Canonic hemoglobin-oxygen equilibrium: Reassessing the role of cooperativity

Hemoglobin-oxygen equilibrium is normally studied within the grand-canonical ensemble, which assumes that each hemoglobin molecule is immersed in a reservoir of unbound oxygen molecules in the plasma. We show that this assumption is incorrect inside the RBC (red blood cell or erythrocyte), where the hemoglobin concentration is larger than the concentration of unbound oxygen in plasma. We suggest a better model, where a single hemoglobin and a few oxygen molecules around it reach a canonical equilibrium at a fixed volume (determined from the RBC structure) and a fixed temperature. The basic models of hemoglobin-oxygen equilibrium-Pauling's model and the Monod-Wyman-Changeux model-can be reformulated for this canonical situation. They predict cooperative interaction energies that are significantly lower than predictions of the same models in the grand-canonical ensemble. Larger cooperative energies, in particular, those predicted by the grand-canonical ensemble, lead to instabilities (cascade processes) in oxygen release within the canonical approach. Oxygen-binding fluctuations within this approach are sizably smaller than those in the grand-canonical situation. These results suggest that the hopping diffusion of oxygen from one hemoglobin to another may play a role in oxygen diffusion within the RBC.