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Thermal and Chemical Unfolding of Lysozyme. Multistate Zimm-Bragg Theory versus 2-State Model.

Thermal and chemical unfolding of lysozyme in the presence of guanidineHCl denaturant is a model system to compare the conventional 2-state model of protein unfolding with the multi-state Zimm-Bragg theory. The 2-state model is shown to be the non-cooperative 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 2-state model. Differential scanning calorimetry (DSC) experiments reported in the literature are analysed with both methods. Lysozyme unfolding is associated with a large endothermic enthalpy that decreases significantly upon addition of guanidineHCl. In contrast, the Gibbs free energy of unfolding is small, negative and independent of the guanidineHCl 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 2-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. GuanidineHCl 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 guanidineHCl-to-amino acid stoichiometry at complete lysozyme unfolding. Chemical unfolding isotherms measured with CD spectroscopy are analyzed with both models. The chemical Zimm-Bragg theory is a cooperative molecular model yielding the guanidineHCl 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.