Scheme 1.

Thermodynamic cycles for unfolding. A. The well-known thermodynamic cycle relating two states, native (N) and unfolded (U), at two denaturant concentrations D (top) and D′ (bottom). We use the notation U and U′ for the unfolded state at the two concentrations, to stress that in fact a different ensemble of conformations is sampled in each. Thus, the transfer energy $\mathrm{\Delta }{G}_U^{tr}$ is composed of the enthalpy of transfer and the change in the conformational entropy of the unfolded state ensemble. B. For the calculation of the free energy of collapse, we introduce a new reference state, which is designated the maximally compact denatured state (C). Notice that in general this state does not equal the unfolded state at zero D.