MOLECULAR THERMODYNAMICS OF THE DENATURATION OF LYSOZYME

The macromolecular system where denaturation takes place, is considere d from a molecular thermodynamic point of view as a convolution of a g rand canonical ensemble, gce and a canonical ensemble ce. The former c orresponds to the solute, the latter to the solvent. The properties of this system can be represented by a convoluted partition function obt ained by the product of a grand canonical partition function Z(N), and a canonical partition function, zeta(W). If the experimental equilibr ium 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-d en should be obtained which are a linear function of the absolute temp erature. The slope of the straight line Delta H-den = f(T) is dependen t upon n(W). The experimental equilibrium constant conforms to the mod el. The apparent isobaric heat capacity, C-p,C-app of the solute is ca lculated 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 exper iments, the apparent isobaric heat capacity yields the apparent enthal py Delta H-den of the denaturation process. The enthalpy thus calculat ed Delta H-den should be a linear function of the denaturation tempera ture T-m in agreement with the denaturation enthalpy obtained by deriv ing the logarithm of the denaturation equilibrium constant. In fact, t he 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 re action 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 chan ging 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 depen dence 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 ent halpy 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 w ater molecules. The difference in the number of water molecules is rel ated to the different size of the macromolecules and probably to the p roportional number of hydrophobic residues. The number of water molecu les changes with different substituents. Mutants of wild lysozyme appe ar to involve n(W) = 131.4 and 139.8 for T157A and R96H, respectively. These numbers are in agreement with the increased hydrophobic charact er of the entering groups. The process seems to be related to the form ation of a cage of water molecules around the denatured protein.