Internal dynamics of hydroxymethyl rotation from CH2 cross-correlated dipolar relaxation in methyl-β- -glucopyranoside

Conventional relaxation parameters (T₁⁻¹, T₂⁻¹, and NOE), obtained at different temperatures and magnetic fields, are reported for the hydroxymethyl (C6) carbon in methyl-β- -glucopyranoside in a D₂O/DMSO cryosolvent. These data are interpreted with the Lipari–Szabo model. In addition, two-field measurements of longitudinal and spin-locked relaxation rates related to the cross-correlated carbon–proton dipole–dipole interactions for the same carbon are reported. The complete data set consisting the conventional and cross-correlated relaxation parameters is interpreted using a new “hybrid” approach, in which the Lipari–Szabo model for the auto-correlated spectral densities is combined with the two-site jump model for the cross-correlated spectral densities, with the global correlation time as a common parameter. The two-site jump rates thus obtained are in reasonable agreement with the ultrasonic relaxation measurements, and have reasonable temperature dependence.     

NMR relaxation interference effects and internal dynamics in gamma-cyclodextrin

Multiple-magnetic field (9.4, 14.1 and 21.1 T) measurements of (13)C spin-lattice and spin-spin relaxation rates, the heteronuclear Overhauser enhancement and cross-correlated relaxation rates (CCRRs) in the methylene groups are reported for gamma-cyclodextrin in water/dimethylsulfoxide solution at 323 and 343K. The CCRRs are obtained from differences in the initial relaxation rates of the components of the CH(2) triplet in the (13)C spectra. The relaxation data are analyzed using the Lipari-Szabo approach and a novel modification of the two-site jump model. According to the latter model, inclusion of the dipolar (CH,CH(')) cross-correlated longitudinal and transverse relaxation is important for estimating the rate of the conformational jumps in the hydroxymethyl group. Using the dynamic information from the jump model, we have also used the differences in the initial relaxation rates for the triplet components to estimate the anisotropy of the chemical shielding tensor.     

Analytical solution to the Lipari-Szabo model based on the reduced spectral density approximation offers a novel protocol for extracting motional parameters.

An analytical solution to the Lipari-Szabo model is derived for isotropic overall tumbling. The parameters of the original Lipari-Szabo model, the order parameter S2 and the effective internal correlation time tau(e), are calculated from two values of the spectral density function. If additionally the spectral density value J(0) is known, the exchange contribution R(ex) term can also be determined. The overall tumbling time tau(c) must be determined in advance, for example, from T1/T2 ratios. The required spectral density values are obtained by reduced spectral density mapping from T1, T2, and NOE measurements. Our computer simulations show that the reduced spectral density mapping is a very good approximation in almost all cases in which the Lipari-Szabo model is applicable. The robustness of the analytical formula to experimental errors is also investigated by extensive computer simulations and is found to be similar to that of the fitting procedures. The derived formulas were applied to the experimental 15N relaxation data of ubiquitin. Our results agree well with the published parameter values of S2 and tau(e), which were obtained from standard fitting procedures. The analytical approach to extract parameters of molecular motions may be more robust than standard analyses and provides a safeguard against spurious fitting results, especially for determining the exchange contribution R(ex).     

Peptide internal motions on nanosecond time scale derived from direct fitting of (13)C and (15)N NMR spectral density functions

NMR relaxation-derived spectral densities provide information on molecular and internal motions occurring on the picosecond to nanosecond time scales. Using (13)C and (15)N NMR relaxation parameters [T(1), T(2), and NOE] acquired at four Larmor frequencies (for (13)C: 62.5, 125, 150, and 200 MHz), spectral densities J(0), J(omega(C)), J(omega(H)), J(omega(H) + omega(C)), J(omega(H) - omega(C)), J(omega(N)), J(omega(H) + omega(N)), and J(omega(H) - omega(N)) were derived as a function of frequency for (15)NH, (13)C(alpha)H, and (13)C(beta)H(3) groups of an alanine residue in an alpha-helix-forming peptide. This extensive relaxation data set has allowed derivation of highly defined (13)C and (15)N spectral density maps. Using Monte Carlo minimization, these maps were fit to a spectral density function of three Lorentzian terms having six motional parameters: tau(0), tau(1), tau(2), c(0), c(1), and c(2), where tau(0), tau(1) and tau(2) are correlation times for overall tumbling and for slower and faster internal motions, and c(0), c(1), and c(2) are their weighting coefficients. Analysis of the high-frequency portion of these maps was particularly informative, especially when deriving motional parameters of the side-chain methyl group for which the order parameter is very small and overall tumbling motions do not dominate the spectral density function. Overall correlation times, tau(0), are found to be in nanosecond range, consistent with values determined using the Lipari-Szabo model-free approach. Internal motional correlation times range from picoseconds for methyl group rotation to nanoseconds for backbone N-H, C(alpha)-H, and C(alpha)-C(beta) bond motions. General application of this approach will allow greater insight into the internal motions in peptides and proteins.     

Conformational dynamics of a metallomesogen studied by 2H-NMR spectroscopy

In this work we present a quantitative analysis of both quadrupolar splittings and deuterium Zeeman and quadrupolar spin-lattice relaxation times reported in the literature for two isotopomers of Azpac, an acetylacetonate derivative of the cyclopalladated 4, 4'-bis(hexyloxy) azoxybenzene. Azpac-d(4) is deuterated at the aromatic rings and Azpac-d(26) is deuterated on the alkoxy chains. The additive potential method is used to model the splittings, while the derived spectral densities are interpreted using the decoupled model in conjunction with the Nordio model. The two side chains are assumed to be noninteracting and identical in their conformations in order to limit the size of the transition rate matrix needed to describe correlated internal bond rotations in the chains. Rotational diffusion constants and internal jump rate constants are derived for this metallomesogen.     

Cross-correlated relaxation for the measurement of angles between tensorial interactions

Theory,experimental aspects, and use in structure calculation of cross-correlated relaxation rates measured on zero- and double-quantum coherences in liquid state NMR are presented. The relative size of the interaction depends on the projection angle between the two tensorial interactions. The tensorial interaction can be either a dipolar interaction or a chemical shift anisotropy relaxation mechanism (CSA). Effects of additional sources of relaxation on the cross-correlated relaxation rates are analyzed. Also, an easy-to-use formalism is given to manipulate different cross-correlated relaxation interactions. The application addresses measurement of the backbone angle psi in a protein by measuring dipole((15)N-(1)H)-dipole((13)C(alpha)-(1)H(alpha)) and CSA((15)N)-dipole((13)C(alpha)-(1)H(alpha)) cross-correlated relaxation rates. It is shown that ambiguities due to the 3 cos(2)θ-1 dependence of one cross-correlated relaxation rate can be overcome by measuring additional cross-correlated relaxation rates. The use of cross-correlated relaxation rates is demonstrated in structure calculations.     

A new approach to visualizing spectral density functions and deriving motional correlation time distributions: applications to an alpha-helix-forming peptide and to a well-folded protein

A new approach to visualizing spectral densities and analyzing NMR relaxation data has been developed. By plotting the spectral density function, J(omega), as F(omega)=2 omega J(omega) on the log-log scale, the distribution of motional correlation times can be easily visualized. F(omega) is calculated from experimental data using a multi-Lorentzian expansion that is insensitive to the number of Lorentzians used and allows contributions from overall tumbling and internal motions to be separated without explicitly determining values for correlation times and their weighting coefficients. To demonstrate the approach, (15)N and (13)C NMR relaxation data have been analyzed for backbone NH and C(alpha)H groups in an alpha-helix-forming peptide 17mer and in a well-folded 138-residue protein, and the functions F(omega) have been calculated and deconvoluted for contributions from overall tumbling and internal motions. Overall tumbling correlation time distribution maxima yield essentially the same overall correlation times obtained using the Lipari-Szabo model and other standard NMR relaxation data analyses. Internal motional correlational times for NH and C(alpha)H bond motions fall in the range from 100 ps to about 1 ns. Slower overall molecular tumbling leads to better separation of internal motional correlation time distributions from those of overall tumbling. The usefulness of the approach rests in its ability to visualize spectral densities and to define and separate frequency distributions for molecular motions.     

The matrix formalism for generalised gradients with time-varying orientation in diffusion NMR

Protein backbone 15N NMR spin relaxation rates are useful in characterizing the protein dynamics and structures. To observe the protein nuclear-spin resonances a pulse sequence has to include a water suppression scheme. There are two commonly employed methods, saturating or dephasing the water spins with pulse field gradients and keeping them unperturbed with flip-back pulses. Here different water suppression methods were incorporated into pulse sequences to measure 15N longitudinal T1 and transversal rotating-frame T1ρ spin relaxation. Unexpectedly the 15N T1 relaxation time constants varied significantly with the choice of water suppression method. For a 25-kDa Escherichiacoli. glutamine binding protein (GlnBP) the T1 values acquired with the pulse sequence containing a water dephasing gradient are on average 20% longer than the ones obtained using a pulse sequence containing the water flip-back pulse. In contrast the two T1ρ data sets are correlated without an apparent offset. The average T1 difference was reduced to 12% when the experimental recycle delay was doubled, while the average T1 values from the flip-back measurements were nearly unchanged. Analysis of spectral signal to noise ratios (s/n) showed the apparent slower 15N relaxation obtained with the water dephasing experiment originated from the differences in 1HN recovery for each relaxation time point. This in turn offset signal reduction from 15N relaxation decay. The artifact becomes noticeable when the measured 15N relaxation time constant is comparable to recycle delay, e.g., the 15N T1 of medium to large proteins. The 15N relaxation rates measured with either water suppression schemes yield reasonable fits to the structure. However, data from the saturated scheme results in significantly lower Model-Free order parameters (=0.81) than the non-saturated ones (=0.88), indicating such order parameters may be previously underestimated.     

Errors in the Measurement of Cross-Correlated Relaxation Rates and How to Avoid Them

Cross-correlated relaxation rates Γ are commonly obtained from constant time experiments by measuring the effect of the desired cross-correlated relaxation on an appropriate coherence during the constant time T. These measurements are affected by systematic errors, which derive from undesired cross-correlated relaxation effects taking place before and after the constant time period T. In this paper we discuss the sources and the size of these errors in an example of two pulse sequences. Higher accuracy of the measured data can be obtained by recording a set of experiments with different T values. Cross-correlated relaxation rates are measured in constant time experiments either from the differential relaxation of multiplet components (J-resolved Γ experiments) or from the efficiency of magnetization transfer between two coherences (quantitative Γ experiments). In this paper we calculate analytically the statistical errors in both J-resolved and quantitative Γ experiments. These formulae provide the basis for the choice of the most efficient experimental approach and parameters for a given measurement time and size of the rate. The optimal constant time T for each method can be calculated and depends on the relaxation properties of the molecule under investigation. Moreover, we will show how to optimize the relative duration of cross and reference experiments in a quantitative Γ approach.     

Characterization of hydrogen bond lengths in Watson-Crick base pairs by cross-correlated relaxation

Hydrogen bond lengths in Watson-Crick base pairs can be characterized by cross-correlated relaxation between 1H chemical shift anisotropy and dipole-dipole coupling of 1H and its hydrogen bond acceptor 15N. As a reference, the cross-correlated relaxation between 1H chemical shift anisotropy and dipole-dipole coupling of 1H and its hydrogen bond donor 15N is used. With the two measured cross-correlated relaxation rates, an apparent hydrogen bond length can be determined, which is composed by the hydrogen bond length multiplied by a term representing the amplitude of inter-base motions. Data are presented for the 15N3-1H3...15N1 hydrogen bonds in A=T base pairs of the Antennapedia homeodomain-DNA complex with a correlation time of global rotational diffusion of 20 ns.     

Characterization of molecular motion in the solid state by carbon-13 spin-lattice relaxation times

Relaxation calculations for rapidly spinning samples show that spin-lattice relaxation time (T(1Z)) anisotropy varies with the angle between the rotor spinning axis and the external field. When the rate of molecular motion is in the extreme narrowing limit, the measurement of T(1Z) anisotropies for two different values of the spinning angle allows the determination of two linear combinations of the three static spectral densities, J(0)(0), J(1)(0), and J(2)(0). These functions are sensitive to molecular geometry and the rate and trajectory of motion. The utility of these linear combinations in the investigation of molecular dynamics in solids has been demonstrated with natural abundance (13)C NMR experiments on ferrocene. In an isolated (13)C-(1,2)H group, the dipole-dipole interaction has the same orientational dependence as the quadrupole interaction. Thus, the spectral densities that are responsible for dipolar relaxation of (13)C are the same as those responsible for deuteron quadrupolar relaxation. For ferrocene-d(10), deuteron T(1Z) and T(1Q) anisotropies and the relaxation time of the (13)C magic angle spinning peak provide sufficient information to determine the orientation dependence of all three individual spectral densities.     

Dipolar Relaxation Times of Tryptophan and Tyrosine in Glycerol and in Proteins: A Direct Evaluation from Their Fluorescence Decays

The dipolar relaxation process induced around tryptophan, indole and tyrosine in viscous media, as well as in several single tryptophan-containing proteins (staphylococcal nuclease, ribonuclease T1, melittin and albumin), has been studied by dynamic fluorescence measurements. A new theoretical model has been developed, including the relaxation dynamics directly in the fluorescence decay function. The phase shift and demodulation data have been fitted with this new algorithm which allows to resolve the different relaxation times influencing the fluorophore excited state. These parameters are in a good agreement with those measured with the traditional time-resolved emission spectroscopy. The results indicate that indeed a correlation exists between the radiative rate change obtained with the new model and the temporal spectral shift reported in the literature. Finally, this new approach has also been extended to the case of superoxide dismutase and phosphofructokinase, allowing to measure the relaxation time even in proteins lacking a temporal spectral shift during the fluorphore's lifetime.     

Simple and accurate determination of global tau(R) in proteins using (13)C or (15)N relaxation data

In the study of protein dynamics by (13)C or (15)N relaxation measurements different models from the Lipari-Szabo formalism are used in order to determine the motion parameters. The global rotational correlation time tau(R) of the molecule must be estimated prior to the analysis. In this Communication, the authors propose a new approach in determining an accurate value for tau(R) in order to realize the best fit of R(2) for the whole sequence of the protein, regardless of the different type of motions atoms may experience. The method first determines the highly structured regions of the sequence. For each corresponding site, the Lipari-Szabo parameters are calculated for R(1) and NOE, using an arbitrary value for tau(R). The chi(2) for R(2), summed over the selected sites, shows a clear minimum, as a function of tau(R). This minimum is used to better estimate a proper value for tau(R).     

A simple method to measure 13CH2 heteronuclear dipolar cross-correlation spectral densities

Here, we report a method to simultaneously determine CH2 cross-correlation spectral densities and T1 relaxation times in the laboratory and rotating frames. To accomplish this, we have employed an indirect approach that is based on measurement of differences in relaxation rates acquired with and without cross-correlation terms. The new method, which can be employed using multidimensional NMR and standard relaxation pulse sequences, is validated experimentally by investigation of a selectively 13C-enriched hexadecapeptide and the uniformly 13C-enriched immunoglobulin-binding domain of streptococcal protein G (GB1). Use of this approach makes determination of CH2 cross-correlation spectral densities in uniformly 13C-enriched proteins now routine and provides novel information concerning their internal motions.     

Spectral densities and nuclear spin relaxation in solids

We investigate the properties of ten spectral densities relevant for nuclear spin relaxation studies in solids. This is preceded by a brief review of nuclear spin relaxation in solids which includes a discussion of the appropriate spin-dependent interactions and the various relaxation rates which can be measured. Also, the link between nuclear spin relaxation and dielectric relaxation is discussed. Where possible and/or appropriate each of the spectral densities is expressed as a continuous distribution of Bloembergen-Purcell-Pound (or Debye) spectral densities 2ξ /(1 + ξ² ω²) for nuclear Larmor angular frequency ω and correlation time ξ. The spectral densities are named after their originators or the shape of the distributions of correlation times or both and are (1) Bloembergen-Purcell-Pound or δ-function, (2) Havriliak-Negami, (3) Cole-Cole, (4) Davidson-Cole, (5) Fang, (6) Fuoss-Kirkwood, (7) Bryn Mawr, (8) Wagner or log-Gaussian, (9) log-Lorentzian, and (10) Fröhlich or energy box. The Havriliak-Negami spectral density is related to the Dissado-Hill theory for dielectric relaxation. The spectral densities are expressed in a way which makes them easy to compare with each other and with experimental data. Many plots of the distributions of correlation times and of the spectral densities vs. various correlation times characterizing the distributions are given.     

High-resolution nonlinear laser spectroscopy of exciton relaxation in GaAs quantum wells

This paper describes measurements of exciton relaxation in GaAs/AlGaAs quantum well structures based on high resolution nonlinear laser spectroscopy. The nonlinear optical measurements show that low energy excitons can be localized by monolayer disorder of the quantum well interface. We show that these excitons migrate between localization sites by phonon assisted migration, leading to spectral diffusion of the excitons. The frequency domain measurements give a direct measure of the quasi-equilibrium exciton spectral redistribution due to exciton energy relaxation, and the temperature dependence of the measured migration rates confirms recent theoretical predictions. The observed line shapes are interpreted based on solutions we obtain to modified Bloch equations which include the effects of spectral diffusion.     

Osmotic and aging effects in caviar oocytes throughout water and lipid changes assessed by 1H NMR T1 and T2 relaxation and MRI

By combining NMR relaxation spectroscopy and magnetic resonance imaging techniques, unsalted (us) and salted (s) caviar (Acipenser transmontanus) oocytes were characterized over a storage period of up to 90 days. The aging and the salting effects on the two major cell constituents, water and lipids, were separately assessed. T1 and T2 decays were interpreted by assuming a two-site exchange model. At Day 0, two water compartments that were not in fast exchange were identified by the T1 relaxation measurements on the us oocytes. In the s samples, T1 decay was monoexponential. During the time of storage, an increment of the free water amount was found for the us oocytes, ascribed to an increased metabolism. T1 and T2 of the s oocytes shortened as a consequence of the osmotic stress produced by salting. Selective images showed the presence of water endowed with different regional mobility that severely changed during the storage. Lipid T1 relaxation decays collected on us and s samples were found to be biexponential, and the T1 values lengthened during storage. In us and s oocytes, the increased lipid mobility with the storage was ascribed to lipolysis. Selective images of us samples showed lipids that were confined to the cytoplasm for up to 60 days of storage.     

Micropore size analysis by NMR in hydrated cement

The understanding of the microstructure of cement remains incomplete. Especially, the progressive setting of the material is still unclear. Micropore size distribution (microstructure) has been investigated by both standard proton nuclear magnetic relaxation (1H-NMR) and field-cycling relaxation in C3S hydrated paste. The non-exponential decay was interpreted as a distribution of discrete relaxation rates. The attribution of T1 is supported by both a spectral and a dispersion curve analyses. These experiments allow us to follow the structuration of the material during setting.     

In vivo relaxation times of gray matter and white matter in spinal cord

In vivo relaxation times and relative spin densities of gray matter (GM) and white matter (WM) of rat spinal cord were measured. Inductively coupled implanted RF coil was used to improve the signal-to-noise ratio required for making these measurements. The estimated relaxation times (in milliseconds) are: T1(GM) = 1021+/-93, T2(GM) = 64+/-3.4, T1(WM) = 1089+/-126, and T2(WM) = 79+/-6.9. The estimated relative spin densities are: rho(GM) = (60+/-2.3)% and rho(WM) = (40+/-2.1)%. The T1 values of GM and white matter are not statistically different. However, the differences in T2 values and spin densities of GM and WM are statistically significant. These in vivo measurements indicate that the observed contrast between GM and WM in spinal cord MR images mainly arises from the differences in the spin density.     

Measurement of dipole-dipole cross-correlated relaxation in fast rotating CH2D groups

Studies of protein dynamics are key to understanding their biological function. NMR relaxation studies of proteins to date have focused primarily on characterizing backbone dynamics. In this paper, we focus on the aliphatic side-chains (Ala, Thr, Val, Leu, and Ile) with the goal of deriving dynamical information on the motion of terminal methyl groups. Dipole-dipole cross-correlated cross-relaxation is analyzed in a fast rotating CH(2)D group, as found in partially deuteriated proteins. In comparison with previous studies on AMX spin systems (methylene C(beta)H(2) groups), the fast rotation of the methyl group makes a number of relaxation pathways efficient, through the coherence C(+)H(1)(+)H(2)(-)+C(+)H(1)(-)H (2)(+). Several pulse schemes were designed to evaluate these relaxation rates: the measured values are small and well predicted by taking into account the complete relaxation network, but they remain strongly influenced by 1H-1H relaxation with all protons in the neighborhood of the CH(2)D moiety. The prospects and limitations of this method are discussed in comparison with 2H relaxation measurements.