MAG-PGSTE: a new STE-based PGSE NMR sequence for the determination of diffusion in magnetically inhomogeneous samples

A new stimulated echo based pulsed gradient spin-echo sequence, MAG-PGSTE, has been developed for the determination of self-diffusion in magnetically inhomogeneous samples. The sequence was tested on two glass bead samples (i.e., 212-300 and <106 microm glass bead packs). The MAG-PGSTE sequence was compared to the MAGSTE (or MPFG) (P.Z. Sun, J.G. Seland, D. Cory, Background gradient suppression in pulsed gradient stimulated echo measurements, J. Magn. Reson. 161 (2003) 168-173; P.Z. Sun, S.A. Smith, J. Zhou, Analysis of the magic asymmetric gradient stimulated echo sequence with shaped gradients, J. Magn. Reson. 171 (2004) 324-329; P.Z. Sun, Improved diffusion measurement in heterogeneous systems using the magic asymmetric gradient stimulated echo (MAGSTE) technique, J. Magn. Reson. 187 (2007) 177-183; P. Galvosas, F. Stallmach, J. K?rger, Background gradient suppression in stimulated echo NMR diffusion studies using magic pulsed field gradient ratios, J. Magn. Reson. 166 (2004) 164-173, P. Galvosas, PFG NMR-Diffusionsuntersuchungen mit ultra-hohen gepulsten magnetischen Feldgradienten an mikropor?sen Materialien, Ph.D. Thesis, Universit?t Leipzig, 2003, P.Z. Sun, Nuclear Magnetic Resonance Microscopy and Diffusion, Ph.D. Thesis, Massachusetts Institute of Technology, 2003] sequence and Cotts 13-interval [R.M. Cotts, M.J.R. Hoch, T. Sun, J.T. Marker, Pulsed field gradient stimulated echo methods for improved NMR diffusion measurements in heterogeneous systems, J. Magn. Reson. 83 (1989) 252-266] sequence using both glass bead samples. The MAG-PGSTE and MAGSTE (or MPFG) sequences outperformed the Cotts 13-interval sequence in the measurement of diffusion coefficients; more interestingly, for the sample with higher background gradients (i.e., the <106 microm glass bead sample), the MAG-PGSTE sequence provided higher signal-to-noise ratios and thus better diffusion measurements than the MAGSTE and Cotts 13-interval sequences. In addition, the MAG-PGSTE sequence provided good characterization of the surface-to-volume ratio for the glass bead samples.     

SOGGY: solvent-optimized double gradient spectroscopy for water suppression. A comparison with some existing techniques

Excitation sculpting, a general method to suppress unwanted magnetization while controlling the phase of the retained signal [T.L. Hwang, A.J. Shaka, Water suppression that works. Excitation sculpting using arbitrary waveforms and pulsed field gradients, J. Magn. Reson. Ser. A 112 (1995) 275-279] is a highly effective method of water suppression for both biological and small molecule NMR spectroscopy. In excitation sculpting, a double pulsed field gradient spin echo forms the core of the sequence and pairing a low-power soft 180 degrees (-x) pulse with a high-power 180 degrees (x) all resonances except the water are flipped and retained, while the water peak is attenuated. By replacing the hard 180 degrees pulse in the double echo with a new phase-alternating composite pulse, broadband and adjustable excitation of large bandwidths with simultaneous high water suppression is obtained. This "Solvent-Optimized Gradient-Gradient Spectroscopy" (SOGGY) sequence is a reliable workhorse method for a wide range of practical situations in NMR spectroscopy, optimizing both solute sensitivity and water suppression.     

Recoupling of chemical-shift anisotropy powder patterns in MAS NMR

A comparison of three different implementations of the chemical-shift recoupling experiment of Tycko et al. [R. Tycko, G. Dabbagh, P.A. Mirau, Determination of chemical-shift-anisotropy lineshapes in a two-dimensional magic-angle-spinning NMR experiment, J. Magn. Reson. 85 (1989) 265-274] is presented. The methods seek to reduce the effects of artefacts resulting from pulse imperfections and residual C-H dipolar coupling in organic solids. An optimised and constant time implementation are shown to give well-defined and artefact free powder pattern lineshapes in the indirectly observed dimension for both sp2 and sp3 carbon sites. Experimental setup is no more demanding than for the original experiment, and can be implemented using standard commercial hardware.     

Measurement of the principal values of the anisotropic diffusion tensor in an unoriented sample by exploiting the chemical shift anisotropy: (19)F PGSE NMR with homonuclear decoupling

NMR methods (S. V. Dvinskikh et al., J. Magn. Reson. 142, 102-110 (2000) and S. V. Dvinskikh and I. Furó, J. Magn. Reson. 144, 142-149 (2000)) that combine PGSE with dipolar decoupling are extended to polycrystalline solids and unoriented liquid crystals. Decoupling suppresses dipolar dephasing not only during the gradient pulses but also under signal acquisition so that the detected spectral shape is dominated by the chemical shift tensor of the selected nucleus. The decay of the spectral intensity at different positions in the powder spectrum provides the diffusion coefficient in sample regions with their crystal axes oriented differently with respect to the direction of the field gradient. Hence, one can obtain the principal values of the diffusion tensor. The method is demonstrated by (19)F PGSE NMR with homonuclear decoupling in a lyotropic lamellar liquid crystal.     

Assessing signal enhancement in distant dipolar field-based sequences

The possibility of improving the signal-to-noise efficiency of NMR signal refocused by long-range dipolar interactions has been discussed recently [R.T. Branca, G. Galiana, W.S. Warren, Signal enhancement in CRAZED experiments, J. Magn. Reson. 187 (2007) 38-43]. For systems where T(1)>T(2), by including an extra radio-frequency pulse in a standard CRAZED sequence, it is possible to increase the available signal by exploiting its sensitivity to T(1) relaxation. Here, we use analytical calculations to investigate the source of this improved signal and determine the maximum enhancement provided by the method.     

Spin Echo Analysis of Restricted Diffusion under Generalized Gradient Waveforms: Planar, Cylindrical, and Spherical Pores with Wall Relaxivity

A simple matrix formalism presented by Callaghan [J. Magn. Reson.129, 74–84 (1997)], and based on the multiple propagator approach of Caprihanet al.[J. Magn. Reson. A118, 94–102 (1996)], allows for the calculation of the echo attenuation,E(q), in spin echo diffusion experiments, for practically all gradient waveforms. We have extended the method to the treatment of restricted diffusion in parallel plate, cylindrical, and spherical geometries, including the effects of fluid–surface interactions. In particular, theq-space coherence curves are presented for the finite-width gradient pulse PGSE experiment and the results of the matrix calculations compare precisely with published computer simulations. It is shown that the use of long gradient pulses (δ a²/D) create the illusion of smaller pores if a narrow pulse approximation is assumed, while ignoring the presence of significant wall relaxation can lead to both an underestimation of the pore dimensions and a misidentification of the pore geometry.     

Double-quantum-filtered rotational-resonance MAS NMR in the presence of large chemical shielding anisotropies

Double-quantum filtration under rotational resonance MAS NMR conditions where the chemical shielding anisotropies involved exceed the differences in isotropic chemical shielding is considered by means of numerical simulations and (13)C MAS NMR experiments. The responses of two different pulse sequences, suitable for double-quantum filtration specifically under rotational resonance conditions, to large chemical shielding anisotropies are compared. In the presence of large chemical shielding anisotropies a very recently introduced pulse sequence (T. Karlsson, M. Edén, H. Luthman, and M. H. Levitt, J. Magn. Reson. 145, 95-107, 2000) suffers losses in double-quantum-filtration efficiencies. The double-quantum-filtration efficiency of another pulse sequence (N. C. Nielsen, F. Creuzet, R. G. Griffin, and M. H. Levitt, J. Chem. Phys. 96, 5668-5677, 1992) is less afflicted by the presence of large chemical shielding anisotropies. Both sequences deliver double-quantum-filtered lineshapes that sensitively reflect chemical shielding tensor orientations. It is further shown that double-quantum-filtered rotational-resonance lineshapes of spin systems composed of more than two spins offer a suitable experimental approach for determining chemical shielding tensor orientations for cases where conventional rotational-resonance experiments are not applicable due to the presence of additional background resonances.     

Specification and visualization of anisotropic interaction tensors in polypeptides and numerical simulations in biological solid-state NMR

Software facilitating numerical simulation of solid-state NMR experiments on polypeptides is presented. The Tcl-controlled SIMMOL program reads in atomic coordinates in the PDB format from which it generates typical or user-defined parameters for the chemical shift, J coupling, quadrupolar coupling, and dipolar coupling tensors. The output is a spin system file for numerical simulations, e.g., using SIMPSON (Bak, Rasmussen, and Nielsen, J. Magn. Reson. 147, 296 (2000)), as well as a 3D visualization of the molecular structure, or selected parts of this, with user-controlled representation of relevant tensors, bonds, atoms, peptide planes, and coordinate systems. The combination of SIMPSON and SIMMOL allows straightforward simulation of the response of advanced solid-state NMR experiments on typical nuclear spin interactions present in polypeptides. Thus, SIMMOL may be considered a "sample changer" to the SIMPSON "computer spectrometer" and proves to be very useful for the design and optimization of pulse sequences for application on uniformly or extensively isotope-labeled peptides where multiple-spin interactions need to be considered. These aspects are demonstrated by optimization and simulation of novel DCP and C7 based 2D N(CO)CA, N(CA)CB, and N(CA)CX MAS correlation experiments for multiple-spin clusters in ubiquitin and by simulation of PISA wheels from PISEMA spectra of uniaxially oriented bacteriorhodopsin and rhodopsin under conditions of finite RF pulses and multiple spin interactions.     

Improved convection compensating pulsed field gradient spin-echo and stimulated-echo methods

The need for convection compensating methods in NMR has been manifested through an increasing number of publications related to the subject over the past few years (J. Magn. Reson. 125, 372 (1997); 132, 13 (1998); 131, 126 (1998); 118, 50 (1996); 133, 379 (1998)). When performing measurements at elevated temperature, small convection currents may give rise to erroneous values of the diffusion coefficient. In work with high resolution NMR spectroscopy, the application of magnetic field gradients also introduces an eddy-current magnetic field which may result in errors in phase and baseline in the FFT-spectra. The eddy current field has been greatly suppressed by the application of bipolar magnetic field gradients. However, when introducing bipolar magnetic field gradients, the pulse sequence is lengthened significantly. This has recently been pointed out as a major drawback because of the loss of coherence and of NMR-signal due to transverse relaxation processes. Here we present modified convection compensating pulsed field gradient double spin echo and double stimulated echo sequences which suppress the eddy-current magnetic field without increasing the duration of the pulse sequences.     

Polynomially scaling spin dynamics II: further state-space compression using Krylov subspace techniques and zero track elimination

We extend the recently proposed state-space restriction (SSR) technique for quantum spin dynamics simulations [Kuprov et al., J. Magn. Reson. 189 (2007) 241-250] to include on-the-fly detection and elimination of unpopulated dimensions from the system density matrix. Further improvements in spin dynamics simulation speed, frequently by several orders of magnitude, are demonstrated. The proposed zero track elimination (ZTE) procedure is computationally inexpensive, reversible, numerically stable and easy to add to any existing simulation code. We demonstrate that it belongs to the same family of Krylov subspace techniques as the well-known Lanczos basis pruning procedure. The combined SSR+ZTE algorithm is recommended for simulations of NMR, EPR and Spin Chemistry experiments on systems containing between 10 and 10(4) coupled spins.     

Efficient 5QMAS NMR of spin-5/2 nuclei: use of fast amplitude-modulated radio-frequency pulses and cogwheel phase cycling

We report here an efficient multiple-quantum magic-angle spinning (MQMAS) pulse sequence involving fast amplitude-modulated (FAM) radio-frequency pulses for excitation and conversion of five-quantum (5Q) coherences of spin-5/2 nuclei. The use of a FAM-I type pulse train for the conversion of 5Q into 1Q coherences proves to be easier to implement experimentally than the earlier suggested use of a FAM-II type sequence [J. Magn. Reson. 154 (2002) 280], while delivering at least equal signal enhancement. Results of numerical simulations and experimental 27Al 5QMAS spectra of aluminium acetylacetonate for different excitation and conversion schemes are compared to substantiate these claims. We also demonstrate the feasibility of acquiring 5QMAS spectra of spin-5/2 systems using cogwheel phase cycling [J. Magn. Reson. 155 (2002) 300] to select the desired coherence pathways. A cogwheel phase cycle of only 57 steps is shown to be as effective as the minimum conventional nested 77-step phase cycle.     

Background gradient suppression in stimulated echo NMR diffusion studies using magic pulsed field gradient ratios

By evaluating the spin echo attenuation for a generalized 13-interval PFG NMR sequence consisting of pulsed field gradients with four different effective intensities (F(p/r) and G(p/r)), magic pulsed field gradient (MPFG) ratios for the prepare (G(p)/F(p)) and the read (G(r)/F(r)) interval are derived, which suppress the cross term between background field gradients and the pulsed field gradients even in the cases where the background field gradients may change during the z-store interval of the pulse sequence. These MPFG ratios depend only on the timing of the pulsed gradients in the pulse sequence and allow a convenient experimental approach to background gradient suppression in NMR diffusion studies with heterogeneous systems, where the local properties of the (internal) background gradients are often unknown. If the pulsed field gradients are centered in the tau-intervals between the pi and pi/2 rf pulses, these two MPFG ratios coincide to eta=G(p/r)/F(p/r)=1-8/[1+(1/3)(delta/tau)(2)]. Since the width of the pulsed field gradients (delta) is bounded by 0< or =delta< or =tau, eta can only be in the range of 5< or =-eta< or =7. The predicted suppression of the unwanted cross terms is demonstrated experimentally using time-dependent external gradients which are controlled in the NMR experiment as well as spatially dependent internal background gradients generated by the magnetic properties of the sample itself. The theoretical and experimental results confirm and extend the approach of Sun et al. (J. Magn. Reson. 161 (2003) 168), who recently introduced a 13-interval type PFG NMR sequence with two asymmetric pulsed magnetic field gradients suitable to suppress unwanted cross terms with spatially dependent background field gradients.     

Nuclear longitudinal relaxation time images by radiofrequency field gradients.

Combination of the Super Fast Inversion Recovery (SUFIR) method (D. Canet, J. Brondeau, and K. Elbayed, J. Magn. Reson. 77, 483 (1988)) and imaging procedures by radiofrequency field gradients (P. Maffei, P. Mutzenhardt, A. Retournard, B. Diter, R. Raulet, J. Brondeau, and D. Canet, J. Magn. Reson. A 107, 40 (1994)) provides spatially resolved maps of longitudinal relaxation times (T1). In addition to accurate T1 values, enhanced spatial resolution is obtained.     

Spin dynamics of polarization inversion spin exchange at the magic angle in multiple spin systems

Polarization inversion spin exchange at the magic angle (PISEMA) [J. Magn. Reson. A 109, 270 (1994)] is an important experiment in NMR structural characterization of membrane proteins in oriented lipid bilayers. This paper presents a theoretical and experimental study of the spin dynamics in PISEMA to investigate the line-narrowing mechanism. The study focuses on the effect of neighboring protons on the spin exchange of a strongly coupled spin pair. The spin exchange is solved analytically for simple spin systems and is numerically simulated for many-spin systems. The results show that the dipolar couplings from the neighboring protons of a strongly coupled spin pair perturb the spin exchange only in the second order, therefore it has little contribution to the linewidth of PISEMA spectra in comparison to the separated-local-field spectra. The effects from proton resonance offset and the mismatch of the Hartmann-Hahn condition are also discussed along with experimental results using model single-crystal samples.     

Volume selective detection by weighted averaging of constant tip angle scans

We propose a method to improve the sensitivity in volume selective detection based on the CARVE excitation sequence (I. Sersa and S. Macura, J. Magn. Reson. 135, 466-477 (1998)) which consists of signal acquisition with constant tip angle excitation and a short phase-encoding gradient pulse. Volume selectivity is achieved using the weighted average of a number of scans whose weights and gradient steps are determined by the shape of the excitation profile. The method is particularly useful for broadband volume selective detection of insensitive spins where the volume selection can be merged with the standard signal averaging process, without compromising the excitation bandwidth or sensitivity.     

The use of sample rotation for minimizing convection effects in self-diffusion NMR measurements.

Undesirable temperature gradients in a NMR sample tube are usually generated by an inappropriate temperature regulation system. We have shown that such convection effects can greatly distort the measurement of translational self-diffusion coefficients. The use of sample spinning helps to minimize such undesirable effects by disruption of convection fluxes due to resulting Coriolis forces that have a strongly stabilizing effect on the conducting state of the system (J. Lounila et al., J. Magn. Reson. A 118, 50 (1996)). This simple trick allows the accurate measurement of diffusion coefficients for a wide range of temperatures and solvents without the need for a convection-compensated NMR pulse sequences or more sophisticated temperature control units. Experimental data obtained for some target compounds dissolved in several common deuterated solvents at different temperatures are reported and discussed.     

Optimizing delays in the MBOB,broadband HMBC,and broadband XLOC NMR pulse sequences

The MBOB, broadband HMBC, and broadband XLOC NMR pulse sequences (A. Meissner and O. W. S?rensen (2000, Magn. Reson. Chem. 38, 981-984; 2001, 39, 49-52)) were introduced as a means of obtaining heteronuclear long-range correlation spectra with broadband excitation over an interval of heteronuclear long-range J coupling constants. However, it is not trivial what combination of delays to choose for a given purpose, particularly if one-bond and long-range correlation spectra are obtained simultaneously as in MBOB. This paper presents a way to determine sets of delays for MBOB, broadband HMBC, and broadband XLOC resolving the problem. The results tabulated suit various ranges of J coupling constants and transverse relaxation times.     

Delayed-focus pulses optimized using simulated annealing

Unlike prefocused pulses and shaped pulses based on the linear response theory, delayed-focus pulses (X.-L. Wu et al., 1991, Magn. Reson. Med. 20, 165--170) produce a selective spin echo after a predefined short delay without using a pi refocusing pulse. In this paper, a series of delayed-focus pulses of different flip angles are proposed based on optimization using Fourier series representation and simulated annealing. The resistance of these delayed-focus pulses to T(2) relaxation is also demonstrated using numerical simulation of Bloch equations.     

Accurate intensities of broad NMR lines from composite pulse experiments

Accurate determination of integral intensities of broad lines is difficult when spin relaxation during the applied pulses cannot be neglected and/or when ringing of the tank circuit interferes with the signal. Here we present an extension of the analytical solution of the generalized Bloch equations (G. A. Morris and P. B. Chilvers, J. Magn. Reson. A 107, 236 (1994)), which is then used to evaluate the signal intensity obtained in a composite pulse experiment designed to cancel ringing effects. Comparing intensities of broad and narrow (81)Br spectral lines tests and proves the accuracy of this approach.