Thermodynamic strategies for stabilizing intermediate states of proteins

This paper presents three theorems pertaining to thermodynamic properties of the intermediate (e.g., molten globule) state of proteins exhibiting such a conformation in the presence of GuHCl or urea. The theorems are proved for the three-state case using the denaturant binding model and the linear extrapolation model; their utility is illustrated via applications to examples in the literature. Theorem One states that the denaturant activity that maximizes the population of a partly folded conformation is at any temperature independent of the Gibbs free energy difference between the intermediate and native states. This result holds for both models of protein-denaturant interaction. The second theorem claims that the population maximum is independent of the denaturant association constant for the denaturant binding model. Theorem Three, which also applies to both models considered here, states that at the temperatures corresponding to the extrema in the population of the intermediate, the enthalpy change of the intermediate is equal to the excess enthalpy function, an experimentally accessible quantity. In the absence of denaturant, the enthalpy change of the intermediate state at the population extrema can be written as a function of the thermodynamic parameters of the unfolded state alone. These results, which can be applied to systems of any number of states under certain conditions, should aid in the optimization of conditions employed for experimental studies of partly organized states of proteins.