The effect of carbon monoxide on haem-facilitated oxygen diffusion

The aim of this paper is to quantify the effect of small quantities of carbon monoxide on the facilitated diffusion of oxygen by haemoglobin in the steady state. It is the first phase in the study of a mathematical model for carbon monoxide poisoning. Here we extend the Wyman model for facilitated diffusion to the case in which there are two ligands. The equations are solved using an asymptotic technique developed by Murray. We obtain accurate analytic approximations for the biologically important quantities of the problem for various percentages of carbon monoxide. These are the concentrations of free oxygen, haemoglobin, oxyhaemoglobin and carboxyhaemoglobin, and hence the saturation of the protein and the facilitated oxygen flux. The major effect of very small quantities of carbon monoxide on the oxygen flux is shown.     

Facilitated diffusion: the elasticity of oxygen supply.

It is well established that the presence of oxygen-carrying proteins such as haemoglobin can facilitate the diffusion of oxygen through a solution. In this paper, it is shown that some properties of a facilitated flow are substantially different from those of unfacilitated flux, including especially the stability of the tension at which the oxygen arrives at the end of the diffusion path. The concept of the “output resistance” of the supply is introduced, and a facilitated pathway is shown to have a lowered resistance. A role for the storage capacity of the bound oxygen reservoir is also developed; it is shown that delivery oxygen tensions are stabilized against transient changes in oxygen demand. In treating the equations of facilitated diffusion, a simplified approach is used to take account of boundary layers in the solution where deviations from oxygen-protein equilibrium are significant. A measure of the thickness and importance of such boundary layers is calculated.     

Morphometry and estimated bulk oxygen diffusion in larvae of Xenopus laevis under chronic carbon monoxide exposure

To understand the mechanisms that allow tadpoles of the African clawed frog Xenopus laevis to develop under conditions of impaired convective transport (hemoglobin poisoning with carbon monoxide), whole animal surface area and volume were measured and bulk oxygen diffusion was modeled at four developmental stages (from initiation of heartbeat to pre-metamorphic climax). Surface area [8.5 mm2 at stages Nieuwkoop-Faber (NF) 33-34 to 70.2 mm2 at stages NF 50-51] and volume (1.8 mm3 at stages NF 33-34 to 35.7 mm3 at stages NF 50-51) measured from volumetric analysis from dual plane images of each animal were not significantly different between treatments. Bulk oxygen radial diffusion was estimated by modeling the larvae as a set of adjacent cylinders with different radii. The model was used to predict the oxygen tension at the water-skin interface at which the oxygen tension in the center of the animal is nil (0.7 kPa at stage NF 33-34 and 14.0 kPa at stage NF 50-51), suggesting that bulk oxygen diffusion is sufficient to meet the metabolic demand up to stages NF 46-47 irrespective of the oxygen tension at the water-skin interface. At NF 50-51 an anoxic core in the animal would appear if bulk oxygen diffusion were the only means of oxygen transport at oxygen tensions below 15 kPa. However, the relative volume of the anoxic core would only exceed 10% of the total volume of the animal only at oxygen tensions below 5 kPa. Therefore, the ten-fold increase in mass between NF 50-51 and metamorphosis would prove insufficient for embryonic oxygen requirements via simple diffusion, and therefore would require additional transport mechanisms.     

Facilitated transport of oxygen in the presence of membranes in the diffusion path.

Most of the experimental observations on facilitated transport have been done with millipore filters, and all the theoretical studies have assumed homogeneous spatial properties. In striated muscle there exist membranes that may impede the diffusion of the carrier myoglobin. In this paper a theoretical study is undertaken to analyze the transport in the presence of membranes in the diffusion path. For the numerical computations physiologically relevant values of the parameters were chosen. The numerical results indicate that the presence of membranes tends to decrease the facilitation. For the nonlinear chemical kinetics of the reaction of oxygen with the carrier, this decrement also depends on the location of the membranes. At the higher oxygen concentration side of each membrane the flow of combined oxygen is transferred to the flow of dissolved oxygen. The reverse process occurs at the lower concentration side. Jump discontinuities of the concentration of the oxygen-carrier compound at each membrane are associated with these transfers. The decrement of facilitation is due to the cumulative effect of these jump discontinuities.     

Binding of oxygen and carbon monoxide to the hemocyanin from the spiny lobster

A high precision, two-dimensional study of oxygen and carbon monoxide binding to Panulirus interruptus hemocyanin has been carried out. Global data analysis of three types of experiments, probing the molecule in its various states of CO and O2 ligation, revealed the entire hexamer to be the basic allosteric unit involved in a two-state mechanism. The co-operativity and linkage of the two ligands are presented in terms of derivative Hill plot surfaces extended along co-ordinates of CO and O2 activities giving a detailed and comprehensive view of the binding behavior. Among the findings is an apparent high co-operativity of carbon monoxide binding at high oxygen activity. The results are discussed in view of a general mechanism for co-operative behavior found in larger hemocyanin aggregates concerning "nested" allosteric interactions.     

Heterogeneous binding of oxygen and carbon monoxide to dissociated molluscan hemocyanin

Functional heterogeneity in O2 or CO binding of sites of dissociated molluscan hemocyanin polypeptide chains (Helix pomatia and Octopus vulgaris) has been estimated by an analysis of accurate noncooperative binding curves. Three types of experiments were performed: pure O2 or CO binding, competitive displacement of one ligand by the other, and simultaneous removal of both gases from protein partially saturated with O2 and CO. The data were analyzed in terms of a model which has two fractions of sites with different properties for O2 and CO. The relative proportion of the different binding sites and their affinity constant values were found by the combined use of the three different procedures. All species show a marked functional heterogeneity of sites for O2 binding, while for CO binding it has been observed only in the case of H. pomatia beta-hemocyanin. Moreover, in all three molluscan hemocyanins examined, the two classes of O2-binding sites, although present in different proportions within the polypeptide chains, display similar affinity constant values. The data reported show a good consistency with results obtained using digested and isolated domains, providing confidence in the analytical procedure used. From comparison of the O2/CO affinity ratios (KO2, KCO) of each class it may be suggested that the difference in O2 affinity of two kinds of binding sites is related to a different local structure of the active sites. The results, moreover, unequivocally confirm that binding and displacement of two gaseous ligands to hemocyanin occur by a simple competitive mechanism, although the binding site is structurally complex and the two ligands are bound with different geometries.