The facilitated diffusion of oxygen by hemoglobin and myoglobin.

We have clarified the use of Wyman's differential equation for the facilitated oxygen flux through a slab of solution of myoglobin or hemoglobin by showing that there is a unique choice of boundary condition on the carrier concentration to be employed in conjunction with it. The singular perturbation solution of Wyman's equation, due to Murrayand Mitchell and Murray, has been extended. By means of it, the paradox of Wittenberg, that the facilitated oxygen flux per mole of heme is apparently independent of the protein carrier, has been resolved.     

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.     

The steady-state transport of oxygen through hemoglobin solutions

The steady-state transport of oxygen through hemoglobin solutions was studied to identify the mechanism of the diffusion augmentation observed at low oxygen tensions. A novel technique employing a platinum-silver oxygen electrode was developed to measure the effective diffusion coefficient of oxygen in steady-state transport. The measurements were made over a wider range of hemoglobin and oxygen concentrations than previously reported. Values of the Brownian motion diffusion coefficient of oxygen in hemoglobin solution were obtained as well as measurements of facilitated transport at low oxygen tensions. Transport rates up to ten times greater than ordinary diffusion rates were found. Predictions of oxygen flux were made assuming that the oxyhemoglobin transport coefficient was equal to the Brownian motion diffusivity which was measured in a separate set of experiments. The close correlation between prediction and experiment indicates that the diffusion of oxyhemoglobin is the mechanism by which steady-state oxygen transport is facilitated.     

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.     

On facilitated oxygen diffusion in muscle tissues.

The role of myoglobin in facilitated diffusion of oxygen in muscle in examined in a tissue model that utilizes a central supplying capillary and a tissue cylinder concentric with the central capillary, and that includes the nonlinear characteristics of the oxygen-hemoglobin dissociation reaction. In contrast to previous work, this model exhibits the effect of blood flow and a realistic, though ideal, tissue-capillary geometry. Solutions of the model equations are obtained by a singular-perturbation technique, and numerical results are discussed for model parameters of physiologic interest. In contrast to the findings of Murray, Rubinow, Taylor, and others, fractional order perturbation terms obtained for the "boundary-layer" regions near the supplying capillaries are quite significant in the overall interpretation of the modeling results. Some closed solutions are found for special cases, and these are contrasted with the full singular-perturbation solution. Interpretations are given for parameters of physiologic interest.     

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.     

The role of facilitated diffusion of oxygen in tissue hypoxia

The evidence that cytochrome P-450 can act as a tissue oxygen carrier is outlined, and a new experimental approach to the measurement of the fraction of oxygen carried this way is described. This fraction is increased when cytochrome P-450 concentration is increased, which occurs on exposure of the experimental animal to hypoxia. This appears to be a new mechanism of tissue acclimation to hypoxia.Presented at the Seventh International Biometeorological Congress, 17–23 August 1975, College Park, Maryland, USA.     

Protein binding of palmitate measured by transmembrane diffusion through polyethylene

Thin polyethylene membranes permit ready diffusion of protonated long-chain fatty acids but are impermeable to protein and ions. This circumstance recommends polyethylene for measuring the free fraction of fatty acids in the presence of a binding protein and for estimating the ionization constant with which to compute the equilibrium constant for the binding of fatty acid anions. As an example of this approach we report the binding of tracer palmitate to bovine albumin and bovine beta-lactoglobulin. We find a binding constant for the high-affinity site on albumin that is close to that calculated by others from heptane:H2O partition ratios. Our procedure is simpler, however, and free of the theoretical objection that heptane may alter the binding characteristics of the protein. Our estimate of the pKa for palmitic acid is 4.9, a finding that conforms to the widely predicted but heretofore unconfirmed expectation that long-chain fatty acids should have a pKa of about 4.8. Unidirectional flux measurements exclude direct exchange of palmitate between albumin and polyethylene.     

Oxygen respiration rates of benthic foraminifera as measured with oxygen microsensors

Oxygen respiration rates of benthic foraminifera are still badly known, mainly because they are difficult to measure. Oxygen respiration rates of seventeen species of benthic foraminifera were measured using microelectrodes and calculated on the basis of the oxygen fluxes measured in the vicinity of the foraminiferal specimens. The results show a wide range of oxygen respiration rates for the different species (from 0.09 to 5.27 nl cell⁻¹ h⁻¹) and a clear correlation with foraminiferal biovolume showed by the power law relationship: R = 3.98 10⁻³ BioVol^0.88 where the oxygen respiration rate (R) is expressed in nl O₂ h⁻¹ and in μm³ biovolume (BioVol) (n = 44, R² = 0.72, F = 114, p < 0.0001). The results expressed per biovolume unit (1.82 to 15.7 nl O₂ 10⁻⁸ μm⁻³ h⁻¹) allow us to compare our data with the previous published data showing similar ranges. A comparison with available data for other microbenthos groups (nematodes, copepods, ostracods, ciliates and flagellates) suggests that benthic foraminifera have a lower oxygen respiration rates per unit biovolume. The total contribution of benthic foraminifera to the aerobic mineralisation of organic matter is estimated for the studied areas. The results suggest that benthic foraminifera play only a minor role (0.5 to 2.5%) in continental shelf environments, which strongly contrasts with their strong contribution to anaerobic organic matter mineralisation, by denitrification, in the same areas.     

Uptake rates of oxygen and sulfide measured with individual Thiomargarita namibiensis cells by using microelectrodes

Gradients of oxygen and sulfide measured towards individual cells of the large nitrate-storing sulfur bacterium Thiomargarita namibiensis showed that in addition to nitrate oxygen is used for oxidation of sulfide. Stable gradients around the cells were found only if acetate was added to the medium at low concentrations.     

The role of facilitated diffusion in oxygen transport by cell-free hemoglobins: implications for the design of hemoglobin-based oxygen carriers

We compared rates of oxygen transport in an in vitro capillary system using red blood cells (RBCs) and cell-free hemoglobins. The axial PO(2) drop down the capillary was calculated using finite-element analysis. RBCs, unmodified hemoglobin (HbA(0)), cross-linked hemoglobin (alpha alpha-Hb) and hemoglobin conjugated to polyethylene-glycol (PEG-Hb) were evaluated. According to their fractional saturation curves, PEG-Hb showed the least desaturation down the capillary, which most closely matched the RBCs; HbA(0) and alpha alpha-Hb showed much greater desaturation. A lumped diffusion parameter, K*, was calculated based on the Fick diffusion equation with a term for facilitated diffusion. The overall rates of oxygen transfer are consistent with hemoglobin diffusion rates according to the Stokes-Einstein Law and with previously measured blood pressure responses in rats. This study provides a conceptual framework for the design of a 'blood substitute' based on mimicking O(2) transport by RBCs to prevent autoregulatory changes in blood flow and pressure.     

A stochastic model for facilitated transport of oxygen through tissue slices

Longmuir and co-workers have reported that respiration of certain tissue slices is approximated by Michaelis-Menten kinetics. From this and other experimental findings, Longmuir proposed that a carrier is involved in tissue oxygen transport. Gold developed a deterministic model to examine this hypothesis. This report presents a stochastic model for a fixed site carrier in a more general framework that includes the stochastic counter-part to Gold's deterministic model as a special case. The kinetics of tissue oxygen consumption predicted by the model are examined for various cases.     

Reaction of acetaldehyde with hemoglobin

Acetaldehyde reacted with hemoglobin at neutral pH and 37 degrees C to form adducts that were stable to dialysis and that were not reduced by sodium borohydride. Hemoglobin tetramers having 2, 3, and probably 4 molar eq of bound aldehyde were isolated by cation exchange chromatography. The sites of attachment of the aldehyde were the free amino groups of the N-terminal valine residues of the alpha and beta chains of hemoglobin. Derivatization of the beta chains caused a greater increase in the acidity of the hemoglobin than did derivatization of the alpha chains. Derivatization of the beta chains was also preferred over that of the alpha chains. Acetaldehyde derivatives of the N-terminal octapeptide of hemoglobin S (beta sT-1 peptide), Val-Gly-Gly, and tetraglycine were formed readily, contained 1 M eq of acetaldehyde/mol of peptide, and were not reduced by sodium borohydride. In contrast, Ala-Pro-Gly failed to form a 1:1 adduct with acetaldehyde. 13C NMR analysis of the peptide adducts formed with [1,2-13C]acetaldehyde indicated that tetrahedral diastereomeric derivatives were produced. The 13C chemical shifts of the adducts formed between hemoglobin and [1,2-13C]acetaldehyde were identical to those of the peptide adducts although resonances from the individual diastereomeric adducts at each hemoglobin site could not be resolved. The results cited above as well as other evidence indicate that acetaldehyde reacts with the amino termini of hemoglobin to form stable cyclic imidazolidinone derivatives. An exchange of acetaldehyde residues between peptides was also documented.     

The anomaly of oxygen diffusion in aqueous xanthan solutions

A membrane-covered polarographic oxygen electrode was used to measure oxygen diffusion coefficients in aqueous polyelectrolyte solutions of xanthan gum, sodium alginate, and sodium carboxymethylcellulose (CMC). In sodium alginate solutions, dilute xanthan solutions, and solutions containing more than 0.3 wt % CMC, oxygen diffusion coefficients decrease with increasing polymer concentrations. Interestingly, in dilute CMC solutions and concentrate xanthan solutions containing more than 0.5 wt % xanthan gum, oxygen diffusion coefficients increase with increasing polymer concentrations, and values exceeding that in pure water are generally observed.