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

Abstract

We consider the statistical mechanics of a full set of two-dimensional protein-like heteropolymers, whose thermodynamics is characterized by the coil-to-globular ($T_θ$) and the folding ($T_f$) transition temperatures. For our model, the typical time scale for reaching the unique native conformation is shown to scale as $τ_f\sim F(M)\exp(σ/σ_0)$, where $σ=1-T_f/T_θ$, $M$ is the number of residues, and $F(M)$ scales algebraically with $M$. We argue that $T_f$ scales linearly with the inverse of entropy of low energy non-native states, whereas $T_θ$ is almost independent of it. As $σ\rightarrow 0$, non-productive intermediates decrease, and the initial rapid collapse of the protein leads to structures resembling the native state. Based solely on {\it accessible} information, $σ$ can be used to predict sequences that fold rapidly.