Ligand binding kinetics of des arginine haemoglobin

Des arginine 141 a haemoglobin (the haemoglobin in which the C-terminal arginine of the a chain has been removed) has a high affinity for oxygen and a reduced co-operativity in its oxygen equilibrium binding. The kinetic consequences of this modification are investigated in this paper. Deoxy des Arg haemoglobin binds carbon monoxide faster than does haemoglobin A, whilst oxy des Arg haemoglobin loses oxygen more slowly. These results are correlated with the oxygen equilibrium binding properties of des Arg haemoglobin. The carbon monoxide binding kinetics have been interpreted as implying a change in the parameter c (of the allosteric model), as well as L, when this arginine is removed from haemoglobin.     

A mathematical model for the computation of carboxyhaemoglobin in human blood as a function of exposure time.

A mathematical model is developed for the carbon monoxide (CO) uptake by the blood by taking into account the molecular diffusion, convection, facilitated diffusion and the non-equilibrium kinetics of CO with haemoglobin. The overall rate for the combination of CO with haemoglobin is derived by including the dissociation of CO from carboxyhaemoglobin (COHb). The resulting coupled system of nonlinear partial differential equation with physiologically relevant initial, entrance and boundary conditions is solved numerically. A fixed point iterative technique is used to deal with nonlinearities. The concentration of COHb in the blood is computed as a function of exposure time and ambient CO concentration. The COHb levels computed from our model are in good agreement with those measured experimentally. Also, results computed from our model give better approximation to the experimental values compared with the results from other models. The time taken by the blood COHb to attain 95% of its equilibrium value is computed. The COHb concentration in the blood increases with the increase in ventilation rate, association rate coefficient of CO with haemoglobin and total haemoglobin content in the blood, and with the decrease in dissociation rate coefficient of CO with haemoglobin and mean capillary blood PO2. It is found that the COHb level in the blood is not affected significantly because of endogenous production of CO in the body under normal condition. However, the effect may be significant in the patients with haemolytic anaemia.     

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.     

A numerical model for the oxygenation of blood in lung capillaries--effect of nth order one-step kinetics of oxygen uptake by haemoglobin

A numerical model is described for the oxygenation of blood in lung capillaries by considering the transport mechanisms of molecular diffusion, convection and the facilitated diffusion due to the presence of haemoglobin. In order to represent the oxygen dissociation curve accurately in the model, the nth order one-step kinetics of oxygen uptake by haemoglobin has been used. The resulting system of coupled, non-linear partial differential equations is solved numerically. It is shown that the blood is required to traverse a larger distance in the capillary before becoming fully oxygenated with nth order one-step kinetics in comparison to first-order one-step kinetics.     

The kinetics of binding of oxygen and carbon monoxide to Gastrophilus haemoglobin

The dimeric haemoglobin in the tracheal cells of the Gastrophilus larva was extracted and purified, and the spectral properties of its oxy- and carbon monoxide adducts are recorded. In dilute solutions the kinetic parameters of binding of oxygen and carbon monoxide were determined. In solutions between 0.1 and 50mum for oxygen k(on) is 1x10(7)m(-1).s(-1) and k(off) is 1s(-1); for carbon monoxide l(on) is 6.5x10(5)m(-1).s(-1) and l(off) is 0.14s(-1). These values are in agreement with previous equilibrium results on oxygen binding and carbon monoxide/oxygen partition. These results are discussed and compared with the known values for other monomeric protohaem proteins.     

Theory of the rotational contribution to facilitated diffusion

Gros and others have recently shown experimentally that the facilitated diffusion of protons carried by a form of haemoglobin is enhanced by rotational diffusion of the carrier, whereas facilitated diffusion of oxygen by the same carrier is not. In this paper the theory of facilitated transport by rotating carriers is developed from first principles. The theory confirms Gros's findings that (i) the rotational contribution appears only when the angle of rotational diffusion over the average time the proton remains bound is small and (ii) under these conditions rotation enhances the normal translational contribution by a factor 1/2 at the lowest carrier concentrations. The theory also shows that there must be a rotational boundary layer.     

A numerical study of the nonsteady transport of gases in the pulmonary capillaries

A mathematical model is formulated for simulating the unsteady transport of gases in the blood flowing through the pulmonary capillaries. The formulation takes into account the transport mechanisms of molecular diffusion, convection and facilitated diffusion of the species due to haemoglobin. A time dependent situation is created by allowing to vary suddenly the partial pressures of the gases either in the venous blood or in the alveolar air. A numerical technique is described to solve the resulting time-dependent system of nonlinear coupled partial differential equations with the physiologically relevant boundary, entrance and initial conditions. The time required by the gases to achieve equilibrium is computed. It is shown that the dissolved oxygen takes longest in reaching equilibration whereas the carbon dioxide is the fastest. The various physiologically relevant unsteady situations have been examined.     

Facilitated diffusion of myoglobin and creatine kinase and reaction-diffusion constraints of aerobic metabolism under steady-state conditions in skeletal muscle

The roles of creatine kinase (CK) and myoglobin (Mb) on steady-state facilitated diffusion and temporal buffering of ATP and oxygen, respectively, are assessed within the context of a reaction-diffusion model of muscle energetics. Comparison of the reaction-diffusion model with experimental data from a wide range of muscle fibers shows that the experimentally observed skeletal muscle fibers are generally not limited by diffusion, and the model further indicates that while some muscle fibers operate near the edge of diffusion limitation, no detectable effects of Mb and CK on the effectiveness factor, a measure of diffusion constraints, are observed under steady-state conditions. However, CK had a significant effect on average ATP concentration over a wide range of rates and length scales within the reaction limited regime. The facilitated diffusion functions of Mb and CK become observable in the model for larger size cells with low mitochondrial volume fraction and for low boundary O(2) concentration and high ATP demand, where the fibers may be limited by diffusion. From the transient analysis it may be concluded that CK primarily functions to temporally buffer ATP as opposed to facilitating diffusion while Mb has a small temporal buffering effect on oxygen but does not play any significant role in steady-state facilitated diffusion in skeletal muscle fibers under most physiologically relevant regions.     

Equilibria and kinetic of oxygen and carbon monoxide binding to the haemoglobin of the South American lungfish,Lepidosiren paradoxa

• 1. The haemoglobin of the South American lungfishLepidosiren paradoxa has a single component.
• 2. The equilibria of this respiratory protein with oxygen have been investigated both in the blood and with the purified haemoglobin. There is a substantial, normal, alkaline Bohr effect and marked sensitivity to organic phosphates in the haemoglobin solutions.
• 3. Studies on the pH dependence of the kinetics of oxygen dissociation can be interpreted in terms of a normal Bohr effect.
• 4. The kinetics of combination of carbon monoxide have an unusual pH dependence.
• 5. These findings are discussed in terms of the two-state model of Monodet al. (1965)

     

PARTICIPATION OF A NON-RESPIRATORY FERROUS COMPLEX DURING MITOSIS IN ROOTS

A systematic survey was undertaken, of the effects of carbon monoxide and hydrogen cyanide (in the presence of 20 per cent oxygen), in darkness and light, on the relative rates of respiration, mitosis, and interphase in pea root tips. The inhibition of respiration by carbon monoxide was light-sensitive, but the inhibition by hydrogen cyanide was light-stable. The inhibitions were presumably due to combination of the inhibitor with the iron of cytochrome oxidase, in its divalent and trivalent forms respectively. In contrast, the inhibitions of mitosis by both poisons proved to be light-sensitive. The light-sensitive inhibition of mitosis by carbon monoxide shows that an iron complex is responsible for the process. That the inhibition of mitosis by hydrogen cyanide is also light-reversible shows that, in contrast with cytochrome oxidase, the mitotic iron complex remains always in the divalent state. The relative affinities of the mitotic ferrous complex, in molar units, were 0.68 for CO/O₂, and 0.37 for HCN/O₂. The properties of the complex are analogous to, yet distinct from, Gastrophilus haemoglobin and reduced cytochrome oxidase. It is considered that the arrest of mitosis by oxygen lack, carbon monoxide, and hydrogen cyanide is definitely due to interference with this unidentified, non-respiratory ferrous complex.     

Steady-State, Hemoglobin-Facilitated O2 Transport in Human Erythrocytes

We measured the rate of oxygen transport through thin (165 µ) films of packed erythrocytes (Hb concentration = 30 g/100 ml). Under optimal conditions steady-state O₂ diffusion was nearly three times that found when the hemoglobin was prevented from acting as a carrier molecule by carbon monoxide binding or high oxygen back pressure. After each experiment we measured hemolysis and found that it averaged less than 1%. Hemolysis could not account for the facilitation, thus proving that facilitated transport of O₂ by hemoglobin can occur in red blood cells. The rate of facilitated transport was identical for Hb solutions of equal concentration to the cells. We interpret this to mean that under the conditions of our experiments the red cell membrane offers no detectable diffusion resistance to O₂ and that the mobility of Hb in intact red cells is the same as in concentrated Hb solution.     

Some factors affecting oxygen uptake by red blood cells in the pulmonary capillaries

In this study we investigate the equations governing the transport of oxygen in pulmonary capillaries. We use a mathematical model consisting of a red blood cell completely surrounded by plasma within a cylindrical pulmonary capillary. This model takes account of convection and diffusion of oxygen through plasma, diffusion of oxygen through the red blood cell, and the reaction between oxygen and haemoglobin molecules. The velocity field within the plasma is calculated by solving the slow flow equations. We investigate the effect on the solution of the governing equations of: (i) mixed-venous blood oxygen partial pressure (the initial conditions); (ii) alveolar gas oxygen partial pressure (the boundary conditions); (iii) neglecting the convection term; and (iv) assuming an instantaneous reaction between the oxygen and haemoglobin molecules. It is found that: (a) equilibrium is reached much more rapidly for high values of mixed-venous blood and alveolar gas oxygen partial pressure; (b) the convection term has a negligible effect on the time taken to reach a prescribed degree of equilibrium; and (c) an instantaneous reaction may be assumed. Explanations are given for each of these results.     

The Secretion of Oxygen into the Swim-bladder of Fish : II. The simultaneous transport of carbon monoxide and oxygen

Toadfish, Opsanus tau, L., were maintained in sea water equilibrated with gas mixtures containing a fixed proportion of oxygen and varying proportions of carbon monoxide. The swim-bladder was emptied by puncture, and, after an interval of 24 or 48 hours, the newly secreted gases were withdrawn and analyzed. Both carbon monoxide and oxygen are accumulated in the swim-bladder at tensions greater than ambient. The ratio of concentrations, carbon monoxide (secreted): carbon monoxide (administered) bears a constant relation to the ratio, oxygen (secreted): oxygen (administered). The value of the partition coefficient describing this relation is (α = 5.44). The two gases are considered to compete for a common intracellular carrier mediating their active transport. The suggestion is advanced that the intracellular oxygen carrier is a hemoglobin. Comparison of the proportions of carboxy- and oxyhemoglobin in the blood with the composition of the secreted gas proves that the secreted gases are not evolved directly from combination with blood hemoglobin. The suggestion is advanced that cellular oxygen secretion occurs in the rete mirabile: the rete may build up large oxygen tensions in the gas gland capillaries. It is suggested that the gas gland acts as a valve impeding back diffusion of gases from the swim-bladder.     

Evidence for partial export of Vitreoscilla hemoglobin into the periplasmic space in Escherichia coli. Implications for protein function

The Vitreoscilla hemoglobin protein has been implicated in earlier studies to serve a globin-like function under oxygen-limited growth conditions. Evidence is presented using fractionation as well as proteinase K accessibility techniques to prove that a considerable amount of this protein is localized in the periplasmic space of the cell. Genetic evidence points towards the existence of information within the N-terminal domain of the protein that plays a role in the process of protein export. However, this sequence is not cleaved in the process of translocation. Analysis of the primary structure of this region reveals several unusual features. Instead of positively charged residues at its amino terminus, it has a negative charge. The overall hydrophobicity of the central region of this sequence is significantly lower than in typical leader peptides due to the presence of a charged residue. In keeping with the likelihood that such an export signal may not be very efficient, a substantial fraction of the total cellular hemoglobin can also be detected in the cytoplasm. Heme is incorporated in both cytoplasmic and periplasmic globin as indicated by the ability of protein from both fractions to bind carbon monoxide. The secretion of this protein into the periplasm raises questions concerning the physiological significance of its localization. Dimensional analysis of a model based on the facilitated diffusion hypothesis, which was initially proposed to account for the effects of eukaryotic globins on oxygen transport, suggests that periplasmic globin can support an additional oxygen flux to the respiratory apparatus that may be physiologically significant.     

On the role of myoglobin in muscle respiration

The presence of myoglobin in red muscle tissue has a marked effect on its respiration because it combines reversibly with oxygen and hence gives rise to facilitated diffusion. In this paper we consider the role of myoglobin in facilitating oxygen diffusion and give quantitative results for the oxygen concentration within a typical muscle fibre. Simple expressions are derived for the critical metabolism for the onset of oxygen debt and the growth and size of the region in oxygen debt when the muscle metabolism exceeds this critical value.The general principle, enunciated by Murray &; Wyman (1971), that the macromolecule, myoglobin here, can only function as a carrier if it is unsaturated in some region of the system is again shown to hold.A singular perturbation procedure is used to analyze the model, the effect of which is to reduce the mathematical problem to that of trivially solving a quadratic algebraic equation for the oxygen concentration in the muscle fibre. Physically one condition which causes this phenomenon to be singular in the mathematical sense is that the relaxation times of the myoglobin-oxygen reaction are small compared with the diffusion time of the myoglobin-oxygen complex.     

Haemoglobins of invertebrate tissues. Nerve haemoglobins of Aphrodite, Aplysia and Halosydna

1. The occurrence of haemoglobin in invertebrate nerves is surveyed. Haemoglobin was observed in the nerves and ganglia of the marine nematode Amphiporus sp. and of the polychaet annelid Halosydna sp. 2. Haemoglobins from the nerve and ganglia of the polychaet annelid Aphrodite aculeata L. and from the nerve of the gastropod mollusc Aplysia californica have been partially purified. The haem in each case was identified as iron protoporphyrin IX. 3. The minimum molecular weight of Aphrodite nerve haemoglobin deduced from the haem content and amino acid analysis is 17090, in agreement with the molecular weight 15600+/-1000 determined by sedimentation equilibrium. 4. The molecular weight of Aplysia nerve haemoglobin was determined by sedimentation equilibrium to be 16400+/-1000. 5. The oxygen dissociation curves are hyperbolic. Half-saturation is achieved at 1.1mm. Hg for Aphrodite nerve haemoglobin and at 4.0mm. Hg for Aplysia nerve haemoglobin. The coefficients for partition between carbon monoxide and oxygen are: Aphrodite nerve haemoglobin, 167; Aplysia nerve haemoglobin, 116. 6. The ferrous haemoglobins combine with cyanide. 7. We conclude that the intracellular haemoglobins of muscle and nerve are similar.     

The process of gas exchange in the pulmonary circulation incorporating the contribution of axial diffusion

A mathematical model is made to describe the process of gas exchange in the pulmonary circulation incorporating the contribution of axial diffusion. The model takes into account the transport mechanisms of molecular diffusion, convection and facilitated diffusion due to the presence of haemoglobin as a carrier of the gases. The mathematical formulation leads to a coupled system of non-linear elliptic partial differential equations. A numerical scheme is described to solve such a system. It is found that the axial diffusion does not have an appreciable effect on the transport of the species in the blood.     

Mathematical modelling of oxygen transport to tissue

 The equations governing oxygen transport from blood to tissue are presented for a cylindrical tissue compartment, with blood flowing along a co–axial cylindrical capillary inside the tissue. These governing equations take account of: (i) the non–linear reactions between oxygen and haemoglobin in blood and between oxygen and myoglobin in tissue; (ii) diffusion of oxygen in both the axial and radial directions; and (iii) convection of haemoglobin and plasma in the capillary. A non–dimensional analysis is carried out to assess some assumptions made in previous studies. It is predicted that: (i) there is a boundary layer for oxygen partial pressure but not for haemoglobin or myoglobin oxygen saturation close to the inflow boundary in the capillary; (ii) axial diffusion may not be neglected everywhere in the model; (iii) the reaction between oxygen and both haemoglobin and myoglobin may be assumed to be instantaneous in nearly all cases; and (iv) the effect of myoglobin is only significant for tissue with a low oxygen partial pressure. These predictions are validated by solving the full equations numerically and are then interpreted physically. Received: 13 October 2000 / Revised version: 12 June 2001 / Published online: 17 May 2002     

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.     

Reaction of carbon monoxide with hemocyanin: Stereochemical effects of a non-bridging ligand

The carbon monoxide binding equilibria and kinetics of a number of molluscan and arthropodal hemocyanins have been investigated employing the visible luminescence of the carbon monoxide-copper complex.Proteins from both phyla, in oligomeric and monomeric form, bind carbon monoxide non-co-operatively; the reaction is largely enthalpy driven is associated with a small unfavourable entropy change.Molluscan hemocyanins display a carbon monoxide affinity (p₅₀ = 1 to 10mm Hg) higher than that of arthropodal hemocyanins (p₅₀ = 100 to 700mm Hg), and only Panulirus interruptus hemocyanin, among those studied here, exhibits a small Bohr effect. The observed differences in equilibrium constant are kinetically reflected in differences in the carbon monoxide dissociation rate constant, which ranges from 20 to 70 s^?1 for molluscan hemocyanins and from 200 to 9000 s^?1 for arthropodal hemocyanins; on the other hand the differences in the combination rate constants between the two phyla are considerably smaller. A comparison of the equilibrium and kinetic results shows some discrepancies between the two sets of data, suggesting that carbon monoxide binding may be governed by a complex mechanism.The correlation between the ligand binding properties and the stereochemistry of the active site is discussed in the light of the knowledge that, while oxygen is bound to both copper atoms in a site, carbon monoxide is a “non-bridging” ligand, being bound to only one of the metals.