16-fold degeneracy of peptide plane orientations from residual dipolar couplings: analytical treatment and implications for protein structure determination

Residual dipolar couplings (RDCs) measured for internally rigid molecular fragments provide important information about the relative orientations of these fragments. Dependent on the symmetry of the alignment tensor and the symmetry of the molecular fragment, however, there generally exist more than one solution for the fragment orientation consistent with the measured RDCs. Analytical solutions are presented that describe the complete set of orientations of internally rigid fragments that are consistent with multiple dipolar couplings measured in a single alignment medium that is rhombic. For the first time, it is shown that, for a planar fragment such as the peptide plane, there generally exist 16 different solutions with their analytical expressions presented explicitly. The presence of these solutions is shown to be highly relevant for standard structure determination protocols using RDCs to refine molecular structures. In particular, when using standard protein structure refinement with RDCs that were measured in a single alignment medium as constraints, it is found that often more than one of the peptide plane solutions is physically viable; i.e., despite being consistent with measured RDCs, the local backbone structure can be incorrect. On the basis of experimental and simulated examples, it is rationalized why protein structures that are refined against RDCs measured in a single medium can have lower resolution (precision) than one would expect on the basis of the experimental accuracy of the RDCs. Conditions are discussed under which the correct solution can be identified.     

Multiple alignment tensors from a denatured protein

The structural content of the denatured state has yet to be fully characterized. In recent years, large residual dipolar couplings (RDCs) from denatured proteins have been observed under alignment conditions produced by bicelles and strained polyacrylamide gels. In this report, we describe efforts to extend our picture of the residual structure in denatured nuclease by measuring RDCs with multiple alignment tensors. Backbone amide 15N-1H RDCs were collected from 4 M urea for a total of eight RDC data sets. The RDCs were analyzed by singular value decomposition (SVD) to determine the number of independent alignment tensors present in the data. On the basis of the resultant singular values and propagated error estimates, it is clear that there are at least three independent alignment tensors. These three independent RDC datasets can be reconstituted as orthogonal linear combinations, (OLC)-RDC datasets, of the eight actually recorded. The first, second, and third OLC-RDC datasets are highly robust to the removal of any single experimental RDC dataset, establishing the presence of three independent alignment tensors, sampled well above the level of experimental uncertainty. The observation that the RDC data span three or more dimensions of the five-dimensional parameter space demonstrates that the ensemble average structure of denatured nuclease must be asymmetric with respect to these three orthogonal principal axes, which is not inconsistent with earlier work demonstrating that it has a nativelike topology.     

Elongated Bacterial Pili as a Versatile Alignment Medium for NMR Spectroscopy

In NMR spectroscopy, residual dipolar couplings (RDCs) have emerged as one of the most exquisite probes of biological structure and dynamics. The measurement of RDCs relies on the partial alignment of the molecule of interest, for example by using a liquid crystal as a solvent. Here, we establish bacterial type 1 pili as an alternative liquid-crystalline alignment medium for the measurement of RDCs. To achieve alignment at pilus concentrations that allow for efficient NMR sample preparation, we elongated wild-type pili by recombinant overproduction of the main structural pilus subunit. Building on the extraordinary stability of type 1 pili against spontaneous dissociation and unfolding, we show that the medium is compatible with challenging experimental conditions such as high temperature, the presence of detergents, organic solvents or very acidic pH, setting it apart from most established alignment media. Using human ubiquitin, HIV-1 TAR RNA and camphor as spectroscopic probes, we demonstrate the applicability of the medium for the determination of RDCs of proteins, nucleic acids and small molecules. Our results show that type 1 pili represent a very useful alternative to existing alignment media and may readily assist the characterization of molecular structure and dynamics by NMR.     

Structure and dynamics of an unfolded protein examined by molecular dynamics simulation

The accurate characterization of the structure and dynamics of proteins in disordered states is a difficult problem at the frontier of structural biology whose solution promises to further our understanding of protein folding and intrinsically disordered proteins. Molecular dynamics (MD) simulations have added considerably to our understanding of folded proteins, but the accuracy with which the force fields used in such simulations can describe disordered proteins is unclear. In this work, using a modern force field, we performed a 200 μs unrestrained MD simulation of the acid-unfolded state of an experimentally well-characterized protein, ACBP, to explore the extent to which state-of-the-art simulation can describe the structural and dynamical features of a disordered protein. By comparing the simulation results with the results of NMR experiments, we demonstrate that the simulation successfully captures important aspects of both the local and global structure. Our simulation was ~2 orders of magnitude longer than those in previous studies of unfolded proteins, a length sufficient to observe repeated formation and breaking of helical structure, which we found to occur on a multimicrosecond time scale. We observed one structural feature that formed but did not break during the simulation, highlighting the difficulty in sampling disordered states. Overall, however, our simulation results are in reasonable agreement with the experimental data, demonstrating that MD simulations can already be useful in describing disordered proteins. Finally, our direct calculation of certain NMR observables from the simulation provides new insight into the general relationship between structural features of disordered proteins and experimental NMR relaxation properties.     

De novo determination of protein backbone structure from residual dipolar couplings using Rosetta

As genome-sequencing projects rapidly increase the database of protein sequences, the gap between known sequences and known structures continues to grow exponentially, increasing the demand to accelerate structure determination methods. Residual dipolar couplings (RDCs) are an attractive source of experimental restraints for NMR structure determination, particularly rapid, high-throughput methods, because they yield both local and long-range orientational information and can be easily measured and assigned once the backbone resonances of a protein have been assigned. While very extensive RDC data sets have been used to determine the structure of ubiquitin, it is unclear to what extent such methods will generalize to larger proteins with less complete data sets. Here we incorporate experimental RDC restraints into Rosetta, an ab initio structure prediction method, and demonstrate that the combined algorithm provides a general method for de novo determination of a variety of protein folds from RDC data. Backbone structures for multiple proteins up to approximately 125 residues in length and spanning a range of topological complexities are rapidly and reproducibly generated using data sets that are insufficient in isolation to uniquely determine the protein fold de novo, although ambiguities and errors are observed for proteins with symmetry about an axis of the alignment tensor. The models generated are not high-resolution structures completely defined by experimental data but are sufficiently accurate to accelerate traditional high-resolution NMR structure determination and provide structure-based functional insights.     

Conformational Ensemble of Disordered Proteins Probed by Solvent Paramagnetic Relaxation Enhancement (sPRE)

Characterization of the conformational ensemble of disordered proteins is highly important for understanding protein folding and aggregation mechanisms, but remains a computational and experimental challenge owing to the dynamic nature of these proteins. New observables that can provide unique insights into transient residual structures in disordered proteins are needed. Here using denatured ubiquitin as a model system, NMR solvent paramagnetic relaxation enhancement (sPRE) measurements provide an accurate and highly sensitive probe for detecting low populations of residual structure in a disordered protein. Furthermore, a new ensemble calculation approach based on sPRE restraints in conjunction with residual dipolar couplings (RDCs) and small‐angle X‐ray scattering (SAXS) is used to define the conformational ensemble of disordered proteins at atomic resolution. The approach presented should be applicable to a wide range of dynamic macromolecules.     

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.     

Residual dipolar coupling measurements of transmembrane proteins using aligned low-q bicelles and high-resolution magic angle spinning NMR spectroscopy

Bicelles are a major medium form to produce weak alignment of soluble proteins for residual dipolar coupling (RDC) measurements. The obstacle to using the same type of bicelles for transmembrane proteins with solution-state NMR spectroscopy is the loss of signals due to the adhesion or penetration of the proteins into large bicelles, resulting in slow protein tumbling. In this study, weak alignment of the second and third transmembrane domains (TM23) of the human glycine receptor (GlyR) was achieved in low-q bicelles (q = DMPC/DHPC). Although protein-free bicelles with such low q would likely show isotropic properties, the insertion of TM23 induced weakly preferred orientations so that the RDC of the embedded protein can be measured. The extent of the alignment increased but the TM23 signal intensity decreased when q was varied from 0.19 to 0.60. A q of 0.50 was found to be an optimal compromise between alignment and the signal-to-noise ratio. In each pair of NMR experiments for RDC measurements, the same sample and pulse sequence were used, with one being performed at high-resolution magic-angle spinning to obtain pure J-couplings without RDC. A meaningful structure refinement in bicelles was possible by iteratively fitting the experimental RDCs to the back-calculated RDCs using the high-resolution NMR structure of GlyR TM23 in trifluoroethanol as the starting template. Combination of this method with the conventional high-resolution NMR in membrane mimicking mixtures of water and organic solvents offers an attractive way to derive structural information for membrane proteins in their native environment.     

Side chain orientation from methyl 1H-1H residual dipolar couplings measured in highly deuterated proteins

High-level deuteration is a prerequisite for the study of high molecular weight systems using liquid-state NMR. Here, we present new experiments for the measurement of proton-proton dipolar couplings in CH(2)D methyl groups of (13)C labeled, highly deuterated (70-80%) proteins. (1)H-(1)H residual dipolar couplings (RDCs) have been measured in two alignment media for 57 out of 70 possible methyl containing residues in the 167-residue flavodoxin-like domain of the E. coli sulfite reductase. These data yield information on the orientation of the methyl symmetry axis with respect to the molecular alignment frame. The alignment tensor characteristics were obtained very accurately from a set of backbone RDCs measured on the same protein sample. To demonstrate that accurate structural information is obtained from these data, the measured methyl RDCs for Valine residues are analyzed in terms of chi(1) torsion angles and stereospecific assignment of the prochiral methyl groups. On the basis of the previously determined backbone solution structure of this protein, the methyl RDC data proved sufficient to determine the chi(1) torsion angles in seven out of nine valines, assuming a single-rotamer model. Methyl RDCs are complementary to other NMR data, for example, methyl-methyl NOE, to determine side chain conformation in high molecular weight systems.     

Mapping the potential energy landscape of intrinsically disordered proteins at amino Acid resolution

Intrinsically disordered regions are predicted to exist in a significant fraction of proteins encoded in eukaryotic genomes. The high levels of conformational plasticity of this class of proteins endows them with unique capacities to act in functional modes not achievable by folded proteins, but also places their molecular characterization beyond the reach of classical structural biology. New techniques are therefore required to understand the relationship between primary sequence and biological function in this class of proteins. Although dependences of some NMR parameters such as chemical shifts (CSs) or residual dipolar couplings (RDCs) on structural propensity are known, so that sampling regimes are often inferred from experimental observation, there is currently no framework that allows for a statistical mapping of the available Ramachandran space of each amino acid in terms of conformational propensity. In this study we develop such an approach, combining highly efficient conformational sampling with ensemble selection to map the backbone conformational sampling of IDPs on a residue specific level. By systematically analyzing the ability of NMR data to map the conformational landscape of disordered proteins, we identify combinations of RDCs and CSs that can be used to raise conformational degeneracies inherent to different data types, and apply these approaches to characterize the conformational behavior of two intrinsically disordered proteins, the K18 domain from Tau protein and N(TAIL) from measles virus nucleoprotein. In both cases, we identify the enhanced populations of turn and helical regions in key regions of the proteins, as well as contiguous strands that show clear and enhanced polyproline II sampling.     

Composite alignment media for the measurement of independent sets of NMR residual dipolar couplings

The measurement of independent sets of NMR residual dipolar couplings (RDCs) in multiple alignment media can provide a detailed view of biomolecular structure and dynamics, yet remains experimentally challenging. It is demonstrated here that independent sets of RDCs can be measured for ubiquitin using just a single alignment medium composed of aligned bacteriophage Pf1 particles embedded in a strained polyacrylamide gel matrix. Using this composite medium, molecular alignment can be modulated by varying the angle between the directors of ordering for the Pf1 and strained gel matrix, or by varying the ionic strength or concentration of the Pf1 particles. This approach offers significant advantages in that greater experimental control can be exercised over the acquisition of multi-alignment RDC data while a homogeneous chemical environment is maintained across all of the measured RDC data.     

Periodicity in residual dipolar couplings and nucleic acid structures

The periodicity in nucleic acid duplex structures is shown to be correlated to the periodicity in residual dipolar couplings (RDCs) in the form of an "RDC wave". This "RDC wave" is characteristic of the alignment of the duplex in the magnetic field, and hence fitting of the data allows the duplex global orientation (, Phi) to be extracted. Further, because the "RDC wave" is fit as a data set of a corresponding secondary structure element, the degeneracy problem is greatly reduced. Consequently, with the global orientation (, Phi) determined, local bond vector conformations are defined. The fit is demonstrated in the examples of the imino RDCs of the negative regulator of splicing RNA fragment (NRS23) and for the C1'H1' RDCs of the Dickerson dodecamer.     

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.     

Measurements of side-chain 13C-13C residual dipolar couplings in uniformly deuterated proteins

13C-only spectroscopy was used to measure multiple residual (13)C-(13)C dipolar couplings (RDCs) in uniformly deuterated and (13)C-labeled proteins. We demonstrate that (13)C-start and (13)C-observe spectra can be routinely used to measure an extensive set of the side-chain residual (13)C-(13)C dipolar couplings upon partial alignment of human ubiquitin in the presence of bacteriophages Pf1. We establish that, among different broadband polarization transfer schemes, the FLOPSY family can be used to exchange magnetization between a J coupled network of spins while largely decoupling dipolar interactions between these spins. An excellent correlation between measured RDCs and the 3D structure of the protein was observed, indicating a potential use of the (13)C-(13)C RDCs in the structure determination of perdeuterated proteins.     

RDC‐enhanced structure calculation of a β‐heptapeptide in methanol

Residual dipolar couplings (RDCs) are a rich source of structural information that goes beyond the range covered by the nuclear Overhauser effect or scalar coupling constants. They can only be measured in partially oriented samples. RDC studies of peptides in organic solvents have so far been focused on samples in chloroform or DMSO. Here, we show that stretched poly(vinyl acetate) can be used for the partial alignment of a linear β‐peptide with proteinogenic side chains in methanol. ¹D_CH, ¹D_NH, and ²D_HH RDCs were collected with this sample and included as restraints in a simulated annealing calculation. Incorporation of RDCs in the structure calculation process improves the long‐range definition in the backbone of the resulting 3₁₄‐helix and uncovers side‐chain mobility. Experimental side‐chain RDCs of the central leucine and valine residues are in good agreement with predicted values from a local three‐state model. Copyright © 2016 John Wiley & Sons, Ltd.     

Magnetic Alignment of Polymer Macro‐Nanodiscs Enables Residual‐Dipolar‐Coupling‐Based High‐Resolution Structural Studies by NMR Spectroscopy

Experimentally measured residual dipolar couplings (RDCs) are highly valuable for atomic‐resolution structural and dynamic studies of molecular systems ranging from small molecules to large proteins by solution NMR spectroscopy. Here we demonstrate the first use of magnetic‐alignment behavior of lyotropic liquid‐crystalline polymer macro‐nanodiscs (>20 nm in diameter) as a novel alignment medium for the measurement of RDCs using high‐resolution NMR. The easy preparation of macro‐nanodiscs, their high stability against pH changes and the presence of divalent metal ions, and their high homogeneity make them an efficient tool to investigate a wide range of molecular systems including natural products, proteins, and RNA.     

Bound-state residual dipolar couplings for rapidly exchanging ligands of His-tagged proteins

The study of bound-state conformations of ligands interacting with proteins is important to the understanding of protein function and the design of drugs that alter function. Traditionally, transferred nuclear Overhauser effects (trNOEs), measured from NMR spectra of ligands in rapid exchange between bound and free states, have been used in these studies, owing to the inherent heavy weighting of bound-state data in the averaged ligand signals. In principle, residual dipolar couplings (RDCs) provide a useful complement to NOE data in that they provide orientational constraints as opposed to distance constraints, but use in ligand-binding applications has been limited due to the absence of heavy weighting of bound-state data. A widely applicable approach to increasing the weighting of bound-state data in averaged RDCs measured on ligands is presented. The approach rests on association of a His-tagged protein with a nickel-chelate-carrying lipid inserted into the lipid bilayer-like alignment media used in the acquisition of RDCs. The approach is validated through the observation of bound-state RDCs for the disaccharide, lactose, bound to the carbohydrate recognition domain of the mammalian lectin, galectin-3.     

Increasing the accuracy of solution NMR structures of membrane proteins by application of residual dipolar couplings. High-resolution structure of outer membrane protein A

The structure determination of membrane proteins is one of the most challenging applications of solution NMR spectroscopy. The paucity of distance information available from the highly deuterated proteins employed requires new approaches in structure determination. Here we demonstrate that significant improvement in the structure accuracy of the membrane protein OmpA can be achieved by refinement with residual dipolar couplings (RDCs). The application of charged polyacrylamide gels allowed us to obtain two alignments and accurately measure numerous heteronuclear dipolar couplings. Furthermore, we have demonstrated that using a large set of RDCs in the refinement can yield a structure with 1 A rms deviation to the backbone of the high-resolution crystal structure. Our simulations with various data sets indicate that dipolar couplings will be critical for obtaining accurate structures of membrane proteins.