Thermal and Chemical Unfolding of Lysozyme. Multistate Zimm-Bragg Theory Versus Two-State Model

Thermal and chemical unfolding of lysozyme in the presence of the guanidine HCl denaturant is a model system to compare the conventional two-state model of protein unfolding with the multistate Zimm-Bragg theory. The two-state model is shown to be the noncooperative limit of the Zimm-Bragg theory. In particular, the Zimm-Bragg theory provides a molecular interpretation of the empirical linear extrapolation method (LEM) of the two-state model. Differential scanning calorimetry (DSC) experiments reported in the literature are analyzed with both methods. Lysozyme unfolding is associated with a large endothermic enthalpy that decreases significantly upon addition of guanidine HCl. In contrast, the Gibbs free energy of unfolding is small, negative, and independent of the guanidine HCl concentration, contradicting, in part, the conclusions of the LEM. The unfolding enthalpy is compensated by an even larger entropy term. The multistate Zimm-Bragg theory predicts a larger conformational enthalpy and a smaller Gibbs free energy than the two-state model. The Zimm-Bragg theory provides the protein cooperativity parameter, the average length of independently folding protein domains, and the Gibbs free energy of unfolding of individual amino acid residues. Guanidine HCl binding to lysozyme is exothermic and counteracts the endothermic unfolding enthalpy. The number of bound denaturant molecules is determined from the decrease in enthalpy and is extrapolated to the guanidine HCl-to-amino acid stoichiometry at complete lysozyme unfolding. Chemical unfolding isotherms measured with circular dichroism (CD) spectroscopy are analyzed with both models. The chemical Zimm-Bragg theory is a cooperative molecular model, yielding the guanidine HCl binding constant and the protein cooperativity parameter. It allows a quantitative comparison between thermal and chemical protein unfolding. The two reactions have almost identical changes in Gibbs free energy. However, thermal unfolding is significantly more cooperative than chemical unfolding. Finally, distinct differences are observed in thermal unfolding between DSC and CD spectroscopy.