LINKED FUNCTIONS IN ALLOSTERIC PROTEINS - EXACT THEORY FOR THE EFFECT OF ORGANIC-PHOSPHATES ON OXYGEN-AFFINITY OF HEMOGLOBIN

A new thermodynamic analysis has been developed for the linkage between binding of two ligands (e.g., oxygen and organic phosphate) to a nondissociating macromolecule (e.g., hemoglobin tetramer). The theory relates the median (X) of an oxygenation curve, measured in the presence of organic phosphate, to any three of the following equilibrium constants: (for binding four oxygens onto the tetramer in the absence of organic phosphate), KD4 (for binding four oxygens onto the tetramer under saturating amounts of organic phosphate), °KD (for binding organic phosphate onto unliganded tetramers), and 4KD (for binding organic phosphate onto fully oxygenated tetramers). In contrast with previous linkage theories [cf. Wyman, J. (1964) Adv. Protein Chem. 19, 223-286], the present development relates observable properties of binding isotherms for one ligand to the total concentrations of the second ligand, and of the macromolecule. In most experimental situations it is the total concentration of the second ligand which is known, whereas the concentration of its free (i.e., unbound) form is not accessible. In the case of human hemoglobin, the new theory opens up the possibility of carrying out interpretable experiments in previously inaccessible regions of the experimental variables where the concentrations of hemoglobin-phosphate complexes and unbound phosphate are of comparable magnitude. Some illustrative applications are presented, and the ranges of validity of the earlier approximate theories have been evaluated. The new theory is found especially pertinent to allosteric systems where binding of an effector molecule occurs with high affinity such as with inositol hexaphosphate binding to human hemoglobin. The theoretical approach employed in this work is general and can be applied to linked binding systems other than hemoglobin. Some examples are mentioned. The relationship of this work to the corresponding theory for subunit polymerization [Ackers, G. K., & Halvorson, H. R. (1974) Proc. Natl. Acad. Sci. U.S.A. 71, 4312-4316; Johnson, M. L., Halvorson, H. R., & Ackers, G. K. (1976) Biochemistry 15, 5363-5371] is discussed, and it is shown how the approach can also be extended to cases of ligand binding linked with conformational equilibria. © 1979, American Chemical Society. All rights reserved.