Evaluating the London Dispersion Coefficients of Protein Force Fields Using the Exchange-Hole Dipole Moment Model

London
dispersion is one of the fundamental interactions involved
in protein folding and dynamics. The popular CHARMM36, Amber ff14sb,
and OPLS-AA force fields represent these interactions through the C6/r6 term of the
Lennard-Jones potential, where the C6 parameters
are assigned empirically. Here, dispersion coefficients of these three
force fields are shown to be roughly 50% larger than values calculated
using the quantum mechanically derived exchange-hole dipole moment
(XDM) model. The CHARMM36 and Amber OL15 force fields for nucleic
acids also exhibit this trend. The hydration energies of the side-chain
models were calculated using REMD-TI for the CHARMM36, Amber ff14sb,
and OPLS-AA force fields. These force fields predict side-chain hydration
energies that are in generally good agreement with the experimental
values, which suggests that the total strength of aqueous dispersion
interactions is correct, despite C6 coefficients
that are considerably larger than XDM predicts. An analytical expression
for the dispersion hydration energy using XDM coefficients shows that
higher-order dispersion terms (i.e., C8 and C10) account for roughly 37.5% of
the hydration energy of methane. This suggests that the C6 dispersion coefficients used in contemporary force fields
are elevated to account for the neglected higher-order terms.