Parametrization of Multiple Pathways in Proteins: Fast Folding versus Tight Transitions

Growing experimental evidence shows that proteins follow one or a few distinct paths when folding. We propose in this paper a procedure to parametrize these observed pathways, and from this parametrization construct effective Hamiltonians for the proteins. We furthermore study the denaturated-native transitions for a wide class of possible effective Hamiltonians based on this scheme, and find that the sharpness (tightness) of the transitions typically are close to their theoretical maximum and thus in quantitative accordance with the sharp folding transition observed for single domain proteins. Finally we demonstrate that realistic folding times are typical for the proposed class of Hamiltonians, and we discuss the implication of the predicted entropy barriers on the temperature dependence of the folding times.