Hidden regularity and universal classification of fast side chain motions in proteins

Proteins display characteristic dynamical signatures that appear to be universal across all proteins regardless of topology and size. Here, we systematically characterize the universal features of fast side chain motions in proteins by examining the conformational energy surfaces of individual residues obtained using enhanced sampling molecular dynamics simulation (618 free energy surfaces obtained from 0.94 μs MD simulation). The side chain conformational free energy surfaces obtained using the adaptive biasing force (ABF) method for a set of eight proteins with different molecular weights and secondary structures are used to determine the methyl axial NMR order parameters (O(axis)(2)), populations of side chain rotamer states (ρ), conformational entropies (S(conf)), probability fluxes, and activation energies for side chain inter-rotameric transitions. The free energy barriers separating side chain rotamer states range from 0.3 to 12 kcal/mol in all proteins and follow a trimodal distribution with an intense peak at ~5 kcal/mol and two shoulders at ~3 and ~7.5 kcal/mol, indicating that some barriers are more favored than others by proteins to maintain a balance between their conformational stability and flexibility. The origin and the influences of the trimodal barrier distribution on the distribution of O(axis)(2) and the side chain conformational entropy are discussed. A hierarchical grading of rotamer states based on the conformational free energy barriers, entropy, and probability flux reveals three distinct classes of side chains in proteins. A unique nonlinear correlation is established between O(axis)(2) and the side chain rotamer populations (ρ). The apparent universality in O(axis)(2) versus ρ correlation, trimodal barrier distribution, and distinct characteristics of three classes of side chains observed among all proteins indicates a hidden regularity (or commonality) in the dynamical heterogeneity of fast side chain motions in proteins.