Ultrafast 2D NMR spectroscopy using a continuous spatial encoding of the spin interactions

A new protocol for acquiring multidimensional NMR spectra within a single scan is introduced and illustrated. The approach relies on applying a pair of frequency-chirped excitation and storage pulses in combination with echoing magnetic field gradients, in order to impart the kind of linear spatial encoding of the NMR interactions that is required by ultrafast 2D NMR spectroscopy. It is found that when dealing with 2D NMR experiments involving a t1 amplitude-modulation of the spin evolution, such continuous encoding scheme presents a number of advantages over alternatives employing discrete excitation pulses. From an experimental standpoint this is mainly reflected by the use of a single pair of bipolar gradients during the course of the indirect-domain encoding, as opposed to the numerous (and more intense) gradient echoes required so far. In terms of the spectral outcome, main advantages of the continuous spatial encoding scheme are the avoidance of "ghost peaks" and of "enveloping effects" associated to the discrete excitation mode. The principles underlying this new spatial encoding protocol are derived, and its applicability is demonstrated with homo- and heteronuclear 2D ultrafast NMR applications on small molecule and on protein samples.     

Spatially encoded NMR and the acquisition of 2D magnetic resonance images within a single scan

An approach that enables the acquisition of multidimensional NMR spectra within a single scan has been recently proposed and demonstrated. The present paper explores the applicability of such ultrafast acquisition schemes toward the collection of two-dimensional magnetic resonance imaging (2D MRI) data. It is shown that ideas enabling the application of these spatially encoded schemes within a spectroscopic setting, can be extended in a straightforward manner to pure imaging. Furthermore, the reliance of the original scheme on a spatial encoding and subsequent decoding of the evolution frequencies endows imaging applications with a greater simplicity and flexibility than their spectroscopic counterparts. The new methodology also offers the possibility of implementing the single-scan acquisition of 2D MRI images using sinusoidal gradients, without having to resort to subsequent interpolation procedures or non-linear sampling of the data. Theoretical derivations on the operational principles and imaging characteristics of a number of sequences based on these ideas are derived, and experimentally validated with a series of 2D MRI results collected on a variety of model phantom samples.     

不均匀场下空间编码超快速高分辨NMR研究进展

二维核磁共振(2D NMR)的提出和发展,为NMR技术的研究和应用提供了广阔的空间. 然而当样品或磁场本身不均匀时,高分辨的2D NMR谱难以获得. 此外,常规2D NMR实验通常需要长的采样时间. 空间编码超快速采样方法利用空间编码技术,只需单次扫描即可获得2D甚至多维NMR谱,极大地缩短了采样时间. 目前相位补偿、相干转移和分子间多量子相干等技术与空间编码技术相结合,已成功实现不均匀场下超快速获得高分辨NMR谱. 该文对不均匀场下空间编码超快速NMR方法进行了介绍,对其未来发展进行了展望.     

Sensitivity losses and line shape modifications due to molecular diffusion in continuous encoding ultrafast 2D NMR experiments

Recent ultrafast techniques make it possible to obtain multidimensional (nD) NMR spectra in a single scan. These ultrafast methods rely on a spatial encoding process based on radiofrequency (RF) pulses applied simultaneously with magnetic field gradients. Numerous approaches have been proposed in the past few years to perform this excitation process, most of them relying on a continuous excitation of the spins throughout the whole sample. However, the resolution and sensitivity of ultrafast nD spectra are often reduced by molecular diffusion effects due to the presence of gradients during the excitation process. In particular, increasing the excitation period is necessary to improve the resolution in the ultrafast dimension, but it leads to high sensitivity losses due to diffusion. In order to understand better and to limit molecular diffusion effects, a detailed theoretical and experimental study of the various continuous ultrafast excitation processes is carried out in the present study. New numerical simulations of ultrafast echo line shapes are presented and compared to experimental data. The evolution of the signal intensity with the excitation process duration is also simulated and compared to experimental intensity losses. The different excitation schemes are compared in order to determine the best excitation conditions to perform 2D ultrafast experiments with optimum resolution and sensitivity. The experimental and theoretical results put in evidence the efficiency of the multi-echo scheme.     

Resolution and sensitivity aspects of ultrafast J-resolved 2D NMR spectra

Recent ultrafast techniques enable nD NMR spectra to be obtained in a single scan. However, resolution enhancement in the ultrafast domain leads to important sensitivity losses and lineshape distortions. In order to understand better resolution and spatial encoding aspects of continuous phase-encoding schemes, a theoretical and experimental comparison of different excitation patterns is carried out. Molecular diffusion appears to be the main cause of signal-to-noise ratio decrease, and a multi-echo excitation scheme is proposed to limit its effects when a good resolution is needed. Results obtained on 2D J-resolved spectra are presented.     

A continuous phase-modulated approach to spatial encoding in ultrafast 2D NMR spectroscopy

Ultrafast 2D NMR replaces the time-domain parametrization usually employed to monitor the indirect-domain spin evolution, with an equivalent encoding along a spatial geometry. When coupled to a gradient-assisted decoding during the acquisition, this enables the collection of complete 2D spectra within a single transient. We have presented elsewhere two strategies for carrying out the spatial encoding underlying ultrafast NMR: a discrete excitation protocol capable of imparting a phase-modulated encoding of the interactions, and a continuous protocol yielding amplitude-modulated signals. The former is general but has associated with it a number of practical complications; the latter is easier to implement but unsuitable for certain 2D NMR acquisitions. The present communication discusses a new protocol that incorporates attractive attributes from both alternatives, imparting a continuous spatial encoding of the interactions yet yielding a phase modulation of the signal. This in turn enables a number of basic experiments that have shown particularly useful in the context of in vivo 2D NMR, including 2D J-resolved and 2D H,H-COSY spectroscopies. It also provides a route to achieving sensitivity-enhanced acquisitions for other homonuclear correlation experiments, such as ultrafast 2D TOCSY. The main features underlying this new spatial encoding protocol are derived, and its potential demonstrated with a series of phase-modulated homonuclear single-scan 2D NMR examples.     

Line shape considerations in ultrafast 2D NMR

We have recently proposed and demonstrated an approach that enables the acquisition of 2D nuclear magnetic resonance (NMR) spectra within a single scan. The approach is based on spatially encoding the spins' evolution along the indirect domain with the aid of a magnetic field gradient, and subsequently decoding this information numerous times over the course of the signal acquisition while spins are subject to a train of gradient echoes. The present paper discusses further considerations pertaining the 2D line shapes arising from this new way of collecting NMR data. Specific issues that are hereby addressed include (i) the effects introduced by fast relaxation onto the spatial encoding process, particularly the line widths and line shapes that will then arise in the frequency domain; (ii) approaches capable of correcting for the mixed-phase kernels resulting in these fast-relaxation cases, corresponding in essence to spatially encoded analogs of the TPPI and hypercomplex time-domain acquisition procedures; (iii) the enveloping characteristics imposed by the use of discrete excitation pulses on the attainable spectral widths along the indirect domain; and (iv) an analysis of the signal-to-noise characteristics of the methodology, with experimental corroborations of theoretical predictions and an illustration of the method's capabilities to analyze protein solutions in the mM-range concentration.     

基于低秩矩阵的非均匀采样NMR波谱重建进展

多维核磁共振（Nuclear Magnetic Resonance，NMR）利用多维波谱来分析分子结构，被广泛用于化学、生物学和医学等领域，但信号采样时间随波谱维度和采样点数增加而迅速增长．非均匀采样通过降低间接维采样点数来加速数据采集，并引入合理的重建方法获得完整的NMR波谱．如何快速重建高质量的波谱，是NMR信号处理研究的前沿．本文主要综述近年来基于低秩矩阵的NMR波谱重建方法的发展．首先介绍了低秩矩阵的相关数学基础；然后从一般低秩矩阵和结构化低秩汉克尔矩阵两个角度来论述重建模型，并讨论相关的NMR波谱应用；最后分析了该技术存在的不足，并展望其未来发展的趋势．     

Accelerated acquisition of high resolution triple-resonance spectra using non-uniform sampling and maximum entropy reconstruction

Non-uniform sampling is shown to provide significant time savings in the acquisition of a suite of three-dimensional NMR experiments utilized for obtaining backbone assignments of H, N, C', CA, and CB nuclei in proteins : HNCO, HN(CA)CO, HNCA, HN(CO)CA, HNCACB, and HN(CO)CACB. Non-uniform sampling means that data were collected for only a subset of all incremented evolution periods, according to a user-specified sampling schedule. When the suite of six 3D experiments was acquired in a uniform fashion for an 11 kDa cytoplasmic domain of a membrane protein at 1.5 mM concentration, a total of 146 h was consumed. With non-uniform sampling, the same experiments were acquired in 32 h and, through subsequent maximum entropy reconstruction, yielded spectra of similar quality to those obtained by conventional Fourier transform of the uniformly acquired data. The experimental time saved with this methodology can significantly accelerate protein structure determination by NMR, particularly when combined with the use of automated assignment software, and enable the study of samples with poor stability at room temperature. Since it is also possible to use the time savings to acquire a greater numbers of scans to increase sensitivity while maintaining high resolution, this methodology will help extend the size limit of proteins accessible to NMR studies, and open the way to studies of samples that suffer from solubility problems.     

单扫描快速采样方法及其在NMR中的应用

单扫描快速采样方法利用空间编码技术,只需单次扫描就能获得二维及多维核磁共振(NMR)谱数据,极大地缩短了二维和多维核磁共振谱的采样时间,有望在NMR领域得到广泛的应用. 该文以离散编码单扫描快速采样方法为例阐明了单扫描快速采样方法的原理,介绍了连续幅度调制、连续相位调制等各种单扫描快速采样新方法及其在NMR领域中的应用, 指出了单扫描快速采样方法的局限性,并对其未来发展进行了展望.     

High-resolution 2D NMR spectra in inhomogeneous fields based on intermolecular multiple-quantum coherences with efficient acquisition schemes

High-resolution 2D NMR spectra in inhomogeneous fields can be achieved by the use of intermolecular multiple-quantum coherences and shearing reconstruction of 3D data. However, the long acquisition time of 3D spectral data is generally unbearable for in vivo applications. To overcome this problem, two pulse sequences dubbed as iDH-COSY and iDH-JRES were proposed in this paper. Although 3D acquisition is still required for the new sequences, the high-resolution 2D spectra can be obtained with a relatively short scanning time utilizing the manipulation of indirect evolution period and sparse sampling. The intermolecular multiple-quantum coherence treatment combined with the raising and lowering operators was applied to derive analytical signal expressions for the new sequences. And the experimental observations agree with the theoretical predictions. Our results show that the new sequences possess bright perspective in the applications on in vivo localized NMR spectroscopy.     

A new detection scheme for ultrafast 2D J-resolved spectroscopy

Recent ultrafast techniques enable 2D NMR spectra to be obtained in a single scan. A modification of the detection scheme involved in this technique is proposed, permitting the achievement of 2D 1H J-resolved spectra in 500 ms. The detection gradient echoes are substituted by spin echoes to obtain spectra where the coupling constants are encoded along the direct nu2 domain. The use of this new J-resolved detection block after continuous phase-encoding excitation schemes is discussed in terms of resolution and sensitivity. J-resolved spectra obtained on cinnamic acid and 3-ethyl bromopropionate are presented, revealing the expected 2D J-patterns with coupling constants as small as 2 Hz.     

基于选择编码的超快速磁共振波谱方法

核磁共振(NMR)波谱技术是当今最有力的谱学工具之一,在化学、生物和医药等众多领域获得重要而广泛的应用．基于时空编码的快速采样方法自2002年Frydman小组提出后,大大增强了高维磁共振波谱的采样效率．在某一些应用体系中,存在若干个强度远超于其他谱峰的情况,很容易由于动态增益不足而检测不到某些较弱的谱峰,而往往这些较弱的谱峰包含着感兴趣的信息．且在实际的化学生物应用中,存在选择性感兴趣检测的情况,即只需要选择性地观察若干个具有标记作用的谱峰．由于时空编码技术借助于高速切换的双极性梯度来完成解码,因而无法选择性地检测若干个非连续的频点．为解决以上两个问题,该文提出一种选择编码的时空编码方法,即在序列中施加选择性脉冲,选择性破坏某些谱峰的编码过程,使之不能在解码期解码,从而简化谱图,实现选择性压制或者非连续频点的感兴趣检测．如果把选择性反转脉冲换为硬反转脉冲加选择性反转脉冲,则最终的谱图中只出现被选择性脉冲选中的谱峰．理论分析及相关的实验验证了这种方法的可行性和有效性.     

Single-scan 2D DOSY NMR spectroscopy

Spatial encoding is a particular kind of spin manipulation that enables the acquisition of multidimensional NMR spectra within a single scan. This encoding has been shown to possess a general applicability and to enable the completion of arbitrary nD NMR acquisitions within a single transient. The present study explores its potential towards the acquisition of 2D DOSY spectra, where the indirect dimension is meant to encode molecular displacements rather than a coherent spin evolution. We find that in its simplest form this extension shows similarities with methods that have been recently discussed for the single-scan acquisition of this kind of traces; still, a number of advantageous features are also evidenced by the “ultrafast” modality hereby introduced. The principles underlying the operation of this new single-scan 2D DOSY approach are discussed, its use is illustrated with a variety of sequences and of samples, the limitations of this new experiment are noted, and potential extensions of the methodology are mentioned.     

Application of Maximum Entropy reconstruction to PISEMA spectra

Maximum Entropy reconstruction is applied to two-dimensional PISEMA spectra of stationary samples of peptide crystals and proteins in magnetically aligned virus particles and membrane bilayers. Improvements in signal-to-noise ratios were observed with minimal distortion of the spectra when Maximum Entropy reconstruction was applied to non-linearly sampled data in the indirect dimension. Maximum Entropy reconstruction was also applied in the direct dimension by selecting sub-sets of data from the free induction decays. Because the noise is uncorrelated in the spectra obtained by Maximum Entropy reconstruction of data with different non-linear sampling schedules, it is possible to improve the signal-to-noise ratios by co-addition of multiple spectra derived from one experimental data set. The combined application of Maximum Entropy to data in the indirect and direct dimensions has the potential to lead to substantial reductions in the total amount of experimental time required for acquisition of data in multidimensional NMR experiments.     

Ultrafast hetero-nuclear 2D J-resolved spectroscopy

Ultrafast techniques enable the acquisition of 2D NMR spectra in a single scan. In this study, we propose a new ultrafast experiment designed to record hetero-nuclear (1)H-(13)C J-resolved spectra in a fraction of a second. The approach is based on continuous constant-time phase modulated spatial encoding followed by a J-resolved detection scheme. An optional isotopic filter is implemented to remove the signal arising from (1)H bound to (12)C. While the most evident application of the technique proposed in this paper is the direct measurement of one bond scalar (13)C-(1)H couplings for structural elucidation purposes, it also offers interesting potentialities for measuring (13)C isotopic enrichments in metabolic samples. The main features of this methodology are presented, and the analytical performances of the ultrafast hetero-nuclear J-resolved pulse sequence are evaluated on model samples.     

Interlaced Fourier transformation of ultrafast 2D NMR data

A new protocol for processing the data arising in ultrafast 2D NMR is discussed and exemplified, based on the interlaced Fourier transformation. This approach is capable of dealing in a single, combined fashion, with the two mirror-imaged interferograms arising in this kind of experiment as a result of the acquisition of a train of magnetic field gradient echoes. By combining all the acquired data points into a common Fourier processing procedure the spectral width along the direct-acquisition domain becomes effectively doubled, giving the opportunity of employing acquisition gradients that are approximately half as strong as hitherto required. This in turn should lead to an overall enhancement in the signal-to-noise ratio of the experiment of ca. 2, as well as to improvements in the achievable digital resolution. These expectations were tested by carrying out a series of homo- and heteronuclear ultrafast 2D NMR acquisitions, and found systematically fulfilled. The robustness and conditions that allow the interlaced numerical procedure to be implemented in routine analytical applications were explored and are briefly discussed.     

Spatially resolved multidimensional NMR spectroscopy within a single scan

We have recently demonstrated that the spatial encoding of internal nuclear magnetic resonance (NMR) spin interactions can be exploited to collect multidimensional NMR spectra within a single scan. Such experiments rely on an inhomogeneous spatial excitation of the spins throughout the sample, and lead to indirect-domain peaks via a constructive interference among the spatially resolved spin-packets that are thus created. The shape of the resulting indirect-domain echo peaks approaches a Sinc function when the chemical's distribution is uniform, but will depart from this function otherwise. It is hereby shown that a Fourier analysis of either the diagonal- or the cross-peaks resolved in these single-scan two-dimensional (2D) NMR experiments can in fact provide a weighted spatial distribution of the analyte originating such peak, thus opening up the possibility of completing spatially resolved multidimensional NMR measurements within a fraction of a second. Principles of this new mode of analysis are discussed, and examples where the potential of spatially resolved ultrafast 2D NMR spectroscopy is brought to bear are presented. Potential extensions of this approach to higher dimensions are also briefly addressed.