Protein folding funnels: the nature of the transition state ensemble.

BACKGROUND

Energy landscape theory predicts that the folding funnel for a small fast-folding alpha-helical protein will have a transition state half-way to the native state. Estimates of the position of the transition state along an appropriate reaction coordinate can be obtained from linear free energy relationships observed for folding and unfolding rate constants as a function of denaturant concentration. The experimental results of Huang and Oas for lambda repressor, Fersht and collaborators for C12, and Gray and collaborators for cytochrome c indicate a free energy barrier midway between the folded and unfolded regions. This barrier arises from an entropic bottleneck for the folding process.

RESULTS

In keeping with the experimental results, lattice simulations based on the folding funnel description show that the transition state is not just a single conformation, but rather an ensemble of a relatively large number of configurations that can be described by specific values of one or a few order parameters (e.g. the fraction of native contacts). Analysis of this transition state or bottleneck region from our lattice simulations and from atomistic models for small alpha-helical proteins by Boczko and Brooks indicates a broad distribution for native contact participation in the transition state ensemble centered around 50%. Importantly, however, the lattice-simulated transition state ensemble does include some particularly hot contacts, as seen in the experiments, which have been termed by others a folding nucleus.

CONCLUSIONS

Linear free energy relations provide a crude spectroscopy of the transition state, allowing us to infer the values of a reaction coordinate based on the fraction of native contacts. This bottleneck may be thought of as a collection of delocalized nuclei where different native contacts will have different degrees of participation. The agreement between the experimental results and the theoretical predictions provides strong support for the landscape analysis.