Solid‐State NMR Measurements of Asymmetric Dipolar Couplings Provide Insight into Protein Side‐Chain Motion

Abstract

Understanding conformational flexibility is of critical importance for understanding protein function, folding, and interactions with other proteins and ligands. NMR spectroscopy is an important tool for such investigations in solution and increasingly also in the solid state since it allows siteresolved studies of dynamic processes. An experimental characterization of all motional modes of a protein is a great challenge and simplified models are necessary. In NMR studies of dynamics, motional amplitudes are generally expressed in terms of a single order parameter, discarding the details of the motion, such as the motional asymmetry. Herein, we show a significant extension of this description, by detecting asymmetric motion of side chains in a protein in the solid state. Dipolar couplings are particularly powerful probes of local molecular dynamics in the solid state. In the absence of motion, the tensor describing the dipolar interaction between two nuclei is a traceless axially symmetric second-rank tensor. It can be characterized by a single parameter, namely its anisotropy dD,rigid which depends only on the internuclear distance and isotope type of the nuclei involved (for the definition see the Supporting Information). In the presence of “fast” motional processes, in other words, processes with a correlation time shorter than approximately 1/dD,rigid, (typically 10–100 ms), the dipolar coupling tensor becomes partially averaged. In the case of a motional process with threefold (C3) or higher symmetry, for example, an isotropic motion within a cone, the averaged tensor remains axially symmetric and is fully characterized by the effective anisotropy dD which has a reduced value compared to dD,rigid. In this case, the motional amplitude can be expressed by a single order parameter S= dD/dD,rigid. However, in the case of a general fast motion, the characterization solely by S is incomplete because the averaged dipolar tensor is no longer axially symmetric and one additional tensor parameter, the asymmetry hD, is needed for a complete description (for the definition, see the Supporting Information). The asymmetry hD varies between zero (symmetric tensor) and one. [5a]