The finite size effects and the two-state paradigm of protein folding

The coil to globule transition of the polypeptide chain is the physical phenomenon behind the folding of globular proteins. Globular proteins with a single domain usually consist of about 30 to 100 amino acid residues, and this finite size extends the transition interval of the coil-globule phase transition. Based on the pedantic derivation of the two-state model, we introduce the number of amino acid residues of a polypeptide chain as a parameter in the expressions for two cooperativity measures and reveal their physical significance. We conclude that the $k_2$ measure, related to the degeneracy of the denatured state, describes the number of cooperative units involved in the transition; additionally is found that the famous condition $k_2=1$ is just the necessary condition to classify the protein as the two-state folder. We also find that $\Omega_c$ is simply proportional to the square of the transition interval. This fact allows us to perform the classical size scaling analysis of the coil-globule phase transition. Moreover, these two measures are shown to describe different characteristics of protein folding.