A metabolic control analysis of kinetic controls in ATP free energy metabolism in contracting skeletal muscle

Reduced expression of mitochondrial complex I subunit Ndufs2 does not impact healthspan in mice

Aging in mammals leads to reduction in genes encoding the 45-subunit mitochondrial electron transport chain complex I. It has been hypothesized that normal aging and age-related diseases such as Parkinson’s disease are in part due to modest decrease in expression of mitochondrial complex I subunits. By contrast, diminishing expression of mitochondrial complex I genes in lower organisms increases lifespan. Furthermore, metformin, a putative complex I inhibitor, increases healthspan in mice and humans. In the present study, we investigated whether loss of one allele of Ndufs2, the catalytic subunit of mitochondrial complex I, impacts healthspan and lifespan in mice. Our results indicate that Ndufs2 hemizygous mice (Ndufs2^+/−) show no overt impairment in aging-related motor function, learning, tissue histology, organismal metabolism, or sensitivity to metformin in a C57BL6/J background. Despite a significant reduction of Ndufs2 mRNA, the mice do not demonstrate a significant decrease in complex I function. However, there are detectable transcriptomic changes in individual cell types and tissues due to loss of one allele of Ndufs2. Our data indicate that a 50% decline in mRNA of the core mitochondrial complex I subunit Ndufs2 is neither beneficial nor detrimental to healthspan.

Oxidative phosphorylation K0.5ADP in vitro depends on substrate oxidative capacity: Insights from a luciferase-based assay to evaluate ADP kinetic parameters

The K_0.5ADP of oxidative phosphorylation (OxPhos) identifies the cytosolic ADP concentration which elicits one-half the maximum OxPhos rate. This kinetic parameter is commonly measured to assess mitochondrial metabolic control sensitivity. Here we describe a luciferase-based assay to evaluate the ADP kinetic parameters of mitochondrial ATP production from OxPhos, adenylate kinase (AK), and creatine kinase (CK). The high sensitivity, reproducibility, and throughput of the microplate-based assay enabled a comprehensive kinetic assessment of all three pathways in mitochondria isolated from mouse liver, kidney, heart, and skeletal muscle. Carboxyatractyloside titrations were also performed with the assay to estimate the flux control strength of the adenine nucleotide translocase (ANT) over OxPhos in human skeletal muscle mitochondria. ANT flux control coefficients were 0.91 ± 0.07, 0.83 ± 0.06, and 0.51 ± 0.07 at ADP concentrations of 6.25, 12.5, and 25 μM, respectively, an [ADP] range which spanned the K_0.5ADP. The oxidative capacity of substrate combinations added to drive OxPhos was found to dramatically influence ADP kinetics in mitochondria from several tissues. In mouse skeletal muscle ten different substrate combinations elicited a 7-fold range of OxPhos V_max, which correlated positively (R² = 0.963) with K_0.5ADP values ranging from 2.3 ± 0.2 μM to 11.9 ± 0.6 μM. We propose that substrate-enhanced capacity to generate the protonmotive force increases the OxPhos K_0.5ADP because flux control at ANT increases, thus K_0.5ADP rises toward the dissociation constant, K_dADP, of ADP-ANT binding. The findings are discussed in the context of top-down metabolic control analysis.

A Simple Hydraulic Analog Model of Oxidative Phosphorylation

Mitochondrial oxidative phosphorylation is the primary source of cellular energy transduction in mammals. This energy conversion involves dozens of enzymatic reactions, energetic intermediates, and the dynamic interactions among them. With the goal of providing greater insight into the complex thermodynamics and kinetics ("thermokinetics") of mitochondrial energy transduction, a simple hydraulic analog model of oxidative phosphorylation is presented. In the hydraulic model, water tanks represent the forward and back "pressures" exerted by thermodynamic driving forces: the matrix redox potential (ΔGredox), the electrochemical potential for protons across the mitochondrial inner membrane (ΔGH), and the free energy of adenosine 5'-triphosphate (ATP) (ΔGATP). Net water flow proceeds from tanks with higher water pressure to tanks with lower pressure through "enzyme pipes" whose diameters represent the conductances (effective activities) of the proteins that catalyze the energy transfer. These enzyme pipes include the reactions of dehydrogenase enzymes, the electron transport chain (ETC), and the combined action of ATP synthase plus the ATP-adenosine 5'-diphosphate exchanger that spans the inner membrane. In addition, reactive oxygen species production is included in the model as a leak that is driven out of the ETC pipe by high pressure (high ΔGredox) and a proton leak dependent on the ΔGH for both its driving force and the conductance of the leak pathway. Model water pressures and flows are shown to simulate thermodynamic forces and metabolic fluxes that have been experimentally observed in mammalian skeletal muscle in response to acute exercise, chronic endurance training, and reduced substrate availability, as well as account for the thermokinetic behavior of mitochondria from fast- and slow-twitch skeletal muscle and the metabolic capacitance of the creatine kinase reaction.

Open-Loop Control of Oxidative Phosphorylation in Skeletal and Cardiac Muscle Mitochondria by Ca(2.)

In cardiac muscle, mitochondrial ATP synthesis is driven by demand for ATP through feedback from the products of ATP hydrolysis. However, in skeletal muscle at higher workloads there is an apparent contribution of open-loop stimulation of ATP synthesis. Open-loop control is defined as modulation of flux through a biochemical pathway by a moiety, which is not a reactant or a product of the biochemical reactions in the pathway. The role of calcium, which is known to stimulate the activity of mitochondrial dehydrogenases, as an open-loop controller, was investigated in isolated cardiac and skeletal muscle mitochondria. The kinetics of NADH synthesis and respiration, feedback from ATP hydrolysis products, and stimulation by calcium were characterized in isolated mitochondria to test the hypothesis that calcium has a stimulatory role in skeletal muscle mitochondria not apparent in cardiac mitochondria. A range of respiratory states were obtained in cardiac and skeletal muscle mitochondria utilizing physiologically relevant concentrations of pyruvate and malate, and flux of respiration, NAD(P)H fluorescence, and rhodamine 123 fluorescence were measured over a range of extra mitochondrial calcium concentrations. We found that under these conditions calcium stimulates NADH synthesis in skeletal muscle mitochondria but not in cardiac mitochondria.

Improving the physiological realism of experimental models

The Virtual Physiological Human (VPH) project aims to develop integrative, explanatory and predictive computational models (C-Models) as numerical investigational tools to study disease, identify and design effective therapies and provide an in silico platform for drug screening. Ultimately, these models rely on the analysis and integration of experimental data. As such, the success of VPH depends on the availability of physiologically realistic experimental models (E-Models) of human organ function that can be parametrized to test the numerical models. Here, the current state of suitable E-models, ranging from in vitro non-human cell organelles to in vivo human organ systems, is discussed. Specifically, challenges and recent progress in improving the physiological realism of E-models that may benefit the VPH project are highlighted and discussed using examples from the field of research on cardiovascular disease, musculoskeletal disorders, diabetes and Parkinson's disease.

Altered Energetics of Exercise Explain Risk of Rhabdomyolysis in Very Long-Chain Acyl-CoA Dehydrogenase Deficiency

Rhabdomyolysis is common in very long-chain acyl-CoA dehydrogenase deficiency (VLCADD) and other metabolic myopathies, but its pathogenic basis is poorly understood. Here, we show that prolonged bicycling exercise against a standardized moderate workload in VLCADD patients is associated with threefold bigger changes in phosphocreatine (PCr) and inorganic phosphate (Pi) concentrations in quadriceps muscle and twofold lower changes in plasma acetyl-carnitine levels than in healthy subjects. This result is consistent with the hypothesis that muscle ATP homeostasis during exercise is compromised in VLCADD. However, the measured rates of PCr and Pi recovery post-exercise showed that the mitochondrial capacity for ATP synthesis in VLCADD muscle was normal. Mathematical modeling of oxidative ATP metabolism in muscle composed of three different fiber types indicated that the observed altered energy balance during submaximal exercise in VLCADD patients may be explained by a slow-to-fast shift in quadriceps fiber-type composition corresponding to 30% of the slow-twitch fiber-type pool in healthy quadriceps muscle. This study demonstrates for the first time that quadriceps energy balance during exercise in VLCADD patients is altered but not because of failing mitochondrial function. Our findings provide new clues to understanding the risk of rhabdomyolysis following exercise in human VLCADD.

Quantification of skeletal muscle mitochondrial function by 31P magnetic resonance spectroscopy techniques: a quantitative review

Magnetic resonance spectroscopy (MRS) can give information about cellular metabolism in vivo which is difficult to obtain in other ways. In skeletal muscle, non-invasive (31) P MRS measurements of the post-exercise recovery kinetics of pH, [PCr], [Pi] and [ADP] contain valuable information about muscle mitochondrial function and cellular pH homeostasis in vivo, but quantitative interpretation depends on understanding the underlying physiology. Here, by giving examples of the analysis of (31) P MRS recovery data, by some simple computational simulation, and by extensively comparing data from published studies using both (31) P MRS and invasive direct measurements of muscle O2 consumption in a common analytical framework, we consider what can be learnt quantitatively about mitochondrial metabolism in skeletal muscle using MRS-based methodology. We explore some technical and conceptual limitations of current methods, and point out some aspects of the physiology which are still incompletely understood.

Fiber-type-specific sensitivities and phenotypic adaptations to dietary fat overload differentially impact fast- versus slow-twitch muscle contractile function in C57BL/6J mice

High-fat diets (HFDs) have been shown to interfere with skeletal muscle energy metabolism and cause peripheral insulin resistance. However, understanding of HFD impact on skeletal muscle primary function, i.e., contractile performance, is limited. Male C57BL/6J mice were fed HFD containing lard (HFL) or palm oil (HFP), or low-fat diet (LFD) for 5weeks. Fast-twitch (FT) extensor digitorum longus (EDL) and slow-twitch (ST) soleus muscles were characterized with respect to contractile function and selected biochemical features. In FT EDL muscle, a 30%-50% increase in fatty acid (FA) content and doubling of long-chain acylcarnitine (C14-C18) content in response to HFL and HFP feeding were accompanied by increase in protein levels of peroxisome proliferator-activated receptor-γ coactivator-1α, mitochondrial oxidative phosphorylation complexes and acyl-CoA dehydrogenases involved in mitochondrial FA β-oxidation. Peak force of FT EDL twitch and tetanic contractions was unaltered, but the relaxation time (RT) of twitch contractions was 30% slower compared to LFD controls. The latter was caused by accumulation of lipid intermediates rather than changes in the expression levels of proteins involved in calcium handling. In ST soleus muscle, no evidence for lipid overload was found in any HFD group. However, particularly in HFP group, the peak force of twitch and tetanic contractions was reduced, but RT was faster than LFD controls. The latter was associated with a fast-to-slow shift in troponin T isoform expression. Taken together, these data highlight fiber-type-specific sensitivities and phenotypic adaptations to dietary lipid overload that differentially impact fast- versus slow-twitch skeletal muscle contractile function.

Optimal experiment design for model selection in biochemical networks

Background

Mathematical modeling is often used to formalize hypotheses on how a biochemical network operates by discriminating between competing models. Bayesian model selection offers a way to determine the amount of evidence that data provides to support one model over the other while favoring simple models. In practice, the amount of experimental data is often insufficient to make a clear distinction between competing models. Often one would like to perform a new experiment which would discriminate between competing hypotheses.

Results

We developed a novel method to perform Optimal Experiment Design to predict which experiments would most effectively allow model selection. A Bayesian approach is applied to infer model parameter distributions. These distributions are sampled and used to simulate from multivariate predictive densities. The method is based on a k-Nearest Neighbor estimate of the Jensen Shannon divergence between the multivariate predictive densities of competing models.

Conclusions

We show that the method successfully uses predictive differences to enable model selection by applying it to several test cases. Because the design criterion is based on predictive distributions, which can be computed for a wide range of model quantities, the approach is very flexible. The method reveals specific combinations of experiments which improve discriminability even in cases where data is scarce. The proposed approach can be used in conjunction with existing Bayesian methodologies where (approximate) posteriors have been determined, making use of relations that exist within the inferred posteriors.

Exercise: Kinetic considerations for gas exchange

The activities of daily living typically occur at metabolic rates below the maximum rate of aerobic energy production. Such activity is characteristic of the nonsteady state, where energy demands, and consequential physiological responses, are in constant flux. The dynamics of the integrated physiological processes during these activities determine the degree to which exercise can be supported through rates of O₂ utilization and CO₂ clearance appropriate for their demands and, as such, provide a physiological framework for the notion of exercise intensity. The rate at which O₂ exchange responds to meet the changing energy demands of exercise--its kinetics--is dependent on the ability of the pulmonary, circulatory, and muscle bioenergetic systems to respond appropriately. Slow response kinetics in pulmonary O₂ uptake predispose toward a greater necessity for substrate-level energy supply, processes that are limited in their capacity, challenge system homeostasis and hence contribute to exercise intolerance. This review provides a physiological systems perspective of pulmonary gas exchange kinetics: from an integrative view on the control of muscle oxygen consumption kinetics to the dissociation of cellular respiration from its pulmonary expression by the circulatory dynamics and the gas capacitance of the lungs, blood, and tissues. The intensity dependence of gas exchange kinetics is discussed in relation to constant, intermittent, and ramped work rate changes. The influence of heterogeneity in the kinetic matching of O₂ delivery to utilization is presented in reference to exercise tolerance in endurance-trained athletes, the elderly, and patients with chronic heart or lung disease.

Parameter uncertainty in biochemical models described by ordinary differential equations

Improved mechanistic understanding of biochemical networks is one of the driving ambitions of Systems Biology. Computational modeling allows the integration of various sources of experimental data in order to put this conceptual understanding to the test in a quantitative manner. The aim of computational modeling is to obtain both predictive as well as explanatory models for complex phenomena, hereby providing useful approximations of reality with varying levels of detail. As the complexity required to describe different system increases, so does the need for determining how well such predictions can be made. Despite efforts to make tools for uncertainty analysis available to the field, these methods have not yet found widespread use in the field of Systems Biology. Additionally, the suitability of the different methods strongly depends on the problem and system under investigation. This review provides an introduction to some of the techniques available as well as gives an overview of the state-of-the-art methods for parameter uncertainty analysis.

Functional classification of skeletal muscle networks. I. Normal physiology

Extensive measurements of the parts list of human skeletal muscle through transcriptomics and other phenotypic assays offer the opportunity to reconstruct detailed functional models. Through integration of vast amounts of data present in databases and extant knowledge of muscle function combined with robust analyses that include a clustering approach, we present both a protein parts list and network models for skeletal muscle function. The model comprises the four key functional family networks that coexist within a functional space; namely, excitation-activation family (forward pathways that transmit a motoneuronal command signal into the spatial volume of the cell and then use Ca(2+) fluxes to bind Ca(2+) to troponin C sites on F-actin filaments, plus transmembrane pumps that maintain transmission capacity); mechanical transmission family (a sophisticated three-dimensional mechanical apparatus that bidirectionally couples the millions of actin-myosin nanomotors with external axial tensile forces at insertion sites); metabolic and bioenergetics family (pathways that supply energy for the skeletal muscle function under widely varying demands and provide for other cellular processes); and signaling-production family (which represents various sensing, signal transduction, and nuclear infrastructure that controls the turn over and structural integrity and regulates the maintenance, regeneration, and remodeling of the muscle). Within each family, we identify subfamilies that function as a unit through analysis of large-scale transcription profiles of muscle and other tissues. This comprehensive network model provides a framework for exploring functional mechanisms of the skeletal muscle in normal and pathophysiology, as well as for quantitative modeling.

Model analysis of the relationship between intracellular PO2 and energy demand in skeletal muscle

On the basis of experimental studies, the intracellular O(2) (iPo(2))-work rate (WR) relationship in skeletal muscle is not unique. One study found that iPo(2) reached a plateau at 60% of maximal WR, while another found that iPo(2) decreased linearly at higher WR, inferring capillary permeability-surface area (PS) and blood-tissue O(2) gradient, respectively, as alternative dominant factors for determining O(2) diffusion changes during exercise. This relationship is affected by several factors, including O(2) delivery and oxidative and glycolytic capacities of the muscle. In this study, these factors are examined using a mechanistic, mathematical model to analyze experimental data from contracting skeletal muscle and predict the effects of muscle contraction on O(2) transport, glycogenolysis, and iPo(2). The model describes convection, O(2) diffusion, and cellular metabolism, including anaerobic glycogenolysis. Consequently, the model simulates iPo(2) in response to muscle contraction under a variety of experimental conditions. The model was validated by comparison of simulations of O(2) uptake with corresponding experimental responses of electrically stimulated canine muscle under different O(2) content, blood flow, and contraction intensities. The model allows hypothetical variation of PS, glycogenolytic capacity, and blood flow and predictions of the distinctive effects of these factors on the iPo(2)-contraction intensity relationship in canine muscle. Although PS is the main factor regulating O(2) diffusion rate, model simulations indicate that PS and O(2) gradient have essential roles, depending on the specific conditions. Furthermore, the model predicts that different convection and diffusion patterns and metabolic factors may be responsible for different iPo(2)-WR relationships in humans.

Mitochondrial function in sparrow pectoralis muscle

Flying birds couple a high daily energy turnover with double-digit millimolar blood glucose concentrations and insulin resistance. Unlike mammalian muscle, flight muscle predominantly relies on lipid oxidation during locomotion at high fractions of aerobic capacity, and birds outlive mammals of similar body mass by a factor of three or more. Despite these intriguing functional differences, few data are available comparing fuel oxidation and free radical production in avian and mammalian skeletal muscle mitochondria. Thus we isolated mitochondria from English sparrow pectoralis and rat mixed hindlimb muscles. Maximal O2 consumption and net H2O2 release were measured in the presence of several oxidative substrate combinations. Additionally, NAD- and FAD-linked electron transport chain (ETC) capacity was examined in sonicated mitochondria. Sparrow mitochondria oxidized palmitoyl-l-carnitine 1.9-fold faster than rat mitochondria and could not oxidize glycerol-3-phosphate, while both species oxidized pyruvate, glutamate and malate–aspartate shuttle substrates at similar rates. Net H2O2 release was not significantly different between species and was highest when glycolytic substrates were oxidized. Sonicated sparrow mitochondria oxidized NADH and succinate over 1.8 times faster than rat mitochondria. The high ETC catalytic potential relative to matrix substrate dehydrogenases in sparrow mitochondria suggests a lower matrix redox potential is necessary to drive a given O2 consumption rate. This may contribute to preferential reliance on lipid oxidation, which may result in lower in vivo reactive oxygen species production in birds compared with mammals.

Acute and chronic effects of bupivacaine on muscle energetics during contraction in vivo: a modular metabolic control analysis

Bupivacaine is a widely used anaesthetic injected locally in clinical practice for short-term neurotransmission blockade. However, persistent side effects on mitochondrial integrity have been demonstrated in muscle parts surrounding the injection site. We use the precise language of metabolic control analysis in the present study to describe in vivo consequences of bupivacaine injection on muscle energetics during contraction. We define a model system of muscle energy metabolism in rats with a sciatic nerve catheter that consists of two modules of reactions, ATP/PCr (phosphocreatine) supply and ATP/PCr demand, linked by the common intermediate PCr detected in vivo by 31P-MRS (magnetic resonance spectroscopy). Measured system variables were [PCr] (intermediate) and contraction (flux). We first applied regulation analysis to quantify acute effects of bupivacaine. After bupivacaine injection, contraction decreased by 15.7% and, concomitantly, [PCr] increased by 11.2%. The regulation analysis quantified that demand was in fact directly inhibited by bupivacaine (−21.3%), causing an increase in PCr. This increase in PCr indirectly reduced mitochondrial activity (−22.4%). Globally, the decrease in contractions was almost fully explained by inhibition of demand (−17.0%) without significant effect through energy supply. Finally we applied elasticity analysis to quantify chronic effects of bupivacaine iterative injections. The absence of a difference in elasticities obtained in treated rats when compared with healthy control rats clearly shows the absence of dysfunction in energetic control of muscle contraction energetics. The present study constitutes the first and direct evidence that bupivacaine myotoxicity is compromised by other factors during contraction in vivo, and illustrates the interest of modular approaches to appreciate simple rules governing bioenergetic systems when affected by drugs.

Computational modeling of mitochondrial energy transduction

Mitochondria are the power plant of the heart, burning fat and sugars to supply the muscle with the adenosine triphosphate (ATP) free energy that drives contraction and relaxation during each heart beat. This function was first captured in a mathematical model in 1967. Today, interest in such a model has been rekindled by ongoing in silico integrative physiology efforts such as the Cardiac Physiome project. Here, the status of the field of computational modeling of mitochondrial ATP synthetic function is reviewed.

Advanced stoichiometric analysis of metabolic networks of mammalian systems

Metabolic engineering tools have been widely applied to living organisms to gain a comprehensive understanding about cellular networks and to improve cellular properties. Metabolic flux analysis (MFA), flux balance analysis (FBA), and metabolic pathway analysis (MPA) are among the most popular tools in stoichiometric network analysis. Although application of these tools into well-known microbial systems is extensive in the literature, various barriers prevent them from being utilized in mammalian cells. Limited experimental data, complex regulatory mechanisms, and the requirement of more complex nutrient media are some major obstacles in mammalian cell systems. However, mammalian cells have been used to produce therapeutic proteins, to characterize disease states or related abnormal metabolic conditions, and to analyze the toxicological effects of some medicinally important drugs. Therefore, there is a growing need for extending metabolic engineering principles to mammalian cells in order to understand their underlying metabolic functions. In this review article, advanced metabolic engineering tools developed for stoichiometric analysis including MFA, FBA, and MPA are described. Applications of these tools in mammalian cells are discussed in detail, and the challenges and opportunities are highlighted.

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)).

Fuel oxidation at the walk-to-run-transition in humans

Multiple factors (including anthropometric, kinetic, mechanical, kinematic, perceptual, and energetic factors) are likely to play a role in the walk-to-run transition in humans. The primary purpose of the present study was to consider an additional factor, the metabolic fuel source. Indirect calorimetry was used to measure fuel oxidation, and perception of effort was recorded as 10 overnight-fasted adults locomoted on a level treadmill at speeds progressing from 1.56 to 2.46 m s(-1) in increments of 0.11 m s(-1) and 10.0 minutes under 3 conditions: (1) unconstrained choice of gait, (2) walking at all speeds, and (3) running at all speeds. The preferred transition speed was 2.08 ± 0.03 m s(-1). Gait transition from walking to running increased oxygen consumption rate, decreased the perception of effort, and decreased the rate of carbohydrate oxidation. We propose that, in an evolutionary context, gait transition, guided by the perception of effort, can be viewed as a carbohydrate-sparing strategy.

Similar mitochondrial activation kinetics in wild-type and creatine kinase-deficient fast-twitch muscle indicate significant Pi control of respiration

Past simulations of oxidative ATP metabolism in skeletal muscle have predicted that elimination of the creatine kinase (CK) reaction should result in dramatically faster oxygen consumption dynamics during transitions in ATP turnover rate. This hypothesis was investigated. Oxygen consumption of fast-twitch (FT) muscle isolated from wild-type (WT) and transgenic mice deficient in the myoplasmic (M) and mitochondrial (Mi) CK isoforms (MiM CK(-/-)) were measured at 20°C at rest and during electrical stimulation. MiM CK(-/-) muscle oxygen consumption activation kinetics during a step change in contraction rate were 30% faster than WT (time constant 53 ± 3 vs. 69 ± 4 s, respectively; mean ± SE, n = 8 and 6, respectively). MiM CK(-/-) muscle oxygen consumption deactivation kinetics were 380% faster than WT (time constant 74 ± 4 s vs. 264 ± 4 s, respectively). Next, the experiments were simulated using a computational model of the oxidative ATP metabolic network in FT muscle featuring ADP and Pi feedback control of mitochondrial respiration (J. A. L. Jeneson, J. P. Schmitz, N. A. van den Broek, N. A. van Riel, P. A. Hilbers, K. Nicolay, J. J. Prompers. Am J Physiol Endocrinol Metab 297: E774-E784, 2009) that was reparameterized for 20°C. Elimination of Pi control via clamping of the mitochondrial Pi concentration at 10 mM reproduced past simulation results of dramatically faster kinetics in CK(-/-) muscle, while inclusion of Pi control qualitatively explained the experimental observations. On this basis, it was concluded that previous studies of the CK-deficient FT muscle phenotype underestimated the contribution of Pi to mitochondrial respiratory control.

Reaction-diffusion constraints in living tissue: effectiveness factors in skeletal muscle design

A mathematical model was developed to analyze the effects of intracellular diffusion of O(2) and high-energy phosphate metabolites on aerobic energy metabolism in skeletal muscle. We tested the hypotheses that in a range of muscle fibers from different species (1) aerobic metabolism was not diffusion limited and (2) that fibers had a combination of rate and fiber size that placed them at the brink of substantial diffusion limitation. A simplified chemical reaction rate law for mitochondrial oxidative phosphorylation was developed utilizing a published detailed model of isolated mitochondrial function. This rate law was then used as a boundary condition in a reaction-diffusion model that was further simplified using the volume averaging method and solved to determine the rates of oxidative phosphorylation as functions of the volume fraction of mitochondria, the size of the muscle cell, and the amount of oxygen delivered by the capillaries. The effectiveness factor, which is the ratio of reaction rate in the system with finite rates of diffusion to those in the absence of any diffusion limitations, defined the regions where intracellular diffusion of metabolites and O(2) may limit aerobic metabolism in both very small, highly oxidative fibers as well as in larger fibers with lower aerobic capacity. Comparison of model analysis with experimental data revealed that none of the fibers was strongly limited by diffusion, as expected. However, while some fibers were near substantial diffusion limitation, most were well within the domain of reaction control of aerobic metabolic rate. This may constitute a safety factor in muscle that provides a level of protection from diffusion constraints under conditions such as hypoxia.

Protein composition and function of red and white skeletal muscle mitochondria

Red and white muscles are faced with very different energetic demands. However, it is unclear whether relative mitochondrial protein expression is different between muscle types. Mitochondria from red and white porcine skeletal muscle were isolated with a Percoll gradient. Differences in protein composition were determined using blue native (BN)-PAGE, two-dimensional differential in gel electrophoresis (2D DIGE), optical spectroscopy, and isobaric tag for relative and absolute quantitation (iTRAQ). Complex IV and V activities were compared using BN-PAGE in-gel activity assays, and maximal mitochondrial respiration rates were assessed using pyruvate (P) + malate (M), glutamate (G) + M, and palmitoyl-carnitine (PC) + M. Without the Percoll step, major cytosolic protein contamination was noted for white mitochondria. Upon removal of contamination, very few protein differences were observed between red and white mitochondria. BN-PAGE showed no differences in the subunit composition of Complexes I-V or the activities of Complexes IV and V. iTRAQ analysis detected 358 mitochondrial proteins, 69 statistically different. Physiological significance may be lower: at a 25% difference, 48 proteins were detected; at 50%, 14 proteins were detected; and 3 proteins were detected at a 100%. Thus any changes could be argued to be physiologically modest. One area of difference was fat metabolism where four β-oxidation enzymes were ∼25% higher in red mitochondria. This was correlated with a 40% higher rate of PC+M oxidation in red mitochondria compared with white mitochondria with no differences in P+M and G+M oxidation. These data suggest that metabolic demand differences between red and white muscle fibers are primarily matched by the number of mitochondria and not by significant alterations in the mitochondria themselves.

Interactive effects of cadmium and hypoxia on metabolic responses and bacterial loads of eastern oysters Crassostrea virginica Gmelin

Pollution by toxic metals including cadmium (Cd) and hypoxia are important stressors in estuaries and coastal waters which may interactively affect sessile benthic organisms, such as oysters. We studied metabolic responses to prolonged hypoxic acclimation (2 weeks at 5% O2) in control and Cd-exposed (30 d at 50 μg L(-1) Cd) oysters Crassostrea virginica, and analyzed the effects of these stressors on abundance of Vibrio spp. in oysters. Hypoxia-acclimated oysters retained normal standard metabolic rates (SMR) at 5% O2, in contrast to a decline of SMR observed during acute hypoxia. However, oysters spent more time actively ventilating in hypoxia than normoxia resulting in enhanced Cd uptake and 2.7-fold higher tissue Cd burdens in hypoxia. Cd exposure led to a significant decrease in tissue glycogen stores, increase in free glucose levels and elevated activity of glycolytic enzymes (hexokinase and aldolase) indicating a greater dependence on carbohydrate catabolism. A compensatory increase in activities of two key mitochondrial enzymes (citrate synthase and cytochrome c oxidase) was found during prolonged hypoxia in control oysters but suppressed in Cd-exposed ones. Cd exposure also resulted in a significant increase in abundance of Vibrio parahaemolyticus and Vibrio vulnificus levels during normoxia and hypoxia, respectively. Overall, Cd- and hypoxia-induced changes in metabolic profile, Cd accumulation and bacterial flora of oysters indicate that these stressors can synergistically impact energy homeostasis, performance and survival of oysters in polluted estuaries and have significant consequences for transfer of Cd and bacterial pathogens to the higher levels of the food chain.

Increased reactive oxygen species production and lower abundance of complex I subunits and carnitine palmitoyltransferase 1B protein despite normal mitochondrial respiration in insulin-resistant human skeletal muscle

OBJECTIVE

The contribution of mitochondrial dysfunction to skeletal muscle insulin resistance remains elusive. Comparative proteomics are being applied to generate new hypotheses in human biology and were applied here to isolated mitochondria to identify novel changes in mitochondrial protein abundance present in insulin-resistant muscle.

RESEARCH DESIGN AND METHODS

Mitochondria were isolated from vastus lateralis muscle from lean and insulin-sensitive individuals and from obese and insulin-resistant individuals who were otherwise healthy. Respiration and reactive oxygen species (ROS) production rates were measured in vitro. Relative abundances of proteins detected by mass spectrometry were determined using a normalized spectral abundance factor method.

RESULTS

NADH- and FADH(2)-linked maximal respiration rates were similar between lean and obese individuals. Rates of pyruvate and palmitoyl-DL-carnitine (both including malate) ROS production were significantly higher in obesity. Mitochondria from obese individuals maintained higher (more negative) extramitochondrial ATP free energy at low metabolic flux, suggesting that stronger mitochondrial thermodynamic driving forces may underlie the higher ROS production. Tandem mass spectrometry identified protein abundance differences per mitochondrial mass in insulin resistance, including lower abundance of complex I subunits and enzymes involved in the oxidation of branched-chain amino acids (BCAA) and fatty acids (e.g., carnitine palmitoyltransferase 1B).

CONCLUSIONS

We provide data suggesting normal oxidative capacity of mitochondria in insulin-resistant skeletal muscle in parallel with high rates of ROS production. Furthermore, we show specific abundance differences in proteins involved in fat and BCAA oxidation that might contribute to the accumulation of lipid and BCAA frequently associated with the pathogenesis of insulin resistance.

Regulation of skeletal muscle oxidative capacity and insulin signaling by the mitochondrial rhomboid protease PARL

Type 2 diabetes mellitus (T2DM) and aging are characterized by insulin resistance and impaired mitochondrial energetics. In lower organisms, remodeling by the protease pcp1 (PARL ortholog) maintains the function and lifecycle of mitochondria. We examined whether variation in PARL protein content is associated with mitochondrial abnormalities and insulin resistance. PARL mRNA and mitochondrial mass were both reduced in elderly subjects and in subjects with T2DM. Muscle knockdown of PARL in mice resulted in malformed mitochondrial cristae, lower mitochondrial content, decreased PGC1alpha protein levels, and impaired insulin signaling. Suppression of PARL protein in healthy myotubes lowered mitochondrial mass and insulin-stimulated glycogen synthesis and increased reactive oxygen species production. We propose that lower PARL expression may contribute to the mitochondrial abnormalities seen in aging and T2DM.

Application of the principles of systems biology and Wiener's cybernetics for analysis of regulation of energy fluxes in muscle cells in vivo

The mechanisms of regulation of respiration and energy fluxes in the cells are analyzed based on the concepts of systems biology, non-equilibrium steady state kinetics and applications of Wiener’s cybernetic principles of feedback regulation. Under physiological conditions cardiac function is governed by the Frank-Starling law and the main metabolic characteristic of cardiac muscle cells is metabolic homeostasis, when both workload and respiration rate can be changed manifold at constant intracellular level of phosphocreatine and ATP in the cells. This is not observed in skeletal muscles. Controversies in theoretical explanations of these observations are analyzed. Experimental studies of permeabilized fibers from human skeletal muscle vastus lateralis and adult rat cardiomyocytes showed that the respiration rate is always an apparent hyperbolic but not a sigmoid function of ADP concentration. It is our conclusion that realistic explanations of regulation of energy fluxes in muscle cells require systemic approaches including application of the feedback theory of Wiener’s cybernetics in combination with detailed experimental research. Such an analysis reveals the importance of limited permeability of mitochondrial outer membrane for ADP due to interactions of mitochondria with cytoskeleton resulting in quasi-linear dependence of respiration rate on amplitude of cyclic changes in cytoplasmic ADP concentrations. The system of compartmentalized creatine kinase (CK) isoenzymes functionally coupled to ANT and ATPases, and mitochondrial-cytoskeletal interactions separate energy fluxes (mass and energy transfer) from signalling (information transfer) within dissipative metabolic structures – intracellular energetic units (ICEU). Due to the non-equilibrium state of CK reactions, intracellular ATP utilization and mitochondrial ATP regeneration are interconnected by the PCr flux from mitochondria. The feedback regulation of respiration occurring via cyclic fluctuations of cytosolic ADP, Pi and Cr/PCr ensures metabolic stability necessary for normal function of cardiac cells.

The O2 cost of the tension-time integral in isolated single myocytes during fatigue

One proposed explanation for the Vo(2) slow component is that lower-threshold motor units may fatigue and develop little or no tension but continue to use O(2), thereby resulting in a dissociation of cellular respiration from force generation. The present study used intact isolated single myocytes with differing fatigue resistance profiles to investigate the relationship between fatigue, tension development, and aerobic metabolism. Single Xenopus skeletal muscle myofibers were allocated to a fast-fatiguing (FF) or a slow-fatiguing (SF) group, based on the contraction frequency required to elicit a fall in tension to 60% of peak. Phosphorescence quenching of a porphyrin compound was used to determine Delta intracellular Po(2) (Pi(O(2)); a proxy for Vo(2)), and developed isometric tension was monitored to allow calculation of the time-integrated tension (TxT). Although peak DeltaPi(O(2)) was not different between groups (P = 0.36), peak tension was lower (P < 0.05) in SF vs. FF (1.97 +/- 0. 17 V vs. 2. 73 +/- 0.30 V, respectively) and time to 60% of peak tension was significantly longer in SF vs. FF (242 +/- 10 s vs. 203 +/- 10 s, respectively). Before fatigue, both DeltaPi(O(2)) and TxT rose proportionally with contraction frequency in SF and FF, resulting in DeltaPi(O(2))/TxT being identical between groups. At fatigue, TxT fell dramatically in both groups, but DeltaPi(O(2)) decreased proportionately only in the FF group, resulting in an increase in DeltaPi(O(2))/TxT in the SF group relative to the prefatigue condition. These data show that more fatigue-resistant fibers maintain aerobic metabolism as they fatigue, resulting in an increased O(2) cost of contractions that could contribute to the Vo(2) slow component seen in whole body exercise.

Structure-function relationships in feedback regulation of energy fluxes in vivo in health and disease: mitochondrial interactosome

The aim of this review is to analyze the results of experimental research of mechanisms of regulation of mitochondrial respiration in cardiac and skeletal muscle cells in vivo obtained by using the permeabilized cell technique. Such an analysis in the framework of Molecular Systems Bioenergetics shows that the mechanisms of regulation of energy fluxes depend on the structural organization of the cells and interaction of mitochondria with cytoskeletal elements. Two types of cells of cardiac phenotype with very different structures were analyzed: adult cardiomyocytes and continuously dividing cancerous HL-1 cells. In cardiomyocytes mitochondria are arranged very regularly, and show rapid configuration changes of inner membrane but no fusion or fission, diffusion of ADP and ATP is restricted mostly at the level of mitochondrial outer membrane due to an interaction of heterodimeric tubulin with voltage dependent anion channel, VDAC. VDAC with associated tubulin forms a supercomplex, Mitochondrial Interactosome, with mitochondrial creatine kinase, MtCK, which is structurally and functionally coupled to ATP synthasome. Due to selectively limited permeability of VDAC for adenine nucleotides, mitochondrial respiration rate depends almost linearly upon the changes of cytoplasmic ADP concentration in their physiological range. Functional coupling of MtCK with ATP synthasome amplifies this signal by recycling adenine nucleotides in mitochondria coupled to effective phosphocreatine synthesis. In cancerous HL-1 cells this complex is significantly modified: tubulin is replaced by hexokinase and MtCK is lacking, resulting in direct utilization of mitochondrial ATP for glycolytic lactate production and in this way contributing in the mechanism of the Warburg effect. Systemic analysis of changes in the integrated system of energy metabolism is also helpful for better understanding of pathogenesis of many other diseases.

Modular regulation analysis of integrative effects of hypoxia on the energetics of contracting skeletal muscle in vivo

In the exercising muscle, acute reduction in ambient oxygen impairs muscle contraction because of the effects of hypoxia on mitochondrial ATP supply. The less marked impairment reported after long-term exposure to hypoxia points to changes in the regulation of the energetic system of contraction in HC (hypoxic conditioned) animals. This energetic system is conceptually defined here as two modules: the ATP/PCr (phosphocreatine)-producer and the ATP/PCr-consumer connected by energetic intermediates. Modular control analysis that combines top-down control analysis with non-invasive 31P-NMR spectroscopy was used to describe the effects of hypoxia on each module and their adaptation. Modulations of steady levels of ATP turnover (indirectly assessed as force output) and muscle PCr were obtained in HC rats (6 weeks at 10.5% O2) compared with N (normoxic) rats. Modular control and regulation analyses quantified the elasticity to PCr of each module in N and HC rats as well as the direct effect of acute hypoxia on the ATP/PCr-producer module. Similar elasticities in N and HC rats indicate the absence of response to long-term hypoxia in internal regulations of the ATP supply and demand pathways. The less marked impairment of contraction by acute hypoxia in HC rats (-9+/-6% versus -17+/-14% in N rats, P<0.05) was therefore fully explained by a lower direct effect (HC -31+/-13% versus N -44+/-23%, P<0.05) of acute hypoxia on mitochondrial ATP supply. This points to a positive adaptation to chronic hypoxia. Modular control analysis in vivo may provide powerful tools to find out improved function (alternatively dysfunction) at the system level in conditioned animals.

Regulation of respiration controlled by mitochondrial creatine kinase in permeabilized cardiac cells in situ. Importance of system level properties

The main focus of this investigation is steady state kinetics of regulation of mitochondrial respiration in permeabilized cardiomyocytes in situ. Complete kinetic analysis of the regulation of respiration by mitochondrial creatine kinase was performed in the presence of pyruvate kinase and phosphoenolpyruvate to simulate interaction of mitochondria with glycolytic enzymes. Such a system analysis revealed striking differences in kinetic behaviour of the MtCK-activated mitochondrial respiration in situ and in vitro. Apparent dissociation constants of MgATP from its binary and ternary complexes with MtCK, Kia and Ka (1.94+/-0.86 mM and 2.04+/-0.14 mM, correspondingly) were increased by several orders of magnitude in situ in comparison with same constants in vitro (0.44+/-0.08 mM and 0.016+/-0.01 mM, respectively). Apparent dissociation constants of creatine, Kib and Kb (2.12+/-0.21 mM 2.17+/-0.40 Mm, correspondingly) were significantly decreased in situ in comparison with in vitro mitochondria (28+/-7 mM and 5+/-1.2 mM, respectively). Dissociation constant for phosphocreatine was not changed. These data may indicate selective restriction of metabolites' diffusion at the level of mitochondrial outer membrane. It is concluded that mechanisms of the regulation of respiration and energy fluxes in vivo are system level properties which depend on intracellular interactions of mitochondria with cytoskeleton, intracellular MgATPases and cytoplasmic glycolytic system.

Control and regulation of integrated mitochondrial function in metabolic and transport networks

The pattern of flux and concentration control coefficients in an integrated mitochondrial energetics model is examined by applying a generalized matrix method of control analysis to calculate control coefficients, as well as response coefficients The computational model of Cortassa et al. encompasses oxidative phosphorylation, the TCA cycle, and Ca²⁺ dynamics. Control of ATP synthesis, TCA cycle, and ANT fluxes were found to be distributed among various mitochondrial processes. Control is shared by processes associated with ATP/ADP production and transport, as well as by Ca²⁺ dynamics. The calculation also analyzed the control of the concentrations of key regulatory ions and metabolites (Ca²⁺, NADH, ADP). The approach we have used demonstrates how properties of integrated systems may be understood through applications of computational modeling and control analysis.

Control and regulation of mitochondrial energetics in an integrated model of cardiomyocyte function

Understanding the regulation and control of complex networks of reactions requires analytical tools that take into account the interactions between individual network components controlling global network function. Here, we apply a generalized matrix method of control analysis to calculate flux and concentration control coefficients, as well as response coefficients, in an integrated model of excitation-contraction (EC) coupling and mitochondrial energetics (ECME model) in the cardiac ventricular myocyte. Control and regulation of oxygen consumption (V(O2)) was first assessed in a mitochondrion model, and then in the integrated cardiac myocyte model under resting and working conditions. The results demonstrate that in the ECME model, control of respiration is distributed among cytoplasmic ATPases and mitochondrial processes. The magnitude of control by cytoplasmic ATPases increases under working conditions. The model prediction that the respiratory chain exerts strong positive control on V(O2) (control coefficient 0.89) was corroborated experimentally in cardiac trabeculae utilizing the inhibitor titration method. In the model, mitochondrial respiration displayed the highest response coefficients with respect to the concentration of cytoplasmic ATP. This was due to the high elasticity of ANT flux toward ATP in the cytoplasm. The analysis reveals the complex interdependence of sarcolemmal, cytoplasmic, and mitochondrial processes that contribute to the control of energy supply and demand in the heart. Moreover, by visualizing the structure of control of the metabolic network of the myocyte, we provide support for the emerging concept of control by diffuse loops, in which action on the network (e.g., by a pharmacological agent) may bring about changes in processes without obvious direct mechanistic links between them.

Mitochondrial function in physically active elders with sarcopenia

Physical activity is reported to protect against sarcopenia and preserve mitochondrial function. Healthy normal lean (NL: n=15) and sarcopenic (SS: n=9) participants were recruited based on body composition (DXA, Lunar DPX), age, and physical activity. Gastrocnemius mitochondrial function was assessed by (31)P MRS using steady-state exercise in a 4T Bruker Biospin. Total work (429.3+/-160.2J vs. 851.0+/-211.7J, p<0.001) and muscle volume (p=0.006) were lower in SS, although these variables were not correlated (NL r=-0.31, p=0.33, SS r=(0.03, p=0.93). In the SS resting ATP/ADP was lower (p=0.03) and ATP hydrolysis higher (p=0.02) at rest. Free energy ATP hydrolysis was greater at the end of exercise (p=0.02) and [ADP] relative to total work output was higher in SS (ANCOVA, p=0.005). [PCr] recovery kinetics were not different between the groups. Adjusting these parameters for differences in total work output and muscle volume did not explain these findings. These data suggest that aerobic metabolism in physically active older adults with sarcopenia is mildly impaired at rest and during modest levels of exercise where acidosis was avoided. Muscle energetics is coordinated at multiple cellular levels and further studies are needed to determine the loci/locus of energy instability in sarcopenia.

High energy phosphate concentrations and AMPK phosphorylation in skeletal muscle from mice with inherited differences in hypoxic exercise tolerance

The effect of chronic hypobaric hypoxia (1/2 atmospheric pressure) on high energy phosphate (HEP) compounds was investigated in slow (soleus; SOL) and fast twitch (extensor digitorum longus; EDL) muscle from 3 strains of mice with large differences in hypoxic exercise tolerance (HET). Phosphocreatine concentration ([PCr]) decreased 16-29% following hypoxia in EDL and SOL in all strains, while [ADP] and [AMP] increased. In the EDL, HET was negatively correlated with the PCr/ATP ratio and positively correlated with the ATP/P(i) ratio. The free energy of ATP hydrolysis (DeltaG(obs)) remained constant despite the substantial changes that occurred in HEP profiles. The alteration of HEP set points and preservation of DeltaG(obs) are consistent with the notion that (1) maximal rates of steady-state ATP turnover are reduced under hypoxia, and (2) HEP perturbations during rest to work transitions are reduced in skeletal muscle from hypoxia acclimated animals. We therefore expected a lower phosphorylation ratio of AMP-activated protein kinase (AMPK-P/AMPK) during stimulation in hypoxic acclimated animals. However, neither the resting nor stimulated AMPK-P/AMPK was influenced by hypoxia, although there were significant differences among strains.

In vivo modular control analysis of energy metabolism in contracting skeletal muscle

We used (31)P MRS (magnetic resonance spectroscopy) measurements of energetic intermediates [ATP, P(i) and PCr (phosphocreatine)] in combination with the analytical tools of metabolic control analysis to study in vivo energy metabolism in the contracting skeletal muscle of anaesthetized rats over a broad range of workload. According to our recent MoCA (modular control analysis) used to describe regulatory mechanisms in beating heart, we defined the energetic system of muscle contraction as two modules (PCr-Producer and PCr-Consumer) connected by the energetic intermediates. Hypoxia and electrical stimulation were used in this in vivo study as reasonably selective modulations of Producer and Consumer respectively. As quantified by elasticity coefficients, the sensitivities of each module to PCr determine the control of steady-state contractile activity and metabolite concentrations. The magnitude of the elasticity of the producer was high (4.3+/-0.6) at low workloads and decreased 5-fold (to 0.9+/-0.2) at high workloads. By contrast, the elasticity of the consumer remained low (0.5-1.2) over the range of metabolic rates studied. The control exerted by each module over contraction was calculated from these elasticities. The control of contraction was found on the consumer at low workloads and then swung to the producer, due to the workload-dependent decrease in the elasticity of producer. The workload-dependent elasticity and control pattern of energy production in muscle is a major difference from heart. Since module rate and elasticity depend on the concentrations of substrates and products, the absence of homoeostasis of the energetic intermediates in muscle, by contrast with heart, is probably the origin of the workload-dependent elasticity of the producer module.

Control over the contribution of the mitochondrial membrane potential (DeltaPsi) and proton gradient (DeltapH) to the protonmotive force (Deltap). In silico studies

The protonmotive force across the inner mitochondrial membrane (Deltap) has two components: membrane potential (DeltaPsi) and the gradient of proton concentration (DeltapH). The computer model of oxidative phosphorylation developed previously by Korzeniewski et al. (Korzeniewski, B., Noma, A., and Matsuoka, S. (2005) Biophys. Chem. 116, 145-157) was modified by including the K+ uniport, K+/H+ exchange across the inner mitochondrial membrane, and membrane capacitance to replace the fixed DeltaPsi/DeltapH ratio used previously with a variable one determined mechanistically. The extended model gave good agreement with experimental results. Computer simulations showed that the contribution of DeltaPsi and DeltapH to Deltap is determined by the ratio of the rate constants of the K+ uniport and K+/H+ exchange and not by the absolute values of these constants. The value of Deltap is mostly controlled by ATP usage. The metabolic control over the DeltaPsi/DeltapH ratio is exerted mostly by K+ uniport and K+/H+ exchange in the presence of these processes, and by the ATP usage, ATP/ADP carrier, and phosphate carrier in the absence of them. The K+ circulation across the inner mitochondrial membrane is controlled mainly by K+ uniport and K+/H+ exchange, whereas H+ circulation by ATP usage. It is demonstrated that the secondary K+ ion transport is not necessary for maintaining the physiological DeltaPsi/DeltapH ratio.

Phosphate metabolite concentrations and ATP hydrolysis potential in normal and ischaemic hearts

To understand how cardiac ATP and CrP remain stable with changes in work rate - a phenomenon that has eluded mechanistic explanation for decades - data from (31)phosphate-magnetic resonance spectroscopy ((31)P-MRS) are analysed to estimate cytoplasmic and mitochondrial phosphate metabolite concentrations in the normal state, during high cardiac workstates, during acute ischaemia and reactive hyperaemic recovery. Analysis is based on simulating distributed heterogeneous oxygen transport in the myocardium integrated with a detailed model of cardiac energy metabolism. The model predicts that baseline myocardial free inorganic phosphate (P(i)) concentration in the canine myocyte cytoplasm - a variable not accessible to direct non-invasive measurement - is approximately 0.29 mm and increases to 2.3 mm near maximal cardiac oxygen consumption. During acute ischaemia (from ligation of the left anterior descending artery) P(i) increases to approximately 3.1 mm and ATP consumption in the ischaemic tissue is reduced quickly to less than half its baseline value before the creatine phosphate (CrP) pool is 18% depleted. It is determined from these experiments that the maximal rate of oxygen consumption of the heart is an emergent property and is limited not simply by the maximal rate of ATP synthesis, but by the maximal rate at which ATP can be synthesized at a potential at which it can be utilized. The critical free energy of ATP hydrolysis for cardiac contraction that is consistent with these findings is approximately -63.5 kJ mol(-1). Based on theoretical findings, we hypothesize that inorganic phosphate is both the primary feedback signal for stimulating oxidative phosphorylation in vivo and also the most significant product of ATP hydrolysis in limiting the capacity of the heart to hydrolyse ATP in vivo. Due to the lack of precise quantification of P(i) in vivo, these hypotheses and associated model predictions remain to be carefully tested experimentally.

Elucidating the interactions between the adhesive and transcriptional functions of -catenin in normal and cancerous cells

Wnt signalling is involved in a wide range of physiological and pathological processes. The presence of an extracellular Wnt stimulus induces cytoplasmic stabilisation and nuclear translocation of beta-catenin, a protein that also plays an essential role in cadherin-mediated adhesion. Two main hypotheses have been proposed concerning the balance between beta-catenin's adhesive and transcriptional functions: either beta-catenin's fate is determined by competition between its binding partners, or Wnt induces folding of beta-catenin into a conformation allocated preferentially to transcription. The experimental data supporting each hypotheses remain inconclusive. In this paper we present a new mathematical model of the Wnt pathway that incorporates beta-catenin's dual function. We use this model to carry out a series of in silico experiments and compare the behaviour of systems governed by each hypothesis. Our analytical results and model simulations provide further insight into the current understanding of Wnt signalling and, in particular, reveal differences in the response of the two modes of interaction between adhesion and signalling in certain in silico settings. We also exploit our model to investigate the impact of the mutations most commonly observed in human colorectal cancer. Simulations show that the amount of functional APC required to maintain a normal phenotype increases with increasing strength of the Wnt signal, a result which illustrates that the environment can substantially influence both tumour initiation and phenotype.

Control over action potential, calcium peak and average fluxes in the cyclic quasi-steady-state ion transport system in cardiac myocytes: in silico studies

MCA (metabolic control analysis) was originally developed to deal with steady-state systems. In the present theoretical study, the control analysis is applied to the cyclic quasi-steady-state system of ion transport in cardiac myocytes. It is demonstrated that the metabolic control of particular components (channels, exchangers, pumps) of the system over such quasi-steady-state variables as action potential amplitude, action potential duration, area under the Ca2+ peak and average fluxes through particular channels during one oscillation period can be defined and calculated. It is shown that the control over particular variables in the analysed, periodical system is distributed among many (potentially all) components of the system. Nevertheless, some components seem to exert much more control than other components, and different variables are controlled to the greatest extent by different channels. Finally, it is hypothesized that the Na+ and K+ transport system exerts a significant control over the Ca2+ transport system, but not vice versa.

Skeletal muscle energetics with PNMR: personal views and historic perspectives

This article reviews historical and current NMR approaches to describing in vivo bioenergetics of skeletal muscles in normal and diseased populations. It draws upon the first author's more than 70 years of personal experience in enzyme kinetics and the last author's physiological approaches. The development of in vivo PNMR jointly with researchers around the world is described. It is explained how non-invasive PNMR has advanced human exercise biochemistry, physiology and pathology. Further, after a brief explanation of bioenergetics with PNMR on creatine kinase, anerobic glycolysis and mitochondrial oxidative phosphorylation, some basic and controversial subjects are focused upon, and the authors' view of the subjects are offered, with questions and answers. Some of the research has been introduced in exercise physiology. Future directions of NMR on bioenergetics, as a part of system biological approaches, are indicated.

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.

Metabolic control over the oxygen consumption flux in intact skeletal muscle: in silico studies

It has been postulated previously that a direct activation of all oxidative phosphorylation complexes in parallel with the activation of ATP usage and substrate dehydrogenation (the so-called each-step activation) is the main mechanism responsible for adjusting the rate of ATP production by mitochondria to the current energy demand during rest-to-work transition in intact skeletal muscle in vivo. The present in silico study, using a computer model of oxidative phosphorylation developed previously, analyzes the impact of the each-step-activation mechanism on the distribution of control (defined within Metabolic Control Analysis) over the oxygen consumption flux among the components of the bioenergetic system in intact oxidative skeletal muscle at different energy demands. It is demonstrated that in the absence of each-step activation, the oxidative phosphorylation complexes take over from ATP usage most of the control over the respiration rate and oxidative ATP production at higher (but still physiological) energy demands. This leads to a saturation of oxidative phosphorylation, impossibility of a further acceleration of oxidative ATP synthesis, and dramatic drop in the phosphorylation potential. On the other hand, the each-step-activation mechanism allows maintenance of a high degree of the control exerted by ATP usage over the ATP turnover and oxygen consumption flux even at high energy demands and thus enables a potentially very large increase in ATP turnover. It is also shown that low oxygen concentration shifts the metabolic control from ATP usage to cytochrome oxidase and thus limits the oxidative ATP production.

A computational model integrating electrophysiology, contraction, and mitochondrial bioenergetics in the ventricular myocyte

An intricate network of reactions is involved in matching energy supply with demand in the heart. This complexity arises because energy production both modulates and is modulated by the electrophysiological and contractile activity of the cardiac myocyte. Here, we present an integrated mathematical model of the cardiac cell that links excitation-contraction coupling with mitochondrial energy generation. The dynamics of the model are described by a system of 50 ordinary differential equations. The formulation explicitly incorporates cytoplasmic ATP-consuming processes associated with force generation and ion transport, as well as the creatine kinase reaction. Changes in the electrical and contractile activity of the myocyte are coupled to mitochondrial energetics through the ATP, Ca2+, and Na+ concentrations in the myoplasmic and mitochondrial matrix compartments. The pseudo steady-state relationship between force and oxygen consumption at various stimulus frequencies and external Ca2+ concentrations is reproduced in both model simulations and direct experiments in cardiac trabeculae under normoxic conditions, recapitulating the linearity between cardiac work and respiration in the heart. Importantly, the model can also reproduce the rapid time-dependent changes in mitochondrial NADH and Ca2+ in response to abrupt changes in workload. The steady-state and dynamic responses of the model were conferred by ADP-dependent stimulation of mitochondrial oxidative phosphorylation and Ca2+ -dependent regulation of Krebs cycle dehydrogenases, illustrating how the model can be used as a tool for investigating mechanisms underlying metabolic control in the heart.

Nitric oxide and mitochondrial biogenesis: a key to long-term regulation of cellular metabolism

Mitochondria, the site of oxidative energy metabolism in eukariotic cells, are a highly organised structure endowed with different enzymes and reactions localized in discrete membranes and aqueous compartments. Mitochondrial function is regulated in complex ways by several agonists and environmental conditions, through activation of specific transcription factors and signalling pathways. A key player in this scenario is nitric oxide (NO). Its binding to cytochrome c oxidase in the mitochondrial respiratory chain, which is reversible and in competition with oxygen, plays a role in acute oxygen sensing and in the cell response to hypoxia. Evidence of the last two years showed that NO has also long-term effects, leading to biogenesis of functionally active mitochondria, that complement its oxygen sensing function. Mitochondrial biogenesis is triggered by NO through activation of guanylate cyclase and generation of cyclic GMP, and yields formation of functionally active mitochondria. Thus, the combined action of NO at its two known intracellular receptors, cytochrome c oxidase and guanylate cyclase, appears to play a role in coupling energy generation with energy demand. This may explain why dysregulation of the NO signalling pathway is often associated with the pathogenesis of metabolic disorders.

Fuel oxidation during human walking

Human adults walk at a characteristic speed, but the mechanisms responsible for this ubiquitous and reproducible behavior remain unknown. In this study, preferred walking speed (PWS) was 4.7 +/- 0.1 km h -1 in 12 overnight-fasted adults, mean age 30.0 +/- 2.6 years. Indirect calorimetry was used to measure fuel oxidation during level treadmill walking from 3.2 to 7.2 km h -1 progressively increased at increments of 0.8 km h -1 and 10.0-min intervals. Corroborating many previous reports, the O2 cost of transport (mL O2 kg -1 km -1 ) was numerically lowest at 4.8 km h -1 , near PWS, but was not significantly different than 5.6 km h -1 . The impact of walking speed on the fuel selection of skeletal muscle was much more dramatic. At speeds less than or equal to PWS, muscle carbohydrate (CHO) oxidation rates were quite low, in the range that could be matched by gluconeogenesis. Above 4.8 km h -1 , CHO oxidation rate increased abruptly and tracked the perception of effort (RPE). Stepwise linear regression revealed that CHO oxidation explained 70% of the variance in RPE, and speed provided an additional 4%. In contrast, the other variables included in the analysis, fat oxidation rate, heart rate, and O2 cost of transport, contributed no additional explained variance in RPE. We conclude that PWS is just below a threshold speed, above which CHO oxidation abruptly increases. The central nervous system may be guided by the perception of effort in selecting a PWS that minimizes dependence on CHO oxidation. We further conclude that skeletal muscle metabolic control is an important factor to be taken into account by the central nervous system motor control of human locomotion.

Mitochondrial affinity for ADP is twofold lower in creatine kinase knock-out muscles. Possible role in rescuing cellular energy homeostasis

Adaptations of the kinetic properties of mitochondria in striated muscle lacking cytosolic (M) and/or mitochondrial (Mi) creatine kinase (CK) isoforms in comparison to wild-type (WT) were investigated in vitro. Intact mitochondria were isolated from heart and gastrocnemius muscle of WT and single- and double CK-knock-out mice strains (cytosolic (M-CK-/-), mitochondrial (Mi-CK-/-) and double knock-out (MiM-CK-/-), respectively). Maximal ADP-stimulated oxygen consumption flux (State3 Vmax; nmol O2 x mg mitochondrial protein(-1) x min(-1)) and ADP affinity (K50ADP; microM) were determined by respirometry. State 3 Vmax and of M-CK-/- and MiM-CK-/- gastrocnemius mitochondria were twofold higher than those of WT, but were unchanged for Mi-CK-/-. For mutant cardiac mitochondria, only the of mitochondria isolated from the MiM-CK-/- phenotype was different (i.e. twofold higher) than that of WT. The implications of these adaptations for striated muscle function were explored by constructing force-flow relations of skeletal muscle respiration. It was found that the identified shift in affinity towards higher ADP concentrations in MiM-CK-/- muscle genotypes may contribute to linear mitochondrial control of the reduced cytosolic ATP free energy potentials in these phenotypes.

CK flux or direct ATP transfer: versatility of energy transfer pathways evidenced by NMR in the perfused heart

How the myocardium is able to permanently coordinate its intracellular fluxes of ATP synthesis, transfer and utilization is difficult to investigate in the whole organ due to the cellular complexity. The adult myocardium represents a paradigm of an energetically compartmented cell since 50% of total CK activity is bound in the vicinity of other enzymes (myofibrillar sarcolemmal and sarcoplasmic reticulum ATPases as well as mitochondrial adenine nucleotide translocator, ANT). Such vicinity of enzymes is well known in vitro as well as in preparations of skinned fibers to influence the kinetic properties of these enzymes and thus the functioning of the subcellular organelles. Intracellular compartmentation has often been neglected in the NMR analysis of CK kinetics in the whole organ. It is indeed a methodological challenge to reveal subcellular kinetics in a working organ by a global approach such as NMR. To get insight in the energy transfer pathway in the perfused rat heart, we developed a combined analysis of several protocols of magnetization transfer associated with biochemical data and quantitatively evaluated which scheme of energetic exchange best describes the NMR data. This allows to show the kinetic compartmentation of subcellular CKs and to quantify their fluxes. Interestingly, we could show that the energy transfer pathway shifts from the phosphocreatine shuttle in the oxygenated perfused heart to a direct ATP diffusion from mitochondria to cytosol under moderate inhibition of ATP synthesis. Furthermore using NMR measured fluxes and the known kinetic properties of the enzymes, it is possible to model the system, estimate local ADP concentrations and propose hypothesis for the versatility of energy transfer pathway. In the normoxic heart, a 3-fold ADP gradient was found between mitochondrial intermembrane space, cytosol and ADP in the vicinity of ATPases. The shift from PCr to ATP transport observed when ATP synthesis decreases might result from a balance in the activity of two populations of ANT, either coupled or uncoupled to CK. We believe this NMR approach could be a valuable tool to reinvestigate the control of respiration by ADP in the whole heart reconciling the biochemical knowledge of mitochondrial obtained in vitro or in skinned fibers with data on the whole heart as well as to identify the implication of bioenergetics in the pathological heart.