  We introduce a method to bring nearly atomistic resolution to coarse-grained
models, and we apply the method to proteins. Using a small number of
coarse-grained sites (about one per eight atoms) but assigning an independent
three-dimensional orientation to each site, we preferentially integrate out
stiff degrees of freedom (bond lengths and angles, as well as dihedral angles
in rings) that are accurately approximated by their average values, while
retaining soft degrees of freedom (unconstrained dihedral angles) mostly
responsible for conformational variability. We demonstrate that our scheme
retains nearly atomistic resolution by mapping all experimental protein
configurations in the Protein Data Bank onto coarse-grained configurations,
then analytically backmapping those configurations back to all-atom
configurations. This roundtrip mapping throws away all information associated
with the eliminated (stiff) degrees of freedom except for their average values,
which we use to construct optimal backmapping functions. Despite the 4:1
reduction in the number of degrees of freedom, we find that heavy atoms move
only 0.051 angstroms on average during the roundtrip mapping, while hydrogens
move 0.179 angstroms on average, an unprecedented combination of efficiency and
accuracy among coarse-grained protein models. We discuss the advantages of such
a high-resolution model for parameterizing effective interactions and
accurately calculating observables through direct or multiscale simulations.
