text: In cooperativity, the initial ligand binding affects the host's affinity for subsequent ligands. In positive cooperativity, the first binding event enhances the affinity of the host for another ligand. Examples of positive and negative cooperativity are hemoglobin and aspartate receptor, respectively.
  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: . 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
  where:
  : = free energy of binding A
  : = free energy of binding B
  : = free energy of binding for A and B tethered
  : = sum of the free energies of binding
  It is considered that if  more than the sum of  and , it is positively cooperative. If  is less, then it is negatively cooperative.
  Host–guest chemistry is not limited to receptor-lingand interactions. It is also demonstrated in ion-pairing systems. Such interactions are studied in an aqueous media utilizing synthetic organometallic hosts and organic guest molecules. For example, a poly-cationic receptor containing copper (the host) is coordinated with molecules such as tetracarboxylates, tricarballate, aspartate, and acetate (the guests). This study illustrates that entropy rather than enthalpy determines the binding energy of the system leading to negative cooperativity. The large change in entropy originates from the displacement of solvent molecules surrounding the ligand and the receptor. When multiple acetates bind to the receptor, it releases more water molecules to the environment than a tetracarboxylate. This led to a decrease in free energy implying that the system is cooperating negatively. In a similar study, utilizing guanidinium and Cu(II) and polycarboxylate guests, it is demonstrated that positive cooperatively is largely determined by enthalpy. In addition to thermodynamic studies, host–guest chemistry also has biological applications.