Computer optimized spectral aliasing in the indirect dimension of (1)H-(13)C heteronuclear 2D NMR experiments. A new algorithm and examples of applications to small molecules

A new algorithm for optimizing spectral width in the indirect dimension of heteronuclear 2D experiments is introduced. It takes a list of carbon chemical shifts as input and calculates the optimal spectral width and number of time increments to use in the carbon dimension of 2D experiments such as HSQC, HMBC, etc. When using optimized conditions where signals are better distributed along the carbon dimension, the number of time increments needed to resolve all of the signals is reduced by one to two orders of magnitude. This decreases the experimental time by the same factors and makes the acquisition of spectra such as HSQC-TOCSY, HSQC-NOESY, etc. more practical. The new algorithm allows users to limit the maximal t(1) evolution time when relaxation is a concern, and can take lists of carbons that do not need to be resolved. For any carbon, insights regarding the position of signals in the proton dimension increase the efficiency of the optimization by allowing the overlap of pairs of carbons with incompatible proton dispersions. The application of a second optimization using a fully-resolved spectrum as a source of proton dispersion for the carbons allows the number of time increments to be reduced further. Application to cyclosporine A shows that the time taken to acquire fully resolved HSQC spectra can be 126 times less than would be required in a full-width spectrum with the same resolution. The most interesting applications concern experiments where series of HSQC-based experiments have to be acquired, for example in relaxation time measurements. It is shown that the acquisition of quickly acquired series of selective-TOCSY-HSQC can facilitate assignment in carbohydrates. Computer-optimized spectral aliasing (COSA) generally requires no modification of the pulse sequence and can therefore be easily applied by non specialists.     

Ultra-high resolution 3D NMR spectra from limited-size data sets

The advantage of the filter diagonalization method (FDM) for analysis of triple-resonance NMR experiments is demonstrated by application to a 3D constant time (CT) HNCO experiment. With a 15N-,13C-labeled human ubiquitin sample (1.0 mM), high spectral resolution was obtained at 500 MHz in 25 min with only 6-8 increments in each of the CT dimensions. This data set size is about a factor of 50-100 smaller than typically required, yet FDM analysis results in a fully resolved spectrum with a sharp peak for each HNCO resonance. Unlike Fourier transform (FT) processing, in which spectral resolution in each dimension is inversely proportional to the acquisition time in this dimension, FDM is a true multi-dimensional method; the resolution in all dimensions is determined by the total information content of the entire signal. As the CT dimensions of the 3D HNCO signal have approximate time-reversal symmetry, they can each be doubled by combining the usual four hyper-complex data sets. This apparent quadrupling of the data is important to the success of the method. Thus, whenever raw sensitivity is not limiting, well-resolved n-dimensional spectra can now be obtained in a small fraction of the usual time. Alternatively, to maximize sensitivity, evolution periods of faster relaxing nuclei may be radically shortened, the total required resolution being obtained through chemical shift encoding of other, more slowly relaxing, spins. Improvements similar to those illustrated with a 3D HNCO spectrum are expected for other triple-resonance spectra, where CT evolution in the indirect dimensions is implemented.     

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.     

通过HSQC和1H,13C-COSY叠合增强二维谱分辨率的方法

通常二维谱F₁维分辨率较差,F₂维分辨率较好. 即HSQC实验¹³C维度分辨率较差,¹H维度分辨率较好. 而¹H, ¹³C-COSY实验¹³C维度分辨率较好,¹H维度分辨率较差. 提出一种通过HSQC和¹H, ¹³C-COSY叠合,取较弱的值储存并显示的方法增强分辨率,采用Bruker Topspin软件AU程序实现. 该方法在不明显增加采样时间的情况下,可显著增强分辨率,信噪比也没有降低. 同时抑制了F₁噪声. 处理后,谱图美观清晰.     

Sensitivity-enhanced IPAP experiments for measuring one-bond C–C and C–H residual dipolar couplings in proteins

Sensitivity-enhanced 2D IPAP experiments using the accordion principle for measuring one-bond 13C'-13Calpha and 1Halpha-13Calpha dipolar couplings in proteins are presented. The resolution of the resulting spectra is identical to that of the decoupled HSQC spectra and the sensitivity of the corresponding 1D acquisitions are only slightly lower than those obtained with 3D HNCO and 3D HN(COCA)HA pulse sequences due to an additional delay 2Delta. For cases of limited resolution in the 2D 15N-1HN HSQC spectrum the current pulse sequences can easily be modified into 3D versions by introducing a poorly digitized third dimension, if so desired. The experiments described here are a valuable addition to the suites available for determination of residual dipolar couplings in biological systems.     

Sensitivity-enhanced IPAP experiments for measuring one-bond 13C'-13Calpha and 13Calpha-1Halpha residual dipolar couplings in proteins

Sensitivity-enhanced 2D IPAP experiments using the accordion principle for measuring one-bond 13C'-13Calpha and 1Halpha-13Calpha dipolar couplings in proteins are presented. The resolution of the resulting spectra is identical to that of the decoupled HSQC spectra and the sensitivity of the corresponding 1D acquisitions are only slightly lower than those obtained with 3D HNCO and 3D HN(COCA)HA pulse sequences due to an additional delay 2Delta. For cases of limited resolution in the 2D 15N-1HN HSQC spectrum the current pulse sequences can easily be modified into 3D versions by introducing a poorly digitized third dimension, if so desired. The experiments described here are a valuable addition to the suites available for determination of residual dipolar couplings in biological systems.     

Two-dimensional one pulse MAS of half-integer quadrupolar nuclei

We show that the two-dimensional one pulse (TOP) representation of magic-angle spinning nuclear magnetic resonance data of half-integer quadrupolar nuclei has significant advantages over the conventional one-dimensional spectrum. The TOP spectrum, which correlates NMR frequency to spinning sideband order, provides a rapid determination of the number of sites as well as the size of the their quadrupolar coupling. Additionally, synchronous acquisition spectra of the central and satellite transition resonances can be separated by different projections of the TOP spectrum, with higher resolution spectra often found in the satellite transitions projection. A previously perceived problem of centerband aliasing in TOP can be eliminated with an algorithm that uses larger subspectral widths and the sideband order dimension to distinguish centerbands from sidebands.     

Improving spectral resolution in spatial encoding dimension of single-scan nuclear magnetic resonance 2D spin echo correlated spectroscopy

The spatial encoding technique can be used to accelerate the acquisition of multi-dimensional nuclear magnetic resonance spectra. However, with this technique, we have to make trade-offs between the spectral width and the resolution in the spatial encoding dimension (F1 dimension), resulting in the difficulty of covering large spectral widths while preserving acceptable resolutions for spatial encoding spectra. In this study, a selective shifting method is proposed to overcome the aforementioned drawback. This method is capable of narrowing spectral widths and improving spectral resolutions in spatial encoding dimensions by selectively shifting certain peaks in spectra of the ultrafast version of spin echo correlated spectroscopy (UFSECSY). This method can also serve as a powerful tool to obtain high-resolution correlated spectra in inhomogeneous magnetic fields for its resistance to any inhomogeneity in the F1 dimension inherited from UFSECSY. Theoretical derivations and experiments have been carried out to demonstrate performances of the proposed method. Results show that the spectral width in spatial encoding dimension can be reduced by shortening distances between cross peaks and axial peaks with the proposed method and the expected resolution improvement can be achieved. Finally, the shifting-absent spectrum can be recovered readily by post-processing.     

A new sequence for the MQMAS/HETCOR experiment

Two-dimensional (2D) multiple quantum MAS (magic angle spinning) spectroscopy has been combined with cross-polarisation to obtain a heteronuclear correlation spectrum between a quadrupolar spin-3/2 and a spin-1/2 nucleus. The advantage over the conventional correlation experiment is the increased resolution obtained in the multiple quantum dimension. Pure absorption 2D spectra can be obtained by implementing a zero quantum filter between the evolution of multiple quanta and the subsequent cross-polarisation step. The current experiment shows a considerable improvement in sensitivity compared to a previously introduced sequence.     

The multidimensional filter diagonalization method

The theory and numerical aspects of the recently developed multidimensional version of the filter diagonalization method (FDM) are described in detail. FDM can construct various "ersatz" or "hybrid" spectra from multidimensional time signals. Spectral resolution is not limited by the time-frequency uncertainty principle in each separate frequency dimension, but rather by the total joint information content of the signal, i.e., N(total) = N(1) x N(2) x vertical ellipsis x N(D), where some of the interferometric dimensions do not have to be represented by more than a few (e.g., two) time increments. It is shown that FDM can be used to compute various reduced-dimensionality projections of a high-dimensional spectrum directly, i.e., avoiding construction of the latter. A subsequent paper (J. Magn. Reson. 144, 357-366 (2000)) is concerned with applications of the method to 2D, 3D, and 4D NMR experiments.     

Rapid high-resolution four-dimensional NMR spectroscopy using the filter diagonalization method and its advantages for detailed structural elucidation of oligosaccharides

Four-dimensional nuclear magnetic resonance spectroscopy with high resolution of signals in the indirect dimensions is reported as an implementation of the filter diagonalization method (FDM). Using an oligosaccharide derivatized with 13C-labeled acetyl isotags, a four-dimensional constant-time pulse sequence was tailored for conjoint use with the FDM. Results demonstrate that high resolution in all dimensions can be achieved using a relatively short experimental time period (19 h), even though the spectrum is highly congested in the direct and all three indirect dimensions. The combined use of isotags, constant-time pulse sequences, and FDM permits rapid isolation of sugar ring proton spin systems in multiple dimensions and enables all endocyclic J-couplings to be simply measured, the key goal to assigning sugar stereochemistry and anomeric configuration. A general method for rapid, unambiguous elucidation of spin systems in oligosaccharides has been a long-sought goal of carbohydrate NMR, and isotags combined with the FDM now enable this to be easily performed. Additional general advantages of the FDM program for generating high-resolution 2D slices in any dimension from a 4D spectrum are emphasized.     

Phase-sensitive spectral estimation by the hybrid filter diagonalization method

A more robust way to obtain a high-resolution multidimensional NMR spectrum from limited data sets is described. The Filter Diagonalization Method (FDM) is used to analyze phase-modulated data and cast the spectrum in terms of phase-sensitive Lorentzian "phase-twist" peaks. These spectra are then used to obtain absorption-mode phase-sensitive spectra. In contrast to earlier implementations of multidimensional FDM, the absolute phase of the data need not be known beforehand, and linear phase corrections in each frequency dimension are possible, if they are required. Regularization is employed to improve the conditioning of the linear algebra problems that must be solved to obtain the spectral estimate. While regularization smoothes away noise and small peaks, a hybrid method allows the true noise floor to be correctly represented in the final result. Line shape transformation to a Gaussian-like shape improves the clarity of the spectra, and is achieved by a conventional Lorentzian-to-Gaussian transformation in the time-domain, after inverse Fourier transformation of the FDM spectra. The results obtained highlight the danger of not using proper phase-sensitive line shapes in the spectral estimate. The advantages of the new method for the spectral estimate are the following: (i) the spectrum can be phased by conventional means after it is obtained; (ii) there is a true and accurate noise floor; and (iii) there is some indication of the quality of fit in each local region of the spectrum. The method is illustrated with 2D NMR data for the first time, but is applicable to n-dimensional data without any restriction on the number of time/frequency dimensions.     

基于核磁共振的统计全相关谱在大鼠肾脏组织中的应用

生物组织是基于NMR的代谢组学研究的主要对象之一，广泛应用于分子病理学、毒理学、生物医学等众多领域. 但是，为了保证测定的准确，组织的NMR实验往往需要在较低的温度下和较短时间内完成，以防止由于组织内酶的降解和扩散而导致的某些代谢物质的分析信息被破坏. 统计全相关谱(Statistical Total Correlation Spectroscopy, STOCSY)是依靠一维谱来实现二维谱的一些功能的方法，不需要额外的实验时间，已经被广泛应用于代谢组学研究中. 本文采用STOCSY方法，通过对一系列¹H高分辨魔角旋转谱的统计分析和计算，得到了肾脏组织的准二维相关谱，其中共振峰之间的相关较为准确的反应了物质之间的耦合信息，为物质的归属提供了帮助.     

The Multidimensional Filter Diagonalization Method: II. Application to 2D Projections of 2D, 3D, and 4D NMR Experiments

The theory of the multidimensional filter diagonalization method (FDM) described in the previous paper (V. A. Mandelshtam, 2000, J. Magn. Reson. 144, 343–356 (2000)) is applied to NMR time signals with up to four independent time variables. Direct projections of the multidimensional time signals produce new kinds of 2D spectra. The resolution obtained by FDM can be far superior to that obtained by conventional phase-sensitive FT processing, and correlation peaks in heteronuclear and homonuclear experiments can be condensed to sharp singlets, removing all spin–spin couplings. Examples of singlet-HSQC and singlet-TOCSY spectra show big gains in resolution. It is not necessary to have a finely digitized spectrum, in which the individual multiplet components are resolved, for the methods to work. Examples of FDM spectra, ranging from simple organic molecules and steroids to metalloproteins, are shown.     

Fast high-resolution 2D correlation spectroscopy in inhomogeneous fields via Hadamard intermolecular multiple quantum coherences technique

Recently, a method based on intermolecular multiple quantum coherences (iMQCs) has been proposed to obtain high-resolution 2D COSY spectra in inhomogeneous fields via 3D acquisitions. However, the very long acquisition time prevents its practical application. To overcome this shortage, the Hadamard technique was applied for the iMQC method in this paper. For the new pulse sequence, the direct frequency-domain excitation is used in the first indirect detection dimension, so the 3D acquisition was replaced by an array of 2D acquisitions. The acquisition time can be reduced to 10 min. The resulting spectra retain useful structural information including chemical shifts and multiplet patterns of J coupling even when the inhomogeneous line broadening leads to overlap of neighboring diagonal resonances in the conventional COSY spectrum. The experimental results are consistent with the theoretical predictions and computer simulations. The new sequence may provide a time-efficient way for the studies of chemical solution in inhomogeneous fields.     

Two-dimensional ENDOR-ESEEM correlation spectroscopy

A two-dimensional (2D) experiment that correlates electron-nuclear double resonance (ENDOR) and electron spin-echo envelope modulation (ESEEM) frequencies, useful for unraveling and assigning ENDOR and ESEEM spectra from different paramagnetic centers with overlapping EPR spectra, is presented. The pulse sequence employed is similar to the Davies ENDOR experiment with the exception that the two-pulse echo detection is replaced by a stimulated echo detection in order to enhance the resolution in the ESEEM dimension. The two-dimensional data set is acquired by measuring the ENDOR spectrum as a function of the time interval T between the last two microwave pulses of the stimulated echo detection scheme. This produces a series of ENDOR spectra with amplitudes that are modulated with T. Fourier transformation (FT) with respect to T then generates a 2D spectrum with cross peaks connecting spectral lines of the ESEEM and ENDOR spectra that belong to the same paramagnetic center. Projections along the vertical and horizontal axes give the three-pulse FT-ESEEM and ENDOR spectra, respectively. The feasibility of the experiment was tested by simulating 2D ENDOR-ESEEM correlation spectra of a system consisting of an electron spin (S = (1/2)) coupled to two nuclei (I(1) = I(2) = (1/2)), taking into account experimental conditions such as pulse durations and off-resonance irradiation frequencies. The experiment is demonstrated on a single crystal of Cu(2+) doped l-histidine (Cu-His), containing two symmetrically related Cu(2+) sites that at an arbitrary orientation exhibit overlapping ESEEM and ENDOR spectra. While the ESEEM spectrum is relatively simple and arises primarily from one weakly coupled (14)N, the ENDOR spectrum is very crowded due to contributions from two nonequivalent nitrogens, two chlorides, and a relatively large number of protons. The simple ESEEM projection of the 2D ENDOR-ESEEM correlation spectrum is then used to disentangle the ENDOR spectrum and resolve two sets of lines corresponding to the different sites. Copyright 2000 Academic Press.     

基于温度变量的四维荧光光谱的石油类污染物测定

三维荧光光谱结合多元校正分析对石油类污染物复杂多组分体系测定方法多谱图混叠,且易受到空白荧光和干扰物荧光影响降低了测定准确性。提出在三维荧光光谱中增加一维温度信息构造激发波长-发射波长-温度-样品（EEM-temperature data array）的四维荧光光谱数据阵列,应用四线性成分模型建立高维荧光光谱定性定量分析的方法。实验证明在15～25 ℃温度范围内,矿物油荧光光谱轮廓形状不随温度变化,而其强度随温度线性变化,满足四线性要求,这为构建四维荧光光谱发展高维数据的三阶校正提取更丰富的有效信息提供了可能。三阶校正不仅可以在干扰物共存的情况下对感兴趣组份进行定量测定,即具有“二阶优势”,还具有更高的选择性和灵敏性,可以对高共线性和背景干扰的重叠光谱表现更好的解析能力,即“三阶优势”。对0#柴油、97#汽油和机油为混合油待测组分,腐殖酸为水体干扰组分组成的复杂体系污染油样品为进行实验,得到的三维荧光光谱利用平行因子（PARAFAC）算法和交替惩罚三线性分解（APTLD）算法进行二阶校正分析,将三维荧光光谱在温度方向上堆叠构成增加温度维度的四维荧光光谱数阵,并将其利用四维平行因子算法（4-PARAFAC）和交替惩罚四线性分解（APQLD）算法进行三阶校正分析,比较,0#柴油、97#汽油和机油的预测结果表明增加了影响荧光光谱的温度因素构造的四维荧光光谱提高了有效信息提取能力,四维荧光光谱结合高阶校正算法能提高油种光谱识别和浓度精确检测,较传统的三维荧光光谱分析提高了回收率（recovery rate）和预测均方根误差（root mean square error of prediction,RMSEP）,有利于石油类污染物的有效,准确,实时,绿色环保检测。同时指出了4-PARAFAC和APQLD算法各自的特点及其不同适用环境,为油类污染物检测具体情况提供算法选择依据。引入温度参量的四维荧光光谱结合三阶校正算法的检测技术较三维荧光光谱技术,在组分光谱定性分辨和浓度定量检测方面能对复杂体系油类污染物实现快速有效,绿色无污染地检测,实现“数学分离”更有效代替“化学分离”。     

Indirect covariance NMR spectroscopy of through-bond homo-nuclear correlations for quadrupolar nuclei in solids under high-resolution

Indirect covariance NMR spectroscopy is demonstrated in solids, and we show that it can be used to obtain through-bond 2D homo-nuclear correlation spectra for quadrupolar nuclei under high-resolution. These spectra, generated with indirect covariance from a hetero-nuclear correlation spectrum, are equivalent to those recorded with the through-bond homo-nuclear hetero-nuclear single-quantum correlation (H-HSQC) method very recently proposed. However, the indirect covariance method can save a lot of experiment time, compared to the H-HSQC experiments, which allows introducing a high-resolution quadrupolar filter, thus providing a much better resolution, even on medium-field spectrometers. The covariance concept can be used to generate many different "indirectly-detected" high-resolution homo-nuclear correlation spectra with through-space or through-bond correlations for spin 1/2 or quadrupolar nuclei. We also propose a simple method that decreases the noise in all (direct or indirect) covariance methods.