Relaxation Rate Measurements Research Articles

Measurement of transverse and longitudinal relaxation rates of double-beam atomic magnetometers in geomagnetic environment

Longitudinal relaxation rate (R1) and transverse relaxation rate (R2) are crucial for evaluating the performance of atomic magnetometers. Unfortunately, to the best of our knowledge, methods for measuring R1 and R2 under arbitrary direction of magnetic field have been rarely studied. We propose, for the first time, measurement methods for R1 and R2 in magnetic fields with arbitrary direction. R1 is measured using the linewidth under three axis modulated magnetic field, while R2 is measured based on demodulated dispersive and absorptive curves of the magnetic resonance signal. The experimental results show that the relative mean deviation of R1 and R2 are 2.5% and 3.6%, respectively. The R1 and R2 measurement methods proposed in this paper has advantage of simple to implement and is validity for measurement in magnetic fields with arbitrary direction, which has significant importance for the application of atomic magnetometers in geomagnetic environments.

Pitfalls in measurements of R1 relaxation rates of protein backbone 15N nuclei.

The dynamics of the backbone and side-chains of protein are routinely studied by interpreting experimentally determined 15N spin relaxation rates. R1(15N), the longitudinal relaxation rate, reports on fast motions and encodes, together with the transverse relaxation R2, structural information about the shape of the molecule and the orientation of the amide bond vectors in the internal diffusion frame. Determining error-free 15N longitudinal relaxation rates remains a challenge for small, disordered, and medium-sized proteins. Here, we show that mono-exponential fitting is sufficient, with no statistical preference for bi-exponential fitting up to 800MHz. A detailed comparison of the TROSY and HSQC techniques at medium and high fields showed no statistically significant differences. The least error-prone DD/CSA interference removal technique is the selective inversion of amide signals while avoiding water resonance. The exchange of amide with solvent deuterons appears to affect the rate R1 of solvent-exposed amides in all fields tested and in each DD/CSA interference removal technique in a statistically significant manner. In summary, the most accurate R1(15N) rates in proteins are achieved by selective amide inversion, without the addition of D2O. Importantly, at high magnetic fields stronger than 800MHz, when non-mono-exponential decay is involved, it is advisable to consider elimination of the shortest delays (typically up to 0.32s) or bi-exponential fitting.

Quantitative analysis of the slow exchange process by 19F NMR in the presence of scalar and dipolar couplings: applications to the ribose 2'-19F probe in nucleic acids.

Solution NMR spectroscopy is a particularly powerful technique for characterizing the functional dynamics of biomolecules, which is typically achieved through the quantitative characterization of chemical exchange processes via the measurement of spin relaxation rates. In addition to the conventional nuclei such as 15N and 13C, which are abundant in biomolecules, fluorine-19 (19F) has recently garnered attention and is being widely used as a site-specific spin probe. While 19F offers the advantages of high sensitivity and low background, it can be susceptible to artifacts in quantitative relaxation analyses due to a multitude of dipolar and scalar coupling interactions with nearby 1H spins. In this study, we focused on the ribose 2'-19F spin probe in nucleic acids and investigated the effects of 1H-19F spin interactions on the quantitative characterization of slow exchange processes on the millisecond time scale. We demonstrated that the 1H-19F dipolar coupling can significantly affect the interpretation of 19F chemical exchange saturation transfer (CEST) experiments when 1H decoupling is applied, while the 1H-19F interactions have a lesser impact on Carr-Purcell-Meiboom-Gill relaxation dispersion applications. We also proposed a modified CEST scheme to alleviate these artifacts along with experimental verifications on self-complementary RNA systems. The theoretical framework presented in this study can be widely applied to various 19F spin systems where 1H-19F interactions are operative, further expanding the utility of 19F relaxation-based NMR experiments.

Experimental nuclear quadrupole resonance and computational study of the structurally refined topological semimetal TaSb2

The local electric field gradients and magnetic dynamics of TaSb2 have been studied using Sb121, Sb123, and Ta181 nuclear quadrupole resonance (NQR) with density functional theory (DFT) calculations using XRD-determined crystal structures. By measuring all structurally expected 13 NQR lines, the nuclear quadrupole coupling constant (νQ) and asymmetric parameter (η) for Ta, Sb(1), and Sb(2) sites were obtained. These values are all in good agreement with the presented DFT calculations. Principal axes of the electric field gradients was determined for a single-crystal sample by measuring the angular dependencies of NMR frequency under a weak magnetic field. The unusual temperature dependence of η(T) of Sb(2) hints at the suppressed thermal expansion along the a axis. Spin-lattice relaxation rate (1/T1T) measurements reveal an activated-type behavior and an upturn below 30 K. Neither the low-temperature upturn nor the high-temperature activation-type behaviors are reproduced by the calculated 1/T1T based on the calculated density of states (DOS). On the other hand, the agreement between the calculated DOS and specific heat measurements indicates that the band renormalization is small. This fact indicates that TaSb2 deviates from the simple semimetal scenario, and magnetic excitations are not captured by Fermi liquid theory. Published by the American Physical Society 2024

Precision measurements of relaxation rates of degenerate 1H transitions in methyl groups of small proteins

An NMR experiment is designed for accurate and robust measurement of transverse relaxation rates of degenerate 1H transitions in selectively 13CH3-labeled, deuterated small proteins. The measurement is based on the use of acute (<90°) angle 1H radio-frequency pulses and relies on selection of the slow- and fast-relaxing components of methyl magnetization following the relaxation period in separate experiments. The R2 decay series recorded with selection of the fast-relaxing components serves as a useful complement to the R2 series acquired with selection of the slow-relaxing part, and permits the extension of the range of relative contributions of the fast- and slow-relaxing parts to apparent signal decay. The approach is experimentally verified on 13CH3 methyl groups of the ILV-{13CH3}-labeled protein ubiquitin at 10 °C and 25 °C. The obtained methyl 1H relaxation rates are in remarkably good agreement with the values obtained from well-established NMR techniques.

Development of a compact NMR system to measure pO2 in a tissue-engineered graft

Cellular macroencapsulation devices, known as tissue engineered grafts (TEGs), enable the transplantation of allogeneic cells without the need for life-long systemic immunosuppression. Islet containing TEGs offer promise as a potential functional cure for type 1 diabetes. Previous research has indicated sustained functionality of implanted islets at high density in a TEG requires external supplementary oxygen delivery and an effective tool to monitor TEG oxygen levels. A proven oxygen-measurement approach employs a 19F oxygen probe molecule (a perfluorocarbon) implanted alongside therapeutic cells to enable oxygen- and temperature- dependent NMR relaxometry. Although the approach has proved effective, the clinical translation of 19F oxygen relaxometry for TEG monitoring will be limited by the current inaccessibility and high cost of MRI. Here, we report the development of an affordable, compact, and tabletop 19F NMR relaxometry system for monitoring TEG oxygenation. The system uses a 0.5 T Halbach magnet with a bore diameter (19 cm) capable of accommodating the human arm, a potential site of future TEG implantation. 19F NMR relaxometry was performed while controlling the temperature and oxygenation levels of a TEG using a custom-built perfusion setup. Despite the magnet’s nonuniform field, a pulse sequence of broadband adiabatic full-passage pulses enabled accurate 19F longitudinal relaxation rate (R1) measurements in times as short as ∼2 min (R1 vs oxygen partial pressure and temperature (R2 > 0.98)). The estimated sensitivity of R1 to oxygen changes at 0.5 T was 1.62-fold larger than the sensitivity previously reported for 16.4 T. We conclude that TEG oxygenation monitoring with a compact, tabletop 19F NMR relaxometry system appears feasible.

Comprehensive analysis of relaxation decays from high-resolution relaxometry

Relaxometry consists in measuring relaxation rates over orders of magnitude of magnetic fields to probe motions of complex systems. High-resolution relaxometry (HRR) experiments can be performed on conventional high-field NMR magnets equipped with a sample shuttle. During the experiment, the sample shuttle transfers the sample between the high-field magnetic center and a chosen position in the stray field for relaxation during a variable delay, thus using the stray field as a variable field. As the relaxation delay occurs outside of the probe, HRR experiments cannot rely on the control of cross-relaxation pathways, which is standard in high-field relaxation pulse sequences. Thus, decay rates are not pure relaxation rates, which may impair a reliable description of the dynamics. Previously, we took into account cross-relaxation effects in the analysis of high-resolution relaxometry data by applying a correction factor to relaxometry decay rates in order to estimate relaxation rates. These correction factors were obtained from the iterative simulation of the relaxation decay while the sample lies outside of the probe and a preceding analysis of relaxation rates which relies on the approximation of a priori multi-exponential decays by mono-exponential functions. However, an analysis protocol matching directly experimental and simulated relaxometry decays should be more self consistent and more generally applicable as it can accommodate deviations from mono-exponential decays. Here, we introduce Matching INtensities for the Optimization of Timescales and Amplitudes of motions Under Relaxometry (MINOTAUR), a framework for the analysis of high-resolution relaxometry that takes as input the intensity decays at all fields. This approach uses the full relaxation matrix to calculate intensity decays, allowing complex relaxation pathways to be taken into account. Therefore, it eliminates the need for a correction of decay rates and for fitting multi-exponential decays with mono-exponential functions. The MINOTAUR software is designed as a flexible framework where relaxation matrices and spectral density functions corresponding to various models of motions can be defined on a case-by-case basis. The agreement with our previous analyses of protein side-chain dynamics from carbon-13 relaxation is excellent, while providing a more robust analysis tool. We expect MINOTAUR to become the tool of choice for the analysis of high-resolution relaxometry.

Identifying structural and dynamic changes during the Biliverdin Reductase B catalytic cycle.

Biliverdin Reductase B (BLVRB) is an NADPH-dependent reductase that catalyzes the reduction of multiple substrates and is therefore considered a critical cellular redox regulator. In this study, we sought to address whether both structural and dynamics changes occur between different intermediates of the catalytic cycle and whether these were relegated to just the active site or the entirety of the enzyme. Through X-ray crystallography, we determined the apo BLVRB structure for the first time, revealing subtle global changes compared to the holo structure and identifying the loss of a critical hydrogen bond that "clamps" the R78-loop over the coenzyme. Amide and Cα chemical shift perturbations were used to identify environmental and secondary structural changes between intermediates, with more distant global changes observed upon coenzyme binding compared to substrate interactions. NMR relaxation rate measurements provided insights into the dynamic behavior of BLVRB during the catalytic cycle. Specifically, the inherently dynamic R78-loop that becomes ordered upon coenzyme binding persists through the catalytic cycle while similar regions experience dynamic exchange. However, the dynamic exchange processes were found to differ through the catalytic cycle with several groups of residues exhibiting similar dynamic responses. Finally, both local and distal structural and dynamic changes occur within BLVRB that are dependent solely on the oxidative state of the coenzyme. Thus, through a comprehensive analysis here, this study revealed structural and dynamic alterations in BLVRB through its catalytic cycle that are not simply relegated to the active site, but instead, are allosterically coupled throughout the enzyme.

A Fast Determination Method for Transverse Relaxation Rate of Minimized SERF Atomic Magnetometer

The sensitivity and bandwidth as the primary criteria of spin-exchange relaxation-free (SERF) atomic magnetometer (AM) are closely related to the transverse relaxation rate of atomic ensemble. In this study, we show an effective method for transverse relaxation rate measurement drawing on golden section algorithm. With no requirement of offline fitting, the measuring time of this method is only 7s. This is especially advantageous for reducing measurement errors due to the drifts of spatial magnetic field and light intensity and employing multiple measurements to better monitor the performance of magnetometers. Moreover, the reset after measuring is optimized as the sensitive axis magnetic field correction, ensuring the integrity of measurement while improving the accuracy of magnetic compensation. Furthermore, we find that the acquired experimental data by using this method can be adopted for the evaluation of magnetic field compensation performance and the monitoring of magnetic anomaly states. This determination method for transverse relaxation rate is anticipated to play a greater important role in multi-channel SERF AMs arrays.

Assessment of vibrational-translational relaxation dynamics of methane isotopologues in a wet-nitrogen matrix through QEPAS

Here we report on a study of the non-radiative relaxation dynamic of 12CH4 and 13CH4 in wet nitrogen-based matrixes by using the quartz-enhanced photoacoustic spectroscopy (QEPAS) technique. The dependence of the QEPAS signal on pressure at fixed matrix composition and on H2O concentration at fixed pressure was investigated. We demonstrated that QEPAS measurements can be used to retrieve both the effective relaxation rate in the matrix, and the V-T relaxation rate associated to collisions with nitrogen and water vapor. No significant differences in measured relaxation rates were observed between the two isotopologues.

Calorimetric measurement of nuclear spin-lattice relaxation rate in metals

The quasiparticle density of states in correlated and quantum-critical metals directly probes the effect of electronic correlations on the Fermi surface. Measurements of the nuclear spin-lattice relaxation rate provide one such experimental probe of quasiparticle mass through the electronic density of states. By far the most common way of accessing the spin-lattice relaxation rate is via nuclear magnetic resonance and nuclear quadrupole resonance experiments, which require resonant excitation of nuclear spin transitions. Here we report non-resonant access to spin-lattice relaxation dynamics in AC-calorimetric measurements. The nuclear spin-lattice relaxation rate is inferred in our measurements from its effect on the frequency dispersion of the thermal response of the calorimeter-sample assembly. We use fast, lithographically-defined nanocalorimeters to access the nuclear spin-lattice relaxation times in metallic indium from 0.3~K to 7~K and in magnetic fields up to 35~T.

Sometimes pulses just have to be perfect – An example based on the measurement of amide proton transverse relaxation rates in proteins

The measurement of spin relaxation rates provides a unique avenue for quantifying dynamic processes in biomolecules. In order to simplify analysis of the measurements so that a few key intuitive parameters can be extracted, it is often the case that experiments are designed to eliminate interference effects between different classes of spin relaxation. One example emerges in the measurement of amide proton (1HN) transverse relaxation rates in 15N labeled proteins, where 15N inversion pulses are applied during a relaxation element to eliminate cross-correlated spin relaxation between 1HN-15N dipole-1HN CSA interactions. We show that unless these pulses are essentially perfect, significant oscillations in magnetization decay profiles can be obtained, due to the excitation of multiple-quantum coherences, leading potentially to errors in measured R2 rates. With the recent development of experiments for quantifying electrostatic potentials via amide proton relaxation rates, the need for highly accurate measurement schemes becomes critical. Straightforward modifications to existing pulse sequences are suggested to achieve this goal.

Cascade of Denoising and Mapping Neural Networks for MRI R2* Relaxometry of Iron-Loaded Liver

MRI of effective transverse relaxation rate (R2*) measurement is a reliable method for liver iron concentration quantification. However, R2* mapping can be degraded by noise, especially in the case of iron overload. This study aimed to develop a deep learning method for MRI R2* relaxometry of an iron-loaded liver using a two-stage cascaded neural network. The proposed method, named CadamNet, combines two convolutional neural networks separately designed for image denoising and parameter mapping into a cascade framework, and the physics-based R2* decay model was incorporated in training the mapping network to enforce data consistency further. CadamNet was trained using simulated liver data with Rician noise, which was constructed from clinical liver data. The performance of CadamNet was quantitatively evaluated on simulated data with varying noise levels as well as clinical liver data and compared with the single-stage parameter mapping network (MappingNet) and two conventional model-based R2* mapping methods. CadamNet consistently achieved high-quality R2* maps and outperformed MappingNet at varying noise levels. Compared with conventional R2* mapping methods, CadamNet yielded R2* maps with lower errors, higher quality, and substantially increased efficiency. In conclusion, the proposed CadamNet enables accurate and efficient iron-loaded liver R2* mapping, especially in the presence of severe noise.

Unified Description of Proton NMR Relaxation in Water, Acetonitrile, and Methane from Molecular Dynamics Simulations in the Liquid, Supercritical, and Gas Phases.

A comprehensive calculation of proton NMR relaxation in water, acetonitrile, and methane across a wide range of the phase diagram is provided via ab initio and force-field-based molecular dynamics simulations. The formalism used for the spin-rotation (SR) contribution to relaxation is developed for use with any molecular symmetry and utilizes the full molecular SR tensors, which are calculated from first-principles via Kohn-Sham (KS) DFT. In combination with calculations of the dipolar contribution, near-quantitative agreement with total measured relaxation rates is achieved.

Slice & Dice: nested spin-lattice relaxation measurements.

Spin-lattice relaxation rate (R1) measurements are commonly used to characterize protein dynamics. However, the time needed to collect the data can be quite long due to long relaxation times of the low-gamma nuclei, especially in the solid state. We present a method to collect backbone heavy atom relaxation data by nesting the collection of datasets in the solid state. This method results in a factor of 2 to 2.5 times faster data acquisition for backbone R1 relaxation data for the 13C and 15N sites of proteins.

Characterisation of magnetic relaxation on extremely long timescales.

The use of magnetisation decay measurements to characterise very slow relaxation of the magnetisation in single-molecule magnets is becoming increasingly prevalent as relaxation times move to longer timescales outside of the AC susceptibility range. However, experimental limitations and a poor understanding of the distribution underlying the stretched exponential function, commonly used to model the data, may be leading to misinterpretation of the results. Herein we develop guidelines on the experimental design, data fitting, and analysis required to accurately interpret magnetisation decay measurements. Various measures of the magnetic relaxation rate extracted from magnetisation decay measurements of [Dy(Dtp)2][Al{OC(CF3)3}4] previously characterised by Evans et al., fitted using combinations of fixing or freely fitting different parameters, are compared to those obtained using the innovative square-wave "waveform" technique of Hilgar et al. The waveform technique is comparable to AC susceptometry for measurement of relaxation rates on long timescales. The most reliable measure of the relaxation time for magnetisation decays is found to be the average logarithmic relaxation time, e〈ln[τ]〉, obtained via a fit of the decay trace using a stretched exponential function, where the initial and equilibrium magnetisation are fixed to first measured point and target values respectively. This new definition causes the largest differences to traditional approaches in the presence of large distributions or relaxation rates, with differences up to 50% with β = 0.45, and hence could have a significant impact on the chemical interpretation of magnetic relaxation rates. A necessary step in progressing towards chemical control of magnetic relaxation is the accurate determination of relaxation times, and such large variations in experimental measures stress the need for consistency in fitting and interpretation of magnetisation decays.

NMR Investigation of the Interaction of Three Non-Steroidal Anti-Inflammatory Drugs with Human Serum Albumin.

The understanding of the interaction between non-steroidal anti-inflammatory drugs and human serum albumin plays a fundamental role in the development of new drugs and new therapeutic strategies. Several studies have been performed, nevertheless, the interaction phenomena are still not fully understood. In this work, high-field solution Nuclear Magnetic Resonance (NMR) spectroscopy was applied to compare the strength of the interaction of diclofenac sodium salt, ketorolac tris salt and flurbiprofen sodium salt toward albumin. To this aim, mono- and bi-selective relaxation rate measurements were performed by applying selective π-pulses at the selected frequencies and by following magnetization recovery. On the basis of the dependence of relaxation parameters on albumin concentration, normalized affinity indexes were calculated for several protons of the drugs. Affinity indexes for diclofenac were about five-fold higher in comparison with ketorolac and flurbiprofen. Aromatic moieties of the three drugs and methine protons at the chiral centers of ketorolac and flurbiprofen were more involved in the interaction with albumin. In conclusion, NMR spectroscopy allows not only for the comparison of drug-to-protein affinities but also points out the nature of the drug sites that are more extensively involved in the interaction.

55/52Mn2+ Complexes with a Bispidine-Phosphonate Ligand: High Kinetic Inertness for Imaging Applications.

Bispidine (3,7-diazabicyclo[3.3.1]nonane) provides a rigid and preorganized scaffold that is particularly interesting for the stable and inert complexation of metal ions, especially for their application in medical imaging. In this study, we present the synthesis of two bispidine ligands with N-methanephosphonate (H4L1) and N-methanecarboxylate (H3L2) substituents as well as the physico-chemical properties of the corresponding Mn2+ and Zn2+ complexes. The two complexes [Mn(L1)]2- and [Mn(L2)]- have relatively moderate thermodynamic stability constants according to potentiometric titration data. However, they both display an exceptional kinetic inertness, as assessed by transmetallation experiments in the presence of 50 equiv excess of Zn2+, showing only ∼40 and 20% of dissociation for [Mn(L1)]2- and [Mn(L2)]-, respectively, after 150 days at pH 6 and 37 °C. Proton relaxivities amount to r1 = 4.31 mM-1 s-1 ([Mn(L1)]2-) and 3.64 mM-1 s-1 ([Mn(L2)]-) at 20 MHz, 25 °C, and are remarkable for Mn2+ complexes with one inner-sphere water molecule (q = 1); they are comparable to that of the commercial contrast agent [Gd(DOTA)(H2O)]-. The presence of one inner-sphere water molecule and an associative water exchange mechanism was confirmed by temperature-dependent transverse 17O relaxation rate measurements, which yielded kex298 = 0.12 × 107 and 5.5 × 107 s-1 for the water exchange rate of the phosphonate and the carboxylate complex, respectively. In addition, radiolabeling experiments with 52Mn were also performed with H2(L1)2- showing excellent radiolabeling properties and quantitative complexation at pH 7 in 15 min at room temperature as well as excellent stability of the complex in various biological media over 24 h.

Measurement of 1Hα transverse relaxation rates in proteins: application to solvent PREs.

It has recently been demonstrated that accurate near surface electrostatic potentials can be calculated for proteins from solvent paramagnetic relaxation enhancements (PREs) of amide protons measured using spin labels of similar structures but different charges (Yu et al. in Proc Natl Acad Sci 118(25):e2104020118, 2021). Here we develop methodology for extending such measurements to intrinsically disordered proteins at neutral pH where amide spectra are of very poor quality. Under these conditions it is shown that accurate PRE values can be measured using the haCONHA experiment that has been modified for recording 1Hα transverse relaxation rates. The optimal pulse scheme includes a spin-lock relaxation element for suppression of homonuclear scalar coupled evolution for all 1Hα protons, except those derived from Ser and Thr residues, and minimizes the radiation damping field from water magnetization that would otherwise increase measured relaxation rates. The robustness of the experiment is verified by developing a second approach using a band selective adiabatic decoupling scheme for suppression of scalar coupling modulations during 1Hα relaxation and showing that the measured PRE values from the two methods are in excellent agreement. The near surface electrostatic potential of a 103-residue construct comprising the C-terminal intrinsically disordered region of the RNA-binding protein CAPRIN1 is obtained at pH 5.5 using both 1HN and 1Hα-based relaxation rates, and at pH 7.4 where only 1Hα rates can be quantified, with very good agreement between potentials obtained under all experimental conditions.

Optical pumping and relaxation of atomic population in assorted conditions

Precise control and knowledge over atomic dynamics is central to the advancement of quantum technology. The different experimental conditions namely, atoms in a vacuum, antirelaxation coated and buffer gas filled atomic cells provide complementary platforms for such investigations. The extent of changes in optical pumping, velocity changing collision and hyperfine changing collision rates associated with these conditions are discussed. There is a phenomenal change in the optical density by a factor of >25 times in the presence of a control field in a buffer gas environment. We found confinement induced enhanced optical pumping as the mechanism behind the observed transparency in buffer gas cell. The diffusive velocity of atoms were measured to be ∼25 ± 12 m s−1 and ⩽8 ± 4 m s−1 for antirelaxation coated and buffer gas filled cells respectively. The measurements were carried out for 85Rb atoms in natural isotopic composition using pump–probe spectroscopy. The studies will have useful application in measurements of relaxation rates, quantum memory, quantum repeaters and atomic devices.