Interference between Dipolar and Quadrupolar Interactions in the Slow Tumbling Limit: A Source of Line Shift and Relaxation in 2H-Labeled Compounds

13C NMR Relaxation Analysis of Protein GB3 for the Assessment of Side Chain Dynamics Predictions by Current AMBER and CHARMM Force Fields

Molecular simulations with seven current AMBER- and CHARMM-based force fields yield markedly differing internal bond vector autocorrelation function predictions for many of the 223 methine and methylene H-C bonds of the 56-residue protein GB3. To enable quantification of accuracy, ¹³C R₁, R₂, and heteronuclear NOE relaxation rates have been determined for the methine and stereochemically assigned methylene C^α and C^β positions. With only three experimental relaxation values for each bond vector, central to this analysis is the accuracy with which MD-derived autocorrelation curves can be represented by a 3-parameter equation which, in turn, maps onto the NMR relaxation values. In contrast to the more widely used extended Lipari-Szabo order parameter representation, 95% of these MD-derived internal autocorrelation curves for GB3 can be fitted to within 1.0% rmsd over the time frame from 30 ps to 4 ns by a biexponential Larmor frequency-selective representation (LF-S²). Applying the LF-S² representation to the experimental relaxation rates and uncertainties serves to determine the boundary range for the autocorrelation function of each bond vector consistent with the experimental data. Not surprisingly, all seven force fields predict the autocorrelation functions for the more motionally restricted ¹H^α-¹³C^α and ¹H^β-¹³C^β bond vectors with reasonable accuracy. However, for the ¹H^β-¹³C^β bond vectors exhibiting aggregate order parameter S² values less than 0.85, only 1% of the MD-derived predictions lie with 1 σ of the experimentally determined autocorrelation functions and only 7% within 2 σ. On the other hand, substantial residue type-specific improvements in predictive performance were observed among the recent AMBER force fields. This analysis indicates considerable potential for the use of ¹³C relaxation measurements in guiding the optimization of the side chain dynamics characteristics of protein molecular simulations.

17O NMR studies of organic and biological molecules in aqueous solution and in the solid state

This review describes the latest developments in the field of ¹⁷O NMR spectroscopy of organic and biological molecules both in aqueous solution and in the solid state. In the first part of the review, a general theoretical description of the nuclear quadrupole relaxation process in isotropic liquids is presented at a mathematical level suitable for non-specialists. In addition to the first-order quadrupole interaction, the theory also includes additional relaxation mechanisms such as the second-order quadrupole interaction and its cross correlation with shielding anisotropy. This complete theoretical treatment allows one to assess the transverse relaxation rate (thus the line width) of NMR signals from half-integer quadrupolar nuclei in solution over the entire range of motion. On the basis of this theoretical framework, we discuss general features of quadrupole-central-transition (QCT) NMR, which is a particularly powerful method of studying biomolecules in the slow motion regime. Then we review recent advances in ¹⁷O QCT NMR studies of biological macromolecules in aqueous solution. The second part of the review is concerned with solid-state ¹⁷O NMR studies of organic and biological molecules. As a sequel to the previous review on the same subject [G. Wu, Prog. Nucl. Magn. Reson. Spectrosc. 52 (2008) 118-169], the current review provides a complete coverage of the literature published since 2008 in this area.

Distance-independent Cross-correlated Relaxation and Isotropic Chemical Shift Modulation in Protein Dynamics Studies

Cross-correlated relaxation (CCR) in multiple-quantum coherences differs from other relaxation phenomena in its theoretical ability to be mediated across an infinite distance. The two interfering relaxation mechanisms may be dipolar interactions, chemical shift anisotropies, chemical shift modulations or quadrupolar interactions. These properties make multiple-quantum CCR an attractive probe for structure and dynamics of biomacromolecules not accessible from other measurements. Here, we review the use of multiple-quantum CCR measurements in dynamics studies of proteins. We compile a list of all experiments proposed for CCR rate measurements, provide an overview of the theory with a focus on protein dynamics, and present applications to various protein systems.

Indirect use of deuterium in solution NMR studies of protein structure and hydrogen bonding

A description of the utility of deuteration in protein NMR is provided with an emphasis on quantitative evaluation of the effects of deuteration on a number of NMR parameters of proteins: (1) chemical shifts, (2) scalar coupling constants, (3) relaxation properties (R1 and R2 rates) of nuclei directly attached to one or more deuterons as well as protons of methyl groups in a highly deuterated environment, (4) scalar relaxation of 15N and 13C nuclei in 15N-D and 13C-D spin systems as a measure of hydrogen bonding strength, and (5) NOE-based applications of deuteration in NMR studies of protein structure. The discussion is restricted to the 'indirect' use of deuterium in the sense that the description of NMR parameters and properties of the nuclei affected by nearby deuterons (15N, 13C, 1H) is provided rather than those of deuterium itself.

Accuracy and precision of protein-ligand interaction kinetics determined from chemical shift titrations

NMR-monitored chemical shift titrations for the study of weak protein-ligand interactions represent a rich source of information regarding thermodynamic parameters such as dissociation constants (K ( D )) in the micro- to millimolar range, populations for the free and ligand-bound states, and the kinetics of interconversion between states, which are typically within the fast exchange regime on the NMR timescale. We recently developed two chemical shift titration methods wherein co-variation of the total protein and ligand concentrations gives increased precision for the K ( D ) value of a 1:1 protein-ligand interaction (Markin and Spyracopoulos in J Biomol NMR 53: 125-138, 2012). In this study, we demonstrate that classical line shape analysis applied to a single set of (1)H-(15)N 2D HSQC NMR spectra acquired using precise protein-ligand chemical shift titration methods we developed, produces accurate and precise kinetic parameters such as the off-rate (k ( off )). For experimentally determined kinetics in the fast exchange regime on the NMR timescale, k ( off ) ~ 3,000 s(-1) in this work, the accuracy of classical line shape analysis was determined to be better than 5 % by conducting quantum mechanical NMR simulations of the chemical shift titration methods with the magnetic resonance toolkit GAMMA. Using Monte Carlo simulations, the experimental precision for k ( off ) from line shape analysis of NMR spectra was determined to be 13 %, in agreement with the theoretical precision of 12 % from line shape analysis of the GAMMA simulations in the presence of noise and protein concentration errors. In addition, GAMMA simulations were employed to demonstrate that line shape analysis has the potential to provide reasonably accurate and precise k ( off ) values over a wide range, from 100 to 15,000 s(-1). The validity of line shape analysis for k ( off ) values approaching intermediate exchange (~100 s(-1)), may be facilitated by more accurate K ( D ) measurements from NMR-monitored chemical shift titrations, for which the dependence of K ( D ) on the chemical shift difference (Δω) between free and bound states is extrapolated to Δω = 0. The demonstrated accuracy and precision for k ( off ) will be valuable for the interpretation of biological kinetics in weakly interacting protein-protein networks, where a small change in the magnitude of the underlying kinetics of a given pathway may lead to large changes in the associated downstream signaling cascade.

Quadrupole central transition 17O NMR spectroscopy of biological macromolecules in aqueous solution

We demonstrate a general nuclear magnetic resonance (NMR) spectroscopic approach in obtaining high-resolution (17)O (spin-5/2) NMR spectra for biological macromolecules in aqueous solution. This approach, termed quadrupole central transition (QCT) NMR, is based on the multiexponential relaxation properties of half-integer quadrupolar nuclei in molecules undergoing slow isotropic tumbling motion. Under such a circumstance, Redfield's relaxation theory predicts that the central transition, m(I) = +1/2 ↔ -1/2, can exhibit relatively long transverse relaxation time constants, thus giving rise to relatively narrow spectral lines. Using three robust protein-ligand complexes of size ranging from 65 to 240 kDa, we have obtained (17)O QCT NMR spectra with unprecedented resolution, allowing the chemical environment around the targeted oxygen atoms to be directly probed for the first time. The new QCT approach increases the size limit of molecular systems previously attainable by solution (17)O NMR by nearly 3 orders of magnitude (1000-fold). We have also shown that, when both quadrupole and shielding anisotropy interactions are operative, (17)O QCT NMR spectra display an analogous transverse relaxation optimized spectroscopy type behavior in that the condition for optimal resolution depends on the applied magnetic field. We conclude that, with the currently available moderate and ultrahigh magnetic fields (14 T and higher), this (17)O QCT NMR approach is applicable to a wide variety of biological macromolecules. The new (17)O NMR parameters so obtained for biological molecules are complementary to those obtained from (1)H, (13)C, and (15)N NMR studies.

Variation in quadrupole couplings of alpha deuterons in ubiquitin suggests the presence of C(alpha)-H(alpha)...O=C hydrogen bonds

Nuclear quadrupolar couplings are sensitive probes of hydrogen bonding. Experimental quadrupolar coupling constants of alpha deuterons (D(alpha) QCC) are reported for the residues of human ubiquitin that do not experience large-amplitude internal dynamics on the pico- to nanosecond time scale. Two different methods for D(alpha) QCC estimation are employed: (i) direct estimation of D(alpha) QCC values from R(1) and R(2) (2)H D(alpha) rates using the dynamics parameters (S(C(alpha)-H(alpha))(2)) derived from 1 micros molecular dynamics simulations as well as from (13)C(alpha) relaxation measurements and (ii) indirect measurements via scalar relaxation of the second kind that affects (13)C(alpha) relaxation rates in (13)C(alpha)-D(alpha) spin systems. A relatively large variability of D(alpha) QCC values is produced by both methods. The average value of 170.6 +/- 3 kHz is derived from the combined data set, with D(alpha) QCC values ranging from 159.2 to 177.2 kHz. The set of lowest quadrupolar couplings in all data sets corresponds to the residues that are likely to form weak C(alpha)-H(alpha)...O=C hydrogen bonds as predicted from the analysis of short H(alpha)...O distances in three-dimensional structures of ubiquitin. These D(alpha) nuclei show up to 10 kHz reduction in their QCC values, which is in agreement with earlier solid-state NMR measurements in alpha deuterons of glycine. A statistically significant correlation is observed between the QCC values of alpha-deuterons and the inverse cube of C(alpha)-H(alpha)...O=C distances in ubiquitin.

Deuterium spin probes of backbone order in proteins: 2H NMR relaxation study of deuterated carbon alpha sites

(2)H spin relaxation NMR experiments to study the dynamics of deuterated backbone alpha-positions, D(alpha), are developed. To date, solution-state (2)H relaxation measurements in proteins have been confined to side-chain deuterons-primarily (13)CH(2)D or (13)CHD(2) methyl groups. It is shown that quantification of (2)H relaxation rates at D(alpha) backbone positions and the derivation of associated order parameters of C(alpha)-D(alpha) bond vector motions in small [U-(15)N,(13)C,(2)H]-labeled proteins is feasible with reasonable accuracy. The utility of the developed methodology is demonstrated on a pair of proteins-ubiquitin (8.5 kDa) at 10, 27, and 40 degrees C, and a variant of GB1 (6.5 kDa) at 22 degrees C. In both proteins, the D(alpha)-derived parameters of the global rotational diffusion tensor are in good agreement with those obtained from (15)N relaxation rates. Semiquantitative solution-state NMR measurements yield an average value of the quadrupolar coupling constant, QCC, for D(alpha) sites in proteins equal to 174 kHz. Using a uniform value of QCC for all D(alpha) sites, we show that C(alpha)-D(alpha) bond vectors are motionally distinct from the backbone amide N-H bond vectors, with (2)H-derived squared order parameters of C(alpha)-D(alpha) bond vector motions, S(2)(CalphaDalpha), on average slightly higher than their N-H amides counterparts, S(2)(NH). For ubiquitin, the (2)H-derived backbone mobility compares well with that found in a 1-mus molecular dynamics simulation.

Dipolar dynamic frequency shifts in multiple-quantum spectra of methyl groups in proteins: correlation with side-chain motion

Small deviations from the expected relative positions of multiplet components in double- and zero-quantum 1H-13C methyl correlation maps have been observed in spectra recorded on a 7-kDa protein. These dynamic frequency shifts (DFS) are the result of dipolar cross-correlations that derive from fields produced by the spins within the methyl groups. The shifts have been quantified and compared with values calculated from a Redfield analysis. Good agreement is noted between the signs of the predicted and experimentally observed relative shifts of lines in both F1 and F2 dimensions of spectra, as well as between the magnitudes of the calculated and observed shifts in the F2 (1H) dimension. The experimental DFS values show a reasonable correlation with 2H relaxation-derived measures of methyl side-chain dynamics, as expected from theory. This suggests that in cases where such shifts can be quantified, they can serve as qualitative measures of motion.

NMR relaxation in multipolar AMX systems under spin-locking conditions

A relaxation network has been calculated for multipolar AMX systems under application of a spin-locking RF field. Systems of this type are of interest in the study of proteins with fractional (2)H enrichment. All possible auto- and cross-correlation terms involving dipolar, quadrupolar, and CSA interactions have been taken into account. The results show the presence of spectral densities at zero frequency for interactions associated with the locked nuclei, which are nonvanishing in the absence of fast motions. In addition, the application of a spin-locking field blocks certain cross-correlation interactions, thereby considerably simplifying the relaxation network. Copyright 2000 Academic Press.

NMR relaxation in multipolar AX systems under spin locking conditions

A relaxation matrix has been calculated for a multipolar AX spin system under the on-resonance spin-locking condition. Auto- and cross-correlation terms between dipolar, quadrupolar, and CSA interactions are considered. It is shown that the spin-lock leads to many relaxation pathways being blocked, resulting in a considerably simplified relaxation network. The presence of spectral densities at zero frequency, associated with locked nuclei, allows efficient relaxation also in the absence of fast molecular motions.

Relaxation effects in a system of a spin-1/2 nucleus coupled to a quadrupolar spin subjected to RF irradiation: evaluation of broadband decoupling schemes

We have investigated the suitability and performance of various decoupling methods on systems in which an observed spin-1/2 nucleus I (13C or 15N) is scalar-coupled to a quadrupolar spin S (2H). Simulations and experiments have been conducted by varying the strength of the irradiating radiofrequency (RF) field, RF offset, relaxation times, and decoupling schemes applied in the vicinity of the S-spin resonance. The T1 relaxation of the quadrupolar spin has previously been shown to influence the efficiency of continuous wave (CW) decoupling applied on resonance in such spin systems. Similarly, the performance of broadband decoupling sequences should also be affected by relaxation. However, virtually all of the more commonly used broadband decoupling schemes have been developed without consideration of relaxation effects. As a consequence, it is not obvious how one selects a suitable sequence for decoupling quadrupolar nuclei with exotic relaxation behavior. Herein we demonstrate that, despite its simplicity, WALTZ-16 decoupling is relatively robust under a wide range of conditions. In these systems it performs as well as the more recently developed decoupling schemes for wide bandwidth applications such as GARP-1 and CHIRP-95. It is suggested that in macromolecular motional regimes, broadband deuterium decoupling can be achieved with relatively low RF amplitudes (500-700 Hz) using WALTZ-16 multiple pulse decoupling.

The use of 2H, 13C, 15N multidimensional NMR to study the structure and dynamics of proteins

During the past thirty years, deuterium labeling has been used to improve the resolution and sensitivity of protein NMR spectra used in a wide variety of applications. Most recently, the combination of triple resonance experiments and 2H, 13C, 15N labeled samples has been critical to the solution structure determination of several proteins with molecular weights on the order of 30 kDa. Here we review the developments in isotopic labeling strategies, NMR pulse sequences, and structure-determination protocols that have facilitated this advance and hold promise for future NMR-based structural studies of even larger systems. As well, we detail recent progress in the use of solution 2H NMR methods to probe the dynamics of protein sidechains.

Electron spin-nuclear spin cross-correlation effects on multiplet splittings in paramagnetic proteins

The effects of cross-correlation between Curie spin-nuclear dipole and nuclear dipole-nuclear dipole interactions on the linewidths and resonance frequencies of the individual lines of an AX multiplet in paramagnetic systems have been calculated. The implication of the relaxation-induced frequency shift of the lines (dynamic frequency shift) for the accurate measurement of residual dipolar couplings in field-oriented systems has been discussed. Our simulations indicate that these effects may play a role in the precise measurement of residual dipolar couplings in systems which belong to the small and intermediate tumbling regime, i.e., correlation times less than 5 ns.

Dynamic frequency shifts of complexed ligands: An NMR study of D--1-13C,1-2H-glucose complexed to the Escherichia coli periplasmic glucose/galactose receptor

The 13C multiplet structure of D--1-13C,1-2H-glucose complexed to the Escherichia coli periplasmic glucose/galactose receptor has been studied as a function of temperature. Asymmetric multiplet patterns observed are shown to arise from dynamic frequency shifts. Multiplet asymmetry contributions resulting from shift anisotropy-dipolar cross correlations were found to be small, with optimal fits of the data corresponding to small, negative values of the correlation factor, chiCD-CSA. Additional broadening at higher temperatures most probably results from ligand exchange between free and complexed states. Effects of internal motion are also considered theoretically, and indicate that the order parameter for the bound glucose is >/=0.9.

Solution NMR characterization of hydrogen bonds in a protein by indirect measurement of deuterium quadrupole couplings

Hydrogen bonds stabilize protein and nucleic acid structure, but little direct spectroscopic data have been available for characterizing these critical interactions in biological macromolecules. It is demonstrated that the electric field gradient at the nucleus of an amide hydrogen can be determined residue-specific by measurement of 15N NMR relaxation times in proteins dissolved in D2O, and uniformly enriched with 13C and 15N. In D2O, all backbone amide protons can be exchanged with solvent deuterons, and the T1 relaxation rate of a deuteron is dominated by its quadrupole coupling constant (QCC), which is directly proportional to the electric field gradient at the nucleus. 2HN T1 relaxation can be measured quantitatively through its effect on the T2 relaxation of its directly attached 15N. QCC values calculated from 2HN T1 and previously reported spectral densities correlate with the inverse cube of the X-ray crystal structure-derived hydrogen bond lengths: QCC = 228 + Sigmai 130 cos alphai/ri3 kHz, where alpha is the N-H...Oi angle and r is the backbone-backbone (N-)H...Oi(=C) hydrogen bond distance in ângstroms.