De novo determination of bond orientations and order parameters from residual dipolar couplings with high accuracy

We report the de novo determination of 15N-1H bond orientations and motional order parameters for the protein ubiquitin with high accuracy based solely on NMR residual dipolar coupling measurements made in six distinct alignment media. The resulting bond orientations are in agreement with RDC-refined orientations of either solid or solution state coordinates to within approximately 2 degrees , which is also the estimated precision of the resulting orientations. The squared generalized order parameters, which reflect amplitudes of motion spanning the picosecond to millisecond time scales, exhibit a correlation with picosecond time scale order parameters derived from conventional NMR 15N spin relaxation methods. Provided that RDC measurements can be obtained using many different alignment media, this approach (called direct interpretation of dipolar couplings) may significantly impact the attainable accuracy and the molecular weight range accessible to NMR structure determination in the solution state, as well as provide a route for the study of motions occurring on the nanosecond to microsecond time scales, which have been traditionally difficult to study at atomic resolution.     

Lanthanide-binding peptides for NMR measurements of residual dipolar couplings and paramagnetic effects from multiple angles

Lanthanide-binding peptide tags (LBTs) containing a single cysteine residue can be attached to proteins via a disulfide bond, presenting a flexible means of tagging proteins site-specifically with a lanthanide ion. Here we show that cysteine residues placed in different positions of the LBT can be used to expose the protein to different orientations of the magnetic susceptibility anisotropy (delta chi) tensor and to generate different molecular alignments in a magnetic field. Delta chi tensors determined by nuclear magnetic resonance (NMR) spectroscopy for LBT complexes with Yb3+, Tm3+, and Er3+ suggest a rational way of producing alignment tensors with different orientations. In addition, knowledge of the delta chi tensor of LBT allows modeling of the protein-LBT structures. Despite evidence for residual mobility of the LBTs with respect to the protein, the pseudocontact shifts and residual dipolar couplings displayed by proteins disulfide-bonded to LBTs are greater than those achievable with most other lanthanide binding tags.     

Physical interpretation of residual dipolar couplings in neutral aligned media

A novel method is described for rapidly calculating alignment tensors from hydrodynamic shape, required for the prediction of residual dipolar couplings in neutral aligned media. Simulations of alignment were used to show that for steric restriction at a planar surface, the alignment process is dependent on linear hydrodynamic length. However, as discussed, previous methods are not in agreement with this observation. Therefore, the method presented here is the first to provide simple, accurate predictions of the alignment tensor for neutral and dilute media, while being consistent with simulations of alignment. It provides predictions in a fraction of the time of a simulation approach, while aiding physical intuition by providing a direct link between shape and alignment. Not only is this physically gratifying, but it also permits residual dipolar couplings to be applied in demanding situations where simulations of alignment are not desirable, such as in studies of molecular dynamics.     

Evaluation of backbone proton positions and dynamics in a small protein by liquid crystal NMR spectroscopy

NMR measurements of a large set of protein backbone one-bond dipolar couplings have been carried out to refine the structure of the third IgG-binding domain of Protein G (GB3), previously solved by X-ray crystallography at a resolution of 1.1 A. Besides the commonly used bicelle, poly(ethylene glycol), and filamentous phage liquid crystalline media, dipolar couplings were also measured when the protein was aligned inside either positively or negatively charged stretched acrylamide gels. Refinement of the GB3 crystal structure against the (13)C(alpha)-(13)C' and (13)C'-(15)N dipolar couplings improves the agreement between experimental and predicted (15)N-(1)H(N) as well as (13)C(alpha)-(1)H(alpha) dipolar couplings. Evaluation of the peptide bond N-H orientations shows a weak anticorrelation between the deviation of the peptide bond torsion angle omega from 180 degrees and the angle between the N-H vector and the C'-N-C(alpha) plane. The slope of this correlation is -1, indicating that, on average, pyramidalization of the peptide N contributes to small deviations from peptide bond planarity ( = 179.3 +/- 3.1 degrees ) to the same degree as true twisting around the C'-N bond. Although hydrogens are commonly built onto crystal structures assuming the N-H vector orientation falls on the line bisecting the C'-N-C(alpha) angle, a better approximation adjusts the C(alpha)-C'-N-H torsion angle to -2 degrees. The (15)N-(1)H(N) dipolar data do not contradict the commonly accepted motional model where angular fluctuations of the N-H bond orthogonal to the peptide plane are larger than in-plane motions, but the amplitude of angular fluctuations orthogonal the C(alpha)(i-1)-N(i)-C(alpha)(i) plane exceeds that of in-plane motions by at most 10-15 degrees. Dipolar coupling analysis indicates that for most of the GB3 backbone, the amide order parameters, S, are highly homogeneous and vary by less than +/-7%. Evaluation of the H(alpha) proton positions indicates that the average C(alpha)-H(alpha) vector orientation deviates by less than 1 degrees from the direction that makes ideal tetrahedral angles with the C(alpha)-C(beta) and C(alpha)-N vectors.     

Dipolar waves map the structure and topology of helices in membrane proteins

Dipolar waves describe the structure and topology of helices in membrane proteins. The fit of sinusoids with the 3.6 residues per turn period of ideal alpha-helices to experimental measurements of dipolar couplings as a function of residue number makes it possible to simultaneously identify the residues in the helices, detect kinks or curvature in the helices, and determine the absolute rotations and orientations of helices in completely aligned bilayer samples and relative rotations and orientations of helices in a common molecular frame in weakly aligned micelle samples. Since as much as 80% of the structured residues in a membrane protein are in helices, the analysis of dipolar waves provides a significant step toward structure determination of helical membrane proteins by NMR spectroscopy.     

Proton evolved local field solid-state nuclear magnetic resonance using Hadamard encoding: theory and application to membrane proteins

NMR anisotropic parameters such as dipolar couplings and chemical shifts are central to structure and orientation determination of aligned membrane proteins and liquid crystals. Among the separated local field experiments, the proton evolved local field (PELF) scheme is particularly suitable to measure dynamically averaged dipolar couplings and give information on local molecular motions. However, the PELF experiment requires the acquisition of several 2D datasets at different mixing times to optimize the sensitivity for the complete range of dipolar couplings of the resonances in the spectrum. Here, we propose a new PELF experiment that takes the advantage of the Hadamard encoding (HE) to obtain higher sensitivity for a broad range of dipolar couplings using a single 2D experiment. The HE scheme is obtained by selecting the spin operators with phase switching of hard pulses. This approach enables one to detect four spin operators, simultaneously, which can be processed into two 2D spectra covering a broader range of dipolar couplings. The advantages of the new approach are illustrated for a U-(15)N NAL single crystal and the U-(15)N labeled single-pass membrane protein sarcolipin reconstituted in oriented lipid bicelles. The HE-PELF scheme can be implemented in other multidimensional experiments to speed up the characterization of the structure and dynamics of oriented membrane proteins and liquid crystalline samples.     

Probing motions between equivalent RNA domains using magnetic field induced residual dipolar couplings: accounting for correlations between motions and alignment

Approaches developed thus for extracting structural and dynamical information from RDCs have rested on the assumption that motions do not affect molecular alignment. However, it is well established that molecular alignment in ordered media is dependent on conformation, and slowly interconverting conformational substates may exhibit different alignment properties. Neglecting these correlation effects can lead to aberrations in the structural and dynamical analysis of RDCs and diminish the utility of RDCs in probing motions between domains having similar alignment propensities. Here, we introduce a new approach based on measurement of magnetic field induced residual dipolar couplings in nucleic acids which can explicitly take into account such correlations and demonstrate measurements of motions between two "magnetically equivalent" domains in the transactivation response element (TAR) RNA.     

NMR spectroscopy investigation of the cooperative nature of the internal rotational motions in acetophenone.

The proton NMR spectrum of the doubly enriched acetophenone-carbonyl,methyl-13C2 isotopomer dissolved in a liquid-crystalline solvent (LXNMR) was analyzed to yield a data set of 19 dipolar couplings. The presence of so many couplings, and in particular the dependence of some of them on the acetyl carbons enabled the investigation of the structure of the acetyl moiety and of possible cooperative motions about the aryl-carbonyl and carbonyl-methyl bonds. Methodological aspects, and approximations relating to the application of the vibrational correction procedure in the presence of large-amplitude torsional motions, are discussed. Results show that it is possible to discriminate between a continuous and a discrete conformer distribution about the angle phi(1) but not among a few proposed continuous shapes of U(iso)({phi}). In this study, the use of dipolar couplings with a non-negligible contribution from the indirect spin-spin coupling tensor J, (D(C8C9) in our case), for structural determination is extended from rigid to flexible molecules. The 1/2J(aniso)(C8C9) contribution was derived theoretically using the density functional theory linear response (DFT-LR) first-principles calculation of the J(C8C9) spin-spin coupling tensor.     

Simultaneous assignment of all diastereotopic protons in strychnine using RDCs: PELG as alignment medium for organic molecules

The concept of using residual dipolar couplings (RDCs) for the structure determination of organic molecules is applied to the simultaneous assignment of all diastereotopic protons in strychnine. To use this important NMR parameter the molecule has to be aligned in the magnetic field. Here we present a new alignment medium for organic substrates. The optimization of the alignment properties of mixtures of poly-gamma-ethyl-L-glutamate (PELG) and CDCl(3) are described and the alignment properties of PELG at different concentrations are evaluated. A comparison of PELG with poly-gamma-benzyl-L-glutamate (PBLG) shows considerable differences in the magnitude of alignment for strychnine in the two alignment media. PELG induces a lower degree of order and makes the measurement of residual dipolar couplings (RDCs) in strychnine possible. All one-bond C-H RDCs of strychnine in PELG were determined by using 2D heteronuclear single quantum coherence (HSQC) spectroscopy. The strategy for the extraction of RDCs for methylene groups is described in detail. The RDCs and order parameters are used to assign pairs of diastereotopic protons. This methodology can distinguish not only one pair of diastereotopic protons but it can be used to assign all pairs of diastereotopic protons simultaneously. Two different calculation approaches to achieve this task are described in detail.     

Protein alignment by a coexpressed lanthanide-binding tag for the measurement of residual dipolar couplings

A protein fusion construct of human ubiquitin with an N-terminal lanthanide binding tag (LBT) enables observation of long-range orientational restraints in solution NMR from residual dipolar couplings (RDCs) due to paramagnetic alignment of the protein. The paramagnetic lanthanide ions Tb3+, Dy3+, and Tm3+ are shown to bind to the LBT and induce different alignment tensors, in agreement with theory. RDCs, measured relative to the diamagnetic Lu3+, range from -7.6 to 5.5 Hz for Tb3+ and -6.6 to 6.1 Hz for Dy3+, while an opposite alignment tensor is observed for Tm3+ (4.5 to -2.9 Hz) at 800 MHz. Experimental RDCs are in excellent agreement with those predicted on the basis of the X-ray structure of the protein.     

Dipolar waves as NMR maps of protein structure

The anisotropy of nuclear spin interactions results in a unique mapping of structure to the resonance frequencies and split tings observed in NMR spectra, however, the determination of molecular structure from experimentally measured spectral parameters is complicated by angular ambiguities resulting from the symmetry properties of dipole-dipole and chemical shift interactions. This issue can be addressed through the periodicity inherent in secondary structure elements, which can be used as an index of topology. Distinctive wheel-like patterns are observed in two-dimensional 1H-15N heteronuclear dipolar/15N chemical shift PISEMA (polarization inversion spin-exchange at the magic angle) spectra of helical membrane proteins in highly aligned lipid bilayer samples. One-dimensional dipolar waves are an extension of two-dimensional PISA (polarity index slant angle) wheels to map protein structure in NMR spectra of both highly and weakly aligned samples. Dipolar waves describe the periodic wavelike variations of the magnitudes of the static heteronuclear dipolar couplings as a function of residue number in the absence of chemical shift effects. Weakly aligned samples of proteins display these same effects, primarily as residual dipolar couplings (RDCs), in solution NMR spectra. The corresponding properties of the RDCs in solution NMR spectra of weakly aligned helices represent a convergence of solid-state and solution NMR approaches to structure determination.     

High-resolution characterization of liquid-crystalline [60]fullerenes using solid-state nuclear magnetic resonance spectroscopy

Liquid-crystalline materials containing fullerenes are valuable in the development of supramolecular switches and in solar cell technology. In this study, we characterize the liquid-crystalline and dynamic properties of fullerene-containing thermotropic compounds using solid-state natural abundance (13)C NMR experiments under stationary and magic angle spinning sample conditions. Chemical shifts spectra were measured in isotropic, liquid-crystalline nematic and smectic A and crystalline phases using one-dimensional (13)C experiments, while two-dimensional separated local-field experiments were used to measure the (1)H- (13)C dipolar couplings in mesophases. Chemical shift and dipolar coupling parameters were used to characterize the structure and dynamics of the liquid-crystalline dyads. NMR data of fullerene-containing thermotropic liquid crystals are compared to that of basic mesogenic unit and mesomorphic promoter compounds. Our NMR results suggest that the fullerene-ferrocene dyads form highly dynamic liquid-crystalline phases in which molecules rotate fast around the symmetry axis on the characteristic NMR time scale of approximately 10 (-4) s.     

Residue-specific 13C' CSA tensor principal components for ubiquitin: correlation between tensor components and hydrogen bonding

The residue-specific 13C' CSA tensor principal components, sigma(11), sigma(22), sigma(33), and the tensor orientation defined by the rotation angles beta and gamma have been determined by solution NMR for uniformly labeled ubiquitin partially aligned in four different media. Spurious chemical shift deviations due to solvent effects were corrected with an offset calculated by linear regression of the residual dipolar couplings and chemical shifts at increasing alignment strengths. Analysis of this effect revealed no obvious correlation to solvent exposure. Data obtained in solution from a protein offer a better sampling of 13C' CSA for different amino acid types in a complex heterogeneous environment, thereby allowing for the evaluation of structural variables that would be challenging to achieve by other methods. The 13C' CSA principal components cluster about the average values previously determined, and experimental correlations observed between sigma(11), sigma(22) tensorial components and C'O...H(N) hydrogen bonding are discussed. The inverse association of sigma(11) and sigma(22) exemplify the calculated and solid-state NMR observed effect on the tensor components by hydrogen bonding. We also show that 13C' CSA tensors are sensitive to hydrogen-bond length but not hydrogen-bond angle. This differentiation was previously unavailable. Similarly, hydrogen bonding to the conjugated NH of the same peptide plane has no detectable effect. Importantly, the observed weak correlations signify the presence of confounding influences such as nearest-neighbor effects, side-chain conformation, electrostatics, and other long-range factors to the 13C' CSA tensor. These analyses hold future potential for exploration provided that more accurate data from a larger number of proteins and alignments become available.     

Chemical shift tensors of protonated base carbons in helical RNA and DNA from NMR relaxation and liquid crystal measurements

Knowledge of (13)C chemical shift anisotropy (CSA) tensors in nucleotide bases is important for interpretation of NMR relaxation data in terms of local dynamic properties of nucleic acids and for analysis of residual chemical shift anisotropy (RCSA) resulting from weak alignment. CSA tensors for protonated nucleic acid base carbons have been derived from measurements on a uniformly (13)C-enriched helical A-form RNA segment and a helical B-form DNA dodecamer at natural (13)C abundance. The magnitudes of the derived CSA principal values are tightly restricted by the magnetic field dependencies of the (13)C transverse relaxation rates, whereas the tensor orientation and asymmetry follow from quantitative measurements of interference between (13)C-{(1)H} dipolar and (13)C CSA relaxation mechanisms. Changes in the chemical shift between the isotropic and aligned states, Deltadelta, complement these measurements and permit cross-validation. The CSA tensors are determined from the experimental Deltadelta values and relaxation rates, under the assumption that the CSA tensor of any specific carbon in a given type of base is independent of the base position in either the RNA or DNA helix. However, the experimental data indicate that for pyrimidine C(6) carbons in A-form RNA the CSA magnitude is considerably larger than in B-form DNA. This result is supported by quantum chemical calculations and is attributed in part to the close proximity between intranucleotide C(6)H and O(5)' atoms in RNA. The magnitudes of the measured CSA tensors, on average, agree better with previous solid-state NMR results obtained on powdered nucleosides than with prior results from quantum chemical calculations on isolated bases, which depend rather strongly on the level of theory at which the calculations are carried out. In contrast, previously computed orientations of the chemical shift tensors agree well with the present experimental results and exhibit less dependence on the level of theory at which the computations are performed.     

Determination of the packing mode of the coiled-coil domain of cGMP-dependent protein kinase Ialpha in solution using charge-predicted dipolar couplings

Coiled-coil motifs are ubiquitous in biology and play essential roles in protein assembly and molecular recognition. Here, we show that the relative orientation and stoichiometry of coiled-coil proteins in solution can be determined by comparison of residual dipolar couplings (RDCs) measured in charged liquid-crystalline medium with values predicted from the three-dimensional charge distribution of the protein. Comparison of charge-predicted RDCs with a small set of one-bond 1DNH dipolar couplings, measured in the negatively charged liquid-crystalline Pf1 bacteriophage medium, identified the coiled-coil region of the cGMP-dependent protein kinase I as a parallel homodimer in solution and ruled out an antiparallel dimeric or monomeric state. The method is very rapid, applicable to a wide variety of liquid crystals used in biological NMR to date, and can be applied to coiled-coil structures and other proteins with higher order assembly.     

Measurement of long-range cross-correlation rates using a combination of single- and multiple-quantum NMR spectroscopy in one experiment

A method is described to determine long-range cross-correlations between the modulations of an anisotropic chemical shift (e.g., of a C' carbonyl carbon in a protein) and the fluctuations of a weak long-range dipolar interaction (e.g., in cross-correlation between the same C' carbonyl and the H(N) proton of the neighboring amide group). Such long-range correlations are difficult to measure because the corresponding long-range scalar couplings are so small that Redfield's secular approximation is often violated. The method, which combines features of single- and double-quantum NMR spectroscopy, allows one to cancel the effects of dominant short-range dipolar interactions (e.g., between the CSA of the amide nitrogen N and the dipolar coupling to its attached proton H(N)) and is designed so that the secular approximation is rescued even if the scalar coupling between the long-range dipolar coupling partners is very small. The cross-correlation rates thus determined in ubiquitin cover a wide range because of local motions and variations of the CSA tensors.     

Measurement of ribose carbon chemical shift tensors for A-form RNA by liquid crystal NMR spectroscopy

Incomplete motional averaging of chemical shift anisotropy upon weak alignment of nucleic acids and proteins in a magnetic field results in small changes in chemical shift. Knowledge of nucleus-specific chemical shift (CS) tensor magnitudes and orientations is necessary to take full advantage of these measurements in biomolecular structure determination. We report the determination by liquid crystal NMR of the CS tensors for all ribose carbons in A-form helical RNA, using a series of novel 3D NMR pulse sequences for accurate and resolved measurement of the ribose (13)C chemical shifts. The orientation of the riboses relative to the rhombic alignment tensor of the molecule studied, a stem-loop sequence corresponding to helix-35 of 23S rRNA, is known from an extensive set of residual dipolar couplings (RDC), previously used to refine its structure. Singular-value-decomposition fits of the chemical shift changes to this structure, or alternatively to a database of helical RNA X-ray structures, provide the CS tensor for each type of carbon. Quantum chemical calculations complement the experimental results and confirm that the most shielded tensor component lies approximately along the local carbon-oxygen bond axis in all cases and that shielding anisotropy for C3' and C4' is much larger than for C1' and C2', with C5' being intermediate.     

Lipid-ethanol interaction studied by NMR on bicelles

The interaction of ethanol with phospholipids was studied in bicelles at a physiologically relevant ethanol concentration of 20 mM and a lipid content of 14 wt % by high-resolution NMR. Transient association of ethanol with magnetically aligned bicelles imparts a small degree of anisotropy to the solute. This anisotropy allows detection of residual (1)H-(1)H and (1)H-(13)C dipolar couplings, which are superimposed on scalar couplings. Residual (2)H NMR quadrupole splittings of isotope-labeled ethanol were measured as well. The analysis of residual tensorial interactions yielded information on the orientation and motions of ethanol in the membrane-bound state. The fraction of phosphatidylcholine-bound ethanol was determined independently by gas chromatography and NMR. About 4% of ethanol is bound to phosphatidylcholine at a bicelle concentration of 14 wt % at 40 degrees C. Free and bound ethanol are in rapid exchange. The lifetime of ethanol association with phosphatidylcholine membranes is of the order of a few nanoseconds.     

Direct prediction of residual dipolar couplings of small molecules in a stretched gel by stochastic molecular dynamics simulations

Residual dipolar couplings are highly useful NMR parameters for calculating and refining molecular structures, dynamics, and interactions. For some applications, however, it is inevitable that the preferred orientation of a molecule in an alignment medium is calculated a priori. Several methods have been developed to predict molecular orientations and residual dipolar couplings. Being beneficial for macromolecules and selected small‐molecule applications, such approaches lack sufficient accuracy for a large number of organic compounds for which the fine structure and eventually the flexibility of all involved molecules have to be considered or are limited to specific, well‐studied liquid crystals. We introduce a simplified model for detailed all‐atom molecular dynamics calculations with a polymer strand lined up along the principal axis as a new approach to simulate the preferred orientation of small to medium‐sized solutes in polymer‐based, gel‐type alignment media. As is shown by a first example of strychnine in a polystyrene/CDCl₃ gel, the simulations potentially enable the accurate prediction of residual dipolar couplings taking into account structural details and dynamic averaging effects of both the polymer and the solute. Copyright © 2015 John Wiley & Sons, Ltd.