An analytic model for kinetics of hemoglobin reacting with ligand

The saturation function Y(t) descriptive of the kinetics of ligand binding by a biological macromolecule such as hemoglobin can be represented by Y(t) = Yeq ([1 + epsilon][1-exp-(sigma 1t])/([1 + epsilon]-epsilon exp-(sigma 1t]), where Yeq is the fraction of sites bound at equilibrium, and sigma 1 and epsilon are parameters which can be determined by kinetics measurements. If the sites bind independently, fixed functional relations hold between the quantities (Yeq, sigma 1, epsilon). These relations do not hold for cooperative ligand binding. The departures of these quantities from that required by the independent sites relations provide a measure of cooperativity. The present formulation, which includes the approximation that the multiplicity of chemical relaxation processes are dominated by a single one, can be extended for more refined applications.