Many proteins interact specifically and directly with ions and small molecules. Binding of such ligands can be the central activity of a protein, or it can modulate the protein’s other activities. Simple one-to-one ligand binding, in which one protein molecule binds one ligand molecule, is relatively straightforward to investigate. The connections between experimentally measurable equilibrium and rate constants and the standard Gibbs free energy of binding are understood and widely applied.

However, in many cases there are multiple ligand binding sites on a single protein molecule, or the protein oligomerizes.  This creates the potential for ligand binding cooperativity, in which binding at one site affects binding at the remainder. Such cooperativity may be crucial for protein function. The best known example is tetrameric haemoglobin, where each subunit possesses a single oxygen binding site. Oxygen binding to haemoglobin is positively cooperative, which enables effective transport of oxygen from lungs to tissue. A related and still more complex problem is the cooperative binding of substrates by oligomeric enzymes.

Quantitating the site-to-site interactions that give rise to ligand binding cooperativity is difficult and is generally done on a case-by-case basis which complicates comparisons between different studies and different proteins. We aim to use classical and statistical thermodynamic theory to develop systematic models which allow quantification of ligand binding cooperativity for proteins with multiple ligand binding sites. These models can be simplified using symmetry and nearest neighbor approximations to reduce the number of model parameters and increase the tractability for fitting to experimental data.