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

TL;DR

This paper investigates how finite size effects influence the two-state model of protein folding, revealing new physical insights and scaling relations for small globular proteins.

Contribution

It introduces the amino acid residue number as a parameter in two-state model measures, clarifies their physical meanings, and performs size scaling analysis of the coil-globule transition.

Findings

The $k_2$ measure indicates the number of cooperative units involved in folding.

The condition $k_2=1$ is necessary for two-state folder classification.

The size scaling analysis relates transition interval to protein size.

Abstract

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.