Accurate calculation of side chain packing and free energy with applications to protein molecular dynamics

To address the large gap between time scales that can be easily reached by molecular simulations and those required to understand protein dynamics, we present 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 computation results in extremely rapid equilibration and sampling of the Boltzmann distribution. Our method, termed Upside, employs a reduced model involving the three backbone atoms, along with the carbonyl oxygen and amide proton, and a single (oriented) side chain bead having multiple locations reflecting the conformational diversity of the side chain's rotameric states. We also introduce a novel, maximum-likelihood method to parameterize the side chain interactions using protein structures. We demonstrate state-of-the-art accuracy for predicting χ1 rotamer states while consuming only milliseconds of CPU time. Our method enables rapidly equilibrating coarse-grained simulations that can nonetheless contain significant molecular detail. We also show that the resulting free energies of the side chains are sufficiently accurate for de novo folding of some proteins.