Excess Enthalpies of Mixing in Phospholipid-Additive Membranes

Isothermal titration calorimetry (ITC) allows the measurement of composition-dependent mixing heats of amphiphiles. A number of experimental protocols are now established to measure molecular transfer heats between, for example, micellar and lamellar aggregates. This study deals with the principle understanding of the physical effects contributing to the ITC data. The physical state of the mixture is described in terms of the molar excess enthalpy as a function of its composition hE(X). A relation is derived between this system property and the observable heat per mole of titrant (qobs) as qobs ) (Xsyr X)(∂hE/∂X) + hE(X) hE(Xsyr) with X and Xsyr being the mole fractions of one chosen component within the mixed aggregates in the sample cell and in the injection syringe, respectively. According to this differential equation, one may derive information about the second and further derivatives (i.e., the curvature) of the excess enthalpy function. This can serve to construct the hE(X) plot based on the ITC data. We emphasize that for aggregates mixing nonideally (which must be considered rather the rule than the exception) one has to carefully distinguish between observed mixing heats and enthalpic state of the mixture. The formalism is presented at the example of mixtures of the phospholipid POPC and detergents of the type C12EOn with n ) 3-6. For instance, the system C12EO3/POPC was found to show an extremely asymmetric mixing enthalpy function with an attractive part (i.e., hE < 0) for low and a repulsive one for higher detergent contents in the mixed membranes. Such excess enthalpy functions could be modeled by a polynomial equation and discussed in terms of cooperative interactions between the molecules.