Folding mechanisms of individual $β$-hairpins in a Gō model of Pin1 WW domain by all-atom molecular dynamics simulations

This paper examines the folding mechanism of an individual $β$-hairpin in the presence of other hairpins by using an off-lattice model of a small triple-stranded antiparallel $β$-sheet protein, Pin1 WW domain. The turn zipper model and the hydrophobic collapse model originally developed for a single $β$-hairpin in literature is confirmed to be useful in describing $β$-hairpins in model Pin1 WW domain. We find that the mechanism for folding a specific hairpin is independent of whether it folds first or second, but the formation process are significantly dependent on temperature. More specifically, $β1-β2$ hairpin folds via the turn zipper model at a low temperature and the hydrophobic collapse model at a high temperature, while the folding of $β2-β3$ hairpin follows the turn zipper model at both temperatures. The change in folding mechanisms is interpreted by the interplay between contact stability (enthalpy) and loop lengths (entropy), the effect of which is temperature dependent.