Solvent friction effects propagate over the entire protein molecule through low-frequency collective modes

Protein solvation dynamics has been investigated using atom-dependent Langevin friction coefficients derived directly from molecular dynamics (MD) simulations. To determine the effect of solvation on the atomic friction coefficients, solution and vacuum MD simulations were performed for lysozyme and staphylococcal nuclease and analyzed by Langevin mode analysis. The coefficients thus derived are roughly correlated with the atomic solvent-accessible surface area (ASA), as expected from the fact that friction occurs as the result of collisions with solvent molecules. However, a considerable number of atoms with higher friction coefficients are found inside the core region. Hence, the influence of solvent friction propagates into the protein core. The internal coefficients have large contributions from the low-frequency modes, yielding a simple picture of the surface-to-core long-range damping via solvation governed by collective low-frequency modes. To make use of these findings in implicit-solvent modeling, we compare the all-atom friction results with those obtained using Langevin dynamics (LD) with two empirical representations: the constant-friction and the ASA-dependent (Pastor-Karplus) friction models. The constant-friction model overestimates the core and underestimates the surface damping whereas the ASA-dependent friction model, which damps protein atoms only on the solvent-accessible surface, reproduces well the friction coefficients for both the surface and core regions observed in the explicit-solvent MD simulations. Therefore, in LD simulation, the solvent friction coefficients should be imposed only on the protein surface.