Relating side-chain mobility in proteins to rotameric transitions: Insights from molecular dynamics simulations and NMR

The dynamic aspect of proteins is fundamental to understanding protein stability and function. One of the goals of NMR studies of side-chain dynamics in proteins is to relate spin relaxation rates to discrete conformational states and the timescales of interconversion between those states. Reported here is a physical analysis of side-chain dynamics that occur on a timescale commensurate with monitoring by 2H spin relaxation within methyl groups. Motivated by observations made from tens-of-nanoseconds long MD simulations on the small protein eglin c in explicit solvent, we propose a simple molecular mechanics-based model for the motions of side-chain methyl groups. By using a Boltzmann distribution within rotamers, and by considering the transitions between different rotamer states, the model semi-quantitatively correlates the population of rotamer states with 'model-free' order parameters typically fitted from NMR relaxation experiments. Two easy-to-use, analytical expressions are given for converting S2axis' values (order parameter for C-CH3 bond) into side-chain rotamer populations. These predict that S2axis' values below 0.8 result from population of more than one rotameric state. The relations are shown to predict rotameric sampling with reasonable accuracy on the ps-ns timescale for eglin c and are validated for longer timescales on ubiquitin, for which side-chain residual dipolar coupling (RDC) data have been collected