Residual dipolar couplings in protein NMR

Residual dipolar line width in magic-angle spinning proton solid-state NMR

Magic-angle spinning is routinely used to average anisotropic interactions in solid-state nuclear magnetic resonance (NMR). Due to the fact that the homonuclear dipolar Hamiltonian of a strongly coupled spin system does not commute with itself at different time points during the rotation, second-order and higher-order terms lead to a residual dipolar line broadening in the observed resonances. Additional truncation of the residual broadening due to isotropic chemical-shift differences can be observed. We analyze the residual line broadening in coupled proton spin systems based on theoretical calculations of effective Hamiltonians up to third order using Floquet theory and compare these results to numerically obtained effective Hamiltonians in small spin systems. We show that at spinning frequencies beyond 75 kHz, second-order terms dominate the residual line width, leading to a 1 / ω r dependence of the second moment which we use to characterize the line width. However, chemical-shift truncation leads to a partial ω r - 2 dependence of the line width which looks as if third-order effective Hamiltonian terms are contributing significantly. At slower spinning frequencies, cross terms between the chemical shift and the dipolar coupling can contribute in third-order effective Hamiltonians. We show that second-order contributions not only broaden the line, but also lead to a shift of the center of gravity of the line. Experimental data reveal such spinning-frequency-dependent line shifts in proton spectra in model substances that can be explained by line shifts induced by the second-order dipolar Hamiltonian.

The simulation of NMR data of flexible molecules: sagittamide A as an example for MD simulations with orientational constraints

The recently developed MDOC (Molecular Dynamics with Orientational Constraints) simulation is applied for the first time to a fully flexible molecule. MDOC simulations aim to single out the naturally existing configuration of molecules and to elucidate conformer populations. The performance of the method was first demonstrated on a well-studied test case, the five-membered ring lactone (α-methylene-γ-butyrolactone). In the case of sagittamide A, one-bond ¹H-¹³C residual dipolar couplings (RDC) are used as orientational constraints that reorient the molecule or parts of it. In addition, NOE distances and ³J scalar couplings are used as constraints. Five possible configurations of sagittamide A (labelled a to e) are considered. One experimental RDC value per flexible unit was available and this was not sufficient to single out one valid configuration. The problem could be solved by including NOE distances as well as ³J couplings as complementary constraints into the MDOC simulations. In accordance with former investigations, we confirmed the configuration a for the natural product. A detailed analysis of conformers of the central chain of 6 chiral carbon atoms could be given by inspecting the MDOC trajectory. The relative abundance of these conformers is crucial in fulfilling all three sets of constraints.

Hybrid Approaches to Structural Characterization of Conformational Ensembles of Complex Macromolecular Systems Combining NMR Residual Dipolar Couplings and Solution X-ray Scattering

Solving structures or structural ensembles of large macromolecular systems in solution poses a challenging problem. While NMR provides structural information at atomic resolution, increased spectral complexity, chemical shift overlap, and short transverse relaxation times (associated with slow tumbling) render application of the usual techniques that have been so successful for medium sized systems (<50 kDa) difficult. Solution X-ray scattering, on the other hand, is not limited by molecular weight but only provides low resolution structural information related to the overall shape and size of the system under investigation. Here we review how combining atomic resolution structures of smaller domains with sparse experimental data afforded by NMR residual dipolar couplings (which yield both orientational and shape information) and solution X-ray scattering data in rigid-body simulated annealing calculations provides a powerful approach for investigating the structural aspects of conformational dynamics in large multidomain proteins. The application of this hybrid methodology is illustrated for the 128 kDa dimer of bacterial Enzyme I which exists in a variety of open and closed states that are sampled at various points in the catalytic cycles, and for the capsid protein of the human immunodeficiency virus.

The structural and topological analysis of membrane-associated polypeptides by oriented solid-state NMR spectroscopy: established concepts and novel developments

Solid-state NMR spectroscopy is a powerful technique for the investigation of membrane-associated peptides and proteins as well as their interactions with lipids, and a variety of conceptually different approaches have been developed for their study. The technique is unique in allowing for the high-resolution investigation of liquid disordered lipid bilayers representing well the characteristics of natural membranes. Whereas magic angle solid-state NMR spectroscopy follows approaches that are related to those developed for solution NMR spectroscopy the use of static uniaxially oriented samples results in angular constraints which also provide information for the detailed analysis of polypeptide structures. This review introduces this latter concept theoretically and provides a number of examples. Furthermore, ongoing developments combining solid-state NMR spectroscopy with information from solution NMR spectroscopy and molecular modelling as well as exploratory studies using dynamic nuclear polarization solid-state NMR will be presented.

NMR-based homology model for the solution structure of the C-terminal globular domain of EMILIN1

EMILIN1 is a glycoprotein of elastic tissues that has been recently linked to the pathogenesis of hypertension. The protein is formed by different independently folded structural domains whose role has been partially elucidated. In this paper the solution structure, inferred from NMR-based homology modelling of the C-terminal trimeric globular C1q domain (gC1q) of EMILIN1, is reported. The high molecular weight and the homotrimeric structure of the protein required the combined use of highly deuterated (15)N, (13)C-labelled samples and TROSY experiments. Starting from a homology model, the protein structure was refined using heteronuclear residual dipolar couplings, chemical shift patterns, NOEs and H-exchange data. Analysis of the gC1q domain structure of EMILIN1 shows that each protomer of the trimer adopts a nine-stranded beta sandwich folding topology which is related to the conformation observed for other proteins of the family. Distinguishing features, however, include a missing edge-strand and an unstructured 19-residue loop. Although the current data do not allow this loop to be precisely defined, the available evidence is consistent with a flexible segment that protrudes from each subunit of the globular trimeric assembly and plays a key role in inter-molecular interactions between the EMILIN1 gC1q homotrimer and its integrin receptor alpha4beta1.

NMR spectroscopic characterization of the membrane affinity of polyols

Residual dipolar couplings (RDCs) are applied here for the analysis of weak, transient binding events between phosphatidylcholine bilayers and polyols. Large signal responses are observed even for low percentages of 'ligand-receptor complexes', making RDCs a sensitive tool for the analysis of molecular recognition events. The different degree of alignment in solution can be compared as a result of the calculation of the alignment tensor elements. By varying polarity and/or charge of the molecules under investigation, nonspecific hydrophobic effects can be excluded.

Solution structure of the active-centre mutant I14A of the histidine-containing phosphocarrier protein from Staphylococcus carnosus

High-pressure NMR experiments performed on the histidine-containing phosphocarrier protein (HPr) from Staphylococcus carnosus have shown that residue Ile14, which is located in the active-centre loop, exhibits a peculiarly small pressure response. In contrast, the rest of the loop shows strong pressure effects as is expected for typical protein interaction sites. To elucidate the structural role of this residue, the mutant protein HPr(I14A), in which Ile14 is replaced by Ala, was produced and studied by solution NMR spectroscopy. On the basis of 1406 structural restraints including 20 directly detected hydrogen bonds, 49 1H(N)-15N, and 25 1H(N)-1Halpha residual dipolar couplings, a well resolved three-dimensional structure could be determined. The overall fold of the protein is not influenced by the mutation but characteristic conformational changes are introduced into the active-centre loop. They lead to a displacement of the ring system of His15 and a distortion of the N-terminus of the first helix, which supports the histidine ring. In addition, the C-terminal helix is bent because the side chain of Leu86 located at the end of this helix partly fills the hydrophobic cavity created by the mutation. Xenon, which is known to occupy hydrophobic cavities, causes a partial reversal of the mutation-induced structural effects. The observed structural changes explain the reduced phosphocarrier activity of the mutant and agree well with the earlier suggestion that Ile14 represents an anchoring point stabilizing the active-centre loop in its correct conformation.

Application of residual dipolar couplings in organic compounds

Residual dipolar couplings (RDCs) induced by anisotropic media are a powerful tool for the structure determination of biomolecules through NMR spectroscopy. Recent advances have proven it to be a valuable tool for determination of the stereochemistry of organic molecules. By simple inspection or order matrix calculations, RDCs provide unambiguous information about the relative configurations or complete stereochemistry of organic compounds.

Complete Relative Stereochemistry of Multiple Stereocenters Using Only Residual Dipolar Couplings

Residual dipolar couplings (RDCs), in combination with molecular order matrix calculations, were used to unambiguously determine the complete relative stereochemistry of an organic compound with five stereocenters. Three simple one-dimensional experiments were utilized for the measurements of (13)C-(1)H, (13)C-(19)F, (19)F-(1)H, and (1)H-(1)H RDCs. The order matrix calculation was performed on each chiral isomer independently. The fits were evaluated by the comparison of the root-mean-square deviation (rmsd) of calculated and measured RDCs. The order tensor simulations based on two different sets of RDC data collected with phage and bicelles are consistent. The resulting stereochemical assignments of the stereocenters obtained from using only RDCs are in perfect agreement with those obtained from the single-crystal X-ray structure. Six RDCs are found to be necessary to run the simulation, and seven are the minimum to get an acceptable result for the investigated compound. It was also shown that (13)C-(1)H and (1)H-(1)H RDCs, which are the easiest to measure, are also the most important and information-rich data for the order matrix calculation. The effect of each RDC on the calculation depends on the location of the corresponding vector in the structure. The direct RDC of a stereocenter is important to the configuration determination, but the configuration of stereocenters devoid of protons can also be obtained from analysis of nearby RDCs.

Internal consistency of NMR data obtained in partially aligned biomacromolecules

A method of testing structure-related NMR data prior to structure calculations is presented. The test is applicable to second rank tensor interactions (dipolar coupling, anisotropic chemical shielding, and quadrupolar interaction) observed in partially aligned samples of biomacromolecules. The method utilizes the fact that only limited number of frequencies corresponding to the mentioned interactions can be measured independently in a rigid fragment of the macromolecule. Additional values can be predicted as linear combinations of the set of independent frequencies. Internal consistency of sufficiently large sets of frequencies measured in individual molecular fragments is tested by comparing the experimental data with their predicted values. The method requires only knowledge of local geometry (i.e., definition of the interaction tensors in the local coordinate frames of the fragments). No information about the alignment or shape of the molecule is required. The test is best suited for planar fragments. Application to peptide bonds and nucleic acid bases is demonstrated.

A novel method for the determination of stereochemistry in six-membered chairlike rings using residual dipolar couplings

A novel method for the determination of the relative stereochemistry of six-membered chairlike ring molecules by residual dipolar couplings is presented. C-H residual dipolar couplings were used to investigate the relative stereochemistry of 4,6-O-ethylidene-d-glucopyranose. For this and similar systems it is not necessary to acquire redundant dipolar couplings and to calculate the orientation order tensor. The presented methodology is a paradigmatic leap for the determination of the relative stereochemistry or remote stereochemistry in this kind of fused ring system. Residual dipolar coupling data were collected by 1D and 2D direct-measurement heteronuclear multiple quantum coherence (HMQC) spectroscopy. It was demonstrated that direct measurement of HMQC was quick and accurate for small molecules at natural abundance.

Paramagnetically induced residual dipolar couplings for solution structure determination of lanthanide binding proteins

Lanthanides may substitute calcium in calcium-binding proteins, such as, for instance, EF-hand proteins. Paramagnetic lanthanides are capable of orienting the protein in high magnetic fields to an extent similar to that obtained by using orienting devices, and each lanthanide orients according to its magnetic susceptibility tensor. Here, Ce(3+), Tb(3+), Dy(3+), Ho(3+), Er(3+), Tm(3+), Yb(3+) in the C-terminal site of calbindin D(9k) have been investigated. Such systems provide (1)H-(15)N residual dipolar couplings (rdc) which can be used for solution structure determinations. Within the frame of optimizing the use of residual dipolar couplings for efficient solution structure determination, it is proposed here to use a number of lanthanides (e.g., >2) to obtain the orientations of the internuclear vectors with respect to an arbitrary reference system. This is facilitated by the independent knowledge of the magnetic susceptibility anisotropy tensor of each metal, obtained from the analysis of the pseudocontact shifts. A further module of the program PARAMAGNETIC-DYANA, called RDCDYANA-ANGLES, is developed to efficiently incorporate such rdc-derived orientations, instead of the rdc themselves, as constraints in the solution structure calculation. This strategy is absolutely general and can be extended to any other pair of dipole-dipole coupled nuclei. The effect of mobility is also assessed. In principle, information on the mobility can be obtained with a number of lanthanide ions >5, or by combining a smaller number of lanthanide ions with a few orienting devices.