Half-site reactivity, negative cooperativity, and positive cooperativity: quantitative considerations of a plausible model.

The nature of cooperative allosteric interactions has been the source of controversy since the ground-breaking studies of oxygen binding to hemoglobin. Until recently, quantitative examples of a model based on the inherent symmetry and asymmetry of oligomeric proteins have been lacking. This laboratory has used the phenolic ligand binding characteristics of the insulin hexamer to develop the first quantitative model for a symmetry-asymmetry-based cooperativity mechanism. The insulin hexamer possesses positive and negative heterotropic and homotropic interactions involving two classes of sites. In this study, we explore the effects of heterotropic interactions between these sites. We show that application of the pairwise structural asymmetry theory of Seydoux, Malhotra, and Bernhard (SMB) gives excellent agreement between the ligand binding behavior and X-ray crystal structure data. Furthermore, by comparing experimental data with computer simulations, we show that the insulin hexamer can be described by a three-state SMB model involving two positive homotropic cooperative transitions linked by a negative homotropic interaction. The first transition, T3T3' right harpoon over left harpoon T3oR3o, with allosteric constant LoA = [T3T3']/[T3oR3o] and ligand dissociation constant KRo consists of a positive cooperative change from high to low symmetry that results in "half-site reactivity". The second transition, T3oR3o right harpoon over left harpoon R3R3', with allosteric constant LoB = [T3oR3o]/[R3R3'] and ligand dissociation constant KR is a change from low to high symmetry, which is also a positive cooperative process. Treatment of the two transitions as concerted and interconnected processes allows derivation of an equation for the fraction of R-state. Using this equation, the effects of changes in the four physical parameters, LoA, LoB, KR, and KRo, on the ligand binding properties of the insulin hexamer are quantitatively described.