Quantitative Analysis of Nonequilibrium, Denaturant-Dependent Protein Folding Transitions

The free energy of folding of small, one-domain proteins is generally measured with denaturant-induced unfolding/refolding equilibria based on the two-state model of protein folding. There is however an increasing number of reports on proteins that do not attain their folding equilibrium and show, even after long-term incubation, unfolding transitions at high and refolding transitions at low denaturant concentrations. We present a theory for the quantitative description of this nonequilibrium behavior in protein folding, which is exclusively based on the two-state assumption and the exponential dependence of the rate constants of unfolding and refolding on denaturant concentration. Using a hyperstable variant of a pilin domain from E. coli type 1 pili that does not reach its folding equilibrium within several years, we demonstrate that the method provides reliable information on the free energy of folding, the solvent accessibility of the transition state of folding relative to the native and unfolded state, and the rate constants of unfolding and refolding in the absence of denaturant.