Separating structure and dynamics in CSA/DD cross-correlated relaxation: a case study on trehalose and ubiquitin

We present two new sensitivity enhanced gradient NMR experiments for measuring interference effects between chemical shift anisotropy (CSA) and dipolar coupling interactions in a scalar coupled two-spin system in both the laboratory and rotating frames. We apply these methods for quantitative measurement of longitudinal and transverse cross-correlation rates involving interference of (13)C CSA and (13)C-(1)H dipolar coupling in a disaccharide, alpha,alpha-D-trehalose, at natural abundance of (13)C as well as interference of amide (15)N CSA and (15)N-(1)H dipolar coupling in uniformly (15)N-labeled ubiquitin. We demonstrate that the standard heteronuclear T(1), T(2), and steady-state NOE autocorrelation experiments augmented by cross-correlation measurements provide sufficient experimental data to quantitatively separate the structural and dynamic contributions to these relaxation rates when the simplifying assumptions of isotropic overall tumbling and an axially symmetric chemical shift tensor are valid.     

The role of (15)N CSA and CSA/dipole cross-correlation in (15)N relaxation in solid proteins

The influence of the (15)N CSA on (15)N longitudinal relaxation is investigated for an amide group in solid proteins in powder form under MAS. This contribution is determined to be typically 20-33% of the overall longitudinal relaxation rate, at 11.74 and 16.45 T, respectively. The improved treatment is used to analyze the internal dynamics in the protein Crh, in the frame of a motional model of diffusion in a cone, using the explicit average sum approach. Significant variations with respect to the determined dynamics parameters are observed when properly accounting for the contribution of (15)N CSA fluctuations. In general, the fit of experimental data including CSA led to the determination of diffusion times (tau(w)) which are longer than when considering only an (15)N-(1)H dipolar relaxation mechanism. CSA-Dipole cross-correlation is shown to play little or no role in protonated solids, in direct contrast to the liquid state case.     

Measurement of Cross Correlation between Dipolar Coupling and Chemical Shift Anisotropy in the Spin Relaxation ofC,N-Labeled Proteins

We present a simple method for extracting interference effects between chemical shift anisotropy (CSA) and dipolar coupling from spin relaxation measurements in macromolecules, and we apply this method to extracting cross-correlation rates involving interference of amide¹⁵N CSA and¹⁵N–¹H dipolar coupling and interference of carbonyl¹³C′ CSA and¹⁵N–¹³C′ dipolar coupling, in a small protein. A theoretical basis for the interpretation of these rates is presented. While it proves difficult to quantitatively separate the structural and dynamic contributions to these cross-correlation rates in the presence of anisotropic overall tumbling and a nonaxially symmetric chemical shift tensor, some useful qualitative correlations of data with protein structure can be seen when simplifying assumptions are made.     

Separating Structure and Dynamics in CSA/DD Cross-Correlated Relaxation: A Case Study on Trehalose and Ubiquitin

We present two new sensitivity enhanced gradient NMR experiments for measuring interference effects between chemical shift anisotropy (CSA) and dipolar coupling interactions in a scalar coupled two-spin system in both the laboratory and rotating frames. We apply these methods for quantitative measurement of longitudinal and transverse cross-correlation rates involving interference of ¹³C CSA and ¹³C–¹H dipolar coupling in a disaccharide, α,α- -trehalose, at natural abundance of ¹³C as well as interference of amide ¹⁵N CSA and ¹⁵N–¹H dipolar coupling in uniformly ¹⁵N-labeled ubiquitin. We demonstrate that the standard heteronuclear T₁, T₂, and steady-state NOE autocorrelation experiments augmented by cross-correlation measurements provide sufficient experimental data to quantitatively separate the structural and dynamic contributions to these relaxation rates when the simplifying assumptions of isotropic overall tumbling and an axially symmetric chemical shift tensor are valid.     

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.     

Measurement of relaxation rates of N(H) and H(alpha) backbone protons in proteins with tailored initial conditions.

Several methods are presented for the selective determination of spin-lattice and spin-spin relaxation rates of backbone protons in labeled proteins. The relaxation rates of amide protons in (15)N labeled proteins can be measured by using two-way selective cross-polarization (SCP). The measurement of H(alpha) relaxation rates can be achieved by combining this method with homonuclear Hartmann-Hahn transfer using doubly selective irradiation. Various schemes for selective or nonselective inversion of the longitudinal proton magnetization lead to different initial recovery rates. The methods have been applied to lysine K6 in (15)N-labeled human ubiquitin and to leucine L5 in (15)N- and (13)C-labeled octapeptide YG*G*F*LRRI (GFL) in which the marked residues are (15)N- and (13)C-labeled.     

Characterization of 15N chemical shift tensors via 15N-13C REDOR and 1N-1H dipolar-shift CPMAS NMR spectroscopy

As part of our studies on the characterization of 15N chemical shift anisotropy (CSA) via magic angle spinning (MAS) NMR spectroscopy, we have investigated via numerical simulations the sensitivity of two different REDOR experimental protocols to the angles defining the orientation of the 15N-13C' bond vector in the principal axis system of the 15N CSA tensor of the amide nitrogen in a peptide bond. Additionally, employing polycrystalline samples of 15N and 13C', 15N-labeled acetanilide, we have obtained, in a first study of this type, the orientation of the 15N CSA tensor in the molecular frame by orienting the tensor with respect to the 15N-3C' and 15N-1H dipolar vectors via 15N-13C' REDOR and 15N-1H dipolar-shift MAS experiments, respectively.     

Modulation of the distance dependence of paramagnetic relaxation enhancements by CSA x DSA cross-correlation

Paramagnetic metal ions with fast-relaxing electronic spin and anisotropic susceptibility tensor provide a rich source of structural information that can be derived from pseudo-contact shifts, residual dipolar couplings, dipole-dipole Curie spin cross-correlation, and paramagnetic relaxation enhancements. The present study draws attention to a cross-correlation effect between nuclear relaxation due to anisotropic chemical shielding (CSA) and due to the anisotropic dipolar shielding (DSA) caused by the electronic Curie spin. This CSA x DSA cross-correlation contribution seems to have been overlooked in previous interpretations of paramagnetic relaxation enhancements. It is shown to be sufficiently large to compromise the 1/r6 distance dependence usually assumed. The effect cannot experimentally be separated from auto-correlated DSA relaxation. It can increase or decrease the observed paramagnetic relaxation enhancement. Under certain conditions, the effect can dominate the entire paramagnetic relaxation, resulting in nuclear resonances narrower than in the absence of the paramagnetic center. CSAxDSA cross-correlation becomes important when paramagnetic relaxation is predominantly due to the Curie rather than the Solomon mechanism. Therefore the effect is most pronounced for relaxation by metal ions with large magnetic susceptibility and fast-relaxing electron spin. It most strongly affects paramagnetic enhancements of transverse relaxation in macromolecules and of longitudinal relaxation in small molecules.     

Improved Estimation of CSA–Dipolar Coupling Cross-Correlation Rates from Laboratory-Frame Relaxation Experiments

We have investigated the underlying assumptions in estimating cross-correlation rates between chemical shift anisotropy (CSA) and dipolar coupling mechanisms in a scalar-coupled two-spin IS system, from laboratory frame relaxation experiments. It has been shown that for an arbitrary relaxation delay, the difference in relaxation rates of the individual components of an in-phase (or antiphase) doublet is not related to the CSA–dipolar coupling cross-correlation rate in a simple way. This is especially true in the case where the difference in the decay rates of the in-phase and antiphase terms of the density matrix becomes comparable to the magnitude of the scalar coupling between the two spins. Improved means of extracting cross-correlation rates in these cases are presented.     

Modulation of the distance dependence of paramagnetic relaxation enhancements by CSA × DSA cross-correlation

Paramagnetic metal ions with fast-relaxing electronic spin and anisotropic susceptibility tensor provide a rich source of structural information that can be derived from pseudo-contact shifts, residual dipolar couplings, dipole-dipole Curie spin cross-correlation, and paramagnetic relaxation enhancements. The present study draws attention to a cross-correlation effect between nuclear relaxation due to anisotropic chemical shielding (CSA) and due to the anisotropic dipolar shielding (DSA) caused by the electronic Curie spin. This CSA x DSA cross-correlation contribution seems to have been overlooked in previous interpretations of paramagnetic relaxation enhancements. It is shown to be sufficiently large to compromise the 1/r6 distance dependence usually assumed. The effect cannot experimentally be separated from auto-correlated DSA relaxation. It can increase or decrease the observed paramagnetic relaxation enhancement. Under certain conditions, the effect can dominate the entire paramagnetic relaxation, resulting in nuclear resonances narrower than in the absence of the paramagnetic center. CSAxDSA cross-correlation becomes important when paramagnetic relaxation is predominantly due to the Curie rather than the Solomon mechanism. Therefore the effect is most pronounced for relaxation by metal ions with large magnetic susceptibility and fast-relaxing electron spin. It most strongly affects paramagnetic enhancements of transverse relaxation in macromolecules and of longitudinal relaxation in small molecules.     

A 2D MAS solid-state NMR method to recover the amplified heteronuclear dipolar and chemical shift anisotropic interactions

A two-dimensional solid-state NMR method for the measurement of chemical shift anisotropy tensors of X nuclei (15N or 13C) from multiple sites of a polypeptide powder sample is presented. This method employs rotor-synchronized pi pulses to amplify the magnitude of the inhomogeneous X-CSA and 1H-X dipolar coupling interactions. A combination of on-resonance and magic angle rf irradiation of protons is used to vary the ratio of the magnitudes of the 1H-X dipolar and X-CSA interactions which are recovered under MAS, in addition to suppressing the 1H-1H dipolar interactions. The increased number of spinning sidebands in the recovered anisotropic interactions is useful to determine the CSA tensors accurately. The performance of this method is examined for powder samples of N-acetyl-(15)N-L-valine (NAV), N-acetyl-15N-L-valyl-15N-L-leucine (NAVL), and alpha-13C-L-leucine. The sources of experimental errors in the measurement of CSA tensors and the application of the pulse sequences under high-field fast MAS operations are discussed.     

Measurement of Relaxation Rates of N and H Backbone Protons in Proteins with Tailored Initial Conditions

Several methods are presented for the selective determination of spin–lattice and spin–spin relaxation rates of backbone protons in labeled proteins. The relaxation rates of amide protons in ¹⁵N labeled proteins can be measured by using two-way selective cross-polarization (SCP). The measurement of H^α relaxation rates can be achieved by combining this method with homonuclear Hartmann–Hahn transfer using doubly selective irradiation. Various schemes for selective or nonselective inversion of the longitudinal proton magnetization lead to different initial recovery rates. The methods have been applied to lysine K6 in ¹⁵N-labeled human ubiquitin and to leucine L5 in ¹⁵N- and ¹³C-labeled octapeptide YG*G*F*LRRI (GFL) in which the marked residues are ¹⁵N- and ¹³C-labeled.     

Separation of anisotropy and exchange broadening using (15)N CSA-(15)N-(1)H dipole-dipole relaxation cross-correlation experiments

Based on the measurement of cross-correlation rates between (15)N CSA and (15)N-(1)H dipole-dipole relaxation we propose a procedure for separating exchange contributions to transverse relaxation rates (R(2) = 1/T(2)) from effects caused by anisotropic rotational diffusion of the protein molecule. This approach determines the influence of anisotropy and chemical exchange processes independently and therefore circumvents difficulties associated with the currently standard use of T(1)/T(2) ratios to determine the rotational diffusion tensor. We find from computer simulations that, in the presence of even small amounts of internal flexibility, fitting T(1)/T(2) ratios tends to underestimate the anisotropy of overall tumbling. An additional problem exists when the N-H bond vector directions are not distributed homogeneously over the surface of a unit sphere, such as in helix bundles or beta-sheets. Such a case was found in segment 4 of the gelation factor (ABP 120), an F-actin cross-linking protein, in which the diffusion tensor cannot be calculated from T(1)/T(2) ratios. The (15)N CSA tensor of the residues for this beta-sheet protein was found to vary even within secondary structure elements. The use of a common value for the whole protein molecule therefore might be an oversimplification. Using our approach it is immediately apparent that no exchange broadening exists for segment 4 although strongly reduced T(2) relaxation times for several residues could be mistaken as indications for exchange processes.     

Amide proton relaxation measurements employing a highly deuterated protein

Proton NMR longitudinal and transverse relaxation rates of unlabelled proteins are generally dominated by the many 1H-1H dipolar interactions so that spin diffusion, rather than molecular or internal motions, governs longitudinal relaxation. Here, relaxation measurements of backbone amide proton (1H(N)) magnetisations have been carried out employing the 99% 2H, 98% 15N labelled, small 2F2 protein domain in 10%/90% H(2)O/D(2)O solution. Under these conditions, the longitudinal relaxation rates exhibit time constants, T(1)*=1/R(1)* if described by a mono-exponential, within the range of 3.0 to 18.7s-a wide range which indicates that the phenomenon of spin diffusion has been greatly reduced. The majority of 1H(N) nuclei in this sample (pH 4.0 and 5 degrees C) exhibit chemical exchange with solvent that couples their longitudinal relaxation to that of the solvent. For the subset of 1H(N) nuclei not undergoing detectable solvent chemical exchange, the R(1)* rates correlate well with their individual 1H(N,O)/2H(N,O) structural environments. The correlation for corresponding transverse relaxation rates, R(2)* was found to be less good. Longitudinal relaxation measurements in 1%/99% H(2)O/D(2)O solution identify a further subset of 1H(N) nuclei which exhibit essentially indistinguishable R(1)* rates in both 1% and 10% H(2)O, implying that averaging of rates from spin diffusion processes and different 2F2 isotopomer populations are negligible for these 1H(N) sites. In addition to a high sensitivity to structural parameters, model calculations predict 1H(N) relaxation rates to exhibit pronounced sensitivity to internal dynamics.     

On the accurate measurement of amide one-bond 15N-1H couplings in proteins: effects of cross-correlated relaxation, selective pulses and dynamic frequency shifts

Amide one-bond 15N-1H scalar couplings of 15N- and [15N,2H]-isotopically enriched ubiquitin have been measured with the Quantitative J approach by monitoring NMR signal intensity modulation. Scalar couplings of the non-deuterated protein are in average approximately 0.6 Hz larger than values of deuterated ubiquitin. This deviation is 30 times the error derived from experiment reproducibility. Refocusing dipole/dipole cross-correlated relaxation decreases the discrepancy to approximately 0.1 Hz, suggesting that it likely originates from relaxation interference. Alternatively, the subtraction of J values obtained at different magnetic fields largely reduces the relaxation effects. In contrast, the dynamic frequency shift whose main contribution to 1J(15N-1H) arises from 15N chemical shielding anisotropy/NH dipole cross-correlation, is not eliminated by refocusing spin evolution under this interaction. Furthermore, the average difference of 1J(15N-1H) values at two magnetic fields closely agrees with the theoretical expected difference in the dynamic frequency shift.     

Symmetrical reconversion: measuring cross-correlation rates with enhanced accuracy

A new strategy has been developed to measure cross-correlation rates with much enhanced accuracy. The method relies on the use of four complementary experiments. Errors due to pulse miscalibration and to uncontrolled attenuation factors associated with relaxation are cancelled out. Problems due to violations of the secular approximation are greatly alleviated. The method has been applied to the measurement of N/NH (CSA/DD) cross-correlated relaxation rates in human ubiquitin.     

Frequency (250 MHz to 9.2 GHz) and viscosity dependence of electron spin relaxation of triarylmethyl radicals at room temperature

Electron spin relaxation times for four triarylmethyl (trityl) radicals at room temperature were measured by long-pulse saturation recovery, inversion recovery, and electron spin echo at 250 MHz, 1.5, 3.1, and 9.2 GHz in mixtures of water and glycerol. At 250 MHz T(1) is shorter than at X-band and more strongly dependent on viscosity. The enhanced relaxation at 250 MHz is attributed to modulation of electron-proton dipolar coupling by tumbling of the trityl radicals at rates that are comparable to the reciprocal of the resonance frequency. Deuteration of the solvent was used to distinguish relaxation due to solvent protons from the relaxation due to intra-molecular electron-proton interactions at 250 MHz. For trityl-CD(3), which contains no protons, modulation of dipolar interaction with solvent protons dominates T(1). For proton-containing radicals the relative importance of modulation of intra- and inter-molecular proton interactions varies with solution viscosity. The viscosity and frequency dependence of T(1) was modeled based on dipolar interaction with a defined number of protons at specified distances from the unpaired electron. At each of the frequencies examined T(2) decreases with increasing viscosity consistent with contributions from T(1) and from incomplete motional averaging of anisotropic hyperfine interaction.     

Measurement of transverse relaxation in coupled spin systems by semi-selective refocusing: Evidence for interference of CSA and dipolar relaxation

A novel spin-echo experiment is proposed that uses semiselective Gaussian pulse cascades for refocusing in systems with homonuclear couplings. The experiment allows one to obtain evidence of differential T₂ effects due to cross-correlation of proton chemical shift anisotropy and proton-proton dipolar interactions in a small aromatic compound at 9.4 T. The spin-echo experiment is also applied to measure transverse relaxation rates for selected multiplets of the cyclic undecapeptide cyclosporin. Possible extensions to multiple-quantum spin echo-spectroscopy are indicated.     

13C/14N heteronuclear multiple-quantum correlation with rotary resonance and REDOR dipolar recoupling

A two-dimensional (13)C/(14)N heteronuclear multiple quantum correlation (HMQC) experiment using dipolar recoupling under magic-angle spinning (MAS) is described. The experiment is an extension of the recent indirect (13)C detection scheme for measuring (14)N quadrupolar coupling under MAS. The recoupling allows the direct use of the much larger dipolar interaction instead of the small J and residual dipolar couplings for establishing (13)C/(14)N correlations. Two recoupling methods are incorporated into the HMQC sequence, both applying rf only to the observed (13)C spin. The first one uses the REDOR sequence with two pi-pulses per rotor cycle. The second one uses a cw rf field matching the spinning frequency, known as rotary resonance. The effects of CSA, T(2)(') signal loss, MAS frequency and stability and t(1)-noise are compared and discussed.     

Cross-correlation effects involving curie spin relaxation in methyl groups

Cross-correlation effects arising in methyl protons due to the simultaneous presence of dipole-dipole, chemical shift anisotropy, and Curie spin relaxation mechanisms in paramagnetic systems are analyzed. We assess the potential of obtaining structural constraints from the cross-correlation of Curie spin relaxation with dipolar relaxation mechanisms among methyl proton spins. By theoretical analysis and numerical simulations we characterize the transfer functions describing the interconversion processes of different ranks of multispin order. The time dependence of these processes contains a new type of structural information, the orientation of the methyl C(3)-axis with respect to the electron center. Experimental confirmation is found for selected methyl groups in low spin Fe(3+) sperm whale myoglobin.