How Quickly Can a β-Hairpin Fold from Its Transition State?

Understanding the structural nature of the free energy bottleneck(s) encountered in protein folding is essential to elucidating the underlying dynamics and mechanism. For this reason, several techniques, including Phi-value analysis, have previously been developed to infer the structural characteristics of such high free-energy or transition states. Herein we propose that one (or few) appropriately placed backbone and/or side chain cross-linkers, such as disulfides, could be used to populate a thermodynamically accessible conformational state that mimics the folding transition state. Specifically, we test this hypothesis on a model beta-hairpin, Trpzip4, as its folding mechanism has been extensively studied and is well understood. Our results show that cross-linking the two beta-strands near the turn region increases the folding rate by an order of magnitude, to about (500 ns)(-1), whereas cross-linking the termini results in a hyperstable beta-hairpin that has essentially the same folding rate as the uncross-linked peptide. Taken together, these findings suggest that cross-linking is not only a useful strategy to manipulate folding free energy barriers, as shown in other studies, but also, in some cases, it can be used to stabilize a folding transition state analogue and allow for direct assessment of the folding process on the downhill side of the free energy barrier. The calculated free energy landscape of the cross-linked Trpzip4 also supports this picture. An empirical analysis further suggests, when folding of beta-hairpins does not involve a significant free energy barrier, the folding time (tau) follows a power law dependence on the number of hydrogen bonds to be formed (n(H)), namely, tau = tau(0)n(H)(alpha), with tau(0) = 20 ns and alpha = 2.3.