Effects of various types of molecular dynamics on 1D and 2D (2)H NMR studied by random walk simulations

By carrying out random walk simulations we systematically study the effects of various types of complex molecular dynamics on (2)H NMR experiments in solids. More precisely, we calculate one-dimensional (1D) (2)H NMR spectra and the results of two dimensional (2D) (2)H NMR experiments in time domain, taking into account isotropic as well as highly restricted motions which involve rotational jumps about different finite angles. Although the dynamical models are chosen to mimic the primary and secondary relaxation in supercooled liquids and glasses, we do not intend to describe experimental results quantitatively but rather to show general effects appearing for complex reorientations. We carefully investigate whether 2D (2)H NMR in time domain, which was originally designed to measure correlation times of ultraslow motions (tau >/= 1 ms), can be used to obtain shorter tau, too. It is demonstrated that an extension of the time window to tau >/= 10 &mgr;s is possible when dealing with exponential relaxation, but that it will fail if there is a distribution of correlation times G(lgtau). Vice versa, we show that 1D (2)H NMR spectra, usually recorded to look at dynamics with tau in the microsecond regime, are also applicable for studying ultraslow motions provided that the loss of correlation is achieved step by step. Therefore, it is useful to carry out 1D and 2D NMR experiments simultaneously in order to reveal the mechanism of complex molecular motions. In addition, we demonstrate that highly restricted dynamics can be clearly observed in 1D spectra and in 2D NMR in time domain if long solid-echo delays and large evolution times are applied, respectively. Finally, unexpected observations are described which appear in the latter experiment when considering very broad distributions G(lgtau). Because of these effects, time scale and geometry of a considered motion cannot be extracted from a straightforward analysis of experimental results. Copyright 2000 Academic Press.     

Deuterium NMR studies of guest motions in urea inclusion compounds of 1,6-dibromohexane with analytical evaluation of spectra in the fast motion limit

²H NMR (nuclear magnetic resonance) spectroscopy, in conjunction with X-ray diffraction experiments, was used to characterize the guest motions of 1,6-dibromohexane in its urea inclusion compound. These motions are characterized by alkyl chain jumps between two conformations, each approximately gauche to the terminal bromines, which remain stationary. In this distorted urea channel, one conformer is heavily preferred, but thermally activated population of the unfavorable conformer leads to reversible, temperature-dependent changes in the unit cell parameters. Although rapid motions of the guest chain give rise to ambiguities in the interpretation of the²H NMR spectra, fortuitous temperature-independent spectral features of guests containing deuterium at the α, β and γ positions indicate that the guest motion resembles a two-site jump with unequal probabilities. Analytical lineshape calculations on the three sets of²H NMR spectra indicate a single jump mechanism in which the range of jump angles is narrowly prescribed. This NMR model provided a starting point for successful solution and refinement of the crystal structures at 213 and 298 K, which had been complicated by motional disorder.     

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。     

二维核磁共振数据处理与显示系统

详细介绍了我们在386微机上建立的二维NMR数据处理与分析系统,该系统采用菜单驱动方式,具有良好的用户界面,可进行标准的常规二维NMR数据处理与分析,数据处理结果可由标准设备输出或者以文件方式存储以便其它应用软件处理,该系统的建立可使通用微计算机成为有效的核磁共振数据处理站。     

The sites and dynamics of p-xylene guest molecules in Dianin’s inclusion compound; a deuteron NMR study

Single crystals of Dianin’s inclusion compound with methyl and ring deuterated p-xylene guest molecules were grown and studied by FT deuteron NMR. The spectra from the deuterated methyl groups reveal that these groups reorient rapidly down to 12K; thereafter they enter into the tunneling regime. The rings of the p-xylene guests become motionless whenT reaches 110K. By measuring the orientation dependence of the quadrupole splittings, determining from these data the quadrupole coupling tensors of the ring deuterons and relating these tensors to the C-D bond directions we infer the sites of the p-xylene guests in the cages of Dianin’s inclusion compound. We find two sets of independent sites. Each contains three C₃ related individual sites. In each set the population of one of the sites is strongly depleted. The only large-anlge molecular motions are 180° rotational jumps about the long molecular axes. From measurements ofT ₁ we conclude that these jumps are thermally activated,τ ₀ = 5·10^?14 s, ΔE=20 kJ/mol. Additional motions are rapid librations, also about the long molecular axes. Their amplitude increases with increasing temperature, at 300 K it reaches 20°. With 2D-exchange spectra we demonstrate that a p-xylene guest cannot change its site on a timescale of 100 ms and a tempering experiment suggests that this is true on a timescale of several days even atT=371 K.     

The equilibrium unfolding of MerP characterized by multivariate analysis of 2D NMR data

A general problem when analysing NMR spectra that reflect variations in the environment of target molecules is that different resonances are affected to various extents. Often a few resonances that display the largest frequency changes are selected as probes to reflect the examined variation, especially in the case, where the NMR spectra contain numerous resonances. Such a selection is dependent on more or less intuitive judgements and relying on the observed spectral variation being primarily caused by changes in the NMR sample. Second, recording changes observed for a few (albeit significant) resonances is inevitably accompanied by not using all available information in the analysis. Likewise, the commonly used chemical shift mapping (CSM) [Biochemistry 39 (2000) 26, Biochemistry 39 (2000) 12595] constitutes a loss of information since the total variation in the data is not retained in the projection into this single variable. Here, we describe a method for subjecting 2D NMR time-domain data to multivariate analysis and illustrate it with an analysis of multiple NMR experiments recorded at various folding conditions for the protein MerP. The calculated principal components provide an unbiased model of variations in the NMR spectra and they can consequently be processed as NMR data, and all the changes as reflected in the principal components are thereby made available for visual inspection in one single NMR spectrum. This approach is much less laborious than consideration of large numbers of individual spectra, and it greatly increases the interpretative power of the analysis.     

代谢组学数据分析方法及在糖尿病研究中的应用

对NMR波谱数据的统计分析是基于NMR代谢组学研究的关键问题之一. 鉴于NMR波谱信号可以近似为样品中各种成分谱信号的线性叠加,本文将非负矩阵分解(NMF)方法引入基于NMR代谢组学的数据处理中,并与代谢组学中常用的统计方法--主成分分析(PCA)进行比较. 通过NMF和PCA两种方法对健康志愿者与2型糖尿患者血液和尿液的NMR谱图的统计分析,对所获取的特征代谢物进行比较和验证,并探讨了PCA方法可能存在的不足之处及其原因;阐明了NMF方法是基于NMR的代谢组学研究中较理想的数据分析方法. 最后,讨论了基于NMR代谢组学在糖尿病研究中的前景.     

Solid-State NMR Studies on the Guest Ordering and Dynamics in α,ω-Dibromoalkane/Urea Inclusion Compounds

Solid-state nuclear magnetic resonance (NMR) spectroscopy is utilized to study the molecular behavior of 1,10-dibromodecane and 1,11-dibromoundecane in their urea inclusion compounds. The guest dynamics and conformational order are explored by ¹³C cross polarization magic-angle spinning (CP/MAS) and ¹H MAS NMR spectroscopy which confirm an all-trans conformation of the guest chains. Dynamic ²H NMR experiments are carried out on two guest molecules selectively deuterated at both end groups. A quantitative analysis of the experimental data, obtained from variable-temperature line shape, spin–spin and spin–lattice relaxation measurements, shows that both guest molecules undergo similar motions within the investigated temperature range between 100 and 298 K. The combination of nondegenerate 6-site (or 3-site) rotational jumps and small-angle overall chain wobbling provides an appropriate motional model for the guest motions in these compounds. It is found that the populations of the jump sites exhibit a characteristic temperature dependence, although a discontinuity is missing at the solid–solid phase transition. The same holds for the guest motions which also remain unaffected by the change of the urea lattice structure. Rather, a discontinuity of the guest dynamics at about 30 and 10 degrees above the corresponding solid–solid phase transition is observed for 1,10-dibromodecane and 1,11-dibromoundecane in urea, respectively. Likewise, there is no clear evidence for an odd–even effect due to the change of the guest chain length on the molecular properties of the present inclusion compounds. As a general result, it is concluded that the intermolecular interactions in the present materials are stronger than in n-alkane/urea inclusion compounds. Authors' address: Klaus Müller, Institut für Physikalische Chemie, Universit?t Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany     

Deuteron NMR spectra of ammonium ion isotopomers at low temperatures

Partially deuterated ammonium compounds contain ammonium ion isotopomers with relative abundances given by the binomial distribution of protons and deuterons. All isotopomers with deuterons contribute characteristic deuteron NMR spectra at 5K. Experimental NMR spectra were separated and respective contributions of isotopomers were determined. The derived contributions agree with expected values for a given deuteration in the case of ammonium hexafluorophosphate. In ammonium hexachlorotellurate both NH2D2+ and about 50% of NH3D+ ions are rigid, while the remaining NH3D+ perform limited jumps. NHD3+ and ND4+ ions undergo tunnelling rotation, NH3D+ ions perform either jumps about C2 axis or limited jumps, but some stay rigid in ammonium hexachlorostannate. NH2D2+, NHD 3+ and ND4+ undergo rotational tunnelling. In the case of ammonium perchlorate, the NH3D+ ions perform either jumps about C3 axis or limited jumps whilst some remain rigid. Very low values of activation energies were derived for all spectral components from the temperature dependence of their spectra, up to about 20K, which indicates an incoherent tunnelling nature of the observed dynamic processes. The diverse mobility of NH3D+ ions appears to be the most interesting and new feature.     

An NMR investigation using liquid crystalline solvents of the conformations of hindered anisoles,thioanisole and selenoanisole

Dipolar couplings obtained previously by analyzing the proton NMR spectra of samples dissolved in nematic solvents of thioanisole and 4-chloroseleno anisole were interpreted in terms of jumps between symmetry-related forms for the motion about the ring-X and X-CH₃ bonds. Two models were found to fit the data: jumps between four positions of minimum energy having the X-CH₃ bond rotated through ? about 40° out of the ring plane, or jumps between planar and orthogonal structures with unequal weightings. The proton and fluorine dipolar couplings for 2,3,5,6-tetrafluoro anisole were interpreted previously in terms of free rotation about the ring—O bond, but with the assumption that the orientational order parameters are independent of the rotational angle ?. The data for all three molecules is re-interpreted here, plus new data for thioanisole dissolved in a second nematic solvent, using a theoretical model which allows for the dependence of the orientational ordering on ?, thus permitting continuous potentials to be tested, and which also involves fewer variable parameters. This constraining of the model leads to a rejection of the non-planar positions for the minimum in the rotational potential, but leaves two other possible solutions: a two-fold continuous potential for rotation about the ring-X bond with a minimum when the C-X bond is in the ring plane and a maximum when it is at 90°, or a four fold continuous potential with a secondary minimum at 90°. In the case of the tetrafluoro anisole the two-fold potential corresponds to virtually free rotation.     

A new approach to visualizing spectral density functions and deriving motional correlation time distributions: applications to an alpha-helix-forming peptide and to a well-folded protein

A new approach to visualizing spectral densities and analyzing NMR relaxation data has been developed. By plotting the spectral density function, J(omega), as F(omega)=2 omega J(omega) on the log-log scale, the distribution of motional correlation times can be easily visualized. F(omega) is calculated from experimental data using a multi-Lorentzian expansion that is insensitive to the number of Lorentzians used and allows contributions from overall tumbling and internal motions to be separated without explicitly determining values for correlation times and their weighting coefficients. To demonstrate the approach, (15)N and (13)C NMR relaxation data have been analyzed for backbone NH and C(alpha)H groups in an alpha-helix-forming peptide 17mer and in a well-folded 138-residue protein, and the functions F(omega) have been calculated and deconvoluted for contributions from overall tumbling and internal motions. Overall tumbling correlation time distribution maxima yield essentially the same overall correlation times obtained using the Lipari-Szabo model and other standard NMR relaxation data analyses. Internal motional correlational times for NH and C(alpha)H bond motions fall in the range from 100 ps to about 1 ns. Slower overall molecular tumbling leads to better separation of internal motional correlation time distributions from those of overall tumbling. The usefulness of the approach rests in its ability to visualize spectral densities and to define and separate frequency distributions for molecular motions.     

Solid state water motions revealed by deuterium relaxation in 2H2O-synthesized kanemite and 2H2O-hydrated Na+-zeolite A

Deuterium NMR relaxation experiments, low temperature deuterium NMR lineshape analysis, and FTIR spectra are consistent with a new model for solid state jump dynamics of water in (2)H(2)O-synthesized kanemite and (2)H(2)O-hydrated Na(+)-Zeolite A. Exchange occurs between two populations of water: one in which water molecules are directly coordinated to sodium ions and experience C(2) symmetry jumps of their OH bonds, and a population of interstitial water molecules outside the sodium ion coordination sphere that experience tetrahedral jumps of their OH bonds. For both samples the C(2) jump rate is much faster than the tetrahedral jump rate. (2)H NMR relaxation experiments match well with the fast exchange regime of the model over a wide range of temperatures, including room temperature and above. For hydrated Zeolite A, the kinetic activation parameters for the tetrahedral and C(2) symmetry jumps are Delta H tet++=+17 kJ/mol, Delta S tet++=-109 J/(mol K), Delta H C2++=+19 kJ/mol, and Delta S C2++=-20 J/(mol K). For kanemite, Delta H tet++ =+23 kJ/mol, Delta S tet++=-69 J/(mol K), Delta H C2++ =+23 kJ/mol, and Delta S C2++ =-11 J/(mol K).     

Model-Free Analysis of Mixtures by NMR Using Blind Source Separation

The concept of blind source separation is described and examples of its use in 1D and 2D NMR spectroscopy are presented. The goal of this data processing method is to extract the spectra of components molecules when only mixtures are available.     

EASY-GOING deconvolution: combining accurate simulation and evolutionary algorithms for fast deconvolution of solid-state quadrupolar NMR spectra

A fast and accurate fit program is presented for deconvolution of one-dimensional solid-state quadrupolar NMR spectra of powdered materials. Computational costs of the synthesis of theoretical spectra are reduced by the use of libraries containing simulated time/frequency domain data. These libraries are calculated once and with the use of second-party simulation software readily available in the NMR community, to ensure a maximum flexibility and accuracy with respect to experimental conditions. EASY-GOING deconvolution (EGdeconv) is equipped with evolutionary algorithms that provide robust many-parameter fitting and offers efficient parallellised computing. The program supports quantification of relative chemical site abundances and (dis)order in the solid-state by incorporation of (extended) Czjzek and order parameter models. To illustrate EGdeconv's current capabilities, we provide three case studies. Given the program's simple concept it allows a straightforward extension to include other NMR interactions. The program is available as is for 64-bit Linux operating systems.     

Dynamics of the biopolymers in articular cartilage studied by magic angle spinning NMR

To understand the viscoelastic properties of cartilage tissue and for the development of tissue-engineered cartilage, we have studied the physicochemical properties of bovine nasal and pig articular cartilage by¹³C nuclear magnetic resonance (NMR) methods. The major macromolecular components of cartilage can be investigated individually by applying¹³C high-resolution (HR) NMR with scalar decoupling (for the polysaccharide component) and solid-state NMR with dipolar decoupling (for the collagen component). Partially resolved NMR spectra of the cartilage polysaccharides can be obtained by HR¹³C NMR indicating that these polysaccharides are highly mobile. Resonance lines have been assigned to chondroitin sulfate, the most mobile component of cartilage. To characterize time scales of molecular motions, we have measuredT ₁ andT ₂ relaxation times as a function of temperature and analyzed these data by means of a broad distribution of molecular correlation times. Typical correlation times for the large amplitude motions of chondroitin sulfate are of the order of 0.1–10 ns. For the detection and dynamical characterization of the cartilage collagen cross-polarization magic angle spinning (CP MAS) and high-power decoupling are indispensable.¹³C CP MAS spectra of cartilage are dominated by resonances from rigid collagen, while only low-intensity signals from the polysaccharides are observed. The good sensitivity at a magnetic field strength of 17.6 T allows the site-specific investigation of cartilage collagen dynamics by two-dimensional NMR methods. The cartilage collagen is essentially rigid with low-amplitude segmental motions on the fast time scale. Considering the high water content of cartilage and the almost isotropic mobility of the chondroitin sulfate molecules it is remarkable how little this affects the collagen dynamics. The dynamics of cartilage macromolecules is broadly distributed from almost completely rigid to highly mobile, which lends cartilage its mechanical strength and shock-absorbing properties.     

Magic-Angle Spinning NMR and Molecular Mobility in Heterogeneous Systems

Magic-angle sample spinning (MAS) nuclear magnetic resonance (NMR) measurements are treated for heterogeneous systems with nanometer dimensions. An appreciable line narrowing in the MAS NMR spectra of the embedded molecules may be achieved also in the cases when the molecules still possess an appreciable local mobility. It appears that the MAS frequencies are of comparable order of magnitude as the frequencies which characterize the random molecular motional processes and which compete with MAS. It will be shown that this behavior may occur if inhomogeneous local magnetic fields due to susceptibility effects have a dominating influence on the widths and shapes of the resonance NMR lines. Properties of these local fields are described. Spectra simulations are carried for molecules embedded in these heterogeneous systems when the coherent averaging by MAS is superimposed by random local motions. This situation may occur for molecules contained in nanoporous solids and also for heterogeneous systems like membranes and biological tissues with flexible components like water, lipids, and small peptides. Several examples are treated which reveal advantages and limitations of these experiments and their theoretical interpretation.     

Quantitative analysis of NMR spectra with chemometrics

The number of applications of chemometrics to series of NMR spectra is rapidly increasing due to an emerging interest for quantitative NMR spectroscopy e.g. in the pharmaceutical and food industries. This paper gives an analysis of advantages and limitations of applying the two most common chemometric procedures, Principal Component Analysis (PCA) and Multivariate Curve Resolution (MCR), to a designed set of 231 simple alcohol mixture (propanol, butanol and pentanol) (1)H 400 MHz spectra. The study clearly demonstrates that the major advantage of chemometrics is the visualisation of larger data structures which adds a new exploratory dimension to NMR research. While robustness and powerful data visualisation and exploration are the main qualities of the PCA method, the study demonstrates that the bilinear MCR method is an even more powerful method for resolving pure component NMR spectra from mixtures when certain conditions are met.     

Comparative study of motions in dimethylsulfone by noise excitation and solid echo spectroscopy

2H NMR spectra of dimethylsulfone were measured with noise excitation and solid echo NMR spectroscopy in the temperature range from 125 to 355 K. Besides the known fact that broad NMR spectra can be measured with both methods, in comparable times it is shown that for noise excitation, the signal loss is negligible compared to echo spectroscopy in the regime when the correlation times of the motions are of the order of magnitude of the echo pulse spacing. For simulating the dynamic NMR spectra acquired with noise excitation, only the motional process must be taken into account and relaxation can be neglected. Furthermore, the problem of restricted acquisition bandwidth in noise NMR spectroscopy is discussed.