Comments on the use of the order parameters obtained from 2H-NMR to describe the anisotropic motions of the methylene groups of the fatty acyl chains in lipid bilayer membranes

The informational content of a deuteron quadrupole splitting obtained from a methylene group undergoing anisotropic motion is inversely proportional to the degree of symmetry underlying this motion. To accurately assess the power and the limitation of ²H-NMR, the motional symmetry of the methylene groups was strictly examined. From the two orthogonal and geometrical planes of symmetry of a methylene group one was found to remain a plane of symmetry for the motion. The other plane was shown, by a quantitative evaluation, to keep its symmetry property only in first approximation. The direction defined by the intersection of the two orthogonal planes was not found to be a motional axis of axial symmetry (even as a poor assumption). However, to a good approximation the motion of this direction with respect to the bilayer normal can be specified by the deuteron quadrupole splitting arising from the particular geometry of a given methylene group.     

NMR-relaxation in hydrated collagen from the spotted dogfish]

Collagen samples from dog-fish egg case at different water content were studied by the 1H NMR relaxation method. The dependences of the proton spin-lattice and spin-spin relaxation rates on the concentration of water in hydrated native collagen were measured. The fractions of water protons of different mobility and their corresponding spin-spin and spin-lattice relaxation rates were determined in a multi-phase model of water protons in natural biopolymer-water systems. The correlation times were calculated as the characteristics of molecular motion in hydrated collagens with different content of absorbed water. The results obtained were compared with literature data of pulse NMR studies of molecular mobility in other collagen fibers.     

NMR spin grouping and correlation exchange analysis. Application to low hydration NaDNA paracrystals.

The NMR spin-grouping technique is applied to low hydration oriented fibers of NaDNA to study the role of exchange in determining the apparent (observed) spin relaxation of the system. The analysis proceeds in three steps: first, the apparent proton relaxation is measured at high fields, with both selective and nonselective inversion pulse sequences, and in the rotating frame. The spin-grouping technique is used in all spin-lattice relaxation measurements to provide the optimum apparent relaxation characterization of the sample. Next, all apparent results are analyzed for exchange. In this analysis the results from the high field and rotating frame experiments (which probe the exchange at two different time scales) are correlated to determine the inherent (or true) spin relaxation parameters of each of the proton groups in the system. The results of selective inversion T1 measurements are also incorporated into the exchange analysis. Finally, the dynamics of each spin group are inferred from the inherent relaxation characterization. The low hydration NaDNA structure is such that the exchange between the protons on the water and those on the NaDNA is limited, a priori, to dipolar mixing. The results of the exchange analysis indicate that the dipolar mixing between water and NaDNA protons is faster than the spin diffusion within the NaDNA proton group itself. The spin-diffusion on the macromolecule is the bottleneck for the exchange between the water protons and the NaDNA protons. The water protons serve as the relaxation sink both at high fields and in the rotating frame for the total NaDNA-water spin bath. The inherent relaxation of the water is characteristic of water undergoing anisotropic motion with a fast reorientational correlation time about one axis (5 X 10(-10) less than or equal to tau r less than or equal to 8 X 10(-9)S) which is about three orders of magnitude slower than that of water in the bulk; and a slow tumbling correlation time for this axis (1.5 x 10(-7) less than or equal to tau t less than or equal to 8 x 10(-7)S) which is two orders of magnitude slower yet.     

Intrinsic proton relaxation parameters of hydrated polyglycine from two‐dimensional time domain NMR

Proton two‐dimensional time domain nmr involving T₁, T_1ρ, T_1D, and T₂ measurements was applied to hydrated polyglycine powders. The results were analyzed for magnetization exchange and found to be consistent with a general three‐site (glycine–water–glycine) exchange model. The intrinsic glycine and water proton relaxation parameters as well as the three exchange rates were obtained. Estimates of correlation times for water molecule motion at hydration sites are presented. © 1999 John Wiley & Sons, Inc. Biopoly 50: 630–640, 1999     

Oxygen-17 and deuterium nuclear magnetic relaxation studies of lysozyme hydration in solution: field dispersion, concentration, pH/pD, and protein activity dependences

A comparison of 17O and 2H NMR relaxation rates of water in lysozyme solutions as a function of concentration, pH/pD, and magnetic field suggests that only 17O monitors directly the hydration of lysozyme in solution. NMR measurements are for the first time extended to 11.75 T. Lysozyme hydration data are analyzed in terms of an anisotropic, dual-motion model with fast exchange of water between the "bound" and "free" states. The analysis yields 180 mol "bound" water/mol lysozyme and two correlation times of 7.4 ns ("slow") and 29 ps ("fast") for the bound water population at 27 degrees C and pH 5.1, in the absence of salt, assuming anisotropic motions of water with an order parameter value for bound water of 0.12. Under these conditions, the value of the slow correlation time of bound water (7.4 ns) is consistent with the value of 8 ns obtained by frequency-domain fluorescence techniques for the correlation time associated with the lysozyme tumbling motion in solutions without salt. In the presence of 0.1 M NaCl the hydration number increases to 290 mol/mol lysozyme at pD 4.5 and 21 degrees C. The associated correlation times at 21 degrees C in the presence of 0.1 M NaCl are 4.7 ns and 15.5 ps, respectively. The value of the slow correlation time of 4.7 ns is consistent with the calculated value (4.9 ns) for the lysozyme monomer tumbling in solution. The systematic deviations of the relaxation rates, estimated with the single-exponential approximation, from the theoretical, multiexponential nuclear (I' + 1/2) spin relaxation are evaluated at various frequencies for 17O (I = 5/2) with the first-order, linear approximation (25). All NMR relaxation data for hydrated lysozymes are affected by protein activity and are sensitive both to the ionization of protein side chains and to the state of protein aggregation.     

Glycerolipids: common features of molecular motion in bilayers

In the present study, analysis of 2H NMR line-shape and spin-lattice relaxation behavior has been used to investigate the dynamics of several glycolipid and phospholipid bilayers. The gel-phase spectra of these lipids labeled at the C3 position of the glycerol backbone are broad (approximately 90 kHz) and characteristic of fast-limit axially asymmetric motion. Moreover, anisotropic spin-lattice relaxation is observed in all of these systems. The line-shape and relaxation features of the lipids in the gel phase were best simulated by using a fast-limit three-site jump model, with relative site populations of 0.46, 0.34, and 0.20. This motion is associated with an internal jump about the C2-C3 bond of the glycerol backbone. A second motion, rotation about the long axis of the molecule, is needed to account for the observed temperature dependence of the quadrupolar echo amplitude and the spectral line shape above and below the gel to liquid-crystalline phase transition temperature. On the other hand, the gel-phase spectra of phospholipids labeled at the C2 position of the glycerol backbone are also characterized by a fast internal motion, which is simulated by a two-site librational jump. The results indicate that the glycerol backbone dynamics of the glycolipid and phospholipid systems investigated in this study can be described in terms of common fast internal motions and a slower whole molecule axial motion. These results are compared with previous dynamic studies of similar systems.     

Dynamic Structure of Proteins in Solid State. 1H and 13C NMR Relaxation Study

Abstract

Temperature dependencies of ¹H non-selective NMR T₁ and T₂ relaxation times measured at two resonance frequencies and natural abundance ^l3C NMR relaxation times T_l and T_lr measured at room temperature have been studied in a set of dry and wet solid proteins—;Bacterial RNase, lysozyme and Bovine serum albumin (BSA). The proton and carbon data were interpreted in terms of a model supposing three kinds of internal motions in a protein. These are rotation of the methyl protons around the axis of symmetry of the methyl group, and fast and slow oscillations of all atoms. The correlation times of these motions in solid state are found around 10^?11, 10^?9 and 10^?6 s, respectively. All kinds of motion are characterized by the inhomogeneous distribution of the correlation times. The protein dehydration affects only the slow internal motion. The amplitude of the slow motion obtained from the carbon data is substantially less than that obtained from the proton data. This difference can be explained by taking into account different relative inter- and intra- chemical group contributions to the proton and carbon second moments. The comparison of the solid state and solution proton relaxation data showed that the internal protein dynamics in these states is different: the slow motion seems to be few orders of magnitude faster in solution.     

The dynamics of the DNA hydration shell at gigahertz frequencies

We have used Brillouin scattering to measure the linewidths and frequencies of GHz acoustic phonons in Na- and Li-DNA films as a function of temperature between 300 and 140 K for samples that were dry, lightly, and heavily hydrated. The linewidths decrease with falling temperature and water contents, indicating that coupling to a water relaxation is the main source of phonon damping. The strength of the relaxation was determined using measurements of the phonon linewidth as a function of frequency, and confirmed by comparison of measured and calculated spectral profiles. The relaxation strength is anisotropic, being greater for phonons propagating perpendicular to the helix axis. The hydrated DNA exhibits both a rapid relaxation (≤ 10^?11 s per radian) giving rise to a classical f² damping, and a slower motion with a relaxation time that varies from ～ 4 × 10^?11 s per radian (primary hydration shell) to ～ 2 × 10^?12 s per radian (secondary hydration shell) at room temperature. In the frequency interval that bounds these relaxation times (～ 4 to 80 GHz) we expect degrees of freedom associated with the primary hydration shell to be important. The sample with primary hydration follows a simple Arrhenius behavior with ΔH ～ 5 kcal mole^?1. The effective activation energy for the sample with secondary hydration is somewhat higher (indicating a more cooperative water relaxation) and varies strongly with temperature. The elastic moduli change much more than can be accounted for by relaxation, indicating the importance of water motion in softening interatomic potentials. The extent of the softening caused by the “unfreezing” of water motion is similar to the degree of softening caused by hydrating the sample.     

Characterization of the overall and internal dynamics of short oligonucleotides by depolarized dynamic light scattering and NMR relaxation measurements

The dynamics of three synthetic oligonucleotides d(CG)4, d(CG)6, and d(CGCGTTGTTCGCG) of different length and shape were studied in solution by depolarized dynamic light scattering (DDLS) and time-resolved nuclear Overhauser effect cross-relaxation measurements. For cylindrically symmetric molecules the DDLS spectrum is dominated by the rotation of the main symmetry axis of the cylinder. The experimental correlation times describe the rotation of the oligonucleotides under hydrodynamic stick boundary conditions. It is shown that the hydrodynamic theory of Tirado and Garcia de la Torre gives good predictions of the rotational diffusion coefficients of cylindrically symmetric molecules of the small axial ratios studied here. These relations are used to calculate the solution dimensions of the DNA fragments from measured correlation times. The hydrodynamic diameter of the octamer and dodecamer is 20.5 +/- 1.0 A, assuming a rise per base of 3.4 A. The tridecamer, d(CGCGTTGTTCGCG), adopts a hairpin structure with nearly spherical dimensions and a diameter of 23.0 +/- 2.0 A. The DDLS relaxation measurements provide a powerful method for distinguishing between different conformations of the oligonucleotides (e.g., DNA double-helix versus hairpin structure). Furthermore, the rotational correlation times are a very sensitive probe of the length of different fragments. The NMR results reflect the anisotropic motion of the molecules as well as the amount of local internal motion present. The experimental correlation time from NMR is determined by the rotation of both the short and long axes of the oligonucleotide.(ABSTRACT TRUNCATED AT 250 WORDS)     

Pulsed NMR studies of water in striated muscle non-freezing factor of water II. Spin-lattice relaxation times and the dynamics of the non-freezing fraction of water

Spin-lattice relaxation times for the water protons in frog gastrocnemius muscle are reported over the temperature range 193 to 283 °K at Larmor frequencies of 30 and 60 MHz. Results of measurements under similar conditions of the transverse relaxation times are also reported. The relaxation times of the non-freezing 20% of the muscle water are interpreted in terms of water molecules, absorbed on or interacting with the proteins, and which are undergoing anisotropic motion, probably with a distribution of correlation times. Proton spin-lattice relaxation times are also reported for muscles under tension, the tension being produced by loading of the muscles with varying weights.     

Sampling of protein dynamics in nanosecond time scale by 15N NMR relaxation and self-diffusion measurements.

This paper presents a procedure for detection of intermediate nanosecond internal dynamics in globular proteins. The procedure uses 1H-15N relaxation measurements at several spectrometer frequencies and hydrodynamic calculations based on experimental self-diffusion coefficients. New heteronuclear experiments, using pulse field gradients, are introduced for the measurement of translation diffusion coefficients of 15N labeled proteins. An advanced interpretation of recently published (Luginbühl et al., Biochemistry, 36, 7305-7312 (1997)) backbone amide 15N relaxation data, measured at two spectrometers (400 and 750 MHz for 1H) for N-terminal DNA-binding domain (1-63) of 434 repressor, is presented. Non-applicability of commonly used fast (picosecond) dynamics model (FD) was justified by (i) poor fit of relaxation data by the FD model-free spectral density function both for isotropic and anisotropic models of the overall molecular tumbling; (ii) specific dependence of the overall rotation correlation times calculated from T1/T2 ratio on the spectrometer frequency; (iii) mismatch of the ratio of longitudinal 15N relaxation times T1, measured at different spectrometer frequencies, in comparison with that anticipated for the FD model; (iv) significantly underestimated overall rotation correlation time provided by the FD model (5.50+/-0.15 and 5.80+/-0.15 ns for 750 and 400 MHz spectrometer frequency respectively) in comparison with correlation time obtained from hydrodynamics. On the other hand, all relaxation and hydrodynamics data are in good correspondence with the model of intermediate (nanoseconds) dynamics. Overall rotation correlation time of 7.5+/-0.7 ns was calculated from experimental translation self-diffusion rate using hydrodynamics formalism (Garcia de la Torre, J. and Bloomfield, V.A. Quart. Rev. Biophys., 14, 81-139 (1981)). The statistical analysis of 15N relaxation data along with the hydrodynamic consideration clearly revealed that most of the residues in 434(1-63) repressor are involved in the nanosecond internal dynamics characterized by the the mean order parameters of 0.59+/-0.06 and the correlation times of ca. 5 ns.     

1H- and 2H-NMR relaxation in serum albumin solutions

The proton and deuteron relaxation times T1 and T2 were investigated in water and heavy water solutions of fatless human serum albumin. The temperature, concentration and Larmor precession frequency dependences can be well described by the conception of fast exchange in a simple biphasic model of water molecules rotation in the first hydration layer with slight anisotropy of motion. In the protonated systems the intermolecular dipole-dipole relaxation mechanism must be taken into account.     

Anisotropic rotational motions of poly(L-glutamic acid) in the alpha-helix conformation

The anisotropic rotational motion of the backbone and the side chains of poly(L -glutamic acid) in the α-helical structure was investigated using the ¹³C-T₁ and T₂ relaxation times of all carbon atoms with directly attached protons, obtained at a ¹³C-Larmor frequency of 67.89 MHz. The evaluation of the nmr data was carried out according to the previously derived anisotropic diffusion model, in which the macromolecule is considered a rigid rod. The rotation of the backbone is characterized by two diffusion constants, D₁ and D₃, describing the rotation perpendicular to and around the symmetry axis. The additional internal motion of the C^β-methylene group is described as a jump process with a jump rate, k₁, between two allowed rotametric states. Steric considerations indicate that the occupation of the third rotameric position is forbidden. The rotation of the C^γ-methylene group is decribed as a one-dimensional diffusion process around the C^β–C^γ bond. Investigation of the temperature dependence of the relaxation parameters led to the temperature dependence of the dynamic parameters. Activation energies were determined from these data. The dynamic parameters obtained for poly(L -glutamic acid) at 291 K are compared with the corresponding results of a previous study of poly(L -lysine). The development of an anisotropic diffusion model for the motions of the rod-shaped poly(L -lysine) α-helix and its application to the interpretation of the ¹³C-relaxation data of this molecule have already been published previously. In this model, both the overall molecular tumbling and the various internal motions have been characterized by diffusion constants or jump rates typical for each process. These dynamic parameters can be calculated from the spin–lattice relaxation times, the spin–spin relaxation times and the NOE factors of the C^α, C^β, and C^γ nuclei of the polypetide. In the present paper, we describe the application of the above-mentioned dynamic model to the interpretation of ¹³C-relaxation studies of a further homopolypeptide, poly(L -glutamic acid), in the α-helical structure. Furthermore, we studied the temperature dependence of the relaxation times of this polymer and determined the anisotropic diffusion parameters at each temperature. From their temperature dependence and from comparison of our present results with the data of our previous study of poly(L -lysine), we were able to derive new insights into the intramolecular diffusion processes and the excitation of various motions.     

Water and Backbone Dynamics in a Hydrated Protein

Rotational immobilization of proteins permits characterization of the internal peptide and water molecule dynamics by magnetic relaxation dispersion spectroscopy. Using different experimental approaches, we have extended measurements of the magnetic field dependence of the proton-spin-lattice-relaxation rate by one decade from 0.01 to 300 MHz for ¹H and showed that the underlying dynamics driving the protein ¹H spin-lattice relaxation is preserved over 4.5 decades in frequency. This extension is critical to understanding the role of ¹H₂O in the total proton-spin-relaxation process. The fact that the protein-proton-relaxation-dispersion profile is a power law in frequency with constant coefficient and exponent over nearly 5 decades indicates that the characteristics of the native protein structural fluctuations that cause proton nuclear spin-lattice relaxation are remarkably constant over this wide frequency and length-scale interval. Comparison of protein-proton-spin-lattice-relaxation rate constants in protein gels equilibrated with ²H₂O rather than ¹H₂O shows that water protons make an important contribution to the total spin-lattice relaxation in the middle of this frequency range for hydrated proteins because of water molecule dynamics in the time range of tens of ns. This water contribution is with the motion of relatively rare, long-lived, and perhaps buried water molecules constrained by the confinement. The presence of water molecule reorientational dynamics in the tens of ns range that are sufficient to affect the spin-lattice relaxation driven by ¹H dipole-dipole fluctuations should make the local dielectric properties in the protein frequency dependent in a regime relevant to catalytically important kinetic barriers to conformational rearrangements.     

1H-nmr study of water dynamics in hydrated collagen: transverse relaxation-time and diffusion analysis

Water proton transverse relaxation times (T2) and self-diffusion coefficients (D) were measured in randomly oriented hydrated collagen fibers. Three T2 relaxation times were discerned indicating the presence of at least three water fractions in the collagen sample. The D values associated with each water fraction were determined. The diffusion time dependence of D suggests water motion is restricted by macromolecular structure. The experimental results are discussed with reference to the structural properties of hydrated collagen fibers.     

Hydration study of homopolypeptides by (2)H NMR

Deuteron T(1) and T(2) was studied as a function of hydration in homopolyglycine (PG) and homopolyproline (PP). Water deuteron relaxation rates in PG conform to a hydration model involving two types of primary hydration sites where water is directly bonded to the polymer. Once these sites are filled, additional water only bonds to water molecules at the primary sites and in so doing affect their dynamics. PP exhibits an anomalous T(1) and T(2) hydration dependence which has been interpreted in terms of a cooperative water molecule-PP molecule helical conformational rearrangement which occurs once a certain hydration level is reached. The proposal of a water-PP structure is tested using molecular dynamics simulations.     

H and C NMR studies on the temperature-dependent water and protein dynamics in hydrated elastin,myoglobin and collagen

²H NMR spin-lattice relaxation and line-shape analyses are performed to study the temperature-dependent dynamics of water in the hydration shells of myoglobin, elastin, and collagen. The results show that the dynamical behaviors of the hydration waters are similar for these proteins when using comparable hydration levels of h = 0.25–0.43. Since water dynamics is characterized by strongly nonexponential correlation functions, we use a Cole–Cole spectral density for spin-lattice relaxation analysis, leading to correlation times, which are in nice agreement with results for the main dielectric relaxation process observed for various proteins in the literature. The temperature dependence can roughly be described by an Arrhenius law, with the possibility of a weak crossover in the vicinity of 220 K. Near ambient temperatures, the results substantially depend on the exact shape of the spectral density so that deviations from an Arrhenius behavior cannot be excluded in the high-temperature regime. However, for the studied proteins, the data give no evidence for the existence of a sharp fragile-to-strong transition reported for lysozyme at about 220 K. Line-shape analysis reveals that the mechanism for the rotational motion of hydration waters changes in the vicinity of 220 K. For myoglobin, we observe an isotropic motion at high temperatures and an anisotropic large-amplitude motion at low temperatures. Both mechanisms coexist in the vicinity of 220 K. ¹³C CP MAS spectra show that hydration results in enhanced elastin dynamics at ambient temperatures, where the enhancement varies among different amino acids. Upon cooling, the enhanced mobility decreases. Comparison of ²H and ¹³C NMR data reveals that the observed protein dynamics is slower than the water dynamics.     

Rearrangement of the Hydrogen-Bonded Network of the Clathrate Hydrates Encaging Polar Guest

Abstract

Rearrangement process of the hydrogen-bonded network of clathrate hydrate of the polar guest ethylamine is examined by the molecular dynamics simulation. The hydrogen-bonded network rearrangements with reorientation of water or migration of water are observed in the 10 ns trajectories and analyzed in term of a representative connectivity pattern of a time zone longer than a time scale of vibrational motion of molecules. The most frequent rearrangement is the reorientation of single water molecule rotating 180° around its twofold axis in the network unlike Bjerrum's picture of molecular rotation in ice. Migration of water in the host lattice rarely occurs and very long time (several hundred pico second) is required to complete the rearrangement process since cooperative reorientation of many neighboring water is necessarily accompanied. The correlation of reorientational motion of water appears to decay not with the Debye type but rather with a power-law behavior.