Wyman's equation and oxygen flux through the red cell

Wyman's equation of 1966 describes the facilitation of flux of a reversibly bound substrate such as oxygen, consequent on the translational diffusion of the binding protein (the carrier). While Wyman's equation, or some modification of it such as that by Murray 2, may provide a realistic description of the flux of oxygen through a dilute solution of haemoglobin (see also Wittenburg), it is unlikely to be the complete explanation, nor even the basis, for oxygen transport through the intact red cell. The mature erythrocyte contains approximately 350 g/l haemoglobin, and while this suggests that only 35% of the available water volume is actually occupied by the protein, the remaining 65% is unavailable for protein translational diffusion due to the mutual exclusion of the haemoglobin molecules. For this reason we have examined other possible mechanisms whereby haemoglobin may facilitate the translational diffusion of oxygen within the erythrocyte. Possible alternatives include rotational diffusion by the haemoglobins, intracellular shuffling of haemoglobins due to shape changes by the erythrocyte, and haemoglobin rotations and oxygen exchange consequent on the charge change which accompanies substration and desubstration of the haemoglobin molecule. Finally the dipole interactions are shown to generate significant intermolecular attractions between adjacent haemoglobins.