Lysozyme-lysozyme interactions in under- and super-saturated solutions: a simple relation between the second virial coefficients in H2O and D2O

A study of lysozyme-lysozyme interactions by small angle neutron scattering (SANS) as a function of temperature in D2O and in H2O is presented. The interactions are analysed in terms of second virial coefficient. The most remarkable result is that the difference between the temperature dependencies of this quantity in D2O and H2O seems similar to the one we have previously observed for lysozyme solubility in these two solvents. These physicochemical quantities in D2O, the second virial coefficient and solubility, are indeed shifted by approximately 7.2 degrees C relatively to the ones in H2O. This temperature shift, 7.2 degrees C, corresponds to the difference of the temperatures of maximum density of H2O (4 degrees C) and D2O (11.2 degrees C). The interactions are modelled by the DLVO potential, which includes an attractive van der Waals component, proportional to the Hamaker constant A(H) and a repulsive screened electrostatic term, proportional to the net charge of the protein Z(p). The attractive component seems to phenomenologically account for effects due to the water structure, as the Hamaker constant A(H) also appears to be shifted by about 7.2 degrees C.