Cross-correlated relaxation for the measurement of angles between tensorial interactions

Theory,experimental aspects, and use in structure calculation of cross-correlated relaxation rates measured on zero- and double-quantum coherences in liquid state NMR are presented. The relative size of the interaction depends on the projection angle between the two tensorial interactions. The tensorial interaction can be either a dipolar interaction or a chemical shift anisotropy relaxation mechanism (CSA). Effects of additional sources of relaxation on the cross-correlated relaxation rates are analyzed. Also, an easy-to-use formalism is given to manipulate different cross-correlated relaxation interactions. The application addresses measurement of the backbone angle psi in a protein by measuring dipole((15)N-(1)H)-dipole((13)C(alpha)-(1)H(alpha)) and CSA((15)N)-dipole((13)C(alpha)-(1)H(alpha)) cross-correlated relaxation rates. It is shown that ambiguities due to the 3 cos(2)θ-1 dependence of one cross-correlated relaxation rate can be overcome by measuring additional cross-correlated relaxation rates. The use of cross-correlated relaxation rates is demonstrated in structure calculations.     

Hydrogen bonding effects on the (15)N and (1)H shielding tensors in nucleic acid base pairs

The results of systematic ab initio calculations of (15)N and (1)H chemical shielding tensors in the GC base pair as a function of hydrogen bond length are presented for the first time. The hydrogen bond length characterized by the distance r(N...N) between purine N1 and pyrimidine N3 was varied between 2.57 and 3.50 A and the chemical shift tensors were calculated by the sum-over-states density functional perturbation theory. It is shown that the hydrogen bond length has a strong effect on the chemical shielding tensor of both imino proton and nitrogen, on their orientation, and, as a consequence, on the relaxation properties of both nuclei. For a nitrogen nucleus not involved in hydrogen bonding, the shielding tensor is nearly axially symmetric and almost collinear with the bond vector. As the length of the hydrogen bond decreases, the least shielding component sigma(11) deflects from the N-H vector and the shielding tensor becomes increasingly asymmetric. The significance of the presented results for the analysis of relaxation data and the efficiency of TROSY effects together with a summary of the relevant shielding parameters are presented and discussed.     

质子化学位移各向异性的测量

测量质子化学位移各向异性（CSA）有助于表征分子结构与其动力学,但由于¹H-¹H同核偶极耦合相互作用很强及质子各向异性化学位移较小,测量质子化学位移各向异性仍具有巨大挑战,特别是对含有多种质子的生物大分子,如蛋白质.本文简要综述了测量质子化学位移各向异性的方法,包括同核去耦慢速魔角旋转方法、超快魔角旋转方法、对称重耦（RN_n^v）方法、xCSA方法以及量子化学计算方法.我们重点介绍了在高速魔角旋转条件下蛋白质氨基质子化学位移各向异性的测量及它们与氢键长度、蛋白质二级结构之间的关系.     

On the accurate measurement of amide one-bond 15N-1H couplings in proteins: effects of cross-correlated relaxation, selective pulses and dynamic frequency shifts

Amide one-bond 15N-1H scalar couplings of 15N- and [15N,2H]-isotopically enriched ubiquitin have been measured with the Quantitative J approach by monitoring NMR signal intensity modulation. Scalar couplings of the non-deuterated protein are in average approximately 0.6 Hz larger than values of deuterated ubiquitin. This deviation is 30 times the error derived from experiment reproducibility. Refocusing dipole/dipole cross-correlated relaxation decreases the discrepancy to approximately 0.1 Hz, suggesting that it likely originates from relaxation interference. Alternatively, the subtraction of J values obtained at different magnetic fields largely reduces the relaxation effects. In contrast, the dynamic frequency shift whose main contribution to 1J(15N-1H) arises from 15N chemical shielding anisotropy/NH dipole cross-correlation, is not eliminated by refocusing spin evolution under this interaction. Furthermore, the average difference of 1J(15N-1H) values at two magnetic fields closely agrees with the theoretical expected difference in the dynamic frequency shift.     

Proton-detected separated local field spectroscopy

PISEMO, a separated local field experiment that can be performed with either direct (15)N (or (13)C) detection or indirect (1)H detection, is demonstrated on a single crystal of a model peptide. The (1)H signals modulated by (1)H-(15)N heteronuclear dipole-dipole couplings are observed stroboscopically in the windows of the multiple-pulse sequence used to attenuate (1)H-(1)H homonuclear dipole-dipole couplings. (1)H-detection yields spectra with about 2.5 times the signal to noise ratio observed with (15)N-detection under equivalent conditions. Resolution in both the (15)N chemical shift and (1)H-(15)N heteronuclear dipole-dipole coupling dimensions is similar to that observed with PISEMA, however, since only on-resonance pulses are utilized, the bandwidth is better.     

有机磷化合物的NMR研究——Ⅱ0,0-二烷基膦酸酯的1H、13C和31PNMR谱

本文报道了21个0,0一二烷基膦酸酯类化合物的¹H、¹³C和³¹P NMR参数。研究和讨论了不等价的二烷基¹H、¹³C化学位移和磷碳偶合常数与立体化学的关系。测定了(CH₃CH₂O)₂P(O)CH(CH₂NO₂)(p-OCH₃C₆H₄)的¹³C自旋一晶格弛豫时间T₁,二乙基¹³C T₁间的差别,说明在类似化合物中,含有化学位移各向异性对弛豫的贡献。     

3hJ coupling between C(alpha) and H(N) across hydrogen bonds in proteins

J couplings between (13)C(alpha) and (1)H(N) across hydrogen bonds in proteins are reported for the first time, and a two- or three-dimensional NMR technique for their measurement is presented. The technique exploits the TROSY effect, i.e., the degree of interference between dipolar and chemical shift anisotropy relaxation mechanisms, for sensitivity enhancement. The 2D or 3D spectra exhibit E.COSY patterns where the splittings in the (13)CO and (1)H(N) dimensions are (1)J((13)C(alpha), (13)CO) and the desired (3h)J((13)C(alpha), (1)H(N)), respectively. A demonstration of the new method is shown for the (15)N,(13)C-labeled protein chymotrypsin inhibitor 2 where 17 (3h)J((13)C(alpha), (1)H(N)) coupling constants ranging from 0 to 1.4 Hz where identified and all of positive sign.     

New techniques for the measurement of C'N and C'H(N) J coupling constants across hydrogen bonds in proteins

Two new two- or three-dimensional NMR methods for measuring (3h)J(C'N) and (2h)J(C'H) coupling constants across hydrogen bonds in proteins are presented. They are tailored to suit the size of the TROSY effect, i.e., the degree of interference between dipolar and chemical shift anisotropy relaxation mechanisms. The methods edit 2D or 3D spectra into two separate subspectra corresponding to the two possible spin states of the (1)H(N) spin during evolution of (13)CO coherences. This allows (2h)J(C'H) to be measured in an E.COSY-type way while (3h)J(C'N) can be measured in the so-called quantitative way provided a reference spectrum is also recorded. A demonstration of the new methods is shown for the (15)N,(13)C-labeled protein chymotrypsin inhibitor 2.     

Separating structure and dynamics in CSA/DD cross-correlated relaxation: a case study on trehalose and ubiquitin

We present two new sensitivity enhanced gradient NMR experiments for measuring interference effects between chemical shift anisotropy (CSA) and dipolar coupling interactions in a scalar coupled two-spin system in both the laboratory and rotating frames. We apply these methods for quantitative measurement of longitudinal and transverse cross-correlation rates involving interference of (13)C CSA and (13)C-(1)H dipolar coupling in a disaccharide, alpha,alpha-D-trehalose, at natural abundance of (13)C as well as interference of amide (15)N CSA and (15)N-(1)H dipolar coupling in uniformly (15)N-labeled ubiquitin. We demonstrate that the standard heteronuclear T(1), T(2), and steady-state NOE autocorrelation experiments augmented by cross-correlation measurements provide sufficient experimental data to quantitatively separate the structural and dynamic contributions to these relaxation rates when the simplifying assumptions of isotropic overall tumbling and an axially symmetric chemical shift tensor are valid.     

Determination of the backbone torsion psi angle by tensor correlation of chemical shift anisotropy and heteronuclear dipole-dipole interaction

We demonstrate that the backbone torsion psi angle of a uniformly labeled residue can be determined accurately by correlating the chemical shift anisotropy of the carbonyl carbon and the 13C-1H heteronuclear dipole-dipole interaction of the alpha carbon. To obtain the highest sensitivity for the psi angle determination, the following conditions are desired: (i) the recoupling pulse sequences for the CSA and the heteronuclear dipolar interactions are gamma encoded, in which the spatial parts of m=2 are selected; (ii) the homonuclear polarization transfer is based on the scalar spin-spin coupling. Experimental data were obtained for [U-13C, 15N]-alanine and N-acetyl-[U-13C, 15N]-d,l-valine under magic-angle spinning at 25kHz. Only three data points are required for the measurements and the dihedral angles determined are in excellent agreement with the diffraction data.     

Measurement of Cross Correlation between Dipolar Coupling and Chemical Shift Anisotropy in the Spin Relaxation ofC,N-Labeled Proteins

We present a simple method for extracting interference effects between chemical shift anisotropy (CSA) and dipolar coupling from spin relaxation measurements in macromolecules, and we apply this method to extracting cross-correlation rates involving interference of amide¹⁵N CSA and¹⁵N–¹H dipolar coupling and interference of carbonyl¹³C′ CSA and¹⁵N–¹³C′ dipolar coupling, in a small protein. A theoretical basis for the interpretation of these rates is presented. While it proves difficult to quantitatively separate the structural and dynamic contributions to these cross-correlation rates in the presence of anisotropic overall tumbling and a nonaxially symmetric chemical shift tensor, some useful qualitative correlations of data with protein structure can be seen when simplifying assumptions are made.     

Separation of anisotropy and exchange broadening using (15)N CSA-(15)N-(1)H dipole-dipole relaxation cross-correlation experiments

Based on the measurement of cross-correlation rates between (15)N CSA and (15)N-(1)H dipole-dipole relaxation we propose a procedure for separating exchange contributions to transverse relaxation rates (R(2) = 1/T(2)) from effects caused by anisotropic rotational diffusion of the protein molecule. This approach determines the influence of anisotropy and chemical exchange processes independently and therefore circumvents difficulties associated with the currently standard use of T(1)/T(2) ratios to determine the rotational diffusion tensor. We find from computer simulations that, in the presence of even small amounts of internal flexibility, fitting T(1)/T(2) ratios tends to underestimate the anisotropy of overall tumbling. An additional problem exists when the N-H bond vector directions are not distributed homogeneously over the surface of a unit sphere, such as in helix bundles or beta-sheets. Such a case was found in segment 4 of the gelation factor (ABP 120), an F-actin cross-linking protein, in which the diffusion tensor cannot be calculated from T(1)/T(2) ratios. The (15)N CSA tensor of the residues for this beta-sheet protein was found to vary even within secondary structure elements. The use of a common value for the whole protein molecule therefore might be an oversimplification. Using our approach it is immediately apparent that no exchange broadening exists for segment 4 although strongly reduced T(2) relaxation times for several residues could be mistaken as indications for exchange processes.     

Separating Structure and Dynamics in CSA/DD Cross-Correlated Relaxation: A Case Study on Trehalose and Ubiquitin

We present two new sensitivity enhanced gradient NMR experiments for measuring interference effects between chemical shift anisotropy (CSA) and dipolar coupling interactions in a scalar coupled two-spin system in both the laboratory and rotating frames. We apply these methods for quantitative measurement of longitudinal and transverse cross-correlation rates involving interference of ¹³C CSA and ¹³C–¹H dipolar coupling in a disaccharide, α,α- -trehalose, at natural abundance of ¹³C as well as interference of amide ¹⁵N CSA and ¹⁵N–¹H dipolar coupling in uniformly ¹⁵N-labeled ubiquitin. We demonstrate that the standard heteronuclear T₁, T₂, and steady-state NOE autocorrelation experiments augmented by cross-correlation measurements provide sufficient experimental data to quantitatively separate the structural and dynamic contributions to these relaxation rates when the simplifying assumptions of isotropic overall tumbling and an axially symmetric chemical shift tensor are valid.     

Characterization of 15N chemical shift tensors via 15N-13C REDOR and 1N-1H dipolar-shift CPMAS NMR spectroscopy

As part of our studies on the characterization of 15N chemical shift anisotropy (CSA) via magic angle spinning (MAS) NMR spectroscopy, we have investigated via numerical simulations the sensitivity of two different REDOR experimental protocols to the angles defining the orientation of the 15N-13C' bond vector in the principal axis system of the 15N CSA tensor of the amide nitrogen in a peptide bond. Additionally, employing polycrystalline samples of 15N and 13C', 15N-labeled acetanilide, we have obtained, in a first study of this type, the orientation of the 15N CSA tensor in the molecular frame by orienting the tensor with respect to the 15N-3C' and 15N-1H dipolar vectors via 15N-13C' REDOR and 15N-1H dipolar-shift MAS experiments, respectively.     

2H chemical shift anisotropies from high-field 2H MAS NMR spectroscopy

2H chemical shift anisotropies (CSAs) have been determined for the first time for polycrystalline samples employing 2H MAS NMR spectroscopy at high magnetic field strength (14.1 T). The 2H CSA is reflected as distinct asymmetries in the manifold of spinning sidebands (ssbs) observed for the two overlapping single-quantum transitions. Least-squares fitting to the manifold of ssbs allows determination of the 2H CSA parameters along with the quadrupole coupling parameters. This is demonstrated for KD2PO4, ND4D2PO4, KDSO4, KDCO3, alpha-(COOD)2, alpha-(COOD)2.2D2O, and boehmite (AlOOD) which exhibit 2H shift anisotropies in the range 13< or =deltasigma< or =27 ppm. For fixed values of the shift anisotropy and the 2H quadrupole coupling it is shown that the precision of the CSA parameters depends strongly on the asymmetry parameter (etaQ) for the quadrupole coupling tensor, giving the highest precision for etaQ approximately 0. The 2H CSA parameters (deltasigma and etasigma) are in good agreement with 1H CSA data reported in the literature for the corresponding protonated samples from 1H NMR spectra employing various homonuclear decoupling techniques. The determination of 2H quadrupole coupling parameters and 2H (1H) CSAs from the same 2H MAS NMR experiment may be particularly useful in studies of hydrogen bonding since the 2H quadrupole coupling constant and the CSA appear to characterize bond lengths in a hydrogen bond in a different manner.     

先进固体NMR技术研究高分子结构与动力学

随着固体NMR理论和谱仪硬件技术的不断发展,近年来固体NMR技术在高分子多尺度结构与动力学研究领域中正发挥着越来越重要的作用. 多脉冲及高速魔角旋转（MAS）等质子高分辨技术的发展使得高灵敏度的¹H谱可有效地用于高分子化学结构与链间相互作用的检测;基于化学键（J-耦合）相关和通过空间（偶极耦合）相互作用的各种二维异核相关谱NMR新技术,使得复杂高分子的链结构得以严格解析. 基于MAS下同核和异核偶极-偶极相互作用、化学位移各向异性等各向异性相互作用重聚的系列新技术,使得研究者可在采用高分辨¹H或¹³C 检测信号的同时检测准静态下的各向异性相互作用,进而获得与之密切相关的结构和动力学信息. 通过质子偶极滤波技术可有效检测多相聚合物中的界面相与相区尺寸、高分子共混物中的相容性等问题. 在动力学的研究中,通过质子间自旋扩散的有效压制技术和化学位移各向异性的重聚,目前已经可以有效地获取链段上单个化学键的快速局域运动以及链段的超慢分子运动. 上述丰富的多尺度NMR技术可以使研究者在不同空间和时间尺度上对高分子聚合物的微观结构、相分离和动力学行为等进行详细的研究,进而阐明高分子微观结构与宏观性能的关联. 该文以固体NMR中最主要的2类核（¹H和¹³C）的检测技术为主线,简单介绍近年来固体NMR领域的一些最新研究进展及其在高分子结构和动力学研究中的应用.     

Experimental aspects of multidimensional solid-state NMR correlation spectroscopy.

The experimental parameters critical for the implementation of multidimensional solid-state NMR experiments that incorporate heteronuclear spin exchange at the magic angle are discussed. This family of experiments is exemplified by the three-dimensional experiment that correlates the (1)H chemical shift, (1)H-(15)N dipolar coupling, and (15)N chemical shift frequencies. The broadening effects of the homonuclear (1)H-(1)H dipolar couplings are suppressed using flip-flop (phase- and frequency-switched) Lee-Goldburg irradiations in both the (1)H chemical shift and the (1)H-(15)N dipolar coupling dimensions. The experiments are illustrated using the (1)H and (15)N chemical shift and dipolar couplings in a single crystal of (15)N-acetylleucine.     

Measurement of 15N chemical shift anisotropy in a protein dissolved in a dilute liquid crystalline medium with the application of magic angle sample spinning

The chemical shifts of nuclei that have chemical shielding anisotropy, such as the 15N amide in a protein, show significant changes in their chemical shifts when the sample is altered from an isotropic state to an aligned state. Such orientation-dependent chemical shift changes provide information on the magnitudes and orientation of the chemical shielding tensors relative to the molecule's alignment frame. Because of the extremely high sensitivity of the chemical shifts to the sample conditions, the changes in chemical shifts induced by adding aligned bicelles do not arise only from the protein alignment but should also include the accumulated effects of environmental changes including protein-bicelle interactions. With the aim of determining accurate 15N chemical shielding tensor values for solution proteins, here we have used magic angle sample spinning (MAS) to observe discriminately the orientation-dependent changes in the 15N chemical shift. The application of MAS to an aligned bicelle solution removes the torque that aligns the bicelles against the magnetic field. Thus, the application of MAS to a protein in a bicelle solution eliminates only the molecular alignment effect, while keeping all other sample conditions the same. The observed chemical shift differences between experiments with and without MAS therefore provide accurate values of the orientation-dependent 15N chemical shifts. From the values for ubiquitin in a 7.5% (w/v) bicelle medium, we determined the 15N chemical shielding anisotropy (CSA) tensor. For this evaluation, we considered uncertainties in measuring the 1H-15N dipolar couplings and the 15N chemical shifts and also structural noise present in the reference X-ray structure, assuming a random distribution of each NH bond vector in a cone with 5 degrees deviation from the original orientation. Taking into account these types of noise, we determined the average 15N CSA tensor for the residues in ubiquitin as Delta sigma=-162.0+/-4.3 ppm, eta=0.18+/-0.02, and beta=18.6+/-0.5 degrees, assuming a 1H-15N bond length of 1.02 A. These tensor values are consistent with those obtained from solid-state NMR experiments.     

Hydrogen-bonding studies of amino acid side-chains with DNA base pairs

The interactions of the amino acid side-chains arginine (ARG), aspartic acid (ASP), asparagine (ASN), lysine (LYS) and serine (SER) with nucleic acid base pairs have been investigated using theoretical methods. The interaction energy of the short intermolecular N–H?···?N, N–H?···?O, O–H?···?O, O–H?···?N, C–H?···?O and C–H?···?N hydrogen bonds present in both isolated base pairs and complexes and its role in providing stability to the complexes have been explored. The homonuclear interactions are found to be stronger than the heteronuclear interactions. An improper hydrogen bond has been observed for some of the N–H?···?O and N–H?···?N hydrogen-bond interactions with the contraction of the N–H bond varying from 0.001 to 0.0260?Å and the corresponding blue shift of the stretching frequency by 4–291?cm^?1. Localized molecular orbital energy decomposition analysis (LMOEDA) reveals that the major contributions to the energetics are from the long-range polarization (PL) interaction, and the short-range attractive (ES, EX) and repulsive (REP) interactions. The Bader's atoms in molecules (AIM) theory shows good correlation for the electron density and its Laplacian at the bond critical points (BCP) with the N–H?···?N and N–H?···?O hydrogen-bond lengths in the complexes, and gives a proper explanation for the stability of the structure. The charge-transfer from the proton acceptor to the antibonding orbital of the X–H bond in the complexes was studied using natural bond orbital (NBO) analysis.     

Difference between 1H NMR signals of primary amide protons as a simple spectral index of the amide intramolecular hydrogen bond strength

The effect of the intramolecular H‐bonding of the primary amide group on the spectral properties and reactivity of this group towards electrophiles has been studied in systematic rows of 1,2,5,6,7,8‐hexahydro‐7,7‐dimethyl‐2,5‐dioxo‐1‐R‐quinoline‐3‐carboxamides and 2‐aryliminocoumarin‐3‐carboxamides using ¹H and ¹⁵N NMR spectroscopy and the kinetics of model reactions. The upfield signal of the amide proton that is not intramolecularly H‐bonded (H^a) depends on external factors such as solvent nature and concentration. At the same time, the downfield chemical shift of the H^b proton (bonded by the intramolecular hydrogen bond) depends mostly on the strength of the intramolecular H‐bond, which is affected by such internal factor as electron nature of substituent R. The substituent's influence on the H^b proton's chemical shift is more effective in deuterochloroform medium than in DMSO‐d₆ where the intramolecular hydrogen bond is less stable. The value Δδ(H) = δ(H^b) ? δ(H^a) is suggested as a simple comparative spectral index of the intramolecular hydrogen bond strength in these and similar compounds. By contrast, the effect of R on the ¹⁵N NMR chemical shift of the amide nitrogen has turned out to be too small to estimate changes of the electron density at the nitrogen. The effect of the intramolecular H‐bond on the reactivity of the amide group is twofold. When the cleavage of the H‐bond occurs on the rate limiting step it dramatically reduces the reaction rate. In the other case, the strengthening of the H‐bond favors the reaction rate because of the increase of the electron density at the amide nitrogen. Copyright © 2011 John Wiley & Sons, Ltd.