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.     

Numerical simulation of oxygen delivery to muscle tissue in the presence of hemoglobin-based oxygen carriers

This work represents a culmination of research on oxygen transport to muscle tissue, which takes into account oxygen transport due to convection, diffusion, and the kinetics of simultaneous reactions between oxygen and hemoglobin and myoglobin. The effect of adding hemoglobin-based oxygen carriers (HBOCs) to the plasma layer of blood in a single capillary surrounded by muscle tissue based on the geometry of the Krogh tissue cylinder is examined for a range of HBOC oxygen affinity, HBOC concentration, capillary inlet oxygen tension (pO(2)), and hematocrit. The full capillary length of the hamster retractor muscle was modeled under resting (V(max) = 1.57 x 10(-4) mLO(2) mL(-1) s(-1), cell velocity (v(c)) = 0.015 cm/s) and working (V(max) = 1.57 x 10(-3) mLO(2) mL(-1) s(-1), v(c) = 0.075 cm/s) conditions. Two spacings between the red blood cell (RBC) and the capillary wall were examined, corresponding to a capillary with and without an endothelial surface layer. Simulations led to the following conclusions, which lend physiological insight into oxygen transport to muscle tissue in the presence of HBOCs: (1) The reaction kinetics between oxygen and myoglobin in the tissue region, oxygen and HBOCs in the plasma, and oxygen and RBCs in the capillary lumen should not be neglected. (2) Simulation results yielded new insight into possible mechanisms of oxygen transport in the presence of HBOCs. (3) HBOCs may act as a source or sink for oxygen in the capillary and may compete with RBCs for oxygen. (4) HBOCs return oxygen delivery to muscle tissue to normal for varying degrees of hypoxia (inlet capillary pO(2) < 30 mmHg) and anemia (hematocrit < 46%) for the hamster model.     

Role of myoglobin in the oxygen supply to red skeletal muscle.

The contribution of nyoglobin to the oxygen uptake of red skeletal muscle was estimated from the difference in oxygen uptake with and without functional myoglobin. The oxygen uptake of bundles (25 mm long, 0.5 mm mean diameter) of muscle fibers teased from pigeon breast muscle was measured in families of steady states of oxygen pressure from 0 to 250 mm Hg. The oxygen-binding function of myoglobin, in situ in muscle fiber bundles, was abolished by treatment with nitrite of hydroxylamine, which convert oxymyoglobin in situ to high spin ferric myoglobin, or with phenylhydrazine, which converts oxymyoglobin to denatured products, or with 2-hydroxyethylhydrazine, which appears to remove myoglobin from the muslce. The oxygen uptake was again measured. At higher oxygen pressure, where oxygen availability does not limit the respiration of the fiber bundles, oxygen uptake is not affected by any of the four reagents, which is evidence that mitochondrial oxygen uptake is not impaired. At lower oxygen pressure, where oxygen uptake is one-half maximal, the steady state oxygen consumption is roughly halved by abolishing functional myoglobin. Under the steady state conditions studied, the storage function of myoglobin, being static, vanishes and the transport function stands revealed. We conclude from these experiments that myoglobin may transport a significant fraction of the oxygen consumed by muscle mitochondria.     

Effects of Fiber Type and Size on the Heterogeneity of Oxygen Distribution in Exercising Skeletal Muscle

The process of oxygen delivery from capillary to muscle fiber is essential for a tissue with variable oxygen demand, such as skeletal muscle. Oxygen distribution in exercising skeletal muscle is regulated by convective oxygen transport in the blood vessels, oxygen diffusion and consumption in the tissue. Spatial heterogeneities in oxygen supply, such as microvascular architecture and hemodynamic variables, had been observed experimentally and their marked effects on oxygen exchange had been confirmed using mathematical models. In this study, we investigate the effects of heterogeneities in oxygen demand on tissue oxygenation distribution using a multiscale oxygen transport model. Muscles are composed of different ratios of the various fiber types. Each fiber type has characteristic values of several parameters, including fiber size, oxygen consumption, myoglobin concentration, and oxygen diffusivity. Using experimentally measured parameters for different fiber types and applying them to the rat extensor digitorum longus muscle, we evaluated the effects of heterogeneous fiber size and fiber type properties on the oxygen distribution profile. Our simulation results suggest a marked increase in spatial heterogeneity of oxygen due to fiber size distribution in a mixed muscle. Our simulations also suggest that the combined effects of fiber type properties, except size, do not contribute significantly to the tissue oxygen spatial heterogeneity. However, the incorporation of the difference in oxygen consumption rates of different fiber types alone causes higher oxygen heterogeneity compared to control cases with uniform fiber properties. In contrast, incorporating variation in other fiber type-specific properties, such as myoglobin concentration, causes little change in spatial tissue oxygenation profiles.     

Effect of the rate of oxygen consumption on muscle respiration

Summary An important role of myoglobin in red muscle is to facilitate the diffusion of oxygen for metabolism. We consider a model for muscle respiration in which the oxygen consumption is of a MichaelisMenten form. The resulting mathematical model is solved in two different ways with two different boundary conditions. The first uses the singular perturbation method of Murray (1974), while the second, which gives another justication of the simpler procedure, is a direct numerical computation of the full problem.The oxygen tension and saturation are often small. For realistic values of the Michaelis-Menten constant the oxygen tension, the saturation and the radius of the region in which the oxygen tension is negligibly small can be calculated using the constant consumption model of Murray (1974), with corrected boundary conditions (those for a Stefan problem), which in certain circumstances markedly affect the solution.B. A. T. would like to thank the Science Research Council of the United Kingdom for their financial support.     

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.     

Evolution of a "falx lunatica" in demarcation of critically ischemic myocutaneous tissue

Using intravital microscopy in a chronic in vivo mouse model, we studied the demarcation of myocutaneous flaps and evaluated microvascular determinants for tissue survival and necrosis. Chronic ischemia resulted in a transition zone, characterized by a red fringe and a distally adjacent white falx, which defined the demarcation by dividing the proximally normal from the distally necrotic tissue. Tissue survival in the red zone was determined by hyperemia, as indicated by recovery of the transiently reduced functional capillary density, and capillary remodeling, including dilation, hyperperfusion, and increased tortuosity. Angiogenesis and neovascularization were not observed over the 10-day observation period. The white rim distal to the red zone, appearing as "falx lunatica," showed a progressive decrease of functional capillary density similar to that of the necrotic distal area but without desiccation, and thus transparency, of the tissue. Development of the distinct zones of the critically ischemic tissue could be predicted by partial tissue oxygen tension (Pt(O(2))) analysis by the time of flap elevation. The falx lunatica evolved at a Pt(O(2)) between 6.2 +/- 1.3 and 3.8 +/- 0.7 mmHg, whereas tissue necrosis developed at <3.8 +/- 0.7 mmHg. Histological analysis within the falx lunatica revealed interstitial edema formation and muscle fiber nuclear rarefaction but an absence of necrosis. We have thus demonstrated that ischemia-induced necrosis does not demarcate sharply from normal tissue but develops beside a fringe of tissue with capillary remodeling an adjacent falx lunatica that survives despite nutritive capillary perfusion failure, probably by direct oxygen diffusion.     

The flow of sickle-cell blood in the capillaries.

Oxygen tension levels and red cell velocities for the flow of sickle-cell blood in the capillaries are determined by using the Krogh model for oxygen transport and lubrication theory for the cell motion. The coupling and interaction between these arises from the red cell compliance, which is assumed to vary with the oxygen concentration. Microsieving data is used to establish an upper bound for this relationship. Calculations are carried out for a range of capillary sizes, taking into account the rightward shift of the oxyhemoglobin dissociation curve and the reduced hematocrit of sickle-cell blood, and are compared to, as a base case, the flow of normal blood under normal pressure gradient. The results indicate that under normal pressure gradients the oxygen tensions and cell velocities for sickle blood are considerably higher than for normal blood, thus acting against the tendency for cells to sickle, or significantly change their rheological properties, in the capillaries. Under reduced pressure gradients, however, the concentrations and velocities drop dramatically, adding to the likelihood of such shape or flow property changes.     

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.     

Mechanical Properties of the Sarcolemma and Myoplasm in Frog Muscle as a Function of Sarcomere Length

The elastimeter method was applied to the single muscle fiber of the frog semitendinosus to obtain the elastic moduli of the sarcolemma and myoplasm, as well as their relative contributions to resting fiber tension at different extensions. A bleb which was sucked into a flat-mouthed pipette at the fiber surface separated into an external sarcolemmal membrane and a thick inner myoplasmic region. Measurements showed that the sarcolemma does not contribute to intact fiber tension at sarcomere lengths below 3 µ. It was estimated that the sarcolemma contributed on the order of 10% to intact fiber tension at sarcomere lengths between 3 and 3.75 µ, and more so with further extension. Between these sarcomere lengths, the sarcolemma can be linearly extended and has a longitudinal elastic modulus of 5 x 10⁶ dyne/cm² (assuming a thickness of 0.1 µ). Resistance to deformation of the inner bleb region is due to myoplasmic elasticity. The myoplasmic elastic modulus was estimated by use of a model and was used to predict a fiber length-tension curve which agreed approximately with observations.     

Myocardial oxygenation in isolated hearts predicted by an anatomically realistic microvascular transport model

An anatomically realistic model for oxygen transport in cardiac tissue is introduced for analyzing data measured from isolated perfused guinea pig hearts. The model is constructed to match the microvascular anatomy of cardiac tissue based on available morphometric data. Transport in the three-dimensional system (divided into distinct microvascular, interstitial, and parenchymal spaces) is simulated. The model is used to interpret experimental data on mean cardiac tissue myoglobin saturation and to reveal differences in tissue oxygenation between buffer-perfused and red blood cell-perfused isolated hearts. Interpretation of measured mean myoglobin saturation is strongly dependent on the oxygen content of the perfusate (e.g., red blood cell-containing vs. cell-free perfusate). Model calculations match experimental values of mean tissue myoglobin saturation, measured mean myoglobin, and venous oxygen tension and can be used to predict distributions of intracellular oxygen tension. Calculations reveal that approximately 20% of the tissue is hypoxic with an oxygen tension of <0.5 mmHg when the buffer is equilibrated with 95% oxygen to give an arterial oxygen tension of over 600 mmHg. The addition of red blood cells to give a hematocrit of only 5% prevents tissue hypoxia. It is incorrect to assume that the usual buffer-perfused Langendorff heart preparation is adequately oxygenated for flows in the range of < or =10 ml. min-1. ml tissue-1.     

The rate of the deoxygenation reaction limits myoglobin- and hemoglobin-facilitated O₂ diffusion in cells

A mathematical model describing facilitation of O(2) diffusion by the diffusion of myoglobin and hemoglobin is presented. The equations are solved numerically by a finite-difference method for the conditions as they prevail in cardiac and skeletal muscle and in red cells without major simplifications. It is demonstrated that, in the range of intracellular diffusion distances, the degree of facilitation is limited by the rate of the chemical reaction between myglobin or hemoglobin and O(2). The results are presented in the form of relationships between the degree of facilitation and the length of the diffusion path on the basis of the known kinetics of the oxygenation-deoxygenation reactions. It is concluded that the limitation by reaction kinetics reduces the maximally possible facilitated oxygen diffusion in cardiomyoctes by ～50% and in skeletal muscle fibers by ～ 20%. For human red blood cells, a reduction of facilitated O(2) diffusion by 36% is obtained in agreement with previous reports. This indicates that, especially in cardiomyocytes and red cells, chemical equilibrium between myoglobin or hemoglobin and O(2) is far from being established, an assumption that previously has often been made. Although the "O(2) transport function" of myoglobin in cardiac muscle cells thus is severely limited by the chemical reaction kinetics, and to a lesser extent also in skeletal muscle, it is noteworthy that the speed of release of O(2) from MbO(2), the "storage function," is not limited by the reaction kinetics under physiological conditions.     

A theoretical model for oxygen transport in skeletal muscle under conditions of high oxygen demand.

Oxygen transport from capillaries to exercising skeletal muscle is studied by use of a Krogh-type cylinder model. The goal is to predict oxygen consumption under conditions of high demand, on the basis of a consideration of transport processes occurring at the microvascular level. Effects of the decline in oxygen content of blood flowing along capillaries, intravascular resistance to oxygen diffusion, and myoglobin-facilitated diffusion are included. Parameter values are based on human skeletal muscle. The dependence of oxygen consumption on oxygen demand, perfusion, and capillary density are examined. When demand is moderate, the tissue is well oxygenated and consumption is slightly less than demand. When demand is high, capillary oxygen content declines rapidly with axial distance and radial oxygen transport is limited by diffusion resistance within the capillary and the tissue. Under these conditions, much of the tissue is hypoxic, consumption is substantially less than demand, and consumption is strongly dependent on capillary density. Predicted consumption rates are comparable with experimentally observed maximal rates of oxygen consumption.     

Comparison of buffer and red blood cell perfusion of guinea pig heart oxygenation

Myocardial mean myoglobin oxygen saturation was determined spectroscopically from isolated guinea pig hearts perfused with red blood cells during increasing hypoxia. These experiments were undertaken to compare intracellular myoglobin oxygen saturation in isolated hearts perfused with a modest concentration of red blood cells (5% hematocrit) with intracellular myoglobin saturation previously reported from traditional buffer-perfused hearts. Studies were performed at 37 degrees C with hearts paced at 240 beats/min and a constant perfusion pressure of 80 cmH2O. It was found that during perfusion with a hematocrit of 5%, baseline mean myoglobin saturation was 93% compared with 72% during buffer perfusion. Mean myoglobin saturation, ventricular function, and oxygen consumption remained fairly constant for arterial perfusate oxygen tensions above 100 mmHg and then decreased precipitously below 100 mmHg. In contrast, mean myoglobin saturation, ventricular function, and oxygen consumption began to decrease even at high oxygen tension with buffer perfusion. The present results demonstrate that perfusion with 5% red blood cells in the perfusate increases the baseline mean myoglobin saturation and better preserves cardiac function at low oxygen tension relative to buffer perfusion. These results suggest that caution should be used in extrapolating intracellular oxygen dynamics from buffer-perfused to blood-perfused hearts.     

Mitochondrial respiratory control can compensate for intracellular O(2) gradients in cardiomyocytes at low PO(2)

In isolated single cardiomyocytes with moderately elevated mitochondrial respiration, direct evidence for intracellular radial gradients of oxygen concentration was obtained by subcellular spectrophotometry of myoglobin (Mb). When oxygen consumption was increased by carbonyl cyanide m-chlorophenylhydrazone (CCCP) during superfusion of cells with 4% oxygen, PO(2) at the cell core dropped to 2.3 mmHg, whereas Mb near the plasma membrane was almost fully saturated with oxygen. Subcellular NADH fluorometry demonstrated corresponding intracellular heterogeneities of NADH, indicating suppression of mitochondrial oxidative metabolism due to relatively slow intracellular oxygen diffusion. When oxygen consumption was increased by electrical pacing in 2% oxygen, radial oxygen gradients of similar magnitude were demonstrated (cell core PO(2) = 2.6 mmHg). However, an increase in NADH fluorescence at the cell core was not detected. Because CCCP abolished mitochondrial respiratory control while it was intact in electrically paced cardiomyocytes, we conclude that mitochondria with intact respiratory control can sustain electron transfer with reduced oxygen supply. Thus mitochondrial intrinsic regulation can compensate for relatively slow oxygen diffusion within cardiomyocytes.     

The distribution and arrangement of microtubules in mammalian skeletal muscle fibers

The distribution and arrangement of microtubules (MTs) in skeletal muscle fibers of the rat and mouse diaphragm were examined by thin-section electron microscopy. In the central portion of muscle fibers, most MTs ran longitudinally between myofibrils and beneath the sarcolemma, and some MTs ran transversely predominantly at the level of the I band, especially of the A-I junction, thus forming a lattice-like arrangement. At the fiber periphery, MTs were aggregated in the perinuclear region, from which they radiated to take a longitudinal course beneath the sarcolemma and to run in a transverse direction at the I-band level. In the end portion of muscle fibers, MTs were abundant and ran longitudinally into sarcoplasmic processes. MTs were often found to be spatially associated with membranous organelles. Quantitative analyses indicated that the longitudinally running MTs were remarkably more numerous in the peripheral zone of muscle fibers than in the deeper zones. The density of MTs in the central portion was almost the same in both red and white muscle fibers. The density was significantly higher at the fiber ends, though it varied considerably among different fibers. These results are discussed with special reference to the possible involvement of MTs in intracellular transport as well as structural support.     

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     

Localization of ionic conductances in crayfish muscle fibers

Summary Analysis of the changes in membrane potential and conductance of isolated crayfish muscle fibers caused by rapid solution changes leads to the following conclusions. First, the extensive invagination system of this fiber presents a barrier for diffusion between bath and sarcolemma that accounts for the time lag of electrical responses to changes in bath chloride concentration. Morphological data regarding these invaginations were used in a model which simulated the fiber response on an analog computer. Second, the potassium conductance is effectively localized on the sarcolemma in direct contact with the bath (superficial sarcolemma), whereas the chloride conductance is restricted to the invaginations. This distribution of conductances is the reverse of that found in frog muscle.     

Determination of myoglobin concentration and oxidative capacity in cryostat sections of human and rat skeletal muscle fibres and rat cardiomyocytes

Myoglobin plays various roles in oxygen supply to muscle mitochondria. It is difficult, and in some cases impossible, to study the relationship between the myoglobin concentration and the oxidative capacity of individual muscle cells because myoglobin has to be fixed in situ whereas determination of oxidative capacity, for example, succinate dehydrogenase activity, requires unfixed cryostat sections. We have investigated whether a vapour-fixation technique allows the use of serial sections to study the relationship between myoglobin and succinate dehydrogenase activity. The technique is used to study a rat soleus muscle, two human skeletal muscle biopsies and biopsies of two patients with chronic heart failure, and in a control and hypertrophied rat heart. Staining intensities were quantified by microdensitometry. The absorbance values were calibrated using sections cut from gelatine blocks containing known amounts of myoglobin. The results show that it is possible to use serial sections for the determination of the myoglobin concentration and succinate dehydrogenase activity, and indicate that myoglobin can lead to a substantial reduction (18–60%) of the extracellular oxygen tension required to prevent an anoxic core in muscle cells.