Chemical Protein Unfolding - A Simple Cooperative Model

Chemical unfolding with guanidineHCl or urea is a common method to study the conformational stability of proteins. The analysis of unfolding isotherms is usually performed with an empirical linear extrapolation method (LEM). A large positive free energy is assigned to the native protein, which is usually considered to be a minimum of the free energy. The method thus contradicts common expectations. Here, we present a multistate cooperative model that addresses specifically the binding of the denaturant to the protein and the cooperativity of the protein unfolding equilibrium. The model is based on a molecular statistical-mechanical partition function of the ensemble, but simple solutions for the calculation of the binding isotherm and the associated free energy are presented. The model is applied to 23 published unfolding isotherms of small and large proteins. For a given denaturant, the binding constant depends on temperature and pH but shows little protein specificity. Chemical unfolding is less cooperative than thermal unfolding. The cooperativity parameter σ is at least 2 orders of magnitude larger than that of thermal unfolding. The multistate cooperative model predicts zero free energy for the native protein, which becomes strongly negative beyond the midpoint concentration of unfolding. The free energy to unfold a cooperative unit corresponds exactly to the diffusive energy of the denaturant concentration gradient necessary for unfolding. The temperature dependence of unfolding isotherms yields the denaturant-induced unfolding entropy and, in turn, the unfolding enthalpy. The multistate cooperative model provides molecular insight and is as simple to apply as the LEM but avoids the conceptual difficulties of the latter.