Spatial encoding strategies for ultrafast multidimensional nuclear magnetic resonance

Multidimensional spectroscopy plays a central role in contemporary magnetic resonance. A general feature of multidimensional NMR is its inherent multiscan nature, stemming from the methodology's reliance on a series of independent acquisitions to sample the spins' evolutions throughout the indirect time domains. Contrasting this traditional feature, an acquisition scheme has recently been reported that enables the collection of complete of multidimensional NMR data sets within one single scan. Provided that the signals to be observed are sufficiently strong, this new "ultrafast" protocol can thus shorten the acquisition times of multidimensional NMR experiments by several orders of magnitude. This new methodology operates by departing from temporal encoding principles used since the advent of Fourier-transform NMR, replacing them with a spatial encoding of the spin interactions. Spatial encoding operates in turn on the basis of novel radiofrequency irradiation and magnetic field gradient waveform manipulations, designed so as to impart on the sample a coherent spin magnetization pattern that reflects the internal interactions to be measured. Given the central role played by this new kind of spectroscopic-oriented manipulations in ultrafast NMR, we devote this review to surveying different variants that have hitherto been proposed for their implementation. These include both discrete and continuous versions, real- and constant-time implementations, as well as amplitude- and phase-modulated alternatives. The principles underlying these various spatial encoding approaches are treated, their operation is graphically illustrated as well as formally derived within suitable theoretical frameworks, and an in-depth comparison of their line shape characteristics is discussed.     

Single Scan 2D NMR Spectroscopy on a 25 T Bitter Magnet

2D NMR relies on monitoring systematic changes in the phases incurred by spin coherences as a function of an encoding time t(1), whose value changes over the course of independent experiments. The intrinsic multiscan nature of such protocols implies that resistive and/or hybrid magnets, capable of delivering the highest magnetic field strengths but possessing poor temporal stabilities, become unsuitable for 2D NMR acquisitions. It is here shown with a series of homo- and hetero-nuclear examples that such limitations can be bypassed using recently proposed 2D "ultrafast" acquisition schemes, which correlate interactions along all spectral dimensions within a single scan.     

Ultrafast solid-state 2D NMR experiments via orientational encoding

Among the methods proposed in recent years toward the acceleration of multidimensional NMR acquisitions is an "ultrafast" approach, capable of delivering arbitrary 2D correlations within a single scan. This scheme operates by parallelizing the indirect-domain temporal incrementation involved in 2D acquisitions, using as aid an ancillary inhomogeneous frequency broadening acting in combination with a train of frequency-shifted RF pulses. So far, all implementations of this frequency broadening have relied on magnetic field gradients; yet the practical performance of gradient-based approaches is sometimes inadequate-for instance when applied on solid samples subject to magic-angle spinning. In order to deal with these cases, an alternative encoding protocol is here introduced and experimentally exemplified, based on exploiting the intrinsic anisotropy that spin interactions exhibit in the solid state as the ancillary broadening in charge of encoding the interactions to be measured. Principles and preliminary examples of the new orientationally encoded ultrafast 2D NMR principle thus resulting are presented and discussed.     

New developments in the spatial encoding of spin interactions for single‐scan 2D NMR

Single‐scan 2D NMR relies on a spatial axis for encoding the indirect‐domain internal spin interactions. Various strategies have been demonstrated for fulfilling the needs underlying this procedure. All such schemes use gradient‐echoed sequences that leave at their conclusion solely the effects of the internal interactions along the indirect domain; they also include a real‐time scheme that though simple, yields in general mixed‐phase line shapes. The present paper introduces two new proposals geared up for easing the spatial encoding underlying single‐scan 2D NMR methodologies. One of these is capable of delivering dispersive‐free peaks along the indirect domain, and thereby purely‐absorptive 2D line shapes, in amplitude‐encoded experiments. The other demonstrates for the first time, the possibility to obtain single‐scan 2D spectra without echoing the effects of the encoding gradient–simply by applying a single‐pulse frequency sweep to encode the interactions. Both of these modes are compatible with homo‐ and heteronuclear correlations, and exhibit a number of complementary features vis‐à‐vis encoding alternatives that have so far been presented. The overall principles underlying these new spatially encoding protocols are derived, and their performance demonstrated with single‐scan 2D NMR TOCSY and HSQC experiments on model compounds. Copyright © 2009 John Wiley & Sons, Ltd.     

Nuclear magnetic resonance studies of solvent flow through chromatographic columns: effect of packing density on flow patterns

NMR (nuclear magnetic resonance) techniques have been used to measure and characterise solvent flow through chromatographic columns. NMR imaging was used to track an injection of D2O. PGSE (pulsed gradient spin echo) NMR was used to measure the flow-rate dependence of axial and transverse apparent diffusion. A combination of these two techniques (dynamic NMR imaging) gave the spatial distribution of the local velocity and apparent diffusion through a cross-section of the column. Significant column wall effects were observed and these effects were found to be highly dependent upon the column packing density. The column performance was assessed in terms of the HETP (height equivalent to a theoretical plate) determined by the NMR techniques employed.     

Ultrafast-based projection-reconstruction three-dimensional nuclear magnetic resonance spectroscopy

Recent years have witnessed increased efforts toward the accelerated acquisition of multidimensional nuclear magnetic resonance (nD NMR) spectra. Among the methods proposed to speed up these NMR experiments is "projection reconstruction," a scheme based on the acquisition of a reduced number of two-dimensional (2D) NMR data sets constituting cross sections of the nD time domain being sought. Another proposition involves "ultrafast" spectroscopy, capable of completing nD NMR acquisitions within a single scan. Potential limitations of these approaches include the need for a relatively slow 2D-type serial data collection procedure in the former case, and a need for at least n high-performance, linearly independent gradients and a sufficiently high sensitivity in the latter. The present study introduces a new scheme that comes to address these limitations, by combining the basic features of the projection reconstruction and the ultrafast approaches into a single, unified nD NMR experiment. In the resulting method each member within the series of 2D cross sections required by projection reconstruction to deliver the nD NMR spectrum being sought, is acquired within a single scan with the aid of the 2D ultrafast protocol. Full nD NMR spectra can thus become available by backprojecting a small number of 2D sets, collected using a minimum number of scans. Principles, opportunities, and limitations of the resulting approach, together with demonstrations of its practical advantages, are here discussed and illustrated with a series of three-dimensional homo- and heteronuclear NMR correlation experiments.     

"Multi-scan single shot" quantitative 2D NMR: a valuable alternative to fast conventional quantitative 2D NMR

Quantitative Ultrafast (UF) 2D NMR is a very promising methodology enabling the acquisition of 2D spectra in a single scan. The analytical performances of UF 2D NMR have been highly increased in the last few years, however little is known about the sensitivity of ultrafast experiments versus conventional 2D NMR. A fair and relevant comparison has to consider the Signal-to-Noise Ratio (SNR) per unit of time, in order to answer the following question: for a given experiment time, should we run a conventional 2D experiment or is it preferable to accumulate ultrafast acquisitions? To answer this question, we perform here a systematic comparison between accumulated ultrafast experiments and conventional ones, for different experiment durations. Sensitivity issues and other analytical aspects are discussed for the COSY experiment in the context of quantitative analysis. The comparison is first carried out on a model sample, and then extended to model metabolic mixtures. The results highlight the high analytical performance of the "multi-scan single shot" approach versus conventional 2D NMR acquisitions. This result is attributed to the absence of t(1) noise in spatially encoded experiments. The multi-scan single shot approach is particularly interesting for quantitative applications of 2D NMR, whose occurrence in the literature has been greatly increasing in the last few years.     

Ultrafast Multidimensional Laplace NMR Using a Single‐Sided Magnet

Laplace NMR (LNMR) consists of relaxation and diffusion measurements providing detailed information about molecular motion and interaction. Here we demonstrate that ultrafast single‐ and multidimensional LNMR experiments, based on spatial encoding, are viable with low‐field, single‐sided magnets with an inhomogeneous magnetic field. This approach shortens the experiment time by one to two orders of magnitude relative to traditional experiments, and increases the sensitivity per unit time by a factor of three. The reduction of time required to collect multidimensional data opens significant prospects for mobile chemical analysis using NMR. Particularly tantalizing is future use of hyperpolarization to increase sensitivity by orders of magnitude, allowed by single‐scan approach.     

Characterization of (1)H-(1)H distances in a uniformly (2)H,(15)N-labeled SH3 domain by MAS solid-state NMR spectroscopy (section sign)

In this communication, we demonstrate the feasibility of obtaining long-range (1)H-(1)H distance information by MAS solid-state NMR for a microcrystalline, uniformly (2)H,(15)N-labeled sample of a SH3 domain of chicken alpha-spectrin. The experiments yield NOESY-type spectra and rely on the favorable dispersion of the (15)N chemical shifts of the protein backbone. Perdeuteration of nonexchangeable sites is employed to simplify proton spin systems and to obtain multiple structural information. Two mixing schemes, (1)H-(1)H double quantum filtered Post-C7 and (1)H spin diffusion, are implemented to obtain quantitative (1)H-(1)H distance information. Post-C7 and spin diffusion cross-peak buildup rates are discussed for initial-rate fitting and in the framework of n = 0 rotational resonance (rotor driven spin diffusion), respectively. Different deuteration schemes were tested to find conditions where short-range (1)H-(1)H interactions are truncated (e.g., between H(N) and H(alpha)), but long-range interactions are retained (e.g., between H(N) and H(N)).     

Nuclear spin relaxation driven by intermolecular dipolar interactions: the role of solute-solvent pair correlations in the modeling of spectral density functions

Nuclear spin relaxation provides useful information related to the dynamics of molecular systems. When relaxation is driven by intermolecular dipolar interactions, the relevant spectral density functions (SDFs) also have significant contributions, in principle, from distant spins all over the dynamic range typically probed by NMR experiments such as NOESY. In this work, we investigate the intermolecular dipolar spin relaxation as driven by the relative diffusion of solvent and solute molecules taking place under a central force field, and we examine the relevant implications for (preferential) solvation studies. For this purpose, we evaluate the SDFs by employing a numerical approach based on spatial discretization of the time-propagation equation, and we supply an analytical solution for the simplest case of a steplike mean-field potential. Several situations related to different solute-solvent pair correlation functions are examined in terms of static/dynamic effects and relaxation modes, and some conclusions are drawn about the interpretation of NOE measurements. While we confirm previous results concerning the spoiling effect of long-range spins (Halle, B. J. Chem. Phys. 2003, 119, 12372), we also show that SDFs are sufficiently sensitive to pair correlation functions that useful, yet rather complicated, inferences can be made on the nature of the solvation shell.     

Progress in Hyperpolarized Ultrafast 2D NMR Spectroscopy

An important development in the field of NMR spectroscopy has been the advent of hyperpolarization approaches, capable of yielding nuclear spin states whose value exceeds by orders‐of‐magnitude what even the highest‐field spectrometers can afford under Boltzmann equilibrium. Included among these methods is an ex situ dynamic nuclear polarization (DNP) approach, which yields liquid‐phase samples possessing spin polarizations of up to 50 %. Although capable of providing an NMR sensitivity equivalent to the averaging of about 1 000 000 scans, this methodology is constrained to extract its “superspectrum” within a single—or at most a few—transients. This makes it a poor starting point for conventional 2D NMR acquisition experiments, which require a large number of scans that are identical to one another except for the increment of a certain t₁ delay. It has been recently suggested that by merging this ex situ DNP approach with spatially encoded “ultrafast” methods, a suitable starting point could arise for the acquisition of 2D spectra on hyperpolarized liquids. Herein, we describe the experimental principles, potential features, and current limitations of such integration between the two methodologies. For a variety of small molecules, these new hyperpolarized ultrafast experiments can, for equivalent overall durations, provide heteronuclear correlation spectra at significantly lower concentrations than those currently achievable by conventional 2D NMR acquisitions. A variety of challenges still remain to be solved before bringing the full potential of this new integrated 2D NMR approach to fruition; these outstanding issues are discussed.     

Two-dimensional homonuclear chemical shift correlation established by the cross-relaxation driven spin diffusion in solids

A new type of spin diffusion, cross-relaxation driven spin diffusion (CRDSD), is investigated using (15)N NMR on a N-acetyl-L-valyl-L-leucine (NAVL) single crystal under stationary condition. A two-dimensional (2D) pulse sequence that correlates the chemical shifts of (15)N nuclei, with a radio-frequency spin lock on the (15)N channel during the mixing time, is used to observe CRDSD. Experimental results obtained using CRDSD, rf-driven spin diffusion, and proton driven spin diffusion approaches on the NAVL single crystal are compared. Our experimental results suggest that the (15)N spin diffusion rate can be enhanced by about 1000 times using CRDSD than by the normal proton driven spin diffusion. Interestingly, the required spin-locking rf field strength for CRDSD is much lower than that used for the rf-driven spin diffusion experiments. The cross-peak patterns observed in 2D (15)N-(15)N correlation spectra using CRDSD and RFDSD are very different as they arise from different spin-spin interactions. A detailed theory describing CRDSD and RFDSD processes is also presented using a thermodynamic model. The speedy spin diffusion process rendered by the CRDSD approach will be useful to assign resonances from a uniformly (15)N or (13)C labeled proteins and peptides, particularly in aligned samples.     

Magnetic field dependence of spatial frequency encoding NMR as probed on an oligosaccharide

The magnetic field dependence of spatial frequency encoding NMR techniques is addressed through a detailed analysis of ¹H NMR spectra acquired under spatial frequency encoding on an oligomeric saccharide sample. In particular, the influence of the strength of the static magnetic field on spectral and spatial resolutions that are key features of this method is investigated. For this purpose, we report the acquisition of correlation experiments implementing broadband homodecoupling or J‐edited spin evolutions, and we discuss the resolution enhancements that are provided by these techniques at two different magnetic fields. We show that performing these experiments at higher field improves the performance of high resolution NMR techniques based on a spatial frequency encoding. The significant resolution enhancements observed on the correlation spectra acquired at very high field make them valuable analytical tools that are suitable for the assignment of ¹H chemical shifts and scalar couplings in molecules with highly crowded spectrum such as carbohydrates. Copyright © 2015 John Wiley & Sons, Ltd.     

Spatial encoding and the acquisition of high-resolution NMR spectra in inhomogeneous magnetic fields

A scheme enabling the acquisition of high-resolution nuclear magnetic resonance (NMR) spectra within inhomogeneous magnetic fields is introduced and exemplified. The scheme is based on the spatial encoding protocol recently introduced for collecting multidimensional NMR data within a single scan, which retrieves spectral information via interference phenomena between spin packets located at distinct positions within the sample. This in turn enables compensating for field inhomogeneities over the sample as a whole by shifting the phases of the radio-frequency pulses involved in the spatial encoding, rather than by demanding an extreme uniformity in the employed magnetic field. The upper tolerable field inhomogeneity limit thus becomes orders of magnitude higher than that in conventional time-domain acquisitions. No particular spatial dependencies are demanded by the new scheme, which can yield its high-resolution results on a single-scan basis.     

Ultrafast two-dimensional NMR spectroscopy using constant acquisition gradients

Multidimensional NMR spectroscopy plays an important role in the characterization of molecular structure and dynamics. A new methodology for acquiring this kind of spectra has been recently demonstrated, endowed with the potential to compress arbitrary multidimensional NMR acquisitions into a single scan. This "ultrafast" nD acquisition protocol is based on a spatiotemporal encoding of the indirect-domain spin evolution, followed by a repetitive decoding and re-encoding of the information thus stored employing a train of alternating-sign gradients. Such train of switching gradients extending throughout the course of the data acquisition may pose extreme demands on a magnetic resonance system, particularly when dealing with nonshielded gradients, strong eddy currents, or rapidly relaxing spin systems. Limits to the in vivo applicability of such fast-switching scheme may also arise due to gradient-induced perineural stimulation. The present study describes a new approach to ultrafast nD NMR that reduces the number of gradient switchings during the acquisition period to zero, leading in essence to a constant-gradient acquisition scheme. This approach operates on the basis of a novel spatiotemporal encoding including discrete, temporally overlapping, frequency-shifted pulses. Principles and examples of this new approach are given; sensitivity limitations and signal-enhancing prospects of such constant-gradient acquisitions are also discussed and exemplified.     

Ultrafast Single-Scan 2D NMR Spectroscopic Detection of a PHIP-Hyperpolarized Protease Inhibitor

Two-dimensional NMR spectroscopy is one of the most important spectroscopic tools for the investigation of biological macromolecules. However, due to the low sensitivity of NMR spectroscopy, it takes usually from several minutes to many hours to record such spectra. Here, the possibility of detecting a bioactive derivative of the sunflower trypsin inhibitor-1 (SFTI-1), a tetradecapeptide, by combining parahydrogen-induced polarization (PHIP) and ultrafast 2D NMR spectroscopy is shown. The PHIP activity of the inhibitor was achieved by labeling with O-propargyl-l -tyrosine. In 1D PHIP experiments a signal enhancement of a factor of approximately 1200 compared to standard NMR was found. This enhancement permits measurement of 2D NMR correlation spectra of low-concentrated SFTI-1 in less than 10 seconds, employing ultrafast single-scan 2D NMR detection. As experimental examples PHIP-assisted ultrafast single-scan TOCSY spectra of SFTI-1 are shown.     

Implementation and Characterization of Flow Injection in Dissolution Dynamic Nuclear Polarization NMR Spectroscopy

The use of dissolution dynamic nuclear polarization (D ‐DNP) offers substantially increased signals in liquid‐state NMR spectroscopy. A challenge in realizing this potential lies in the transfer of the hyperpolarized sample to the NMR detector without loss of hyperpolarization. Here, the use of a flow injection method using high‐pressure liquid leads to improved performance compared to the more common gas‐driven injection, by suppressing residual fluid motions during the NMR experiment while still achieving a short injection time. Apparent diffusion coefficients are determined from pulsed field gradient echo measurements, and are shown to fall below 1.5 times the value of a static sample within 0.8 s. Due to the single‐scan nature of D ‐DNP, pulsed field gradients are often the only choice for coherence selection or encoding, but their application requires stationary fluid. Sample delivery driven by a high‐pressure liquid will improve the applicability of these types of D‐DNP advanced experiments.     

Multidimensional spatial-spectral holographic interpretation of NMR photography

A spectral holographic interpretation arises naturally in nuclear magnetic resonance (NMR) photography from either the intrinsic chemical shift anisotropy of the spin system or the field inhomogeneity due to the applied spatial encoding gradients. We can thus think of NMR photography as arising from a "diffraction" off a spatial-spectral holographic grating. The spatial holographic component arises from a high dielectric constant (>50) of the NMR medium at high field strength (>4 T) when the excitation wavelength is commensurate with the size of the NMR sample; otherwise, it is a volume spectral holographic grating. In this paper, the NMR localized spectroscopy (imaging) equation is derived from the principles of spatial-spectral holography. Holographic properties of storage and programmable time delay and time reversal are shown to follow naturally from this viewpoint and are experimentally demonstrated in an inhomogeneously broadened NMR sample. These ideas are shown to be extendable to complex signal processing functions such as recognition, correlations, and triple products.     

Single-scan NMR spectroscopy at arbitrary dimensions

Multidimensional nuclear magnetic resonance (NMR) provides one of the foremost analytical tools available to elucidate the structure and dynamics of complex molecules in their native states. Executing this kind of experiment generally requires collecting an n-dimensional time-domain signal S, from which the spectrum arises via an appropriate Fourier analysis of its various time variables. This time-domain signal is actually measured directly only along one of the time axes, while the effects introduced by the remaining time variables are monitored via a parametric incrementation of their values throughout independent experiments. Two-dimensional (2D) NMR experiments thus usually require longer acquisition times than unidimensional experiments, 3D NMR is orders-of-magnitude more time consuming than 2D spectroscopy, etc. Very recently, we proposed and demonstrated an approach whereby data acquisition in 2D NMR can be parallelized, enabling the collection of complete 2D spectral sets within a single transient. The present paper discusses the extension of this 2D NMR methodology to an arbitrary number of dimensions. The principles of the ensuing ultrafast n-dimensional NMR approach are described, and a variety of homo- and heteronuclear 3D and 4D NMR spectra collected within a fraction of a second are presented.     

1H‐19F REDOR‐filtered NMR spin diffusion measurements of domain size in heterogeneous polymers

Solid state NMR spectroscopy is inherently sensitive to chemical structure and composition and thus makes an ideal method to probe the heterogeneity of multicomponent polymers. Specifically, NMR spin diffusion experiments can be used to extract reliable information about spatial domain sizes on multiple length scales, provided that magnetization selection of one domain can be achieved. In this paper, we demonstrate the preferential filtering of protons in fluorinated domains during NMR spin diffusion experiments using ¹H‐¹⁹F heteronuclear dipolar dephasing based on rotational echo double resonance (REDOR) MAS NMR techniques. Three pulse sequence variations are demonstrated based on the different nuclei detected: direct ¹H detection, plus both ¹H?¹³C cross polarization and ¹H?¹⁹F cross polarization detection schemes. This ¹H‐¹⁹F REDOR‐filtered spin diffusion method was used to measure fluorinated domain sizes for a complex polymer blend. The efficacy of the REDOR‐based spin filter does not rely on spin relaxation behavior or chemical shift differences and thus is applicable for performing NMR spin diffusion experiments in samples where traditional magnetization filters may prove unsuccessful. This REDOR‐filtered NMR spin diffusion method can also be extended to other samples where a heteronuclear spin pair exists that is unique to the domain of interest.