Reappraisal of diffusion, solubility, and consumption of oxygen in frog skeletal muscle, with applications to muscle energy balance

A model of anemic tissue perfusion after blood transfusion shows critical role of endothelial response to shear stress stimuli

Although some of the cardiovascular responses to changes in hematocrit (Hct) are not fully quantified experimentally, available information is sufficient to build a mathematical model of the consequences of treating anemia by introducing RBCs into the circulation via blood transfusion. We present such a model, which describes how the treatment of normovolemic anemia with blood transfusion impacts oxygen (O₂) delivery (DO₂, the product of blood O₂ content and arterial blood flow) by the microcirculation. Our analysis accounts for the differential response of the endothelium to the wall shear stress (WSS) stimulus, changes in nitric oxide (NO) production due to modification of blood viscosity caused by alterations of both hematocrit (Hct) and cell free layer thickness, as well as for their combined effects on microvascular blood flow and DO₂. Our model shows that transfusions of 1- and 2-unit of blood have a minimal effect on DO₂ if the microcirculation is unresponsive to the WSS stimulus for NO production that causes vasodilatation increasing blood flow and DO₂. Conversely, in a fully WSS responsive organism, blood transfusion significantly enhances blood flow and DO₂, because increased viscosity stimulates endothelial NO production causing vasodilatation. This finding suggests that evaluation of a patients' pretransfusion endothelial WSS responsiveness should be beneficial in determining the optimal transfusion requirements for treating patients with anemia.NEW & NOTEWORTHY Transfusion of 1 or 2 units of blood accounts for about 3/4 of the world blood consumption of 119 million units per year, whereas a current world demand deficit is on the order of 100 million units. Therefore, factors supporting the practice of transfusing 1 unit instead of 2 are of interest, given their potential to expand the number of interventions without increasing blood availability. Our mathematical model provides a physiological support for this practice.

Localized Oxygen Exchange Platform for Intravital Video Microscopy Investigations of Microvascular Oxygen Regulation

Intravital microscopy has proven to be a powerful tool for studying microvascular physiology. In this study, we propose a gas exchange system compatible with intravital microscopy that can be used to impose gas perturbations to small localized regions in skeletal muscles or other tissues that can be imaged using conventional inverted microscopes. We demonstrated the effectiveness of this system by locally manipulating oxygen concentrations in rat extensor digitorum longus muscle and measuring the resulting vascular responses. A computational model of oxygen transport was used to partially validate the localization of oxygen changes in the tissue, and oxygen saturation of red blood cells flowing through capillaries were measured as a surrogate for local tissue oxygenation. Overall, we have demonstrated that this approach can be used to study dynamic and spatial responses to local oxygen challenges to the microenvironment of skeletal muscle.

August Krogh's theory of muscle microvascular control and oxygen delivery: a paradigm shift based on new data

August Krogh twice won the prestigious international Steegen Prize, for nitrogen metabolism (1906) and overturning the concept of active transport of gases across the pulmonary epithelium (1910). Despite this, at the beginning of 1920, the consummate experimentalist was relatively unknown worldwide and even among his own University of Copenhagen faculty. But, in early 1919, he had submitted three papers to Dr Langley, then editor of The Journal of Physiology in England. These papers coalesced anatomical observations of skeletal muscle capillary numbers with O₂ diffusion theory to propose a novel active role for capillaries that explained the prodigious increase in blood-muscle O₂ flux from rest to exercise. Despite his own appraisal of the first two papers as "rather dull" to his friend, the eminent Cambridge respiratory physiologist, Joseph Barcroft, Krogh believed that the third one, dealing with O₂ supply and capillary regulation, was"interesting". These papers, which won Krogh an unopposed Nobel Prize for Physiology or Medicine in 1920, form the foundation for this review. They single-handedly transformed the role of capillaries from passive conduit and exchange vessels, functioning at the mercy of their upstream arterioles, into independent contractile units that were predominantly closed at rest and opened actively during muscle contractions in a process he termed 'capillary recruitment'. Herein we examine Krogh's findings and some of the experimental difficulties he faced. In particular, the boundary conditions selected for his model (e.g. heavily anaesthetized animals, negligible intramyocyte O₂ partial pressure, binary open-closed capillary function) have not withstood the test of time. Subsequently, we update the reader with intervening discoveries that underpin our current understanding of muscle microcirculatory control and place a retrospectroscope on Krogh's discoveries. The perspective is presented that the imprimatur of the Nobel Prize, in this instance, may have led scientists to discount compelling evidence. Much as he and Marie Krogh demonstrated that active transport of gases across the blood-gas barrier was unnecessary in the lung, capillaries in skeletal muscle do not open and close spontaneously or actively, nor is this necessary to account for the increase in blood-muscle O₂ flux during exercise. Thus, a contemporary model of capillary function features most muscle capillaries supporting blood flow at rest, and, rather than capillaries actively vasodilating from rest to exercise, increased blood-myocyte O₂ flux occurs predominantly via elevating red blood cell and plasma flux in already flowing capillaries. Krogh is lauded for his brilliance as an experimentalist and for raising scientific questions that led to fertile avenues of investigation, including the study of microvascular function.

Is the teleost heart oxygen limited? - Insights using "hyperoxic" incubations of contracting cardiac tissue from rainbow trout

Considerable effort has been devoted to understanding the negative effects of reduced PO₂ on cardiac function. Much less is known about the impacts of elevated PO₂ (hyperoxia) on cardiac performance and energetics, especially in fishes. The fish heart is of particular interest because cardiac dependence on oxygen is extremely variable between species and the early evolution of fish occurred when atmospheric PO₂ was higher than current conditions. Although extracellular PO₂ is variable and normally does not exceed 21 kPa, recent evidence suggests that teleost cardiac function is stimulated at supraphysiological PO₂ values. The purpose of this study was to address whether cardiac contractility and energy metabolism is responsive to elevated PO₂ values in sexually-immature female rainbow trout. Isometric force development (contractility) and oxygen consumption (V̇O₂) were recorded in electrically-paced ventricular preparations. Contractility and V̇O₂decreased when superfusate PO₂ was decreased from ~70 kPa to 57 kPa or 45 kPa. However, PO₂ calculated at the preparation core was always above 18 kPa. This estimate, along with complete recovery of contractility and V̇O₂ at ~70 kPa, suggests that decreases observed in cardiac performance were not due to tissue hypoxia at the lower PO₂ levels. In conclusion, the heart of female rainbow trout may be oxygen-limited in vitro and this study raises new questions about the choice of appropriate PO₂ for experimentation, the relevance of elevated and varying PO₂ to measurements of cardiac performance, and the possible existence of an oxygen sensor within rainbow trout cardiomyocytes.

Oxygen dependence of respiration in rat spinotrapezius muscle contracting at 0.5-8 twitches per second

The oxygen dependence of respiration was obtained in situ in microscopic regions of rat spinotrapezius muscle for different levels of metabolic activity produced by electrical stimulation at rates from 0.5 to 8 Hz. The rate of O₂ consumption (V̇o₂) was measured with phosphorescence quenching microscopy (PQM) as the rate of O₂ disappearance in a muscle with rapid flow arrest. The phosphorescent oxygen probe was loaded into the interstitial space of the muscle to give O₂ tension (Po₂) in the interstitium. A set of sigmoid curves relating the Po₂ dependence of V̇o₂ was obtained with a Po₂-dependent region below a characteristic Po₂ (~30 mmHg) and a Po₂-independent region above this Po₂. The V̇o₂(Po₂) plots were fit by the Hill equation containing O₂ demand (rest to 8 Hz: 216 ± 26 to 636 ± 77 nl O₂/cm³ s) and the Po₂ value corresponding to O₂ demand/2 (rest to 8 Hz: 22 ± 4 to 11 ± 1 mmHg). The initial Po₂ and V̇o₂ pairs of values measured at the moment of flow arrest formed a straight line, determining the rate of oxygen supply. This line had a negative slope, equal to the oxygen conductance for the O₂ supply chain. For each level of tissue blood flow the set of possible values of Po₂ and V̇o₂ consists of the intersection points between this O₂ supply line and the set of V̇o₂ curves. An electrical analogy for the intraorgan O₂ supply and consumption is an inverting transistor amplifier, which allows the use of graphic analysis methods for prediction of the behavior of the oxygen processing system in organs. NEW & NOTEWORTHY The sigmoidal shape of curves describing oxygen dependence of muscle respiration varies from basal to maximal workload and characterizes the oxidative metabolism of muscle. The rate of O₂ supply depends on extracellular O₂ tension and is determined by the overall oxygen conductance in the muscle. The dynamics of oxygen consumption is determined by the supply line that intersects the oxygen demand curves. An electrical analogy for the oxygen supply/consumption system is an inverting transistor amplifier.

The Relation Between Capillary Transit Times and Hemoglobin Saturation Heterogeneity. Part 1: Theoretical Models

Capillary dysfunction impairs oxygen supply to parenchymal cells and often occurs in Alzheimer's disease, diabetes and aging. Disturbed capillary flow patterns have been shown to limit the efficacy of oxygen extraction and can be quantified using capillary transit time heterogeneity (CTH). However, the transit time of red blood cells (RBCs) through the microvasculature is not a direct measure of their capacity for oxygen delivery. Here we examine the relation between CTH and capillary outflow saturation heterogeneity (COSH), which is the heterogeneity of blood oxygen content at the venous end of capillaries. Models for the evolution of hemoglobin saturation heterogeneity (HSH) in capillary networks were developed and validated using a computational model with moving RBCs. Two representative situations were selected: a Krogh cylinder geometry with heterogeneous hemoglobin saturation (HS) at the inflow, and a parallel array of four capillaries. The heterogeneity of HS after converging capillary bifurcations was found to exponentially decrease with a time scale of 0.15-0.21 s due to diffusive interaction between RBCs. Similarly, the HS difference between parallel capillaries also drops exponentially with a time scale of 0.12-0.19 s. These decay times are substantially smaller than measured RBC transit times and only weakly depend on the distance between microvessels. This work shows that diffusive interaction strongly reduces COSH on a small spatial scale. Therefore, we conclude that CTH influences COSH yet does not determine it. The second part of this study will focus on simulations in microvascular networks from the rodent cerebral cortex. Actual estimates of COSH and CTH will then be given.

Two-photon microscopy measurement of cerebral metabolic rate of oxygen using periarteriolar oxygen concentration gradients

The cerebral metabolic rate of oxygen ([Formula: see text]) is an essential parameter for evaluating brain function and pathophysiology. However, the currently available approaches for quantifying [Formula: see text] rely on complex multimodal imaging and mathematical modeling. Here, we introduce a method that allows estimation of [Formula: see text] based on a single measurement modality-two-photon imaging of the partial pressure of oxygen ([Formula: see text]) in cortical tissue. We employed two-photon phosphorescence lifetime microscopy (2PLM) and the oxygen-sensitive nanoprobe PtP-C343 to map the tissue [Formula: see text] distribution around cortical penetrating arterioles. [Formula: see text] is subsequently estimated by fitting the changes of tissue [Formula: see text] around arterioles with the Krogh cylinder model of oxygen diffusion. We measured the baseline [Formula: see text] in anesthetized rats and modulated tissue [Formula: see text] levels by manipulating the depth of anesthesia. This method provides [Formula: see text] measurements localized within [Formula: see text] and it may provide oxygen consumption measurements in individual cortical layers or within confined cortical regions, such as in ischemic penumbra and the foci of functional activation.

Energetics of contraction

Muscles convert energy from ATP into useful work, which can be used to move limbs and to transport ions across membranes. The energy not converted into work appears as heat. At the start of contraction heat is also produced when Ca(2+) binds to troponin-C and to parvalbumin. Muscles use ATP throughout an isometric contraction at a rate that depends on duration of stimulation, muscle type, temperature and muscle length. Between 30% and 40% of the ATP used during isometric contraction fuels the pumping Ca(2+) and Na(+) out of the myoplasm. When shortening, muscles produce less force than in an isometric contraction but use ATP at a higher rate and when lengthening force output is higher than the isometric force but rate of ATP splitting is lower. Efficiency quantifies the fraction of the energy provided by ATP that is converted into external work. Each ATP molecule provides 100 zJ of energy that can potentially be converted into work. The mechanics of the myosin cross-bridge are such that at most 50 zJ of work can be done in one ATP consuming cycle; that is, the maximum efficiency of a cross-bridge is ∼50%. Cross-bridges in tortoise muscle approach this limit, producing over 90% of the possible work per cycle. Other muscles are less efficient but contract more rapidly and produce more power.

Simultaneous sampling of tissue oxygenation and oxygen consumption in skeletal muscle

Under physiologic conditions, microvascular oxygen delivery appears to be well matched to oxygen consumption in respiring tissues. We present a technique to measure interstitial oxygen tension (PISFO2) and oxygen consumption (VO2) under steady-state conditions, as well as during the transitions from rest to activity and back. Phosphorescence Quenching Microscopy (PQM) was employed with pneumatic compression cycling to achieve 1 to 10 Hz sampling rates of interstitial PO2 and simultaneous recurrent sampling of VO2 (3/min) in the exteriorized rat spinotrapezius muscle. The compression pressure was optimized to 120-130 mmHg without adverse effect on the tissue preparation. A cycle of 5s compression followed by 15s recovery yielded a resting VO2 of 0.98 ± 0.03 ml O2/100 cm(3)min while preserving microvascular oxygen delivery. The measurement system was then used to assess VO2 dependence on PISFO2 at rest and further tested under conditions of isometric muscle contraction to demonstrate a robust ability to monitor the on-kinetics of tissue respiration and the compensatory changes in PISFO2 during contraction and recovery. The temporal and spatial resolution of this approach is well suited to studies seeking to characterize microvascular oxygen supply and demand in thin tissues.

Erythrocyte aggregation may promote uneven spatial distribution of NO/O2 in the downstream vessel of arteriolar bifurcations

This study examined the effect of red blood cell (RBC) aggregation on nitric oxide (NO) and oxygen (O2) distributions in the downstream vessels of arteriolar bifurcations. Particular attention was paid to the inherent formation of asymmetric cell-free layer (CFL) widths in the downstream vessels and its consequential impact on the NO/O2 bioavailability after the bifurcations. A microscopic image-based two-dimensional transient model was used to predict the NO/O2 distribution by utilizing the in vivo CFL width data obtained under non-, normal- and hyper-aggregating conditions at the pseudoshear rate of 15.6±2.0s(-1). In vivo experimental result showed that the asymmetry of CFL widths was enhanced by the elevation in RBC aggregation level. The model demonstrated that NO bioavailability was regulated by the dynamic fluctuation of the local CFL widths, which is corollary to its modulation of wall shear stress. Accordingly, the uneven distribution of NO/O2 was prominent at opposite sides of the arterioles up to six vessel-diameter (6D) away from the bifurcating point, and this was further enhanced by increasing the levels of RBC aggregation. Our findings suggested that RBC aggregation potentially augments both the formation of asymmetric CFL widths and its influence on the uneven distribution of NO/O2 in the downstream flow of an arteriolar bifurcation. The extended heterogeneity of NO/O2 downstream (2D-6D) also implied its potential propagation throughout the entire arteriolar microvasculature.

Two-dimensional transient model for prediction of arteriolar NO/O2 modulation by spatiotemporal variations in cell-free layer width

Despite the significant roles of the cell-free layer (CFL) in balancing nitric oxide (NO) and oxygen (O2) bioavailability in arteriolar tissue, many previous numerical approaches have relied on a one-dimensional (1-D) steady-state model for simplicity. However, these models are unable to demonstrate the influence of spatiotemporal variations in the CFL on the NO/O2 transport under dynamic flow conditions. Therefore, the present study proposes a new two-dimensional (2-D) transient model capable of predicting NO/O2 transport modulated by the spatiotemporal variations in the CFL width. Our model predicted that NO bioavailability was inversely related to the CFL width as expected. The enhancement of NO production by greater wall shear stress with a thinner CFL could dominate the diffusion barrier role of the CFL. In addition, NO/O2 availability along the vascular wall was inhomogeneous and highly regulated by dynamic changes of local CFL width variation. The spatial variations of CFL widths on opposite sides of the arteriole exhibited a significant inverse relation. This asymmetric formation of CFL resulted in a significantly imbalanced NO/O2 bioavailability on opposite sides of the arteriole. The novel integrative methodology presented here substantially highlighted the significance of spatiotemporal variations of the CFL in regulating the bioavailability of NO/O2, and provided further insight about the opposing effects of the CFL on arteriolar NO production.

On-off asymmetries in oxygen consumption kinetics of single Xenopus laevis skeletal muscle fibres suggest higher-order control

The mechanisms controlling skeletal muscle oxygen consumption (V(o)₂) during exercise are not well understood. We determined whether first-order control could explain V(o)₂kinetics at contractions onset (V(o)₂(on)) and cessation (V(o)₂off)) in single skeletal muscle fibres differing in oxdidative capacity, and across stimulation intensities up to V(o)₂(max). Xenopus laevis fibres (n = 21) were suspended in a sealed chamber with a fast response P(o)₂ electrode to measure V(o)₂ every second before, during and after stimulated isometric contractions. A first-order model did not well characterize on-transient V(o)₂ kinetics. Including a time delay (TD) in the model provided a significantly improved characterization than a first-order fit without TD (F-ratio; P < 0.05), and revealed separate 'activation' and 'exponential' phases in 15/21 fibres contracting at V(o)₂(max) (mean ± SD TD: 14 ± 3s). On-transient kinetics (τV(o)₂(on)) was weakly and linearly related to V(o)₂(max) (R² = 0.271, P = 0.015). Off-transient kinetics, however, were first-order, and τV(o)₂(off) was greater in low-oxidative (V(o)₂max < 0.05 nmol mm⁻³s⁻¹ than high-oxidative fibres (V(o)₂(max > 0.10 nmol mm ⁻³ s⁻¹; 170 ± 70 vs. 29 ± 6 s, P < 0.001). 1/ τV(o)₂(off) was proportional to V(o)₂(max) (R² = 0.727, P < 0.001), unlike in the on-transient. The calculated oxygen deficit was larger (P < 0.05) than the post-contraction volume of consumed oxygen at all intensities except V(o)₂(max). These data show a clear dissociation between the kinetic control of V(o)₂at the onset and cessation of contractions and across stimulation intensities. More complex models are therefore required to understand the activation of mitochondrial respiration in skeletal muscle at the start of exercise.

A new method for measuring the oxygen diffusion constant and oxygen consumption rate of arteriolar walls

Oxygen transport is believed to primarily occur via capillaries and depends on the oxygen tension gradient between the vessels and tissues. As blood flows along branching arterioles, the O(2) saturation drops, indicating either consumption or diffusion. The blood flow rate, the O(2) concentration gradient, and Krogh's O(2) diffusion constant (K) of the vessel wall are parameters affecting O(2)delivery. We devised a method for evaluating K of arteriolar wall in vivo using phosphorescence quenching microscopy to measure the partial pressure of oxygen in two areas almost simultaneously. The K value of arteriolar wall (inner diameter, 63.5 ± 11.9 μm; wall thickness, 18.0 ± 1.2 μm) was found to be 6.0 ± 1.2 × 10(-11) (cm(2)/s)(ml O(2)·cm(-3) tissue·mmHg(-1)). The arteriolar wall O(2) consumption rate (M) was 1.5 ± 0.1 (ml O(2)·100 cm(-3) tissue·min(-1)), as calculated using Krogh's diffusion equation. These results suggest that the arteriolar wall consumes a considerable proportion of the O(2) that diffuses through it.

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.

Oxygen dependence of respiration in rat spinotrapezius muscle in situ

The oxygen dependence of respiration in striated muscle in situ was studied by measuring the rate of decrease of interstitial Po(2) [oxygen disappearance curve (ODC)] following rapid arrest of blood flow by pneumatic tissue compression, which ejected red blood cells from the muscle vessels and made the ODC independent from oxygen bound to hemoglobin. After the contribution of photo-consumption of oxygen by the method was evaluated and accounted for, the corrected ODCs were converted into the Po(2) dependence of oxygen consumption, Vo(2), proportional to the rate of Po(2) decrease. Fitting equations obtained from a model of heterogeneous intracellular Po(2) were applied to recover the parameters describing respiration in muscle fibers, with a predicted sigmoidal shape for the dependence of Vo(2) on Po(2). This curve consists of two regions connected by the point for critical Po(2) of the cell (i.e., Po(2) at the sarcolemma when the center of the cell becomes anoxic). The critical Po(2) was below the Po(2) for half-maximal respiratory rate (P(50)) for the cells. In six muscles at rest, the rate of oxygen consumption was 139 ± 6 nl O(2)/cm(3)·s and mitochondrial P(50) was k = 10.5 ± 0.8 mmHg. The range of Po(2) values inside the muscle fibers was found to be 4-5 mmHg at the critical Po(2). The oxygen dependence of respiration can be studied in thin muscles under different experimental conditions. In resting muscle, the critical Po(2) was substantially lower than the interstitial Po(2) of 53 ± 2 mmHg, a finding that indicates that Vo(2) under this circumstance is independent of oxygen supply and is discordant with the conventional hypothesis of metabolic regulation of the oxygen supply to tissue.

Simulation of NO and O2 transport facilitated by polymerized hemoglobin solutions in an arteriole that takes into account wall shear stress-induced NO production

A mathematical model was developed to study nitric oxide (NO) and oxygen (O(2)) transport in an arteriole and surrounding tissues exposed to a mixture of red blood cells (RBCs) and hemoglobin (Hb)-based O(2) carriers (HBOCs). A unique feature of this model is the inclusion of blood vessel wall shear stress-induced production of endothelial-derived NO, which is very sensitive to the viscosity of the RBC and HBOC mixture traversing the blood vessel lumen. Therefore in this study, a series of polymerized bovine Hb (PolyHb) solutions with high viscosity, varying O(2) affinities, NO dioxygenation rate constants and O(2) dissociation rate constants that were previously synthesized and characterized by our group was evaluated via mathematical modeling, in order to investigate the effect of these biophysical properties on the transport of NO and O(2) in an arteriole and its surrounding tissues subjected to anemia with the commercial HBOC Oxyglobin® and cell-free bovine Hb (bHb) serving as appropriate controls. The computer simulation results indicated that transfusion of high viscosity PolyHb solutions promoted blood vessel wall shear stress dependent generation of the vasodilator NO, especially in the blood vessel wall and should transport enough NO inside the smooth muscle layer to activate vasodilation compared to the commercial HBOC Oxyglobin® and cell-free bHb. However, NO scavenging in the arteriole lumen was unavoidable due to the intrinsic high NO dioxygenation rate constant of the HBOCs being studied. This study also observed that all PolyHbs could potentially improve tissue oxygenation under hypoxic conditions, while low O(2) affinity PolyHbs were more effective in oxygenating tissues under normoxic conditions compared with high O(2) affinity PolyHbs. In addition, all ultrahigh molecular weight PolyHbs displayed higher O(2) transfer rates than the commercial HBOC Oxyglobin® and cell-free bHb. Therefore, these results suggest that ultrahigh molecular weight PolyHb solutions could be used as safe and efficacious O(2) carriers for use in transfusion medicine. It also suggests that future generations of PolyHb solutions should possess lower NO dioxygenation reaction rate constants in order to reduce NO scavenging, while maintaining high solution viscosity to take advantage of wall shear stress-induced NO production. Taken together, we suggest that this mathematical model can be used to predict the vasoactivity of HBOCs and help guide the design and optimization of the next generation of HBOCs for use in transfusion medicine.

Effects of cell-free layer formation on NO/O2 bioavailability in small arterioles

We developed a new time-dependent computational model for coupled NO/O(2) transport in small arterioles that incorporates potential physiological responses (temporal changes in NO scavenging rate and O(2) partial pressure in blood lumen and NO production rate in endothelium) to the temporal cell-free layer width variations. Two relations between wall shear stress (WSS) and NO production rate based on the linear and sigmoidal functions were considered in this simulation study. The cell-free layer data used for the simulation were acquired from arteriolar flows (D=48.3 ± 1.9 μm) in the rat cremaster muscles under normal flow conditions (WSS=3.4-5.6 Pa). For both cases of linear and sigmoidal relations, temporal layer width variations were found to be capable of significantly enhancing NO bioavailability and this effect was more pronounced in the latter (P<0.0005) than the former (P<0.005). In contrast, O(2) bioavailability in the arteriolar wall was not considerably altered by the temporal layer width variations, irrespective of the relation. Prominent enhancement (P<0.005) of soluble guanylyl cyclase (sGC) activation in the smooth muscle by the temporal layer width variations were predicted for both relations. The extent of sGC activation was generally lower (P<0.01) in the case of the sigmoidal relation than that of the linear relation, suggesting a lesser tendency for arterioles to dilate with the former.

Sensitivity analysis of reaction-diffusion constraints in muscle energetics

Theoretical and experimental studies of aerobic metabolism on a wide range of skeletal muscle fibers have shown that while all fibers normally function within the reaction control regime, some fibers operate near the transition region where reaction control switches to diffusion control. Thus, the transition region between reaction and diffusion control may define the limits of muscle function, and analysis of factors that affect this transition is therefore needed. In order to assess the role of all important model parameters, a sensitivity analysis (SA) was performed to define the parameter space where muscle fibers transition from reaction to diffusion control. SA, performed on a previously developed reaction-diffusion model, shows that the maximum rate for the ATPase reaction (V(max,ATPase)), boundary oxygen concentration in the capillary supply (O ₂⁰), the mitochondrial volume fraction (ε(mito)), and the diffusion coefficient of oxygen (DO ₂) are the most sensitive parameters affecting this transition to diffusion control. It is demonstrated that fibers are not limited by diffusion for slow reactions (V(max,ATPase)  < 25 mM/min), high oxygen supply for the capillaries (O ₂⁰ ≥ 35 µM), and large amounts of mitochondria (ε(mito) ≥ 0.1). These conditions are applicable to muscle cells spanning a very broad range of animals. Within the diffusion-controlled region, the overall metabolic rate and ATP concentrations have much higher sensitivity to the diffusion coefficient of oxygen than to the diffusion coefficients of the other metabolites (ATP, ADP, P(i)).

The effect of small changes in hematocrit on nitric oxide transport in arterioles

We report the development of a mathematical model that quantifies the effects of small changes in systemic hematocrit (Hct) on the transport of nitric oxide (NO) in the microcirculation. The model consists of coupled transport equations for NO and oxygen (O2) and accounts for both shear-induced NO production by the endothelium and the effect of changing systemic Hct on the rate of NO production and the rate of NO scavenging by red blood cells. To incorporate the dependence of the plasma layer width on changes in Hct, the model couples the hemodynamics of blood in arterioles with NO and O2 transport in the plasma layer. A sensitivity analysis was conducted to determine the effects of uncertain model parameters (the thicknesses of endothelial surface layers and diffusion coefficients of NO and O2 in muscle tissues and vascular walls) on the model's predictions. Our analysis reveals that small increases in Hct may raise NO availability in the vascular wall. This finding sheds new light on the experimental data that show that the blood circulation responds to systematic increases of Hct in a manner that is consistent with increasing NO production followed by a plateau.

Radius-dependent decline of performance in isolated cardiac muscle does not reflect inadequacy of diffusive oxygen supply

The study of cardiac energetics commonly involves the use of isolated muscle preparations (papillary muscles or trabeculae carneae). Their contractile performance has been observed to vary inversely with thickness. This inverse dependence has been attributed, almost without exception, to inadequate diffusion of oxygen into the centers of muscles of large diameter. It is thus commonly hypothesized that the radius-dependent diminution of performance reflects the development of an anoxic core. We tested this hypothesis theoretically by solving a modification of the diffusion equation, in which the rate of oxygen consumption is a sigmoidal function of the partial pressure of oxygen. The model demonstrates that sufficiently thick muscles, operating at sufficiently high rates of oxygen demand or sufficiently low ambient partial pressures of oxygen, will indeed show diminished energetic performance, whether indirectly indexed as stress (force per cross-sectional area) development or as the rate of heat production. However, such simulated behavior requires the adoption of extreme parameter values, often differing by an order of magnitude from their experimental equivalents. We thus conclude that the radius-dependent diminution of muscle performance in vitro cannot be attributed entirely to an insufficient supply of oxygen via diffusion.

Phosphorescence quenching microrespirometry of skeletal muscle in situ

We have developed an optical method for the evaluation of the oxygen consumption (Vo(2)) in microscopic volumes of spinotrapezius muscle. Using phosphorescence quenching microscopy (PQM) for the measurement of interstitial Po(2), together with rapid pneumatic compression of the organ, we recorded the oxygen disappearance curve (ODC) in the muscle of the anesthetized rats. A 0.6-mm diameter area in the tissue, preloaded with the phosphorescent oxygen probe, was excited once a second by a 532-nm Q-switched laser with pulse duration of 15 ns. Each of the evoked phosphorescence decays was analyzed to obtain a sequence of Po(2) values that constituted the ODC. Following flow arrest and tissue compression, the interstitial Po(2) decreased rapidly and the initial slope of the ODC was used to calculate the Vo(2). Special analysis of instrumental factors affecting the ODC was performed, and the resulting model was used for evaluation of Vo(2). The calculation was based on the observation of only a small amount of residual blood in the tissue after compression. The contribution of oxygen photoconsumption by PQM and oxygen inflow from external sources was evaluated in specially designed tests. The average oxygen consumption of the rat spinotrapezius muscle was Vo(2) = 123.4 ± 13.4 (SE) nl O(2)/cm(3) · s (N = 38, within 6 muscles) at a baseline interstitial Po(2) of 50.8 ± 2.9 mmHg. This technique has opened the opportunity for monitoring respiration rates in microscopic volumes of functioning skeletal muscle.

Kinetics of oxygen consumption after a flash of light in the lateral ocellus of the barnacle

Until recently, polarographic methods for measuring the time course of transient changes in the rate of oxygen consumption (DeltaQO(2)) have been applied only to tissue preparations containing thousands of cells. Here, we describe DeltaQO(2) measurements on the lateral ocellus of the barnacle (Balanus eburneus) which contains only three photoreceptor cells. The decrement of partial pressure of oxygen (DeltaPO(2)) elicited by an 80 ms flash of light was measured near the cells with a microelectrode and the DeltaQO(2) was calculated from the DeltaPO(2) using a model of diffusion with spherical symmetry. As shown by mathematical simulation, the exact shape of the preparation is not crucial for our measurements of the time course of the DeltaQO(2). For a given DeltaQO(2), the model describes correctly the attenuation of the DeltaPO(2) measured at increased distances from the preparation. To know more about the mechanisms controlling the DeltaQO(2), we compared it with the electrical response of the photoreceptor cells: both responses have a similar spectral dependence, but only the DeltaQO(2) was abolished by a 10-min exposure to 50 muM dinitrophenol or to 3 mM amytal. We conclude that the DeltaQO(2) reflects an increase in mitochondrial respiration and that it is initiated by the phototransformation of rhodopsin, as was already found in the honeybee drone retina (Dimitracos and Tsacopoulos, 1985; Jones and Tsacopoulos, 1987).

The unique mitochondrial form and function of Antarctic channichthyid icefishes

Antarctic icefishes of the family Channichthyidae are the only vertebrate animals that as adults do not express the circulating oxygen-binding protein hemoglobin (Hb). Six of the 16 family members also lack the intracellular oxygen-binding protein myoglobin (Mb) in the ventricle of their hearts and all lack Mb in oxidative skeletal muscle. The loss of Hb has led to substantial remodeling in the cardiovascular system of icefishes to facilitate adequate oxygenation of tissues. One of the more curious adaptations to the loss of Hb and Mb is an increase in mitochondrial density in cardiac myocytes and oxidative skeletal muscle fibers. The proliferation of mitochondria in the aerobic musculature of icefishes does not arise through a canonical pathway of mitochondrial biogenesis. Rather, the biosynthesis of mitochondrial phospholipids is up-regulated independently of the synthesis of proteins and mitochondrial DNA, and newly-synthesized phospholipids are targeted primarily to the outer-mitochondrial membrane. Consequently, icefish mitochondria have a higher lipid-to-protein ratio compared to those from red-blooded species. Elevated levels of nitric oxide in the blood plasma of icefishes, compared to red-blooded notothenioids, may mediate alterations in mitochondrial density and architecture. Modifications in mitochondrial structure minimally impact state III respiration rates but may significantly enhance intracellular diffusion of oxygen. The rate of oxygen diffusion is greater within the hydrocarbon core of membrane lipids compared to the aqueous cytosol and impeded only by proteins within the lipid bilayer. Thus, the proliferation of icefish's mitochondrial membranes provides an optimal conduit for the intracellular diffusion of oxygen and compensates for the loss of Hb and Mb. Currently little is known about how mitochondrial phospholipid synthesis is regulated and integrated into mitochondrial biogenesis. The unique architecture of the oxidative muscle cells of icefishes highlights the need for further studies in this area.

Myoglobin concentration in skeletal muscle fibers of chronic heart failure patients

The purpose of this study was to determine the myoglobin concentration in skeletal muscle fibers of chronic heart failure (CHF) patients and to calculate the effect of myoglobin on oxygen buffering and facilitated diffusion. Myoglobin concentration, succinate dehydrogenase (SDH) activity, and cross-sectional area of individual muscle fibers from the vastus lateralis of five control and nine CHF patients were determined using calibrated histochemistry. CHF patients compared with control subjects were similar with respect to myoglobin concentration: type I fibers 0.69 +/- 0.11 mM (mean +/- SD), type II fibers 0.52 +/- 0.07 mM in CHF vs. type I fibers 0.70 +/- 0.09 mM, type II fibers 0.49 +/- 0.07 mM in control, whereas SDH activity was significantly lower in CHF in both fiber types (P < 0.01). The myoglobin concentration in type I fibers was higher than in type II fibers (P < 0.01). Consequently, the oxygen buffering capacity, calculated from myoglobin concentration/SDH activity was increased in CHF: type I fibers 11.4 +/- 2.1 s, type II fibers 13.6 +/- 3.9 s in CHF vs. type I fibers 7.8 +/- 0.9 s, type II fibers 7.5 +/- 1.0 s in control, all P < 0.01). The calculated extracellular oxygen tension required to prevent core anoxia (Po2(crit)) in muscle fibers was similar when controls were compared with patients in type I fibers 10.3 +/- 0.9 Torr in CHF and 11.5 +/- 3.3 Torr in control, but was lower in type II fibers of patients 6.1 +/- 2.8 Torr in CHF and 14.7 +/- 6.2 Torr in control, P < 0.01. The lower Po2(crit) of type II fibers may facilitate oxygen extraction from capillaries. Reduced exercise tolerance in CHF is not due to myoglobin deficiency.

The energetic cost of activation in mouse fast-twitch muscle is the same whether measured using reduced filament overlap or N-benzyl-p-toluenesulphonamide

AIM

Force generation and transmembrane ion pumping account for the majority of energy expended by contracting skeletal muscles. Energy turnover for ion pumping, activation energy turnover (E(A)), can be determined by measuring the energy turnover when force generation has been inhibited. Most measurements show that activation accounts for 25-40% of isometric energy turnover. It was recently reported that when force generation in mouse fast-twitch muscle was inhibited using N-benzyl-p-toluenesulphonamide (BTS), activation accounted for as much as 80% of total energy turnover during submaximal contractions. The purpose of this study was to compare E(A) measured by inhibiting force generation by: (1) the conventional method of reducing contractile filament overlap; and (2) pharmacological inhibition using BTS.

METHODS

Experiments were performed in vitro using bundles of fibres from mouse fast-twitch extensor digitorum longus (EDL) muscle. Energy turnover was quantified by measuring the heat produced during 1-s maximal and submaximal tetanic contractions at 20 and 30 degrees C.

RESULTS

E(A) measured using reduced filament overlap was 0.36 +/- 0.04 (n = 8) at 20 degrees C and 0.31 +/- 0.05 (n = 6) at 30 degrees C. The corresponding values measured using BTS in maximal contractions were 0.46 +/- 0.06 and 0.38 +/- 0.06 (n = 6 in both cases). There were no significant differences among these values. E(A) was also no different when measured using BTS in submaximal contractions.

CONCLUSION

Activation energy turnover is the same whether measured using BTS or reduced filament overlap and accounts for slightly more than one-third of isometric energy turnover in mouse EDL muscle.

A multiscale theoretical model for diffusive mass transfer in cellular biological media

An integrated methodology is developed for the theoretical analysis of solute transport and reaction in cellular biological media, such as tissues, microbial flocs, and biofilms. First, the method of local spatial averaging with a weight function is used to establish the equation which describes solute conservation at the cellular biological medium scale, starting with a continuum-based formulation of solute transport at finer spatial scales. Second, an effective-medium model is developed for the self-consistent calculation of the local diffusion coefficient in the cellular biological medium, including the effects of the structural heterogeneity of the extra-cellular space and the reversible adsorption to extra-cellular polymers. The final expression for the local effective diffusion coefficient is: D(Abeta)=lambda(beta)D(Aupsilon), where D(Aupsilon) is the diffusion coefficient in water, and lambda(beta) is a function of the composition and fundamental geometric and physicochemical system properties, including the size of solute molecules, the size of extra-cellular polymer fibers, and the mass permeability of the cell membrane. Furthermore, the analysis sheds some light on the function of the extra-cellular hydrogel as a diffusive barrier to solute molecules approaching the cell membrane, and its implications on the transport of chemotherapeutic agents within a cellular biological medium. Finally, the model predicts the qualitative trend as well as the quantitative variability of a large number of published experimental data on the diffusion coefficient of oxygen in cell-entrapping gels, microbial flocs, biofilms, and mammalian tissues.

Hemoglobin-based O2 carrier O2 affinity and capillary inlet pO2 are important factors that influence O2 transport in a capillary

Hemopure (Biopure; Cambridge, MA) and PolyHeme (Northfield Laboratories; Evanston, IL) are two acellular hemoglobin-based O2 carriers (HBOCs) currently in phase III clinical trials for use as red blood cell substitutes. The most common adverse side effect that these HBOCs exhibit is increased vasoconstriction. Autoregulatory theory has been presented as a possible explanation for this physiological effect, where it is hypothesized that low-affinity HBOCs over-deliver O2 to tissues surrounding arterioles, thereby eliciting vasoconstriction. In this paper, we wanted to investigate HBOC oxygenation of tissue surrounding a capillary, which is the smallest element of the circulatory system. An a priori model has been developed in which the performance of mixtures of acellular HBOCs (synthesized by our group and others) and human red blood cells (hRBCs) has been simulated using a Krogh tissue cylinder model (KTCM) comprising a capillary surrounded by a capillary membrane and skeletal muscle tissue in cylindrical coordinates with specified tissue O2 consumption rates and Michaelis-Menten kinetics. In this study, the total hemoglobin (hRBCs and HBOCs) concentration was kept constant. The HBOCs studied possessed O2 affinities that were higher and lower compared to hRBCs (P50's spanned 5-55 mmHg), and the equilibrium binding/release of oxygen to/from the HBOCs was modeled using the Adair equation. At normoxic inlet pO2's, there was no correlation between O2 flux out of the capillary and the O2 affinity of the HBOC. However, a correlation was found between the average pO2 tension in the capillary and the O2 affinity of the HBOC. Additionally, we studied the change in the O2 equilibrium curve of HBOCs with different O2 affinities over a wide range of inlet pO2's and found that changing the inlet pO2 greatly affected which HBOC, having a unique O2 affinity, best delivered O2 to the surrounding tissue. The analysis of oxygen transport presented could lead to a better prediction of which acellular HBOC is best suited for a specific transfusion application that many times depends on the capillary inlet pO2 tension.

A computational model of oxygen delivery by hemoglobin-based oxygen carriers in three-dimensional microvascular networks

A detailed computational model is developed to simulate oxygen transport from a three-dimensional (3D) microvascular network to the surrounding tissue in the presence of hemoglobin-based oxygen carriers. The model accounts for nonlinear O(2) consumption, myoglobin-facilitated diffusion and nonlinear oxyhemoglobin dissociation in the RBCs and plasma. It also includes a detailed description of intravascular resistance to O(2) transport and is capable of incorporating realistic 3D microvascular network geometries. Simulations in this study were performed using a computer-generated microvascular architecture that mimics morphometric parameters for the hamster cheek pouch retractor muscle. Theoretical results are presented next to corresponding experimental data. Phosphorescence quenching microscopy provided PO(2) measurements at the arteriolar and venular ends of capillaries in the hamster retractor muscle before and after isovolemic hemodilution with three different hemodilutents: a non-oxygen-carrying plasma expander and two hemoglobin solutions with different oxygen affinities. Sample results in a microvascular network show an enhancement of diffusive shunting between arterioles, venules and capillaries and a decrease in hemoglobin's effectiveness for tissue oxygenation when its affinity for O(2) is decreased. Model simulations suggest that microvascular network anatomy can affect the optimal hemoglobin affinity for reducing tissue hypoxia. O(2) transport simulations in realistic representations of microvascular networks should provide a theoretical framework for choosing optimal parameter values in the development of hemoglobin-based blood substitutes.

Modeling of oxygen transport and cellular energetics explains observations on in vivo cardiac energy metabolism

Observations on the relationship between cardiac work rate and the levels of energy metabolites adenosine triphosphate (ATP), adenosine diphosphate (ADP), and phosphocreatine (CrP) have not been satisfactorily explained by theoretical models of cardiac energy metabolism. Specifically, the in vivo stability of ATP, ADP, and CrP levels in response to changes in work and respiratory rate has eluded explanation. Here a previously developed model of mitochondrial oxidative phosphorylation, which was developed based on data obtained from isolated cardiac mitochondria, is integrated with a spatially distributed model of oxygen transport in the myocardium to analyze data obtained from several laboratories over the past two decades. The model includes the components of the respiratory chain, the F₀F₁-ATPase, adenine nucleotide translocase, and the mitochondrial phosphate transporter at the mitochondrial level; adenylate kinase, creatine kinase, and ATP consumption in the cytoplasm; and oxygen transport between capillaries, interstitial fluid, and cardiomyocytes. The integrated model is able to reproduce experimental observations on ATP, ADP, CrP, and inorganic phosphate levels in canine hearts over a range of workload and during coronary hypoperfusion and predicts that cytoplasmic inorganic phosphate level is a key regulator of the rate of mitochondrial respiration at workloads for which the rate of cardiac oxygen consumption is less than or equal to approximately 12 μmol per minute per gram of tissue. At work rates corresponding to oxygen consumption higher than 12 μmol min⁻¹ g⁻¹, model predictions deviate from the experimental data, indicating that at high work rates, additional regulatory mechanisms that are not currently incorporated into the model may be important. Nevertheless, the integrated model explains metabolite levels observed at low to moderate workloads and the changes in metabolite levels and tissue oxygenation observed during graded hypoperfusion. These findings suggest that the observed stability of energy metabolites emerges as a property of a properly constructed model of cardiac substrate transport and mitochondrial metabolism. In addition, the validated model provides quantitative predictions of changes in phosphate metabolites during cardiac ischemia.

To function properly over a range of work rates, the heart must maintain its metabolic energy level within a range that is narrow relative to changes in the rate of energy utilization. Decades of observations have revealed that in cardiac muscle cells, the supply of adenosine triphosphate (ATP)—the primary currency of intracellular energy transfer—is controlled to maintain intracellular concentrations of ATP and related compounds within narrow ranges. Yet the development of a mechanistic understanding of this tight control has lagged behind experimental observation. This paper introduces a computational model that links ATP synthesis in a subcellular body called the mitochondrion with ATP utilization in the cytoplasm, and reveals that the primary control mechanism operating in the system is feedback of substrate concentrations for ATP synthesis. In other words, changes in the concentrations of the products generated by the utilization of ATP in the cell (adenosine diphosphate and inorganic phosphate) effect changes in the rate at which mitochondria utilize those products to resynthesize ATP.

ATP splitting by half the cross-bridges can explain the twitch energetics of mouse papillary muscle

The aim of this study was to quantify the fraction of cross-bridges that cycle during a cardiac twitch. Measurements of the energetics of contracting left ventricular mouse papillary muscle were made in vitro (27 degrees C) using the myothermic technique. Enthalpy output was partitioned into force-dependent and force-independent components using 2,3-butanedione monoxime (BDM) to selectively inhibit cross-bridge cycling. For isometric contractions and a contraction frequency of 2 Hz the net enthalpy output was 5.7 +/- 0.8 mJ g(-1) twitch(-1) and initial enthalpy output was 2.3 +/- 0.3 mJ g(-1) twitch(-1) (n = 11). Assuming that low concentrations of BDM did not affect Ca2+ cycling, force-independent enthalpy output was 18.6 +/- 1.9% (n = 7) of the initial enthalpy output. Enthalpy output decreased with increased contraction frequency but was independent of shortening velocity. On the basis of these values, it was calculated that the twitch energetics were consistent with ATP splitting by half the cross-bridges and the pumping of one Ca2+ into the sarcoplasmic reticulum for every three cross-bridge cycles. The simplest interpretation is that half the cross-bridges completed one ATP-splitting cycle in each twitch. The lack of influence of shortening velocity on energy cost supports the idea that the amount of energy to be used is determined early in a twitch and is not greatly influenced by events that occur during the contraction.

Modelling diffusive O(2) supply to isolated preparations of mammalian skeletal and cardiac muscle

The purpose of this study was to use A. V. Hill's equation describing diffusion of O(2) into cylindrical muscles to assess the adequacy of O(2) supply for commonly used isolated preparations of mammalian cardiac and skeletal muscles. The diffusion equation was solved numerically to give the maximum, steady state O(2) diffusion distances (i.e. the distance from the surface of the muscle to the radial location where P(O(2)) is 0) for both resting and contracting muscles and for a range of temperatures. Non-steady state solutions for the rest-to-work transition were also determined to estimate how long contractile activity could be continued before anoxia develops at the muscle centre. The influence on muscle oxygenation of myoglobin-facilitated O(2) diffusion was also assessed. The analysis was performed for typical sized, whole muscles from adult rats and mice, for frog sartorius muscle and for a range of temperatures. Muscle O(2) consumption rates were taken from the literature. The results indicated that (1) diffusive O(2) supply would be adequate to support resting metabolism of soleus and EDL muscles of rat and mouse but may not be adequate to support the transient high resting metabolic rate of papillary muscles shortly after dissection, (2) during steady contractile activity of soleus and EDL muscles, particularly those from the rat, over a reasonable range of duty cycles, adequate O(2) supply could only be ensured if the radii of preparations was substantially smaller than those of whole muscles and (3) for cardiac muscles, diffusive O(2) supply could only support steady-state metabolism at twitch frequencies <1 Hz for whole papillary muscles from rat and <3 Hz for those from mouse. Reducing experimental temperature markedly enhances O(2) supply to skeletal, but not cardiac, muscle. O(2) supply from myoglobin had only minimal effects on oxygenation under typical isolated muscle conditions.

Krogh's diffusion coefficient for oxygen in isolated Xenopus skeletal muscle fibers and rat myocardial trabeculae at maximum rates of oxygen consumption

The value of the diffusion coefficient for oxygen in muscle is uncertain. The diffusion coefficient is important because it is a determinant of the extracellular oxygen tension at which the core of muscle fibers becomes anoxic (Po(2crit)). Anoxic cores in muscle fibers impair muscular function and may limit adaptation of muscle cells to increased load and/or activity. We used Hill's diffusion equations to determine Krogh's diffusion coefficient (Dalpha) for oxygen in single skeletal muscle fibers from Xenopus laevis at 20 degrees C (n = 6) and in myocardial trabeculae from the rat at 37 degrees C (n = 9). The trabeculae were dissected from the right ventricular myocardium of control (n = 4) and monocrotaline-treated, pulmonary hypertensive rats (n = 5). The cross-sectional area of the preparations, the maximum rate of oxygen consumption (Vo(2 max)), and Po(2crit) were determined. Dalpha increased in the following order: Xenopus muscle fibers Dalpha = 1.23 nM.mm(2).mmHg(-1).s(-1) (SD 0.12), control rat trabeculae Dalpha = 2.29 nM.mm(2).mmHg(-1).s(-1) (SD 0.24) (P = 0.0012 vs. Xenopus), and hypertrophied rat trabeculae Dalpha = 6.0 nM.mm(2).mmHg(-1).s(-1) (SD 2.8) (P = 0.039 vs. control rat trabeculae). Dalpha increased with extracellular space in the preparation (Spearman's rank correlation coefficient = 0.92, P < 0.001). The values for Dalpha indicate that Xenopus muscle fibers cannot reach Vo(2 max) in vivo because Po(2crit) can be higher than arterial Po(2) and that hypertrophied rat cardiomyocytes can become hypoxic at the maximum heart rate.

Resting metabolism of mouse papillary muscle

The aims of this study were to measure the resting metabolic rate of isolated mouse papillary muscles and to determine whether diffusive O2 supply is adequate to support the resting metabolism. Resting metabolism of left ventricular papillary muscles was measured in vitro (27 degrees C) using the myothermic technique. The rate of resting metabolism declined exponentially with time towards a steady value, with a time constant of 18+/-2 min (n=13). There was no alteration in isometric force output during this time. The magnitude of the resting metabolism, which depended inversely on muscle mass, more than doubled following a change in substrate from glucose to pyruvate and was increased 2.5-fold when the osmolarity of the bathing solution was increased by addition of 300 mM sucrose. Addition of 30 mM 2, 3-butanedione monoxime affected neither the time course of the decline in metabolic rate nor the eventual steady value. Analysis of the diffusive oxygen supply to the isolated preparation indicated that small papillary muscles (mass <1 mg), which have a very high resting metabolic rate early in an experiment, are unlikely to be adequately oxygenated.

Effect of dissociating cytosolic calcium and metabolic rate on intracellular PO2 kinetics in single frog myocytes

The purpose of this investigation was to utilize 2,3-butanedione monoxime (BDM; an inhibitor of contractile activation) to dissociate cytosolic [Ca(2+)] ([Ca(2+)](c)) from the putative respiratory regulators that arise from muscle contraction-induced ATP utilization in order to determine the relative contribution of [Ca(2+)](c) on intracellular P(O(2)) (P(iO(2))) kinetics during the transition from rest to contractions in single skeletal myocytes isolated from Xenopus laevis lumbrical muscle. Myocytes were subjected to electrically induced isometric tetanic contractions (0.25 Hz; 2-min bouts) while peak tension and either [Ca(2+)](c) (n= 7; ratiometric fluorescence microscopy) or P(iO(2)) (n= 7; phosphorescence microscopy) was measured continuously. Cells were studied under both control and 3 mm BDM conditions in randomized order. Initial (control, 100 +/- 0%; BDM, 72.6 +/- 4.6%), midpoint (control, 86.7 +/- 1.8%; BDM, 61.6 +/- 4.1%) and end (control, 85.0 +/- 2.8%; BDM, 57.5 +/- 5.0%) peak tensions (normalized to initial control values) were significantly reduced (P < 0.05) with BDM compared with control (n= 14). Despite the reduced peak tension, peak [Ca(2+)](c) was not altered (P > 0.05) between control and BDM trials. Thus, the peak tension-to-peak [Ca(2+)](c) ratio was reduced with BDM compared with control. The absolute fall in P(iO(2)) with contractions, which is proportional to the rise in , was significantly reduced with BDM (13.2 +/- 1.3 mmHg) compared with control (22.0 +/- 2.0 mmHg). However, P(iO(2)) onset kinetics (i.e. mean response time (MRT)) was not altered between BDM (66.8 +/- 8.0 s) and control (64.9 +/- 6.3 s) trials. Therefore, the initial rate of change (defined as the fall in P(iO(2))/MRT) was significantly slower in BDM fibres compared with control. These data demonstrate in these isolated single skeletal muscle fibres that unchanged peak [Ca(2+)](c) in the face of reduced metabolic feedback from the contractile sites evoked with BDM did not alter P(iO(2)) onset kinetics in isolated single frog myocytes, suggesting that metabolic signals arising from the contractile sites play a more substantial role than [Ca(2+)](c) in the signalling pathway to oxidative phosphorylation during the transition from rest to repeated tetanic contractions.

Slow skeletal muscles of the mouse have greater initial efficiency than fast muscles but the same net efficiency

The aim of this study was to determine whether the net efficiency of mammalian muscles depends on muscle fibre type. Experiments were performed in vitro (35 degrees C) using bundles of muscle fibres from the slow-twitch soleus and fast-twitch extensor digitorum longus (EDL) muscles of the mouse. The contraction protocol consisted of 10 brief contractions, with a cyclic length change in each contraction cycle. Work output and heat production were measured and enthalpy output (work + heat) was used as the index of energy expenditure. Initial efficiency was defined as the ratio of work output to enthalpy output during the first 1 s of activity. Net efficiency was defined as the ratio of the total work produced in all the contractions to the total, suprabasal enthalpy produced in response to the contraction series, i.e. net efficiency incorporates both initial and recovery metabolism. Initial efficiency was greater in soleus (30 +/- 1%; n=6) than EDL (23 +/- 1%; n=6) but there was no difference in net efficiency between the two muscles (12.6 +/- 0.7% for soleus and 11.7 +/- 0.5% for EDL). Therefore, more recovery heat was produced per unit of initial energy expenditure in soleus than EDL. The calculated efficiency of oxidative phosphorylation was lower in soleus than EDL. The difference in recovery metabolism between soleus and EDL is unlikely to be due to effects of changes in intracellular pH on the enthalpy change associated with PCr hydrolysis. It is suggested that the functionally important specialization of slow-twitch muscle is its low rate of energy use rather than high efficiency.

Mitochondrial coupling in vivo in mouse skeletal muscle

The coupling of mitochondrial ATP synthesis and oxygen consumption (ratio of ATP and oxygen fluxes, P/O) plays a central role in cellular bioenergetics. Reduced P/O values are associated with mitochondrial pathologies that can lead to reduced capacity for ATP synthesis and tissue degeneration. Previous work found a wide range of values for P/O in normal mitochondria. To measure mitochondrial coupling under physiological conditions, we have developed a procedure for determining the P/O of skeletal muscle in vivo. This technique measures ATPase and oxygen consumption rates during ischemia with31P magnetic resonance and optical spectroscopy, respectively. This novel approach allows the independent quantitative measurement of ATPase and oxygen flux rates in intact tissue. The quantitative measurement of oxygen consumption is made possible by our ability to independently measure the saturations of hemoglobin (Hb) and myoglobin (Mb) from optical spectra. Our results indicate that the P/O in skeletal muscle of the mouse hindlimb measured in vivo is 2.16 ± 0.24. The theoretical P/O for resting muscle is 2.33. Systemic treatment with 2,4-dinitrophenol to partially uncouple mitochondria does not affect the ATPase rate in the mouse hindlimb but nearly doubles the rate of oxygen consumption, reducing in vivo P/O to 1.37 ± 0.22. These results indicate that only a small fraction of the oxygen consumption in resting mouse skeletal muscle is nonphosphorylating under physiological conditions, suggesting that mitochondria are more tightly coupled than previously thought.

The dichotomous oxyregulatory behaviour of the planktonic crustaceanDaphnia magna

The dual function of appendage movement (food acquisition, ventilation)proved to be the key to explaining the peculiar oxyregulatory repertoire of the planktonic filter feeder Daphnia magna. Short-term hypoxic exposure experiments with normoxia-acclimated animals under varying food concentrations revealed a dichotomous response pattern with a compensatory tachycardia under food-free conditions and a ventilatory compensation prevailing under food-rich conditions. Food-free, normoxic conditions resulted in maximum appendage beating rates (fa) and half-maximum heart rates (fh), which restricted the scope for oxyregulation to the circulatory system. Food-rich conditions (105algal cells ml-1), on the contrary, had a depressing effect on fa whereas fh increased to 83% of the maximum. In this physiological state, D. magna was able to respond to progressive hypoxia with a compensatory increase in ventilation. A conceptual and mathematical model was developed to analyse the efficiency of ventilatory and circulatory adjustments in improving oxygen transport to tissue. Model predictions showed that an increase in perfusion rate was most effective under both food-free and food-rich conditions in reducing the critical ambient oxygen tension (PO2crit) at which oxygen supply to the tissue started to become impeded. By contrast, a hypothetical increase in ventilation rate had almost no effect on PO2crit under food-free conditions, indicating that appendage movement is driven by nutritive rather than respiratory requirements. However, the model predicted a moderate reduction of PO2crit by hyperventilation under food-rich conditions. Since the regulatory scope for an adjustment in fh was found to be limited in D. magna under these conditions, the increase in ventilation rate is the means of choice for a fed animal to cope with short-term, moderate reductions in ambient oxygen availability. Under long-term and more severe hypoxic conditions, however, the increase in the concentration and oxygen affinity of haemoglobin represents the one and only measure for improving the transport of oxygen from environment to cells.

Maximum rate of oxygen consumption related to succinate dehydrogenase activity in skeletal muscle fibres of chronic heart failure patients and controls

Previous studies indicate that the low maximum rate of oxygen consumption (VO2max) of chronic heart failure (CHF) patients is not because of impaired pump function of the heart. We hypothesize that VO2 during maximum exercise is determined by the total oxidative capacity of skeletal muscle. VO2max of six controls and 14 CHF patients, New York Heart Association class I-III, was determined using an incremental bicycle ergometer test. Cryostat sections of a biopsy from the quadriceps femoris muscle were incubated for succinate dehydrogenase (SDH) using quantitative histochemistry. VO2max (range: 29 ml O2 kg muscle(-1) min(-1) in a class III patient to 118 ml O2 kg muscle(-1) min(-1) in a control subject) correlates with the mean SDH activity of skeletal muscle fibres (r=0.79 or r=0.81, including or excluding oxygen uptake at rest, respectively; P<0.001). The relationship between VO2max and SDH activity is similar to that determined previously using isolated single muscle fibres and myocardial trabeculae under hyperoxic conditions. From the product of SDH activity and the cross-sectional area of the fibre (i.e. spatially integrated SDH activity), it is possible to calculate the maximum oxygen uptake rate per unit muscle fibre length. This uptake rate is linearly related to the number of capillaries per fibre (r=0.76, P<0.001) in all subjects, suggesting that oxidative capacity of skeletal muscle fibres in CHF patients decreases in proportion to the oxygen supply capacity of the microcirculation.

Oxygen regulation and limitation to cellular respiration in mouse skeletal muscle in vivo

In skeletal muscle, intracellular Po2 can fall to as low as 2-3 mmHg. This study tested whether oxygen regulates cellular respiration in this range of oxygen tensions through direct coupling between phosphorylation potential and intracellular Po2. Oxygen may also behave as a simple substrate in cellular respiration that is near saturating levels over most of the physiological range. A novel optical spectroscopic method was used to measure tissue oxygen consumption (Mo2) and intracellular Po2 using the decline in hemoglobin and myoglobin saturation in the ischemic hindlimb muscle of Swiss-Webster mice. 31P magnetic resonance spectroscopic determinations yielded phosphocreatine concentration ([PCr]) and pH in the same muscle volume. Intracellular Po2 fell to <2 mmHg during the ischemic period without a change in the muscle [PCr] or pH. The constant phosphorylation state despite the decline in intracellular Po2 rejects the hypothesis that direct coupling between these two variables results in a regulatory role for oxygen in cellular respiration. A second set of experiments tested the relationship between intracellular Po2 and Mo2. In vivo Mo2 in mouse skeletal muscle was increased by systemic treatment with 2 and 4 mg/kg body wt 2,4-dinitrophenol to partially uncouple mitochondria. Mo2 was not dependent on intracellular Po2 above 3 mmHg in the three groups despite a threefold increase in Mo2. These results indicate that Mo2 and the phosphorylation state of the cell are independent of intracellular Po2 throughout the physiological range of oxygen tensions. Therefore, we reject a regulatory role for oxygen in cellular respiration and conclude that oxygen acts as a simple substrate for respiration under physiological conditions.

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.

Initial mechanical efficiency of isolated cardiac muscle

The aim of this study was to determine whether the initial mechanical efficiency (ratio of work output to initial metabolic cost) of isolated cardiac muscle is over 60%, as has been reported previously, or whether it is approximately 30%, as suggested by an estimate based on the well-established net mechanical efficiency (ratio of work output to total, suprabasal energy cost) of 15%. Determination of initial efficiency required separation of the enthalpy output (i.e. heat + work) into initial and recovery components. The former corresponds to energy produced by reactions that use high-energy phosphates and the latter to energy produced in the regeneration of high-energy phosphates. The two components were separated mathematically. Experiments were performed in vitro (30 degrees C) using preparations dissected from rat left ventricular papillary muscles (N=13). Muscle work output and heat production were measured during a series of 40 contractions using a contraction protocol designed to mimic in vivo papillary muscle activity. Net mechanical efficiency was 13.3+/-0.7%. The total enthalpy output was 2.16 times greater than the initial enthalpy output, so that initial mechanical efficiency was 28.1+/-1.2%.

Effect of extracellular PO2 on the fall in intracellular PO2 in contracting single myocytes

The purpose of this investigation was to study the effects of altered extracellular Po(2) (Pe(O(2))) on the intracellular Po(2) (Pi(O(2))) response to contractions in single skeletal muscle cells. Single myocytes (n = 12) were dissected from lumbrical muscles of adult female Xenopus laevis and injected with 0.5 mM Pd-meso-tetra(4-carboxyphenyl)porphine for assessment of Pi(O(2)) via phosphorescence quenching. At a Pe(O(2)) of approximately 20 (low), approximately 40 (moderate), and approximately 60 (high) Torr, tetanic contractions were induced at a frequency of 0.67 Hz for approximately 2 min with a 5-min recovery between bouts (blocked order design). The Pi(O(2)) response to contractions was characterized by a time delay followed by a monoexponential decline to steady-state (SS) values. The fall in Pi(O(2)) to SS values was significantly greater at each progressively greater Pe(O(2)) (all P < 0.05). The mean response time (time delay + time constant) was significantly faster in the low (35.2 +/- 5.1 s; P < 0.05 vs. high) and moderate (43.3 +/- 6.4 s; P < 0.05 vs. high) compared with high Pe(O(2)) (61.8 +/- 9.4 s) and was correlated positively (r = 0.965) with the net fall in Pi(O(2)). However, the initial rate of change of Pi(O(2)) (calculated as net fall in Pi(O(2))/time constant) was not different (P > 0.05) among Pe(O(2)) trials. These latter data suggest that, over the range of 20-60 Torr, Pe(O(2)) does not play a deterministic role in setting the initial metabolic response to contractions in isolated frog myocytes. Additionally, these results suggest that oxidative phosphorylation in these myoglobin-free myocytes may be compromised by Pe(O(2)) at values nearing 60 Torr.

Calibrated histochemistry applied to oxygen supply and demand in hypertrophied rat myocardium

Oxygen supply and demand of individual cardiomyocytes during the development of myocardial hypertrophy is studied using calibrated histochemical methods. An oxygen diffusion model is used to calculate the critical extracellular oxygen tension (PO(2,crit)) required by cardiomyocytes to prevent hypoxia during hypertrophic growth, and determinants of PO(2,crit) are estimated using calibrated histochemical methods for succinate dehydrogenase activity, cardiomyocyte cross-sectional area, and myoglobin concentration. The model calculation demonstrates that it is essential to calibrate the histochemical methods, so that absolute values for the relevant parameters are obtained. The succinate dehydrogenase activity, which is proportional to the maximum rate of oxygen consumption, and the myoglobin concentration hardly change while the cardiomyocytes grow. The cross-sectional area of the cardiomyocytes, which increases up to threefold in the right ventricular wall due to pulmonary hypertension in monocrotaline-treated rats, is the most important determinant of PO(2,crit) in this model of myocardial hypertrophy. The relationship between oxygen supply and demand at the level of the cardiomyocyte can be investigated using paired determinations of spatially integrated succinate dehydrogenase activity and capillary density. Hypoxia-inducible factor 1alpha can be demonstrated by immunohistochemistry in cardiomyocytes with high PO(2,crit) and increased spatially integrated succinate dehydrogenase activity, indicating that limited oxygen supply affects gene expression in these cells. We conclude that a mismatch of oxygen supply and demand may develop during hypertrophic growth, which can play a role in the transition from myocardial hypertrophy to heart failure.