Methyl dynamics in proteins from NMR slowly relaxing local structure spin relaxation analysis: A new perspective

NMR spin relaxation of (2)H nuclei in (13)CH(2)D groups is a powerful method for studying side-chain motion in proteins. The analysis is typically carried out with the original model-free (MF) approach adapted to methyl dynamics. The latter is described in terms of axial local motions around, and of, the methyl averaging axis, mutually decoupled and independent of the global motion of the protein. Methyl motion is characterized primarily by the axial squared order parameter, S(axis)2, associated with fluctuations of the methyl averaging axis. This view is shown to be oversimplified by applying to typical experimental data the slowly relaxing local structure (SRLS) approach of Polimeno and Freed (Adv. Chem. Phys. 1993, 83, 89) which can be considered the generalization of the MF approach. Neglecting mode coupling and the asymmetry of the local ordering and treating approximately features of local geometry imply inaccurate values of S(axis)2, hence of the residual configurational entropy derived from it. S(axis)2, interpreted as amplitude of motion, was found to range from near disorder to almost complete order. Contrary to this picture, we find with the SRLS approach a moderate distribution in the magnitude of asymmetric local ordering and significant variation in its symmetry. The latter important property can be associated implicitly with the contribution of side-chain rotamer jumps. This is consistent with experimental residual dipolar coupling studies and theoretical work based on molecular dynamics simulations and molecular mechanics considerations. Configurational entropy is obtained in the SRLS approach directly from experimentally determined asymmetric potentials. Inconsistency between order parameters from 2H relaxation and from eta(HC-HH) cross-correlation and increase in order parameters with increasing temperature were observed with the MF approach. These discrepancies are reconciled, and physically tenable temperature dependence is obtained with the SRLS approach.     

Dynamics of an inclusion complex of chloroform and cryptophane-E: evidence for a strongly anisotropic van der Waals bond

The motional dynamics of a van der Waals inclusion complex of cryptophane-E and chloroform has been investigated by a combined NMR exchange and relaxation study. The kinetics of exchange of chloroform between the bulk solution and the complex was investigated by means of proton EXSY measurements. The carbon-13 relaxation of the cryptophane-E host and of the bound chloroform guest was analyzed using the Lipari-Szabo "model-free" approach. For interpretation of the carbon-13 relaxation measurements for chloroform, the chemical-exchange process of complex formation and dissociation had to be taken into account in terms of the modified Bloch equations. It was found that the complex behaves as a single molecule without any significant guest chloroform motion inside the host's cavity.     

A multifaceted approach to the interpretation of NMR order parameters: a case study of a dynamic alpha-helix

The model-free approach (Lipari, G.; Szabo, A. J. Am. Chem. Soc. 1982, 104, 4546-4559; 4559-4570) is the standard method for the analysis of NMR relaxation data from proteins. The method assigns to each interaction vector a generalized order parameter S(2), which is a measure of the spatial restriction that the vector experiences in a molecular reference frame. A variety of techniques for the interpretation of S(2) values and their underlying assumptions are tested here for a dynamic alpha-helix represented by an ensemble of peptide structures that satisfies a set of predefined constraints. A self-consistent picture is developed that characterizes the influence of major determinants, including backbone dihedral angle fluctuations and their correlations, separability of internal and overall motion, the preservation of hydrogen bonds, restricted end-to-end distance fluctuations, locally anisotropic dynamics, and local contacts between interaction vector atoms and their environment. Many of the features parallel experimental NMR and computational observations of helices in proteins. The understanding gained from this model system is expected to contribute toward the ever more detailed interpretation of experimental order parameter profiles.     

A structural mode-coupling approach to 15N NMR relaxation in proteins.

The two-body Slowly Relaxing Local Structure (SRLS) model was applied to (15)N NMR spin relaxation in proteins and compared with the commonly used original and extended model-free (MF) approaches. In MF, the dynamic modes are assumed to be decoupled, local ordering at the N-H sites is represented by generalized order parameters, and internal motions are described by effective correlation times. SRLS accounts for dynamical coupling between the global diffusion of the protein and the internal motion of the N-H bond vector. The local ordering associated with the coupling potential and the internal N-H diffusion are tensors with orientations that may be tilted relative to the global diffusion and magnetic frames. SRLS generates spectral density functions that differ from the MF formulas. The MF spectral densities can be regarded as limiting cases of the SRLS spectral density. SRLS-based model-fitting and model-selection schemes similar to the currently used MF-based ones were devised, and a correspondence between analogous SRLS and model-free parameters was established. It was found that experimental NMR data are sensitive to the presence of mixed modes. Our results showed that MF can significantly overestimate order parameters and underestimate local motion correlation times in proteins. The extent of these digressions in the derived microdynamic parameters is estimated in the various parameter ranges, and correlated with the time scale separation between local and global motions. The SRLS-based analysis was tested extensively on (15)N relaxation data from several isotropically tumbling proteins. The results of SRLS-based fitting are illustrated with RNase H from E. coli, a protein extensively studied previously with MF.     

The nuclear magnetic resonance relaxation data analysis in solids: general R1/R1(ρ) equations and the model-free approach

The advantage of the solid state NMR for studying molecular dynamics is the capability to study slow motions without limitations: in the liquid state, if orienting media are not used, all anisotropic magnetic interactions are averaged out by fast overall Brownian tumbling of a molecule and thus investigation of slow internal conformational motions (e.g., of proteins) in solution can be conducted using only isotropic interactions. One of the main tools for obtaining amplitudes and correlation times of molecular motions in the μs time scale is measuring relaxation rate R(1)(ρ). Yet, there have been a couple of unresolved problems in the quantitative analysis of the relaxation rates. First, when the resonance offset of the spin-lock pulse is used, the spin-lock field can be oriented under an arbitrary angle in respect to B(0). Second, the spin-lock frequency can be comparable or even less than the magic angle spinning rate. Up to now, there have been no equations for R(1)(ρ) that would be applicable for any values of the spin-lock frequency, magic angle spinning rate and resonance offset of the spin-lock pulse. In this work such equations were derived for two most important relaxation mechanisms: heteronuclear dipolar coupling and chemical shift anisotropy. The validity of the equations was checked by numerical simulation of the R(1)(ρ) experiment using SPINEVOLUTION program. In addition to that, the applicability of the well-known model-free approach to the solid state NMR relaxation data analysis was considered. For the wobbling in a cone at 30° and 90° cone angles and two-site jump models, it has been demonstrated that the auto-correlation functions G(0)(t), G(1)(t), G(2)(t), corresponding to different spherical harmonics, for isotropic samples (powders, polycrystals, etc.) are practically the same regardless of the correlation time of motion. This means that the model-free approach which is widely used in liquids can be equally applied, at least assuming these two motional models, to the analysis of the solid state NMR relaxation data.     

Protein side-chain dynamics observed by solution- and solid-state NMR: comparative analysis of methyl 2H relaxation data

Rapid advances in solid-state MAS NMR made it possible to probe protein dynamics on a per-residue basis, similar to solution experiments. In this work we compare methyl 2H relaxation rates measured in the solid and liquid samples of alpha-spectrin SH3 domain. The solution data are treated using a model-free approach to separate the contributions from the overall molecular tumbling and fast internal motion. The latter part forms the basis for comparison with the solid-state data. Although the accuracy of solid-state measurements is limited by deuterium spin diffusion, the results suggest a significant similarity between methyl dynamics in the two samples. This is a potentially important observation, preparing the ground for combined analysis of the dynamics data by solid- and solution-state NMR.     

Changes in dynamics of SRE-RNA on binding to the VTS1p-SAM domain studied by 13C NMR relaxation

RNA recognition by proteins is often accompanied by significant changes in RNA dynamics in addition to conformational changes. However, there are very few studies which characterize the changes in molecular motions in RNA on protein binding. We present a quantitative (13)C NMR relaxation study of the changes in RNA dynamics in the pico-nanosecond time scale and micro-millisecond time scale resulting from interaction of the stem-loop SRE-RNA with the VTS1p-SAM domain. (13)C relaxation rates of the protonated carbons of the nucleotide base and anomeric carbons have been analyzed by employing the model-free formalism, for a fully (13)C/(15)N-labeled sample of the SRE-RNA in the free and protein-bound forms. In the free RNA, the nature of molecular motions are found to be distinctly different in the stem and the loop region. On binding to the protein, the nature of motions becomes more homogeneous throughout the RNA, with many residues showing increased flexibility at the aromatic carbon sites, while the anomeric carbon sites become more rigid. Surprisingly, we also observe indications of a slow collective motion of the RNA in the binding pocket of the protein. The observation of increased motions on binding is interesting in the context of growing evidence that binding does not always lead to motional restrictions and the resulting entropy gain could favor the free energy of association.     

Probing side-chain dynamics in the proteasome by relaxation violated coherence transfer NMR spectroscopy

A pair of experiments is presented for measuring intra-methyl 1H-1H dipolar cross-correlated spin relaxation rates in highly deuterated, methyl protonated proteins with significantly improved sensitivity relative to previously developed experiments that measure dynamics via 1H spin relaxation. In applications to proteins with correlation times in the macromolecular limit, these cross-correlation rates are related directly to order parameters, characterizing the amplitude of motion of methyl-containing side-chains. The experimental approach is validated by comparing extracted order parameters with those obtained via 2H and 13C spin relaxation methods for both protein L (7.5 kDa) and malate synthase G (82 kDa), with excellent correlations obtained. The methodology is applied to study Ile, Leu, and Val side-chain dynamics in a 360 kDa "half-proteasome" complex. In particular, order parameters obtained from the WT complex and from a second complex where the proteasome gating residues are deleted establish that the relative levels of dynamics in each of the two molecules are very similar. It thus becomes clear that there is no communication between gating residues and other regions of the molecule involving pico- to nanosecond time-scale dynamics of these methyl-containing side-chains.     

Nuclear magnetic relaxation and molecular motion in solid lysozyme

Nuclear magnetic relaxation data for both proton and carbon-13 nuclei in solid lysozyme are analysed together to obtain information on local internal motions in protein. For this analysis the “model-free” approach is used. Three types of internal motion appear to determine the observed nuclear relaxation in protein. They may be attributed to local rotations of methyl groups around symmetry axes, the motion of main and side chain atoms like in rigid lattice, and large-amplitude motions of side groups (mainly, methylene groups). Conclusions on hydrated water influence on local dynamics of protein are made.     

Membrane Proteins Have Distinct Fast Internal Motion and Residual Conformational Entropy

The internal motions of integral membrane proteins have largely eluded comprehensive experimental characterization. Here the fast side‐chain dynamics of the α‐helical sensory rhodopsin II and the β‐barrel outer membrane protein W have been investigated in lipid bilayers and detergent micelles by solution NMR relaxation techniques. Despite their differing topologies, both proteins have a similar distribution of methyl‐bearing side‐chain motion that is largely independent of membrane mimetic. The methyl‐bearing side chains of both proteins are, on average, more dynamic in the ps–ns timescale than any soluble protein characterized to date. Accordingly, both proteins retain an extraordinary residual conformational entropy in the folded state, which provides a counterbalance to the absence of the hydrophobic effect. Furthermore, the high conformational entropy could greatly influence the thermodynamics underlying membrane‐protein functions, including ligand binding, allostery, and signaling.     

Nuclear spin relaxation times dispersion in disordered polymer systems

Nuclear spin relaxation reveals a wealth of information concerning motional dynamics and morphology within a polymer system. The conventional breakdown of relaxation into discrete decay components is usually arbitrary and often ambiguous due to strong coupling and spin diffusion between domains. To avoid being limited by pre-determined models, we have explored the utility of maximum entropy regularization scheme to reconstruct the complete NMR spin relaxation distribution continuum. Case studies showed that the three characteristics of the distribution correlate with various aspects of polymer morphology and with physical properties. These positive results suggested that this approach has the potential of yielding profiles on polymer dynamics and information concerning phonon coupling between domains in complex polymer systems which are not previously accessible. Furthermore, the nondestructive nature of NMR gives this approach an extra advantage over conventional tests for “in-situ” studies of polymers.     

Backbone dynamics of proteins studied by two-dimensional heteronuclear NMR spectroscopy and molecular dynamics simulations

To investigate the backbone dynamics of proteins ¹⁵N longitudinal and transverse relaxation experiments combined with {¹H, ¹⁵N{ NOE measurements together with molecular dynamics simulations were carried out using ribonuclease T₁ and the complex of ribonuclease T₁ with 2′GMP as a model protein. The intensity decay of individual amide cross peaks in a series of (¹H, ¹⁵N)HSQC spectra with appropriate relaxation periods was fitted to a single exponential by using a simplex algorithm in order to obtain ¹⁵N T₁ and T₂ relaxation times. The relaxation times were analyzed in terms of the “model-free” approach introduced by Lipari and Szabo. In addition, a nanosecond molecular dynamics (MD ) simulation of ribonuclease T₁ and its 2′GMP complex in water was carried out. The angular reorientations of the backbone amide groups were classified with several coordinate frames following a transformation of NH vector trajectories. In this study, NH librations and backbone dihedral angle fluctuations were distinguished. The NH bond librations were found to be similar for all amides as characterized by correlation times of librational motions in a subpicosecond scale. The angular amplitudes of these motions were found to be about 10°–12° for out-of-plane displacements and 3°–5° for the in-plane displacement. The contributions from the much slower backbone dihedral angle fluctuations strongly depend on the secondary structure. The dependence of the amplitude of local motion on the residue location in the backbone is in good agreement with the results of NMR relaxation measurements and the X-ray data. The protein dynamics is characterized by a highly restricted local motion of those parts of the backbone with defined secondary structure as well as by a high flexibility in loop regions. Comparison of the MD and NMR data of the free liganded enzyme ribonuclease T₁ clearly indicates a restriction of the mobility within certain regions of the backbone upon inhibitor binding. © 1996 John Wiley & Sons, Inc.     

Dynamics and conformations of PEO chains chemically bonded on silica: comparison between 1H and 2H NMR

1H NMR was used to study the motion of monomer units in a layer of poly(ethylene oxide) chains grafted on silica. First, the dependence of the relaxation times on the grafting ratios is discussed qualitatively from a phenomenological point of view. Next, the NMR line narrowing effect by high-speed rotation is observed in the same samples with different grafting ratios. The magic angle spinning technique permits determination of two correlation times for each grafting ratio: tau(c) characteristic of an environment with a fast motion and tau(l) characteristic of an environment with a slow motion. In addition, the dynamics of these grafted chains are investigated by deuterium NMR (2H NMR), which is sensitive to the anisotropy of molecular motion. The evolution has been studied for two extreme grafting ratios and each time as a function of temperature. The anisotropy is more marked at low temperatures and for a low grafting ratio. The results are consistent with the 1H NMR relaxation times measured as a function of temperature.     

Damped torsional oscillator model for polymer molecules

At present the widely used model for explaining viscoelastic and dielectric properties of polymer solutions is that of Rouse and Bueche. Here the polymer molecule is considered as an array of Gaussian subunits, each of which acts as an entropy spring. The motion of these segments is damped by the viscous drag of the surrounding solvent (RB model). An alternative model is presented, in which the segments are torsional oscillators consisting of two or three backbone links, and the damping is due to hindered internal rotation (DTO model). The mathematical treatment of these two models is essentially identical, but the physical interpretation of the constants used is very different. The DTO model has previously been applied by one of us to the interpretation of viscoelastic data. It is here applied to the interpretation of dielectric loss data. It is shown that dielectric measurements in dilute solution should very readily discriminate between the two approaches. Finally it is shown that the relaxation time computed from the DTO model is in closer agreement with published NMR data on poly(propylene oxide) 2025, than is the RB relaxation time. The postulates of the DTO model appear to be confirmed for this low molecular weight polymer. An even more sensitive distinction should be available by studies of the relaxation time as a function of polymer concentration.     

An improved picture of methyl dynamics in proteins from slowly relaxing local structure analysis of 2H spin relaxation

Protein dynamics is intimately related to biological function. Core dynamics is usually studied with 2H spin relaxation of the 13CDH2 group, analyzed traditionally with the model-free (MF) approach. We showed recently that MF is oversimplified in several respects. This includes the assumption that the local motion of the dynamic probe and the global motion of the protein are decoupled, the local geometry is simple, and the local ordering is axially symmetric. Because of these simplifications MF has yielded a puzzling picture where the methyl rotation axis is moving rapidly with amplitudes ranging from nearly complete disorder to nearly complete order in tightly packed protein cores. Our conclusions emerged from applying to methyl dynamics in proteins the slowly relaxing local structure (SRLS) approach of Polimeno and Freed (Polimeno, A.; Freed, J. H. J. Phys. Chem. 1995, 99, 10995-11006.), which can be considered the generalization of MF, with all the simplifications mentioned above removed. The SRLS picture derived here for the B1 immunoglobulin binding domain of peptostreptococcal protein L, studied over the temperature range of 15-45 degrees C, is fundamentally different from the MF picture. Thus, methyl dynamics is characterized structurally by rhombic local potentials with varying symmetries and dynamically by tenfold slower rates of local motion. On average, potential rhombicity decreases, mode-coupling increases, and the rate of local motion increases with increasing temperature. The average activation energy for local motion is 2.0 +/- 0.2 kcal/mol. Mode-coupling affects the analysis even at 15 degrees C. The accuracy of the results is improved by including in the experimental data set relaxation rates associated with rank 2 coherences.     

Relaxation spectrometry in solid polymers based on NMR and EPR measurements

Wide distribution of relaxation times is taken into consideration in determination of the activation energy of the molecular motion associated with the motional narrowings of line widths of magnetic resonance spectra. The molecular motion of rotational vibration around the chain axis of polyethylene in urea-polyethylene inclusion complex is examined. Relaxation spectra can be obtained from the data of the motional narrowings of EPR and NMR by assuming the activation energy as a parameter. Also, the representative relaxation times corresponding to EPR and NMR observations can be estimated. These relaxation times give us an activation energy since EPR and NMR observations correspond to different time constants of observations. The activation energy estimated from the data of the representative correlation times is identical with the activation energy obtained as a parameter in determination of the identical relaxation spectrum from the data of motional narrowings of EPR and NMR observations.     

The high-potential flavin and heme of nitric oxide synthase are not magnetically linked: implications for electron transfer

Background: The homodimeric nitric oxide synthase (NOS) catalyzes conversion of l-arginine to l-citrulline and nitric oxide. Each subunit contains two flavins and one protoporphyrin IX heme. A key component of the reaction is the transfer of electrons from the flavins to the heme. The NOS gene encodes two domains linked by a short helix containing a calmodulin-recognition sequence. The reductase domain binds the flavin cofactors, while the oxygenase domain binds heme and l-arginine and additionally mediates the dimerization of the NOS subunits. We investigated the origin of the unusual magnetic properties (rapid-spin relaxation) of an air-stable free radical localized to a reductase domain flavin cofactor.Results: We characterized the air-stable flavin in wild-type NOS, both in the presence and absence of calcium and calmodulin, the imidazole-bound heme complex of wild-type NOS, the NOS Cys415→Ala mutant, and the isolated reductase domain. All preparations of NOS had the same flavin electron-spin relaxation behavior. No half-field transitions or temperature-dependent changes in the linewidth of the radical spin signal were detected.Conclusions: These data suggest that the observed relaxation enhancement of the NOS flavin radical is caused by the environment provided by the reductase domain. No magnetic interaction between the heme and flavin cofactors was detected, suggesting that the flavin and heme centers are probably separated by more than 15 A.     

低剂量铅对大鼠脑组织一氧化氮合酶表达及活性的影响

为探讨低水平铅损伤记忆功能的作用机理，采用ＮＡＤＰＨ－黄递酶组织化学方法和＾３Ｈ－瓜氨酸生成生物检测技术，观察了新生大鼠在４００ｍｇ／Ｌ醋酸铅染毒４０天后对脑组织内一氧化氮合酶表达及活性的影响。结果显示大脑皮质一氧化氮合酶阳性神经元数量明显减少（Ｐ〈０．０５），在海马区脑组织内一氧化氮合酶活性降低５４．４％。结论：低水平铅暴露后可抑制大鼠脑组织内一氧化氮合酶的表达及活性。     

13C NMR spectroscopy of 13C1-labeled octanethiol-protected Au nanoparticles: shifts,relaxations, and particle-size effect

We report here an investigation of metal-ligand interactions in nanoparticles with 13C NMR, using a labeled 13C1-octanethiol, a protecting ligand for self-assembled monolayer (SAM) systems, in which close proximity of the 13C1 to the metal surface serves as an effective probe for the changing electronic environment. Several remarkable results have been obtained: as the metal core size increases from 1.6 to 4.0 nm, the 13C1 spectrum is downshifted from 40.5 to 53 ppm, and the spin-spin relaxation rate, T2-1, increases while the spin-lattice relaxation ratio decreases. Although the spin-lattice relaxation may be due to particle tumbling and ligand motion in the liquid state, the main source of the spin-spin relaxation, and NMR shift, is most possibly due to the changing electronic properties of the metal core.