Before revision:  It is shown by first inferring interactions from protein sequences and then from Monte Carlo samples that the fields and couplings can be well recovered by the group L_1 and the ModAdam method. However, the distribution of evolutionary energies over natural proteins is shifted towards lower energies from that of Monte Carlo samples, indicating that there may be higher-order interactions to favor natural sequences .
After revision:  It is shown by first inferring interactions from protein sequences and then from Monte Carlo samples that the fields and couplings can be well recovered , but that recovering the pairwise correlations in the resolution of a total energy is harder for the natural proteins than for the protein-like sequences. Selective temperature for folding/structural constrains in protein evolution is also estimated .