J. Mol. Biol. (1974) 82, 231-265


A General Approach to Co-operativity and its Application to the Oxygen Equilibrium of Hemoglobin and its Effectors


Harvard-M.I. T. Program in Health Sciences and Technology,

Department of Chemistry, and Department of Physics

Massachusetts Institute of Technology

Cambridge, Mass. 02139, U.S.A.

(Received 12 June 1972, and in revised form 14 May 1973)

A general model of co-operativity is developed and solved explicitly; it combines the concepts of preferential binding and quaternary constraints (due to Monod, Wyman & Changeux), nearest -neighbor subunit interactions (due to Koshland), and changes in subunit aggregation (due to Briehl). For this reason, the general model can explain systems which previous models cannot – e.g. the model of Monod, Wyman & Changeux cannot explain negative co-operativity, the model of Koshland cannot treat situations where quaternary conformation is observed to be coupled to ligand binding, and the model of Briehl cannot explain co-operativity when no change in the level of subunit aggregation occurs. This general model of co-operativity reduces in special limits to these previous models. Still another limiting case corresponds to the Perutz description of hemoglobin, a "mixed" system thought to exhibit characteristics of several previous models.

Four distinct types of effector are defined and incorporated in the model. By calculating binding curves, and explicitly comparing them with experimental data concerning the inhibition of hemoglobin oxygenation by 2,3-diphosphoglycerate (P2GIyc), one finds: (a) that P2GIyc binding not only stabilizes the deoxy quaternary conformation of hemoglobin but also increases the strength of molecular (i.e. quaternary) constraints; (b) that the oxygen binding affinity is higher for the subunits than for the subunits but that the and subunits are practically equivalent with respect to the P2GIyc binding equilibrium and molecular constraints; (c) that the quaternary conformation changes from the deoxy to the oxy form at about the third oxygenation, depending only slightly on P2GIyc concentration; (d) that the detailed dependence of the four Adair parameter's and of the apparent free energy of interaction on the free P2GIyc concentration can be easily calculated; and (e) that the model describes biphasic oxygenation curves very well and can explain the dependence of the Hill coefficient, nH, on P2GIyc concentration, on pH, and on ionic strength.

The model is also used to describe the dependence of the oxygen equilibrium on hemoglobin concentration for very dilute solutions of HbA (normal adult hemoglobin) and for lamprey hemoglobin. It is found that oxygenated HbA dissociates more readily than deoxygenated HbA, primarily because the dimer has a very high oxygen affinity; the fact that the stability of the oxy quaternary conformation of the tetramer is somewhat lower than that of the deoxy quaternary conformation is relatively unimportant. For lamprey hemoglobin it is found that there is some tetramer present but one cannot tell whether the tetramer is co-operative like the HbA tetramer.

The model is finally applied to dimeric mollusc myoglobin, in order to try to determine the mechanism of co-operativity in this system from the temperature dependence of the oxygen equilibrium. This attempt proved unsuccessful in the temperature range of the data available.