Narrowing the gap between experimental and computational determination of methyl group dynamics in proteins

Nuclear magnetic resonance (NMR) spin relaxation has become the mainstay technique to sample protein dynamics at atomic resolution, expanding its repertoire from backbone 15N to side-chain 2H probes. At the same time, molecular dynamics (MD) simulations have become increasingly powerful to study protein dynamics due to steady improvements of physical models, algorithms, and computational power. Good agreement between generalized Lipari-Szabo order parameters derived from experiment and MD simulation has been observed for the backbone dynamics of a number of proteins. However, the agreement for the more dynamic side-chains, as probed by methyl group relaxation, was much worse. Here, we use T4 lysozyme (T4L), a protein with moderate tumbling anisotropy, to showcase a number of improvements that reduce this gap by a combined evaluation of NMR relaxation experiments and MD simulations. By applying a protein force field with accurate methyl group rotation barriers in combination with a solvation model that yields correct protein rotational diffusion times, we find that properly accounting for anisotropic protein tumbling is an important factor to improve the match between NMR and MD in terms of methyl axis order parameters, spectral densities, and relaxation rates. The best agreement with the experimentally measured relaxation rates is obtained by a posteriori fitting the appropriate internal time correlation functions, truncated by anisotropic overall tumbling. In addition, MD simulations led us to account for a hitherto unrealized artifact in deuterium relaxation experiments arising from strong coupling for leucine residues in uniformly 13C-enriched proteins. For T4L, the improved analysis reduced the RMSD between MD and NMR derived methyl axis order parameters from 0.19 to 0.11. At the level of the spectral density functions, the improvements allow us to extract the most accurate parameters that describe protein side-chain dynamics. Further improvement is challenging not only due to force field and sampling limitations in MD, but also due to inherent limitations of the Lipari-Szabo model to capture complex dynamics.