In recent years, the thermodynamic properties of cooperativity have been studied in order to define mathematical parameters that distinguish positive or negative cooperativity. The traditional Gibbs free energy equation states: formula_85. However, to quantify cooperativity in a host–guest system, the binding energy needs to be considered. The schematic on the right shows the binding of A, binding of B, positive cooperative binding of A–B, and lastly, negative cooperative binding of A–B. Therefore, an alternate form of the Gibbs free energy equation would be