Kinetics of co-operative ligand binding in proteins: the effects of organic phosphates on hemoglobin oxygenation.

A master equation approach to the kinetics of co-operative ligand binding reactions in proteins is developed. As a specific example, equations based on the Perutz description are applied to several reactions of hemoglobin, both in the absence and in the presence of organic phosphates. The observed time dependence of 0, binding to stripped hemoglobin is fitted with a total of four parameters, of which two are held fixed at values determined from the experimentally measured rate constants for the last step of ligand binding. An analysis of Gibson’s data (1970a) for oxygen-binding kinetics of unstripped hemoglobin shows that phosphate binding not only stabilizes the deoxy quaternary conformation of hemoglobin but also increases both the strength of the quaternary conformational constraints and the kinetic time scaling parameter for the deoxy quaternary conformation. A single set of five parameters is used to fit the deoxygenation data of Salhany et al. ( 1970) in the presence of varying concentrations of PzGlyc 8. The five para meters are determined by fitting the theory to the data in the absence of P,Glyc and at a single concentration of P,Glyc. The predictive ability of the model is then tested by using these same parameter values to calculate the curves for intermediate P,Glyc concentrations, and then comparing the predicted curves with experimental data. Whereas deoxygenation data in the presence of PsGlyc can be fitted with the subunits considered as equivalent, we find that E, fl subunit, inequivalence is particularly important in interpreting deoxygenation data in the presence of the inhibitor, IHP. Since the phosphate dependence of the reaction is explicitly included, the model can also describe biphasic deoxygenation, as observed by Gray & Gibson (1971) for the deoxygenation reaction in the presence of IHP. In the deoxygenation reaction, the quaternary conformation is found to change from oxy to deoxy just prior to the release of the second oxygen molecule : the switch occurs somewhat earlier in the presence of organic phosphates. As a consequence of this switch, the release of oxygen lags behind the binding of organic phosphates; the lag is more pronounced for IHP than for P,Glyc. The analogous result of MacQuarrie & Gibson (1972) concerning the lag between the release of HPT and binding of CO is well reproduced; the fractional saturation