A new approach for applying residual dipolar couplings as restraints in structure elucidation

Residual dipolar couplings are useful global structural restraints. The dipolar couplings define the orientation of a vector with respect to the alignment tensor. Although the size of the alignment tensor can be derived from the distribution of the experimental dipolar couplings, its orientation with respect to the coordinate system of the molecule is unknown at the beginning of structure determination. This causes convergence problems in the simulated annealing process. We therefore propose a protocol that translates dipolar couplings into intervector projection angles, which are independent of the orientation of the alignment tensor with respect to the molecule. These restraints can be used during the whole simulated annealing protocol.     

Structural characterization of unfolded states of apomyoglobin using residual dipolar couplings

The conformational propensities of unfolded states of apomyoglobin have been investigated by measurement of residual dipolar couplings between (15)N and (1)H in backbone amide groups. Weak alignment of apomyoglobin in acid and urea-unfolded states was induced with both stretched and compressed polyacrylamide gels. In 8 M urea solution at pH 2.3, conditions under which apomyoglobin contains no detectable secondary or tertiary structure, significant residual dipolar couplings of uniform sign were observed for all residues. At pH 2.3 in the absence of urea, a change in the magnitude and/or sign of the residual dipolar couplings occurs in local regions of the polypeptide where there is a high propensity for helical secondary structure. These results are interpreted on the basis of the statistical properties of the unfolded polypeptide chain, viewed as a polymer of statistical segments. For a folded protein, the magnitude and sign of the residual dipolar couplings depend on the orientation of each bond vector relative to the alignment tensor of the entire molecule, which reorients as a single entity. For unfolded proteins, there is no global alignment tensor; instead, residual dipolar couplings are attributed to alignment of the statistical segments or of transient elements of secondary structure. For apomyoglobin in 8 M urea, the backbone is highly extended, with phi and psi dihedral angles favoring the beta or P(II) regions. Each statistical segment has a highly anisotropic shape, with the N-H bond vectors approximately perpendicular to the long axis, and becomes weakly aligned in the anisotropic environment of the strained acrylamide gels. Local regions of enhanced flexibility or chain compaction are characterized by a decrease in the magnitude of the residual dipolar couplings. The formation of a small population of helical structure in the acid-denatured state of apomyoglobin leads to a change in sign of the residual dipolar couplings in local regions of the polypeptide; the population of helix estimated from the residual dipolar couplings is in excellent agreement with that determined from chemical shifts. The alignment model described here for apomyoglobin can also explain the pattern of residual dipolar couplings reported previously for denatured states of staphylococcal nuclease and other proteins. In conjunction with other NMR experiments, residual dipolar couplings can provide valuable insights into the dynamic conformational propensities of unfolded and partly folded states of proteins and thereby help to chart the upper reaches of the folding landscape.     

Determination of residual dipolar couplings in homonuclear MOCCA-SIAM experiments

In solutions with partial molecular alignment, anisotropic magnetic interactions such as the chemical shift anisotropy, the electric quadrupole interaction, and the magnetic dipole-dipole interaction are no longer averaged out to zero in contrast to isotropic solutions. The resulting residual anisotropic magnetic interactions are increasingly used in biological NMR studies for the determination of 3D structures of proteins and other biomolecules. In the present paper we propose a new approach allowing the measurement of residual H^N-H dipolar couplings of non-isotope enriched proteins based on the application of the MOCCA-SIAM experiment. This experiment allows the measurement of homonuclear coupling constants with an accuracy of ca. ±0.2 Hz and is therefore particularly well suited to determine residual dipolar couplings at relatively low degrees of molecular orientation. The agreement between experimentally determined residual H^N-H couplings and calculated values is demonstrated for BPTI.     

A unifying probabilistic framework for analyzing residual dipolar couplings

Residual dipolar couplings provide complementary information to the nuclear Overhauser effect measurements that are traditionally used in biomolecular structure determination by NMR. In a de novo structure determination, however, lack of knowledge about the degree and orientation of molecular alignment complicates the analysis of dipolar coupling data. We present a probabilistic framework for analyzing residual dipolar couplings and demonstrate that it is possible to estimate the atomic coordinates, the complete molecular alignment tensor, and the error of the couplings simultaneously. As a by-product, we also obtain estimates of the uncertainty in the coordinates and the alignment tensor. We show that our approach encompasses existing methods for determining the alignment tensor as special cases, including least squares estimation, histogram fitting, and elimination of an explicit alignment tensor in the restraint energy.     

Sensitivity-optimized experiment for the measurement of residual dipolar couplings between amide protons

High signal to noise is a necessity for the quantification of NMR spectral parameters to be translated into accurate and precise restraints on protein structure and dynamics. An important source of long-range structural information is obtained from ¹H–¹H residual dipolar couplings (RDCs) measured for weakly aligned molecules. For sensitivity reasons, such measurements are generally performed on highly deuterated protein samples. Here we show that high sensitivity is also obtained for protonated protein samples if the pulse schemes are optimized in terms of longitudinal relaxation efficiency and J-mismatch compensated coherence transfer. The new sensitivity-optimized quantitative J-correlation experiment yields important signal gains reaching factors of 1.5 to 8 for individual correlation peaks when compared to previously proposed pulse schemes. Paul Schanda and Ewen Lescop contributed equally to this work.     

Conformational studies of blood group A and blood group B oligosaccharides using NMR residual dipolar couplings

The conformations of two synthetic trisaccharides of blood group A and B (alpha-L-Fucp-(1-->2)-[alpha-D-GalpNAc-(1-->3)]-alpha-D-Galp and alpha-L-Fucp-(1-->2)-[alpha-D-Galp-(1-->3)]-alpha-D-Galp, respectively) and of a type A tetrasaccharide alditol, Fucp-(1-->2)-[alpha-D-GalpNAc-(1-->3)]-beta-D-Galp-(1-->3)-GalNAc-ol, were studied by NMR measurements of one-bond C-H residual dipolar couplings in partially oriented liquid crystal solutions. The conformations of the three oligosaccharides were analyzed by generating thousands of structures using a Monte-Carlo method. Two different strategies were applied to calculate theoretical dipolar couplings for these structures. In the first method, the orientation of the molecule was calculated from the optimal fit of the molecular model to the experimental data, while in the second method the orientation tensor was calculated directly from the moment of inertia of the molecular model. Both methods of analysis give similar results but with slightly better agreement with experiment for the former one. The analysis of the results implies a single unique conformation for both blood group epitopes in solution in disagreement with theoretical models suggesting the existence of two conformers in solution.     

Direct structure refinement of high molecular weight proteins against residual dipolar couplings and carbonyl chemical shift changes upon alignment: an application to maltose binding protein

The global fold of maltose binding protein in complex with -cyclodextrin has been determined using a CNS-based torsion angle molecular dynamics protocol involving direct refinement against dipolar couplings and carbonyl chemical shift changes that occur upon alignment. The shift changes have been included as structural restraints using a new module, CANI, that has been incorporated into CNS. Force constants and timesteps have been determined that are particularly effective in structure refinement applications involving high molecular weight proteins with small to moderate numbers of NOE restraints. Solution structures of the N- and C-domains of MBP calculated with this new protocol are within 2 Å of the X-ray conformation.     

Measuring membrane protein bond orientations in nanodiscs via residual dipolar couplings

Membrane proteins are involved in numerous vital biological processes. To understand membrane protein functionality, accurate structural information is required. Usually, structure determination and dynamics of membrane proteins are studied in micelles using either solution state NMR or X‐ray crystallography. Even though invaluable information has been obtained by this approach, micelles are known to be far from ideal mimics of biological membranes often causing the loss or decrease of membrane protein activity. Recently, nanodiscs, which are composed of a lipid bilayer surrounded by apolipoproteins, have been introduced as a more physiological alternative than micelles for NMR investigations on membrane proteins. Here, we show that membrane protein bond orientations in nanodiscs can be obtained by measuring residual dipolar couplings (RDCs) with the outer membrane protein OmpX embedded in nanodiscs using Pf1 phage as an alignment medium. The presented collection of membrane protein RDCs in nanodiscs represents an important step toward more comprehensive structural and dynamical NMR‐based investigations of membrane proteins in a natural bilayer environment.     

Characterization of protein dynamics from residual dipolar couplings using the three dimensional Gaussian axial fluctuation model

Residual dipolar couplings are potentially very powerful probes of slower protein motions, providing access to dynamic events occurring on functionally important timescales up to the millisecond. One recent approach uses the three dimensional Gaussian Axial Fluctuation model (3D GAF) to determine the major directional modes and associated amplitudes of motions along the peptide chain. In this study we have used standard and accelerated molecular dynamics simulations to determine the accuracy of 3D GAF-based approaches in characterizing the nature and extent of local molecular motions. We compare modes determined directly from the trajectories with motional parameterization derived from RDCs simulated from the same trajectories. Three approaches are tested, that either suppose a known three-dimensional structure, simultaneously determine backbone structure and dynamics, or determine dynamic modes in the absence of a structural model. The results demonstrate the robustness of the 3D GAF analysis even in the presence of large-scale motions, and illustrate the remarkably quantitative nature of the extracted amplitudes. These observations suggest that the approach can be generally used for the study of functionally interesting biomolecular motions.     

Conformational studies of Lewis X and Lewis A trisaccharides using NMR residual dipolar couplings.

The conformations of the histo-blood group carbohydrate antigens Lewis X (Le(x)) and Lewis A (Le(a)) were studied by NMR measurements of one-bond C-H residual dipolar couplings in partially oriented liquid crystal solutions. A strategy for rapid calculation of the difference between theoretical and experimental dipolar couplings of a large number of model structures generated by computer simulations was developed, resulting in an accurate model structure for the compounds. Monte Carlo simulations were used to generate models for the trisaccharides, and orientations of each model were sought that could reproduce the experimental residual dipolar coupling values. For both, Le(a) and Le(x), single low energy models giving excellent agreement with experiment were found, implying a compact rigidly folded conformation for both trisaccharides. The new approach was also applied to the pentasaccharides lacto-N-fucopentaose 2 (LNF-2) and lacto-N-fucopentaose 3 (LNF-3) proving its consistency and robustness. For describing the conformation of tightly folded oligosaccharides, a definition for characterization of ring planes in pyranoside chairs is proposed and applied to the analysis of the relation between the fucose and galactose residues in the epitopes, revealing the structural similarity between them.     

Use of residual dipolar couplings as restraints in ab initio protein structure prediction

NMR residual dipolar couplings (RDCs), in the form of the projection angles between the respective internuclear bond vectors, are used as structural restraints in the ab initio structure prediction of a test set of six proteins. The restraints are applied using a recently developed SICHO (SIde-CHain-Only) lattice protein model that employs a replica exchange Monte Carlo (MC) algorithm to search conformational space. Using a small number of RDC restraints, the quality of the predicted structures is improved as reflected by lower RMSD/dRMSD (root mean square deviation/distance root mean square deviation) values from the corresponding native structures and by the higher correlation of the most cooperative mode of motion of each predicted structure with that of the native structure. The latter, in particular, has possible implications for the structure-based functional analysis of predicted structures.     

Rapid and accurate structure determination of coiled-coil domains using NMR dipolar couplings: application to cGMP-dependent protein kinase Ialpha

Coiled-coil motifs play essential roles in protein assembly and molecular recognition, and are therefore the targets of many ongoing structural and functional studies. However, owing to the dynamic nature of many of the smaller coiled-coil domains, crystallization for X-ray studies is very challenging. Determination of elongated structures using standard NMR approaches is inefficient and usually yields low-resolution structures due to accumulation of small errors over long distances. Here we describe a solution NMR approach based on residual dipolar couplings (RDCs) for rapid and accurate structure determination of coiled-coil dimers. Using this approach, we were able to determine the high-resolution structure of the coiled-coil domain of cGMP-dependent protein kinase Ialpha, a protein of previously unknown structure that is critical for physiological relaxation of vascular smooth muscle. This approach can be extended to solve coiled-coil structures with higher order assemblies.     

Determination of helical membrane protein topology using residual dipolar couplings and exhaustive search algorithm: application to phospholamban

Dipolar waves are distinct hallmarks of both the secondary and tertiary structures of alpha-helical proteins that are immobilized in membrane bilayers or embedded in anisotropic media. We present a simple, semi-empirical approach that exploits the modulation of the amplitude and average of dipolar waves to determine the topology of alpha-helical proteins. Moreover, we describe the application of this method for the structural determination of a detergent solubilized membrane protein, phospholamban (PLB) that is involved in calcium regulation of cardiac muscle. When combined with high-resolution solid-state NMR data, this method can serve as a fast route for determining the topology of helical membrane proteins solubilized in detergent micelles.     

Observation of residual dipolar couplings in short peptides

Residual dipolar couplings provide information on the orientation of individual bond vectors with respect to a unique set of molecular axes. We report that short peptides from 2 to 15 amino acids in length of arbitrary sequence exhibit a modest range of residual dipolar couplings when aligned in either strained polyacrylamide gels or alkyl-PEG bicelles. The absence of significant line broadening in gels suggests peptides align predominantly through steric interactions with the polyacrylamide matrix. However, broadening of NMR lines for a subset of residues aligned in bicelles indicates some peptides bind weakly to these lipid disks, yet a weak negative correlation between the couplings measured in gels and bicelles is consistent with steric hindrance playing a role in both media. The observation of dipolar couplings for peptides of length 10-15 suggests the statistical segment lengths of polypeptide chains must often be >10-15 residues, with data from denatured proteins indicating even larger values. Presumably, local side-chain backbone interactions severely restrict chain flexibility, with the cumulative effect of many such restrictions giving rise to biases in chain direction that may persist for the entire length of a protein chain. Comparison of experimental dipolar couplings for peptides with couplings calculated for ensembles of conformations generated by molecular dynamics should permit evaluation of the accuracy of molecular mechanics potentials in reproducing sequence-specific preferences for phi and psi angles.     

Theoretical framework for NMR residual dipolar couplings in unfolded proteins

A theoretical framework for the prediction of nuclear magnetic resonance (NMR) residual dipolar couplings (RDCs) in unfolded proteins under weakly aligning conditions is presented. The unfolded polypeptide chain is modeled as a random flight chain while the alignment medium is represented by a set of regularly arranged obstacles. For the case of bicelles oriented perpendicular to the magnetic field, a closed-form analytical result is derived. With the obtained analytical expression the RDCs are readily accessible for any locus along the chain, for chains of differing length, and for varying bicelle concentrations. The two general features predicted by the model are (i) RDCs in the center segments of a polypeptide chain are larger than RDCs in the end segments, resulting in a bell-shaped sequential distribution of RDCs, and (ii) couplings are larger for shorter chains than for longer chains at a given bicelle concentration. Experimental data available from the literature confirm the first prediction of the model, providing a tool for recognizing fully unfolded polypeptide chains. With less certainty experimental data appear to support the second prediction as well. However, more systematic experimental studies are needed in order to validate or disprove the predictions of the model. The presented framework is an important step towards a solid theoretical foundation for the analysis of experimentally measured RDCs in unfolded proteins in the case of alignment media such as polyacrylamide gels and neutral bicelle systems which align biomacromolecules by a steric mechanism. Various improvements and generalizations are possible within the suggested approach.     

Exact solutions for chemical bond orientations from residual dipolar couplings

New methods for determining chemical structures from residual dipolar couplings are presented. The fundamental dipolar coupling equation is converted to an elliptical equation in the principal alignment frame. This elliptical equation is then combined with other angular or dipolar coupling constraints to form simple polynomial equations that define discrete solutions for the unit vector(s). The methods are illustrated with residual dipolar coupling data on ubiquitin taken in a single anisotropic medium. The protein backbone is divided into its rigid groups (namely, its peptide planes and C frames), which may be solved for independently. A simple procedure for recombining these independent solutions results in backbone dihedral angles and that resemble those of the known native structure. Subsequent refinement of these - angles by the ROSETTA program produces a structure of ubiquitin that agrees with the known native structure to 1.1 Å C rmsd.     

Influence of the fluctuations of the alignment tensor on the analysis of the structure and dynamics of proteins using residual dipolar couplings

It has been suggested that the fluctuations of the alignment tensor can affect the results of procedures for characterizing the structure and the dynamics of proteins using residual dipolar couplings. We show here that the very significant fluctuations of the steric alignment tensor caused by the dynamics of proteins can be safely ignored when they do not correlate with those of the bond vectors. A detailed analysis of these correlations in the protein ubiquitin reveals that their effects are negligible for the analysis of backbone motions within secondary structure elements, but also that they may be significant in turns, loops and side chains, especially for bond vectors that have small residual dipolar couplings. Our results suggest that methods that explicitly consider the motions of the alignment tensor will be needed to study the large-scale structural fluctuations that take place on the millisecond timescale, which are often important for the biological function of proteins, from residual dipolar coupling measurements.     

De novo determination of internuclear vector orientations from residual dipolar couplings measured in three independent alignment media

The straightforward interpretation of solution state residual dipolar couplings (RDCs) in terms of internuclear vector orientations generally requires prior knowledge of the alignment tensor, which in turn is normally estimated using a structural model. We have developed a protocol which allows the requirement for prior structural knowledge to be dispensed with as long as RDC measurements can be made in three independent alignment media. This approach, called Rigid Structure from Dipolar Couplings (RSDC), allows vector orientations and alignment tensors to be determined de novo from just three independent sets of RDCs. It is shown that complications arising from the existence of multiple solutions can be overcome by careful consideration of alignment tensor magnitudes in addition to the agreement between measured and calculated RDCs. Extensive simulations as well applications to the proteins ubiquitin and Staphylococcal protein GB1 demonstrate that this method can provide robust determinations of alignment tensors and amide N-H bond orientations often with better than 10 degrees accuracy, even in the presence of modest levels of internal dynamics.     

Structural characterization of a mannose-binding protein-trimannoside complex using residual dipolar couplings

The ligand-binding properties of a 53 kDa homomultimeric trimer from mannose-binding protein (MBP) have been investigated using residual dipolar couplings (RDCs) that are easily measured from NMR spectra of the ligand and isotopically labeled protein. Using a limited set of 1H-15N backbone amide NMR assignments for MBP and orientational information derived from the RDC measurements in aligned media, an order tensor for MBP has been determined that is consistent with symmetry-based predictions of an axially symmetric system. 13C-1H couplings for a bound trisaccharide ligand, methyl 3,6-di-O-(alpha-D-mannopyranosyl)-alpha-D-mannopyranoside (trimannoside) have been determined at natural abundance and used as orientational constraints. The bound ligand geometry and orientational constraints allowed docking of the trimannoside ligand in the binding site of MBP to produce a structural model for MBP-oligosaccharide interactions.     

Overcoming the problems associated with poor spectra quality of the protein kinase Byr2 using residual dipolar couplings

For the Ras-binding domain of the protein kinase Byr2, only a limited number of NOE contacts could be initially assigned unambiguously, as the quality of the NOESY spectra was too poor. However, the use of residual (1)H-(15)N dipolar couplings in the beginning of the structure determination process allows to overcome this problem. We used a three-step recipe for this procedure. A previously unknown structure could be calculated reasonably well with only a limited number of unambiguously assigned NOE contacts.