The folding of lattice proteins with single amino acid substitutions was studied using a statistical mechanical model for protein folding. All possible single amino acid substitutions were analyzed for two different native conformations, and two amino acid sequences foldable to the given native conformation were considered for each native conformation. First, the transition temperature change ΔT m(ξ i) with the conformational energy change ΔE(ξ i) caused by the substitution of the amino acid residue type ξ i at the i-th residue was examined. Although both ΔE(ξ i) and ΔT m(ξ i) strongly depend on the amino acid sequence (as a result, these two changes for the two proteins with different amino acid sequences foldable to the same native conformation differ considerably from each other), it is indicated that the correlations between ΔE(ξ i) and ΔT m(ξ i) for the given residue i of the two proteins are mainly determined by their native conformations and are less dependent on their amino acid sequences. We classified the residues into three groups according to the coefficient of regression χ i of ΔT m(ξ i) on ΔE(ξ i), i.e., the susceptibility of the conformational stability to the amino acid substitutions. Some of the residues in two of the three groups, which have clear correlations between ΔE(ξ i) and ΔT m(ξ i) but have different χ i's, are clustered to form domains in the native conformations. The residues in the third group, in which ΔT m(ξ i) is independent of ΔE(ξ i), are located in the loop and terminal regions. Secondly, φ(η, ξ i), which is defined by referring to the Φ value that characterizes the transition state, but into which the progress variable of protein folding η is introduced in this study, was examined for the mutants described above. It is shown that φ(η, ξ i) can reveal the states of individual amino acid residues and characterize their cooperative behaviors not only in the transition state but also at various stages of the folding process.
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