Chemical Shift Anisotropy Relaxation Mechanisms Research Articles

Dynamics in Flexible Pillar[n]arenes Probed by Solid-State NMR.

Pillar[n]arenes are supramolecular assemblies that can perform a range of technologically important molecular separations which are enabled by their molecular flexibility. Here, we probe dynamical behavior by performing a range of variable-temperature solid-state NMR experiments on microcrystalline perethylated pillar[n]arene (n = 5, 6) and the corresponding three pillar[6]arene xylene adducts in the 100–350 K range. This was achieved either by measuring site-selective motional averaged 13C 1H heteronuclear dipolar couplings and subsequently accessing order parameters or by determining 1H and 13C spin–lattice relaxation times and extracting correlation times based on dipolar and/or chemical shift anisotropy relaxation mechanisms. We demonstrate fast motional regimes at room temperature and highlight a significant difference in dynamics between the core of the pillar[n]arenes, the protruding flexible ethoxy groups, and the adsorbed xylene guest. Additionally, unexpected and sizable 13C 1H heteronuclear dipolar couplings for a quaternary carbon were observed for p-xylene adsorbed in pillar[6]arene only, indicating a strong host–guest interaction and establishing the p-xylene location inside the host, confirming structural refinements.

Aromatic 19 F-13 C TROSY-[19 F, 13 C]-Pyrimidine Labeling for NMR Spectroscopy of RNA.

We present the access to [5‐19F, 5‐13C]‐uridine and ‐cytidine phosphoramidites for the production of site‐specifically modified RNAs up to 65 nucleotides (nts). The amidites were used to introduce [5‐19F, 5‐13C]‐pyrimidine labels into five RNAs—the 30 nt human immunodeficiency virus trans activation response (HIV TAR) 2 RNA, the 61 nt human hepatitis B virus ϵ (hHBV ϵ) RNA, the 49 nt SAM VI riboswitch aptamer domain from B. angulatum, the 29 nt apical stem loop of the pre‐microRNA (miRNA) 21 and the 59 nt full length pre‐miRNA 21. The main stimulus to introduce the aromatic 19F–13C‐spin topology into RNA comes from a work of Boeszoermenyi et al., in which the dipole‐dipole interaction and the chemical shift anisotropy relaxation mechanisms cancel each other leading to advantageous TROSY properties shown for aromatic protein sidechains. This aromatic 13C–19F labeling scheme is now transferred to RNA. We provide a protocol for the resonance assignment by solid phase synthesis based on diluted [5‐19F, 5‐13C]/[5‐19F] pyrimidine labeling. For the 61 nt hHBV ϵ we find a beneficial 19F–13C TROSY enhancement, which should be even more pronounced in larger RNAs and will facilitate the NMR studies of larger RNAs. The [19F, 13C]‐labeling of the SAM VI aptamer domain and the pre‐miRNA 21 further opens the possibility to use the biorthogonal stable isotope reporter nuclei in in vivo NMR to observe ligand binding and microRNA processing in a biological relevant setting.

Temperature dependence of fast carbonyl backbone dynamics in chicken villin headpiece subdomain

Temperature-dependence of protein dynamics can provide information on details of the free energy landscape by probing the characteristics of the potential responsible for the fluctuations. We have investigated the temperature-dependence of picosecond to nanosecond backbone dynamics at carbonyl carbon sites in chicken villin headpiece subdomain protein using a combination of three NMR relaxation rates: (13)C' longitudinal rate, and two cross-correlated rates involving dipolar and chemical shift anisotropy (CSA) relaxation mechanisms, (13)C'/(13)C'-(13)C(α) CSA/dipolar and (13)C'/(13)C'-(15)N CSA/dipolar. Order parameters have been extracted using the Lipari-Szabo model-free approach assuming a separation of the time scales of internal and molecular motions in the 2-16°C temperature range. There is a gradual deviation from this assumption from lower to higher temperatures, such that above 16°C the separation of the time scales is inconsistent with the experimental data and, thus, the Lipari-Szabo formalism can not be applied. While there are variations among the residues, on the average the order parameters indicate a markedly steeper temperature dependence at backbone carbonyl carbons compared to that probed at amide nitrogens in an earlier study. This strongly advocates for probing sites other than amide nitrogen for accurate characterization of the potential and other thermodynamics characteristics of protein backbone.

Nuclear spin relaxation due to chemical shift anisotropy of gas-phase 129Xe

Nuclear spin relaxation provides detailed dynamical information on molecular systems and materials. Here, first-principles modeling of the chemical shift anisotropy (CSA) relaxation time for the prototypic monoatomic (129)Xe gas is carried out, both complementing and predicting the results of NMR measurements. Our approach is based on molecular dynamics simulations combined with pre-parametrized ab initio binary nuclear shielding tensors, an "NMR force field". By using the Redfield relaxation formalism, the simulated CSA time correlation functions lead to spectral density functions that, for the first time, quantitatively determine the experimental spin-lattice relaxation times T(1). The quality requirements on both the Xe-Xe interaction potential and binary shielding tensor are investigated in the context of CSA T(1). Persistent dimers Xe(2) are found to be responsible for the CSA relaxation mechanism in the low-density limit of the gas, completely in line with the earlier experimental findings.

New probes of ligand flexibility in drug design: transferred (13)C CSA-dipolar cross-correlated relaxation at natural abundance.

Understanding the impact of molecular flexibility remains an important outstanding problem in rational drug design. Toward this end, we present new NMR relaxation methods that describe ligand flexibility at the atomic level. Specifically, we measure natural abundance (13)C cross-correlated relaxation parameters for ligands in rapid exchange between the free and receptor-bound states. The rapid exchange transfers the bound state relaxation parameters to the free state, such that a comparison of relaxation rates in the absence and presence of protein receptor yields site-specific information concerning the bound ligand flexibility. We perform these measurements for aromatic carbons, which are highly prevalent in drug-like molecules and demonstrate significant cross-correlated relaxation between the (13)C-(1)H dipole-dipole (DD) and (13)C chemical shift anisotropy (CSA) relaxation mechanisms. Our use of natural abundance measurements addresses the practical difficulties of obtaining isotope-labeled ligands in pharmaceutical research settings. We demonstrate our methods on a small ligand of the 42 kDa kinase domain of the p38 MAP kinase. We show that exchange-transferred cross-correlated relaxation measurements are not only sensitive probes of bound ligand flexibility but also offer complementary advantages over standard R(1) = 1/T(1) and R(2) = 1/T(2) measurements. The ligand flexibility profiles obtained from the relaxation data can help assess the influence of dynamics on ligand potency or pharmacokinetic properties or both, and thereby include inherent molecular flexibility in drug design.

Cross-correlated relaxation for measurement of angles between tensorial interactions

c Theory, experimental aspects, and use in structure calculation of cross-correlated relaxation rates measured on zeroand doublequantum 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 c in a protein by measuring dipole(N–H)–dipole(C–H) and CSA(N)–dipole(C– H) cross-correlated relaxation rates. It is shown that ambiguities due to the 3 cosu-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. © 2000 Academic Press

Current approaches for the study of large proteins by NMR

An overview of current methods employed for characterizing larger (>25 kDa) proteins by NMR is presented. These techniques include: the attenuation of T 2 relaxation effects by offsetting dipole–dipole and chemical shift anisotropy relaxation mechanisms (TROSY); the extraction of residual dipolar couplings from partially oriented molecules; the elimination of relaxation pathways by incorporating deuterium nuclei into protein samples; the easing of resonance overlap by isotopically labeling only specific protein segments; and the decrease of rotational correlation times by dissolving proteins in low viscosity solvents.

A sequential HNCA NMR pulse sequence for protein backbone assignment.

The conventional HNCA pulse sequence suffers from the ambiguity that it cannot distinguish inter- and intraresidue correlations because the one-bond and two-bond J(NC(alpha)) coupling constants are of similar magnitude. This paper presents a novel pulse sequence, sequential HNCA, that leads to a spectrum exhibiting exclusively interresidue correlations. This important sequential information has so far usually been obtained by an HN(CO)CA experiment that for medium field strengths typically also is more sensitive than HNCA. However, for increasing static magnetic fields the chemical shift anisotropy relaxation mechanism of carbonyl carbons becomes more and more efficient, leading to a degradation of the HN(CO)CA sensitivity. Hence there is a point where the sequential HNCA experiment becomes the most sensitive option for sequential N-C(alpha) correlation.

Anisotropic Reorientational Dynamics of Toluene in Neat Liquid. A 13C Nuclear Magnetic Relaxation Study

The reorientational motion of toluene in neat liquid was examined by using 13C nuclear magnetic relaxation. The temperature-dependent dipolar spin−lattice relaxation rates and cross-correlation rates between the dipolar and the chemical-shift anisotropy relaxation mechanisms were measured for different 13C nuclei in the molecule over a temperature range of 253 to 318 K. Assuming the molecular frame to show an anisotropic rotational motion, we found three different rotational diffusion constants about the molecular rotation axes. Reorientation velocities about the C2 axis and the axis perpendicular to the molecular plane were of comparable magnitude, but change their ratio in the temperature range investigated in this study. The reorientation about the axis in the molecular plane and perpendicular to the C2 axis was found to be approximately 2 to 3 times slower. The rotational diffusion constants were fitted to an Arrhenius equation, and activation energies from 3.5 to 9.1 kJ mol-1 were found. Furthermore, correlation times for the reorientation of different 13C−1H bonds, spin−lattice relaxation rates for the chemical-shift anisotropy and spin-rotation mechanisms were also derived for the different 13C nuclei.

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.

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 ψ in a protein by measuring dipole(15N–1H)–dipole(13Cα–1Hα) and CSA(15N)–dipole(13Cα–1Hα) cross-correlated relaxation rates. It is shown that ambiguities due to the 3 cos2θ-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.

Quantitative Measurement of Cross-Correlations between 15N and 13CO Chemical Shift Anisotropy Relaxation Mechanisms by Multiple Quantum NMR

This paper describes an experiment that allows the quantitative measurement of the CSA−CSA cross-correlation between backbone 15N and 13CO nuclei in uniformly enriched proteins. The CSA−CSA cross-correlation is obtained from the cross-peak intensity ratios of the double- and the zero-quantum components observed with a modified triple-quantum 2D CT-HNCO experiment. In addition, the 1HN−15N/1HN−13CO dipole−dipole cross-correlation was measured without relying on resolved scalar couplings using a complementary quantum 2D CT-HNCO experiment. The cross-correlation rates measured for the protein binase (12.3 kDa) were obtained with high precision but show a surprisingly large range of values. Calculations show that this range is at least partially caused by dynamical processes. The potential use of this information to characterize internal anisotropic motion is discussed.

Influence of cross-correlation between the chemical shift anisotropies of pairs of nuclei on multiple-quantum relaxation rates in macromolecules

The relaxation of multiple-quantum coherence due to intramolecular dipole–dipole and chemical shift anisotropy (CSA) relaxation mechanisms is described. It is shown that cross-correlation between the CSAs of the active spins can affect the relaxation of 1 H– 15 N two-spin coherences in the protein backbone. An experiment that enables this effect to be monitored is discussed. Data are presented for perdeuterated 15 N -labelled human dynamic light chain 1 protein (hdlc1). An analysis of the results yields a value for the CSA of the active 1 H .

Sensitivity Improvement of Transverse Relaxation-Optimized Spectroscopy

Procedures are described for significantly improving the sensitivity of the recently proposed TROSY (transverse relaxation-optimized spectroscopy) experiment (K. Pervushinet al.,1997,Proc. Natl. Acad. Sci. USA94, 12366–12371). The TROSY experiment takes advantage of destructive interference between dipolar and chemical shift anisotropy relaxation mechanisms to achieve substantial reductions in resonance linewidths in heteronuclear correlation spectra; the effect is significant particularly for studies of large molecular weight systems at very high static magnetic field strengths. A2improvement in the sensitivity of the TROSY experiment is achieved by implementation of the PEP (preservation of equivalent pathways) scheme (J. Cavanagh and M. Rance, 1990,J. Magn. Reson.88, 72–85). An additional significant improvement in sensitivity for15N-labeled samples in H2O solution is realized through a simple modification of the1H–15N TROSY pulse sequence to return the water magnetization to its equilibrium position (+zaxis) at the beginning of the acquisition period. Relaxation-induced imbalance between the coherence transfer pathways utilized in the TROSY refocusing period is shown theoretically and experimentally to give rise to additional unanticipated signals in TROSY spectra.

Measurement of 3hJNC' connectivities across hydrogen bonds in a 30 kDa protein.

A method is described which permits detection of 3hJNC' scalar couplings across hydrogen bonds in larger, perdeuterated proteins. The experiment is demonstrated for the uniformly 2H/13C/15N-enriched 30 kDa ribosome inactivating protein MAP30. The 3hJNC' interactions are smaller than 1 Hz, but their detection in an HNCO experiment is made possible through the use of constructive interference between the 15N chemical shift anisotropy and 1H-15N dipole-dipole relaxation mechanisms in a manner similar to that of recently proposed TROSY schemes. Sensitivity of the HNCO experiment depends strongly on the 15N transverse relaxation rate of the downfield 15N multiplet component and on the amide proton T1. In perdeuterated MAP30 at 40 degrees C, the average TROSY T2 was 169 ms at 750 MHz 1H frequency, and a wide range of longitudinal relaxation rates was observed for the amide protons.

Determination of the Protein Backbone Dihedral Angle ψ from a Combination of NMR-Derived Cross-Correlation Spin Relaxation Rates

A sensitive triple resonance NMR experiment is presented for the measurement of the protein backbone dihedral angle ψ based on cross-correlated spin relaxation between 13Cα−1Hα and 15N−1HN dipolar interactions in 15N,13C-labeled proteins. In general, as many as four ψ values can be consistent with a single cross-correlation rate. However, in many cases, the ambiguity can be significantly reduced (for example, from four to two) when a combination of cross-correlation relaxation rates are employed. This is illustrated by considering rates derived from 13Cα−1Hα/15N−1HN dipolar and from 13Cα−1Hα dipolar/carbonyl chemical shift anisotropy relaxation mechanisms for the proteins ubiquitin and CheY. Using a database of ψ values obtained from high-resolution X-ray structures, it is shown that for values in the range −50° ≤ ψ ≤ 40° a single ψ can be obtained to high probability.

The Complete Homogeneous Master Equation for a Heteronuclear Two-Spin System in the Basis of Cartesian Product Operators

The complete homogeneous form of the quantum mechanical master equation for a heteronuclear two-spin system is presented in the basis of Cartesian product operators. The homogeneous master equation is useful since it allows fast, single-step computation of the density operator during pulse sequences, without neglecting relaxation effects. The homogeneous master equation is also a prerequisite for an expansion of the average Hamiltonian theory to include relaxation, thus forming average Liouvillian theory. The coherences of the two-spin system are assumed to be relaxed both by mutual dipole–dipole interaction and by chemical shift anisotropy interaction with the static magnetic field. The cross-correlation between dipole–dipole and chemical shift anisotropy relaxation mechanisms is also considered. To illustrate the applicability of the developed formalism we simulate the overall transfer efficiency of three different inverse detection1H–15N correlation experiments with parameters corresponding to a large protein.

On the calculation of spectral density functions for spin interactions without axial symmetry

Decomposition of an arbitrary cartesian tensor expressed in its principal axis system into two axially symmetric cartesian tensors greatly facilitates the calculation of spectral densities, the latter being the Fourier transform of correlation functions involving elements of those tensors. A straightforward method is given for two motional models: (a) fully anisotropic diffusion rotation, appropriate for rigid molecules; and (b) the “model-free approach,” appropriate for large molecules whose overall reorientation is slow and isotropic, and which undergo, in addition, fast local motions. Although of general applicability, these calculations are devoted here to the chemical shift anisotropy relaxation mechanism, especially in cross-correlation spectral densities involving the dipolar interaction. ©1998 John Wiley & Sons, Inc. Concepts Magn Reson 10: 291–297, 1998

A Sensitive Pulse Scheme for Measuring the Backbone Dihedral Angle psi Based on Cross-correlation Between (13)C (alpha)- (1)Halpha Dipolar and Carbonyl Chemical Shift Anisotropy Relaxation Interactions.

A pulse scheme for measuring cross-correlation between 13Calpha-1Halpha dipolar and carbonyl chemical shift anisotropy relaxation mechanisms is presented from which the protein backbone dihedral angle psi is measured. The method offers significant sensitivity gains relative to our recently published scheme for measuring psi based on this cross-correlation effect [Yang et al. (1997) J. Am. Chem. Soc., 119, 11938-11940]. The utility of the method is demonstrated with an application to a 42 kDa complex of 15N,13C-labeled maltose binding protein and beta-cyclodextrin.

Motional properties of E. Coli polysaccharide K5 in aqueous solution analyzed by NMR relaxation measurements

13C NMR relaxation measurements at three different magnetic field strengths have been used to analyse the motional properties of a low molecular weight K5 polysaccharide ( ΔUA-[→ 4)-β-d-GlcNAc(1 → 4)-β-d-GlcA(1 → ] n -GlcNAc red) from E. coli. Two-dimensional double INEPT spectra with suppression of cross-correlation effects between dipolar and chemical shift anisotropy relaxation mechanisms were collected in order to determine carbon longitudinal and transverse relaxation times. The values of the overall correlation time and the rate of internal motions were obtained using the model free spectral densities. The data indicate that the overall motion of the molecule is non-isotropic and can be approximated with the symmetric top model with an axial ratio of ≈ 22. The magnitude of the generalized order parameter ( S 2 ≈ 0.8) and the internal motion correlation time ( τ e ≈ 30 ps) differ from those found for iduronic acid-containing glycosaminoglycans and suggest that the internal motions in K5 polysaccharide are more limited.