Dynamics of oxygen transport in erythrocytes

Distribution dynamics of oxygen tension throughout the erythrocyte volume was calculated by means of a mathematical model describing the dynamics of oxygen transport in the erythrocyte, its shape, diffusion resistance of hemoglobin solution. The pattern of the dissociation curve of oxyhemoglobin being taken into account. The model is presented as a system of differential equations in partial derivatives. Its solution was performed on an electron computer by a net method. Sharp jumps of pO2 inside the erythrocyte at its fast movements in the media with different partial pressure of O2 were shown. A quantitative relationship was found between the rate of physico-chemical reactions of oxygen binding and yield by hemoglobin and the level of hemoglobin saturation with oxygen.     

Tissue oxygenation and perfusion in inferior pedicle reduction mammaplasty by near-infrared reflection spectroscopy and color-coded duplex sonography

Near-infrared reflection spectroscopy has been used in various experimental and clinical settings to investigate tissue perfusion and oxygenation noninvasively. Its application in plastic surgery has only recently been reported. The current study used near-infrared reflection spectroscopy to monitor cutaneous microcirculation in breast skin flaps after inferior pedicle reduction mammaplasty. Thirty patients underwent bilateral reduction mammaplasty by a modified Robbins technique. Near-infrared reflection spectroscopy measurements were performed preoperatively and postoperatively at several defined positions of the breast. The reflection spectroscopy system was capable of detecting absolute values of total hemoglobin in milligrams per milliliter of tissue and tissue hemoglobin oxygen saturation in percent. Color-coded duplex sonography was used to visualize nutrient vessels of the inferior dermoglandular pedicle and to measure systolic peak flow in the arteries supplying the nipple-areola complex. Reflection spectroscopy values were examined for changes during the postoperative course. Reflection spectroscopy and duplex sonography values were analyzed for differences between patients with normal and compromised skin flap perfusion and wound healing, which was assessed clinically and by ultrasound. Preoperative reflection spectroscopy values demonstrated local, regional, and interindividual variations. Postoperatively, characteristic changes of tissue hemoglobin oxygen saturation and total hemoglobin were observed in all patients during the 2-week follow-up. Reflection spectroscopy values differed significantly between breast and nipple-areola skin. Tissue hemoglobin oxygen saturation was significantly lower, and total hemoglobin significantly higher, in patients with impaired wound healing compared with patients having normal wound healing. However, systolic peak flow in arteries of the inferior dermoglandular pedicle did not reveal differences between patients with impaired or normal wound healing of the nipple-areola complex. Near-infrared reflection spectroscopy allows the detection of hemoglobin content and oxygenation in skin flaps. Changes in tissue hemoglobin oxygen saturation and total hemoglobin reflect hemodynamic changes in skin flaps during normal and pathological wound healing. Because of considerable intraindividual and interindividual variations, trend values seem to be superior to single measurements. Although in this study, near-infrared reflection spectroscopy was capable of distinguishing between normal and impaired perfusion in skin flaps in a clinical model, its future implication may be the early detection of vascular compromise in free flaps.     

Study of chemically modified hemoglobin as an artificial oxygen carrier in the model of hemorrhagic shock in dogs]

Hemodynamic and gas-transporting properties of the chemically modified hemoglobin solution have been studied on the model of hemorrhagic shock in dog. It has been shown that the polymerized hemoglobin solution exerts the hemodynamic action just as the plasma substitute "polyglucin" does. However, in contrast to the latter, polyhemoglobin circulating in the vascular bed for a prolonged period of time increases the blood oxygen capacity and oxygen delivery to tissues with the resultant increase in body total oxygen taking-up.     

Dynamics of oxygen unloading from sickle erythrocytes.

The objective of this work is to theoretically model oxygen unloading in sickle red cells. This has been done by combining into a single model diffusive transport mechanisms, which have been well-studied for normal red cells, and the hemoglobin polymerization process, which has been previously been studied for deoxyhemoglobin-S solutions and sickle cells in near-equilibrium situations. The resulting model equations allow us to study the important processes of oxygen delivery and polymerization simultaneously. The equations have been solved numerically by a finite-difference technique. The oxygen unloading curve for sickle erythrocytes is biphasic in nature. The rate of unloading depends in a complicated way on (a) the kinetics of hemoglobin S polymerization, (b) the kinetics of hemoglobin deoxygenation, and (c) the diffusive transport of both free oxygen and oxy-hemoglobin. These processes interact. For example, the hemoglobin S polymer interferes with the transport of both free oxygen and unpolymerized oxy-hemoglobin, and this is accounted for in the model by diffusivities which depend on the polymer and solution hemoglobin concentration. Other parameters which influence the interaction of these processes are the concentration of 2,3-diphosphoglycerate and total hemoglobin concentration. By comparing our model predictions for oxygen unloading with simpler predictions based on equilibrium oxygen affinities, we conclude that the relative rate of oxygen unloading of cells with different physical properties cannot be correctly predicted from the equilibrium affinities. To describe the unloading process, a kinetic calculation of the sort we give here is required.     

Peripheral skin temperature effects on muscle oxygen levels

In both hot and cold environments, tissue oxygen saturation levels may affect muscle performance. Using near-infrared spectroscopy, muscle oxygen saturation (StO2) and total hemoglobin levels were measured during exercise. Lowering skin temperature caused a greater StO2 and total hemoglobin decrease by 16% and 15.9%, respectively, compared to controls. Increasing skin temperature resulted in a smaller decrease in both StO2 and total hemoglobin by 12.2% and 8.2%, respectively, compared to controls. These data indicate that warming the skin will cause less of decrease in StO2 and total hemoglobin, while cooling the skin has the opposite effect.     

High and low oxygen affinity conformations of T state hemoglobin

To understand the interplay between tertiary and quaternary transitions associated with hemoglobin function and regulation, oxygen binding curves were obtained for hemoglobin A fixed in the T quaternary state by encapsulation in wet porous silica gels. At pH 7.0 and 15 degrees C, the oxygen pressure at half saturation (p50) was measured to be 12.4 +/- 0.2 and 139 +/- 4 torr for hemoglobin gels prepared in the absence and presence of the strong allosteric effectors inositol hexaphosphate and bezafibrate, respectively. Both values are in excellent agreement with those found for the binding of the first oxygen to hemoglobin in solution under similar experimental conditions. The corresponding Hill coefficients of hemoglobin gels were 0.94 +/- 0.02 and 0.93 +/- 0.03, indicating, in the frame of the Monod, Wyman, and Changeux model, that high and low oxygen-affinity tertiary T-state conformations have been isolated in a pure form. The values, slightly lower than unity, reflect the different oxygen affinity of alpha- and beta-hemes. Significantly, hemoglobin encapsulated in the presence of the weak effector phosphate led to gels that show intermediate oxygen affinity and Hill coefficients of 0.7 to 0.8. The heterogeneous oxygen binding results from the presence of a mixture of the high and low oxygen-affinity T states. The Bohr effect was measured for hemoglobin gels containing the pure conformations and found to be more pronounced for the high-affinity T state and almost absent for the low-affinity T state. These findings indicate that the functional properties of the T quaternary state result from the contribution of two distinct, interconverting conformations, characterized by a 10-fold difference in oxygen affinity and a different extent of tertiary Bohr effect. The very small degree of T-state cooperativity observed in solution and in the crystalline state might arise from a ligand-induced perturbation of the distribution between the high- and low-affinity T-state conformations.     

Solubilities and Diffusivities of Oxygen in Hemolyzed Human Blood Solutions

By continuous absorption and by bubble collapse methods respectively, the solubilities and diffusion coefficients of oxygen in water and in dilute solutions of human hemoglobin (1.11, 2.22, and 4.44 wt%) have been determined at one atmosphere and 10°, 20°, 30°, 40°, 50°, and 60°C. Measured equilibrium constants, oxygen/hemoglobin ratios and isochoric heats of solution have been interpreted in terms of various mechanisms for oxygen-hemoglobin interaction. Oxygen diffusivities obtained experimentally for the hemolyzed blood solutions have been found to compare favorably with those predicted by a model of facilitated transport proposed by Houghton (1966). The diffusion measurements indicate that, while kinetic phenomena cannot be ignored, the over-all rate of exchange of oxygen with hemoglobin is not a controlling factor in facilitated diffusion. Anomalous equilibrium constants and temperature coefficients have been observed in the most dilute hemoglobin solution at the lowest temperatures.     

Nonequilibrium-Facilitated Oxygen Transport in Hemoglobin Solution

We have used the quasi-linearization method to obtain numerical solutions to the equations which describe steady-state diffusion of oxygen through layers of hemoglobin solution. The numerical solutions show how the facilitated flux of oxygen depends upon the layer thickness, reaction-rate coefficients, and other parameters of the system. The results indicate that steady-state oxygen diffusion in layers of hemoglobin solution, similar to those studied by Scholander, should be adequately described by the models which assume chemical equilibrium exists throughout the layer, but for layers of concentrated hemoglobin solution about the thickness of a human erythrocyte, the facilitation of oxygen diffusion should be much less than the equilibrium models predict.     

Mechanical characterisation of in vivo human skin using a 3D force-sensitive micro-robot and finite element analysis

The complex mechanical properties of skin have been the subject of much study in recent years. Several experimental methods developed to measure the mechanical properties of skin in vivo, such as suction or torsion, are unable to measure skin’s anisotropic characteristics. An experiment characterising the mechanical properties of in vivo human skin using a novel force-sensitive micro-robot is presented. The micro-robot applied in-plane deformations to the anterior forearm and the posterior upper arm. The behaviour of the skin in each area is highly nonlinear, anisotropic, and viscoelastic. The response of the upper arm skin is very dependent on the orientation of the arm. A finite element model consisting of an Ogden strain energy function and quasi-linear viscoelasticity was developed to simulate the experiments. An orthogonal initial stress field, representing the in vivo skin tension, was used as an additional model parameter. The model simulated the experiments accurately with an error-of-fit of 17.5% for the anterior lower forearm area, 6.5% for the anterior upper forearm and 9.3% for the posterior upper arm. The maximum in vivo tension in each area determined by the model was 6.2 Nm⁻¹ in the anterior lower forearm, 11.4 Nm⁻¹ in anterior upper forearm and 5.6 Nm⁻¹ in the posterior upper arm. The results also show that a finite element model with a neo-Hookean strain energy function cannot simulate the experiments with the same accuracy.     

A mechanism for indirect allosteric action of charged effectors

A mechanism for indirect allosteric action of charged effectors on substrate binding to a macromolecule is proposed. It is accounted for by electrostatic interaction among effectors in the solution, away from their receptors. The possibility of the mechanism proposed is tested in the allosteric action of univalent salt and 2,3-diphosphoglycerate on oxygen binding to hemoglobin. A model for electrostatic interaction between these two effectors in the solution and for their overall effect on oxygen binding is introduced. The 2,3-diphosphoglycerate binding constant to deoxygenated hemoglobin as a function of univalent salt concentration and the median ligand activity as a function of the concentration of univalent salt and 2,3-diphoshoglycerate are calculated and compared with experimental data. The obtained results indicate that electrostatic interaction in the solution may significantly contribute to indirect allosteric action of charged effectors. Partly presented at the “11th FEBS Meeting” in Copenhagen, August 1977     

On the determination of species fractions from ligand-binding data. Application to human hemoglobin

A method outlined in a previous study (S.J. Gill, H.T. Gaud, J. Wyman and G. Barisas, Biophys. Chem. 8 (1978) 53) is applied for the determination of species fractions from ligand-binding data for the oxygen reaction with human hemoglobin. The results obtained by this alternative approach, which is based on the solution of a system of linear equations, are consistent with those obtained using nonlinear least-squares analysis.     

In vitro kinetics of oxygen transport in erythrocyte suspension or unmodified hemoglobin solution from human and other animals

Oxygen transport behavior in erythrocyte suspension or in hemoglobin solution was studied as a potential therapeutic model for the clinical treatment of blood loss, and this can also provide physiological data with which to evaluate blood substitutes. In the present project, we examined the in vitro kinetics of hemoglobin binding to and releasing oxygen, to provide detailed oxygen-flux measurements for unmodified hemoglobin solutions and erythrocyte suspensions in human, as well as other vertebrates. An in vitro method was used, based on a widely used artificial system, with the oxygen saturation level being detected in real time. Results from this study indicated that the kinetic curves of human erythrocyte suspensions and hemoglobin solutions were either S-shaped or hyperbolic, respectively. Based on these curves, the significance of T(50) emerged in our investigation, where T(50) is defined as the time needed for 50% hemoglobin to be saturated with oxygen, and reflects the efficiency with which hemoglobin carries oxygen. This parameter may be used to diagnose blood diseases, and could be a standard for evaluating blood substitutes. In this study, we also compared the T(50) of 4 species of vertebrates, and found that it shows a distinct efficiency of oxygen binding related to species, and potentially reveals the evolutionary function of hemoglobin and its possible adaptation to the environment.     

Nanobiotechnological modification of hemoglobin and enzymes from this laboratory

Polyhemoglobin is formed by the nanobiotechnological assembling of hemoglobin molecules into soluble nanodimension complex. A further step involves the nanobiotechnological assembly of hemoglobin, catalase and superoxide dismutase into a soluble nanodimension complex. This acts both as oxygen carrier and antioxidant to prevent the oxidative effects of hemoglobin. A further step is the preparation of nanodimension artificial red blood cells that contain hemoglobin and all the enzymes present in red blood cells. Other approaches include a polyhemoglobin-fibrinogen that acts as an oxygen carrier with platelet-like activity, and a polyhemoglobin-tyrosinase to retard the growth of a fatal skin cancer, melanoma.     

A compartmental model for oxygen transport in brain microcirculation in the presence of blood substitutes

A compartmental model is developed for oxygen (O(2)) transport in brain microcirculation in the presence of blood substitutes (hemoglobin-based oxygen carriers). The cerebrovascular bed is represented as a series of vascular compartments, on the basis of diameters, surrounded by a tissue compartment. A mixture of red blood cells (RBC) and plasma/extracellular hemoglobin solution flows through the vascular bed from the arterioles through the capillaries to the venules. Oxygen is transported by convection in the vascular compartments and by diffusion in the surrounding tissue where it is utilized. Intravascular resistance and the diffusive loss of oxygen from the arterioles to the tissue are incorporated in the model. The model predicts that most of the O(2) transport occurs at the level of capillaries. Results computed from the present model in the presence of hemoglobin-based oxygen carriers are consistent with those obtained from the earlier validated model (Sharan et al., 1989, 1998a) on oxygen transport in brain circulation in the absence of extracellular hemoglobin. We have found that: (a) precapillary PO(2) gradients increase as PO(2) in the arterial blood increases, P(50 p) (oxygen tension at 50% saturation of hemoglobin with O(2) in plasma) decreases, i.e. O(2) affinity of the extracellular hemoglobin is increased, the flow rate of the mixture decreases, hematocrit decreases at constant flow, metabolic rate increases, and intravascular transport resistance in the arterioles is neglected; (b) precapillary PO(2) gradients are not sensitive to (i) intracapillary transport resistance, (ii) cooperativity (n(p)) of hemoglobin with oxygen in plasma, (iii) hemoglobin concentration in the plasma and (iv) hematocrit when accounting for viscosity variation in the flow; (c) tissue PO(2) is not sensitive to the variation of intravascular transport resistance in the arterioles. We also found that tissue PO(2) is a non-monotonic function of the Hill coefficient n(p) for the extracellular hemoglobin with a maximum occurring when n(p) equals the blood Hill coefficient. The results of the computations give estimates of the magnitudes of the increases in tissue PO(2) as arterial PO(2) increases,P(50 p) increases, flow rate increases, hematocrit increases, hemoglobin concentration in the plasma increases, metabolic rate decreases, the capillary mass transfer coefficient increases or the intracapillary transport resistance decreases.     

A reaction cell for simultaneous measurements of fluorescence and absorption in a hemoglobin solution at various oxygen pressures

An apparatus was constructed to carry out measurements of fluorescence, optical absorption and oxygen partial pressure in a hemoglobin or other solution simultaneously, and its performance was examined. This apparatus has a rhombiform optical cell in place of the usual square optical cell used in commercially available spectrofluorometers. Fluorescence emitted at the region near the cell surface in the solution could be detected satisfactorily and easily even if the solution had strong light absorption bands at both the excitation and the emission wavelengths in the presence of high concentrations of a chromophore. This apparatus was particularly effective for studies on the interactions of a fluorescent allosteric effector with hemoglobin at various degrees of deoxygenation. Consequently, it was proved experimentally that the fluorescence of β-naphthyl triphosphate bound to hemoglobin is completely quenched. Moreover, simultaneous and continuous measurements of the oxygen-binding equilibrium of hemoglobin and the allosteric effector-binding to hemoglobin as a function of oxygen partial pressure could be satisfactorily carried out, and it is confirmed that β-naphthyl triphosphate binds not only to deoxyhemoglobin but also to fully oxygenated hemoglobin and lowers strongly the oxygen affinity of hemoglobin as an allosteric effector.     

A quantitative framework for the design of acellular hemoglobins as blood substitutes: implications of dynamic flow conditions

The delivery of oxygen to tissue by cell-free carriers eliminates intraluminal barriers associated with red blood cells. This is important in arterioles, since arteriolar tone controls capillary perfusion. We describe a mathematical model for O(2) transport by hemoglobin solutions and red blood cells flowing through arteriolar-sized tubes to optimize values of p50, Hill number, hemoglobin molecular diffusivity and concentration. Oxygen release is evaluated by including an extra-luminal resistance term to reflect tissue oxygen consumption. For low consumption (i.e., high resistance to O(2) release) a hemoglobin solution with p50=15 mmHg, n=1, D(HBO2)=3 x 10(-7) cm(2)/s delivers O(2) at a rate similar to that of red blood cells. For high consumption, the p50 must be decreased to 5 mmHg. The model predicts that regardless of size, hemoglobin solutions with higher p50 will present excess O(2) to arteriolar walls. Oversupply of O(2) to arteriolar walls may cause constriction and paradoxically reduced capillary perfusion.     

Evaluation and propagation of confidence intervals in nonlinear, asymmetrical variance spaces. Analysis of ligand-binding data

Two problems that are often overlooked in studies employing nonlinear least-squares techniques for parameter estimation are confidence-interval estimation and propagation. When the parameters are correlated, the variance space and consequently the confidence intervals are nonlinear and asymmetrical. The presented mathematical method for the evaluation of confidence intervals and error propagation addresses these problems. The examples employed to demonstrate these methods include linear least-squares and the nonlinear least-squares analysis of ligand-binding problems, such as hormone receptor interactions and oxygen binding to human hemoglobin. The mathematical procedures have proven very useful for analyzing the molecular mechanism of cooperativity in human hemoglobin (Johnson, M. L., and G. K. Ackers, 1982. Biochemistry 21:201-211).     

Nonequilibrium Thermodynamic Analysis of the Coupling between Active Sodium Transport and Oxygen Consumption

Sodium transport and oxygen consumption have been simultaneously studied in the short-circuited toad skin. A constant stoichiometric ratio was observed in each skin under control condition (NaCl-Ringer's solution bathing both sides of the skin) and after block of sodium transport by ouabain. During alterations of sodium transport by removal and addition of K to the internal solution the stoichiometric ratio is constant although having a value higher than that observed in other untreated skins. The coupling between active sodium transport and oxygen consumption was studied after a theoretical nonequilibrium thermodynamic model. Studies were made of the influence of Na chemical potential difference across the skin on the rates of Na transport and oxygen consumption. A linear relationship was observed between the rates of Na transport and oxygen consumption and the Na chemical potential difference. Assuming the Onsager relationship to be valid, the three phenomenological coefficients which describe the system were evaluated. Transient increases in the rate of sodium transport and oxygen consumption were observed after a transitory block of sodium transport by removal of Na from the external solution. Cyanide blocks completely the rate of oxygen consumption in less than 2 min and the short-circuit current measured after that time decays exponentially with time, suggesting a depletion of ATP from a single compartment.     

Net charge and oxygen affinity of human hemoglobin are independent of hemoglobin concentration

The dependence of net charge and oxygen affinity of human hemoglobin upon hemoglobin concentration was reinvestigated. In contrast to earlier reports from various laboratories, both functional properties of hemoglobin were found to be independent of hemoglobin concentration. Two findings indicate a concentration-independent net charge of carbonmonoxy hemoglobin at pH 6.6: (A) The pH value of a given carbonmonoty hemoglobin solution remains constant at 6.6 when the hemoglobin concentration is raised from 10 to 40 g/dl, indicating that there is no change in protonation of titratable groups of hemoglobin: (b) the net charge of carbonmonoxy hemoglobin as estimated from the Donnan distribution of 22Na+ shows no dependence on hemoglobin concentration in this concentration range. The oxygen affinity of human hemoglobin was determined from measurements of oxygen concentrations in equilibrated samples using a Lex-O2-Con apparatus (Lexington Instruments, Waltham, Mass.). P50 averaged 11.4 mm Hg at 37 degrees C, pH = 7.2, and ionic strength approximately 0.15. Neither P50 nor Hill's n showed any variation with hemoglobin concentrations increasing from 10 to 40 g/dl.