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 (T-f) transition temperatures. For our model, the typical time scale for reaching the unique native conformation is shown to scale as tau(f) similar to exp[sigma/sigma(0)]. We argue that T-f scales linearly with the inverse of entropy of low-energy non-native states, whereas T-theta is almost independent of it. As sigma-->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, sigma can be used to predict sequences that fold rapidly.