Randomization improves sparse sampling in multidimensional NMR

While a number of strategies have been developed to reduce data collection requirements for multidimensional NMR based on non-Fourier methods of spectrum analysis, there is an increasing awareness that the principal differences in the performance of these methods is attributable to the sampling strategies employed, and not the method of spectrum analysis per se. The ability of maximum entropy reconstruction to utilize essentially arbitrary sampling schemes makes it a useful platform for comparative analysis of sampling strategies. Here we use maximum entropy reconstruction to demonstrate that artifacts characteristic of sparse sampling result from regularity in the sampling pattern, and that they can be substantially reduced by introducing a degree of randomness to an otherwise regular sampling scheme, without requiring additional sampling.     

SEnD NMR: Sensitivity Enhanced n-Dimensional NMR

Sparse sampling offers tremendous potential for overcoming the time limitations imposed by traditional Cartesian sampling of indirectly detected dimensions of multidimensional NMR data. However, in many instances sensitivity rather than time remains of foremost importance when collecting data on protein samples. Here we explore how to optimize the collection of radial sampled multidimensional NMR data to achieve maximal signal-to-noise. A method is presented that exploits a rigorous definition of the minimal set of radial sampling angles required to resolve all peaks of interest in combination with a fundamental statistical property of radial sampled data. The approach appears general and can achieve a substantial sensitivity advantage over Cartesian sampling for the same total data acquisition time. Termed Sensitivity Enhanced n-Dimensional or SEnD NMR, the method involves three basic steps. First, data collection is optimized using routines to determine a minimal set of radial sampling angles required to resolve frequencies in the radially sampled chemical shift evolution dimensions. Second, appropriate combinations of experimental parameters (transients and increments) are defined by simple statistical considerations in order to optimize signal-to-noise in single angle frequency domain spectra. Finally, the data is processed with a direct multidimensional Fourier transform and a statistical artifact and noise removal step is employed.     

Fast multidimensional NMR: radial sampling of evolution space

Multidimensional NMR spectroscopy can be speeded up by limited radial sampling of the time-domain evolution data. The resulting frequency-domain projections are used to reconstruct the full NMR spectrum. New algorithms are proposed to suppress back-projection artifacts while retaining optimum sensitivity. The method is illustrated by experiments on the 900 MHz HNCO spectrum of a protein, HasA.     

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．     

多维核磁共振数据在通用计算机上的处理与三维谱的观测

本文分析、讨论了利用外部通用计算机处理核磁共振数据的方法及程序,包括数据格式转换,一维、二维、三维谱的数据处理,谱图的显示及输出,并以VAX机为例实现了三维谱的观测。文中还详细讨论了编程的原理和一些技术细节。     

Phasing arbitrarily sampled multidimensional NMR data

The recent re-introduction of the two-dimensional Fourier transformation (2D-FT) has allows for the transformation of arbitrarily sampled time domain signals. In this respect, radial sampling, where two incremented time dimensions (t(1) and t(2)) are sampled such that t(1)=taucosalpha and t(2)=tausinalpha, is especially appealing because of the relatively small leakage artifacts that occur upon Fourier transformation. Unfortunately radially sampled time domain data results in a fundamental artifact in the frequency domain manifested as a ridge of intensity extending through the peak positions perpendicular to +/- the radial sampling angle. Successful removal of the ridge artifacts using existing algorithms requires absorptive line shapes. Here we present two procedures for retrospective phase correction of arbitrarily sampled data.     

基于近似l0范数最小化的NMR波谱稀疏重建算法

在核磁共振（NMR）波谱中,过长的数据采集时间会使很多化学以及分子生物学领域的高分辨率多维谱应用难以实现. 传统的解决办法是使用随机非均匀采样代替奈奎斯特采样,但这样会使谱图质量受损. 压缩传感的出现为此提供了更好的解决办法,合适的压缩传感重建算法可以通过很少的随机非均匀采样将谱图高质量的重建出来. 该文先介绍了一种可用于谱图重建的压缩传感重建算法,名为“平滑l₀范数最小化法”,然后针对该算法对采样噪声鲁棒性较差的缺点进行了改进. 通过将改进后的算法与原算法在一维实数域信号以及NMR波谱信号重建实验中进行对比后表明,改进后的算法对噪声的鲁棒性明显提高,并能获得更好的重建性能.     

三维NMR谱

３ＤＮＭＲ谱是２ＤＮＭＲ谱附加一个时间周期扩展而成，３ＤＮＭＲ共振峰的重叠降低，并且灵敏度与常规的２ＤＮＯＥＳＹ实验大体相当，采集３ＤＮＭＲ数据组所需时间太长，因此迄今为止，该方法的实际应用只局限于那些浓度相当高的样品。尽管目前还十分费时，但很可能３ＤＮＭＲ不久即可成为常规的ＮＭＲ技术。     

Two-dimensional Fourier transform of arbitrarily sampled NMR data sets

A new procedure for Fourier transform with respect to more than one time variable simultaneously is proposed for NMR data processing. In the case of two-dimensional transform the spectrum is calculated for pairs of frequencies, instead of conventional sequence of one-dimensional transforms. Therefore, it enables one to Fourier transform arbitrarily sampled time domain and thus allows for analysis of high dimensionality spectra acquired in a short time. The proposed method is not limited to radial sampling, it requires only to fulfill the Nyquist theorem considering two or more time domains at the same time. We show the application of new approach to the 3D HNCO spectrum acquired for protein sample with radial and spiral time domain sampling.     

Sampling of the NMR time domain along concentric rings

We present a novel approach to sampling the NMR time domain, whereby the sampling points are aligned on concentric rings, which we term concentric ring sampling (CRS). Radial sampling constitutes a special case of CRS where each ring has the same number of points and the same relative orientation. We derive theoretically that the most efficient CRS approach is to place progressively more points on rings of larger radius, with the number of points growing linearly with the radius, a method that we call linearly increasing CRS (LCRS). For cases of significant undersampling to reduce measurement time, a randomized LCRS (RLCRS) is also described. A theoretical treatment of these approaches is provided, including an assessment of artifacts and sensitivity. The analytical treatment of sensitivity also addresses the sensitivity of radially sampled data processed by Fourier transform. Optimized CRS approaches are found to produce artifact-free spectra of the same resolution as Cartesian sampling, for the same measurement time. Additionally, optimized approaches consistently yield fewer and smaller artifacts than radial sampling, and have a sensitivity equal to Cartesian and better than radial sampling. We demonstrate the method using numerical simulations, as well as a 3D HNCO experiment on protein G B1 domain.     

Solvent Magnetization Artifacts in High-Field NMR Studies of Macromolecular Hydration

With the use of high magnetic fields and improved quality factor ratings of the probeheads in modern NMR spectrometers, radiation damping becomes more and more important. In addition, the demagnetizing field effect from protonated solvents gains significance with the increase of the magnetic field strength. During a typical NMR pulse sequence the magnetic fields caused by these effects become time-dependent, which makes the system nonlinear and may, for example, measurably influence the precession frequencies of all nuclei in the sample. Since radiation damping can affect signals that are several kilohertz away from the solvent resonance, the amplitude, phase, and frequency of the desired signals can be disturbed so as to give rise to spectral artifacts. In particular when difference methods are used to obtain the final spectrum, the data sets may be severely deteriorated by such artifacts. This paper investigates effects from the demagnetizing field and from radiation damping with a selection of pulse sequences in use for studies of macromolecular hydration, and strategies are described for the detection and elimination of the ensuing artifacts.     

Narrow peaks and high dimensionalities: Exploiting the advantages of random sampling

Level of artifacts in spectra obtained by Multidimensional Fourier Transform has been studied, considering randomly sampled signals of high dimensionality and long evolution times. It has been shown theoretically and experimentally, that this level is dependent on the number of time domain samples, but not on its relation to the number of points required in appropriate conventional experiment. Independence of the evolution time domain size (in the terms of both: dimensionality and evolution time reached), suggests that random sampling should be used rather to design new techniques with large time domain than to accelerate standard experiments. 5D HC(CC-TOCSY)CONH has been presented as the example of such approach. The feature of Multidimensional Fourier Transform, namely the possibility of calculating spectral values at arbitrary chosen frequency points, allowed easy examination of resulting spectrum. We present the example of such approach, referred to as Sparse Multidimensional Fourier Transform.     

Defining the sampling space in multidimensional NMR experiments: What should the maximum sampling time be?

Efficient sampling of signals is a key issue for multiple-dimensional NMR experiments to establish the best ratio between experiment time and spectral quality. Focussing on the most widely used sampling strategy using standard rectangular sampling and data analysis by Fourier transformation, a central question is concerned with determining the optimal maximum sampling time in the individual dimensions. The spectral resolution depends directly on this choice, as do the overall experiment times when addressing the indirect dimensions. We present a theoretical, numerical, and experimental analysis of the sampling space problem and propose approaches to efficient sampling for typical cases.     

由NMR获取原子间距离约束计算蛋白质三维结构

提出一种以核磁共振(NMR)技术获取蛋白质分子多肽链中原于对(主要是H—H对)的距离约束,来计算蛋白质在溶液中的三维结构的方法。这种方法把肽平面之间的二面角当作独立变量,通过从局部到整体逐渐最优化的方法使适当构造的目标函数最小,计算出这些二面角,以及主链每个残基上六种原子N、H~N、C~α、H~α、C′、O的空间坐标.本方法已编写成计算程序DISNMA,并以碱性胰蛋白酶抑制剂(BPTI)为标准结构,得到了很好的验证.     

Optimized 3D-NMR sampling for resonance assignment of partially unfolded proteins

Resonance assignment of NMR spectra of unstructured proteins is made difficult by severe overlap due to the lack of secondary structure. Fortunately, this drawback is partially counterbalanced by the narrow line-widths due to the internal flexibility. Alternate sampling schemes can be used to achieve better resolution in less experimental time. Deterministic schemes (such as radial sampling) suffer however from the presence of systematic artifacts. Random acquisition patterns can alleviate this problem by randomizing the artifacts. We show in this communication that quantitative well-resolved spectra can be obtained, provided that the data points are properly weighted before FT. These weights can be evaluated using the concept of Voronoi cells associated with the data points. The introduced artifacts do not affect the direct surrounding of the peaks and thus do not alter the amplitude and frequency of the signals. This procedure is illustrated on 60-residue viral protein, which lacks any persistent secondary structure and thus exhibits major signal overlap.     

Signal identification in NMR spectra with coupled evolution periods

Novel multidimensional NMR experiments rely on modified time-domain sampling schemes to provide significant savings of experimental time. Several approaches are based on the coupling of evolution times resulting in a reduction of the dimensionality of the recorded spectra, and a concomitant saving of experimental time. We present a consistent and general tool, called EVOCOUP, for the analysis of these reduced dimensionality spectra. The approach is flexible in the sense that the input can consist of various forms of reduced dimensionality spectra, that any piece of information can be removed (provided enough information is left), e.g., signals undetectable due to poor signal-to-noise or covered by artifacts, and that it can be applied to spectra involving any number of nuclei. The use of a general optimization procedure and an appropriate target function provides for a robust approach with well-defined results and ensures optimal use of redundant information normally present in the input. Spectral overlap in the directly detected dimension is resolved in a fully automated manner, avoiding the assessment of signal quality and its use in combinatorial trials. The positions of all peaks in a corresponding full-dimensional spectrum are obtained without need for reconstruction of this spectrum. In a systematic analysis of a complete spectrum recorded for the 14 kDa protein azurin and involving five different nuclei, only four spin systems were missed and no false spins systems were detected.     

由NMR获取原子间距离约束计算蛋白质三维结构

提出一种以核磁共振(NMR)技术获取蛋白质分子多肽链中原于对(主要是H-H对)的距离约束,来计算蛋白质在溶液中的三维结构的方法。这种方法把肽平面之间的二面角当作独立变量,通过从局部到整体逐渐最优化的方法使适当构造的目标函数最小,计算出这些二面角,以及主链每个残基上六种原子N、H^N、C^α、H^α、C'、O的空间坐标.本方法已编写成计算程序DISNMA,并以碱性胰蛋白酶抑制剂(BPTI)为标准结构,得到了很好的验证.     

四维NMR谱

尽管３ＤＮＭＲ谱的分辨率有所提高，但解释较大的三维异核ＮＭＲ谱时，仍存在含糊性。因此，人们希望通过增加维数进一步提高分辨率，在最近几年中出现了４ＤＮＭＲ谱，４ＤＮＭＲ谱常常是说明２ＤＮＭＲ谱的方法，４ＤＮＭＲ实验可简单地看作是由三个２ＤＮＭＲ实验所组成，新的４ＤＮＭＲ技术仍在不断地发展，已有许多将４ＤＮＭＲ谱应用于蛋白质及核酸研究的报道。     

Dual-Compensating Composite Inversion Pulses for NMR

Dual-compensating composite inversion pulses described as Wigner rotation matrix has been proposed for NMR optimization. The main FORTRAN program was modified to carry out optimization of the composite pulses, and the subroutine DULSJ and DSLEQ were programed instead of “IMSL” library DBCLSJ to calculate Jacobian and Levenberg-Marquardt iteration equations. Pulse and phase angles with respect to positive and negative resonance off-set were optimized on the multidimensional surface in search for the optimal parameters. It was found that the results obtained by the proposed method are better than other exsisting pulse sequences.