Chi(1) rotamer populations and angles of mobile surface side chains are accurately predicted by a torsion angle database potential of mean force

The equilibrium angles and distributions of chi(1) rotamers for mobile surface side chains of the small, 63-residue, B1 domain of protein L have been calculated from the static crystal structure by rigid body/torsion angle simulated annealing using a torsion angle database potential of mean force and compared to those deduced by Monte Carlo analysis of side chain residual dipolar couplings measured in solution. Good agreement between theory and experiment is observed, indicating that for side chains undergoing rotamer averaging that is fast on the chemical shift time scale, the equilibrium angles and distribution of chi(1) rotamers are largely determined by the backbone phi/psi torsion angles.     

Chi1 torsion angle dynamics in proteins from dipolar couplings.

Experiments are presented for the measurement of one-bond carbon-proton dipolar coupling values at CH and CH2 ositions in 13C-labeled, approximately 50% fractionally deuterated proteins. 13Cbeta-1Hbeta dipolar couplings have been measured for 38 of 49 possible residues in the 63-amino-acid B1 domain of peptostreptococcal protein L in two aligning media and interpreted in the context of side-chain chi1 torsion angle dynamics. The beta protons for 18 of the 25 beta-methylene-containing amino acids for which dipolar data are available can be unambiguously stereoassigned, and for those residues which are best fit to a single rotamer model the chi(1) angles obtained deviate from crystal structure values by only 5.2 degrees (rmsd). The results for 11 other residues are significantly better fit by a model that assumes jumps between the three canonical (chi1 approximately -60 degrees, 60 degrees, 180 degrees ) rotamers. Relative populations of the rotamers are determined to within +/-6% uncertainty on average and correlate with dihedral angles observed for the three molecules in the crystal asymmetric unit. Entropic penalties for quenching chi1 jumps are considered for six mobile residues thought to be involved in binding to human immunoglobulins. This study demonstrates that dipolar couplings may be used to characterize both the conformation of static residues and side-chain motion with high precision.     

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.     

CHARMM36 all‐atom additive protein force field: Validation based on comparison to NMR data

Protein structure and dynamics can be characterized on the atomistic level with both nuclear magnetic resonance (NMR) experiments and molecular dynamics (MD) simulations. Here, we quantify the ability of the recently presented CHARMM36 (C36) force field (FF) to reproduce various NMR observables using MD simulations. The studied NMR properties include backbone scalar couplings across hydrogen bonds, residual dipolar couplings (RDCs) and relaxation order parameter, as well as scalar couplings, RDCs, and order parameters for side‐chain amino‐ and methyl‐containing groups. It is shown that the C36 FF leads to better correlation with experimental data compared to the CHARMM22/CMAP FF and suggest using C36 in protein simulations. Although both CHARMM FFs contains the same nonbond parameters, our results show how the changes in the internal parameters associated with the peptide backbone via CMAP and the χ₁ and χ₂ dihedral parameters leads to improved treatment of the analyzed nonbond interactions. This highlights the importance of proper treatment of the internal covalent components in modeling nonbond interactions with molecular mechanics FFs. © 2013 Wiley Periodicals, Inc.     

J-GFT NMR for precise measurement of mutually correlated nuclear spin-spin couplings

G-matrix Fourier transform (GFT) NMR spectroscopy is presented for accurate and precise measurement of chemical shifts and nuclear spin-spin couplings correlated according to spin system. The new approach, named "J-GFT NMR", is based on a largely extended GFT NMR formalism and promises to have a broad impact on projection NMR spectroscopy. Specifically, constant-time J-GFT (6,2)D (HA-CA-CO)-N-HN was implemented for simultaneous measurement of five mutually correlated NMR parameters, that is, 15N backbone chemical shifts and the four one-bond spin-spin couplings 13Calpha-1Halpha, 13Calpha-13C', 15N-13C', and 15N-1HNu. The experiment was applied for measuring residual dipolar couplings (RDCs) in an 8 kDa protein Z-domain aligned with Pf1 phages. Comparison with RDC values extracted from conventional NMR experiments reveals that RDCs are measured with high precision and accuracy, which is attributable to the facts that (i) the use of constant time evolution ensures that signals do not broaden whenever multiple RDCs are jointly measured in a single dimension and (ii) RDCs are multiply encoded in the multiplets arising from the joint sampling. This corresponds to measuring the couplings multiple times in a statistically independent manner. A key feature of J-GFT NMR, i.e., the correlation of couplings according to spin systems without reference to sequential resonance assignments, promises to be particularly valuable for rapid identification of backbone conformation and classification of protein fold families on the basis of statistical analysis of dipolar couplings.     

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.     

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.     

Insights into the mobility of methyl-bearing side chains in proteins from (3)J(CC) and (3)J(CN) couplings

Side-chain dynamics in proteins can be characterized by the NMR measurement of (13)C and (2)H relaxation rates. Evaluation of the corresponding spectral densities limits the slowest motions that can be studied quantitatively to the time scale on which the overall molecular tumbling takes place. A different measure for the degree of side-chain order about the C(alpha)-C(beta) bond (chi(1) angle) can be derived from (3)J(C)(')(-)(C)(gamma) and (3)J(N)(-)(C)(gamma) couplings. These couplings can be measured at high accuracy, in particular for Thr, Ile, and Val residues. In conjunction with the known backbone structures of ubiquitin and the third IgG-binding domain of protein G, and an extensive set of (13)C-(1)H side-chain dipolar coupling measurements in oriented media, these (3)J couplings were used to parametrize empirical Karplus relationships for (3)J(C)(')(-)(C)(gamma) and (3)J(N)(-)(C)(gamma). These Karplus curves agree well with results from DFT calculations, including an unusual phase shift, which causes the maximum (3)J(CC) and (3)J(CN) couplings to occur for dihedral angles slightly smaller than 180 degrees, particularly noticeable in Thr residues. The new Karplus curves permit determination of rotamer populations for the chi(1) torsion angles. Similar rotamer populations can be derived from side-chain dipolar couplings. Conversion of these rotamer populations into generalized order parameters, S(J)(2) and S(D)(2), provides a view of side-chain dynamics that is complementary to that obtained from (13)C and (2)H relaxation. On average, results agree well with literature values for (2)H-relaxation-derived S(rel)(2) values in ubiquitin and HIV protease, but also identify a fraction of residues for which S(J,D)(2) < S(rel)(2). This indicates that some of the rotameric averaging occurs on a time scale too slow to be observable in traditional relaxation measurements.     

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.     

Stretched poly(methyl methacrylate) gel aligns small organic molecules in chloroform. stereochemical analysis and diastereotopic proton NMR assignment in ludartin using residual dipolar couplings and 3J coupling constant analysis

Poly(methyl methacrylate) (PMMA) gels prepared by copolymerizing methyl methacrylate (MMA) and various amounts of ethylene glycol dimethacrylate (EGDMA) in the presence of the radical initiator V-70 (2,2'-azobis(2,4-dimethyl-4-methoxyvaleronitrile)) can orient small organic molecules when swollen in NMR tubes with CDCl(3). The aligning properties of the stretched PMMA gels were evaluated by monitoring the quadrupolar splitting of the (2)H NMR signal of CDCl(3), and the aligning degree is proportional to the cross-linking density. Natural abundance one-bond (1)H-(13)C residual dipolar couplings (RDCs) for menthol measured in the gels depended on the cross-link density. The stereochemistry and assignment of the diastereotopic protons of the gastroprotective and nonsteroidal aromatase inhibitor sesquiterpene lactone ludartin, isolated from Stevia yaconensis var. subeglandulosa, were unambiguously determined using a combination of natural abundance one-bond (1)H-(13)C RDCs measured in a PMMA gel and a (3)J coupling constant analysis.     

Residual-Chemical-Shift-Anisotropy-Based Enantiodifferentiation in Lyotropic Liquid Crystalline Phases Based on Helically Chiral Polyacetylenes

Anisotropic NMR spectroscopy, revealing residual dipolar couplings (RDCs) and residual chemical shift anisotropies (RCSAs) has emerged as a powerful tool to determine the configurations of synthetic and complex natural compounds. The deduction of the absolute in addition to the relative configuration is one of the primary goals in the field. Therefore, the investigation of the enantiodiscriminating capabilities of chiral alignment media becomes essential. While RDCs and RCSAs are now used for the determination of the relative configuration routinely, RCSAs have not been measured in chiral alignment media such as chiral liquid crystals. Herein, we present this application by measuring RCSAs for chiral analytes such as indanol and isopinocampheol in the lyotropic liquid crystalline phase of an L-valine derived helically chiral polyacetylenes. We have also demonstrated that a single 1D ¹³C−{¹H} NMR spectrum suffices to get the RCSAs circumventing the necessity to acquire two spectra at two alignment conditions.     

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.     

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.     

Dipolar couplings in multiple alignments suggest alpha helical motion in ubiquitin

Recently, residual dipolar couplings (RDCs) of backbone N-HN vectors measured in 11 different alignment media were analyzed with respect to structure and dynamics in a model-free way in terms of generalized order parameters and motional anisotropies. The anisotropies in the central alpha-helix were found to be strikingly uniformly distributed. In this communication, these parameters are further interpreted in terms of physically feasible cooperative reorientational motion of the helix with respect to the core of the protein. The RDCs are compatible with a model in which all N-HN vectors of the alpha-helix of ubiquitin exhibit correlated anisotropic excursions with amplitudes of 21 degrees and 12 degrees along two orthogonal directions x' ' and y' ' of a coordinate system C' ', if z' ' represents the helix axis. Such motion contradicts neither NOE data nor molecular force-field calculations.     

Protein alignment by a coexpressed lanthanide-binding tag for the measurement of residual dipolar couplings

A protein fusion construct of human ubiquitin with an N-terminal lanthanide binding tag (LBT) enables observation of long-range orientational restraints in solution NMR from residual dipolar couplings (RDCs) due to paramagnetic alignment of the protein. The paramagnetic lanthanide ions Tb3+, Dy3+, and Tm3+ are shown to bind to the LBT and induce different alignment tensors, in agreement with theory. RDCs, measured relative to the diamagnetic Lu3+, range from -7.6 to 5.5 Hz for Tb3+ and -6.6 to 6.1 Hz for Dy3+, while an opposite alignment tensor is observed for Tm3+ (4.5 to -2.9 Hz) at 800 MHz. Experimental RDCs are in excellent agreement with those predicted on the basis of the X-ray structure of the protein.     

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.     

Probing Long‐Range Anisotropic Interactions: a General and Sign‐Sensitive Strategy to Measure 1H–1H Residual Dipolar Couplings as a Key Advance for Organic Structure Determination

Residual dipolar couplings (RDCs) are amongst the most powerful NMR parameters for organic structure elucidation. In order to maximize their effectiveness in increasingly complex cases such as flexible compounds, a maximum of RDCs between nuclei sampling a large distribution of orientations is needed, including sign information. For this, the easily accessible one‐bond ¹H–¹³C RDCs alone often fall short. Long‐range ¹H–¹H RDCs are both abundant and typically sample highly complementary orientations, but accessing them in a sign‐sensitive way has been severely obstructed due to the overflow of ¹H–¹H couplings. Here, we present a generally applicable strategy that allows the measurement of a large number of ¹H–¹H RDCs, including their signs, which is based on a combination of an improved PSYCHEDELIC method and a new selective constant‐time β‐COSY experiment. The potential of ¹H–¹H RDCs to better determine molecular alignment and to discriminate between enantiomers and diastereomers is demonstrated.     

Protein Backbone 1H(N)-13Calpha and 15N-13Calpha residual dipolar and J couplings: new constraints for NMR structure determination

A simple, sensitivity-enhanced experiment was devised for accurate measurement of backbone 15N-13Calpha and 1HN-13Calpha couplings in proteins. The measured residual dipolar couplings 2DHCA, 1DNCA, 3DHCA, and 2DNCA for protein GB1 display very good agreement with the refined NMR structure (PDB code: 3GB1). A Karplus-type relationship between the one-bond 1JNCA couplings and the backbone dihedral psi angles holds, and on the basis of the two-bond 2JNCA couplings a secondary structure index can be established.