Investigation of backbone dynamics and local geometry of bio-molecules using calculated NMR chemical shifts and anisotropies

Abstract

Prerequisite for chemical shift (CS) and CS tensor calculations are highly refined structures defining the molecular surroundings of the nuclei under study. Here, we present geometry optimizations with ¹³C and ¹⁵N CS constraints for large bio-molecules like peptides and proteins. The method discussed here provides both, refined structures and chemical shift tensors. Furthermore, since the experimental resonances of aligned systems are related to CS tensors, they strongly depend on the orientation and motion of molecules, their fragments, functional groups and moieties. For efficient CS calculations we apply a semi-empirical approach—the bond polarization theory (BPT). The BPT relies on linear bond polarization parameters and we present a new set of parameters based on ab initio second-order Møller–Plesset perturbation theory calculations. The new parametrization extends the applicability of the BPT approach to a wide range of organic molecules and bio-polymers. Here, the method has been applied to the protein ubiquitin and the membrane-active peptide gramicidin A (dimer) in oriented bilayers. The calculated ¹³C and ¹⁵N CS values of best-refined structures published until now gave a large scatter with respect to the experiment. It will be shown that BPT CS optimizations can reduce these errors to values near the experimental uncertainty. In combination with molecular dynamics with orientational constraints it is possible to study motional dynamics and BPT calculations can provide residual chemical shift anisotropies.