Simple expressions of the nuclear relaxation rate enhancement due to quadrupole nuclei in slowly tumbling molecules

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.

Water Dynamics in Highly Concentrated Protein Systems-Insight from Nuclear Magnetic Resonance Relaxometry

¹H spin-lattice relaxation experiments have been performed for water-Bovine Serum Albumin (BSA) mixtures, including 20%wt and 40%wt of BSA. The experiments have been carried out in a frequency range encompassing three orders of magnitude, from 10 kHz to 10 MHz, versus temperature. The relaxation data have been thoroughly analyzed in terms of several relaxation models with the purpose of revealing the mechanisms of water motion. For this purpose, four relaxation models have been used: the data have been decomposed into relaxation contributions expressed in terms of Lorentzian spectral densities, then three-dimensional translation diffusion has been assumed, next two-dimensional surface diffusion has been considered, and eventually, a model of surface diffusion mediated by acts of adsorption to the surface has been employed. In this way, it has been demonstrated that the last concept is the most plausible. Parameters describing the dynamics in a quantitative manner have been determined and discussed.

On the Observation of 14N Quadrupole Resonance Transitions in Water Proton NMR Relaxometry Dispersion Curves: The Case of a Labile NH Grouping in a Semirigid Molecular Moiety

The electric field gradient tensor (considered here at the level of a nitrogen nucleus) can be described by two parameters: the largest element in the (X,Y,Z) principal axis system, denoted by V_ZZ (leading to the nuclear quadrupole coupling), and the asymmetry parameter η = (|V_YY| - |V_XX|)/|V_ZZ| with |V_ZZ| > |V_YY| > |V_XX|. The frequencies of the three nitrogen-14 nuclear quadrupole resonance (NQR) transitions depend on both parameters but, for sensitivity reasons, their determination may be especially difficult and time consuming. For a partly rigid NH grouping with a labile proton, water nuclear magnetic resonance (NMR) relaxometry curves may exhibit these three transitions (dubbed quadrupolar dips or quadrupole relaxation enhancement (QRE)), provided that the NH grouping belongs to a moiety possessing a sufficient degree of ordering. Their line shape leads to the correlation time describing mainly the motion of the NH grouping (the proton of which being in exchange with water protons), and their amplitude can be interpreted in terms of an effective NH distance. This approach is applied to a hydrogel, where separate NQR lines are observed for the different types of water existing in this system. Furthermore, the analysis of experimental data allows one to determine the nuclear quadrupole coupling in the protonated and deprotonated forms of this molecular moiety involving a labile NH grouping.

Fast-field-cycling NMR at very low magnetic fields: water molecular dynamic biomarkers of glioma cell invasion and migration

Our objective was to study NMR relaxometry of glioma invasion/migration at very low field (<2 mT) by fast-field-cycling NMR (FFC-NMR) and to decipher the pathophysiological processes of glioma that are responsible for relaxation changes in order to open a new diagnostic method that can be extended to imaging. The phenotypes of two new glioma mouse models, Glio6 and Glio96, were characterized by T_2w -MRI, HE histology, Ki-67 immunohistochemistry (IHC) and CXCR4 RT-qPCR, and were compared with the U87 model. R₁ dispersions of glioma tissues were acquired at low field (0.1 mT-0.8 T) ex vivo and were fitted with Lorentzian and power-law models to extract FFC biomarkers related to the molecular dynamics of water. In order to decipher relaxation changes, three main invasion/migration pathophysiological processes were studied: hypoxia, H₂ O₂ function and the water-channel aquaporin-4 (AQP4). Glio6 and Glio96 were characterized with invasion/migration phenotype and U87 with high cell proliferation as a solid glioma. At very low field, invasion/migration versus proliferation was characterized by a decrease in the relaxation-rate constant (ΔR₁  ≈ -32% at 0.1 mT) and correlation time (≈-40%). These decreases corroborated the AQP4-IHC overexpression (Glio6/Glio96: +92%/+46%), suggesting rapid transcytolemmal water exchange, which was confirmed by the intracellular water-lifetime τ_IN decrease (Δτ_IN  ≈ -30%). In functional experiments, AQP4 expression, τ_IN and the relaxation-rate constant at very low field were all found to be sensitive to hypoxia and to H₂ O₂ stimuli. At very low field the role of water exchanges in relaxation modulation was confirmed, and for the first time it was linked to the glioma invasion/migration and to its main pathophysiological processes: hypoxia, H₂ O₂ redox signaling and AQP4 expression. The method appears appropriate to evaluate the effect of drugs that can target these pathophysiological mechanisms. Finally, FFC-NMR operating at low field is demonstrated to be sensitive to invasion glioma phenotype and can be straightforwardly extended to FFC-MRI as a new cancer invasion imaging method in the clinic.

Connecting Rheological Properties and Molecular Dynamics of Egg-Tempera Paints based on Egg Yolk

Egg-tempera painting is a pictorial technique widely used in the Middle Ages, although poorly studied in its physico-chemical aspects until now. Here we show how NMR relaxometry and rheology can be combined to probe egg-tempera paints and shed new light on their structure and behavior. Based on recipes of the 15th century, model formulations with egg yolk and green earth have been reproduced to characterize the physicochemical properties of this paint at the mesoscopic and macroscopic scales. The rheological measurements highlight a synergetic effect between green earth and egg yolk, induced by the interactions between them and the structural organisation of the system. ¹ H NMR relaxometry emphasizes the presence and the structure of a network formed by the yolk and the pigment.

Nuclear relaxation rate enhancement by a 14N quadrupole nucleus in a fluctuating electric-field gradient

We consider the longitudinal quadrupole relaxation rate enhancement (QRE) of a ¹H nucleus due to the time fluctuations of the local dipolar magnetic field created by a close quadrupole ¹⁴N nucleus, the electric-field gradient (EFG) Hamiltonian of which changes with time because of vibrations/distortions of its chemical environment. The QRE is analytically expressed as a linear combination of the cosine Fourier transforms of the three quantum time auto-correlation functions G_AA(t) of the ¹⁴N spin components along the principal axes A = X, Y, and Z of the mean (time-averaged) EFG Hamiltonian. Denoting the three transition frequencies between the energy levels of this mean Hamiltonian by ν_A, the functions G_AA(t) oscillate at frequencies ν_A + s_A/(2π) with mono-exponential decays of relaxation times τ_A, where the frequency dynamic shifts s_A and the relaxation times τ_A are closed expressions of the magnitude of the fluctuations of the instantaneous EFG Hamiltonian about its mean and of the characteristic fluctuation time. Thus, the theoretical QRE is the sum of three Lorentzian peaks centered at ν_A + s_A/(2π) with full widths at half maxima 1/(πτ_A). The predicted peak widths are nearly equal. The predicted dynamic shifts of the peaks are much smaller than their widths and amazingly keep proportional to the transition frequencies ν_A for reasonably fast EFG fluctuations. The theory is further improved by correcting the transition frequencies by the ¹⁴N Zeeman effects of second order. It is successfully applied to reinterpret the QRE pattern measured by Broche, Ashcroft, and Lurie [Magn. Reson. Med. 68, 358 (2012)] in normal cartilage.

Water Dynamics in Whey-Protein-Based Composite Hydrogels by Means of NMR Relaxometry

Whey-protein-isolate-based composite hydrogels with encapsulated black carrot (Daucus carota) extract were prepared by heat-induced gelation. The hydrogels were blended with gum tragacanth, pectin and xanthan gum polysaccharides for modulating their properties. 1H spin-lattice relaxation experiments were performed in a broad frequency range, from 4 kHz to 30 MHz, to obtain insight into the influence of the different polysaccharides and of the presence of black carrot on dynamical properties of water molecules in the hydrogel network. The 1H spin-lattice relaxation data were decomposed into relaxation contributions associated with confined and free water fractions. The population of the confined water fraction and the value of the translation diffusion coefficient of water molecules in the vicinity of the macromolecular network were quantitatively determined on the basis of the relaxation data. Moreover, it was demonstrated that the translation diffusion is highly anisotropic (two-dimensional, 2D).

A new method for investigating osteoarthritis using Fast Field-Cycling nuclear magnetic resonance

Osteoarthritis in synovial joints remains a major cause of long-term disability worldwide, with symptoms produced by the progressive deterioration of the articular cartilage. The earliest cartilage changes are thought to be alteration in its main protein components, namely proteoglycan and collagen. Loss of proteoglycans bound in the collagen matrix which maintain hydration and stiffness of the structure is followed by collagen degradation and loss. The development of new treatments for early osteoarthritis is limited by the lack of accurate biomarkers to assess the loss of proteoglycan. One potential biomarker is magnetic resonance imaging (MRI). We present the results of a novel MRI methodology, Fast Field-Cycling (FFC), to assess changes in critical proteins by demonstrating clear quantifiable differences in signal from normal and osteoarthritic human cartilage for in vitro measurements. We further tested proteoglycan extracted cartilage and the key components individually. Three clear signals were identified, two of which are related predominantly to the collagen component of cartilage and the third, a unique very short-lived signal, is directly related to proteoglycan content; we have not seen this in any other tissue type. In addition, we present the first volunteer human scan from our whole-body FFC scanner where articular cartilage measurements are in keeping with those we have shown in tissue samples. This new clinical imaging modality offers the prospect of non-invasive monitoring of human cartilage in vivo and hence the assessment of potential treatments for osteoarthritis. Keywords: Fast Field-Cycling NMR; human hyaline cartilage; Osteoarthritis; T1 dispersion; quadrupolar peaks; protein interactions.

Monitoring tissue implants by field-cycling 1H-MRI via the detection of changes in the 14N-quadrupolar-peak from imidazole moieties incorporated in a "smart" scaffold material

This study is focused on the development of innovative sensors to non-invasively monitor the tissue implant status by Fast-Field-Cycling Magnetic Resonance Imaging (FFC-MRI). These sensors are based on oligo-histidine moieties that are conjugated to PLGA polymers representing the structural matrix for cells hosting scaffolds. The presence of 14N atoms of histidine causes a quadrupolar relaxation enhancement (also called Quadrupolar Peak, QP) at 1.39 MHz. This QP falls at a frequency well distinct from the QPs generated by endogenous semisolid proteins. The relaxation enhancement is pH dependent in the range 6.5-7.5, thus it acts as a reporter of the scaffold integrity as it progressively degrades upon lowering the microenvironmental pH. The ability of this new sensors to generate contrast in an image obtained at 1.39 MHz on a FFC-MRI scanner is assessed. A good biocompatibility of the histidine-containing scaffolds is observed after its surgical implantation in healthy mice. Over time the scaffold is colonized by endogenous fibroblasts and this process is accompanied by a progressive decrease of the intensity of the relaxation peak. In respect to the clinically used contrast agents this material has the advantage of generating contrast without the use of potentially toxic paramagnetic metal ions.

Towards applying NMR relaxometry as a diagnostic tool for bone and soft tissue sarcomas: a pilot study

This work explores what Fast Field-Cycling Nuclear Magnetic Resonance (FFC-NMR) relaxometry brings for the study of sarcoma to guide future in vivo analyses of patients. We present the results of an ex vivo pilot study involving 10 cases of biopsy-proven sarcoma and we propose a quantitative method to analyse 1H NMR relaxation dispersion profiles based on a model-free approach describing the main dynamical processes in the tissues and assessing the amplitude of the Quadrupole Relaxation Enhancement effects due to 14N. This approach showed five distinct groups of dispersion profiles indicating five discrete categories of sarcoma, with differences attributable to microstructure and rigidity. Data from tissues surrounding sarcomas indicated very significant variations with the proximity to tumour, which may be attributed to varying water content but also to tissue remodelling processes due to the sarcoma. This pilot study illustrates the potential of FFC relaxometry for the detection and characterisation of sarcoma.

A close view of the organic linker in a MOF: structural insights from a combined 1H NMR relaxometry and computational investigation

The organic linker in a metal organic framework (MOF) affects its adsorption behavior and performance, and its structure and dynamics play a role in the modulation of the adsorption properties. In this work, the combination of ¹H nuclear magnetic resonance (NMR) longitudinal relaxometry and theoretical calculations allowed details of the structure and dynamics of the organic linker in the NH₂-MIL-125 MOF to be obtained. In particular, fast field cycling (FFC) NMR, applied here for the first time on MOFs, was used to disclose the dynamics of the amino group and its electronic environment through the analysis of the ¹⁴N quadrupole relaxation peaks, observed in the frequency interval 0.5-5 MHz, at different temperatures from 25 to 110 °C. The line width of the peaks allowed a lower boundary on the rotational correlation time of the N-H bonds to be set, whereas relevant changes in the amplitudes were interpreted in terms of a change in the orientation of the ¹⁴N averaged electric field gradient tensor. The experimental findings were complemented by quantum chemistry calculations and classical molecular dynamics simulations.

Slow dynamics of solid proteins - Nuclear magnetic resonance relaxometry versus dielectric spectroscopy

¹H Nuclear Magnetic Resonance (NMR) relaxometry and Dielectric Spectroscopy (DS) have been exploited to investigate the dynamics of solid proteins. The experiments have been carried out in the frequency range of about 10 kHz-40 MHz for NMR relaxometry and 10^-2Hz-20 MHz for DS. The data sets have been analyzed in terms of theoretical models allowing for a comparison of the correlation times revealed by NMR relaxometry and DS. The ¹H spin-lattice relaxation profiles have been decomposed into relaxation contributions associated with ¹H-¹H and ¹H-¹⁴N dipole - dipole interactions. The ¹H-¹H relaxation contribution has been interpreted in terms of three dynamical processes of time scales of 10^-6s, 10^-7s and 10^-8s. It has turned out that the correlation times do not differ much among proteins and they are only weakly dependent on temperature. The analysis of DS relaxation spectra has also revealed three motional processes characterized by correlation times that considerably depend on temperature in contrast to those obtained from the ¹H relaxation. This finding suggest that for solid proteins there is a contribution to the ¹H spin-lattice relaxation associated with a kind of motion that is not probed in DS as it does not lead to a reorientation of the electric dipole moment.

Fast field-cycling magnetic resonance detection of intracellular ultra-small iron oxide particles in vitro: Proof-of-concept

PURPOSE

Inflammation is central in disease pathophysiology and accurate methods for its detection and quantification are increasingly required to guide diagnosis and therapy. Here we explored the ability of Fast Field-Cycling Magnetic Resonance (FFC-MR) in quantifying the signal of ultra-small superparamagnetic iron oxide particles (USPIO) phagocytosed by J774 macrophage-like cells as a proof-of-principle.

METHODS

Relaxation rates were measured in suspensions of J774 macrophage-like cells loaded with USPIO (0-200 μg/ml Fe as ferumoxytol), using a 0.25 T FFC benchtop relaxometer and a human whole-body, in-house built 0.2 T FFC-MR prototype system with a custom test tube coil. Identical non-imaging, saturation recovery pulse sequence with 90° flip angle and 20 different evolution fields selected logarithmically between 80 μT and 0.2 T (3.4 kHz and 8.51 MHz proton Larmor frequency [PLF] respectively). Results were compared with imaging flow cytometry quantification of side scatter intensity and USPIO-occupied cell area. A reference colorimetric iron assay was used.

RESULTS

The T1 dispersion curves derived from FFC-MR were excellent in detecting USPIO at all concentrations examined (0-200 μg/ml Fe as ferumoxytol) vs. control cells, p ≤ 0.001. FFC-NMR was capable of reliably detecting cellular iron content as low as 1.12 ng/µg cell protein, validated using a colorimetric assay. FFC-MR was comparable to imaging flow cytometry quantification of side scatter intensity but superior to USPIO-occupied cell area, the latter being only sensitive at exposures ≥ 10 µg/ml USPIO.

CONCLUSIONS

We demonstrated for the first time that FFC-MR is capable of quantitative assessment of intra-cellular iron which will have important implications for the use of USPIO in a variety of biological applications, including the study of inflammation.

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.

A whole-body Fast Field-Cycling scanner for clinical molecular imaging studies

Fast Field-Cycling (FFC) is a well-established Nuclear Magnetic Resonance (NMR) technique that exploits varying magnetic fields to quantify molecular motion over a wide range of time scales, providing rich structural information from nanometres to micrometres, non-invasively. Previous work demonstrated great potential for FFC-NMR biomarkers in medical applications; our research group has now ported this technology to medical imaging by designing a whole-body FFC Magnetic Resonance Imaging (FFC-MRI) scanner capable of performing accurate measurements non-invasively over the entire body, using signals from water and fat protons. This is a unique tool to explore new biomarkers related to disease-induced tissue remodelling. Our approach required making radical changes in the design, construction and control of MRI hardware so that the magnetic field is switched within 12.5 ms to reach any field strength from 50 μT to 0.2 T, providing clinically useful images within minutes. Pilot studies demonstrated endogenous field-dependant contrast in biological tissues in good agreement with reference data from other imaging modalities, confirming that our system can perform multiscale structural imaging of biological tissues, from nanometres to micrometres. It is now possible to confirm ex vivo results obtained from previous clinical studies, offering applications in diagnosis, staging and monitoring treatment for cancer, stroke, osteoarthritis and oedema.

Multi-quantum quadrupole relaxation enhancement effects in 209Bi compounds

¹H spin-lattice nuclear magnetic resonance relaxation experiments have been performed for triphenylbismuth dichloride (C₁₈H₁₅BiCl₂) and phenylbismuth dichloride (C₆H₅BiCl₂) in powder. The frequency range of 20-128 MHz has been covered. Due to ¹H-²⁰⁹Bi dipole-dipole interactions, a rich set of pronounced Quadrupole Relaxation Enhancement (QRE) peaks (quadrupole peaks) has been observed. The QRE patterns for both compounds have been explained in terms of single- and double-quantum transitions of the participating nuclei. The analysis has revealed a complex, quantum-mechanical mechanism of the QRE effects. The mechanism goes far beyond the simple explanation of the existence of three quadrupole peaks for ¹⁴N reported in literature. The analysis has been supported by nuclear quadrupole resonance results that independently provided the ²⁰⁹Bi quadrupole parameters (amplitude of the quadrupole coupling constant and asymmetry parameter).

Correction of environmental magnetic fields for the acquisition of Nuclear magnetic relaxation dispersion profiles below Earth's field

T₁ relaxation times can be measured at a range of magnetic field strengths by Fast Field-Cycling (FFC) NMR relaxometry to provide T₁-dispersion curves. These are valuable tools for the investigation of material properties as they provide information about molecular dynamics non-invasively. However, accessing information at fields below 230 μT (10kHz proton Larmor frequency) requires careful correction of unwanted environmental magnetic fields. In this work a novel method is proposed that compensates for the environmental fields on a FFC-NMR relaxometer and extends the acquisition of Nuclear Magnetic Relaxation Dispersion profiles to 2.3μT (extremely low field region), with direct application in the study of slow molecular motions. Our method is an improvement of an existing technique, reported by Anoardo and Ferrante in 2003, which exploits the non-adiabatic behaviour of the magnetisation in rapidly-varying magnetic fields and makes use of the oscillation of the signal amplitude to estimate the field strength. This increases the accuracy in measuring the environmental fields and allows predicting the optimal correction values by applying simple equations to fit the data acquired. Validation of the method is performed by comparisons with well-known dispersion curves obtained from polymers and benzene.