Rate of beta-structure formation in polypeptides.

An explanation is suggested for why a marginally stable beta-structure folds extremely slowly; it is predicted that even a small increase in stability drastically accelerates beta-folding. According to the theory, this folding is a first-order phase transition, and the rate-limiting step is nucleation. The rate-determining "nucleus" (transition state) is the smallest beta-sheet that is sufficiently large to provide an overall free energy reduction during subsequent folding. If the stability of the beta-structure is low, the nucleus is large and possesses a high free energy due to having a large perimeter. When the net stability of the final beta-structure increases (due to either an increase of the beta-sheet stability or a decrease in stability of the competing structures, e.g., alpha-helices), the size and energy of a nucleus decrease and the rate of folding increases exponentially. This must result in a fast folding of polypeptides enriched by beta-forming residues (e.g., protein chains). The theory is developed for intramolecular beta-structure, but it can also explain the overall features of intermolecular beta-folding; it is applicable both to antiparallel and parallel beta-sheets. The difference in folding of beta-sheets, alpha-helices, and proteins is discussed.