A Criterion That Determines Fast Folding of Proteins: A Model Study

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We consider the statistical mechanics of a full set of two-dimensional protein-like heteropolymers, whose thermodynamics is characterized by the coil-to-globular (Tθ) and the folding (Tf) transition temperatures. For our model, the typical time scale for reaching the unique native conformation is shown to scale as τf F(M)(σ/σ₀), where σ=1-Tf/Tθ, M is the number of residues, and F(M) scales algebraically with M. We argue that Tf scales linearly with the inverse of entropy of low energy non-native states, whereas Tθ is almost independent of it. As σ→ 0, non-productive intermediates decrease, and the initial rapid collapse of the protein leads to structures resembling the native state. Based solely on accessible information, σ can be used to predict sequences that fold rapidly.