A probabilistic approach to cooperativity of ligand binding by a polyvalent molecule

Cooperativity of ligand binding is defined operationally in terms of the Hill parameter n, whose values uniquely define the shape of the binding curve. When n is everywhere equal to 1 the system behaves as if the sites were all the same and independent. If at any point n is unequal to 1 the system is either cooperative (n > 1) or anticooperative (n < 1) at that point. This means that the binding of ligand at any site is influenced by the presence or absence of ligand at other sites. In the present paper this influence is formulated in terms of probabilities of the various binding events and of conditional probabilities which relate them. The result is a network of linked probabilities which determine the cooperativity or anticooperativity of the system. This probabilistic formulation supplements the more usual one in terms of free energies and places the subject in a broader perspective.