  Coarse-graining is a powerful tool for extending the reach of dynamic models
of proteins and other biological macromolecules. Topological coarse-graining,
in which biomolecules or sets thereof are represented via graph structures, is
a particularly useful way of obtaining highly compressed representations of
molecular structure, and simulations operating via such representations can
achieve substantial computational savings. A drawback of coarse-graining,
however, is the loss of atomistic detail - an effect that is especially acute
for topological representations such as protein structure networks (PSNs).
Here, we introduce an approach based on a combination of machine learning and
physically-guided refinement for inferring atomic coordinates from PSNs. This
"neural upscaling" procedure exploits the constraints implied by PSNs on
possible configurations, as well as differences in the likelihood of observing
different configurations with the same PSN. Using a 1 $\mu$s atomistic
molecular dynamics trajectory of A$\beta_{1-40}$, we show that neural upscaling
is able to effectively recapitulate detailed structural information for
intrinsically disordered proteins, being particularly successful in recovering
features such as transient secondary structure. These results suggest that
scalable network-based models for protein structure and dynamics may be used in
settings where atomistic detail is desired, with upscaling employed to impute
atomic coordinates from PSNs.
