Ionization of clusters. IV. Cooperativity and allosterism derived from shared clusters in macromolecules

Clusters of ionizable groups are examined for conditions that develop cooperativity (1) on the binding of protons, and (2) on the binding of an associated ligand when the clusters are shared between domains or subunits in macromolecules. Cooperative binding isotherms for protons have long been observed (but not emphasized as cooperative binding) when studies have been done on clusters for the evaluation of metal ion complexation [A. E. Martell & M. Calvin (1952) Chemistry of the Metal Chelate Compounds, Prentice-Hall, Englewood Cliffs, New Jersey]. Reactions are formulated in this paper to show that anions, chelating to positively charged clusters, are also capable of developing the cooperative binding of protons. Extension of these simple reactions to those where clusters of ionizable groups are shared between domains of macromolecules provides models for cooperative binding, which include the allosteric, Bohr, anion, and cation effects in proteins.