Double-quantum Coherence Research Articles

Effective dipolar couplings determined by dipolar dephasing of double-quantum coherences

It is shown how homonuclear distances and homonuclear dipolar lattice sums between spin-1/2 nuclei can be measured by a pulsed solid-state NMR experiment under magic-angle spinning conditions. The presented technique is based on double-quantum coherence filtering. Instead of measuring a build-up of double-quantum coherence the pulse sequence is designed to dephase double-quantum coherence. This is achieved by exciting double-quantum coherence either with the help of the through-space dipolar coupling or the through-bond dipolar coupling while the dephasing relies on the through-space dipolar coupling as selected by a γ-encoded pulse sequence from the C/ R symmetry class. Since dephasing curves can be normalized on zero dephasing, it is possible to analyze the initial dephasing regime and hence determine dipolar lattice sums (effective dipolar couplings) in multiple-spin systems. A formula for the effective dipolar coupling is derived theoretically and validated by numerical calculations and experiments on crystalline model compounds for 13C and 31P spin systems. The double-quantum dephasing experiment can be combined with constant-time data sampling to compensate for relaxation effects, consequently only two experimental data points are necessary for a single distance measurement. The phase cycling overhead for the constant-time experiment is minimal because a short cogwheel phase cycle exists. A 2D implementation is demonstrated on [ 13C 3]alanine.

Mixed Frequency/Time Domain Optical Analogues of Heteronuclear Multidimensional NMR

Ultrafast spectroscopy is dominated by time domain methods such as pump-probe and, more recently, 2D-IR spectroscopies. In this paper, we demonstrate that a mixed frequency/time domain ultrafast four wave mixing (FWM) approach not only provides similar capabilities, but it also provides optical analogues of multiple- and zero-quantum heteronuclear nuclear magnetic resonance (NMR). The method requires phase coherence between the excitation pulses only over the dephasing time of the coherences. It uses twelve coherence pathways that include four with populations, four with zero-quantum coherences, and four with double-quantum coherences. Each pathway provides different capabilities. The population pathways correspond to those of two-dimensional (2D) time domain spectroscopies, while the double- and zero-quantum coherence pathways access the coherent dynamics of coupled quantum states. The three spectral and two temporal dimensions enable the isolation and characterization of the spectral correlations between different vibrational and/or electronic states, coherence and population relaxation rates, and coupling strengths. Quantum-level interference between the direct and free-induction decay components gives a spectral resolution that exceeds that of the excitation pulses. Appropriate parameter choices allow isolation of individual coherence pathways. The mixed frequency/time domain approach allows one to access any set of quantum states with coherent multidimensional spectroscopy.

Detection of correlated dynamics on multiple timescales by measurement of the differential relaxation of zero- and double-quantum coherences involving sidechain methyl groups in proteins

Multiple effects may lead to significant differences between the relaxation rates of zero-quantum coherences (ZQC) and double-quantum coherences (DQC) generated between a pair of nuclei in solution. These include the interference between the anisotropic chemical shifts of the two nuclei participating in formation of the ZQC or DQC, the individual dipolar interactions of each of the two nuclei with the same proton, and the slow modulation of the isotropic chemical shifts of the two nuclei due to conformational exchange. Motional events that occur on a timescale much faster than the rotational correlation time (ps–ns) influence the first two effects, while the third results from processes that occur on a far slower timescale (μs–ms). An analysis of the differential relaxation of ZQC and DQC is thus informative about dynamics on the fast as well as the slow timescales. We present here an experiment that probes the differential relaxation of ZQC and DQC involving methyl groups in protein sidechains as an extension to our recently proposed experiments for the protein backbone. We have applied the methodology to 15N, 13C-labeled ubiquitin and used a detailed analysis of the measured relaxation rates using a simple single-axis diffusion model to probe the motional restriction of the C nextH next bond vector where C next is the carbon that is directly bonded to a sidechain methyl carbon (C methyl). Comparison of the present results with the motional restriction of the C nextC methyl bond ( S axis 2 ) reveals that the single-axis diffusion model, while valid in the fringes of the protein and for shorter chain amino acids, proves inadequate in the central protein core for long chain, asymmetrically branched amino acids where more complex motional models are necessary, as is the inclusion of the possibility of correlation between multiple motional modes. In addition, the present measurements report on the modulation of isotropic chemical shifts due to motion on the μs–ms timescale. Three Leu residues (8, 50, and 56) are found to display these effects. These residues lie in regions where chemical shift modulation had been detected previously both in the backbone and sidechain regions of ubiquitin.

Photo-oxidation of diglycine in confined media: Relaxation of longitudinal magnetization in spin correlated radical pairs

Time-resolved electron paramagnetic resonance spectra (X-band) of correlated radical pairs created in AOT reverse micelles are presented and simulated using the microreactor model. They are discussed in terms of the two-site model with a particular emphasis on longitudinal relaxation mechanisms. The geminate radical pair is created by photo-oxidation of dyglicine by the excited triplet states of an anthraquinone salt. The strong chemically induced electron spin polarization observed is due to three mechanisms: TM, RPM, and SCRPM. Relative contributions from these mechanisms depend on the water pool volume and the time of observation. There are three types of longitudinal relaxation in radical pairs. The first is relaxation of the RPM induced longitudinal magnetization in spin correlated radical pairs. The second is the longitudinal relaxation in radical pairs which are not correlated (with a zero value of the double quantum coherence). In such pairs, the generation of longitudinal magnetization due to RPM is impossible, and the spin-selective recombination of the pairs is ineffective. Under all experimental conditions, the first type of relaxation is slower than the second type. For both, the physical mechanism leading to relaxation is modulation of the Heisenberg electron spin exchange interaction. This is an internal relaxation process. The third relaxation type occurs in radical pairs due to ordinary longitudinal relaxation in non-interacting radicals. Normally, relaxation of the third type is the slowest of the three. This explains time and micelle size dependence of the relative contribution of RPM into TREPR spectra. It seems reasonable to suggest that the creation of the initial spin state populations is partially adiabatic.

New double quantum coherence filter for localized detection of glutathione in vivo

In this work, a new double quantum filter for glutathione (GSH) editing is introduced, combined with the point-resolved spectroscopy localization sequence (PRESS), and demonstrated in vivo. Compared to the conventional double quantum coherence filter, the new filter has two major advantages. First, it eliminates the need for calibration scans for optimizing the signal yield, making it more efficient and convenient for routine use. Second, it removes the influence of water saturation pulses on the GSH yield, further improving its accuracy. With this method, GSH concentrations in the left and right parietal lobes of five healthy volunteers were determined to be 0.91+/-0.16 mM and 0.89+/-0.16 mM, respectively, in agreement with previous studies.

Effects of Protein–pheromone Complexation on Correlated Chemical Shift Modulations

Major urinary protein (MUP) is a pheromone-carrying protein of the lipocalin family. Previous studies by isothermal titration calorimetry (ITC) show that the affinity of MUP for the pheromone 2-methoxy-3-isobutylpyrazine (IBMP) is mainly driven by enthalpy, with a small unfavourable entropic contribution. Entropic terms can be attributed in part to changes in internal motions of the protein upon binding. Slow internal motions can lead to correlated or anti-correlated modulations of the isotropic chemical shifts of carbonyl C' and amide N nuclei. Correlated chemical shift modulations (CSM/CSM) in MUP have been determined by measuring differences of the transverse relaxation rates of zero- and double-quantum coherences ZQC{C'N} and DQC{C'N}, and by accounting for the effects of correlated fluctuations of dipole-dipole couplings (DD/DD) and chemical shift anisotropies (CSA/CSA). The latter can be predicted from tensor parameters of C' and N nuclei that have been determined in earlier work. The effects of complexation on slow time-scale protein dynamics can be determined by comparing the temperature dependence of the relaxation rates of APO-MUP (i.e., without ligand) and HOLO-MUP (i.e., with IBMP as a ligand).

Slow Diffusion by Singlet State NMR Spectroscopy

Small diffusion coefficients can be measured by using populations of singlet states that have a relaxation time constant, T(s), which can be much longer than the longitudinal relaxation time, T1. Spatial information can be encoded with pulsed field gradients in the manner of stimulated echo sequences. Singlet states can be excited via double-quantum coherences to enhance the efficiency of phase encoding and decoding.

Double quantum coherence electron spin resonance on coupled Cu(II)–Cu(II) electron spins

We demonstrate for the first time the ability to generate double quantum coherences (DQCs) for the case of Cu(II). We show that small splittings (∼7 MHz) from the Cu(II)–Cu(II) electron–electron magnetic dipolar interaction can be reliably resolved even though the inhomogeneously broadened Cu(II) linewidth is ∼2 GHz. A Cu(II)–Cu(II) distance of 2.0 nm was measured on a model peptide system, thus, demonstrating that distances on the nanometer scale may be measured using DQC electron spin resonance (ESR).

Rotor-synchronized acquisition of quadrupolar satellite-transition NMR spectra: practical aspects and double-quantum filtration

The very broad resonances of quadrupolar (spin I > 1/2) nuclei are resolved by magic angle spinning (MAS) into a large number of spinning sidebands, each of which often remains anisotropically broadened. The quadrupolar interaction can be removed to a first-order approximation if the MAS NMR spectrum is acquired in a rotor-synchronized fashion, aliasing the spinning sidebands onto a centreband and thereby increasing the signal-to-noise ratio in the resulting, possibly second-order broadened, spectrum. We discuss the practical aspects of this rotor-synchronization in the direct ( t 2) time domain, demonstrating that the audiofrequency filters in the receiver section of the spectrometer have a significant impact on the precise timings needed in the experiment. We also introduce a novel double-quantum filtered rotor-synchronized experiment for half-integer spin quadrupolar (spin I = 3/2, 5/2, etc.) nuclei that makes use of central-transition-selective inversion pulses to both excite and reconvert double-quantum coherences and yields a simplified spectrum containing only the ST 1 ( m I = ± 1/2 ↔ ± 3/2) satellite-transition lineshapes. For spin I = 5/2 nuclei, such as 17O and 27Al, this spectrum may exhibit a significant resolution increase over the conventional central-transition spectrum.

Brain γ‐aminobutyric acid measurement by proton double‐quantum filtering with selective J rewinding

An optimized single-shot proton double-quantum (DQ) filter for the quantification of gamma-aminobutyric acid (GABA) levels in human brain is reported. It is demonstrated that creation of DQ coherences following dual-resonance-selective refocusing gives a theoretical editing efficiency of 50% for the detection of the GABA resonance at 3.01 ppm. The sequence times are optimized with both numerical and experimental analyses of the editing performance, giving an experimental editing efficiency of 42%. It is acknowledged that homocarnosine is partially coedited, leading to a 20% contribution to the edited signal; however, macromolecule contamination is negligible in vivo under these experimental conditions. The GABA concentration in human prefrontal cortex is estimated to be 0.8 +/- 0.1 micromol/g (mean +/- SD, n = 6), with reference to the internal standard creatine at 9 micromol/g.

Functional magnetic resonance imaging with intermolecular double‐quantum coherences at 3 T

Functional magnetic resonance imaging (fMRI) based on the selection of intermolecular double-quantum coherences (iDQC) was performed with a standard birdcage coil at 3 T in a group of normal human volunteers. Suppression of spurious signal contributions from unwanted coherence-transfer pathways was achieved by combining a two-step phase cycle and a long repetition time of 5 s. A gradient-recalled echo iDQC sequence (echo time, T(E) = 80 ms) yielded robust activation with a visual paradigm. Maximum z-scores were about half of those observed with conventional blood-oxygen level dependent fMRI, whereas the functional signal change increased by more than a factor of 5. No activation was obtained with a spin-echo iDQC sequence (T(E) = 160 ms), in which dephasing accumulated during the evolution period was fully rephased by an appropriate delay time. It is hypothesized that substantial inherent diffusion weighting of the iDQC technique efficiently suppresses intravascular contributions to the functional contrast. A consistent quantitative explanation of the observed amount of signal change currently remains speculative.

Crossed-coil detection of two-photon excited nuclear quadrupole resonance

Applying a recently developed theoretical framework for determining two-photon excitation Hamiltonians using average Hamiltonian theory, we calculate the excitation produced by half-resonant irradiation of the pure quadrupole resonance of a spin-3/2 system. This formalism provides expressions for the single-quantum and double-quantum nutation frequencies as well as the Bloch–Siegert shift. The dependence of the excitation strength on RF field orientation and the appearance of the free-induction signal along an axis perpendicular to the excitation field provide an unmistakable signature of two-photon excitation. We demonstrate single- and double-quantum excitation in an axially symmetric system using 35Cl in a single crystal of potassium chlorate ( ω Q = 28 MHz) with crossed-coil detection. A rotation plot verifies the orientation dependence of the two-photon excitation, and double-quantum coherences are observed directly with the application of a static external magnetic field.

Site directed spin labelling and pulsed dipolar electron paramagnetic resonance (doubleelectron–electron resonance) of force activation in muscle

The recent development of site specific spin labelling and advances in pulsedelectron paramagnetic resonance (EPR) have established spin labelling as a viablestructural biology technique. Specific protein sites or whole domains can beselectively targeted for spin labelling by cysteine mutagenesis. The secondarystructure of the proteins is determined from the trends in EPR signals of labelsattached to consecutive residues. Solvent accessibility or label mobility displayperiodicities along the labelled polypeptide chain that are characteristic ofβ-strands (periodicityof 2 residues) or α-helices (3.6 residues). Low-resolution 3D structure of proteins is determined from thedistance restraints. Two spin labels placed within 60–70 Å of each other create a local dipolarfield experienced by the other spin labels. The strength of this field is related to theinterspin distance, . The dipolar field can be measured by the broadening of the EPR lines for the shortdistances (8–20 Å) or for the longer distances (17–70 Å) by the pulsed EPR methods, doubleelectron–electron resonance (DEER) and double quantum coherence (DQC). A brief reviewof the methodology and its applications to the multisubunit muscle protein troponin ispresented below.

Orientational dependence of intermolecular double quantum coherence (iDQC) signal from tendon tissue

The proton signal changes as the long axis of tendon tissue is rotated with respect to the main magnetic field (B(0)). The orientational changes in the tendon signal obtained using the correlation spectroscopy revamped by asymmetric z-gradient echo detection (CRAZED) sequence, which allows the effects of intermolecular dipolar interactions to be observed, were investigated and compared with the orientational changes of the signals produced using correlation spectroscopy (COSY), spin-echo (SE), and one-pulse sequences. The intermolecular double quantum coherence (iDQC) signal obtained using the CRAZED sequence showed a variation in the signal from tendon tissue, with sharper peaks and greater relative differences between minimum and maximum signal values compared to the variations in the signal obtained from the COSY, SE, and one-pulse sequences. This result is attributed to the orientational dependence of the transverse relaxation rate of single (SQC) and double (DQH) quantum coherences R(2) and R(2,2), respectively.

Rotating‐frame intermolecular double‐quantum spin‐lattice relaxation T1ρ, DQC‐weighted magnetic resonance imaging

In this study, spin-locking techniques were added as a part of intermolecular multiple-quantum experiments, thereby introducing the concept of rotating-frame intermolecular double-quantum spin-lattice relaxation, T(1rho, DQC). A novel magnetic resonance imaging methodology based on intermolecular multiple-quantum coherences is demonstrated on a 7.05-T microimaging scanner. The results clearly reveal that the intermolecular double-quantum coherence T(1rho, DQC)-weighted imaging technique provides an alternative contrast mechanism to conventional imaging.

Multiplet patterns due to co-existing intermolecular dipolar and intramolecular scalar couplings in liquid nuclear magnetic resonance

When both intermolecular dipolar couplings (D couplings) and intramolecular scalar couplings (J couplings) exist in a highly polarized multiple-spin liquid, some forbidden nuclear magnetic resonance signals originating from intermolecular multiple-quantum coherences may become observable. Moreover, their multiplet patterns are quite different from what are observed in a multiple-spin system with J couplings only. In this paper, these forbidden resonance peaks and unique multiplet patterns are studied theoretically and experimentally. For comparison and verification, an I2S3+X spin system is chosen as an example to present five types of signal patterns from the interactions of D and J couplings with either selective or non-selective radio-frequency pulse sequences for double-quantum coherences. The multiplet pattern rules for a more general IpSq+Xk (p,q,k = 1,2,3,...) spin system are derived as well. It is demonstrated that some unusual multiplet amplitude patterns such as (1:0:–1) may ``magnify'' J splittings, allowing more accurate measurement of J coupling in the case of small J coupling constants and/or in inhomogeneous fields. It is shown that the theoretical predictions, computer simulations and experimental observations are all in agreement with one another very well.

The determination of pair distance distributions by pulsed ESR using Tikhonov regularization

Pulsed ESR techniques with the aid of site-directed spin labeling have proven useful in providing unique structural information about proteins. The determination of distance distributions in electron spin pairs directly from the dipolar time evolution of the pulsed ESR signals by means of the Tikhonov regularization method is reported. The difficulties connected with numerically inverting this ill-posed mathematical problem are clearly illustrated. The Tikhonov regularization with the regularization parameter determined by the L-curve criterion is then described and tested to confirm its accuracy and reliability. The method is applied to recent experimental results on doubly labeled proteins that have been studied using two pulsed ESR techniques, double quantum coherence (DQC) ESR and double electron–electron resonance (DEER). The extracted distance distributions are able to provide valuable information about the conformational constraints in various partially folded states of proteins. This study supplies a mathematically reliable method for extracting pair distributions from pulsed ESR experimental data and has extended the use of pulsed ESR to provide results of greater value for structural biology.

Spin-Labeled Gramicidin A: Channel Formation and Dissociation

Gramicidin A was studied by continuous wave electron spin resonance (CW-ESR) and by double-quantum coherence electron spin resonance (DQC-ESR) in several lipid membranes (using samples that were macroscopically aligned by isopotential spin-dry ultracentrifugation) and vesicles. As a reporter group, the nitroxide spin-label was attached at the C-terminus yielding the spin-labeled product (GAsl). ESR spectra of aligned membranes containing GAsl show strong orientation dependence. In DPPC and DSPC membranes at room temperature the spectral shape is consistent with high ordering, which, in conjunction with the observed high polarity of the environment of the nitroxide, is interpreted in terms of the nitroxide moiety being close to the membrane surface. In contrast, spectra of GAsl in DMPC membranes indicate deeper embedding and tilt of the NO group. The GAsl spectrum in the DPPC membrane at 35°C (the gel to P β phase transition) exhibits sharp changes, and above this temperature becomes similar to that of DMPC. The dipolar spectrum from DQC-ESR clearly indicates the presence of pairs in DMPC membranes. This is not the case for DPPC, rapidly frozen from the gel phase; however, there are hints of aggregation. The interspin distance in the pairs is 30.9 Å, in good agreement with estimates for the head-to-head GAsl dimer (the channel-forming conformation), which matches the hydrophobic thickness of the DMPC bilayer. Both DPPC and DSPC, apparently as a result of hydrophobic mismatch between the dimer length and bilayer thickness, do not favor the channel formation in the gel phase. In the P β and L α phases of DPPC (above 35°C) the channel dimer forms, as evidenced by the DQC-ESR dipolar spectrum after rapid freezing. It is associated with a lateral expansion of lipid molecules and a concomitant decrease in bilayer thickness, which reduces the hydrophobic mismatch. A comparison with studies of dimer formation by other physical techniques indicates the desirability of using low concentrations of GA (∼0.4–1 mol %) accessible to the ESR methods employed in the study, since this yields non-interacting dimer channels.

Separation and characterization of different signals from intermolecular three-spin orders in solution NMR

In this paper, signals originating from a pure specific coherence of intermolecular three-spin orders were separated and characterized experimentally in highly polarized two-component spin systems. A modified CRAZED sequence with selective radio-frequency excitation was designed to separate the small signals from the strong conventional single-spin single-quantum signals. General theoretical expressions of the pulse sequence with arbitrary flip angle pulses were derived using dipolar field treatment. The expressions were used to predict the relaxation and diffusion properties and optimal experimental parameters such as flip angles. For the first time, relaxation and diffusion properties of pure intermolecular single-quantum, double-quantum, and triple-quantum coherences of three-spin orders were characterized and analyzed in one-dimensional experiments. All experimental observations are in excellent agreement with the theoretical predictions. The theoretical results show that the quantum-mechanical treatment leads to exactly the same predictions as the dipolar field treatment. The quantitative study of intermolecular multiple-quantum coherences of three-spin orders presented herein provides a better understanding of their mechanisms.

Two-dimensional nuclear magnetic resonance spectroscopy in optically pumped semiconductors

Optical pumping enhanced double quantum nuclear spin coherences were detected in bulk GaAs and InP by two-dimensional NMR. The stimulation of the coherences was achieved using a single non-selective resonant RF pulse. This is unusual because stimulation of such coherences from a spin system at thermal equilibrium in high field would normally require a minimum of two pulses. A density matrix analysis, combined with a time-resolved study of the build-up of the double quantum coherence in GaAs, suggests that the enhancement of the double quantum coherence amplitude stems from optical pumping of dipolar nuclear spin order.