Model-free analysis of protein backbone motion from residual dipolar couplings

On the basis of the measurement of NH residual dipolar couplings (RDCs) in 11 different alignment media, an RDC-based order parameter is derived for each residue in the protein ubiquitin. Dipolar couplings are motionally averaged in the picosecond to millisecond time range and, therefore, reflect motion slower than the inverse overall tumbling correlation time of the protein. It is found that there is considerable motion that is slower than the correlation time and could not be detected with previous NMR methodology. Amplitudes and anisotropies of the motion can be derived from the model-free analysis. The method can be applied provided that at least five sufficiently different alignment media can be found for the biomolecule under investigation.     

De novo determination of bond orientations and order parameters from residual dipolar couplings with high accuracy

We report the de novo determination of 15N-1H bond orientations and motional order parameters for the protein ubiquitin with high accuracy based solely on NMR residual dipolar coupling measurements made in six distinct alignment media. The resulting bond orientations are in agreement with RDC-refined orientations of either solid or solution state coordinates to within approximately 2 degrees , which is also the estimated precision of the resulting orientations. The squared generalized order parameters, which reflect amplitudes of motion spanning the picosecond to millisecond time scales, exhibit a correlation with picosecond time scale order parameters derived from conventional NMR 15N spin relaxation methods. Provided that RDC measurements can be obtained using many different alignment media, this approach (called direct interpretation of dipolar couplings) may significantly impact the attainable accuracy and the molecular weight range accessible to NMR structure determination in the solution state, as well as provide a route for the study of motions occurring on the nanosecond to microsecond time scales, which have been traditionally difficult to study at atomic resolution.     

Simultaneous definition of high resolution protein structure and backbone conformational dynamics using NMR residual dipolar couplings.

Despite the importance of molecular dynamics for biological activity, most approaches to protein structure determination, whether based on crystallographic or solution studies, propose three-dimensional atomic representations of a single configuration that take no account of conformational fluctuation. Non-averaged anisotropic NMR interactions, such as residual dipolar couplings, that become measurable under conditions of weak alignment, provide sensitive probes of both molecular structure and dynamics. Residual dipolar couplings are becoming increasingly powerful for the study of proteins in solution. In this minireview we present their use for the simultaneous determination of protein structure and dynamics.     

Direct structure determination using residual dipolar couplings: reaction-site conformation of methionine sulfoxide reductase in solution

Residual dipolar couplings (RDC) from partially aligned molecules provide long-range structural data and are thus particularly well adapted to rapid structure validation or protein fold recognition. Extensive measurements in two alignment media can also provide precise de novo structure from RDC alone. We have applied a novel combination of these approaches to the study of methionine sulfoxide reductase (MsrA) from Erwinia chrysanthemi, a 27 kDa enzyme essential for repairing oxidative stress damage. The tertiary fold was initially validated by comparing backbone RDC to expected values from the crystal structure of the homologous MsrA from Escherichia coli. Good agreement was found throughout the chain, verifying the overall topology of the molecule, with the exception of the catalytically important peptide P196-L202, where strong and systematic RDC violation was observed. No evidence for local differential mobility in this region was detected, implying that the structure of the strand differs in the two molecules. We have therefore applied the de novo approach meccano to determine the conformation of this peptide using only RDC. A single conformation is found that is in agreement with all measured data. The aligned peptide can be docked onto the expected covalence of the rest of the template molecule while respecting its strictly defined relative orientation. In contrast to the structure of MsrA from E. coli, the reactive side chain of Cys200 is oriented toward the interior of the molecule and therefore closer to the catalytic Cys53, obviating the need for previously proposed conformational reorganization prior to formation of this disulfide intermediate. This analysis requires only backbone assignment and uses unambiguously assigned and readily measurable structural data, thereby greatly economizing investigation time compared to established nuclear Overhauser effect- (nOe-) based structure calculation methods.     

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.     

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.     

Calculation of residual dipolar couplings from disordered state ensembles using local alignment

Residual dipolar couplings (RDCs) have been observed in disordered states of several proteins. While their nonuniform values were initially surprising, it has been shown that reasonable approximation of experimental RDCs can be obtained using simple statistical coil models and assuming global alignment of each structure, provided that many thousands of conformers are averaged. Here we show that, by using short local alignment tensors, we can achieve good agreement between experimental and simulated RDCs with far fewer structures than required when using global alignment. This makes the possibility of using RDCs as direct restraints in structural calculations of disordered proteins much more feasible. In addition, it provides insight into the nature of RDCs in disordered states, suggesting that they are primarily reporting on local structure.     

On the origin of residual dipolar couplings from denatured proteins

Effects of steric obstruction on random flight chains are examined. Spatial probability distributions are elaborated to calculate residual dipolar couplings and residual chemical shift anisotropy, parameters that are acquired by NMR spectroscopy from solutes dissolved in dilute liquid crystals. Calculations yield chain length and residue position-dependent values in good agreement with simulations to provide understanding of recently acquired data from denatured proteins.     

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.     

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.     

Conformational analysis of a flexible oligosaccharide using residual dipolar couplings.

We present a new approach to the analysis of the conformational and the motional properties of an oligosaccharide, methyl 3,6-di-O-(alpha-D-mannopyranosyl)-alpha-D-mannopyranoside. The approach relies on an order matrix analysis of residual dipolar couplings in the solution state. By combining a number of different types of couplings, (1)D(CH), (2)D(CH), and D(HH), an order matrix is solved for each ring of the trimannoside. The resulting order parameters indicate the internal motion at the alpha (1,3) linkage to be limited, while significant motion is suggested at the alpha (1,6) linkage. Two structures for the trimannoside were determined by aligning the order tensor principal axes obtained from two different orienting media, bicelles and phage. The very similar conformations at the alpha (1,3) linkage of these two structures confirm that the internal motion at the alpha (1,3) linkage is small and the conformation is a good representation of a single preferred structure. The different conformations at the alpha (1,6) linkage suggest that the motional amplitudes are large and the conformations must be viewed as virtual conformers. Compared with traditional NMR methods, data acquisition is easy and data analysis is straightforward.     

1H-1H dipolar couplings provide a unique probe of RNA backbone structure

A NMR method is described that permits simultaneous measurement of the geminal 2JH1H2 + 2DH1H2 splitting and the sum of the 1JCH1 + 1DCH1 + 1JCH2 + 1DCH2 couplings for methylene groups, where 2DH1H2 and 1DCH are residual dipolar couplings, occurring when molecules are weakly oriented relative to the magnetic field. By suppressing either the upfield or downfield half of the 1H-1H geminal doublet, the experiment yields improved resolution relative to regular two-dimensional 1H-13C correlation spectra, making it applicable to systems of considerable complexity. The method is demonstrated for measurement of all 2DH5'H5' couplings in a 24-nucleotide 13C-enriched RNA stem loop structure, weakly aligned in liquid crystalline Pf1. The method is equally applicable to methylene groups in 13C-labeled proteins and to natural abundance samples of smaller molecules.     

Molecular structure extracted from residual dipolar couplings: diphenylmethane dissolved in a nematic liquid crystal

This paper describes an analysis of 1H-1H residual dipolar couplings (RDCs) in diphenylmethane (DPM) dissolved in a nematic liquid crystal, reported by Celebre et al. [J. Chem. Phys. 118, 6417 (2003)]. In that article, the conformational distribution function for DPM was extracted from the RDCs, using the additive potential (AP) model which is based on the molecular-field theory. The AP approach is a powerful, and frequently used, tool for analysis of the nuclear-magnetic-resonance (NMR) parameters in liquid crystals. It requires, however, a priori knowledge of the functional form of the torsional potential, which may even for a simple molecule, such as DPM, be complicated to determine. Here, we analyze the same set of the RDCs using our APME procedure, which is a hybrid model based on the AP approach and maximum entropy (ME) theory. The APME procedure does not require any assumptions about the functional form of the torsional potential and, in contrast with the ME method, is applicable to weakly ordered systems. In the investigation reported in the present study, the results from the APME analysis are in good agreement with the AP interpretation, whereas the ME approach essentially fails in the extraction of the conformational distribution function for DPM.     

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.