Computation of relaxation matrix elements from incomplete NOESY data sets

Summary The structural determination of biological molecules in solution by NMR relies on the determination of a set of interatomic distances obtained by measurement of intramolecular nuclear Overhauser effects (NOE). It is shown in this paper that it is possible to obtain the accurate relaxation rate (and hence the interatomic distance) from the direct measurement of a single NOE signal. The precise analysis of a NOESY peak evolution with respect to the mixing time allows the evaluation of the relaxation parameters for the pair of spins under consideration. This is done without any assumption on the relaxation of unmeasured spins, or on the movement of the molecule. The theoretical basis of this method is presented. In order to evaluate the proposed method, a simulated case on the protein BPTI is studied, which shows that the method performs very well even in the case of noisy data sets.     

Conformational analysis of the Sda determinant-containing tetrasaccharide and two mimics in aqueous solution by using 1H NMR ROESY spectroscopy in combination with MD simulations

The conformational behaviour of the spacer-linked synthetic Sd^a tetrasaccharide -d-GalpNAc-(14)-[-Neu5Ac-(23)]--d-Galp-(14)--d-GlcpNAc-(1O)(CH₂)₅NH₂ (1) and the two mimics -d-Galp-(14)-[-Neu5Ac-(23)]--d-Galp-(14)--d-GlcpNAc-(1O)(CH₂)₅NH₂ (2) and -d-GlcpNAc-(14)-[-Neu5Ac-(23)]--d-Galp-(14)--d-GlcpNAc-(1O)(CH₂)₅NH₂ (3) were investigated by ¹H NMR spectroscopy in combination with molecular dynamics (MD) simulations in water. Experimental 2D ¹H ROESY cross-peak intensities (ROEs) of the tetrasaccharides were compared with calculated ROEs derived from MD trajectories using the CROSREL program. Analysis of these data indicated that the oligosaccharidic skeletons of the compounds 1–3 are rather rigid, especially the -d-Hex(NAc)-(14)-[-Neu5Ac-(23)]--d-Galp fragments. The - Neu5-Ac-(23)--d-Galp linkage occurred in two different energy minima in the three-dimensional structure of the compounds 1–3 in aqueous solution. Experimental data and dynamics simulations supported the finding that the higher energy rotamer (CHEAT forcefield) was abundant in compounds 1 and 3 due to the existence of a hydrogen bond between the carboxyl group of the sialic acid and the acetamido group of the terminal monosaccharide (GalNAc or GlcNAc) unit. The conformational similarity between 1 and 3 leads to the suggestion that also their activities will be alike.     

Solution conformation and dynamics of a tetrasaccharide related to the LewisX antigen deduced by NMR relaxation measurements

¹H-NMR cross-relaxation rates and nonselectivelongitudinal relaxation times have been obtained at two magnetic fields (7.0and 11.8 T) and at a variety of temperatures for the branchedtetrasaccharide methyl3-O--N-acetyl-galactosaminyl--galactopyranosyl-(14)[3-O--fucosyl]-glucopyranoside (1), an inhibitor of astrocyte growth. Inaddition, ¹³C-NMR relaxation data have also been recorded atboth fields. The ¹H-NMR relaxation data have been interpretedusing different motional models to obtain proton–proton correlationtimes. The results indicate that the GalNAc and Fuc rings display moreextensive local motion than the two inner Glc and Gal moieties, since thosepresent significantly shorter local correlation times. The¹³C-NMR relaxation parameters have been interpreted in termsof the Lipari–Szabo model-free approach. Thus, order parameters andinternal motion correlation times have been deduced. As obtained for the¹H-NMR relaxation data, the two outer residues possess smallerorder parameters than the two inner rings. Internal correlation times are inthe order of 100 ps. The hydroxymethyl groups have also different behaviour,with the exocyclic carbon on the glucopyranoside unit showing the highestS². Molecular dynamics simulations using a solvated systemhave also been performed and internal motion correlation functions have beendeduced from these calculations. Order parameters and interproton distanceshave been compared to those inferred from the NMR measurements. The obtainedresults are in fair agreement with the experimental data.     

Conformational analysis of two xylose-containing N-glycans in aqueous solution by using 1H NMR ROESY and NOESY spectroscopy in combination with MD simulations

The conformational behavior of the synthetic hexa- and heptasaccharide methyl beta-glycosides alpha-D-Manp-(1 --> 6)-[alpha-D-Manp-(1 --> 3)-][beta-D-Xylp-(1 --> 2)-]beta-D-Manp-(1 --> 4)-beta-D-GlcpNAc-(1 --> 4)-beta-D-GlcpNAc-(1 --> OMe and alpha-D-Manp-(1 --> 6)-[alpha-D-Manp-(1 --> 3)-][beta-D-Xylp-(1 --> 2)-]beta-D-Manp-(1 --> 4)-beta-D-GlcpNAc-(1 --> 4)-[alpha-L-Fucp-(1 --> 6)-]beta-D-GlcpNAc-(1 --> OMe, representing the xylosylated and the xylosylated alpha-(1 --> 6)-fucosylated core structures of N-glycans in alpha(D)-hemocyanin of the snail Helix pomatia, respectively, were investigated by 1H NMR spectroscopy in combination with molecular dynamics (MD) simulations in water. 1H and 13C chemical shifts of the oligosaccharides were assigned using 1H-(1)H COSY, TOCSY, and NOESY, and 1H-(13)C HMQC techniques. Experimental 2D 1H cross-peak intensities from one series of NOESY and one series of ROESY experiments of the two oligosaccharides were compared with calculated values derived from MD trajectories using the CROSREL program, yielding information about the conformation of each glycosidic linkage of the methyl glycosides. The flexibility of the linkages was described by generalized order parameters and internal rotation correlation times. Analysis of the data indicated that several conformations are likely to exist for the alpha-D-Man-(1 --> 6)-beta-D-Man, the alpha-L-Fuc-(1 --> 6)-beta-D-GlcNAc, and the alpha-D-Man-(1 --> 3)-beta-D-Man linkage, whereas the beta-D-Xyl-(1 --> 2)-beta-D-Man-(1 --> 4)-beta-D-GlcNAc-(1 --> 4)-beta-D-GlcNAc fragment occurs in one rigid conformation. No significant differences were found between the corresponding structural elements in both methyl glycosides. NOESY and ROESY experiments proved to be suitable for providing the experimental data required, however, due to more overlap within the ROESY spectra, reducing the accuracy of the analysis, NOESY spectral analysis is preferred.     

Conformational analysis of an EP24.15 inhibitor by NMR and molecular modelling

Summary The enzyme thimet oligopeptidase (EC3.4.24.15, EP24.15) is responsible for the hydrolysis of a number of neuropeptides. Despite much research examining its substrate specificity, little is known about the conformational requirements of its active site. We have used 1D¹H and 2D TOCSY NMR experiments to assign the proton resonances of the EP24.15 inhibitor,N-[1-(R, S)-carboxy-3-phenylpropyl]-Ala-Ala-Tyr-p-aminobenzoate (cFP), and 2D ROESY NMR to investigate whether cFP exhibits any conformational preferences in CD₃OD and in aqueous CD₃OD. Molecular modelling of charged cFP in the gaseous phase generated a number of conformations that were consistent with the NMR data obtained in CD₃OD. Analogous modelling on the uncharged cFP did not result in conformations consistent with any of the NMR data, but did suggest that, under non-polar conditions, cFP could adopt a hairpin conformation which would allow simultaneous coordination of the two carboxyl groups of cFP to the zinc ion in the active site of EP24.15.     

Two-dimensional rotating-frame Overhauser spectroscopy (ROESY) and (13)C NMR study of the interactions between maltodextrin and an anionic surfactant

Rotational frame nuclear Overhauser effect spectroscopy (ROESY) and (13)C NMR measurements were carried out to study the molecular interaction between maltodextrin, a digestive byproduct of starch, and an anionic surfactant. Significant differences in chemical shifts were observed when sodium dodecyl sulfate (SDS) was introduced into the maltodextrin (DE 10) solutions. (13)C NMR measurement indicated that there were downfield shifts and broadening of peaks, especially in the region of 75-81 and 100-103 ppm, which were assigned to carbons 1 and 4 of the d-glucopyranose residues of maltodextrin, respectively. ROESY spectra indicated cross-peaks between the SDS and maltodextrin protons. These peaks can arise only in the case of the designated SDS protons and maltodextrin protons being less than 0.5 nm apart for a substantial period of time. The most intense cross-peaks are those between the central CH(2) protons of SDS near 1.2 ppm and the maltodextrin protons ranging from 3.5 to 3.9 ppm. The SDS-H3 CH(2) protons were resolved from the bulk of the SDS protons, with peaks and shoulders at 1.25 ppm, which indicated an especially strong interaction of the SDS hydrophobic tail with MD6 and some less intense interactions with MD2, 4, and 5.     

Larmor frequency selective model free analysis of protein NMR relaxation

Summary The Lipari-Szabo dynamical formalism is extended by setting the time constants of the Lorentzian terms to and . This analysis is compared to the earlier proposed three-parameter extended model free formalism with regard to the range of equivalence and the advantages of the simplified two-parameter (S _inff ^sup2 ,S _infH ^sup2 ) and (S _inff ^sup2 ,S _infN ^sup2 ) representations. Spectral density components are calculated and compared to those obtained from the spectral density analysis formalism. Protein relaxation data, commonly analyzed in terms of the two-parameter representation, may correspond to a dynamically heterogeneous behaviour that is more appropriately represented in terms of a fast limit order parameter and a second, lower frequency order parameter.     

Complete relaxation matrix refinement of NMR structures of proteins using analytically calculated dihedral angle derivatives of NOE intensities

Summary A new method for refining three-dimensional (3D) NMR structures of proteins is described, which takes account of the complete relaxation pathways. Derivatives of the NOE intensities with respect to the dihedral angles are analytically calculated, and efficiently evaluated with the use of a filter technique for identifying the dominant terms of these derivatives. This new method was implemented in the distance geometry program DIANA. As an initial test, we refined 30 rigid distorted helical structures, using a simulated data set of NOE distance constraints for a rigid standard -helix. The final root-mean-square deviations of the refined structures relative to the standard helix were less than 0.1 Å, and the R-factors dropped from values between 7% and 32% to values of less than 0.5% in all cases, which compares favorably with the results from distance geometry calculations. In particular, because spin diffusion was not explicitly considered in the evaluation of exact¹H–¹H distances corresponding to the simulated NOE intensities, a group of nearly identical distance geometry structures was obtained which had about 0.5 Å root-mean-square deviation from the standard -helix. Further test calculations using an experimental NOE data set recorded for the protein trypsin inhibitor K showed that the complete relaxation matrix refinement procedure in the DIANA program is functional also with systems of practical interest.Abbreviations RMSD root-mean-square deviation - NOE nuclear Overhauser enhancement - NOESY 2-dimensional nuclear Overhauser enhancement spectroscopy - CPU central processing unit     

Investigations of peptide hydration using NMR and molecular dynamics simulations: A study of effects of water on the conformation and dynamics of antamanide

Summary The influence of water binding on the conformational dynamics of the cyclic decapeptide antamanide dissolved in the model lipophilic environment chloroform is investigated by NMR relaxation measurements. The water-peptide complex has a lifetime of 35 s at 250 K, which is longer than typical lifetimes of water-peptide complexes reported in aqueous solution. In addition, there is a rapid intracomplex mobility that probably involves librational motions of the bound water or water molecules hopping between different binding sites. Water binding restricts the flexibility of antamanide. The experimental findings are compared with GROMOS molecular dynamics simulations of antamanide with up to eight bound water molecules. Within the simulation time of 600 ps, no water molecule leaves the complex. Additionally, the simulations show a reduced flexibility for the complex in comparison with uncomplexed antamanide. Thus, there is a qualitative agreement between the experimental NMR results and the computer simulations.     

Full Length Vpu from HIV-1: Combining Molecular Dynamics Simulations with NMR Spectroscopy

Abstract

Based on structures made available by solution NMR, molecular models of the protein Vpu from HIV-1 were built and refined by 6 ns MD simulations in a fully hydrated lipid bilayer. Vpu is an 81 amino acid type I integral membrane protein encoded by the human immunodeficiency virus type-1 (HIV-1) and closely related simian immunodeficiency viruses (SIVs). Its role is to amplify viral release. Upon phosphorylation, the cytoplasmic domain adopts a more compact shape with helices 2 and 3 becoming almost parallel to each other. A loss of helicity for several residues belonging to the helices adjacent to both ends of the loop region containing serines 53 and 57 is observed. A fourth helix, present in one of the NMR-based structures of the cytoplasmic domain and located near the C-terminus, is lost upon phosphorylation.     

Conformational analysis of an EP24.15 inhibitor by NMR and molecular modelling

The enzyme thimet oligopeptidase (EC3.4.24.15, EP24.15) is responsible for the hydrolysis of a number of neuropeptides. Despite much research examining its substrate specificity, little is known about the conformational requirements of its active site. We have used 1D ¹H and 2D TOCSY NMR experiments to assign the proton resonances of the EP24.15 inhibitor, N-[1-(R,S)-carboxy-3-phenylpropyl]-Ala-Ala-Tyr-p-aminobenzoate (cFP), and 2D ROESY NMR to investigate whether cFP exhibits any conformational preferences in CD₃OD and in aqueous CD₃OD. Molecular modelling of charged cFP in the gaseous phase generated a number of conformations that were consistent with the NMR data obtained in CD₃OD. Analogous modelling on the uncharged cFP did not result in conformations consistent with any of the NMR data, but did suggest that, under non-polar conditions, cFP could adopt a hairpin conformation which would allow simultaneous coordination of the two carboxyl groups of cFP to the zinc ion in the active site of EP24.15.     

Conformational analysis of an anti-androgenic, (E,E)-8-hydroxygermacrene B,using NOESY and dynamic NMR spectroscopy

(E,E)-8-Hydroxygermacrene B was prepared by ketone reduction of germacrone, a naturally occurring compound from Curcuma aeruginosa Roxb. with NaBH₄ at low temperature (4 °C). This compound showed remarkable in vitro anti-androgenic activity (IC₅₀ 0.15 ± 0.022 mM) applicable to male baldness treatments. NMR analysis at −50 °C indicated that there were four conformational isomers of (E,E)-8-hydroxygermacrene B in a ratio of 48:40:8:4. The major conformers were assigned by ¹H NMR and 2D-NOESY NMR spectroscopy as having methyl groups at C-10 and C-4 in up–down (UD) orientations (48% predominance) and UU (40%). ¹H NMR spectra implied another two minor conformers with these methyls having DU (8%) and DD (4%) orientations.     

MUNIN: Application of three-way decomposition to the analysis of heteronuclear NMR relaxation data**

MUNIN (Multidimensional NMR Spectra Interpretation), a recently introduced approach exploiting the mathematical concept of three-way decomposition, is proposed for separation and quantitative relaxation measurements of strongly overlapped resonances in sets of heteronuclear two-dimensional spectra that result from typical relaxation experiments. The approach is general and may also be applied to sets of two-dimensional spectra with arbitrary modulation along the third dimension (e.g., J-coupling, diffusion). Here, the method is applied for the analysis of ¹⁵N rotating frame relaxation data.     

Internal dynamics of d(CGCAAATTTGCG)2: a comparison of NMR relaxation measurements with a molecular dynamics simulation

We report the analysis of a 250 ps molecular dynamics simulation of the dodecamer d(CGCAAATTT-GCG)₂ immersed in a rectangular box of 3469 water molecules with 22 Na⁺ counterions. The internal dynamics of the molecule were investigated by studying the relevant autocorrelation functions related to the ¹³C-NMR relaxation parameters of the C1′-H1′ bonds of the sugar rings. The calculated effective correlation times τ _e (∼13 ps) and the order parameter S² (∼0.82) of the Lipari and Szabo formalism (Lipari and Szabo 1982a, b) are in satisfactory agreement with those determined previously by NMR (Gaudin et al. 1995, 1996). ¹H-¹H NOE buildups have also been measured experimentally and agree with those computed from the simulation. These results validate the simulation, and a more detailed analysis of the internal dynamics of the dodecamer was undertaken. Analysis of the distributions and of the autocorrelation functions of the glycosidic angle flucuations χ shows that the rotational motion of the sugar rings about their glycosidic bond conforms to a restricted diffusion mechanism. The amplitude of the motions and the diffusion constant are 20° and 17.10⁹ rad²s^–1 respectively. These values are in good agreement with ¹³C NMR data. Furthermore the simulation allows us to rule out another model also consistent with the experiment, consisting of a two-state jump between a syn and an anti conformation. Received: 19 November 1996 / Accepted: 17 March 1997     

基于修正的转移概率方法进行城市景观动态研究——以南昌市区为例

利用南昌市1988～2000年期间5个时段的TM卫星影像数据编制了景观组分类型图,并通过叠图分析统计了全部组分类型在4个比较时段的转移概率矩阵。在此基础上构建了组分转入、转出贡献率和特定转移过程贡献率等3个动态分析参数,对南昌市的景观动态变化特征和驱动机制进行了研究。结果显示,城市化引发的建设用地规模急剧膨胀是工作区内景观结构在研究时段内急剧调整的主要原因;农业经营的稳定性需要作为一种重要驱动因素,在农业用地大量流失的同时,使其它景观组分向农田转移成为优势性转移过程类型;地形和水文变化对于林地和水体等组分变化具有次要约束性影响,但对于一些特定优势转移过程的出现则具有决定性作用。研究结果还证实了所提出的3种基于组分转移概率矩阵的量化参数在景观动态变化特征和驱动机制研究中的合理性和有效性。     

A suite of Mathematica notebooks for the analysis of protein main chain 15N NMR relaxation data

A suite of Mathematica notebooks has been designed to ease the analysis of protein main chain ¹⁵N NMR relaxation data collected at a single magnetic field strength. Individual notebooks were developed to perform the following tasks: nonlinear fitting of ¹⁵N-T ₁ and -T ₂ relaxation decays to a two parameter exponential decay, calculation of the principal components of the inertia tensor from protein structural coordinates, nonlinear optimization of the principal components and orientation of the axially symmetric rotational diffusion tensor, model-free analysis of ¹⁵N-T ₁, -T ₂, and {¹H}–¹⁵N NOE data, and reduced spectral density analysis of the relaxation data. The principle features of the notebooks include use of a minimal number of input files, integrated notebook data management, ease of use, cross-platform compatibility, automatic visualization of results and generation of high-quality graphics, and output of analyses in text format.L. Spyracopoulos is an AHFMR Medical Research Senior Scholar     

13C标记代谢流分析中天然稳定性同位素修正矩阵构建方法及应用

稳定性同位素¹³C标记实验是分析细胞代谢流的一种重要手段,主要通过质谱检测胞内代谢物中¹³C标记的同位素分布,并作为胞内代谢流计算时的约束条件,进而通过代谢流分析算法得到相应代谢网络中的通量分布。然而在自然界中,并非只有C元素存在天然稳定性同位素¹³C,其他元素如O元素也有其天然稳定性同位素¹⁷O、¹⁸O等,这使得质谱方法所测得的同位素分布中会夹杂除¹³C标记之外的其他元素的同位素信息,特别是分子中含有较多其他元素的分子,这将导致很大的实验误差,因此需要在进行代谢流计算前进行质谱数据的矫正。本研究提出了一种基于Python语言的天然同位素修正矩阵的构建方法,用于修正同位素分布测量值中由于天然同位素分布引起的测定误差。文中提出的基本修正矩阵幂方法用于构建各元素修正矩阵,结构简单、易于编码实现,可直接应用于¹³C代谢流分析软件数据前处理。将该修正方法应用于¹³C标记的黑曲霉（Aspergillus niger）胞内代谢流分析,结果表明本研究提出的方法准确有效,为准确获取微生物胞内代谢流分析提供了可靠的数据修正方法。