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.     

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.     

A model study of intracellular oxygen gradients in a myoglobin-containing skeletal muscle fiber.

A theoretical two-dimensional model is used to investigate oxygen gradients in a red skeletal muscle fiber. The model describes the steady state, free and myoglobin-facilitated diffusion of oxygen into a respiring cylindrical muscle fiber cross section. The oxygen tension at the sarcolemma is assumed to vary along the sarcolemma as an approximation to the discrete capillary oxygen supply around the fiber. Maximal oxygen gradients are studied by considering parameters relevant to a maximally-respiring red muscle fiber. The model predicts that angular variations in the oxygen tension imposed at the sarcolemma due to the discrete capillary sources do not penetrate deeply into the fiber over a range of physiological values for myoglobin concentration, diffusion coefficients, number of surrounding capillaries, and oxygen tension level at the sarcolemma. Also, the oxygen tension in the core of the fiber is determined by the average oxygen tension at the sarcolemma. The drop in oxygen tension from fiber periphery to core, however, does depend significantly on the myoglobin concentration, the oxygen tension level at the sarcolemma, and the oxygen and myoglobin diffusivities. This dependence is summarized by calculating the minimum average sarcolemmal oxygen tension for maximal respiration without the development of an intracellular anoxic region. For a myoglobin-rich muscle fiber (0.5 mM myoglobin), the model predicts that maximal oxygen consumption can proceed with a relatively flat (less than 5 mm Hg) oxygen tension drop from fiber periphery to core over a large range for diffusion coefficients.     

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.     

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.     

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.     

The histochemical demonstration of myoglobin and succinic dehydrogenase activity in the tibialis anterior muscle of the rabbit

Summary The staining reactions for myoglobin and succinic dehydrogenase activity in the tibialis anterior of the rabbit demonstrate four types of muscle fibre. These may be distinguished by their intensity of staining for myoglobin and the distribution of the mitochondria shown by the dehydrogenase reaction.The large fibres (70–80 m diameter) which contain many mitochondria evenly scattered throughout the fibre contain much myoglobin. Smaller fibres (45–60 m diameter) which show an identical staining reaction for the dehydrogenase reaction contain less myoglobin. This suggests that myoglobin may be present to aid the diffusion of oxygen into muscle fibres.     

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.     

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.     

Distal heme pocket regulation of ligand binding and stability in soybean leghemoglobin

Leghemoglobins facilitate diffusion of oxygen through root tissue to a bacterial terminal oxidase in much the same way that myoglobin transports oxygen from blood to muscle cell mitochondria. Leghemoglobin serves an additional role as an oxygen scavenger to prevent inhibition of nitrogen fixation. For this purpose, the oxygen affinity of soybean leghemoglobin is 20-fold greater than myoglobin, resulting from an 8-fold faster association rate constant combined with a 3-fold slower dissociation rate constant. Although the biochemical mechanism used by myoglobin to bind oxygen has been described in elegant detail, an explanation for the difference in affinity between these two structurally similar proteins is not obvious. The present work demonstrates that, despite their similar structures, leghemoglobin uses methods different from myoglobin to regulate ligand affinity. Oxygen and carbon monoxide binding to a comprehensive set of leghemoglobin distal heme pocket mutant proteins in comparison to their myoglobin counterparts has revealed some of these mechanisms. The "distal histidine" provides a crucial hydrogen bond to stabilize oxygen in myoglobin but has little effect on bound oxygen in leghemoglobin and is retained mainly for reasons of protein stability and prevention of heme loss. Furthermore, soybean leghemoglobin uses an unusual combination of HisE7 and TyrB10 to sustain a weak stabilizing interaction with bound oxygen. Thus, the leghemoglobin distal heme pocket provides a much lower barrier to oxygen association than occurs in myoglobin and oxygen dissociation is regulated from the proximal heme pocket.     

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.     

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.     

Maintenance of myoglobin concentration in human skeletal muscle after heavy resistance training

The aim of this study was to determine the effects of 8 weeks of resistance training (RT) on the myoglobin concentration ([Mb]) in human skeletal muscle, and to compare the change in the [Mb] in two different RT protocols. The two types of protocol used were interval RT (IRT) of moderate to low intensity with a high number of repetitions and a short recovery time, and repetition RT (RRT) of high intensity with a low number of repetitions and a long recovery time. A group of 11 healthy male adults voluntarily participated in this study and were divided into IRT (n = 6) and RRT (n = 5) groups. Both training protocols were carried out twice a week for 8 weeks. At the completion of the training period, the one-repetition maximal force values and isometric force were increased significantly in all the subjects, by about 38.8% and 26.0%, respectively (P < 0.01). The muscle fibre composition was unchanged by the 8 weeks of training. The muscle fibre cross-sectional areas were increased significantly by both types of training in all fibre types (I, IIa and IIb, mean + 16.1 %, P < 0.05). The [Mb] showed no significant changes at the completion of the training [IRT from 4.63 (SD 0.63) to 4.48 (SD 0.72), RRT from 4.47 (SD 0.75) to 4.24 (SD 0.80) mg x g(-1) wet tissue] despite a significant decrease in citrate synthase activity [IRT from 5.27 (SD 1.45) to 4.49 (SD 1.48), RRT from 5.33 (SD 2.09) to 4.85 (SD 1.87) micromol x min(-1) x g(-1) wet tissue; P < 0.05] observed after both protocols. These results suggested that myoglobin and mitochondria enzymes were regulated by different mechanisms in response to either type of RT. Moreover, the maintained [Mb] in hypertrophied muscle should preserve oxygen transport from capillaries to mitochondria even when diffusion distance is increased.     

Mathematical modeling of myoglobin facilitated transport of oxygen in devices containing myoglobin-expressing cells

Low pO(2) is perhaps the most significant factor in artificial pancreas failure. In these environments, not only is the beta cell production of insulin reduced, but the cell death rate is also significantly higher. Mathematical models are developed to test the feasibility of facilitated oxygen transport in enhancing O(2) flux to genetically engineered cells in a bioartificial device such as a pancreas. For this device, it is proposed that beta cells be genetically engineered to express myoglobin throughout the cell. In addition, the significance of including myoglobin throughout the alginate matrix present to provide immuno-protection for the transplanted cells is considered. The mathematical analysis predicts that myoglobin facilitated oxygen transport has the potential of increasing the oxygen concentration at the centre of a cluster of cells (islet) with an effective radius of 100 microm by 50%. These theoretical models for myoglobin facilitated oxygen transport with homogeneous Michaelis-Menten consumption also indicate that including myoglobin in the alginate gel would beneficially improve the flux of oxygen to the transplanted cells.     

How does the eye breathe? Evidence for neuroglobin-mediated oxygen supply in the mammalian retina

Visual performance of the vertebrate eye requires large amounts of oxygen, and thus the retina is one of the highest oxygen-consuming tissues of the body. Here we show that neuroglobin, a neuron-specific respiratory protein distantly related to hemoglobin and myoglobin, is present at high amounts in the mouse retina (approximately 100 microm). The estimated concentration of neuroglobin in the retina is thus about 100-fold higher than in the brain and is in the same range as that of myoglobin in the muscle. Neuroglobin is expressed in all neurons of the retina but not in the retinal pigment epithelium. Neuroglobin mRNA was detected in the perikarya of the nuclear and ganglion layers of the neuronal retina, whereas the protein was present mainly in the plexiform layers and in the ellipsoid region of photoreceptor inner segment. The distribution of neuroglobin correlates with the subcellular localization of mitochondria and with the relative oxygen demands, as the plexiform layers and the inner segment consume most of the retinal oxygen. These findings suggest that neuroglobin supplies oxygen to the retina, similar to myoglobin in the myocardium and the skeletal muscle.     

A computational study of the effect of vasomotion on oxygen transport from capillary networks

The objective of this study was to investigate the effect of arteriolar vasomotion on oxygen transport from capillary networks. A computational model was used to calculate blood flow and oxygen transport from a simulated network of striated muscle capillaries. For varying tissue oxygen consumption rates, the importance of the frequency and amplitude of vasomotion-induced blood flow oscillations was studied. The effect of myoglobin on oxygen delivery during vasomotion was also examined. In the absence of myoglobin, it was found that when consumption is high enough to produce regions of hypoxia under steady flow conditions, vasomotion-induced flow oscillations can significantly increase tissue oxygenation and decrease oxygen transport heterogeneity. The largest effect was seen for low-frequency, high-amplitude oscillations (1.5-3 cycles min(-1), 90% of steady-state velocity). By contrast, at physiological tissue myoglobin concentrations, vasomotion did not improve tissue oxygenation. This unexpected finding is due to the buffering effect of myoglobin, suggesting that in highly aerobic muscles short-term storage of oxygen is more important than the possibility of increasing transport through vasomotion.     

Myoglobin and mitochondria: a relationship bound by oxygen and nitric oxide

Since their initial discovery over a century ago, our knowledge of the functions of myoglobin and the mitochondrion has gradually evolved. The mitochondrion, once thought to be solely responsible for energy production, is now known to be an integral redox and apoptotic signal transducer within the cell. Likewise, myoglobin, traditionally thought of only as an oxygen store, has emerged as a physiological catalyst that can modulate reactive oxygen species levels, facilitate oxygen diffusion and scavenge or generate nitric oxide (NO) depending on oxygen tensions within the cell. By virtue of its unique ability to regulate O(2) and NO levels within the cell, myoglobin can modulate mitochondrial function in energy-demanding tissues such as the beating heart and exercising muscle. In this review, we present the conventional functions of myoglobin and mitochondria, and describe how these roles have been reassessed and advanced, particularly in the context of NO and nitrite signaling. We present the mechanisms by which mitochondria and myoglobin regulate one another within the cell through their interactions with NO and oxygen and discuss the implications of these interactions in terms of health and disease.     

Reduction of anoxia through myoglobin-facilitated diffusion of oxygen.

At relatively low perfusion rates, anoxic regions may occur in tissue even though oxygen remains in the blood as it leaves the capillary at the venous end. In this paper a mathematical theory of facilitated diffusion is developed and used to determine the extent to which myoglobin increases the removal of oxygen from blood and aids in the reduction or elimination of regions of anoxia.     

Model of nitric oxide diffusion in an arteriole: impact of hemoglobin-based blood substitutes

Administration of hemoglobin-based oxygen carriers (HBOCs) frequently results in vasoconstriction that is primarily attributed to the scavenging of endothelium-derived nitric oxide (NO) by cell-free hemoglobin. The ensuing pressor response could be caused by the high NO reactivity of HBOC in the vascular lumen and/or the extravasation of hemoglobin molecules. There is a need for quantitative understanding of the NO interaction with HBOC in the blood vessels. We developed a detailed mathematical model of NO diffusion and reaction in the presence of an HBOC for an arteriolar-size vessel. The HBOC reactivity with NO and degree of extravasation was studied in the range of 2-58 x 10(6) M(-1) x s(-1) and 0-100%, respectively. The model predictions showed that the addition of HBOC reduced the smooth muscle (SM) NO concentration in the activation range (12-28 nM) for soluble guanylate cyclase, a major determinant of SM contraction. The SM NO concentration was significantly reduced when the extravasation of HBOC molecules was considered. The myoglobin present in the parenchymal cells scavenges NO, which reduces the SM NO concentration.