Spin-lock Experiments Research Articles

Optimal control theory techniques for nitrogen vacancy ensembles in single crystal diamond

Nitrogen vacancy centre ensembles are excellent candidates for quantum sensors due to their vector magnetometry capabilities, deployability at room temperature and simple optical initialization and readout. This work describes the engineering and characterization methods required to control all four principle axis systems (P.A.S.) of NV ensembles in a single crystal diamond without an applied static magnetic field. Circularly polarized microwaves enable arbitrary simultaneous control with spin-locking experiments and collective control using optimal control theory (OCT) in a (100) diamond. These techniques may be further improved and integrated to realize high-sensitivity NV-based quantum sensing devices using all four P.A.S. systems.

A brisk walk through the fields of relaxation, saturation, and exchange: From solid state NMR to in-vivo imaging

Novel MRI contrast methods, such as Chemical Exchange Saturation Transfer (CEST), rely on previously developed theory and approaches, often introduced first in solidstate NMR. Understanding or at least connecting the basic principles and original works to the modern-day contrast methods in MRI is instructive. The work brings together concepts in relaxation, saturation, and spin lock experiments in the dynamic (exchanging) systems. The work describes how basic principles and theory are translated and being applied to MRI contrast, including MT and CEST. Finally, we review select papers generalizing concepts of relaxation under periodic RF.

Microsecond Motion of the Bacterial Transporter EmrE in Lipid Bilayers.

The bacterial transporter EmrE is a homo-dimeric membrane protein that effluxes cationic polyaromatic substrates against the concentration gradient by coupling to proton transport. As the archetype of the small multidrug resistance family of transporters, EmrE structure and dynamics provide atomic insights into the mechanism of transport by this family of proteins. We recently determined high-resolution structures of EmrE in complex with a cationic substrate, tetra(4-fluorophenyl)phosphonium (F4-TPP+), using solid-state NMR spectroscopy and an S64V-EmrE mutant. The substrate-bound protein exhibits distinct structures at acidic and basic pH, reflecting changes upon binding or release of a proton from residue E14, respectively. To obtain insight into the protein dynamics that mediate substrate transport, here we measure 15N rotating-frame spin-lattice relaxation (R1ρ) rates of F4-TPP+-bound S64V-EmrE in lipid bilayers under magic-angle spinning (MAS). Using perdeuterated and back-exchanged protein and 1H-detected 15N spin-lock experiments under 55 kHz MAS, we measured 15N R1ρ rates site-specifically. Many residues show spin-lock field-dependent 15N R1ρ relaxation rates. This relaxation dispersion indicates the presence of backbone motions at a rate of about 6000 s-1 at 280 K for the protein at both acidic and basic pH. This motional rate is 3 orders of magnitude faster than the alternating access rate but is within the range estimated for substrate binding. We propose that these microsecond motions may allow EmrE to sample different conformations to facilitate substrate binding and release from the transport pore.

Neuronal current imaging: An experimental method to investigate electrical currents in dogs with idiopathic epilepsy.

BackgroundThe diagnosis of idiopathic epilepsy (IE) in dogs is based on exclusion of other potential causes of seizures. Recently, a novel magnetic resonance imaging (MRI) sequence that utilizes a variant of the rotary saturation approach has been suggested to detect weak transient magnetic field oscillations generated by neuronal currents in humans with epilepsy.Hypothesis/ObjectivesEffects on the magnetic field evoked by intrinsic epileptic activity can be detected by MRI in the canine brain. As proof‐of‐concept, the novel MRI sequence to detect neuronal currents was applied in dogs.AnimalsTwelve dogs with IE and 5 control dogs without a history of epileptic seizures were examined.MethodsProspective case‐control study as proof‐of‐concept. All dogs underwent a clinical neurological examination, scalp electroencephalography, cerebrospinal fluid analysis, and MRI. The MRI examination included a spin‐locking (SL) experiment applying a low‐power on‐resonance radiofrequency pulse in a predefined frequency domain in the range of oscillations generated by the epileptogenic tissue.ResultsIn 11 of 12 dogs with IE, rotary saturation effects were detected by the MRI sequence. Four of 5 control dogs did not show rotary saturation effects. One control dog with a diagnosis of neuronal ceroid lipofuscinosis had SL‐related effects, but did not have epileptic seizures clinically.Conclusions and Clinical ImportanceThe proposed MRI method detected neuronal currents in dogs with epileptic seizures and represents a potential new line of research to investigate neuronal currents possibly related to IE in dogs.

Rapid measurement of heteronuclear transverse relaxation rates using non-uniformly sampled R1ρ accordion experiments.

Multidimensional, heteronuclear NMR relaxation methods are used extensively to characterize the dynamics of biological macromolecules. Acquisition of relaxation datasets on proteins typically requires significant measurement time, often several days. Accordion spectroscopy offers a powerful means to shorten relaxation rate measurements by encoding the "relaxation dimension" into the indirect evolution period in multidimensional experiments. Time savings can also be achieved by non-uniform sampling (NUS) of multidimensional NMR data, which is used increasingly to improve spectral resolution or increase sensitivity per unit time. However, NUS is not commonly implemented in relaxation experiments, because most reconstruction algorithms are inherently nonlinear, leading to problems when estimating signal intensities, relaxation rate constants and their error bounds. We have previously shown how to avoid these shortcomings by combining accordion spectroscopy with NUS, followed by data reconstruction using sparse exponential mode analysis, thereby achieving a dramatic decrease in the total length of longitudinal relaxation experiments. Here, we present the corresponding transverse relaxation experiment, taking into account the special considerations required for its successful implementation in the framework of the accordion-NUS approach. We attain the highest possible precision in the relaxation rate constants by optimizing the NUS scheme with respect to the Cramér-Rao lower bound of the variance of the estimated parameter, given the total number of sampling points and the spectrum-specific signal characteristics. The resulting accordion-NUS relaxation experiment achieves comparable precision in the parameter estimates compared to conventional CPMG (Carr-Purcell-Meiboom-Gill) or spin-lock experiments while saving an order of magnitude in experiment time.

Application of Floquet-Magnus and Fer expansion approaches during spin-locking radiation in solid-state NMR

We apply and compare two potential expansion schemes that are developing in the field of NMR, namely, the Floquet-Magnus and Fer expansions. We use these expansion schemes for the calculation of effective Hamiltonians and propagators. We present an important iterative approach for the Floquet-Magnus expansion. While both approaches are powerful methods, there are subtle differences among them. To understand these differences, we performed explicit calculations for the multiple-pulse spin-locking experiment. Our work unifies and generalizes existing results of Floquet-Magnus and Fer approaches and delivers illustrations of novel springs that boost previous applications that are based on the classical information.

Chemical Exchange.

The phenomenon of chemical or conformational exchange in NMR spectroscopy has enabled detailed characterization of time-dependent aspects of biomolecular function, including folding, molecular recognition, allostery, and catalysis, on timescales from microsecond to second. Importantly, NMR methods based on a variety of spin relaxation parameters have been developed that provide quantitative information on interconversion kinetics, thermodynamic properties, and structural features of molecular states populated to a fraction of a percent at equilibrium and otherwise unobservable by other NMR approaches. The ongoing development of more sophisticated experimental techniques and the necessity to apply these methods to larger and more complex molecular systems engenders a corresponding need for theoretical advances describing such techniques and facilitating data analysis in applications. This review surveys current aspects of the theory of chemical exchange, as utilized in ZZ-exchange; Hahn and Carr-Purcell-Meiboom-Gill (CPMG) spin-echo; and R1ρ, chemical exchange saturation transfer (CEST), and dark state saturation transfer (DEST) spin-locking experiments. The review emphasizes theoretical results for kinetic topologies with more than two interconverting states, both to obtain compact analytical forms suitable for data analysis and to establish conditions for distinguishability between alternative kinetic schemes.

CEST imaging at 9.4 T using adjusted adiabatic spin‐lock pulses for on‐ and off‐resonant T1⍴‐dominated Z‐spectrum acquisition

The CEST experiment, with its correlation to rare proton species that are in exchange with the water pool, is very similar to the off-resonant water spin-lock (SL) experiment. In particular, low-power SL Z-spectrum acquisition allows insight into T1ρ and exchange effects with decreased direct water saturation. Because the available SL methods either require high B1 power or are instable in the presence of strong B1 and B0 inhomogeneity present at ultra-high fields, the goal of this study was to find a robust adiabatic SL pulse for on- and off-resonant application in the human brain at 9.4T. A series of Bloch simulations were used to find optimal pulse shape parameters of an adjusted hyperbolic secant pulse applicable in the low power regime typically used for exchange-weighted SL experiments. The optimized pulse was implemented and tested in phantom and in vivo experiments on a 9.4T human scanner for on- and off-resonant T1ρ - and Z-spectrum measurements. The simulation yielded a feasible pulse shape, which yielded robust images, less sensitivity to B1 and B0 inhomogeneity compared with previous SL approaches and less direct water saturation, as well as a higher chemical exchange weighting compared with conventional CEST approaches. By adapting a pulse shape for low-power SL experiments, we were able to acquire robust on- and off-resonant adiabatic SL prepared images in vivo at 9.4T. This development leads directly to SL Z-spectrum acquisition, beneficial for chemical-exchange-weighted MRI.

Theoretical investigations of quantum correlations in NMR multiple-pulse spin-locking experiments

Quantum correlations are investigated theoretically in a two-spin system with the dipole-dipole interactions in the NMR multiple-pulse spin-locking experiments. We consider two schemes of the multiple-pulse spin-locking. The first scheme consists of $\pi/2$-pulses only and the delays between the pulses can differ. The second scheme contains $\varphi$-pulses ($0<\varphi<\pi$) and has equal delays between them. We calculate entanglement for both schemes for an initial separable state. We show that entanglement is absent for the first scheme at equal delays between $\pi/2$-pulses at arbitraty temperatures. Entanglement emerges after several periods of the pulse sequence in the second scheme at $\varphi=\pi/4$ at milliKelvin temperatures. The necessary number of the periods increases with increasing temperature. We demonstrate the dependence of entanglement on the number of the periods of the multiple-pulse sequence. Quantum discord is obtained for the first scheme of the multiple-pulse spin-locking experiment at different temperatures.

Radiofrequency fields in MAS solid state NMR probes

We present a detailed analysis of the radiofrequency (RF) field over full volume of a rotor that is generated in a solenoid coil. On top of the usually considered static distribution of amplitudes along the coil axis we describe dynamic radial RF inhomogeneities induced by sample rotation. During magic angle spinning (MAS), the mechanical rotation of the sample about the magic angle, a spin packet travels through areas of different RF fields and experiences periodical modulations of both the RF amplitude and the phase. These modulations become particularly severe at the end regions of the coil where the relative RF amplitude varies up to ±25% and the RF phase changes within ±30°. Using extensive numerical simulations we demonstrate effects of RF inhomogeneity on pulse calibration and for the ramped CP experiment performed at a wide range of MAS rates. In addition, we review various methods to map RF fields using a B0 gradient along the sample (rotor axis) for imaging purposes. Under such a gradient, a nutation experiment provides directly the RF amplitude distribution, a cross polarization experiment images the correlation of the RF fields on the two channels according to the Hartmann-Hahn matching condition, while a spin-lock experiment allows to calibrate the RF amplitude employing the rotary resonance recoupling condition.Knowledge of the RF field distribution in a coil provides key to understand its effects on performance of a pulse sequence at the spectrometer and enables to set robustness requirements in the experimental design.

Spin-locking of half-integer quadrupolar nuclei in NMR of solids: The far off-resonance case

Spin-locking of spin I=3/2 and I=5/2 nuclei in the presence of large resonance offsets has been studied using both approximate and exact theoretical approaches and, in the case of I=3/2, experimentally. We show the variety of coherences and population states produced in a far off-resonance spin-locking NMR experiment (one consisting solely of a spin-locking pulse) and how these vary with the radiofrequency field strength and offset frequency. Under magic angle spinning (MAS) conditions and in the “adiabatic limit”, these spin-locked states acquire a time dependence. We discuss the rotor-driven interconversion of the spin-locked states, using an exact density matrix approach to confirm the results of the approximate model. Using conventional and multiple-quantum filtered spin-locking 23Na (I=3/2) NMR experiments under both static and MAS conditions, we confirm the results of the theoretical calculations, demonstrating the applicability of the approximate theoretical model to the far off-resonance case. This simplified model includes only the effects of the initial rapid dephasing of coherences that occurs at the start of the spin-locking period and its success in reproducing both experimental and exact simulation data indicates that it is this dephasing that is the dominant phenomenon in NMR spin-locking of quadrupolar nuclei, as we have previously found for the on-resonance and near-resonance cases. Potentially, far off-resonance spin-locking of quadrupolar nuclei could be of interest in experiments such as cross polarisation as a consequence of the spin-locking pulse being applied to a better defined initial state (the thermal equilibrium bulk magnetisation aligned along the z-axis) than can be created in a powdered solid with a selective radiofrequency pulse, where the effect of the pulse depends on the orientation of the individual crystallites.

Adiabatically prepared spin-lock approach for T1ρ-based dynamic glucose enhanced MRI at ultrahigh fields.

Chemical exchange sensitive spin-lock and related techniques allow to observe the uptake of administered D-glucose in vivo. The exchange-weighting increases with the magnetic field strength, but inhomogeneities in the radiofrequency (RF) field at ultrahigh field whole-body scanners lead to artifacts in conventional spin-lock experiments. Thus, our aim was the development of an adiabatically prepared T1ρ -based imaging sequence applicable to studies of glucose metabolism in tumor patients at ultrahigh field strengths. An adiabatically prepared on-resonant spin-lock approach was realized at a 7 Tesla whole-body scanner and compared with conventional spin-lock. The insensitivity to RF field inhomogeneities as well as the chemical exchange sensitivity of the approach was investigated in simulations, model solutions and in the human brain. The suggested spin-lock approach was shown to be feasible for in vivo application at ultrahigh field whole-body scanners and showed substantially improved image quality compared with conventional spin-lock. The sensitivity of the presented method to glucose was verified in model solutions and a glucose contrast was observed in a glioblastoma patient after intravenous administration of glucose solution. An adiabatically prepared spin-lock preparation was presented that enables a homogeneous and chemical exchange sensitive T1ρ -based imaging at ultra-high field whole-body scanners, e.g., for T1ρ -based dynamic glucose enhanced MRI. Magn Reson Med 78:215-225, 2017. © 2016 International Society for Magnetic Resonance in Medicine.

Pulsed Dynamic Nuclear Polarization with Trityl Radicals.

Continuous-wave (CW) dynamic nuclear polarization (DNP) is now established as a method of choice to enhance the sensitivity in a variety of NMR experiments. Nevertheless, there remains a need for the development of more efficient methods to transfer polarization from electrons to nuclei. Of particular interest are pulsed DNP methods because they enable a rapid and efficient polarization transfer that, in contrast with CW DNP methods, is not attenuated at high magnetic fields. Here we report nuclear spin orientation via electron spin-locking (NOVEL) experiments using the polarizing agent trityl OX063 in glycerol/water at a temperature of 80 K and a magnetic field of 0.34 T. (1)H NMR signal enhancements up to 430 are observed, and the buildup of the local polarization occurs in a few hundred nanoseconds. Thus, NOVEL can efficiently dynamically polarize (1)H atoms in a system that is of general interest to the solid-state DNP NMR community. This is a first, important step toward the general application of pulsed DNP at higher fields.

Investigation of intermolecular double-quantum off-resonance longitudinal relaxation in the tilted rotating frame

A modified correlation spectroscopy revamped by asymmetric z-gradients echo detection (CRAZED) sequence was applied to investigate the behavior of intermolecular double-quantum longitudinal relaxation processes in the tilted rotating frame. Theoretical formalism based on dipolar field theory was presented in detail. Spectroscopic measurements and quantitative analysis demonstrated that the signal intensities and intermolecular double-quantum off-resonance longitudinal relaxation time in the rotating frame (T1ρ,DQCeff) are inversely correlated with the tilt angle (θ), while positively correlated with the effective frequency of spin-locking field (ωe). Magnetic resonance imaging experiments of an agarose phantom also prove the validity of the theoretical analysis and demonstrated the feasibility of imaging based on T1ρ,DQCeff. The rotating-frame double-quantum relaxation measurements are useful for probing slow-motion molecules and this study provides the guidance for optimization of the spin-lock experiments.

Selective magnetic resonance imaging of magnetic nanoparticles by acoustically induced rotary saturation.

The goal of this study was to introduce a new method to selectively detect iron oxide contrast agents using an acoustic wave to perturb the spin-locked water signal in the vicinity of the magnetic particles. The acoustic drive can be modulated externally to turn the effect on and off, allowing sensitive and quantitative statistical comparison and removal of confounding image background variations. We demonstrated the effect in spin-locking experiments using piezoelectric actuators to generate vibrational displacements of iron oxide samples. We observed a resonant behavior of the signal changes with respect to the acoustic frequency where iron oxide is present. We characterized the effect as a function of actuator displacement and contrast agent concentration. The resonant effect allowed us to generate block-design "modulation response maps" indicating the contrast agent's location, as well as positive contrast images with suppressed background signal. We found that the acoustically induced rotary saturation (AIRS) effect stayed approximately constant across acoustic frequency and behaved monotonically over actuator displacement and contrast agent concentration. AIRS is a promising method capable of using acoustic vibrations to modulate the contrast from iron oxide nanoparticles and thus perform selective detection of the contrast agents, potentially enabling more accurate visualization of contrast agents in clinical and research settings.

Chemical exchange in biomacromolecules: Past, present, and future

The perspective reviews quantitative investigations of chemical exchange phenomena in proteins and other biological macromolecules using NMR spectroscopy, particularly relaxation dispersion methods. The emphasis is on techniques and applications that quantify the populations, interconversion kinetics, and structural features of sparsely populated conformational states in equilibrium with a highly populated ground state. Applications to folding, molecular recognition, catalysis, and allostery by proteins and nucleic acids are highlighted.

Exchange‐dependent relaxation in the rotating frame for slow and intermediate exchange – modeling off‐resonant spin‐lock and chemical exchange saturation transfer

Chemical exchange observed by NMR saturation transfer (CEST) and spin-lock (SL) experiments provide an MRI contrast by indirect detection of exchanging protons. The determination of the relative concentrations and exchange rates is commonly achieved by numerical integration of the Bloch-McConnell equations. We derive an analytical solution of the Bloch-McConnell equations that describes the magnetization of coupled spin populations under radiofrequency irradiation. As CEST and off-resonant SL are equivalent, their steady-state magnetization and dynamics can be predicted by the same single eigenvalue: the longitudinal relaxation rate in the rotating frame R1ρ . For the case of slowly exchanging systems, e.g. amide protons, the saturation of the small proton pool is affected by transverse relaxation (R2b ). It turns out, that R2b is also significant for intermediate exchange, such as amine- or hydroxyl-exchange or paramagnetic CEST agents, if pools are only partially saturated. We propose a solution for R1ρ that includes R2 of the exchanging pool by extending existing approaches, and verify it by numerical simulations. With the appropriate projection factors, we obtain an analytical solution for CEST and SL for nonzero R2 of the exchanging pool, exchange rates in the range 1-10(4) Hz, B1 from 0.1 to 20 μT and arbitrary chemical shift differences between the exchanging pools, whilst considering the dilution by direct water saturation across the entire Z-spectra. This allows the optimization of irradiation parameters and the quantification of pH-dependent exchange rates and metabolite concentrations. In addition, we propose evaluation methods that correct for concomitant direct saturation effects. It is shown that existing theoretical treatments for CEST are special cases of this approach.

Measurement of the signs of methyl 13C chemical shift differences between interconverting ground and excited protein states by R 1ρ : an application to αB-crystallin

Carr-Purcell-Meiboom-Gill relaxation dispersion (CPMG RD) NMR spectroscopy has emerged as a powerful tool for quantifying the kinetics and thermodynamics of millisecond time-scale exchange processes involving the interconversion between a visible ground state and one or more minor, sparsely populated invisible 'excited' conformational states. Recently it has also become possible to determine atomic resolution structural models of excited states using a wide array of CPMG RD approaches. Analysis of CPMG RD datasets provides the magnitudes of the chemical shift differences between the ground and excited states, Δϖ, but not the sign. In order to obtain detailed structural insights from, for example, excited state chemical shifts and residual dipolar coupling measurements, these signs are required. Here we present an NMR experiment for obtaining signs of (13)C chemical shift differences of (13)CH(3) methyl groups using weak field off-resonance R(1ρ) relaxation measurements. The accuracy of the method is established by using an exchanging system where the invisible, excited state can be converted to the visible, ground state by altering sample conditions so that the signs of Δϖ values obtained from the spin-lock approach can be validated against those measured directly. Further, the spin-lock experiments are compared with the established H(S/M)QC approach for measuring signs of chemical shift differences and the relative strengths of each method are discussed. In the case of the 650 kDa human αB-crystallin complex where there are large transverse relaxation differences between ground and excited state spins the R(1ρ) method is shown to be superior to more 'traditional' experiments for sign determination.

Radiofrequency pulse sequences which compensate their own imperfections

Radiofrequency pulse sequences are described which have the same overall effect as a single 90° or 180° pulse but which compensate the undesirable effects of resonance offset and spatial inhomogeneity of the radiofrequency field H 1. These “composite” pulses are built up from a small number of conventional pulses which rotate the nuclear magnetization vectors about different axes in the rotating frame, while in the intervals between pulses a limited amount of free precession may be allowed to occur. Insight into the way in which pulse imperfections are compensated is obtained by computer simulation of trajectories of families of nuclear spin “isochromats” representing a distribution of H 1 intensity or resonance offset. Composite 90° pulses are suggested as a method of reducing systematic errors in spin-lattice relaxation times derived from progressive saturation or saturation-recovery experiments, and as the preparation pulse of a spin-locking experiment. A test of the effectiveness of the composite 180° pulse sequence has been made by using it for population inversion in a spin-lattice relaxation measurement, where T 1 is derived from the null point in the recovery curve, a technique known to be very sensitive to pulse imperfections.

Spin-locking versus chemical exchange saturation transfer MRI for investigating chemical exchange process between water and labile metabolite protons

Chemical exchange saturation transfer (CEST) and spin-locking (SL) experiments were both able to probe the exchange process between protons of nonequivalent chemical environments. To compare the characteristics of the CEST and SL approaches in the study of chemical exchange effects, we performed CEST and SL experiments at varied pH and concentrated metabolite phantoms with exchangeable amide, amine, and hydroxyl protons at 9.4 T. Our results show that: (i) on-resonance SL is most sensitive to chemical exchanges in the intermediate-exchange regime and is able to detect hydroxyl and amine protons on a millimolar concentration scale. Off-resonance SL and CEST approaches are sensitive to slow-exchanging protons when an optimal SL or saturation pulse power matches the exchanging rate, respectively. (ii) Offset frequency-dependent SL and CEST spectra are very similar and can be explained well with an SL model recently developed by Trott and Palmer (J Magn Reson 2002;154:157-160). (iii) The exchange rate and population of metabolite protons can be determined from offset-dependent SL or CEST spectra or from on-resonance SL relaxation dispersion measurements. (iv) The asymmetry of the magnetization transfer ratio (MTR(asym)) is highly dependent on the choice of saturation pulse power. In the intermediate-exchange regime, MTR(asym) becomes complicated and should be interpreted with care.