The macromolecular system where denaturation takes place, is considered from a molecular thermodynamic point of view as a convolution of a grand canonical ensemble, gce and a canonical ensemble ce. The former corresponds to the solute, the latter to the solvent. The properties of this system can be represented by a convoluted partition function obtained by the product of a grand canonical partition function Z(N), and a canonical partition function, zeta(W). If the experimental equilibrium constant, K-den = [D-hyd]/[N] is substituted for Z(N) and [W](nW) for zeta(W), the convoluted partition function is K-0 = K-den [W](nW), where [W] is the concentration of the solvent in the bulk and n(W) is the number of water molecules involved in the reaction. According to this model, by calculating the derivative partial derivative In K-den/partial derivative(1/T), values of the denaturation enthalpy Delta H-den should be obtained which are a linear function of the absolute temperature. The slope of the straight line Delta H-den = f(T) is dependent upon n(W). The experimental equilibrium constant conforms to the model. The apparent isobaric heat capacity, C-p,C-app of the solute is calculated by double mixed derivation of In Z(N) with respect to In[W](-nW) and In T. By integration between two temperatures, as in DSC experiments, the apparent isobaric heat capacity yields the apparent enthalpy Delta H-den of the denaturation process. The enthalpy thus calculated Delta H-den should be a linear function of the denaturation temperature T-m in agreement with the denaturation enthalpy obtained by deriving the logarithm of the denaturation equilibrium constant. In fact, the heat supplied is comprehensive of the enthalpy due to the change of the conformation of the protein from native to denatured Delta H-conf, of the hydration enthalpy, Delta H-hyd, and of a term, n(W)C(p,W) T-m, due to the heat absorbed by n(W) water molecules involved in the reaction Delta H-den = Delta H-conf + Delta H-hyd + n(W) C-p,C-W T-m The hen egg white lysozyme (mol. wt. 14 100 Da) changes the denaturation enthalpy, and correspondingly the denaturation temperature T-m by changing the pH or the concentration of denaturant. The influence of pH is related to changes in the structure of the solvent rather than to an actual reaction process. In accordance with this hypothesis, the dependence of the denaturation enthalpy either from In T or from pH or from denaturant concentration follows the same law. Values of Delta H-den for hen egg white lysozyme plotted as the function of temperature give a unique straight line with slope corresponding to n(W) = 88.9 water molecules. The same treatment has been applied to the denaturation enthalpy for wild lysozyme of the bacteriophage T4 (mol, wt. 700 Da), as determined in DSC experiments. The slope of line yields n(W) = 122.0 water molecules. The difference in the number of water molecules is related to the different size of the macromolecules and probably to the proportional number of hydrophobic residues. The number of water molecules changes with different substituents. Mutants of wild lysozyme appear to involve n(W) = 131.4 and 139.8 for T157A and R96H, respectively. These numbers are in agreement with the increased hydrophobic character of the entering groups. The process seems to be related to the formation of a cage of water molecules around the denatured protein.
