  Recent studies attracted the attention on the inherent structure landscape
(ISL) approach as a reduced description of proteins allowing to map their full
thermodynamic properties. However, the analysis has been so far limited to a
single topology of a two-state folding protein, and the simplifying assumptions
of the method have not been examined. In this work, we construct the
thermodynamics of four two-state folding proteins of different sizes and
secondary structure by MD simulations using the ISL method, and critically
examine possible limitations of the method. Our results show that the ISL
approach correctly describes the thermodynamics function, such as the specific
heat, on a qualitative level. Using both analytical and numerical methods, we
show that some quantitative limitations cannot be overcome with enhanced
sampling or the inclusion of harmonic corrections.
