  Atomistic force fields that are tuned to describe folded proteins predict
overly compact structures for intrinsically disordered proteins (IDPs). To
correct this, improvements in force fields to better model IDPs are usually
paired with scattering models for validation against experiments. For
scattering calculations, protein configurations from all-atom simulations are
used within the continuum-solvent model CRYSOL for comparison with experiments.
To check this approach, we develop an equation to evaluate the radius of
gyration (Rg) for any defined inner-hydration shell thickness given all-atom
simulation data. Rg based on an explicit description of hydration waters
compares well with the reference value of Rg obtained using Guinier analysis of
the all-atom scattering model. However, these internally consistent estimates
disagree with Rg from CRYSOL for the same definition of the inner-shell. CRYSOL
can over-predict Rg by up to 2.5 Angstroms. We rationalize the reason for this
behavior and highlight the consequences for force field design.
