Transport of oxygen in solutions of hemoglobin and myoglobin

Abstract

A method to solve numerically the diffusion-reaction equations that describe the steady state transport of oxygen through solutions of hemoglobin and myoglobin is presented. The method has a rather general range of applicability; in particular, it does not depend on the assumption of near chemical equilibrium. In the first part of the paper the chemical kinetics are described by the single step reaction P + X ⇌ PX. The nature of the method allows for its extension to more complex situations. In the latter part of the paper, it is extended to take into account the cooperative properties induced by the four step reaction (Adair) of the hemoglobin-oxygen chemical kinetics. The method will be extended in reports forthcoming to include the nonhomogeneous spatial parameters as they occur in the striated muscle. An analysis of the available experimental information is presented here. The results confirm those from previous analysis that the experimental facilitated transport of oxygen can be accounted for by the simultaneous diffusion of oxygen, the protein, and the oxygen-protein compound plus their chemical interaction. The magnitude of the facilitated transport of oxygen for the model that includes the cooperative properties of hemoglobin is compared with the one for the model associated with the single step reaction. Some features contained in the former, that are not available in the single step model, are shown to favor the facilitated transport. The results for hemoglobin as it occurs in the red cells make it plausible that facilitation may contribute to the transport of oxygen in the red cell inside the systemic capillaries.