Tension at the heme: a mathematical treatment of hemoglobin cooperativity

The unique feature of this model is that both the fractional saturation and the free energy change are handled within the framework of the tension-displacement mechanism for hemoglobin co-operativity proposed by Perutz (1970, 1972), i.e. heme iron movement and associated changes in the protein globin internal tension, tau. Physically, tau is the force applied by the protein globin on the proximal histidine, preventing the iron stereochemistry from attaining the geometry preferred in the bound state. It is assumed that a change in position of the heme iron on ligand binding displaces the protein globin proportionately, thereby decreasing tau at neighboring sites; the resulting energy change is assumed to be delocalized throughout the flexible protein globin rather than localized at the heme group per se. The physical interpretation of the model parameters has important implications with regard to data analysis: first, structural data is used to fix the molecular displacements lt and lr; second, jt/jr provides a measure of the protein's intrinsic (i.e. tau = 0) affinity for the bound ligand, and third the set [Ei] is a property of the hemoglobin molecule only and can be determined, in principle, using structural data and optical absorption spectra. The calculated protein globin internal tension in the tense, unbound state (approximately 2 X 10(-5) dyne), determined from the fractional saturation data of Joels & Pugh (1958), is very similar (approximately 3.2 X 10(-5) dyne) to the value estimated by Hopfield (1973) from free energy considerations.