Deuterium Relaxation Research Articles

Deuterium spin relaxation of fractionally deuterated ribonuclease H using paired 475 and 950MHz NMR spectrometers.

Deuterium (2H) spin relaxation of 13CH2D methyl groups has been widely applied to investigate picosecond-to-nanosecond conformational dynamics in proteins by solution-state NMR spectroscopy. The B0 dependence of the 2H spin relaxation rates is represented by a linear relationship between the spectral density function at three discrete frequencies J(0), J(ωD) and J(2ωD). In this study, the linear relation between 2H relaxation rates at B0 fields separated by a factor of two and the interpolation of rates at intermediate frequencies are combined for a more robust approach for spectral density mapping. The general usefulness of the approach is demonstrated on a fractionally deuterated (55%) and alternate 13C-12C labeled sample of E. coli RNase H. Deuterium relaxation rate constants (R1, R1ρ, RQ, RAP) were measured for 57 well-resolved 13CH2D moieties in RNase H at 1H frequencies of 475MHz, 500MHz, 900MHz, and 950MHz. The spectral density mapping of the 475/950MHz data combination was performed independently and jointly to validate the expected relationship between data recorded at B0 fields separated by a factor of two. The final analysis was performed by jointly analyzing 475/950MHz rates with 700MHz rates interpolated from 500/900MHz data to yield six J(ωD) values for each methyl peak. The J(ω) profile for each peak was fit to the original (τM, Sf2, τf) or extended model-free function (τM, Sf2, Ss2, τf, τs) to obtain optimized dynamic parameters.

Fitting Side-Chain NMR Relaxation Data Using Molecular Simulations.

Proteins display a wealth of dynamical motions that can be probed using both experiments and simulations. We present an approach to integrate side-chain NMR relaxation measurements with molecular dynamics simulations to study the structure and dynamics of these motions. The approach, which we term ABSURDer (average block selection using relaxation data with entropy restraints), can be used to find a set of trajectories that are in agreement with relaxation measurements. We apply the method to deuterium relaxation measurements in T4 lysozyme and show how it can be used to integrate the accuracy of the NMR measurements with the molecular models of protein dynamics afforded by the simulations. We show how fitting of dynamic quantities leads to improved agreement with static properties and highlight areas needed for further improvements of the approach.

Accurate Methyl Group Dynamics in Protein Simulations with AMBER Force Fields.

An approach is presented to directly simulate the dynamics of methyl groups in protein side-chains, as accessible via NMR spin relaxation measurements, by all-atom MD simulations. The method, which does not rely on NMR information or any system-specific adjustable parameters, is based on calculating the time-correlation functions (TCFs) of the C-H bonds in methyl groups and explicitly takes the truncation of the TCFs due to overall tumbling of the molecule into account. Using ubiquitin as a model protein, we show (i) that an accurate description of the methyl dynamics requires reparametrization of the potential energy barriers of methyl group rotation in the AMBER ff99SB*-ILDN force field (and related parameter sets), which was done with CCSD(T) coupled cluster calculations of isolated dipeptides as reference, and (ii) that the TIP4P/2005 solvation model yields overall tumbling correlation times that are in close agreement with experimental data. The methyl axis squared order parameters Saxis2 and associated correlation times τf, obtained within the Lipari-Szabo formalism, are in good agreement with the values derived from NMR deuterium relaxation experiments. Importantly, the relaxation rates and spectral densities derived from MD and NMR agree as well, enabling a direct comparison without assumptions inherent to simplified motional models.

Enhanced spectral density mapping through combined multiple-field deuterium 13CH2D methyl spin relaxation NMR spectroscopy.

Quadrupolar relaxation of 2H (D) nuclear spins is a powerful probe of conformational dynamics in biological macromolecules. Deuterium relaxation rate constants are determined by the spectral density function for reorientation of the C-D bond vector at zero, single-quantum, and double-quantum 2H frequencies. In the present work, 2H relaxation rate constants were measured for an E. coli ribonuclease H [U-2H, 15N] ILV-[13CH2D] sample using 400, 500, 800, and 900 MHz NMR spectrometers and analyzed by three approaches to determine spectral density values. First, data recorded at each static magnetic field were analyzed independently. Second, data recorded at 400 and 800 MHz were analyzed jointly and data recorded at other fields were analyzed independently. Third, data recorded at 400 and 500 MHz were interpolated to 450 MHz, and the resulting two pairs of data, corresponding to 400 MHz/800 MHz and 450 MHz/900 MHz, were analyzed jointly. The second and third approaches rely on the identity between the double quantum frequency at the lower field and the single quantum frequency at the higher field. Spectral density values for 32 of the 48 resolvable ILV methyl resonances were fit by the Lipari-Szabo model-free formalism and used to validate the three methods. The three spectral density mapping methods performed equally well in cross validation with data recorded at 700 MHz. However, the third method yielded approximately 10-15% more precise estimates of model-free parameters and consequently provides a general strategy for analysis of 2H spin relaxation data in biological macromolecules.

Molecular Dynamics of Cyclodextrins in Water Solutions from NMR Deuterium Relaxation: Implications for Cyclodextrin Aggregation.

The aggregation of the most common natural cyclodextrins (α-, β-, and γ-) in aqueous solutions is addressed by studying the CD-CD interactions using deuterium relaxation rates for deuterium labeled CDs. Relaxation times (T1) and their corresponding relaxation rates (R1 = 1/T1) provide information about the rotational correlation times of CDs and serve as a proxy for solute-solute interactions. Measured T1's for α-, β-, and γ-CD at the lowest CD concentrations were in agreement with predictions of a hydrodynamic model for toroids, in particular with regard to the dependence of T1 on CD size. On the other hand, the dependence of T1's with respect to the increase in CD concentration could not be explained by hydrodynamic or direct interaction between CD molecules, and it is suggested that there is an equilibrium between monomeric and dimeric CD to account for the observed concentration dependence. No evidence in favor of large aggregates of CDs involving a non-negligible fraction was found for the investigated CDs.

Communication: Dissolution DNP reveals a long-lived deuterium spin state imbalance in methyl groups.

We report the generation and observation of long-lived spin states in deuterated methyl groups by dissolution DNP. These states are based on population imbalances between manifolds of spin states corresponding to irreducible representations of the C3v point group and feature strongly dampened quadrupolar relaxation. Their lifetime depends on the activation energies of methyl group rotation. With dissolution DNP, we can reduce the deuterium relaxation rate by a factor up to 20, thereby extending the experimentally available time window. The intrinsic limitation of NMR spectroscopy of quadrupolar spins by short relaxation times can thus be alleviated.

Dynamic Nuclear Polarization and Relaxation of H and D Atoms in Solid Mixtures of Hydrogen Isotopes

We report on a study of Dynamic Nuclear Polarization and electron and nuclear spin relaxation of atomic hydrogen and deuterium in solid molecular matrices of H$_{2}$, D$_{2}$, and HD mixtures. The electron and nuclear spin relaxation times ($T_{1e}$ and $T_{1N}$) were measured within the temperature range 0.15-2.5$\,$K in a magnetic field of 4.6 T, conditions which ensure a high polarization of electron spins. We found that $T_{1e}$ is nearly temperature independent in this temperature range, while $T_{1N}$ decreased by 2 orders of magnitude. Such strong temperature dependence is typical for the nuclear Orbach mechanism of relaxation via the electron spins. We found that the nuclear spins of H atoms in solid D$_{2}$ and D$_{2}:$HD can be efficiently polarized by the Overhauser effect. Pumping the forbidden transitions of H atoms also leads to DNP, with the efficiency strongly dependent on the concentration of D atoms. This behaviour indicates the Cross effect mechanism of the DNP and nuclear relaxation, which turns out to be well resolved in the conditions of our experiments. Efficient DNP of H atoms was also observed when pumping the middle D line located in center of the ESR spectrum. This phenomenon can be explained in terms of clusters or pairs of H atoms with strong exchange interaction. These clusters have partially allowed transitions in the center of the ESR spectrum and DNP may be created via the resolved Cross effect.

An SRLS Study of 2H Methyl-Moiety Relaxation and Related Conformational Entropy in Free and Peptide-Bound PLCγ1C SH2.

The two-body (protein and probe) coupled-rotator slowly relaxing local structure (SRLS) approach for NMR relaxation in proteins is extended to derive conformational entropy, Ŝ. This version of SRLS is applied to deuterium relaxation from the C-CDH2 bonds of free and peptide-bound PLCγ1C SH2. Local C-CDH2 motion is described by a correlation time for local diffusion, τ2, and a Maier-Saupe potential, u. On average, τ2, which largely fulfills τ2 ≪ τ1 (τ1 - correlation time for global tumbling), is 270 ± 41 ps and u is 2 ± 0.1 kBT. The PLCγ1C SH2 data were analyzed previously with the model-free (MF) method. SRLS is a generalization of MF, assumed so far to yield the latter for τ2 ≪ τ1 and simple local geometry. Despite these conditions being fulfilled, we find here that τ2 and u differ substantially from their MF counterparts. This is shown to stem from MF (a) disregarding mode-coupling of the first type (see below) and (b) parametrizing the methyl-moiety-related spectral density function (SDF). Our main interest lies in ΔŜ, the conformational entropy difference between the peptide-bound and free PLCγ1C SH2 forms. We find that ΔŜ is rendered inaccurate in MF because factors a and b above impair the accuracy of Saxis, the parameter on which the calculation of ΔŜ is based. Conformational entropy was obtained previously using various simple system-specific models. SRLS is unique in obtaining this important thermodynamic quantity based on a general physically well-defined local potential. It is also unique in its ability to extract the information inherent in 2H relaxation parameters from methyl moieties in protein with accuracy commensurate with data sensitivity.

The unusual internal motion of the villin headpiece subdomain.

The thermostable 36-residue subdomain of the villin headpiece (HP36) is the smallest known cooperatively folding protein. Although the folding and internal dynamics of HP36 and close variants have been extensively studied, there has not been a comprehensive investigation of side-chain motion in this protein. Here, the fast motion of methyl-bearing amino acid side chains is explored over a range of temperatures using site-resolved solution nuclear magnetic resonance deuterium relaxation. The squared generalized order parameters of methyl groups extensively spatially segregate according to motional classes. This has not been observed before in any protein studied using this methodology. The class segregation is preserved from 275 to 305 K. Motions detected in Helix 3 suggest a fast timescale of conformational heterogeneity that has not been previously observed but is consistent with a range of folding and dynamics studies. Finally, a comparison between the order parameters in solution with previous results based on solid-state nuclear magnetic resonance deuterium line shape analysis of HP36 in partially hydrated powders shows a clear disagreement for half of the sites. This result has significant implications for the interpretation of data derived from a variety of approaches that rely on partially hydrated protein samples.

The Behavior of Water in Collagen and Hydroxyapatite Sites of Cortical Bone: Fracture, Mechanical Wear, and Load Bearing Studies.

The mechanical properties of cortical bone, which is largely comprised of collagen, hydroxyapatite, and water, are known to hinge on hydration. Recently, the characteristics of water in bone have drawn attention as potential markers of bone quality. We report on the dynamics, diffusion, population, and exchange of water in cortical bone by NMR relaxation and diffusion methodologies. Relaxation measurements over timescales ranging from 0.001 to 4.2 s reveal two distinguishable water environments. Systematic exposure to ethylenediaminetetraacetic acid or collagenase reveals one peak in our 2D relaxation map belonging to water present in the hydroxyapatite rich environment, and a second peak with shorter relaxation times arising from a collagen rich site. Diffusion-T2 measurements allowed for direct measurement of the diffusion coefficient of water in all observable reservoirs. Further, deuterium relaxation methods were applied to study cortical bone under an applied force, following mechanical wear or fracture. The tumbling correlation times of water reduce in all three cases, indicating that water dynamics may be used as a probe of bone quality. Lastly, changes in the relative populations and correlation times of water in bone under an applied force suggest that load bearing occurs largely in the collagen rich environment and is reversible.

Probing Side-Chain Dynamics in Proteins by the Measurement of Nine Deuterium Relaxation Rates Per Methyl Group

We demonstrate the feasibility of the measurement of up to nine deuterium spin relaxation rates in 13CHD2 and 13CH2D methyl isotopomers of small proteins. In addition to five measurable 2H relaxation rates in a 13CH2D methyl group (Millet, O.; Muhandiram, D. R.; Skrynnikov, N. R.; Kay, L. E. J. Am. Chem. Soc. 2002, 124, 6439-48), the measurement of additional four rates of (nearly) single-exponentially decaying magnetization terms in methyl groups of the 13CHD2 variety is reported. Consistency relationships between 2H spin relaxation rates measured in the two different types of methyl groups are derived and verified experimentally for a subset of methyl-containing side chains in the protein ubiquitin. A detailed comparison of methyl-bearing side-chain dynamics parameters obtained from relaxation measurements in 13CH2D and 13CHD2 methyls of ubiquitin at 10, 27, and 40 °C reveals that transverse 2H relaxation rates in 13CHD2 groups are reliable and accurate reporters of the amplitudes of methyl 3-fold axis motions (S(axis)2) for protein molecules with global molecular tumbling times τ(C) >~9 ns. For smaller molecules, simple correction of transverse 2H relaxation rates in 13CHD2 groups is sufficient for the derivation of robust measures of order. Residue-specific distributions of S(axis)2 are consistent with atomic-detail molecular dynamics (MD) results. Both 13CHD2- and 13CH2D-derived S(axis)2 values are in good overall agreement with those obtained from 1 μs MD simulations at all the three temperatures, although some differences in the site-specific temperature dependence between MD- and 2H-relaxation-derived S(axis)2 values are observed.

Extreme-Values Statistics and Dynamics of Water at Protein Interfaces

Immobilized proteins present a unique interface with water. The water translational diffusive motions affect the high-frequency dynamics and the nuclear spin-lattice relaxation as with all surfaces; however, rare binding sites for water in protein systems add very low-frequency components to the dynamics spectrum. Water binding sites in protein systems are not identical, thus distributions of free energies and consequent dynamics are expected. (2)H(2)O spin-lattice relaxation rate measurements as a function of magnetic field strength characterize the local rotational fluctuations for protein-bound water molecules. The measurements are sensitive to dynamics down to the kilohertz range. To account for the data, we show that the extreme-values statistics of rare events, i.e., water dynamics in rare binding sites, implies an exponential distribution of activation energies for the strongest binding events. In turn, for an activated dynamical process, the exponential energy distribution leads to a Pareto distribution for the reorientational correlation times and a power law in the Larmor frequency for the (2)H(2)O spin-lattice relaxation rate constants at low field strengths. The most strongly held water molecules escape from rare binding sites in times on the order of microseconds, which interrupts the intramolecular correlations and causes a plateau in the spin-lattice relaxation rate at very low magnetic field strengths. We examine the magnetic relaxation dispersion (MRD) data using two simple but related models: a protein-bound environment for water characterized by a single potential well and a protein-bound environment characterized by a double potential well where the potential functions for the local motions of the bound-state water are of different depth. This analysis is applied to D(2)O deuterium spin-lattice relaxation on cross-linked albumin and lysozyme, which is dominated by the intramolecular relaxation driven by the dynamical modulation of the nuclear electric quadrupole coupling. We also separate the intramolecular from the intermolecular contribution to water proton spin-lattice relaxation by isotope dilution and show that the intramolecular proton data map onto the deuterium relaxation by a scale factor implied by the relative strength of the quadrupole and dipolar couplings. The temperature and pH dependence of the magnetic relaxation dispersion are complex and accounted for by changing only the weighting factors in a superposition of contributions from single-well and double-well contributions. These experiments show that the reorientational dynamics spectrum for water, in and on a protein, is characterized by a strongly asymmetric distribution with a long-time tail that extends at least to microseconds.

Counterion Effects and Dynamics of Parathion in Anionic Lyomesophases

Ingestion of parathion produces catastrophic effects on mammals. Transformed into paraoxon, it inhibits acetylcholinesterase, producing acetylcholine accumulation. The distribution, orientation, and dynamics of parathion in different hydrophobic bilayer environments is interesting from both ecological and biological perspectives. A study of parathion-d4 dissolved in two nematic discotic lyotropic liquid crystals made of sodium and cesium decylsulfate (CsDS and NaDS)/decanol (10% 1,1-dideuterodecanol)/water (0.1% D2O)/M2SO4 (M = Na+, Cs+), is presented. Deuterium quadrupole splittings and relaxation times of all deuteriated species were measured. Parathion is strongly attached to both aggregates, increasing the alignment of CsDS and decreasing the alignment of NaDS. Molecular dynamics trajectories were calculated for both mesophases. CsDS appears more neutralized than NaDS. Despite the surface charge, parathion is associated to both aggregates, located near the interface, with the nitro group oriented to the headgroups and the ethoxy chains toward the hydrophobic core. When included in the CsDS interface, it stabilizes the system by shielding repulsive electrostatic interactions among headgroups. Included in NaDS, parathion induces an increase in the distance among counterions and sulfate headgroups, thus decreasing the degree of order.

Intermediate rate atomic trajectories of RNA by solid-state NMR spectroscopy.

Many RNAs undergo large conformational changes in response to the binding of proteins and small molecules. However, when RNA functional dynamics occur in the nanosecond-microsecond time scale, they become invisible to traditional solution NMR relaxation methods. Residual dipolar coupling methods have revealed the presence of extensive nanosecond-microsecond domain motions in HIV-1 TAR RNA, but this technique lacks information on the rates of motions. We have used solid-state deuterium NMR to quantitatively describe trajectories of key residues in TAR by exploiting the sensitivity of this technique to motions that occur in the nanosecond-microsecond regime. Deuterium line shape and relaxation data were used to model motions of residues within the TAR binding interface. The resulting motional models indicate two functionally essential bases within the single-stranded bulge sample both the free and Tat-bound conformations on the microsecond time scale in the complete absence of the protein. Thus, our results strongly support a conformational capture mechanism for recognition: the protein does not induce a new RNA structure, but instead captures an already-populated conformation.

Redox-Dependent Domain Rearrangement of Protein Disulfide Isomerase Coupled with Exposure of Its Substrate-Binding Hydrophobic Surface

Protein disulfide isomerase (PDI) is a major protein in the endoplasmic reticulum, operating as an essential folding catalyst and molecular chaperone for disulfide-containing proteins by catalyzing the formation, rearrangement, and breakage of their disulfide bridges. This enzyme has a modular structure with four thioredoxin-like domains, a, b, b', and a', along with a C-terminal extension. The homologous a and a' domains contain one cysteine pair in their active site directly involved in thiol-disulfide exchange reactions, while the b' domain putatively provides a primary binding site for unstructured regions of the substrate polypeptides. Here, we report a redox-dependent intramolecular rearrangement of the b' and a' domains of PDI from Humicola insolens, a thermophilic fungus, elucidated by combined use of nuclear magnetic resonance (NMR) and small-angle X-ray scattering (SAXS) methods. Our NMR data showed that the substrates bound to a hydrophobic surface spanning these two domains, which became more exposed to the solvent upon oxidation of the active site of the a' domain. The hydrogen-deuterium exchange and relaxation data indicated that the redox state of the a' domain influences the dynamic properties of the b' domain. Moreover, the SAXS profiles revealed that oxidation of the a' active site causes segregation of the two domains. On the basis of these data, we propose a mechanistic model of PDI action; the a' domain transfers its own disulfide bond into the unfolded protein accommodated on the hydrophobic surface of the substrate-binding region, which consequently changes into a "closed" form releasing the oxidized substrate.

Nuclear relaxation and critical fluctuations in membranes containing cholesterol

Nuclear resonance frequencies in bilayer membranes depend on lipid composition. Our calculations describe the combined effects of composition fluctuations and diffusion on nuclear relaxation near a miscibility critical point. Both tracer and gradient diffusion are included. The calculations involve correlation functions and a correlation length xi=xi(0)T/(T-T(c)), where T-T(c) is temperature above the critical temperature and xi(0) is a parameter of molecular length. Several correlation functions are examined, each of which is related in some degree to the Ising model correlation function. These correlation functions are used in the calculation of transverse deuterium relaxation rates in magic angle spinning and quadrupole echo experiments. The calculations are compared with experiments that report maxima in deuterium and proton nuclear relaxation rates at the critical temperature [Veatch et al., Proc. Nat. Acad. Sci. U.S.A. 104, 17650 (2007)]. One Ising-model-related correlation function yields a maximum 1/T(2) relaxation rate at the critical temperature for both magic angle spinning and quadrupole echo experiments. The calculated rates at the critical temperature are close to the experimental rates. The rate maxima involve relatively rapid tracer diffusion in a static composition gradient over distances of up to 10-100 nm.

Fast structural dynamics in reduced and oxidized cytochrome c

The sub-nanosecond structural dynamics of reduced and oxidized cytochrome c were characterized. Dynamic properties of the protein backbone measured by amide (15)N relaxation and side chains measured by the deuterium relaxation of methyl groups change little upon change in the redox state. These results imply that the solvent reorganization energy associated with electron transfer is small, consistent with previous theoretical analyses. The relative rigidity of both redox states also implies that dynamic relief of destructive electron transfer pathway interference is not operational in free cytochrome c.

Solid state water motions revealed by deuterium relaxation in 2H 2O-synthesized kanemite and 2H 2O-hydrated Na +-Zeolite A

Deuterium NMR relaxation experiments, low temperature deuterium NMR lineshape analysis, and FTIR spectra are consistent with a new model for solid state jump dynamics of water in 2H 2O-synthesized kanemite and 2H 2O-hydrated Na +-Zeolite A. Exchange occurs between two populations of water: one in which water molecules are directly coordinated to sodium ions and experience C 2 symmetry jumps of their OH bonds, and a population of interstitial water molecules outside the sodium ion coordination sphere that experience tetrahedral jumps of their OH bonds. For both samples the C 2 jump rate is much faster than the tetrahedral jump rate. 2H NMR relaxation experiments match well with the fast exchange regime of the model over a wide range of temperatures, including room temperature and above. For hydrated Zeolite A, the kinetic activation parameters for the tetrahedral and C 2 symmetry jumps are Δ H tet ‡ = +17 kJ/mol, Δ S tet ‡ = −109 J/(mol K), Δ H C 2 ‡ = + 19 kJ / mol , and Δ S C 2 ‡ = - 20 J / ( mol K ) . For kanemite, Δ H tet ‡ = +23 kJ/mol, Δ S tet ‡ = −69 J/(mol K), Δ H C 2 ‡ = + 23 kJ/mol , and Δ S C 2 ‡ = - 11 J / ( mol K ) .

Re-Evaluation of the Model-Free Analysis of Fast Internal Motion in Proteins Using NMR Relaxation

NMR spin relaxation retains a central role in the characterization of the fast internal motion of proteins and their complexes. Knowledge of the distribution and amplitude of the motion of amino acid side chains is critical for the interpretation of the dynamical proxy for the residual conformational entropy of proteins, which can potentially significantly contribute to the entropy of protein function. A popular treatment of NMR relaxation phenomena in macromolecules dissolved in liquids is the so-called model-free approach of Lipari and Szabo. The robustness of the mode-free approach has recently been strongly criticized and the remarkable range and structural context of the internal motion of proteins, characterized by such NMR relaxation techniques, attributed to artifacts arising from the model-free treatment, particularly with respect to the symmetry of the underlying motion. We develop an objective quantification of both spatial and temporal asymmetry of motion and re-examine the foundation of the model-free treatment. Concerns regarding the robustness of the model-free approach to asymmetric motion appear to be generally unwarranted. The generalized order parameter is robustly recovered. The sensitivity of the model-free treatment to asymmetric motion is restricted to the effective correlation time, which is by definition a normalized quantity and not a true time constant and therefore of much less interest in this context. With renewed confidence in the model-free approach, we then examine the microscopic distribution of side chain motion in the complex between calcium-saturated calmodulin and the calmodulin-binding domain of the endothelial nitric oxide synthase. Deuterium relaxation is used to characterize the motion of methyl groups in the complex. A remarkable range of Lipari-Szabo model-free generalized order parameters are seen with little correlation with basic structural parameters such as the depth of burial. These results are contrasted with the homologous complex with the neuronal nitric oxide synthase calmodulin-binding domain, which has distinctly different thermodynamic origins for high affinity binding.

Deuterium Magnetic Relaxation Process during the Polymerization of Hemoglobin S

The deuterium and the proton spin–spin relaxation times are investigated at 4 MHz in partially deuterated samples of hemoglobin A and S at 36 °C during spontaneous deoxygenation. Deuterium relaxation shows a sigmoidal behavior describing the three characteristic phases of hemoglobin S (HbS) polymerization. The coincidence between the behaviors of deuterium and proton relaxation supports the dominant effect of agglutination on macromolecular mobility. Evidences of an increase of the internal electric field gradient and the appearance of a modified charge distribution inside the HbS solution, as a result of the polymerization process under spontaneous deoxygenation, were not found.