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. In the preceding manuscript, we analyzed dimensionless free energy changes, \Delta \psi_N (= \Delta G_N /  k_B T_s ), due to single nucleotide mutations, for which the total interaction \psi_N of a sequence was estimated from a multiple sequence alignment . Based on this analyis, we study the equilibrium state of protein stability in a monoclonal approximation, in which protein evolution proceeds with single amino acid substitutions fixed at a time in a population.
After 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 selective temperature. Thus, 4N_e m (1 - 1 / k_B T_s ), due to single nucleotide mutations, for which the total interaction \psi_N of a sequence was estimated from a multiple sequence alignment . Based on this analyis, we study the equilibrium state of protein stability in a monoclonal approximation, in which protein evolution proceeds with single amino acid substitutions fixed at a time in a population.