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.     

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.     

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.     

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.     

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.     

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.     

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.     

Refinement of d(GCGAAGC) hairpin structure using one- and two-bond residual dipolar couplings

The structure of the ¹³C,¹⁵N-labeled d(GCGAAGC) hairpin, as determined by NMR spectroscopy and refined using molecular dynamics with NOE-derived distances, torsion angles, and residual dipolar couplings (RDCs), is presented. Although the studied molecule is of small size, it is demonstrated that the incorporation of diminutive RDCs can significantly improve local structure determination of regions undefined by the conventional restraints. Very good correlation between the experimental and back-calculated small one- and two-bond ¹H-¹³C, ¹H-¹⁵N, ¹³C-¹³C and ¹³C-¹⁵N coupling constants has been attained. The final structures clearly show typical features of the miniloop architecture. The structure is discussed in context of the extraordinary stability of the d(GCGAAGC) hairpin, which originates from a complex interplay between the aromatic base stacking and hydrogen bonding interactions.     

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.     

A liquid crystalline medium for measuring residual dipolar couplings over a wide range of temperatures

A mixture of dilauroyl phosphatidylcholine (DLPC) and 3-(cholamidopropyl)dimethylammonio-2-hydroxyl-1-propane sulfonate (CHAPSO) in water forms disc shaped bicelles that become ordered at high magnetic fields over a wide range of temperatures. As illustrated for the FK506 binding protein (FKBP), large residual dipolar couplings can be measured for proteins dissolved in low concentrations (5% w/v) of a DLPC/CHAPSO medium at a molar ratio of 4.2:1. This system is especially useful for measuring residual dipolar couplings for molecules that are only stable at low temperatures.     

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.     

Assessment of molecular structure using frame-independent orientational restraints derived from residual dipolar couplings

Residual dipolar couplings measured in weakly aligning liquid-crystalline solvent contain valuable information on the structure of biomolecules in solution. Here we demonstrate that dipolar couplings (DCs) can be used to derive a comprehensive set of pairwise angular restraints that do not depend on the orientation of the alignment tensor principal axes. These restraints can be used to assess the agreement between a trial protein structure and a set of experimental dipolar couplings by means of a graphic representation termed a `DC consistency map'. Importantly, these maps can be used to recognize structural elements consistent with the experimental DC data and to identify structural parameters that require further refinement, which could prove important for the success of DC-based structure calculations. This approach is illustrated for the 42 kDa maltodextrin-binding protein.     

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.     

Accurate measurement of residual dipolar couplings in anisotropic phase

The determination of residual dipolar couplings (RDCs) by quantitative J spectroscopy methods such as Heteronuclear Single Quantum Correlation with Phase Encoded Coupling (HSQC-PEC) is prone to systematic errors that may be caused by differential attenuation during the conversion of orthogonal density operator components into observable terms. The attenuation may be caused by miscalibration of radio-frequency pulses and by relaxation effects. A simple method is presented that allows one to remove most of these systematic errors without losses in sensitivity or resolution.     

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.     

Evaluation of the influence of anisotropic indirect nuclear spin-spin coupling tensors on effective residual dipolar couplings for model peptides

Residual dipolar couplings (RDCs) observed between nuclear spins in molecules in partially oriented media have become a valuable source of information for NMR spectroscopists seeking to structurally characterize biological macromolecules. Examination of the form of the direct (D) and indirect (J) nuclear spin-spin coupling Hamiltonians indicates that all observed RDCs contain an unknown contribution from the anisotropic part of J (J) in addition to the direct dipolar contribution, D _PQ. Here, we evaluate the influence of J on RDCs through a series of DFT calculations on model peptides. Very small corrections to one-bond RDCs measured between heavy atoms in peptides and proteins are recommended: +0.51% for N-C spin pairs, and +0.45% for C-C spin pairs. The corrections to RDCs involving at least one proton are negligible. This latter point is likely to be equally applicable to nucleic acids and oligosaccharides in addition to peptides and proteins. Finally, the orientations of the J(N, C) and J(C, C) tensors in the molecular framework are reported for glycylglycine.     

A novel interactive tool for rigid-body modeling of multi-domain macromolecules using residual dipolar couplings

Residual dipolar couplings (RDC), measured by dissolving proteins in dilute liquid crystal media, or by studying naturally paramagnetic molecules, have rapidly become established as routine measurements in the investigation of the structure of macromolecules by NMR. One of the most obvious applications of the previously inaccessible long-range angular information afforded by RDC is the accurate definition of domain orientation in multi-module macromolecules or complexes. In this paper we describe a novel program developed to allow the determination of alignment tensor parameters for individual or multiple domains in macromolecules from residual dipolar couplings and to facilitate their manipulation to construct low-resolution models of macromolecular structure. For multi-domain systems the program determines the relative orientation of individual structured domains, and provides graphical user-driven rigid-body modeling of the different modules relative to the common tensorial frame. Translational freedom in the common frame, and equivalent rotations about the diagonalized (x,y,z) axes are used to position the different modules in the common frame to find a model in best agreement with experimentally measured couplings alone or in combination with additional experimental or covalent information.     

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.     

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.     

Refinement of the solution structure of the heparin-binding domain of vascular endothelial growth factor using residual dipolar couplings

Previous NMR structural studies of the heparin-binding domain of vascular endothelial growth factor (VEGF₁₆₅) revealed a novel fold comprising two subdomains, each containing two disulfide bridges and a short two-stranded antiparallel -sheet. The mutual orientation of the two subdomains was poorly defined by the NMR data. Heteronuclear relaxation data suggested that this disorder resulted from a relative lack of experimental restraints due to the limited size of the interface, rather than inherent high-frequency flexibility. Refinement of the structure using ¹H^N-¹⁵N residual dipolar coupling restraints results in significantly improved definition of the relative subdomain orientations.