A theoretical search for folding/unfolding nuclei in three-dimensional protein structures

When a protein folds or unfolds, it has to pass through many half-folded mi crostates, Only a few of them can be seen experimentally. In a two-state tr ansition proceeding with no accumulation of metastable intermediates [Fersh t, A. R. (1995) Curr. Opin. Struct. Biol. 5, 79-84], only the semifolded mi crostates corresponding to the transition state can be outlined; they influ ence the folding/unfolding kinetics. Our aim is to calculate them, provided the three-dimensional protein structure is given. The presented approach f ollows from the capillarity theory of protein folding and unfolding [Wolyne s, P. G. (1997) Proc. Natl. Acad. Sci. USA 94, 6170-6175]. The approach is based on a search for free-energy saddle point(s) on a network of protein u nfolding pathways. Under some approximations, this search is rapidly perfor med by dynamic programming and, despite its relative simplicity, gives a go od correlation with experiment. The computed folding nuclei look like ensem bles of those compact and closely packed parts of the three-dimensional nat ive folds that contain a small number of disordered protruding loops. Their estimated free energy is consistent with the rapid (within seconds) foldin g and unfolding of small proteins at the point of thermodynamic equilibrium between the native fold and the coil.