Nesting: Hierarchies of allosteric ii

A generalization of the allosteric model is presented that incorporates a hierarchy of conformational equilibria. Such a formulation draws upon structural organi- zation already seen in many large macromolecular systems. The functional binding properties of the macromolecule reflect conformational equilibria at each structural level. Appropri- ate "nested" models are used to interpret structural features and functional aspects of two hemocyanin systems with a large number (12 and 24) of binding sites. Structures of large biological macromolecules commonly show a hierarchical organization of subunits, in which a small number of subunits form "building block" assemblies that themselves build up progressively to form the holomole- cule. In proteins the subunits are often well defined as poly- peptide chains. In nucleic acids the subunits could be thought of as the nucleotide residues that are base-paired at one level of structure and chained together and stacked into a helix at a higher level. Macromolecules with these charac- teristics often present a challenge to modeling in terms of function. It is the purpose of this paper to suggest a thermo- dynamic framework for considering functional aspects of such organization. Examples of hierarchy in structural organization are found readily in the oxygen-carrying proteins of arthropods and mollusks, the hemocyanins. In certain hemocyanin mole- cules as many as 160 ligand-binding sites are arranged in highly repetitive structures and substructures (1). An advan- tage of this arrangement in terms of function may be en- hancement of the total cooperativity of ligand binding, aris- ing from the large number of interacting sites; another may be extension of the range of cooperative binding, enabling the macromolecule to operate with different cooperativities in different regions of ligand activity (2). The ligand-binding curves of such molecules are often complex (2-9) and cannot be readily explained by simple models of allosteric interac- tion.