Before revision:  Combining this finding with the knowledge of protein folding, we derive a correspondence between protein fitness and folding free energy, i.e., 4N_e m (1 - 1/(2N)) and -\Delta G_{ND}/k_B T_s  , where \Delta G_{ND} \equiv G_N - G_D, G_N and G_D are the native and denatured free energies, and T_s is the effective temperatureof natural selection.
After revision:  On the other hand, the probability distribution of sequences with maximum entropy that satisfies a given amino acid composition at each site and a given pairwise amino acid frequency at each site pair is a Boltzmann distribution with \exp( - 1/(2N)) and -\Delta G_{ND}/k_B T_s , where \Delta G_{ND} \equiv G_N - G_D, G_N and G_D are the native and denatured free energies, and T_s is the effective temperatureof natural selection.