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.     

Reference deconvolution. Elimination of distortions arising from reference line truncation

Reference deconvolution (G. A. Morris; J. Magn. Reson. 80, 547 (1988)) or reference lineshape adjustment (J. M. Wouters and G. A. Petersson, J. Magn. Reson. 28,81 (1977); J. M. Wouters, G. A. Petersson, W. C. Agosta, F. H. Field, W. A. Gibbons, H. Wyssbrod, and D. Cowburn, J. Magn. Reson. 28, 93 (1977)) relies on extracting the signal of a known reference material from an experimental spectrum and using a comparison between the experimental reference signal and that predicted by theory to correct instrumental contributions to the full experimental spectrum. Truncation of the reference line can produce unwanted artifacts and distortions in the final spectrum. The source of these anomalies usually lies in the dispersion-mode rather than in the absorption-mode data, as discontinuities are formed when the dispersion “wings” are truncated. These discontinuities can be reduced by a numerical extrapolation covering the lost region; this is sufficient to provide adequate results in most cases, but fails where spectra have baseline errors. A method of recreating the full dispersion signal directly from the corresponding adsorption data, based on the Hilbert transform relationship between the real and imaginary parts of a Fourier transform, is demonstrated here. This method results in the removal of truncation distortions from the deconvoluted spectrum, thus extending the range of application of the reference deconvolution technique.     

Iterative analysis of strong coupling effects in semiselective J spectroscopy

A computer program for the iterative analysis of semiselective J spectra (A. Bax, J. Magn. Reson.52, 330 (1983)) is described, and experimental and calculated f₁ cross sections through semiselective 2D J spectra for the three-spin system of fumaric acid monoethyl ester and the five-spin system of thiophene are compared.     

Spectral simulations incorporating gradient coherence selection.

Computer-aided methods can considerably simplify the use of the product operator formalism for theoretical analysis of NMR phenomena, which otherwise becomes unwieldy for anything but simple spin systems and pulse sequences. In this report, two previously available programming approaches using symbolic algebra (J. Shriver, Concepts Magn. Reson. 4, 1-33, 1992) and numerical simulation using object-oriented programming (S. A. Smith, T. O. Levante, B. H. Meier, and R. R. Ernst, J. Magn. Reson. A 106, 75-105, 1994) have been extended to include the use of gradient operators for simulation of spatially localized NMR spectroscopy and gradient coherence selection. These methods are demonstrated using an analysis of the response of an AX(3) spin system to the STEAM pulse sequence and verified with experimental measurements on lactate.     

The multidimensional filter diagonalization method

The theory and numerical aspects of the recently developed multidimensional version of the filter diagonalization method (FDM) are described in detail. FDM can construct various "ersatz" or "hybrid" spectra from multidimensional time signals. Spectral resolution is not limited by the time-frequency uncertainty principle in each separate frequency dimension, but rather by the total joint information content of the signal, i.e., N(total) = N(1) x N(2) x vertical ellipsis x N(D), where some of the interferometric dimensions do not have to be represented by more than a few (e.g., two) time increments. It is shown that FDM can be used to compute various reduced-dimensionality projections of a high-dimensional spectrum directly, i.e., avoiding construction of the latter. A subsequent paper (J. Magn. Reson. 144, 357-366 (2000)) is concerned with applications of the method to 2D, 3D, and 4D NMR experiments.     

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.     

A Three-Component Model for Magnetization Transfer. Solution by Projection-Operator Technique,and Application to Cartilage

A projection-operator technique is applied to a general three-component model for magnetization transfer, extending our previous two-component model [R. S. Adler and H. N. Yeung,J. Magn. Reson. A104,321 (1993), and H. N. Yeung, R. S. Adler, and S. D. Swanson,J. Magn. Reson. A106,37 (1994)]. The PO technique provides an elegant means of deriving a simple, effective rate equation in which there is natural separation of relaxation and source terms and allows incorporation of Redfield–Provotorov theory without any additional assumptions or restrictive conditions. The PO technique is extended to incorporate more general, multicomponent models. The three-component model is used to fit experimental data from samples of human hyaline cartilage and fibrocartilage. The fits of the three-component model are compared to the fits of the two-component model.     

A J-multiplied HMQC (MJ-HMQC) experiment for measuring (3)J(HNHalpha) coupling constants

The J-multiplied HSQC experiment (MJ-HSQC: S. Heikkinen et al., J. Magn. Reson 137, 243 (1999)) amplifies J coupling constants m times and allows direct observation of the (3)J(HNHalpha) coupling constants of peptides and proteins (<10 kDa). The drawbacks to this method are line broadening in the f(1)-dimension and lower sensitivity. In the J-multiplied HMQC (MJ-HMQC) experiment described here, the PEP-HSQC pulse sequence is replaced by a sensitivity-enhanced HMQC section, and the total decay time for the J-coupling and the chemical shift evolution is shortened by a period of t(1). This experiment affords narrower linewidth and enhances the sensitivity by 34%, on an average of 105 well-isolated peaks, when compared with the MJ-HSQC experiment.     

Improved measurement of (3)J(H(alpha)(i),N(i+1)) coupling constants in H(2)O dissolved proteins.

A modification to the recently proposed alpha/beta-HN(CO)CA-J TROSY pulse sequence (P. Permi et al., J. Magn. Reson. 146, 255-259 (2000)) makes it possible to determine (3)J(H(alpha)(i), N(i+1)) coupling constants from a single E.COSY-type cross-peak pattern rather than from two (1)H(alpha) spin-state-edited subspectra. Advantages are increased (15)N resolution, critical to extracting accurate (1)H(alpha)-(15)N coupling constants, and minimized differential relaxation due to nested (13)C(alpha) and (15)N evolution periods. Application of the improved pulse sequence to Desulfovibrio vulgaris flavodoxin results in (3)J(H(alpha)(i), N(i+1)) values being systematically larger than those obtained with the original scheme. Parametrization of the coupling dependence on the protein backbone torsion angle psi yields the Karplus relation (3)J(H(alpha)(i), N(i+1))=-1.00 cos(2)(psi-120 degrees )+0.65 cos(psi-120 degrees )-0.15 Hz, with a residual root-mean-square difference of 0.13 Hz between measured and back-calculated coupling constants. The curve compares with data derived from ubiquitin (A. C. Wang and A. Bax, J. Am. Chem. Soc. 117, 1810-1813 (1995)), although spanning a slightly larger range of J values in flavodoxin. The orientation of the Ala39/Ser40 peptide link, forming a type-II beta-turn in flavodoxin, is twisted against X-ray-derived torsions by approximately 10 degrees in the NMR structure as evident from the analysis of straight phi- and psi-related (3)J coupling constants. The remaining deviation of some experimental values from the prediction is likely to be due to strong hydrogen bonding, substituent effects, or the additional dependence on the adjacent torsions straight phi.     

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.     

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.     

Removal of zero-quantum peaks from 1D selective TOCSY and NOESY spectra

Selective 1D TOCSY and NOESY experiments are widely used for structure determination. However, they often give distorted peak shapes owing to coherence transfer though zero-quantum coherence (ZQ) which cannot be suppressed by conventional phase cycling or pulse-field gradients. This paper demonstrates that ZQ contributions can be removed from selective 1D spectra by introducing a ZQ evolution time, as previously demonstrated for 2D NOESY spectra by Wang et al. [A three-dimensional method for the separation of zero-quantum coherence and NOE in NOESY spectra, J. Magn. Reson. A 102 (1993) 116-121]. This approach is simple to implement and robust, and is not demanding of spectrometer hardware. Using a new approach to phase cycling described here, spectra can be acquired in a similar time to spectra without a ZQ evolution time.     

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.     

Magnetic resonance imaging of rigid polymers at elevated temperatures with SPRITE

Magnetic resonance imaging has rarely been applied to rigid polymeric materials, due primarily to the strong dipolar coupling and short signal lifetimes inherent in these materials. SPRITE (single point ramped imaging withT ₁ enhancement) (B. J. Balcom, R. P. MacGregor, S. D. Beyea, D. P. Green, R. L. Armstrong, T. W. Bremner: J. Magn. Reson. A123, 131–134, 1996) is particularly well suited to imaging solid materials. With SPRITE, the only requirement is thatT ₂^* be long enough so that the signal can be phase-encoded. The minimum phase encoding time is limited by the maximum gradient strength available and by the instrument deadtime. At present this is usually tens of microseconds and will only improve with refinements in technology. We have used the SPRITE sequence in conjunction with raising the sample temperature to obtain images of rigid polymers that have largely frustrated conventional imaging methods. This approach provides a straightforward and reliable method for imaging a class of samples that, up until now, have been very difficult to image.     

The filtering approach to solvent peak suppression in MRS: a critical review

Suppressing the solvent peak is important in many applications of biomedical NMR spectroscopy in order to quantify the metabolites with a great accuracy. Among the postprocessing methods proposed in the literature, many deal with the concept of filtering. However, several proposals lack a theoretical perspective and some have not been explicitly applied to quantification problems. The present article is intended to bridge this gap: five methods are analyzed from a theoretical perspective. Subsequently the different methods are applied to the same set of data, and then the latter are quantified using the model fitting method AMARES. With our set, the scheme proposed by T. Sundin et al. (J. Magn. Reson. 139(2), 189-204 (1999)) proved to be the most reliable method.     

The Multidimensional Filter Diagonalization Method: II. Application to 2D Projections of 2D, 3D, and 4D NMR Experiments

The theory of the multidimensional filter diagonalization method (FDM) described in the previous paper (V. A. Mandelshtam, 2000, J. Magn. Reson. 144, 343–356 (2000)) is applied to NMR time signals with up to four independent time variables. Direct projections of the multidimensional time signals produce new kinds of 2D spectra. The resolution obtained by FDM can be far superior to that obtained by conventional phase-sensitive FT processing, and correlation peaks in heteronuclear and homonuclear experiments can be condensed to sharp singlets, removing all spin–spin couplings. Examples of singlet-HSQC and singlet-TOCSY spectra show big gains in resolution. It is not necessary to have a finely digitized spectrum, in which the individual multiplet components are resolved, for the methods to work. Examples of FDM spectra, ranging from simple organic molecules and steroids to metalloproteins, are shown.     

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.     

On neglecting chemical exchange when correcting in vivo (31)P MRS data for partial saturation: commentary on: "Pitfalls in the measurement of metabolite concentrations using the one-pulse experiment in in Vivo NMR"

This article replies to Spencer et al. (J. Magn. Reson. 149, 251--257, 2001) concerning the degree to which chemical exchange affects partial saturation corrections using saturation factors. Considering the important case of in vivo (31)P NMR, we employ differential analysis to demonstrate a broad range of experimental conditions over which chemical exchange minimally affects saturation factors, and near-optimum signal-to-noise ratio is preserved. The analysis contradicts Spencer et al.'s broad claim that chemical exchange results in a strong dependence of saturation factors upon M(0)'s and T(1) and exchange parameters. For Spencer et al.'s example of a dynamic (31)P NMR experiment in which phosphocreatine varies 20-fold, we show that our strategy of measuring saturation factors at the start and end of the study reduces errors in saturation corrections to 2% for the high-energy phosphates.