Free energy coupling within macromolecules. The chemical work of ligand binding at the individual sites in co-operative systems.

Individual-site binding curves such as those obtainable from techniques of DNase footprinting or nuclear magnetic resonance spectroscopy can be used to monitor structurally localized events within biopolymers. This paper discusses thermodynamic aspects of individual-site ligand binding for co-operative systems where the binding of ligand at a local site is coupled to binding of the same ligand species at other sites within the macromolecule. Individual-site binding isotherms have the following properties. (1) They provide a direct indication of the role played by the particular site in the overall binding reaction. (2) They can be used to determine the energetic contribution of loading the site regardless of the complexity of the system. (3) They can be used to resolve microscopic equilibrium constants and co-operativity constants in cases where the classical isotherm is incapable of such resolution. The microscopic constants bear a complex relation to the chemical work of loading each individual site. For a system with two interacting sites we derive analytical relationships between the individual-site loading energies and the microscopic constants. These relationships prescribe, for any values of the microscopic constants, how the co-operative energy is partitioned between events at the two sites. At fixed ligand activity the binding free energy can be estimated directly from an individual-site isotherm. This quantity, which is also a composite of the microscopic constants, provides a useful measure of site--site interaction. Several examples and applications are discussed for these properties of individual-site binding reactions.