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.     

Bicelle-based liquid crystals for NMR-measurement of dipolar couplings at acidic and basic pH values

It is demonstrated that mixtures of ditetradecyl- phosphatidylcholine or didodecyl-phoshatidylcholine and dihexyl- phosphatidylcholine in water form lyotropic liquid crystalline phases under similar conditions as previously reported for bicelles consisting of dimyristoyl-phosphatidylcholine (DMPC) and dihexanoyl- phosphatidylcholine (DHPC). The carboxy-ester bonds present in DMPC and DHPC are replaced by ether linkages in their alkyl analogs, which prevents acid- or base-catalyzed hydrolysis of these compounds. 15N-1H dipolar couplings measured for ubiquitin over the 2.3–10.4pH range indicate that this protein retains a backbone conformation which is very similar to its structure at pH 6.5 over this entire range.     

Characterization of surfactant liquid crystal phases suitable for molecular alignment and measurement of dipolar couplings

Media employed for imparting partial alignment onto solute molecules have recently attracted considerable attention, since they permit the measurement of NMR parameters for solute biomolecules commonly associated with solid state NMR. Here we characterize a medium which is based on a quasi-ternary surfactant system comprising cetylpyridinium bromide/hexanol/sodium bromide. We demonstrate that dilute solutions of this system can exist in liquid crystalline phases which orient in the magnetic field and allow the measurement of residual dipolar couplings under a variety of conditions. The present system is extremely versatile and robust, tolerating different buffer conditions, temperature ranges and concentrations.     

Recognition of protein folds via dipolar couplings

Alignment of proteins in dilute liquid crystalline medium gives rise to residual dipolar couplings which provide orientational information of vectors connecting the interacting nuclei. Considering that proteins are mainly composed of regular secondary structures in a finite number of different mutual orientations, main chain dipolar couplings appear sufficient to reveal structural resemblance. Similarity between dipolar couplings measured from a protein and corresponding values computed from a known structure imply homologous structures. For dissimilar structures the agreement between experimental and calculated dipolar couplings remains poor. In this way protein folds can be readily recognized prior to a comprehensive structure determination. This approach has been demonstrated by showing the similarity in fold between the hitherto unknown structure of calerythrin and sarcoplasmic calcium-binding proteins from Nereis diversicolor and Branchiostoma lanceolatum with known crystal structures.     

Improved low pH bicelle system for orienting macromolecules over a wide temperature range

We have prepared and characterized a novel bicelle system composed of 1,2-di-O-dodecyl-sn-glycero-3-phos- phocholine (DIODPC) and 3-(chloramidopropyl)dimethylammonio-2-hydroxyl-1-propane sulfonate (CHAPSO). At the optimal DIODPC/CHAPSO molar ratio of 4.3:1, this medium becomes magnetically oriented from pH 6.5 down to pH 1.0. Unlike previously reported bicelle preparations, these bicelles are chemically stable at low pH and are capable of inducing protein alignment, as illustrated by the large residual dipolar couplings measured for rusticyanin from Thiobacillus ferrooxidans at pH 2.1. The DIODPC/CHAPSO system is particularly useful for measuring residual dipolar couplings of macromolecules that require very acidic conditions.     

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.     

Measurement of dipolar couplings in a transducin peptide fragment weakly bound to oriented photo-activated rhodopsin

Rhodopsin-containing disks, isolated from rod outer segments of bovine retina, align at high magnetic fields with their membrane normal parallel to the magnetic field. After light-activation of rhodopsin, transient binding of the C-terminal transducin undecapeptide, selectively labeled with ¹⁵N at Leu⁵ and Gly⁹, results in residual dipolar contributions to the ¹J_NH splittings for these two residues. Both residues show ¹J_NH splittings which are smaller than in the dark-adapted or rhodopsin-free sample, and return to their isotropic values at a rate determined by the decay of the meta II state of rhodopsin. The dipolar couplings indicate that in the bound state, N-H vectors of Leu⁵ and Gly⁹ make angles of 48±4° and 40±8°, respectively, with the disk normal. These `transferred' dipolar couplings potentially offer a useful method for studying the conformation and orientation of flexible, low affinity ligands when bound to oriented integral membrane receptors.     

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.     

Multiplet component separation for measurement of methyl 13C-1H dipolar couplings in weakly aligned proteins

A simple spectral editing procedure is described that generates separate subspectra for the methyl ¹³C-¹H₃ multiplet components of ¹H-¹³C HSQC spectra. The editing procedure relies on co-addition of in-phase and antiphase spectra and yields ¹H-coupled constant-time HSQC subspectra for the methyl region that have the simplicity of the regular decoupled CT-HSQC spectrum. Resulting spectra permit rapid and reliable measurement of ¹H-¹³C J and dipolar couplings. The editing procedure is illustrated for a Ca²⁺-calmodulin sample in isotropic and liquid crystalline phases.     

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.     

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.     

Study of conformational rearrangement and refinement of structural homology models by the use of heteronuclear dipolar couplings

For an increasing fraction of proteins whose structures are being studied, sequence homology to known structures permits building of low resolution structural models. It is demonstrated that dipolar couplings, measured in a liquid crystalline medium, not only can validate such structural models, but also refine them. Here, experimental ¹H-¹⁵N, ¹H-¹³C, and ¹³C-¹³C dipolar couplings are shown to decrease the backbone rmsd between various homology models of calmodulin (CaM) and its crystal structure. Starting from a model of the Ca²⁺-saturated C-terminal domain of CaM, built from the structure of Ca²⁺-free recoverin on the basis of remote sequence homology, dipolar couplings are used to decrease the rmsd between the model and the crystal structure from 5.0 to 1.25 Å. A better starting model, built from the crystal structure of Ca²⁺-saturated parvalbumin, decreases in rmsd from 1.25 to 0.93 Å. Similarly, starting from the structure of the Ca²⁺-ligated CaM N-terminal domain, experimental dipolar couplings measured for the Ca²⁺-free form decrease the backbone rmsd relative to the refined solution structure of apo-CaM from 4.2 to 1.0 Å.     

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.     

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.     

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.     

A simple apparatus for generating stretched polyacrylamide gels, yielding uniform alignment of proteins and detergent micelles*

Compressed and stretched polyacrylamide hydrogels previously have been shown to offer a robust method for aligning proteins. A simple, funnel-like apparatus is described for generating uniformly stretched hydrogels. For prolate-shaped proteins, gels stretched in the direction of the magnetic field yield two-fold larger alignment than gels compressed to the same aspect ratio in this direction. Empirically, protein alignment is found to be proportional to (c–2.3)² [(d_o/d_N)³-1], where d_o and d_N are the diameters of the cylindrical gels before and after stretching, respectively, and c is the polyacrylamide weight fraction in percent. Low gel densities, in the 4–7% range, are found to have minimal effects on macromolecular rotational correlation times, _c, and no effect of the compression ratio on _c could be discerned over the range studied (d_o/d_N le1.4). Application is demonstrated for a sample containing the first Ig-binding domain of protein G, and for a detergent-solubilized peptide.     

Overall structure and sugar dynamics of a DNA dodecamer from homo- and heteronuclear dipolar couplings and 31P chemical shift anisotropy

The solution structure of d(CGCGAATTCGCG)₂ has been determined on the basis of an exceptionally large set of residual dipolar couplings. In addition to the heteronuclear ¹³C-¹H and ¹⁵N-¹H and qualitative homonuclear ¹H-¹H dipolar couplings, previously measured in bicelle medium, more than 300 quantitative ¹H-¹H and 22 ³¹P-¹H dipolar restraints were obtained in liquid crystalline Pf1 medium, and 22 ³¹P chemical shift anisotropy restraints. High quality DNA structures can be obtained solely on the basis of these new restraints, and these structures are in close agreement with those calculated previously on the basis of ¹³C-¹H and ¹⁵N-¹H dipolar couplings. In the newly calculated structures, ³¹P-¹H dipolar and ³Jsub H3 P sub couplings and ³¹P CSA data restrain the phosphodiester backbone torsion angles. The final structure represents a quite regular B-form helix with a modest bending of 10°, which is essentially independent of whether or not electrostatic terms are used in the calculation. Combined, the number of homo- and heteronuclear dipolar couplings significantly exceeds the number of degrees of freedom in the system. Results indicate that the dipolar coupling data cannot be fit by a single structure, but are compatible with the presence of rapid equilibria between C2-endo and C3-endo deoxyribose puckers (sugar switching). The C2-H2/H2 dipolar couplings in B-form DNA are particularly sensitive to sugar pucker and yield the largest discrepancies when fit to a single structure. To resolve these discrepancies, we suggest a simplified dipolar coupling analysis that yields N/S equilibria for the ribose sugar puckers, which are in good agreement with previous analyses of NMR J_HH couplings, with a population of the minor C3-endo form higher for pyrimidines than for purines.     

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.     

Transverse relaxation optimised spin-state selective NMR experiments for measurement of residual dipolar couplings

Three transverse relaxation optimised NMR experiments (TROSY) for the measurement of scalar and dipolar couplings suitable for proteins dissolved in aqueous iso- and anisotropic solutions are described. The triple-spin-state-selective experiments yield couplings between ¹H^N-¹³C, ¹⁵N-¹³C, ¹H^N-¹³C _i–1, ¹⁵N-¹³C _i–1, ¹H^N-¹³C_i–1, ¹⁵N-¹³C_i–1, and ¹³C_i–1-¹³C _i–1 without introducing nonessential spectral crowding compared with an ordinary two-dimensional ¹⁵N-¹H correlation spectrum and without requiring explicit knowledge of carbon assignments. This set of /-J-TROSY experiments is most useful for perdeuterated proteins in studies of structure–activity relationships by NMR to observe, in addition to epitopes for ligands, also conformational changes induced by binding of ligands.     

Sign determination of dipolar couplings in field-oriented bicelles by variable angle sample spinning (VASS)

Residual dipolar couplings are being increasingly used as structural constraints for NMR studies of biomolecules. A problem arises when dipolar coupling contributions are larger than scalar contributions for a given spin pair, as is commonly observed in solid state NMR studies, in that signs of dipolar couplings cannot easily be determined. Here the sign ambiguities of dipolar couplings in field-oriented bicelles are resolved by variable angle sample spinning (VASS) techniques. The director behavior of field-oriented bicelles (DMPC/DHPC, DMPC/CHAPSO) in VASS is studied by ³¹P NMR. A stable configuration occurs when the spinning angle is smaller than the magic angle, 54.7°, and the director (or bicelle normal) of the disks is mainly distributed in a plane perpendicular to the rotation axis. Since the dipolar couplings depend on how the bicelles are oriented with respect to the magnetic field, it is shown that the dipolar interaction can be scaled to the same order as the J-coupling by moving the spinning axis from 0° toward 54.7°. Thus the relative sign of dipolar and scalar couplings can be determined.