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 measure, defined as the ratio of van ’t Hoff and calorimetric enthalpy is related to the degeneracy of the denatured state and describes the number of cooperative units involved in the transition; additionally, it is found that the widely discussed is just the necessary condition to classify the protein as the two-state folder. We also find that , a quantity not limited from above and growing with system size, 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.
Highlights
From the point of view of polymer physics, the folding of a protein is similar to the coil-globule transition of a short polypeptide chain [1]
If there are no finite size effects or heterogeneity, the order parameter at the transition point undergoes an abrupt all-or-none transformation
The situation of the idealized first order phase transition with correlations that extend throughout the system and lead to the discontinuity of the order parameter corresponds to infinite cooperativity and the zero transition interval
Summary
From the point of view of polymer physics, the folding of a protein is similar to the coil-globule transition of a short polypeptide chain [1]. If there are long-range interactions present in the system, the formation of secondary structures can change the effective stiffness of the polypeptide chain, increase stability, and promote the coil-globule transition at equal external conditions. Indirect support for such a mechanism arises from the fact that both the coil-helix transition and protein folding occur at the same interval of external parameters [7]. Using the Taylor expansion cut at first order, it is possible to approximate the order parameter as fDappr with the help of the tangent at the transition point: fD(T)
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