The statistical mechanical theory of the structural transitions of proteins is developed in accordance with the island model by considering the hydrophobic interactions and the entropy factors while connecting the two hydrophobic residues. The proteins treated here are apo-α-lactalbumin (1B9O), lysozyme (1LZ1), ferrocytochrome c (1CYC), cytochrome c (isozyme 1) (1YCC), chymotrypsin inhibitor 2 (2CI2), and ubiquitin (1UBQ). Among them, according to the experiments, 2CI2 and 1UBQ do not exhibit intermediate structures (two-state model), but others do exhibit intermediate structures that are sometimes termed molten globules (three-state model). The theory related to these facts is given in terms of the island model, specifically 1B9O and 1LZ1. The stability or instability of the intermediate structures is explained by the effects of entropy during folding and the amino acid sequence. The intermediate structure is composed of several stable islands, which become unstable during unfolding.
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