Free energy approximations in simple lattice proteins
  This work addresses the question of whether it is possible to define simple pair-wise interaction terms to approximate free energies of proteins or polymers. Rather than ask how reliable a potential of mean force is, one can ask how reliable it could possibly be. In a two-dimensional, infinite lattice model system one can calculate exact free energies by exhaustive enumeration. A series of approximations were fitted to exact results to assess the feasibility and utility of pair-wise free energy terms. Approximating the true free energy with pair-wise interactions gives a poor fit with little transferability between systems of different size. Adding extra artificial terms to the approximation yields better fits, but does not improve the ability to generalise from one system size to another. Further, one cannot distinguish folding from non-folding sequences via the approximated free energies. Most usefully, the methodology shows how one can assess the utility of various terms in lattice protein/polymer models. 
Dirk Reith, Thomas Huber, Florian Mueller-Plathe and Andrew E. Torda