Transforming between discrete and continuous angle distribution models: application to protein χ₁ torsions

Conformational Populations of β-(1→4) O-Glycosidic Linkages Using Redundant NMR J-Couplings and Circular Statistics

Twelve disaccharides containing β-(1→4) linkages and displaying systematic structural variations in the vicinity of these linkages were selectively labeled with ¹³C to facilitate measurements of multiple NMR spin-spin (scalar; J) coupling constants (J_CH and J_CC values) across their O-glycosidic linkages. Ensembles of spin-couplings (²J_COC, ³J_COCH, ³J_COCC) sensitive to the two linkage torsion angles, phi (ϕ) and psi (ψ), were analyzed by using parametrized equations obtained from density functional theory (DFT) calculations, Fredholm theory, and circular statistics to calculate experiment-based rotamer populations for ϕ and ψ in each disaccharide. With the statistical program MA'AT, torsion angles ϕ and ψ were modeled as a single von Mises distribution, which yielded two parameters, the mean position and the circular standard deviation (CSD) for each angle. The NMR-derived rotamer populations were compared to those obtained from 1 μs aqueous molecular dynamics (MD) simulations and crystallographic database statistical analyses. Conformer populations obtained exclusively from the MA'AT treatment of redundant J-couplings were in very good agreement with those obtained from the MD simulations, providing evidence that conformational populations can be determined by NMR for mobile molecular elements such as O-glycosidic linkages with minimal input from theory. The approach also provides an experimental means to validate the conformational preferences predicted from MD simulations. The conformational behaviors of ϕ in the 12 disaccharides were very similar, but those of ψ varied significantly, allowing a classification of the 12 disaccharides based on preferred linkage conformation in solution.

Side Chain Conformational Distributions of a Small Protein Derived from Model-Free Analysis of a Large Set of Residual Dipolar Couplings

Accurate quantitative measurement of structural dispersion in proteins remains a prime challenge to both X-ray crystallography and NMR spectroscopy. Here we use a model-free approach based on measurement of many residual dipolar couplings (RDCs) in differentially orienting aqueous liquid crystalline solutions to obtain the side chain χ₁ distribution sampled by each residue in solution. Applied to the small well-ordered model protein GB3, our approach reveals that the RDC data are compatible with a single narrow distribution of side chain χ₁ angles for only about 40% of the residues. For more than half of the residues, populations greater than 10% for a second rotamer are observed, and four residues require sampling of three rotameric states to fit the RDC data. In virtually all cases, sampled χ₁ values are found to center closely around ideal g^–, g⁺ and t rotameric angles, even though no rotamer restraint is used when deriving the sampled angles. The root-mean-square difference between experimental ³J_HαHβ couplings and those predicted by the Haasnoot-parametrized, motion-adjusted Karplus equation reduces from 2.05 to 0.75 Hz when using the new rotamer analysis instead of the 1.1-Å X-ray structure as input for the dihedral angles. A comparison between observed and predicted ³J_HαHβ values suggests that the root-mean-square amplitude of χ₁ angle fluctuations within a given rotamer well is ca. 20°. The quantitatively defined side chain rotamer equilibria obtained from our study set new benchmarks for evaluating improved molecular dynamics force fields, and also will enable further development of quantitative relations between side chain chemical shift and structure.

Protein backbone and sidechain torsion angles predicted from NMR chemical shifts using artificial neural networks

A new program, TALOS-N, is introduced for predicting protein backbone torsion angles from NMR chemical shifts. The program relies far more extensively on the use of trained artificial neural networks than its predecessor, TALOS+. Validation on an independent set of proteins indicates that backbone torsion angles can be predicted for a larger, ≥90 % fraction of the residues, with an error rate smaller than ca 3.5 %, using an acceptance criterion that is nearly two-fold tighter than that used previously, and a root mean square difference between predicted and crystallographically observed (ϕ, ψ) torsion angles of ca 12º. TALOS-N also reports sidechain χ(1) rotameric states for about 50 % of the residues, and a consistency with reference structures of 89 %. The program includes a neural network trained to identify secondary structure from residue sequence and chemical shifts.