A New Two-Dimensional Pulse Sequence for T2* Measurements of Protons in C Isotopomers

A new two-dimensional pulse sequence for T₂* measurement of protons directly coupled to ¹³C spins is proposed. The sequence measures the tranverse relaxation time of heteronuclear proton single-quantum coherence under conditions of free precession and is therefore well suited to evaluate relaxation losses of proton magnetization during preparation delays of heteronuclear pulse experiments in analytical NMR. The relevant part of the pulse sequence can be inserted as a “building block” into any direct or inverse detecting H,C correlation pulse sequence if proton spin–spin relaxation is to be investigated. In this contribution, the building block is inserted into a HETCOR as well as into a HMQC pulse sequence. Experimental results for the HETCOR-based sequence are given.     

Analysis of protein/ligand interactions with NMR diffusion measurements: the importance of eliminating the protein background

Pulsed-field gradient nuclear magnetic resonance (PFG-NMR) is a well-established method for the determination of translational diffusion coefficients. Recently, this method has found applicability in the combinatorial arena with the introduction of affinity NMR for characterizing protein/ligand interactions. Although affinity NMR has been reported to be an effective method for the identification of active compounds in a complex mixture, there are limitations of this method. We have developed a simple mathematical model to predict optimum concentration ratios of the ligand and protein in order to observe maximum changes in the ligand diffusion coefficient upon protein binding. The ligand/protein systems of L-tryptophan and ibuprofen binding to human serum albumin were chosen to demonstrate the usefulness of this model. However, even when the conditions of the mathematical model are satisfied, the spectral background arising from the protein in proton-detected experiments can be problematic. To this end, we have employed spectral subtraction of the protein spectrum to yield ligand diffusion coefficients that are in agreement with those predicted by simulation.     

Solid state proton imaging detected by quadrupole resonance

A double resonance method for imaging of solid materials containing quadrupole nuclei via the coupled protons is reported. The technique uses a static field gradient to encode the position on the protons and the method of double resonance spin-echo to detect the occurrence of proton resonances by affecting the zero-field echo signal from the quadrupole system. The double resonance imaging method offers the advantages of higher spatial resolution and straightforward image reconstruction for powder samples compared with rotating-frame and Zeeman-perturbated nuclear quadrupole resonance encoding techniques.     

Tailored HCCH-TOCSY experiment for resonance assignment in the proximity of a paramagnetic center

The presence of a paramagnetic center may disturb both coherent and incoherent communication between nuclear spins that are affected, to some extent, by the hyperfine interaction. This is a limiting factor to an extensive use of paramagnetic probes in NMR spectroscopy to enhance partial alignment and to exploit cross correlation effects and pseudocontact shifts. We propose here an HCCH-TOCSY experiment tailored to identify spin systems involving resonances that are partly or completely affected by hyperfine interaction. The efficiency of polarization transfer steps when fast relaxing nuclei are involved is discussed. The sequence is tested for the protein Calbindin D(9k), in which one of the two native Ca2+ ions is replaced by the paramagnetic Ce3+ ion as well as for the oxidized form of cytochrome b(562).     

H Spectroscopy without Solvent Suppression: Characterization of Signal Modulations at Short Echo Times

While most proton (¹H) spectra acquired in vivo utilize selective suppression of the solvent signal for more sensitive detection of signals from the dilute metabolites, recent reports have demonstrated the feasibility and advantages of collecting in vivo data without solvent attenuation. When these acquisitions are performed at short echo times, the presence of frequency modulations of the water resonance may become an obstacle to the identification and quantitation of metabolite resonances. The present report addresses the characteristics, origin, and elimination of these sidebands. Sideband amplitudes were measured as a function of delay time between gradient pulse and data collection, as a function of gradient pulse amplitude, and as a function of spatial location of the sample for each of the three orthogonal gradient sets. Acoustic acquisitions were performed to demonstrate the correlation between mechanical vibration resonances and the frequencies of MR sidebands. A mathematical framework is developed and compared with the experimental results. This derivation is based on the theory that these frequency modulations are induced by magnetic field fluctuations generated by the transient oscillations of gradient coils.     

Sensitivity enhancement in structural measurements by solid state NMR through pulsed spin locking

Free induction decay (FID) signals in solid state NMR measurements performed with magic angle spinning can often be extended in time by factors on the order of 10 by a simple pulsed spin locking technique. The sensitivity of a structural measurement in which the structural information is contained in the dependence of the integrated FID amplitude on a preceding evolution period can therefore be enhanced substantially by pulsed spin locking in the signal detection period. We demonstrate sensitivity enhancements in a variety of solid state NMR techniques that are applicable to selectively isotopically labeled samples, including 13C-15N rotational echo double resonance (REDOR), 13C-13C dipolar recoupling measurements using the constant-time finite-pulse radio-frequency-driven recoupling (fpRFDR-CT) and constant-time double-quantum-filtered dipolar recoupling (CTDQFD) techniques, and torsion angle measurements using the double quantum chemical shift anisotropy (DQCSA) technique. Further, we demonstrate that the structural information in the solid state NMR data is not distorted by pulsed spin locking in the detection period.     

An improved method for suppressing protein background in PFG NMR experiments to determine ligand diffusion coefficients in the presence of receptor

In NMR diffusion experiments to study ligand-protein binding equilibria, the spectral background due to broad protein resonances can contribute significantly to the measured ligand signal intensity resulting in erroneous binding affinities. One method to suppress the protein spectral background involves coupling a CPMG pulse train before or after the BPPSTE pulse sequence to allow for differential T(2) relaxation of the broad protein resonances. Here, we present an improved method, the Gradient Phase Encoded Spin-lock (GraPES) experiment that integrates the relaxation filter into the diffusion period. Compared with sequential CPMG-BPPSTE pulse sequences, GraPES offers effective suppression of the protein background with improved signal-to-noise ratios and shorter experiment times.     

Generation and Application of Ultra-High-Intensity Magnetic Field Gradient Pulses for NMR Spectroscopy

Two different concepts of gradient current power supplies are introduced, which are suitable for the generation of ultra-high intensity pulsed magnetic field gradients of alternating polarity. The first system consists of a directly binary coded current source (DBCCS). It yields current pulses of up to ±120 A and a maximum voltage across the gradient coil of ±400 V. The second system consists of two TECHRON 8606 power supplies in push–pull configuration (PSPPC). It yields current pulses of up to ±100 A and a maximum voltage across the gradient coil of ±300 V. In combination with actively shielded anti-Helmholtz gradient coils, both systems are used routinely in NMR diffusion studies with unipolar pulsed field gradients of up to 35 T/m. Until now, alternating pulsed field gradient experiments were successfully performed with gradient intensities of up to ±25 T/m (DBCCS) and ±35 T/m (PSPPC), respectively. Based on the observation of the NMR spin echo in the presence of a small read gradient, procedures to test the stability and the matching of such ultra-high pulsed field gradient intensities as well as an automated routine for the compensation of possible mismatches are introduced. The results of these procedures are reported for the PSPPC system.     

Numerical simulation of one- and two-dimensional ESEEM experiments

Numerical simulation has become an indispensable tool for the interpretation of pulse EPR experiments. In this work it is shown how automatic orientation selection, grouping of operator factors, and direct selection and elimination of coherences can be used to improve the efficiency of time-domain simulations of one- and two-dimensional electron spin echo envelope modulation (ESEEM) spectra. The program allows for the computation of magnetic interactions of any symmetry and can be used to simulate spin systems with an arbitrary number of nuclei with any spin quantum number. Experimental restrictions due to finite microwave pulse lengths are addressed and the enhancement of forbidden coherences by microwave pulse matching is illustrated. A comparison of simulated and experimental HYSCORE (hyperfine sublevel correlation) spectra of ordered and disordered systems with varying complexity shows good qualitative agreement.     

GAMMA simulations of stray field responses: slice thickness and pulse calibration

A stray field (STRAFI) module has been added to the GAMMA magnetic resonance simulation platform in order to facilitate computational investigations of NMR experiments in large static field gradients that are on the order of 50 T/m. The package has been used to examine system response during echo trains generated by the application of shaped pulses. The associated echo amplitude maxima and effective slice thickness are presented. A new accurate method for STRAFI pulse calibration based on relative echo amplitudes is proposed.     

Dynamics of Spin I=3/2 under Spin-Locking Conditions in an Ordered Environment

We have derived approximate analytic solutions to the master equation describing the evolution of the spin I=3/2 density operator in the presence of a radio-frequency (RF) field and both static and fluctuating quadrupolar interactions. Spectra resulting from Fourier transformation of the evolutions of the on-resonance spin-locked magnetization into the various coherences display two satellite pairs and, in some cases, a central line. The central line is generally trimodal, consisting of a narrow component related to a slowly relaxing mode and two broad components pertaining to two faster relaxing modes. The rates of the fast modes are sensitive to slow molecular motion. Neither the amplitude nor the width of the narrow component is affected by the magnitude of the static coupling, whereas the corresponding features of the broad components depend in a rather complicated manner on the spin-lock field strength and static quadrupolar interaction. Under certain experimental conditions, the dependencies of the amplitudes on the dynamics are seen to vanish and the relaxation rates reduce to relatively simple expressions. One of the promising emerging features is the fact that the evolutions into the selectively detected quadrupolar spin polarization order and the rank-two double-quantum coherence do not exhibit a slowly relaxing mode and are particularly sensitive to slow molecular motion. Furthermore, these coherences can only be excited in the presence of a static coupling and this makes it possible to discern nuclei in anisotropic from those in isotropic environment. The feasibility of the spin-lock pulse sequences with limited RF power and a nonvanishing average electric field gradient has been demonstrated through experiments on sodium in a dense lyotropic DNA liquid crystal.     

Measurement of Small One-Bond Proton–Carbon Residual Dipolar Coupling Constants in Partially Oriented C Natural Abundance Oligosaccharide Samples: Analysis of Heteronuclear JCH-Modulated Spectra with the BIRD Inversion Pulse

Two 2D J-modulated HSQC-based experiments were designed for precise determination of small residual dipolar one-bond carbon–proton coupling constants in ¹³C natural abundance carbohydrates. Crucial to the precision of a few hundredths of Hz achieved by these methods was the use of long modulation intervals and BIRD pulses, which acted as semiselective inversion pulses. The BIRD pulses eliminated effective evolution of all but ¹J_CH couplings, resulting in signal modulation that can be described by simple modulation functions. A thorough analysis of such modulation functions for a typical four-spin carbohydrate spin system was performed for both experiments. The results showed that the evolution of the ¹H–¹H and long-range ¹H–¹³C couplings during the BIRD pulses did not necessitate the introduction of more complicated modulation functions. The effects of pulse imperfections were also inspected. While weakly coupled spin systems can be analyzed by simple fitting of cross peak intensities, in strongly coupled spin systems the evolution of the density matrix needs to be considered in order to analyse data accurately. However, if strong coupling effects are modest the errors in coupling constants determined by the “weak coupling” analysis are of similar magnitudes in oriented and isotropic samples and are partially cancelled during dipolar coupling calculation. Simple criteria have been established as to when the strong coupling treatment needs to be invoked.     

Imaging the long-range dipolar field in structured liquid state samples

We describe imaging experiments in which the pattern of the dipolar field generated by spatially modulated nuclear magnetization is directly visualized in simply structured phantoms. Two types of experiment have been carried out at 11.7 T using (1)H NMR signals. In the first, the field from a single spin species is imaged via its own NMR signal. In the second, the NMR signal from one spin species is used to image the field generated by a second species. The field patterns measured in these experiments correspond well with those calculated using simple theoretical expressions for the dipolar field. The results also directly demonstrate the spatial sensitivity of the signal generated using dipolar field effects, indicating that the range of the field depends upon the inverse of the spatial frequency with which the magnetization is modulated.     

Non-CPMG Fast Spin Echo with full signal

The standard Fast Spin Echo sequence used in MR imaging relies on the CPMG condition. A consequence of this condition is that only one component of the transverse magnetization can be measured. To counter this, some phase modulation schemes (XY, MLEV.) for the pulse train have been proposed, but they are useful only over a very restricted range, close to pi, of the refocusing pulse rotation angle. Some other solutions not relying on phase modulation have also been suggested, but they destroy one half the available signal. Revisiting the phase modulation approach, J. Murdoch ("Second SMR Scientific Meeting," p. 1145, 1994) suggested that a quadratic phase modulation could generate a train of classical echoes. We show here that indeed a quadratic phase modulation has a very suitable property: after an adequate change of frame, the dynamic of the system composed of all the protons situated in one pixel can be seen as stationary. If the parameter of the quadratic phase modulation is well chosen, it is then possible to put the dynamic system in a combination of two suitable states and obtain a signal identical to the signal of a classical spin echo, at least for nutation of the refocusing pulse higher than, approximately, two radians.     

Analytical Planar Mixing Transfer Functions for Two Coupled Spin-1 Nuclei

Analytical coherence transfer functions are presented for spin systems consisting of two spins 1 under planar mixing conditions. Compared to isotropic mixing experiments, larger transfer amplitudes are found and differences in the multiplet patterns are discussed.     

Product Operator Theory for Spin‐5/2 Nuclei: Application to 2D J‐Resolved NMR Spectroscopy

Product operator theory is a simple quantum mechanical method that has often been used to analytically describe multi‐pulse NMR experiments for weakly coupled spin systems. Considering the existence of 2D‐J resolved NMR spectra of aqueous solutions containing S = 5/2 nuclear spins, the product operator formalism has been extended to the weakly coupled IS (I = 1/2, S = 5/2) spin system. The evolution of I_x, I_y, I_xS_z and I_yS_z product operators under spin–spin coupling Hamiltonian are given here. The analytical results obtained are applied to the well‐known gated decoupler pulse sequence for heteronuclear 2D‐J resolved NMR spectroscopy.     

Convection compensated electrophoretic NMR

A novel method of convection compensated ENMR (CC-ENMR) has been developed to detect electrophoretic motion of ionic species in the presence of bulk solution convection. This was accomplished using a gradient moment nulling technique to remove spectral artifacts from heat-induced convection and using the polarity switch of the applied electric field to retain spin phase modulations due to electrophoretic flow. Experiments were carried out with a mixture of 100 mM L-aspartic acid and 100 mM 4,9-dioxa-1,12-dodecanediamine to demonstrate this new method of ENMR. CC-ENMR enhances our previously developed capillary array ENMR (CA-ENMR) in solving the convection problem. The combined CA- and CC-ENMR approach strengthens the potential of multidimensional ENMR in simultaneous structural determination of coexisting proteins and protein conformations in biological buffer solutions of high ionic strength. Structural mapping of interacting proteins during biochemical reactions becomes possible in the future using ENMR techniques, which may have a profound impact on the understanding of biological events, including protein folding, genetic control, and signal transduction in general.     

Improved Broadband Inversion Performance for NMR in Liquids

New NMR broadband inversion pulses that compensate both for resonance offset and radiofrequency (RF) inhomogeneity are described. The approach described is a straightforward computer optimization of an initial digitized waveform generated from either a constant-amplitude frequency sweep or from an existing composite inversion pulse. Problems with convergence to local minima are alleviated by the way the optimization is carried out. For a given duration and maximum allowable RF field strength B₁ (but not necessarily given RMS power deposition), the resultant broadband inversion pulse (BIP) shows superior inversion compared to inversion pulses obtained from previous methods, including adiabatic inversion pulses. Any existing BIP can be systematically elaborated to build up longer inversion pulses that perform over larger and larger bandwidths. The resulting pulse need not be adiabatic throughout its duration or across the entire operational bandwidth.     

Sequential HNCACB and CBCANH protein NMR pulse sequences

The pulse sequences HNCACB and CBCANH correlating side chain C(beta) resonances with amide resonances in the protein backbone do not distinguish between inter- and intraresidue correlations. The new pulse sequences sequential HNCACB and sequential CBCANH make this distinction by suppressing coherence transfer between 13C(alpha) and 15N via the one-bond J(NC(alpha)) coupling so that only the sequential correlations are observed in the spectrum. The experimental results of applying sequential HNCACB in a clean-TROSY-adapted implementation to the protein Chymotrypsin Inhibitor 2 at 800 MHz are presented.