NMR-Based Configurational Assignments of Natural Products: Gibbs Sampling and Bayesian Inference Using Floating Chirality Distance Geometry Calculations

Floating chirality restrained distance geometry (fc-rDG) calculations are used to directly evolve structures from NMR data such as NOE-derived intramolecular distances or anisotropic residual dipolar couplings (RDCs). In contrast to evaluating pre-calculated structures against NMR restraints, multiple configurations (diastereomers) and conformations are generated automatically within the experimental limits. In this report, we show that the “unphysical” rDG pseudo energies defined from NMR violations bear statistical significance, which allows assigning probabilities to configurational assignments made that are fully compatible with the method of Bayesian inference. These “diastereomeric differentiabilities” then even become almost independent of the actual values of the force constants used to model the restraints originating from NOE or RDC data.

Global Structure of the Intrinsically Disordered Protein Tau Emerges from its Local Structure

The paradigmatic disordered protein tau plays an important role in neuronal function and neurodegenerative diseases. To disentangle the factors controlling the balance between functional and disease-associated conformational states, we build a structural ensemble of the tau K18 fragment containing the four pseudorepeat domains involved in both microtubule binding and amyloid fibril formation. We assemble 129-residue-long tau K18 chains at atomic resolution from an extensive fragment library constructed with molecular dynamics simulations. We introduce a reweighted hierarchical chain growth (RHCG) algorithm that integrates experimental data reporting on the local structure into the assembly process in a systematic manner. By combining Bayesian ensemble refinement with importance sampling, we obtain well-defined ensembles and overcome the problem of exponentially varying weights in the integrative modeling of long-chain polymeric molecules. The resulting tau K18 ensembles capture nuclear magnetic resonance (NMR) chemical shift and J-coupling measurements. Without further fitting, we achieve excellent agreement with measurements of NMR residual dipolar couplings. The good agreement with experimental measures of global structures such as single-molecule Förster resonance energy transfer (FRET) efficiencies is improved further by ensemble refinement. By comparing wild-type and mutant ensembles, we show that pathogenic single-point P301 mutations shift the population from the turn-like conformations of the functional microtubule-bound state to the extended conformations of disease-associated tau fibrils. RHCG thus provides us with an atomically resolved view of the population equilibrium between functional and aggregation-prone states of tau K18, and demonstrates that global structural characteristics of this intrinsically disordered protein emerge from its local structure.

The Flexibility of Oligosaccharides Unveiled Through Residual Dipolar Coupling Analysis

The intrinsic flexibility of glycans complicates the study of their structures and dynamics, which are often important for their biological function. NMR has provided insights into the conformational, dynamic and recognition features of glycans, but suffers from severe chemical shift degeneracy. We employed labelled glycans to explore the conformational behaviour of a β(1-6)-Glc hexasaccharide model through residual dipolar couplings (RDCs). RDC delivered information on the relative orientation of specific residues along the glycan chain and provided experimental clues for the existence of certain geometries. The use of two different aligning media demonstrated the adaptability of flexible oligosaccharide structures to different environments.

Tandem domain structure determination based on a systematic enumeration of conformations

Protein structure determination is undergoing a change of perspective due to the larger importance taken in biology by the disordered regions of biomolecules. In such cases, the convergence criterion is more difficult to set up and the size of the conformational space is a obstacle to exhaustive exploration. A pipeline is proposed here to exhaustively sample protein conformations using backbone angle limits obtained by nuclear magnetic resonance (NMR), and then to determine the populations of conformations. The pipeline is applied to a tandem domain of the protein whirlin. An original approach, derived from a reformulation of the Distance Geometry Problem is used to enumerate the conformations of the linker connecting the two domains. Specifically designed procedure then permit to assemble the domains to the linker conformations and to optimize the tandem domain conformations with respect to two sets of NMR measurements: residual dipolar couplings and paramagnetic resonance enhancements. The relative populations of optimized conformations are finally determined by fitting small angle X-ray scattering (SAXS) data. The most populated conformation of the tandem domain is a semi-closed one, fully closed and more extended conformations being in minority, in agreement with previous observations. The SAXS and NMR data show different influences on the determination of populations.

An Integrative Approach to Determine 3D Protein Structures Using Sparse Paramagnetic NMR Data and Physical Modeling

Paramagnetic nuclear magnetic resonance (NMR) methods have emerged as powerful tools for structure determination of large, sparsely protonated proteins. However traditional applications face several challenges, including a need for large datasets to offset the sparsity of restraints, the difficulty in accounting for the conformational heterogeneity of the spin-label, and noisy experimental data. Here we propose an integrative approach to structure determination combining sparse paramagnetic NMR with physical modelling to infer approximate protein structural ensembles. We use calmodulin in complex with the smooth muscle myosin light chain kinase peptide as a model system. Despite acquiring data from samples labeled only at the backbone amide positions, we are able to produce an ensemble with an average RMSD of ∼2.8 Å from a reference X-ray crystal structure. Our approach requires only backbone chemical shifts and measurements of the paramagnetic relaxation enhancement and residual dipolar couplings that can be obtained from sparsely labeled samples.

Incomplete Data Sets in the Model Free Analysis of Experimental Residual Dipolar Couplings in Small Organic Compounds

Residual dipolar couplings (RDCs) contain information on the relative arrangement and dynamics of internuclear spin vectors in chemical compounds. The recently introduced software TITANIA implements the MFA and extracts structure and dynamics parameters directly from experimental RDCs to facilitate <i>de novo</i> structure refinement for small organic compounds. Herein, we focus on the challenges faced with experimentally inaccessible data often encountered for small organic compounds leading to voids in the RDC matrix and the concomitant effects on the structure refinement. It is shown that RDC data sets obtained experimentally from currently available alignment media and measurement methods are of sufficient quality to allow relative configuration determination even when the relative configuration of the analyte is completely unknown.<br>

TITANIA: Model Free Interpretation of Residual Dipolar Couplings in the context of Organic Compounds

The direct use of RDCs as restraint to construct structures based on RDCs is proposed for organic compounds. It uses the vector and dynamics information available in multi alignment data sets directly for the joint determination of conformation and configuration of organic compounds. We show that employing these data even a flat or random start structure converges into the correctly configured structure when employing multiple alignment data sets in our iterative procedure. <br>