Protein Dynamics in the Solid State from ²H NMR Line Shape Analysis. II. MOMD Applied to C-D and C-CD₃ Probes

Deuterium line shape analysis from mobile C-D and C-CD₃ groups has emerged as a particularly useful tool for studying dynamics in the solid state. The theoretical models devised so far consist typically of sets of independent dynamic modes. Each such mode is simple and usually case-specific. In this scenario, model improvement entails adding yet another mode (thereby changing the overall model), comparison of different cases is difficult, and ambiguity is unavoidable. We recently developed the microscopic order macroscopic disorder (MOMD) approach as a single-mode alternative. In MOMD, the local spatial restrictions are expressed by an anisotropic potential, the local motion by a diffusion tensor, and the local molecular geometry by relative (magnetic and model-related) tensor orientations, all of adjustable symmetry. This approach provides a consistent method of analysis, thus resolving the issues above. In this study, we apply MOMD to PS-adsorbed LKα14 peptide and dimethylammonium tetraphenylborate (C-CD₃ and N-CD₃ dynamics, respectively), as well as HhaI methyltransferase target DNA and phase III of benzene-6-hexanoate (C-D dynamics). The success with fitting these four disparate cases, as well as the two cases in the previous report, demonstrates the generality of this MOMD-based approach. In this study, C-D and C-CD₃ are both found to execute axial diffusion (rates R_⊥ and R_∥) in the presence of a rhombic potential given by the L = 2 spherical harmonics (coefficients c²₀ and c²₂). R_⊥ (R_∥) is in the 10²-10³ (10⁴-10⁵) s^-1 range, and c²₀ and c²₂ are on the order of 2-3 k_BT. Specific parameter values are determined for each mobile site. The diffusion and quadrupolar tensors are tilted at either 120° (consistent with trans-gauche isomerization) or nearly 110.5° (consistent with methyl exchange). Future prospects include extension of the MOMD formalism to include MAS, and application to ¹⁵N and ¹³C nuclei.