium phosphite gly·H3PO3 crystal

Electron spin-lattice relaxation has been measured for PO₃^2- radical in glycinium phosphite gly·H₃PO₃ crystal and its deuterated analogue in temperature range 40-300 K. Angular dependence of the relaxation rate was measured in three crystal planes at room temperature. The Debye cut-off temperature has been calculated as Θ_D = 97 K, which indicates that the temperature dependence of 1/T₁ is governed by radical local vibrations localized in optical phonon modes range. Theories of possible 1/T₁ angular dependence are reviewed. The anisotropy of spin-lattice relaxation rate in our crystal is assumed to be a result of local magnetic field fluctuations due to electron-proton dipolar coupling. Theoretical evaluation of 1/T₁ were performed for coupling with protons at distances up to 0.46 nm. Not perfect agreement was found with motion correlation time τ_c = 2·10^-9 s.

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.

Translational dynamics of water at the phospholipid interface

The residual water-proton magnetic relaxation dispersion profile obtained from suspensions of phospholipid vesicles in deuterium oxide was found to be a logarithmic function of the proton Larmor frequency at high magnetic field strengths, and independent of Larmor frequency at low magnetic field strengths. The residual proton relaxation is caused by dipole-dipole coupling between the residual water proton in otherwise deuterated water and the phospholipid protons. The logarithmic dependence on magnetic field strength is the signature of water-proton diffusive exploration on the interface that is approximately two-dimensionally constrained. Application of relaxation theory for two-dimensional diffusion to the spin-lattice relaxation data yields a translational correlation time of approximately 70 ps for water diffusing in the interface of 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) vesicles.

A 207Pb NMR Study of Beta"-Alumina

We report results of a nuclear magnetic resonance (NMR) study of lead(II) cations in β"-alumina. Measurements of line positions and spin-lattice relaxation times (T1) as a function of temperature are presented. The results show that Pb ions possess both static and dynamic disorder in low and intermediate temperature regimes, respectively. Also, a comparison is made between Lorentzian and logarithmic spectral density functions, from which we conclude that the latter provides a better fit to the dataat short correlation times (ωºτºα). The logarithmic form has been proposed to describe diffusive motion in 2-dimensional conductors.

Motions and relaxations of confined liquids

When a liquid is confined in a narrow gap (as near a cell membrane, in a lubricated contact between solids, or in a porous medium), new dynamic behavior emerges. The effective shear viscosity is enhanced compared to the bulk, relaxation times are prolonged, and nonlinear responses set in at lower shear rates. These effects are more prominent, the thinner the liquid film. They appear to be the manifestation of collective motions. The flow of liquids under extreme confinement cannot be understood simply by intuitive extrapolation of bulk properties. Practical consequences are possible in areas from tribology and materials processing to membrane physics.

Dimensionality of diffusive exploration at the protein interface in solution

The dynamics of water are critically important to the energies of interaction between proteins and substrates and determine the efficiency of transport at the interface. The magnetic field dependence of the nuclear spin-lattice relaxation rate constant 1/T(1) of water protons provides a direct characterization of water diffusional dynamics at the protein interface. We find that the surface-average translational correlation time is 30-40 ps and the magnetic field dependence of the water proton 1/T(1) is characteristic of two-dimensional diffusion of water in the protein interfacial region. The reduced dimensionality substantially increases the intermolecular re-encounter probability and the efficiency of the surface exploration by the small molecule, water in this case. We propose a comprehensive theory of the translational effects of a small diffusing particle confined in the vicinity of a spherical macromolecule as a function of the relative size of the two particles. We show that the change in the apparent dimensionality of the diffusive exploration is a general result of the small diffusing particle encountering a much larger particle that presents a diffusion barrier. Examination of the effects of the size of the confinement relative to the macromolecule size reveals that the reduced dimensionality characterizing the small-molecule diffusion persists to remarkably small radius ratios. The experimental results on several different proteins in solution support the proposed theoretical model, which may be generalized to other small-particle-large-body systems like vesicles and micelles.

T1-relaxation of 129Xe on metal single crystal surfaces-multilayer experiments on iridium and monolayer considerations

The surface of a typical laboratory single crystal has about 10(15) surface atoms or adsorption sites, respectively, and is thus far out of reach for conventional NMR experiments using thermal polarization. It should however be in reach for NMR of adsorbed laser polarized (hyperpolarized) 129Xe, which is produced by spin transfer from optically pumped rubidium. With multilayer experiments of xenon adsorbed on an iridium surface we do not only demonstrate that monolayer sensitivity has been obtained, we also show that such surface experiments can be performed under ultra high vacuum conditions with the crystal being mounted in a typical surface analysis chamber on a manipulator with far-reaching sample heating and cooling abilities. With only four spectra summed up we present an NMR signal from at most 4x10(14) atoms of 129Xe, four layers of naturally abundant xenon, respectively. The fact that no monolayer signal has been measured so far is explained by a fast Korringa relaxation due to the Fermi contact interaction of the 129Xe nuclei with the electrons of the metal substrate. T(1)-relaxation times in the order of several ms have been calculated using all electron density functional theory for several metal substrates.

Magnetic cross-relaxation and chemical exchange between microporous solid and mobile liquid phases

Nuclear magnetic spin-lattice relaxation rates are reported as a function of magnetic field strength, pH, and temperature for water protons in Sephadex gels. The water proton rates report the relaxation profile characteristic of the solid at high pH values. At lower pH values, the relaxation rate is limited by a slow chemical exchange process that makes the relaxation rate independent of magnetic field at low field strengths. In cases where the proton exchange rate does not limit the total relaxation rate, the magnetic field dependence of the relaxation rate is given by a power law of the type R = Av-B, where B is 0.75 except at pH 11 where the data are better represented with B = 0.5. The exchange events important for the water proton relaxation are represented as a two-stage process in which water within the pores of the gel exchanges protons and magnetization with the solid spin system rapidly compared with the rate at which the water within the pores exchanges with the bulk water phase.

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

Heisenberg spin exchange rates and dipole-dipole spin lattice relaxation rates for deuterated 14N- and 15N-spin labels bound selectively to the histidine His15 and to the lysines Lys13, 96, 97 of the lysozyme molecule have been determined with the aid of electron spin resonance spectroscopy. The results can be interpreted in terms of a two dimensional translational diffusion of the nitroxide tips of the spin labels along the protein surface within restricted surface areas. The spin labels are regarded as models for long amino acid side chains and as probes for the dynamics of protein and water in the vicinity of the protein surface. The translational diffusion coefficient DII is reduced by a factor of between six and thirty compared to the value for T = 295 K is given by (1.3 +/- 0.6) x 10 -10m2s-1 greater than or equal to DII greater than or equal to (2.4 +/- 0.3) x 10-11M2s-1.

Water-proton nuclear magnetic relaxation in heterogeneous systems: hydrated lysozyme results

Spin-lattice relaxation rates of water protons in hydrated immobilized lysozyme are measured as a function of magnetic field strength. The dependence of water relaxation versus hydration is presented from 35 to 55% by weight water content. The water-proton relaxation is directly coupled to that of the protein and the coupling exists in the absence of chemical exchange. A model is applied where relaxation within the two proton phases is coupled through a dipolar cross-relaxation mechanism as well as chemical exchange. The observed amplitudes of the water-proton relaxation profiles scale with the ratio of protein to water protons as well as the protein-proton relaxation rate. The field dependence of the protein-proton spin-lattice relaxation is presented in the presence of D2O where a cross-relaxation coupling is absent. The coupled relaxation model accounts well for the NMR relaxation data as a function of magnetic field strength which is similar to measurements on other heterogeneous systems such as tissues.

The magnetic field dependence of proton spin relaxation in tissues

The magnetic field dependence of water-proton relaxation is reported for a simple protein solution, a cross-linked protein solution, and a series of rat tissues, fresh, dried and rehydrated. The shape of the magnetic field dependence associated with water proton relaxation in tissues is accounted for by magnetic dipole-dipole interactions between the mobile water spins and the immobile spin populations of the nonrotating components of the tissue coupling the behavior of the immobilized spin system to that of the mobile water spin system. The effect of this coupling is to impart the field dependence of the relaxation associated with the immobilized spin population to that of the mobile water spins that are observed in most relaxation and imaging experiments.

Orientation and vertical fluctuations of spin-labeled analogues of cholesterol and androstanol in phospholipid bilayers

We have used ESR and NMR linewidth broadening by spin-labels to determine the overall orientation of spin-labeled analogues of cholesterol and androstanol in egg lecithin bilayers. While the cholesterol analogues were found to have a single orientation in each monolayer, with the acyl chain pointing towards the center of the bilayer, the androstanol analogue appeared, at least in sonicated vesicles, to experience two opposite orientations in the same monolayer, very likely with a rapid reorientation. The possibility of rapid vertical fluctuations of the sterol molecules within the phospholipid bilayer is also discussed.