Dynamics of oxygen unloading from sickle erythrocytes

The objective of this work is to theoretically model oxygen unloading in sickle red cells. This has been done by combining into a single model diffusive transport mechanisms, which have been well-studied for normal red cells, and the hemoglobin polymerization process, which has been previously been studied for deoxyhemoglobin-S solutions and sickle cells in near-equilibrium situations. The resulting model equations allow us to study the important processes of oxygen delivery and polymerization simultaneously. The equations have been solved numerically by a finite-difference technique. The oxygen unloading curve for sickle erythrocytes is biphasic in nature. The rate of unloading depends in a complicated way on (a) the kinetics of hemoglobin S polymerization, (b) the kinetics of hemoglobin deoxygenation, and (c) the diffusive transport of both free oxygen and oxy-hemoglobin. These processes interact. For example, the hemoglobin S polymer interferes with the transport of both free oxygen and unpolymerized oxy-hemoglobin, and this is accounted for in the model by diffusivities which depend on the polymer and solution hemoglobin concentration. Other parameters which influence the interaction of these processes are the concentration of 2,3-diphosphoglycerate and total hemoglobin concentration. By comparing our model predictions for oxygen unloading with simpler predictions based on equilibrium oxygen affinities, we conclude that the relative rate of oxygen unloading of cells with different physical properties cannot be correctly predicted from the equilibrium affinities. To describe the unloading process, a kinetic calculation of the sort we give here is required.