The effects of molecular diffusion in ultrafast two-dimensional nuclear magnetic resonance

The so-called "ultrafast" nuclear magnetic resonance (NMR) methods enable the collection of multidimensional spectra within a single scan. These experiments operate by replacing traditional t(1) time increments, with a series of combined radiofrequency-irradiation/magnetic-field-gradient manipulations that spatially encode the effects of the indirect-domain spin interactions. Barring the presence of sizable displacements, the spatial patterns thus imparted can be read out following a mixing period with the aid of oscillating acquisition gradients, leading to a train of t(2)-modulated echoes carrying in their positions and phases the indirect- and the direct-domain spin interactions. Both the initial spatial encoding as well as the subsequent spatial decoding procedures underlying ultrafast NMR were designed under the assumption that spins remain static within the sample during their execution. Most often this is not the case, and motion-related effects can be expected to affect the outcome of these experiments. The present paper focuses on analyzing the effects of diffusion in ultrafast two-dimensional (2D) NMR. Toward this end both analytical and numerical formalisms are derived, capable of dealing with the nonuniform spin manipulations, macroscopic sample sizes, and microscopic displacements involved in this kind of sequences. After experimentally validating the correctness of these formalisms these were used to analyze the effects of diffusion for a variety of cases, including ultrafast experiments on both rapidly and slowly diffusing molecules. A series of prototypical schemes were considered including discrete and continuous encoding modes, constant- and real-time manipulations, homo- and heteronuclear acquisitions, and single versus multiple quantum modalities. The effects of molecular diffusion were also compared against typical relaxation-driven losses as they happen in these various prototypical situations; from all these situations, general guidelines for choosing the optimal ultrafast 2D NMR scheme for a particular sample and condition could be deduced.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

UltraSOFAST HMQC NMR and the repetitive acquisition of 2D protein spectra at Hz rates

Following unidirectional biophysical events such as the folding of proteins or the equilibration of binding interactions, requires experimental methods that yield information at both atomic-level resolution and at high repetition rates. Toward this end a number of different approaches enabling the rapid acquisition of 2D NMR spectra have been recently introduced, including spatially encoded "ultrafast" 2D NMR spectroscopy and SOFAST HMQC NMR. Whereas the former accelerates acquisitions by reducing the number of scans that are necessary for completing arbitrary 2D NMR experiments, the latter operates by reducing the delay between consecutive scans while preserving sensitivity. Given the complementarities between these two approaches it seems natural to combine them into a single tool, enabling the acquisition of full 2D protein NMR spectra at high repetition rates. We demonstrate here this capability with the introduction of "ultraSOFAST" HMQC NMR, a spatially encoded and relaxation-optimized approach that can provide 2D protein correlation spectra at approximately 1 s repetition rates for samples in the approximately 2 mM concentration range. The principles, relative advantages, and current limitations of this new approach are discussed, and its application is exemplified with a study of the fast hydrogen-deuterium exchange characterizing amide sites in Ubiquitin.     

Sub-second 2D NMR spectroscopy at sub-millimolar concentrations

A recently proposed protocol enables the acquisition of two-dimensional nuclear magnetic resonance (2D NMR) spectra within a single scan. A promising application opened up by this new data acquisition mode concerns its combination with active nuclear polarization methods, whereby spectroscopy is carried out on analytes whose spin magnetizations have been significantly enhanced over their Boltzmann thermal values. The present paper explores the potential of such combination, with the acquisition of peptide and protein 2D NMR 1H correlation spectra recorded after the samples had been subject to laser-driven chemically induced dynamic nuclear polarization (CIDNP). It is demonstrated that the speed and sensitivity enhancement afforded by these combined processes enables the acquisition of quality 2D NMR data sets within a fraction of a second, at analyte concentrations that are under 1 mM.     

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.     

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.     

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.     

How to face the low intrinsic sensitivity of 2D heteronuclear NMR with fast repetition techniques: go faster to go higher!

Nuclear magnetic resonance (NMR) is one of the most widely used analytical techniques in numerous domains where molecules are objects of investigation. However, major limitations of multidimensional NMR experiments come from their low sensitivity and from the long times needed for their acquisition. In order to overcome such limitations, fast repetition NMR techniques allowed for the reduction of 2D experimental time and for the conversion of the gained time into a higher number of scans leading to a better sensitivity. Thus, fast repetition 2D heteronuclear NMR techniques have allowed new advances in NMR, especially to access infomation on low abundant nuclei, to enhance the detection of low concentrated compounds and to probe weak interactions like hydrogen bonds at natural abundance. Copyright © 2017 John Wiley & Sons, Ltd.     

A simple approach for phase-modulated single-scan 2D NMR spectroscopy

Conventional NMR spectroscopy techniques require long acquisition times due to the recovery time between the repeated excitations necessary for each increment of the evolution times in the indirectly detected dimensions. Here we outline a pulse sequence element for gradient-assisted ultrafast multidimensional NMR spectroscopy using frequency-modulated 'chirp' pulses to generate phase-modulated magnetization in an indirectly detected spectral dimension. The potential of this sequence element is demonstrated by acquiring a correlation spectroscopy (COSY) spectrum in 96 ms. This new pulse sequence element is an extension of ultrafast spectroscopy techniques based on the generation of amplitude modulation of the NMR signal in the indirectly detected spectral dimensions. The use of phase modulation instead of amplitude modulation helps broaden the applicability and may provide an increase of sensitivity in some experiments due to the ability to distinguish between positive and negative frequency offsets relative to the carrier frequency of the sequence element.     

Monitoring mechanistic details in the synthesis of pyrimidines via real-time, ultrafast multidimensional NMR spectroscopy

Recent years have witnessed unprecedented advances in the development of fast multidimensional NMR acquisition techniques. This progress could open valuable new opportunities for the elucidation of chemical and biochemical processes. This study demonstrates one such capability, with the first real-time Two-dimensional (2D) dynamic analysis of a complex organic reaction relying on unlabeled substrates. Implementing such measurements required the development of new ultrafast 2D methods, capable of monitoring multiple spectral regions of interest as the reaction progressed. The alternate application of these acquisitions in an interleaved, excitation-optimized fashion, allowed us to extract new structural and dynamic insight concerning the reaction between aliphatic ketones and triflic anhydride in the presence of nitriles to yield alkylpyrimidines. Up to 2500 2D NMR data sets were thus collected over the course of this nearly 100 min long reaction, in an approach resembling that used in functional magnetic resonance imaging. With the aid of these new frequency-selective low-gradient strength experiments, supplemented by chemical shift calculations of the spectral coordinates observed in the 2D heteronuclear correlations, previously postulated intermediates involved in the alkylpyrimidine formation process could be confirmed, and hitherto undetected ones were revealed. The potential and limitations of the resulting methods are discussed.     

Proton evolved local field solid-state nuclear magnetic resonance using Hadamard encoding: theory and application to membrane proteins

NMR anisotropic parameters such as dipolar couplings and chemical shifts are central to structure and orientation determination of aligned membrane proteins and liquid crystals. Among the separated local field experiments, the proton evolved local field (PELF) scheme is particularly suitable to measure dynamically averaged dipolar couplings and give information on local molecular motions. However, the PELF experiment requires the acquisition of several 2D datasets at different mixing times to optimize the sensitivity for the complete range of dipolar couplings of the resonances in the spectrum. Here, we propose a new PELF experiment that takes the advantage of the Hadamard encoding (HE) to obtain higher sensitivity for a broad range of dipolar couplings using a single 2D experiment. The HE scheme is obtained by selecting the spin operators with phase switching of hard pulses. This approach enables one to detect four spin operators, simultaneously, which can be processed into two 2D spectra covering a broader range of dipolar couplings. The advantages of the new approach are illustrated for a U-(15)N NAL single crystal and the U-(15)N labeled single-pass membrane protein sarcolipin reconstituted in oriented lipid bicelles. The HE-PELF scheme can be implemented in other multidimensional experiments to speed up the characterization of the structure and dynamics of oriented membrane proteins and liquid crystalline samples.     

Real-time monitoring of chemical transformations by ultrafast 2D NMR spectroscopy

An approach enabling the acquisition of 2D nuclear magnetic resonance (NMR) spectra within a single scan has been recently proposed. A promising application opened up by this "ultrafast" data acquisition format concerns the monitoring of chemical transformations as they happen, in real time. The present paper illustrates some of this potential with two examples: (i) following an H/D exchange process that occurs upon dissolving a protonated protein in D2O, and (ii) real-time in situ tracking of a transient Meisenheimer complex that forms upon rapidly mixing two organic reactants inside the NMR observation tube. The first of these measurements involved acquiring a train of 2D 1H-15N HSQC NMR spectra separated by ca. 4 s; following an initial dead time, this allowed us to monitor the kinetics of hydrogen exchange in ubiquitin at a site-resolved level. The second approach enabled us to observe, within ca. 2 s after the triggering of the reaction, a competition between thermodynamic and kinetic controls via changes in a series of 2D TOCSY patterns. The real-time dynamic experiments hereby introduced thus add to an increasing family of fast characterization techniques based on 2D NMR; their potential and limitations are briefly discussed.     

Real-time 2D NMR identification of analytes undergoing continuous chromatographic separation

We have recently proposed and demonstrated an approach that enables the acquisition of multidimensional nuclear magnetic resonance (NMR) spectra within a single scan. A promising application opened up by this new accelerated form of data acquisition concerns the possibility of monitoring in real time the chemical nature of analytes subject to a continuous flow. The present paper illustrates such potential, with the real-time acquisition of a series of 2D 1H NMR spectra arising from a mixture of compounds subject to a continuous liquid chromatography (LC) separation. This real-time 2D NMR identification of chemicals eluted minutes apart under usual LC-NMR conditions differs from the way in which LC-2D NMR has hitherto been carried out, which relies on stopped-flow modes of operations whereby fractions are first collected and then subject to individual, aliquot-by-aliquot analyses. The real-time LC-2D NMR experiment hereby introduced can be implemented in a straightforward manner using modern commercial LC-NMR hardware, thus opening up immediate possibilities in high-throughput characterizations of complex molecules.     

Feasibility of Ultrafast High‐Resolution Spectroscopy in the Analysis of Molecular‐Mobility‐Restricted Samples in Deuterium‐Free Environments

The feasibility of ultrafast high‐resolution intermolecular multiple‐quantum coherence (UF‐iMQC) spectroscopy for the direct analysis of molecular‐mobility‐restricted samples that are not suitable for magic‐angle spinning, such as a jelly, hand soap, and marrow, is presented. Most components could be directly detected in their original state within 1 min without the need for tedious sample preparation processes. When we use conventional liquid nuclear magnetic resonance (NMR) method to study these systems, the spectral information could not be retrieved owing to the intrinsic inhomogeneous magnetic fields caused by sample inhomogeneity. In addition, the possibility for UF‐iMQC‐based quantifications is shown. The examples presented in this paper demonstrate the potential of UF iMQC NMR for food safety inspection, for quality testing of daily‐life supplies, or in assisting medical diagnosis.