Hemoglobin-facilitated diffusion of oxygen: Interfacial and thickness effects

The equations of facilitated diffusion were solved numerically for steady state diffusion of oxygen across membranes of hemoglobin and myoglobin. An interfacial resistance was included in the boundary conditions and the dependence of the solutions on membrane thickness and interfacial conductance was studied. The data of Wittenberg on millipore membranes was fitted adequately if a tortuosity factor for the millipore membranes was taken into account. Comparison of the solutions with Wittenberg's data shows that the interfacial conductances must be large, 10-8 mole/cm2-sec-mm Hg or larger. More accurate estimates of interfacial conductance could be obtained from data on thin membranes, 1-5 [mu], but such data are not available. It was found that the concentration profiles are not independent of thickness and that the facilitation decreases as the membrane thickness decreases. The latter occurs even for zero interfacial resistance and hence cannot be attributed to a back pressure effect. The effect is present because the dissociation reaction at the low PO2 boundary increasingly becomes the limiting factor in the establishment of the steady state as L decreases.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/34087/1/0000368.pd

The physiological role of myoglobin: More than a problem in reaction-diffusion kinetics

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/24916/1/0000343.pd

Nonequilibrium facilitated diffusion of oxygen through membranes of aqueous cobaltodihistidine

1. 1. The reversible reaction of oxygen wit colbatodihistidine to from oxy-bis-(cobaltodihistidine) in aqueous solutions was used as a model system to study the characteristics of facilitated diffusion in membranes. The cobaltodihistidine molecule served as the model carrier species, and the unequal diffusivities of the two carrier forms as well as a two-step reaction mechanism added a degree of complexity not treated in previous studies.2. 2. Facilitation of the oxygen flux through the membrane increased with oxygen gradients but also showed saturation effects at high oxygen partial pressures. Facilitation was proportional to (membrane thickness)-0.92 in the range of 50-280 [mu], adn to total carrier concentration up to 0.030 M cobaltohistidine. There was no further increase in facilitation at higher carrier concentration because of the solubility limit for cobaltohistidine. Facilitation increased with temperature and showed an apparent activation energy of 4.44 kcal/mole. Maximum facilitation was found in a pH region near neutrality.3. 3. The facilitated fluxes were about one-third of the magnitude predicted by a simple model which assumes chemical equilibrium throughout the film but could be accurately predicted by a complete model which allows for a finite reaction rate within the membrane. The correct equations and boundary conditions for both the equilibrium and nonequilibrium models are delineated, as well as numerical techniques for obtaining solutions. The total carrier concentration, free plus complexed, is not necessarily uniform throughout each position in the membrane, but the integrated carrier concentration profile across the membrane is a constant.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/32719/1/0000086.pd

Models of lon and substrate cotransport and the effect of the membrane potential

The implications of a carrier model of ion and substrate cotransport are worked out. Each carrier is assumed to have one ion and one substrate binding site. The model includes features that have not been included in previously published models. These features are the effect of the membrane potential and of the assumption that all carrier forms, with or without bound substrate and with or without various bound ions, can cross the membrane. The model is of a two-state (gate-type) carrier with transition rate constants. In one state the carrier interacts with outer bulk phase; in the other state it interacts with the inner bulk phase. Equilibrium in the reactions between ion, substrate, and carrier is assumed at each surface.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/34163/1/0000451.pd

Numerical study of oxygen uptake by layers of hemoglobin solution

Numerical solutions have been obtained for the equations describing O2 uptake by layers of concentrated hemoglobin solution 0.25, 0.5, 1, 1.6, 2, 3.6, 5, 10, and 20 [mu] thick. The results indicate that the diffusion of oxyhemoglobin has almost no effect on the rate of oxygenation of the 0.25 [mu] layer, but its influence increases with increasing layer thickness, so that it shortens the time required to reach 50% saturation in the 1.6 [mu] layer by 23 % and in the 5[mu] layer by 34%. For the 1.6 [mu] layer, which might be considered a model red blood cell, the results suggest that the rate at which O2 reacts with hemoglobin is of primary importance early in the uptake process, but that later the diffusion of O2 into the deeper parts of the layer becomes rate-limiting.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/32682/1/0000049.pd