  To address the large gap between time scales that can be easily reached by
molecular simulations and those required to understand protein dynamics, we
propose a rapid self-consistent approximation of the side chain free energy at
every integration step. In analogy with the adiabatic Born-Oppenheimer
approximation for electronic structure, the protein backbone dynamics are
simulated as preceding according to the dictates of the free energy of an
instantaneously-equilibrated side chain potential. The side chain free energy
is computed on the fly, allowing the protein backbone dynamics to traverse a
greatly smoothed energetic landscape. This results in extremely rapid
equilibration and sampling of the Boltzmann distribution. Because our method
employs a reduced model involving single-bead side chains, we also provide a
novel, maximum-likelihood method to parameterize the side chain model using
input data from high resolution protein crystal structures. We demonstrate
state-of-the-art accuracy for predicting $\chi_1$ rotamer states while
consuming only milliseconds of CPU time. We also show that the resulting free
energies of side chains is sufficiently accurate for de novo folding of some
proteins.
