Reaction rates of oxygen with hemoglobin measured by non-equilibrium facilitated oxygen diffusion through hemoglobin solutions

The purpose of this study was to verify the concept of non-equilibrium facilitated oxygen diffusion. This work succeeds our previous study, where facilitated oxygen diffusion by hemoglobin was measured at conditions of chemical equilibrium, and which yielded diffusion coefficients of hemoglobin and of oxygen. In the present work chemical non-equilibrium was induced using very thin diffusion layers. As a result, facilitation was decreased as predicted by theory. Thus, this work presents the first experimental demonstration of non-equilibrium facilitated oxygen diffusion. In addition, association and dissociation rate parameters of the reaction between oxygen and bovine and human hemoglobin were calculated and the effect of the homotropic and heterotropic interactions on each rate parameter was demonstrated. The results indicate that the homotropic interaction--which leads to increasing oxygen affinity with increasing oxygenation--is predominantly due to an increase in the association rate. The heterotropic interaction--which leads to decreasing oxygen affinity by anionic ligands--appears to be effected in two ways. Cl- increases the dissociation rate. In contrast, 2,3-diphosphoglycerate decreases the association rate.     

Theory of hemoglobin facilitated oxygen transport

The transport of oxygen in a hemoglobin-saturated medium is theoretically investigated using classical transport theory. It is found that all the chemical complexes can be expressed as a single function of oxygen pressure. A potential difference together with apH shift is predicted to occur across the medium. This research was supported by the United States Public Health Service Training Grant No. 5-T1-GM-833 from the National Institute of General Medical Sciences. This research was supported by a United States Public Health Service Research Career Program Award 5-K6-GM-18,420 from the National Institute of General Medical Sciences.     

Acute oxygen supply by infusion of hemoglobin solutions.

Preparations of 6% human hemoglobin have been investigated for 4 years. While the oxygen dissociation curve is shifted to the left, the hemoglobin solution has been shown to deliver oxygen adequately to the tissues in animal studies. Intracorporeal fate has been investigated by 131-I tagging, and the hemoglobin has not been found to accumulate in the tissues. Intravascular half-life has varied between 1.5 and 3.5 hours.     

A steady-state model of maximal oxygen and carbon dioxide transport in anuran amphibians

A steady-state model, incorporating pulmonary ventilation, pulmonary diffusion capacity, cardiovascular transport capacity, and tissue diffusion capacity, was developed to describe the maximal O2 and CO2 transport capacity for an anuran amphibian (Bufo). Solution of the model by iterative calculation closely predicted 1) the empirical maximal O2 consumption (VO2max) for Bufo, 2) variation in empirical VO2max for three other genera (Rana, Xenopus, Scaphiopus), and the empirically observed effects on VO2max of 3) hypobaric hypoxia, 4) artificially induced anemia, and 5) beta-blockade of heart rate increment with activity. The model indicates that cardiovascular transport is the rate-limiting step to VO2max in amphibians and that an increase in circulatory O2 transport is a major physiological adaptation for increasing total aerobic capacity. CO2 transport and body fluid PCO2 values were primarily determined by pulmonary ventilatory capacity, and to a lesser extent by cardiovascular transport. The model should be generally applicable to other terrestrial vertebrates.     

Analysis of hemoglobin oxygen equilibrium curves. Are unique solutions possible?

As a hemoglobin tetramer is oxygenated, it converts from a form with low ligand affinity to a high-affinity structure. This allosteric transition occurs in partially liganded molecules, typically after two or three ligands are bound. As a result of the co-operative nature of the process, the populations of the partially liganded forms are low. The relative proportions and precise properties of these intermediate substrates are therefore difficult to measure and are subject to controversy. The problem is compounded by compensating effects; for example, over-estimation of the oxygen affinity of triply liganded forms will result in under-estimation of the proportion of these species. Specifically, published values for the oxygen affinity of the triply liganded species vary for identical conditions by a factor of more than 6. In analyses based on the highest affinity values, the triply liganded species virtually disappears. However, this affinity is usually calculated from the last few per cent of the oxygenation curve, and this part of the curve is extremely sensitive to the normalization of the data. We conclude that unique solutions for the ligand affinity and substrate populations may be impossible to achieve, and that unusual mechanisms based on particular combinations of parameters, therefore, should be viewed with caution.     

Ambipolarity condition and possibility of multivalued steady-state solutions to transport equations in stellarators

The possibility of steady-state multivalued solutions to transport equations in stellarators is considered. It is shown that the ambipolarity condition is necessary but not sufficient to find the ambipolar electric field, because the functions entering into it (the plasma density and temperature, as well as their spatial derivatives) depend on the ambipolar field. To do this correctly, it is necessary to solve the full set of time-independent transport equations (including diffusion and heat conduction equations). The possible existence of multivalued solutions to this set of equations is analyzed numerically. It is shown that, under certain conditions that depend on the form and magnitude of particle and heat sources, such solutions can exist. Their form is determined by the initial value of the ambipolar field, the source magnitudes, and the boundary conditions. Discontinuous solutions in which the radial profile of the ambipolar field undergoes jumps are found. In this case, however, the particle and energy fluxes remain continuous, because the discontinuities of the electric field are balanced by the discontinuities of the density and temperature gradients.     

The role of proteins in a dipole model for steady-state ionic transport through biological membranes.

The steady-state current-voltage characteristics of biological membranes are analyzed for means of an application of the electrodiffusion theory to the passage of ions through "dielectric pores", with orientable dipoles at the pore-water interfaces. A detailed evaluation of the electrostatic potential barrier shows, indeed, that the ions have practically no chance to penetrate into the phospholipid bilayer, but that they can cross the membrane through local protein inclusions, of high dielectric constant. A "gating mechanism" can be provided, moreover, by a change of the potential barrier, resulting from a dipole reorientation at the pore-water interface. Dipole-dipole interactions are opposed to the orienting effect of an applied field, but they can be neglected when the separation between the dipoles exceeds a certain critical value. The high polarizability of the pore material leads to an amplification of the effect of an applied field on the orientable dipoles. It is therefore possible to achieve a satisfactory agreement with the experimental results of Gilbert and Ehrenstein (Biophys. J., 9: 447, 1969) for the squid axon, and, in particular, to account for the width of the negative resistance regions with a relatively small value for the length of the orientable dipoles.     

Studies on the “facilitated flux” of oxygen through hemoglobin solutions using a polarographic method

The phenomenon of hemoglobin-facilitated O₂ diffusion was studied by a polarographic method.

Polarograms relative to the reduction process of O₂ have been obtained at pH 7.2 (phosphate buffer, 30°) in the presence of various hemoglobin concentrations (Hb_tot*) and at various O₂ partial pressures (from 8 to 360 mm Hg).

Analogous experiments were performed at pH 6.4 and 8.1 (at constant ionic strength). Graphs of the limiting current values (at E = −1.5 V versus the saturated calomel electrode), relative to the overall reduction process of oxygen, plotted versus P_O2 (at Hb_tot* = constant), show some characteristic trends. The influence of pH on the features of the experimental curves is discussed.

Experimental results suggest that the diffusions of O₂, oxyhemoglobin and hemoglobin, as well as the kinetics of dissociation and association of O₂ with hemoglobin, are effective in determining the “facilitated flux”.

The corresponding nonlinear differential system is solved under some simplifying assumptions, and an expression for the flux, and consequently for the current, is obtained which is consistent with the experimental findings.

Furthermore, it is shown that the dissociation curve of oxyhemoglobin can be obtained from these polarographic experiments on the basis of this theory. Agreement with tensiometric data was satisfactory.