Model-Free Approach to the Dynamic Interpretation of Residual Dipolar Couplings in Globular Proteins

Abstract

The effects of internal motions on residual dipolar NMR couplings of proteins partially aligned in a liquid-crystalline environment are analyzed using a 10 ns molecular dynamics (MD) computer simulation of ubiquitin. For a set of alignment tensors with different orientations and rhombicities, MD-averaged dipolar couplings are determined and subsequently interpreted for different scenarios in terms of effective alignment tensors, average orientations of dipolar vectors, and intramolecular reorientational vector distributions. Analytical relationships are derived that reflect similarities and differences between motional scaling of dipolar couplings and scaling of dipolar relaxation data (NMR order parameters). Application of the self-consistent procedure presented here to dipolar coupling measurements of biomolecules aligned in different liquid-crystalline media should allow one to extract in a "model-free" way average orientations of dipolar vectors and specific aspects of their motions.

Protein dynamics and function from solution state NMR spectroscopy

“…This suggests that ubiquitin's ability to bind to a very wide range of proteins is partly due to an appreciable degree of structural plasticity in its apo state. RDCs Tolman et al 1995) are sensitive to motions that occur over ps to ms (Meiler et al 2001(Meiler et al , 2001(Meiler et al , 1997Peti et al 2002) and thus fill a gap between the time windows that can be studied using Lipari-Szabo order parameters (Lipari & Szabo, 1982a, b) (sub-τ c motion) and relaxation dispersion experiments (Loria et al 1999;Tollinger et al 2001) (between 50 µs and 100 ms). In an extensive RDC-based study, the laboratories of Griesinger and de Groot developed a method (denoted EROS) that enabled a precise determination of a structural ensemble of apo ubiquitin that is sensitive to motions in the ps-to ms-regime (Lakomek et al 2005(Lakomek et al , 2008b; this regime is henceforth referred to as the supra-τ c regime.…”

“…RDCs are sensitive to motions that are either faster or slower than the protein's rotational correlation time (τ m ), so order parameters derived from RDCs are sensitive to motions occurring over time scales ranging from ps to ms. This was demonstrated in a study on ubiquitin in which RDC-derived order parameters (Meiler et al 2001) were consistently found to be smaller than the corresponding Lipari-Szabo order parameters (Lakomek et al 2005). RDCs have provided particularly important results in studies on IDPs.…”

Identification of slow correlated motions in proteins using residual dipolar and hydrogen-bond scalar couplings

“…Residual dipolar couplings (RDCs) report on averages over longer time scales (up to the millisecond range) and therefore encode key information for understanding slower protein motions over a very broad time scale (15,16). Recent studies have exploited the orientational averaging properties of RDCs to characterize the amplitude and direction of motions of NH vectors (17)(18)(19) or to study local variations in position and dynamics of the amide proton (20,21). Despite this activity, key questions remain concerning the nature and amplitude of slower backbone motions on the peptide chain (22), whose resolution is not only fundamental to our understanding of protein function but also important for the accurate incorporation of conformational disorder into protein structure elucidation (23).…”

Modélisation de la dynamique de la chaîne peptidique des protéines en solution par RMN à travers les couplages dipolaires

“…L'équation 17 est linéaire par rapportà la moyenne dynamique des cinq harmoniques. Si les couplages D jk d'une même paire de spinétaient mesurés dans cinq (ou plus) tenseurs d'alignement connus {A a , A r , 1 , 2 , 3 }, les cinq valeurs Y 2,M pourraientêtre déterminées en résolvant le système linéaire constituéà partir de l'équation 17, sans recours aux modèles géométriques [17,19]. Cependant, il est difficile d'obtenir la mesure d'un couplage dans plus de 5 milieux différents et le cas de l'ubiquitine reste exceptionnel.…”

“…Les récentes contributions se servant des couplages dipolaires résiduels pourétudier les moyennes conformationnelles ont utilisé des approches sans contrainte géométrique (model free) pour caractériser les propriétés de réorientation des vecteurs N-N H [17][18][19][20]. La direction et l'amplitude de l'échantillonnage angulaire du vecteur internucléaire sont décrits: soit purementà partir d'harmoniques sphériques moyennées de deuxième ordre Y 2M , qui sont ensuite déterminées explicitement; soità partir de matrices décrivant aussi bien l'information structurale que dynamique,à déterminer aussi.…”