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.     

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.     

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.     

Reorientational eigenmode dynamics: a combined MD/NMR relaxation analysis method for flexible parts in globular proteins

An approach is presented for the interpretation of heteronuclear NMR spin relaxation data in mobile protein parts in terms of reorientational eigenmode dynamics. The method is based on the covariance matrix of the spatial functions of the nuclear spin interactions that cause relaxation expressed as spherical harmonics of rank 2. The approach was applied to characterize the dynamics of a loop region of ubiquitin. The covariance matrix was determined from a conformational ensemble generated by a 5 ns molecular dynamics simulation. It was found that the time correlation functions of the dominant eigenmodes decay in good approximation with a single correlation time. From the reorientational eigenmodes, their eigenvalues, and correlation times, NMR relaxation data were calculated in accordance with Bloch-Wangsness-Redfield relaxation theory and directly compared with experimental (15)N relaxation parameters. Using a fitting procedure, agreement between calculated and experimental data was improved significantly by adjusting eigenvalues and correlation times of the dominant modes. The presented procedure provides detailed information on correlated reorientational dynamics of flexible parts in globular proteins. The covariance matrix was linked to the covariance matrix of backbone dihedral angle fluctuations, allowing one to study the motional behavior of these degrees of freedom on nano- and subnanosecond time scales.     

Simulated and NMR-derived backbone dynamics of a protein with significant flexibility: a comparison of spectral densities for the betaARK1 PH domain.

A 7.6 ns molecular dynamics trajectory of the betaARK1 PH domain in explicit water with appropriate ions was calculated at 300 K. Spectral densities at omega = 0, omega(N), and 0.87omega(H) and the model-free parameters were evaluated from the experimental as well as the simulated data, taking the anisotropic overall motion of the protein into account. Experimental and simulated spectral densities are in reasonable general agreement for NH bond vectors, where the corresponding motions have converged within the simulation time. A sufficient sampling of the motions for NH bonds within flexible parts of the protein requires a longer simulation time. The simulated spectral densities J(0) and J(omega(N)) are, on average, 4.5% and 16% lower than the experimental data; the corresponding numbers for the core residues are about 6%; the high-frequency spectral densities J(0.87omega(H)) are lower by, on average, 16% (21% for the core). The simulated order parameters, S(2), are also lower, although the overall disagreement between the simulation and experiment is less pronounced: 1% for all residues and 6% for the core. The observed systematic decrease of simulated spectral density and the order parameters compared to the experimental data can be partially attributed to the ultrafast librational motion of the NH bonds with respect to their peptide plane, which was analyzed in detail. This systematic difference is most pronounced for J(0.87omega(H)), which appears to be most sensitive to the slow, subnanosecond time scale of internal motion, whereas J(0) and J(omega(N)) are dominated by the overall rotational tumbling of the protein. Similar discrepancies are observed between the experimentally measured (15)N relaxation parameters (R(1), R(2), NOE) and their values calculated from the simulated spectral densities. The analysis of spectral densities provides additional information regarding the comparison of the simulated and experimental data, not available from the model-free analysis.     

Spin relaxation effects in photochemically induced dynamic nuclear polarization spectroscopy of nuclei with strongly anisotropic hyperfine couplings

We describe experimental results and theoretical models for nuclear and electron spin relaxation processes occurring during the evolution of 19F-labeled geminate radical pairs on a nanosecond time scale. In magnetic fields of over 10 T, electron-nucleus dipolar cross-relaxation and longitudinal DeltaHFC-Deltag (hyperfine coupling anisotropy--g-tensor anisotropy) cross-correlation are shown to be negligibly slow. The dominant relaxation process is transverse DeltaHFC-Deltag cross-correlation, which is shown to lead to an inversion in the geminate 19F chemically induced dynamic nuclear polarization (CIDNP) phase for sufficiently large rotational correlation times. This inversion has recently been observed experimentally and used as a probe of local mobility in partially denatured proteins (Khan, F.; et al. J. Am. Chem. Soc. 2006, 128, 10729-10737). The essential feature of the spin dynamics model employed here is the use of the complete spin state space and the complete relaxation superoperator. On the basis of the results reported, we recommend this approach for reliable treatment of magnetokinetic systems in which relaxation effects are important.     

Theory for spin-lattice relaxation of spin probes on weakly deformable DNA

The weakly bending rod (WBR) model of double-stranded DNA (dsDNA) is adapted to analyze the internal dynamics of dsDNA as observed in electron paramagnetic resonance (EPR) measurements of the spin-lattice relaxation rate, R(1e), for spin probes rigidly attached to nucleic acid-bases. The WBR theory developed in this work models dsDNA base-pairs as diffusing rigid cylindrical discs connected by bending and twisting springs whose elastic force constants are kappa and alpha, respectively. Angular correlation functions for both rotational displacement and velocity are developed in detail so as to compute values for R(1e) due to four relaxation mechanisms: the chemical shift anisotropy (CSA), the electron-nuclear dipolar (END), the spin rotation (SR), and the generalized spin diffusion (GSD) relaxation processes. Measured spin-lattice relaxation rates in dsDNA under 50 bp in length are much faster than those calculated for the same DNAs modeled as rigid rods. The simplest way to account for this difference is by allowing for internal flexibility in models of DNA. Because of this discrepancy, we derive expressions for the spectral densities due to CSA, END, and SR mechanisms directly from a weakly bending rod model for DNA. Special emphasis in this development is given to the SR mechanism because of the lack of such detail in previous treatments. The theory developed in this paper provides a framework for computing relaxation rates from the WBR model to compare with magnetic resonance relaxation data and to ascertain the twisting and bending force constants that characterize DNA.     

Orientational order and dynamics of molecules in the nematic phase 4-trans-(4-trans-n-propylcyclohexyl)cyclohexanenitrile

A sample of 4-trans-(4-trans-n-propylcyclohexyl)cyclohexanenitrile (CCH3) has been synthesized containing six deuterons randomly distributed between axial and equatorial positions in the cyanylated ring. The local orientational order parameters for axes fixed in this ring have been measured by obtaining the deuterium N.M.R. spectrum. The results show that the lack of symmetry and flexibility of the molecule affect the order matrix. The biaxiality in the local order matrix is small and could be close to zero, depending on the location, as yet unknown, of the principal axes. The spectral densities J₁(ω) and J₂(ω) have been measured for a sample oriented with the director orthogonal to B₀. It is shown that these spectral densities cannot be explained by the mechanism of relaxation being caused solely by director fluctuations. It is also not possible to explain the spectral densities by invoking only small-step rotational diffusion. A combination of these two relaxation mechanisms does fit the data.     

Enthalpy recovery in glassy materials: heterogeneous versus homogenous models

Models of enthalpy relaxations of glasses are the basis for understanding physical aging, scanning calorimetry, and other phenomena that involve non-equilibrium and non-linear dynamics. We compare models in terms of the nature of the relaxation dynamics, heterogeneous versus homogeneous, with focus on the Kovacs-Aklonis-Hutchinson-Ramos (KAHR) and the Tool-Narayanaswamy-Moynihan (TNM) approaches. Of particular interest is identifying the situations for which experimental data are capable of discriminating the heterogeneous from the homogeneous scenario. The ad hoc assumption of a single fictive temperature, T(f), is common to many models, including KAHR and TNM. It is shown that only for such single-T(f) models, enthalpy relaxation of a glass is a two-point correlation function in reduced time, implying that experimental results are not decisive regarding the underlying nature of the dynamics of enthalpy relaxation. We also find that the restriction of the common TNM model to a Kohlrausch-Williams-Watts type relaxation pattern limits the applicability of this approach, as the particular choice regarding the distribution of relaxation times is a more critical factor compared with isothermal relaxation experiments. As a result, significant improvements in fitting calorimetry data can be achieved with subtle adjustments in the underlying relaxation time distribution.     

Nuclear magnetic resonance and dielectric noise study of spectral densities and correlation functions in the glass forming monoalcohol 2-ethyl-1-hexanol

The spectral densities related to various relaxation processes of the glass former 2-ethyl-1-hexanol (2E1H), a monohydroxy alcohol, are probed using several nuclear magnetic resonance (NMR) experiments as well as via dielectric noise spectroscopy (DNS). On the basis of the spectral density relating to voltage fluctuations, i.e., without the application of external electrical fields, DNS enables the detection of the structural relaxation and of the prominent, about two decades slower Debye process. The NMR-detected spectral density, sensitive to the orientational fluctuations of the hydroxyl deuteron, also reveals dynamics slower than the structural relaxation, but not as slow as the Debye process. Rotational and translational correlation functions of 2E1H are probed using stimulated-echo NMR techniques which could only resolve the structural dynamics or faster processes. The experimental results are discussed with reference to models that were suggested to describe the dynamics in supercooled alcohols.     

How to measure absolute P3HT crystallinity via 13C CPMAS NMR

We outline the details of acquiring quantitative ¹³C cross‐polarization magic angle spinning (CPMAS) nuclear magnetic resonance on the most ubiquitous polymer for organic electronic applications, poly(3‐hexylthiophene) (P3HT), despite other groups' claims that CPMAS of P3HT is strictly nonquantitative. We lay out the optimal experimental conditions for measuring crystallinity in P3HT, which is a parameter that has proven to be critical in the electrical performance of P3HT‐containing organic photovoltaics but remains difficult to measure by scattering/diffraction and optical methods despite considerable efforts. Herein, we overview the spectral acquisition conditions of the two P3HT films with different crystallinities (0.47 and 0.55) and point out that because of the chemical similarity of P3HT to other alkyl side chain, highly conjugated main chain polymers, our protocol could straightforwardly be extended to other organic electronic materials. Variable temperature ¹H NMR results are shown as well, which (i) yield insight into the molecular dynamics of P3HT, (ii) add context for spectral editing techniques as applied to quantifying crystallinity, and (iii) show why T_1ρ^H, the ¹H spin–lattice relaxation time in the rotating frame, is a more optimal relaxation filter for distinguishing between crystalline and noncrystalline phases of highly conjugated alkyl side‐chain polymers than other relaxation times such as the ¹H spin–spin relaxation time, T₂^H, and the spin–lattice relaxation time in the toggling frame, T_1xz^H. A 7 ms T_1ρ^H spin lock filter, prior to CPMAS, allows for spectroscopic separation of crystalline and noncrystalline ¹³C nuclear magnetic resonance signals. Published 2016. This article is a U.S. Government work and is in the public domain in the USA.     

NMR relaxation parameters of a Lennard-Jones fluid from molecular-dynamics simulations

Ensembles of soft spheres or of Lennard-Jones atoms were studied by molecular dynamics at reduced temperatures from 0.8 to 3, and radial distribution functions, diffusion coefficients, and magnetic dipole-dipole correlation functions were measured as functions of system size. The expected relation between the values of the correlation functions at zero lag time and the integrals of the radial distribution was verified for each system. The measured correlation functions were compared with theoretical expressions derived by [Ayant et al., J. Phys. (Paris) 36, 991 (1975)] and by [Hwang and Freed, J. Chem. Phys. 63, 4017 (1975)]. It was shown that, in order to recover the long-time behavior characteristic of diffusion-controlled relaxation processes, the simulation must comprise at least 10 000 particles. By fitting the simulation results to the Hwang-Freed function, independent values of the diffusion coefficient were obtained, similar but not identical to those computed using the Green-Kubo formalism. The spectral densities of the dipole-dipole interaction were computed as Fourier transforms of the correlation functions. These quantities are less sensitive to model imperfections and reproduce quite well the values derived from theory. The dimensionless spin-lattice and spin-spin relaxation rates were derived from the spectral densities. It was shown that the spin-lattice (longitudinal) relaxation rate goes through a maximum as the temperature increases, while the spin-spin (transverse) rate decreases monotonously.     

NMR paramagnetic relaxation due to the S=5/2 complex, Fe(III)-(tetra-p-sulfonatophenyl)porphyrin: central role of the tetragonal fourth-order zero-field splitting interaction

The metalloporphyrins, Me-TSPP [Me=Cr(III), Mn(III), Mn(II), Fe(III), and TSPP=meso-(tetra-p-sulfonatophenyl)porphyrin], which possess electron spins S=3/2, 2, 5/2, and 5/2, respectively, comprise an important series of model systems for mechanistic studies of NMR paramagnetic relaxation enhancement (NMR-PRE). For these S>1/2 spin systems, the NMR-PRE depends critically on the detailed form of the zero-field splitting (zfs) tensor. We report the results of experimental and theoretical studies of the NMR relaxation mechanism associated with Fe(III)-TSPP, a spin 5/2 complex for which the overall zfs is relatively large (D approximately = 10 cm(-1)). A comparison of experimental data with spin dynamics simulations shows that the primary determinant of the shape of the magnetic relaxation dispersion profile of the water proton R1 is the tetragonal fourth-order component of the zfs tensor. The relaxation mechanism, which has not previously been described, is a consequence of zfs-induced mixing of the spin eigenfunctions of adjacent Kramers doublets. We have also investigated the magnetic-field dependence of electron-spin relaxation for S=5/2 in the presence of a large zfs, such as occurs in Fe(III)-TSPP. Calculations show that field dependence of this kind is suppressed in the vicinity of the zfs limit, in agreement with observation.     

Determination of carbon-13 chemical shielding tensor in the liquid state by combining NMR relaxation experiments and quantum chemical calculations

Based on multifield NMR relaxation measurements and quantum chemistry calculations, a strategy aiming at the determination of the chemical shielding tensor (CST) in the liquid state is described. Brownian motions in the liquid state restrict the direct observation of CST to a third of its trace (isotropic shift), and even if CST can be probed indirectly through some spin relaxation rates (specific longitudinal relaxation rates, dipolar chemical shift anisotropy (CSA) cross-correlation rates), an insufficient number of experimental parameters prevents its complete determination. This lack of information can be compensated by using quantum chemical calculations so as to obtain the molecular CST orientation even if a relatively modest level of computation is used. As relaxation parameters involve a dynamic part, a prerequisite is the determination of the molecular anisotropic reorientation which can be obtained independently from dipolar cross-relaxation rates. A polycyclic molecule exhibiting a well-characterized anisotropic reorientation serves as an example for such a study, and some (but not all) carbon-13 chemical shielding tensors can be accurately determined. A comparison with solid-state NMR data and numerous chemical quantum calculations are presented.     

Exciton states of dynamic DNA double helices: alternating dCdG sequences

The present communication deals with the excited states of the alternating DNA oligomer (dCdG)5.(dCdG)5 which correspond to the UV absorption band around 260 nm. Their properties are studied in the frame of the exciton theory, combining molecular dynamics simulations and quantum chemistry data. It is shown that the dipolar coupling undergoes important variations with the site and the helix geometry. In contrast, the energy of the monomer transitions within the double helix is not sensitive to the local environment. It is thus considered to be distributed over Gaussian curves whose maximum and width are derived from the experimental absorption spectra of nucleosides in aqueous solution. The influence of the spectral width on the excited state delocalization and the absorption spectra is much stronger than that of the oligomer plasticity. About half of the excited states are delocalized over at least two bases. Many of them result from the mixing of different monomer states and extend on both strands. The trends found in the simulated spectra, when going from non-interacting monomers to the duplex, are in agreement with experimental observations. Conformational changes enhance the diversity of the states which can be populated upon excitation at a given energy. The states with larger spatial extent are located close to the maximum of the absorption spectrum.     

A new spin probe of protein dynamics: nitrogen relaxation in 15N-2H amide groups

(15)N spin relaxation data have provided a wealth of information on protein dynamics in solution. Standard R(1), R(1)(rho), and NOE experiments aimed at (15)N[(1)H] amide moieties are complemented in this work by HA(CACO)N-type experiments allowing the measurement of nitrogen R(1) and R(1)(rho) rates at deuterated (15)N[(2)D] sites. Difference rates obtained using this approach, R(1)((15)N[(1)H]) - R(1)((15)N[(2)D]) and R(2)((15)N[(1)H]) - R(2)((15)N[(2)D]), depend exclusively on dipolar interactions and are insensitive to (15)N CSA and R(ex) relaxation mechanisms. The methodology has been tested on a sample of peptostreptococcal protein L (63 residues) prepared in 50% H(2)O-50% D(2)O solvent. The results from the new and conventional experiments are found to be consistent, with respect to both local backbone dynamics and overall protein tumbling. Combining several data sets permits evaluation of the spectral density J(omega(D) + omega(N)) for each amide site. This spectral density samples a uniquely low frequency (26 MHz at a 500 MHz field) and, therefore, is expected to be highly useful for characterizing nanosecond time scale local motions. The spectral density mapping demonstrates that, in the case of protein L, J(omega(D) + omega(N)) values are compatible with the Lipari-Szabo interpretation of backbone dynamics based on the conventional (15)N relaxation data.     

Deuterium spin probes of side-chain dynamics in proteins. 2. Spectral density mapping and identification of nanosecond time-scale side-chain motions

In the previous paper in this issue we have demonstrated that it is possible to measure the five different relaxation rates of a deuteron in (13)CH(2)D methyl groups of (13)C-labeled, fractionally deuterated proteins. The extensive set of data acquired in these experiments provides an opportunity to investigate side-chain dynamics in proteins at a level of detail that heretofore was not possible. The data, acquired on the B1 domain of peptostreptococcal protein L, include 16 (9) relaxation measurements at 4 (2) different magnetic field strengths, 25 degrees C (5 degrees C). These data are shown to be self-consistent and are analyzed using a spectral density mapping procedure which allows extraction of values of the spectral density function at a number of frequencies with no assumptions about the underlying dynamics. Dynamics data from 31 of 35 methyls in the protein for which data could be obtained were well-fitted using the two-parameter Lipari-Szabo model (Lipari, G.; Szabo, A. J. Am. Chem. Soc. 1982, 104, 4546). The data from the remaining 4 methyls can be fitted using a three-parameter version of the Lipari-Szabo model that takes into account, in a simple manner, additional nanosecond time-scale local dynamics. This interpretation is supported by analysis of a molecular dynamics trajectory where spectral density profiles calculated for side-chain methyl sites reflect the influence of slower (nanosecond) time-scale motions involving jumps between rotameric wells. A discussion of the minimum number of relaxation measurements that are necessary to extract the full complement of dynamics information is presented along with an interpretation of the extracted dynamics parameters.     

NMR investigations on dynamical aspects of aging processes in elastomers

Proton spin relaxation measurements have been used to investigate the effect of aging on local and coherent segmental dynamics in cis-1,4-polybutadiene samples. The polymer chains in bulk polybutadiene were crosslinked by exposure to ionizing radiation. The transition of the ¹H-n.m.r. signal from a liquidlike spin system response to a solidlike one is due to crosslinking and network formation by the irradiation and depends on the radiation dose. It is shown that the radiation yields changes in the constrained defect diffusion processes modelling the chain dynamics. Correlation time and memory time for the local and coherent segmental motion strongly depend on radiation dose.     

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.