A criterion that determines fast folding of proteins: A model study

We consider the statistical mechanics of a full set of two-dimensional protein-like heteropolymers, whose thermodynamics is characterized by the coil-to-globular ($T_\theta$) and the folding (Tf) transition temperatures. For our model, the typical time scale for reaching the unique native conformation is shown to scale as $\tau_{\rm f}\sim \exp[\sigma/\sigma_0]$. We argue that Tf scales linearly with the inverse of entropy of low-energy non-native states, whereas $T_\theta$ is almost independent of it. As $\sigma\rightarrow 0$, non-productive intermediates decrease, and the initial rapid collapse of the protein leads to structures resembling the native state. Based solely on thermodynamic information, σ can be used to predict sequences that fold rapidly