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.     

Evaluation of uncertainty in alignment tensors obtained from dipolar couplings

Residual dipolar couplings and their corresponding alignment tensors are useful for structural analysis of macromolecules. The error in an alignment tensor, derived from residual dipolar couplings on the basis of a known structure, is determined not only by the accuracy of the measured couplings but also by the uncertainty in the structure (structural noise). This dependence is evaluated quantitatively on the basis of simulated structures using Monte-Carlo type analyses. When large numbers of dipolar couplings are available, structural noise is found to result in a systematic underestimate of the magnitude of the alignment tensor. Particularly in cases where only few dipolar couplings are available, structural noise can cause significant errors in best-fitted alignment tensor values, making determination of the relative orientation of small fragments and evaluation of local backbone mobility from dipolar couplings difficult. An example for the protein ubiquitin demonstrates the inherent limitations in characterizing motions on the basis of local alignment tensor magnitudes.     

Simple multidimensional NMR experiments to obtain different types of one-bond dipolar couplings simultaneously

In order to measure residual dipolar couplings, the molecule under study has to be partially oriented in the presence of the magnetic field. It has been observed that some protein samples are not stable under the conditions imposed by the orienting media. If different types of dipolar couplings are measured sequentially, their values will not agree with a unique alignment tensor that is changing slowly over time. This could bias the structure calculation. It would be more appropriate to obtain different types of dipolar couplings simultaneously, such that all the data correspond to one effective alignment tensor. We describe here a general NMR strategy designed to do so, that can be adapted to various existing pulse sequences.     

NMR: prediction of molecular alignment from structure using the PALES software

Orientational restraints such as residual dipolar couplings promise to overcome many of the problems that traditionally limited liquid-state nuclear magnetic resonance spectroscopy. Recently, we developed methods to predict a molecular alignment tensor and thus residual dipolar couplings for a given molecular structure. This provides many new opportunities for the study of the structure and dynamics of proteins, nucleic acids, oligosaccharides and small molecules. This protocol details the use of the software PALES (Prediction of AlignmEnt from Structure) for prediction of an alignment tensor from a known three-dimensional (3D) coordinate file of a solute. The method is applicable to alignment of molecules in many neutral and charged orienting media and takes into account the molecular shape and 3D charge distribution of the molecule.     

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.     

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.     

A graphical method for analyzing distance restraints using residual dipolar couplings for structure determination of symmetric protein homo-oligomers

High-resolution structure determination of homo-oligomeric protein complexes remains a daunting task for NMR spectroscopists. Although isotope-filtered experiments allow separation of intermolecular NOEs from intramolecular NOEs and determination of the structure of each subunit within the oligomeric state, degenerate chemical shifts of equivalent nuclei from different subunits make it difficult to assign intermolecular NOEs to nuclei from specific pairs of subunits with certainty, hindering structural analysis of the oligomeric state. Here, we introduce a graphical method, DISCO, for the analysis of intermolecular distance restraints and structure determination of symmetric homo-oligomers using residual dipolar couplings. Based on knowledge that the symmetry axis of an oligomeric complex must be parallel to an eigenvector of the alignment tensor of residual dipolar couplings, we can represent distance restraints as annuli in a plane encoding the parameters of the symmetry axis. Oligomeric protein structures with the best restraint satisfaction correspond to regions of this plane with the greatest number of overlapping annuli. This graphical analysis yields a technique to characterize the complete set of oligomeric structures satisfying the distance restraints and to quantitatively evaluate the contribution of each distance restraint. We demonstrate our method for the trimeric E. coli diacylglycerol kinase, addressing the challenges in obtaining subunit assignments for distance restraints. We also demonstrate our method on a dimeric mutant of the immunoglobulin-binding domain B1 of streptococcal protein G to show the resilience of our method to ambiguous atom assignments. In both studies, DISCO computed oligomer structures with high accuracy despite using ambiguously assigned distance restraints.     

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.     

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 constraints from residual tensorial couplings in high resolution NMR without an explicit term for the alignment tensor

Structural restraints from residual tensorial couplings in high resolution NMR are usually incorporated into molecular structure calculation programs by an energy penalty function which depends on the knowledge of the alignment tensor. Here, we show that the alignment tensor enters in linear form into such a function. Therefore, the explicit appearance of the alignment tensor can be eliminated from the penalty function. This avoids the necessity of a determination of magnitude and rhombicity of the alignment tensor in the absence of structural information. The price for this procedure is a slightly shallower energy landscape. Simulations in the vicinity of the energy minimum for the backbone of human ubiquitin show that the reduction in curvature is on the order of a few percent.     

Residual dipolar couplings in nucleic acid structure determination

Solution NMR spectroscopy of nucleic acids has been limited by the short-range nature of the nuclear Overhauser effect and scalar coupling restraints normally used in structure determination. The addition of residual dipolar couplings, obtained from slightly oriented mixtures, provides bond vector angles relative to a universal alignment tensor. The accurate determination of helix curvature, domain orientation and the stoichiometry of homomultimeric nucleic acid complexes is now possible.     

Improving the Accuracy of NMR Structures of Large Proteins Using Pseudocontact Shifts as Long-Range Restraints

We demonstrate improved accuracy in protein structure determination for large (>/=30 kDa), deuterated proteins (e.g. STAT4(NT)) via the combination of pseudocontact shifts for amide and methyl protons with the available NOEs in methyl-protonated proteins. The improved accuracy is cross validated by Q-factors determined from residual dipolar couplings measured as a result of magnetic susceptibility alignment. The paramagnet is introduced via binding to thiol-reactive EDTA, and multiple sites can be serially engineered to obtain data from alternative orientations of the paramagnetic anisotropic susceptibility tensor. The technique is advantageous for systems where the target protein has strong interactions with known alignment media.     

The importance of being ordered: improving NMR structures using residual dipolar couplings

Residual dipolar couplings arise from small degrees of alignment of molecules in a magnetic field. Most biomolecules lack sufficient intrinsic magnetic susceptibility anisotropies for practical purposes; however, alignment can be achieved using dilute aqueous phospholipid mixtures, colloidal suspensions of rod-shaped viruses, complex phases of surfactant systems and strained gels. The stability of the liquid crystalline phases varies with respect to temperature range, pH variation and time and is critically dependent on sample composition and experimental conditions. The magnitude of the residual dipolar couplings depends upon the degree of ordering and allows the determination of the corresponding inter-nuclear vectors with respect to the molecule's alignment frame. Inclusion of dipolar constraints into NMR structure calculations leads to improved precision and accuracy of the resulting structures, especially in cases where the information content provided by traditional NOE constraints is limited. In addition, rapid evaluation of backbone protein folds and determination of the relative orientations of individual components in multi-molecular complexes have become feasible. Dipolar coupling based strategies may well emerge as the most critical developments, in establishing NMR as a valuable and competitive methodology in the structural genomics initiative.     

Principal component method for assessing structural heterogeneity across multiple alignment media

The recent availability of residual dipolar coupling measurements in a variety of different alignment media raises the question to what extent biomolecular structure and dynamics are differentially affected by their presence. A computational method is presented that allows the sensitive assessment of such changes using dipolar couplings measured in six or more alignment media. The method is based on a principal component analysis of the covariance matrix of the dipolar couplings. It does not require a priori structural or dynamic information nor knowledge of the alignment tensors and their orientations. In the absence of experimental errors, the covariance matrix has at most five nonzero eigenvalues if the structure and dynamics of the biomolecule is the same in all media. In contrast, differential structural and dynamic changes lead to additional nonzero eigenvalues. Characteristic features of the eigenvalue distribution in the absence and presence of noise are discussed using dipolar coupling data calculated from conformational ensembles taken from a molecular dynamics trajectory of native ubiquitin.     

Solution structure of calcium-saturated cardiac troponin C bound to cardiac troponin I

Cardiac troponin C (TnC) is composed of two globular domains connected by a flexible linker. In solution, linker flexibility results in an ill defined orientation of the two globular domains relative to one another. We have previously shown a decrease in linker flexibility in response to cardiac troponin I (cTnI) binding. To investigate the relative orientation of calcium-saturated TnC domains when bound to cTnI, (1)H-(15)N residual dipolar couplings were measured in two different alignment media. Similarity in alignment tensor orientation for the two TnC domains supports restriction of domain motion in the presence of cTnI. The relative spatial orientation of TnC domains bound to TnI was calculated from measured residual dipolar couplings and long-range distance restraints utilizing a rigid body molecular dynamics protocol. The relative domain orientation is such that hydrophobic pockets face each other, forming a latch to constrain separate helical segments of TnI. We have utilized this structure to successfully explain the observed functional consequences of linker region deletion mutants. Together, these studies suggest that, although linker plasticity is important, the ability of TnC to function in muscle contraction can be correlated with a preferred domain orientation and interdomain distance.     

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.     

The utility of residual dipolar couplings in detecting motion in carbohydrates: application to sucrose

The solution structure and dynamics of sucrose are examined using a combination of NMR residual dipolar coupling and molecular mechanics force fields. It is found that the alignment tensors of the individual rings are different, and that fitting 35 measured residual dipolar couplings to structures with specific phi, psi values indicates the presence of three major conformations: phi, psi=(120 degrees ,270 degrees), (45 degrees, 300 degrees) and (90 degrees ,180 degrees). Furthermore, fitting two structures simultaneously to the 35 residual dipolar couplings results in a substantial improvement in the fits. The existence of multiple conformations having similar stabilities is a strong indication of motion, due to the interconversion among these states. Results from four molecular mechanics force fields are in general agreement with the experimental results. However, there are major disagreements between force fields. Because fits of residual dipolar couplings to structures are dependent on the force field used to calculate the structures, multiple force fields were used to interpret NMR data. It is demonstrated that the pucker of the fructofuranosyl ring affects the calculated potential energy surface, and the fit to the residual dipolar couplings data. Previously published 13C nuclear relaxation results suggesting that sucrose is rigid are not inconsistent with the present results when motional timescales are considered.     

DipoCoup: A versatile program for 3D-structure homology comparison based on residual dipolar couplings and pseudocontact shifts

A program, DipoCoup, is presented that allows to search the protein data bank for proteins which have a three dimensional fold that is at least partially homologous to a protein under investigation. The three dimensional homology search uses secondary structure alignment based on chemical shifts and dipolar couplings or pseudocontact shifts for the three dimensional orientation of secondary structure elements. Moreover, the program offers additional tools for handling and analyzing dipolar couplings.