NMR diffusometry and the short gradient pulse limit approximation

In NMR diffusometry, one often uses the short gradient pulse (SGP) limit approximation in the interpretation of data from systems with restricted diffusion. The SGP limit approximation means that the gradient pulse length, delta, is so short that the spins do not diffuse during the pulse duration, but this condition is rarely met. If the length scale of the pores corresponds to the molecular mean square displacement during the gradient pulse, the measured echo intensities become a function of the gradient pulse length. Here, we have studied highly concentrated emulsions to show how the length of the gradient pulse influences NMR diffusion experiments. We have focused on molecules confined to one pore and molecules that can migrate through the porous system. For the former the echo decays give smaller pores than the actual case and for the latter we show large changes in echo decay depending on the gradient pulse length, everything else being equal.     

Solvent-localized NMR spectroscopy using the distant dipolar field: a method for NMR separations with a single gradient

Solvent-localized NMR (SOLO) is a new method which allows the separation of NMR spectra of substances dissolved in different solvents. It uses the selective HOMOGENIZED pulse sequence to produce a two-dimensional NMR spectrum resulting from intermolecular zero-quantum coherences in one distinct solvent. The detected signal is locally refocused by the action of the distant dipolar field, which is created by a frequency selective pulse only in regions containing the selected solvent. The prerequisites are that the different solvents have sufficiently different chemical shifts to be excited separately and that compartments with different solvents are spatially separated by more than the typical diffusion distance. Here, the method is demonstrated for the solvents water and DMSO on a length scale of 0.5 mm. Because signal in the spectra is refocused locally, SOLO is insensitive to variations in the magnetic field which may result from inhomogeneities or structures in the sample. This makes applications in strongly structured samples possible. SOLO is the first method that achieves localization of NMR signal with a single gradient pulse. Therefore, it can be used in conventional NMR spectrometers with one-axis gradient systems and lends itself to a wide range of applications including in vivo NMR.     

Refocussing of chemical and paramagnetic shift anisotropies in 2H NMR using the quadrupolar-echo experiment

A simple two-pulse spin-echo experiment is shown to refocus inhomogeneous broadening arising from both chemical and/or paramagnetic shift anisotropy and a first-order I=1 quadrupolar interaction. The method is shown to yield ²H NMR spectra of a paramagnetic solid (CuCl₂ · 2D₂O) and of a non-paramagnetic solid (D₂C₂O₄ · 2D₂O) that are significantly less distorted than those provided by the conventional quadrupolar-echo method. The technique will thus prove useful in studies of motion and dynamics where detailed analysis of the ²H lineshape is performed.     

Measurement of membrane permeability to slowly penetrating molecules by a pulse gradient NMR method

A nuclear magnetic resonance study of differentiation between molecules in the extra- and intracellular media is presented. The method is based on the fact that the cell membrane restricts the diffusion of a molecule inside the cell allowing observation of this restricted diffusion by a pulse gradient NMR technique. Membrane permeability to slowly penetrating molecules may be studied using this gradient technique, without otherwise disturbing the system, as illustrated by the measurement of Li⁺ uptake by human red blood cells.     

A 2D MAS solid-state NMR method to recover the amplified heteronuclear dipolar and chemical shift anisotropic interactions

A two-dimensional solid-state NMR method for the measurement of chemical shift anisotropy tensors of X nuclei (15N or 13C) from multiple sites of a polypeptide powder sample is presented. This method employs rotor-synchronized pi pulses to amplify the magnitude of the inhomogeneous X-CSA and 1H-X dipolar coupling interactions. A combination of on-resonance and magic angle rf irradiation of protons is used to vary the ratio of the magnitudes of the 1H-X dipolar and X-CSA interactions which are recovered under MAS, in addition to suppressing the 1H-1H dipolar interactions. The increased number of spinning sidebands in the recovered anisotropic interactions is useful to determine the CSA tensors accurately. The performance of this method is examined for powder samples of N-acetyl-(15)N-L-valine (NAV), N-acetyl-15N-L-valyl-15N-L-leucine (NAVL), and alpha-13C-L-leucine. The sources of experimental errors in the measurement of CSA tensors and the application of the pulse sequences under high-field fast MAS operations are discussed.     

Spectral characterization of diffusion with chemical shift resolution: Highly concentrated water-in-oil emulsion

We present a modulated gradient spin-echo method, which uses a train of sinusoidally shaped gradient pulses separated by 180° radio-frequency (RF) pulses. The RF pulses efficiently refocus chemical shifts and de-phasing due to susceptibility differences, resulting in undistorted, high-resolution diffusion weighted spectra. This allows for the simultaneous spectral characterization of the diffusion of several molecular species with different chemical shifts. The technique is robust against susceptibility artifacts, field inhomogeneity and imperfections in the gradient generating equipment. The feasibility of the technique is demonstrated by measuring the diffusion of water, oil, and water-soluble salt in a highly concentrated water-in-oil emulsion. The diffusion of water and salt reveal precise information about the droplet size distribution below the μm-range. Common droplet size distribution explains both the data for water with finite long-range diffusion and the data for salt with negligible long-range diffusion. The results of water diffusion show that the technique is efficient in deconvolving the effects of molecular exchange between droplets and restricted diffusion within droplets. The effects of water exchange suggest that droplets of different sizes are uniformly distributed within the sample.     

Criteria to average out the chemical shift anisotropy in solid-state NMR when irradiated with BABA I,BABA II,and C7 radiofrequency pulse sequences

Floquet–Magnus expansion is used to study the effect of chemical shift anisotropy in solid-state NMR of rotating solids. The chemical shift interaction is irradiated with two types of radiofrequency pulse sequences: BABA and C7. The criteria for the chemical shift anisotropy to be averaged out in each rotor period are obtained.     

Determination of pore space shape and size in porous systems using NMR diffusometry. Beyond the short gradient pulse approximation

The influence of finite length gradient pulses on NMR diffusion experiments on liquids confined to diffuse between two parallel planes is investigated. It is experimentally verified that the pore size decreases when determined using finite gradient pulses if the results are analyzed within the short gradient pulse approximation. The results are analyzed using the matrix formulation. The observed minima in the echo decay profiles are considerably less sharp than theoretical analysis would indicate and we suggest that this is due to the presence of a distribution of pore sizes in the sample. In addition, effects due to the presence of background gradients are discussed. It is argued that effects due to the finite length gradient pulses are relatively minor and in realistic applications the effects due to inhomogeneities in pore sizes and effects due to background gradients will constitute more serious problems in pore size determinations by means of NMR diffusometry.     

Enhanced spectral resolution by high-dimensional NMR using the filter diagonalization method and "hidden" dimensions

High-dimensional (HD) NMR spectra have poorer digital resolution than low-dimensional (LD) spectra, for a fixed amount of experiment time. This has led to "reduced-dimensionality" strategies, in which several LD projections of the HD NMR spectrum are acquired, each with higher digital resolution; an approximate HD spectrum is then inferred by some means. We propose a strategy that moves in the opposite direction, by adding more time dimensions to increase the information content of the data set, even if only a very sparse time grid is used in each dimension. The full HD time-domain data can be analyzed by the filter diagonalization method (FDM), yielding very narrow resonances along all of the frequency axes, even those with sparse sampling. Integrating over the added dimensions of HD FDM NMR spectra reconstitutes LD spectra with enhanced resolution, often more quickly than direct acquisition of the LD spectrum with a larger number of grid points in each of the fewer dimensions. If the extra-dimensions do not appear in the final spectrum, and are used solely to boost information content, we propose the moniker hidden-dimension NMR. This work shows that HD peaks have unmistakable frequency signatures that can be detected as single HD objects by an appropriate algorithm, even though their patterns would be tricky for a human operator to visualize or recognize, and even if digital resolution in an HD FT spectrum is very coarse compared with natural line widths.     

Towards rapid and unique curve resolution of low-field NMR relaxation data: trilinear SLICING versus two-dimensional curve fitting

In this work an alternative method, named SLICING, for two-dimensional and noniterative T(2) decomposition of low-field pulsed NMR data (LF-NMR) is proposed and examined. The method is based on the Direct Exponential Curve Resolution Algorithm (DECRA) proposed by W. Windig and A. Antalek (1997, Chemom. Intell. Lab. Syst.37, 241-254) and takes advantage of the fact that exponential decay functions, when translated in time, retain their characteristic relaxation times while only their relative amounts or concentrations change. By such simple translations (slicing) it is possible to create a new "pseudo" direction in the relaxation data and thus facilitate application of trilinear (multiway) data-analytical methods. For the application on LF-NMR relaxation data, the method has two basic requirements in practice: (1) two or more samples must be analyzed simultaneously and (2) all samples must contain the same qualities (i.e., identical sets of distinct T(2) values). In return, if these requirements are fulfilled, the SLICING (trilinear decomposition) method provides very fast and unique curve-resolution of multiexponential LF-NMR relaxation curves and, as a spin-off, calibrations to reference data referring to individual proton components require only scaling of the resulting unique concentrations. In this work the performance of the SLICING method (including multiple slicing schemes) is compared to a traditional two-dimensional curve fitting algorithm named MATRIXFIT through application to simulated data in a large-scale exhaustive experimental design and the results validated by application to two small real data sets. Finally a new algorithm, Principal Phase Correction (PPC) based on principal component analysis, is proposed for phase rotation of CPMG quadrature data, an important prerequisite to optimal SLICING analysis.     

Correlating fast and slow chemical shift spinning sideband patterns in solid-state NMR

An experiment is presented that enables the measurement of small chemical shift anisotropy tensors under fast magic-angle spinning (MAS). The two-dimensional spectra obtained give a fast MAS sideband pattern in the directly observed dimension with the spinning sideband intensities equivalent to the chemical shift anisotropy scaled by a factor of N, or equivalently the sample spinning frequency scaled by 1/N, in the indirectly observed dimension. The scaling factor may be arbitrarily varied by changing the number and timings of the rotor synchronized pi-pulses used. Desirable features of the experiment include a fixed length pulse sequence and efficient sampling of the indirectly observed dimension. In addition, neither quadrature detection in the indirect dimension nor storage periods are required, consequently no signal intensity is discarded by the pulse sequence. The experiment is demonstrated using (31)P NMR of sodium phosphate and (13)C NMR of fumaric acid monoethyl ester for which a scaling factor of N=10.2 was employed.     

A method to distinguish between chemical shift and susceptibility effects in NMR microscopy and its application to insect larvae

We propose a simple method of distinguishing Zeeman broadening arising from susceptibility inhomogeneity and chemical shift variation, applicable to NMR microscopy. The method is based on the use of a specially built probehead in which orthogonal sample alignment is possible using the same radiofrequency (RF) coil. This allows the investigation of alignment effects in image distortion and relies on the fact that the isotropic chemical shift is invariant under reorientation, whereas the susceptibility-related local field will depend strongly on relative orientation of bounding surfaces with the external polarizing field. We apply this approach to the study of a simple phantom, and an insect larva (Spodoptera litura Fabricius), demonstrating in the latter case that susceptibility variations are sufficiently small to allow chemical shift imaging on a scale greater than 1 ppm.     

Detection of homonuclear decoupled in vivo proton NMR spectra using constant time chemical shift encoding: CT-PRESS

A new pulse sequence, termed CT-PRESS, is presented, which allows the detection of in vivo ¹H NMR spectra with effective homonuclear decoupling. A PRESS sequence with a short echo-time TE, used for spatial localization, is supplemented by an additional 180° pulse. The temporal position of this 180° pulse is shifted within a series of experiments, while the time interval between signal excitation and detection is kept constant. CT-PRESS is a two-dimensional (2D) spectroscopic experiment as far as data acquisition and processing are concerned, although only diagonal signals are generated in the 2D spectrum. However, since the principle of constant time chemical shift encoding is used in the t₁ domain, effective homonuclear decoupling is obtained by projecting the 2D spectrum onto the corresponding f₁ axis. Thus, good spectral resolution and high signal-to-noise ratio are obtained. The main advantage, as compared to localized 2D J-resolved MRS, is that optimized experiments can be performed for coupled resonances of interest by choosing the sequence parameters dependent on the type of multiplets, the J-coupling constants and T₂. Major fields of application will be parametric studies on coupled resonances, (e.g., T₁, diffusion behavior or magnetization transfer) and/or the detection of spatial and temporal changes of metabolites with coupled spin systes.     

Comparative analysis of NMR chemical shift predictions for proteins in the solid phase

A comparative analysis of nuclear chemical shift predictions of proteins in the solid state by rapid algorithms trained on and verified with solution-state NMR assignments is presented. The precision of predictions by four dedicated computer programs (SHIFTS, PROSHIFTS, SHIFTX and SPARTA) was found to be close to values obtained for proteins in solution. Correlation coefficients depend on the NMR nucleus (N, C′, C^α and C^β) and on secondary structure (β-strand, random coil and α-helix), but also on the molecular environment (membrane-integral or not). The findings establish a quantitative basis for using chemical shift prediction programs for solid-state NMR applications. On the other hand, prediction inaccuracies identified for certain resonance kind, residue type, and molecular environment point to possible areas of methodological improvement.