Isothermal titration calorimetry: application of the gibbs-duhem equation to the study of the relationship between forward and reverse titrations

In this work we rigorously demonstrate that, in dilute solutions, the partial enthalpy of interaction of the ligand can be measured by a forward titration and that the partial enthalpy of interaction of the macromolecule with the ligand can be calculated from the Gibbs-Duhem equation. Using a reverse titration, it is possible to experimentally obtain the partial enthalpy of interaction of the macromolecule and to calculate that of the ligand. Based on this fact, we propose a thermodynamic criterion to experimentally discern when the forward process is equal to or different from the reverse process: they are equal (or different) if the interaction partial enthalpies obtained experimentally are equal to (or different from) those calculated from the Gibbs-Duhem equation. The above criterion is applied to four systems taken from the literature. The first system features the interaction between a bilayer and a surfactant. The second system features a binding interaction with two binding sites that are equivalent and independent. The final two systems feature binding interactions with two non-equivalent binding sites.