On optima: the case of myoglobin-facilitated oxygen diffusion

The process of myoglobin/leghemoglobin-facilitated oxygen diffusion is adapted to function in different environments in diverse organisms. We enquire how the functional parameters of the process are optimized in particular organisms. The ligand-binding properties of the proteins, myoglobin and plant symbiotic hemoglobins, we discover, suggest that they have been adapted under genetic selection pressure for optimal performance. Since carrier-mediated oxygen transport has probably evolved independantly many times, adaptation of diverse proteins for a common functionality exemplifies the process of convergent evolution. The progenitor proteins may be built on the myoglobin scaffold or may be very different.     

Effect of temperature on the myoglobin-facilitated transport of oxygen in skeletal muscle.

An analysis of thermal effects on the facilitative transport of oxygen in skeletal muscle fibers is presented. Steady-state mass and energy transport balances are written and solved analytically or numerically using a finite-difference procedure. It is shown that no significant spatial thermal gradients exist due to internal reactions or bulk conduction effects across a muscle fiber. At typical muscle conditions, it is predicted that increased global temperature reduces the fraction of oxygenated myoglobin, increases local oxygen concentrations, and increases the percentage of oxygen flux attributed to oxy-myoglobin. The maximum supportable oxygen consumption rate, mO2max, is defined as the highest consumption rate sustainable without developing anoxic regions at the center of the fiber. By considering only temperature sensitive effects within fibers, mO2max is found to increase slightly with temperature at low temperatures. This increase is due to thermal effects on the diffusion coefficients as opposed to effects associated with the kinetics of the myoglobin-oxygen reaction. If the simulations include the temperature effect associated with oxygen solubility in blood plasma, mO2max decreases with temperature. A sensitivity analysis was performed by varying the values of relevant parameters. The maximum consumption rate was least affected by parameters associated with the kinetic and equilibrium constants and most affected by the diffusion coefficients and the concentration of myoglobin.     

Parameter dependence of myoglobin-facilitated transport of oxygen in the presence of membranes

Some physicochemical entities involved in the facilitated transport of oxygen along a transport path z1 less than or equal to z less than or equal to zn with membranes impermeable to myoglobin at zi, i = 1,...,n, were identified in an earlier paper [Math. Biosci. 95:209 (1989)]. These entities are the partition between the oxygen and oxymyoglobin flows, the flow transfers taking place near a membrane, and the membrane resistance. Expressions for these entities were obtained that explicitly involve the parameters of the system. In this paper, for the case of prescribed boundary oxygen concentrations x1 and xn, these expressions are incorporated into (i) an explicit representation for the facilitated transport value in terms of the difference, E(x1)-E(xn), between the boundary oxymyoglobin equilibrium values and the sum, gamma, of the membrane resistances, and (ii) a representation for the distribution of the membrane oxygen concentrations xi at zi, i = 2,...,n-1. This makes it possible to analyze the manner in which the facilitated transport depends on the parameters. For a physiological range of parameter values, the facilitated transport was found to increase as either the oxygen-myoglobin association rate constant k', the dissociation rate constant k, the oxygen diffusion coefficient, or the oxymyoglobin diffusion coefficient increases. Thus, the facilitated transport does not depend directly on ratios of chemical and diffusion coefficients. Although the increase in the oxygen diffusion coefficient does not per se affect the chemical conductance, it diminishes the membrane resistance through an interface feature, with a resulting increase in the facilitated transport. For a larger range of values of k' and k, the dependences of the facilitated transport on k' and on k are both biphasic and are similar in shape. However, the mechanisms involved are different: The associated changes in E(x1)-E(xn) and in gamma that result from the increase in k' are opposite to those that result from an increase in k. The use of (i) and (ii) permits, also, discrimination between the different roles of the physicochemical entities involved in a given facilitated transport change. In some cases (e.g., the decreasing phase of the facilitated transport as k' increases), this change depends in an essential manner on a secondary modification of the profile xi, i = 1,...,n, along the transport path.     

The effect of myoglobin-facilitated oxygen transport on the basal metabolism of papillary muscle.

A mathematical model of oxygen diffusion into cylindrical papillary muscles is presented. The model partitions total oxygen flux into its simple and myoglobin-facilitated components. The model includes variable sigmoidal, exponential, or hyperbolic functions relating oxygen partial pressure to both fractional myoglobin saturation and rate of oxygen consumption. The behavior of the model was explored for a variety of saturation- and consumption-concentration relations. Facilitation of oxygen transport by myoglobin was considerable as indexed both by the elevation of oxygen partial pressure on the longitudinal axis of the muscle and by the fraction of total oxygen flux at the muscle center contributed by oxymyoglobin. Despite its facilitation of oxygen flux at the muscle center, myoglobin made only a negligible contribution to the total oxygen consumption averaged over the muscle cross-section. Hence the presence of myoglobin fails to explain either the experimentally determined basal metabolism-muscle radius relation or the stretch effect observed in isolated papillary muscle.     

Gas diffusion through wood: implications for oxygen supply

Living tissue in tree stems has to be supplied with oxygen, which can be transported upwards with the transpiration stream; but in times of zero sapflow, the only source is the oxygen stored or diffusing radially through bark and xylem. We measured radial and axial diffusion of oxygen against nitrogen gas in wood of coniferous (Picea abies (L.) Karst. and Taxus baccata L.), ring-porous (Quercus robur L. and Fraxinus excelsior L.) and diffuse-porous (Fagus sylvatica L. and Carpinus betulus L.) trees at different water and gas contents in the laboratory. The diffusion coefficient (D) in radial direction was mostly between 10⁻¹¹ and 10⁻⁷ m² s⁻¹ and was strongly related to the gas content. At 40% gas volume, D increased 5–13-fold in Picea, Taxus and Quercus, 36-fold in Fraxinus, and about 1000-fold in Carpinus and Fagus relative to D at 15% gas volume. In the axial direction, diffusion was 1 or 2 orders of magnitude faster. Between-species differences in diffusion velocities can largely be explained by wood structure. In general, D was lowest in conifers, highest in diffuse-porous and intermediate in ring-porous hardwoods, where the large vessels were mostly blocked by tyloses. Model calculations showed that at very high water content, radial diffusion can be too low to ensure the supply of respiring sapwood with sufficient oxygen and an important function of gas in living stems appears to be the supply of oxygen through storage and diffusion.     

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.     

Measuring oxygen diffusion coefficients with polarographic oxygen electrodes. II. Fermentation Media

Fermentation media consist of a large number of chemicals which composition undergoes alteration during the course of fermentations. In consequence, the conventional methods and correlations for gas diffusion coefficient measurement and prediction cannot be easily applied to such systems. Oxygen diffusion coefficients have been measured in simulated chemical systems as well as in complex solutions of nutrient broth, using the polarographic technique introduced in a previous article. It is identified that sugars and salts are the major factors influencing oxygen diffusion coefficients in these aqueous fermentation media. The effect of salts on oxygen diffusion coefficients in electrolyte solutions has been found to be well correlated with the square root of total ionic strength of electrolyte solutions. The individual effect of glucose and its combined effect with salts are explored in order to reach rational correlations capable of predicting oxygen diffusion coefficients in synthetic fermentation media. For aqueous solutions of glucose plus salts, it is observed that the log-additive relationship can be used to account for the combined effect. Finally, a linear correlation has been established in measuring oxygen diffusion coefficients in aqueous solutions having different concentrations of nutrient broth.     

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.     

Effect of lipid monolayers on diffusion of oxygen through the air/water interface

The dependence of the diffusion current on the depth of immersion of the electrode was studied by polarography using an open platinum electrode. As the electrode was brought from the depth of the liquid phase to its surface, an increase in the current under aerobic conditions was observed, due to diffusion of oxygen through the interface. The formation of lipid monolayers of phosphatidylcholine, stearic acid, hexadecanol, octadecanol, eicosanol, and docosanol on the water surface led to a decrease in diffusion current; the effect being most pronounced at a minimal depth of immersion of the electrode. The maximum value of the relative decrease in diffusion current R was obtained for docosanol monolaers. It was shown that the R value increases with increasing surface pressure in monolayers of phosphatidylcholine and stearic acid. It is assumed that the decrease in diffusion flow of O2 in the presence of monolayers is caused by the formation of an energy barrier that prevents the sorption of O2, which is related to the presence of hydrocarbon chains weakly interacting with oxygen.     

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.     

Reduction of infarct size by cell-permeable oxygen metabolite scavengers.

The timely restoration of blood flow to severely ischemic myocardium limits myocardial infarct size. However, experimental studies demonstrate that the myocardial salvage achieved is suboptimal because of additional injury that occurs during reperfusion, due in part to the generation of reactive oxygen metabolites. Initially, superoxide (O2-) was considered to be the central mediator of reperfusion injury. While there are several potential pathways of O2- generation in reperfused myocardium, O2- is poorly reactive toward tissue biomolecules. However, O2-, in the presence of redox-active metals such as iron, generates .OH or hydroxyl-like species that are highly reactive with cell constituents. Thus, while O2- may initiate reaction sequences leading to myocardial injury, it may not be the actual injurious agent. In vitro studies suggest that oxygen metabolite injury occurs at intracellular sites and involves iron-catalyzed processes. Consistent with this mechanism, extracellular oxygen metabolite scavengers have not convincingly reduced infarct size. However, treatment around the time of reperfusion, after ischemia is well established, with cell-permeable scavengers of .OH reduce infarct size. Results with these cell-permeable agents suggest that in the intact animal during regional ischemia and reperfusion, oxygen metabolite injury also occurs at intracellular sites. Cell-permeable scavenger agents are a promising class of drugs for potential clinical use, though further experimental and toxicologic studies are required.     

In vivo diffusion of lidocaine through tissue expanders.

It has been suggested that the addition of lidocaine to the saline used to fill tissue expanders will reduce the pain often associated with the expansion process. In vitro experiments have shown that lidocaine as it is normally supplied will diffuse through an expander only at a very slow rate, which would probably be inadequate for a clinical effect. We found that the addition of sodium bicarbonate resulted in a substantial increase in the rate of diffusion. Studies in rabbits demonstrated that at a pH of 8.0, 75 percent of the lidocaine dose crossed the silicone elastomer membrane at 24 hours and greater than 95 percent had left the expander at 1 week. We have concluded that intraluminal lidocaine can be effective only when the pH is close to the pKa of lidocaine.     

Photosynthetic electron flow to oxygen and diffusion of hydrogen peroxide through the chloroplast envelope via aquaporins

Light-induced generation of superoxide radicals and hydrogen peroxide in isolated thylakoids has been studied with a lipophilic spin probe, cyclic hydroxylamine 1-hydroxy-4-isobutyramido-2,2,6,6-tetramethylpiperidinium (TMT-H) to detect superoxide radicals, and the spin trap α-(4-pyridyl-1-oxide)-N-tert-butylnitron (4-POBN) to detect hydrogen peroxide-derived hydroxyl radicals. Accumulation of the radical products of the above reactions has been followed using electron paramagnetic resonance. It is found that the increased production of superoxide radicals and hydrogen peroxide in higher light is due to the enhanced production of these species within the thylakoid membrane, rather than outside the membrane. Fluorescent probe Amplex red, which forms fluorescent product, resorufin, in the reaction with hydrogen peroxide, has been used to detect hydrogen peroxide outside isolated chloroplasts using confocal microscopy. Resorufin fluorescence outside the chloroplasts is found to be suppressed by 60% in the presence of the inhibitor of aquaporins, acetazolamide (AZA), indicating that hydrogen peroxide can diffuse through the chloroplast envelope aquaporins. It is demonstrated that AZA also inhibits carbonic anhydrase activity of the isolated envelope. We put forward a hypothesis that carbonic anhydrase presumably can be attached to the envelope aquaporins. This article is part of a Special Issue entitled: Photosynthesis Research for Sustainability: from Natural to Artificial.     

Oxygen diffusion through the venule walls in the rat cerebral cortex during breathing with pure oxygen

Using oxygen microelectrodes, distribution of oxygen tension (pO2) has been studied in venules of the rat brain cortex at normobaric hyperoxia (spontaneous breathing with pure oxygen). It has been shown that inhalation of oxygen results in sharp increase of pO2 in majority of the venules under study. The pO2 distribution along the length of venous microvessels of 7-280 microns in diameter is best approximated by equation: pO2 = 76.44 e-0.0008D, n = 407. The pO2 distribution was characterised by extremely high pO2 values (180-240 mm Hg) in some minute venules. Heterogeneity of pO2 distribution in venous microvessels at hyperoxia was shown to be significantly increased. Profiles of pO2 between neighbouring arterioles and venules were for the first time measured. The data clearly evidenced that O2 diffusional shunting took place between cortical arterioles and venules, provided they were distanced from each other for not over 80-100 microns. Distribution of pO2 in venules has been shown to be dependent on the blood flow in the brain cortical microvessels.     

Accelerative exchange diffusion kinetics of glucose between blood and brain and its relation to transport during anoxia.

An earlier study showed that unidirectional glucose transport from blood to brain decreases during perfusion with anoxic blood (Betz, A. L., Gilboe, D. D. and Drewes, L. R. (1974) Brain Res. 67, 307-316). Brain glucose levels also decrease during anoxia. Therefore, the present study was designed to investigate whether the decreased transport might be the result of decreased accelerative exchange diffusion when brain glucose levels are low. The rate of undirectional transport into brain (v) of D-[6-3H]glucose was studied in 22 isolated, perfused dog brains by means of an indicator dilution technique using 22Na as the intravascular reference. The kinetics of transport were determined over a range of blood glucose concentrations (S1) at each of five different brain glucose levels (S2). The existence of accelerative exchange diffusion for glucose was indicated by a decrease in the intercept (increase of apparent V) of a double reciprocal plot (1/v versus 1/S1) as S2 increased. This phenomenon is consistent with a model for facilitated diffusion in which the mobility of the loaded carrier is greater than that of the unloaded carrier. Although the data predict a decrease in glucose transport during anoxia, the predicted decrease (5%) is less than the observed decrease (35%). It is concluded that the simple mobile-carrier model for facilitated diffusion cannot, by itself, describe all properties of blood-brain glucose transport.