Before revision:  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:  In the preceding manuscript, we analyzed dimensionless free energy changes, \Delta \psi_N (= \Delta G_N / (2N)), -\Delta G_{ND 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.