Calorimetrically-derived parameters for protein interactions with urea and guanidine-HCl are not consistent with denaturant m values

A recent study used calorimetric data and a stoichiometric binding model to derive binding constants, enthalpies, and stoichiometries describing the interaction between proteins and the chemical denaturants, urea and guanidine-HCl (Makhatadze and Privalov, J. Mol. Biol., 226 (1992) 491). In the present study, these parameters have been used to calculate the excess free energy, Delta G(ex), associated with interactions between chemical denaturants and the three proteins examined in the calorimetric study: ribonuclease A, cytochrome c, and lysozyme. This free energy and its dependence on denaturant concentration, the denaturant m value, have then been compared to experimental results from chemical denaturation experiments. The magnitudes of m values calculated from the calorimetric studies are significantly greater, 20 to 100%, than the observed values in urea. Calculated m values for guanidine-HCl range from about 10% greater than observed values for cytochrome c to over 100% greater for lysozyme. Discrepancies between calculated and observed m values are probably attributable to incomplete binding isotherms in the calorimetric studies. An additional issue raised in this study concerns the correlation of m values with changes in accessible surface areas upon unfolding. For proteins that undergo a two-state unfolding reaction, experimental m values can vary by more than a factor of two for a given protein, depending on the solution conditions. This observation suggests that factors beyond changes in accessible surface areas play a major role in determining m values.