Regulation of oxidative phosphorylation in intact mammalian heart in vivo

Kinetic Mathematical Modeling of Oxidative Phosphorylation in Cardiomyocyte Mitochondria

Oxidative phosphorylation (OXPHOS) is an oxygen-dependent process that consumes catabolized nutrients to produce adenosine triphosphate (ATP) to drive energy-dependent biological processes such as excitation-contraction coupling in cardiomyocytes. In addition to in vivo and in vitro experiments, in silico models are valuable for investigating the underlying mechanisms of OXPHOS and predicting its consequences in both physiological and pathological conditions. Here, we compare several prominent kinetic models of OXPHOS in cardiomyocytes. We examine how their mathematical expressions were derived, how their parameters were obtained, the conditions of their experimental counterparts, and the predictions they generated. We aim to explore the general landscape of energy production mechanisms in cardiomyocytes for future in silico models.

Time and charge/pH-dependent activation of K+ channel-mediated K+ influx and K+/H+ exchange in guinea pig heart isolated mitochondria; role in bioenergetic stability

Mitochondria play an important role not only in producing energy for the cell but also for regulating mitochondrial and cell function depending on the cell's needs and environment. Uptake of cations, anions, and substrates requires a stable, polarized transmembrane charge potential (ΔΨ_m). Chemiosmosis requires ion exchangers to remove Na⁺, K⁺, Ca²⁺, PO₄^3-, and other charged species that enter mitochondria. Knowledge of the kinetics of mitochondrial (m) cation channels and exchangers is important in understanding their roles in regulating mitochondrial chemiosmosis and bioenergetics. The influx/efflux of K⁺, the most abundant mitochondrial cation, alters mitochondrial volume and shape by bringing in anions and H₂O by osmosis. The effects of K⁺ uptake through ligand-specific mK⁺ channels stimulated/inhibited by agonists/antagonists on mitochondrial volume (swelling/contraction) are well known. However, a more important role for K⁺ influx is likely its effects on H⁺ cycling and bioenergetics facilitated by mitochondrial (m) K⁺/H⁺ exchange (mKHE), though the kinetics and consequences of K⁺ efflux by KHE are not well described. We hypothesized that a major role of K⁺ influx/efflux is stimulation of respiration via the influx of H⁺ by KHE. We proposed to modulate KHE activity by energizing guinea pig heart isolated mitochondria and by altering the mK⁺ cycle to capture changes in mitochondrial volume, pH_m, ΔΨ_m, and respiration that would reflect a role for H⁺ influx via KHE to regulate bioenergetics. To test this, mitochondria were suspended in a 150 mM K⁺ buffer at pH 6.9, or in a 140 mM Cs⁺ buffer at pH 7.6 or 6.9 with added 10 mM K⁺, minimal Ca²⁺ and free of Na⁺. O₂ content was measured by a Clark electrode, and pH_m, ΔΨ_m, and volume, were measured by fluorescence spectrophotometry and light-scattering. Adding pyruvic acid (PA) alone caused increases in volume and respiration and a rapid decrease in the transmembrane pH gradient (ΔpH_m = pH_in-pH_ext) at pH_ext 6.9> > 7.6, so that ΔΨ_m was charged and maintained. BK_Ca agonist NS1619 and antagonist paxilline modified these effects, and KHE inhibitor quinine and K⁺ ionophore valinomycin depolarized ΔΨ_m. We postulate that K⁺ efflux-induced H⁺ influx via KHE causes an inward H⁺ leak that stimulates respiration, but at buffer pH 6.9 also utilizes the energy of ΔpH_m, the smaller component of the overall proton motive force, ΔμH⁺. Thus ΔpH_m establishes and maintains the ΔΨ_m required for utilization of substrates, entry of all cations, and for oxidative phosphorylation. Thus, K⁺ influx/efflux appears to play a pivotal role in regulating energetics while maintaining mitochondrial ionic balance and volume homeostasis.

Integrative Methods for Studying Cardiac Energetics

The more recent studies of human pathologies have essentially revealed the complexity of the interactions involved at the different levels of integration in organ physiology. Integrated organ thus reveals functional properties not predictable by underlying molecular events. It is therefore obvious that current fine molecular analyses of pathologies should be fruitfully combined with integrative approaches of whole organ function. It follows that an important issue in the comprehension of the link between molecular events in pathologies and whole organ function/dysfunction is the development of new experimental strategies aimed at the study of the integrated organ physiology. Cardiovascular diseases are a good example as heart submitted to ischemic conditions has to cope both with a decreased supply of nutrients and oxygen, and the necessary increased activity required to sustain whole body-including the heart itself-oxygenation.By combining the principles of control analysis with noninvasive ³¹P NMR measurement of the energetic intermediates and simultaneous measurement of heart contractile activity, we developed MoCA (for Modular Control and regulation Analysis), an integrative approach designed to study in situ control and regulation of cardiac energetics during contraction in intact beating perfused isolated heart (Diolez et al., Am J Physiol Regul Integr Comp Physiol 293(1):R13-R19, 2007). Because it gives real access to integrated organ function, MoCA brings out a new type of information-the "elasticities," referring to integrated internal responses to metabolic changes-that may be a key to the understanding of the processes involved in pathologies. MoCA can potentially be used not only to detect the origin of the defects associated with the pathology, but also to provide the quantitative description of the routes by which these defects-or also drugs-modulate global heart function, therefore opening therapeutic perspectives. This review presents selected examples of the applications to isolated intact beating heart that evidence different modes of energetic regulation of cardiac contraction. We also discuss the clinical application by using noninvasive ³¹P cardiac energetics examination under clinical conditions for detection of heart pathologies.

Impaired Energy Production Contributes to Development of Failure in Taurine Deficient Heart

Taurine forms a conjugate in the mitochondria with a uridine residue in the wobble position of tRNALeu(UUR). The resulting product, 5-taurinomethyluridine tRNALeu(UUR), increases the interaction between the UUG codon and AAU anticodon of tRNALeu(UUR), thereby improving the decoding of the UUG codon. We have shown that the protein most affected by the taurine conjugation product is ND6, which is a subunit of complex I of the respiratory chain. Thus, taurine deficiency exhibits reduced respiratory chain function. Based on these findings, we proposed that the taurine deficient heart is energy deficient. To test this idea, hearts were perfused with buffer containing acetate and glucose as substrates. The utilization of both substrates, as well as the utilization of endogenous lipids, was significantly reduced in the taurine deficient heart. This led to a 25% decrease in ATP production, an effect primarily caused by diminished aerobic metabolism and respiratory function. In addition, inefficient oxidative phosphorylation causes a further decrease in ATP generation. The data support the idea that reductions in energy metabolism, including oxidative phosphorylation, ATP generation and high energy phosphate content, contribute to the severity of the cardiomyopathy. The findings are also consistent with the hypothesis that taurine deficiency and reduced myocardial energy content increases mortality of the taurine deficient, failing heart. The clinical implications of these findings are addressed.

Regulation of oxidative phosphorylation is different in electrically- and cortically-stimulated skeletal muscle

A computer model of the skeletal muscle bioenergetic system was used to study the regulation of oxidative phosphorylation (OXPHOS) in electrically-stimulated and cortically-stimulated skeletal muscle. Two types of the dependence of the intensity of each-step activation (ESA) of OXPHOS complexes on ATP usage activity were tested: power-type dependence and saturating-type dependence. The dependence of muscle oxygen consumption ([Formula: see text]), phosphocreatine (PCr), cytosolic ADP, ATP, inorganic phosphate (Pi), pH and τp (characteristic transition time) of the principal component of the muscle [Formula: see text] on-kinetics on the ATP usage activity was simulated for both types of the ESA intensity-ATP usage activity dependence. Computer simulations involving the power-type dependence predict system properties that agree well with experimental data for electrically-stimulated muscle. On the other hand, model predictions for the saturating-type dependence in the presence of the 'additional' ATP usage (postulated previously to underlie the slow component of the VO2 on-kinetics) reproduce well system properties encountered in human skeletal muscle during voluntary exercise. It is postulated that the difference between the regulation and kinetic properties of the system in electrically- and cortically-stimulated muscle is mostly due to the different muscle fibers recruitment pattern. In the former, all fiber types are recruited in parallel already at low power output (PO) values, while in the latter type I fibers (with higher ESA intensity) are stimulated at low PO values, while type II fibers (especially type II b and IIx fibers) with low ESA intensity are recruited predominantly at high PO values.

Modeling oxygen requirements in ischemic cardiomyocytes

Heart disease remains the leading cause of death globally. Although reperfusion following myocardial ischemia can prevent death by restoring nutrient flow, ischemia/reperfusion injury can cause significant heart damage. The mechanisms that drive ischemia/reperfusion injury are not well understood; currently, few methods can predict the state of the cardiac muscle cell and its metabolic conditions during ischemia. Here, we explored the energetic sustainability of cardiomyocytes, using a model for cellular metabolism to predict the levels of ATP following hypoxia. We modeled glycolytic metabolism with a system of coupled ordinary differential equations describing the individual metabolic reactions within the cardiomyocyte over time. Reduced oxygen levels and ATP consumption rates were simulated to characterize metabolite responses to ischemia. By tracking biochemical species within the cell, our model enables prediction of the cell's condition up to the moment of reperfusion. The simulations revealed a distinct transition between energetically sustainable and unsustainable ATP concentrations for various energetic demands. Our model illustrates how even low oxygen concentrations allow the cell to perform essential functions. We found that the oxygen level required for a sustainable level of ATP increases roughly linearly with the ATP consumption rate. An extracellular O₂ concentration of ∼0.007 mm could supply basic energy needs in non-beating cardiomyocytes, suggesting that increased collateral circulation may provide an important source of oxygen to sustain the cardiomyocyte during extended ischemia. Our model provides a time-dependent framework for studying various intervention strategies to change the outcome of reperfusion.

A simulation study on the constancy of cardiac energy metabolites during workload transition

KEY POINTS

The cardiac energy metabolites such as ATP, phosphocreatine, ADP and NADH are kept relatively constant during physiological cardiac workload transition. How this is accomplished is not yet clarified, though Ca²⁺ has been suggested to be one of the possible mechanisms. We constructed a detailed mathematical model of cardiac mitochondria based on experimental data and studied whether known Ca²⁺ -dependent regulation mechanisms play roles in the metabolite constancy. Model simulations revealed that the Ca²⁺ -dependent regulation mechanisms have important roles under the in vitro condition of isolated mitochondria where malate and glutamate were mitochondrial substrates, while they have only a minor role and the composition of substrates has marked influence on the metabolite constancy during workload transition under the simulated in vivo condition where many substrates exist. These results help us understand the regulation mechanisms of cardiac energy metabolism during physiological cardiac workload transition.

ABSTRACT

The cardiac energy metabolites such as ATP, phosphocreatine, ADP and NADH are kept relatively constant over a wide range of cardiac workload, though the mechanisms are not yet clarified. One possible regulator of mitochondrial metabolism is Ca²⁺ , because it activates several mitochondrial enzymes and transporters. Here we constructed a mathematical model of cardiac mitochondria, including oxidative phosphorylation, substrate metabolism and ion/substrate transporters, based on experimental data, and studied whether the Ca²⁺ -dependent activation mechanisms play roles in metabolite constancy. Under the in vitro condition of isolated mitochondria, where malate and glutamate were used as mitochondrial substrates, the model well reproduced the Ca²⁺ and inorganic phosphate (P_i ) dependences of oxygen consumption, NADH level and mitochondrial membrane potential. The Ca²⁺ -dependent activations of the aspartate/glutamate carrier and the F₁ F_o -ATPase, and the P_i -dependent activation of Complex III were key factors in reproducing the experimental data. When the mitochondrial model was implemented in a simple cardiac cell model, simulation of workload transition revealed that cytoplasmic Ca²⁺ concentration ([Ca²⁺ ]_cyt ) within the physiological range markedly increased NADH level. However, the addition of pyruvate or citrate attenuated the Ca²⁺ dependence of NADH during the workload transition. Under the simulated in vivo condition where malate, glutamate, pyruvate, citrate and 2-oxoglutarate were used as mitochondrial substrates, the energy metabolites were more stable during the workload transition and NADH level was almost insensitive to [Ca²⁺ ]_cyt . It was revealed that mitochondrial substrates have a significant influence on metabolite constancy during cardiac workload transition, and Ca²⁺ has only a minor role under physiological conditions.

Faster and stronger manifestation of mitochondrial diseases in skeletal muscle than in heart related to cytosolic inorganic phosphate (Pi) accumulation

A model of the cell bioenergetic system was used to compare the effect of oxidative phosphorylation (OXPHOS) deficiencies in a broad range of moderate ATP demand in skeletal muscle and heart. Computer simulations revealed that kinetic properties of the system are similar in both cases despite the much higher mitochondria content and "basic" OXPHOS activity in heart than in skeletal muscle, because of a much higher each-step activation (ESA) of OXPHOS in skeletal muscle than in heart. Large OXPHOS deficiencies lead in both tissues to a significant decrease in oxygen consumption (V̇o2) and phosphocreatine (PCr) and increase in cytosolic ADP, Pi, and H(+) The main difference between skeletal muscle and heart is a much higher cytosolic Pi concentration in healthy tissue and much higher cytosolic Pi accumulation (level) at low OXPHOS activities in the former, caused by a higher PCr level in healthy tissue (and higher total phosphate pool) and smaller Pi redistribution between cytosol and mitochondria at OXPHOS deficiency. This difference does not depend on ATP demand in a broad range. A much greater Pi increase and PCr decrease during rest-to-moderate work transition in skeletal muscle at OXPHOS deficiencies than at normal OXPHOS activity significantly slows down the V̇o2 on-kinetics. Because high cytosolic Pi concentrations cause fatigue in skeletal muscle and can compromise force generation in skeletal muscle and heart, this system property can contribute to the faster and stronger manifestation of mitochondrial diseases in skeletal muscle than in heart. Shortly, skeletal muscle with large OXPHOS deficiencies becomes fatigued already during low/moderate exercise.

Each-step activation of oxidative phosphorylation is necessary to explain muscle metabolic kinetic responses to exercise and recovery in humans

KEY POINTS

The basic control mechanisms of oxidative phosphorylation (OXPHOS) and glycolysis during work transitions in human skeletal muscle are still a matter of debate. We used simulations of skeletal muscle bioenergetics to identify key system features that contribute to this debate, by comparing kinetic model outputs with experimental human data, including phosphocreatine, pH, pulmonary oxygen uptake and fluxes of ATP production by OXPHOS (vOX), anaerobic glycolysis and creatine kinase in moderate and severe intensity exercise transitions. We found that each-step activation of particular OXPHOS complexes, NADH supply and glycolysis, and strong (third-order) glycolytic inhibition by protons was required to reproduce observed phosphocreatine, pH and vOX kinetics during exercise. A slow decay of each-step activation during recovery, which was slowed further following severe exercise, was necessary to reproduce the experimental findings. Well-tested computer models offer new insight in the control of the human skeletal muscle bioenergetic system during physical exercise.

ABSTRACT

To better understand muscle bioenergetic regulation, a previously-developed model of the skeletal muscle cell bioenergetic system was used to simulate the influence of: (1) each-step activation (ESA) of NADH supply (including glycolysis) and oxidative phosphorylation (OXPHOS) complexes and (2) glycolytic inhibition by protons on the kinetics of ATP synthesis from OXPHOS, anaerobic glycolysis and creatine kinase. Simulations were fitted to previously published experimental data of ATP production fluxes and metabolite concentrations during moderate and severe intensity exercise transitions in bilateral knee extension in humans. Overall, the computer simulations agreed well with experimental results. Specifically, a large (>5-fold) direct activation of all OXPHOS complexes was required to simulate measured phosphocreatine and OXPHOS responses to both moderate and severe intensity exercise. In addition, slow decay of ESA was required to fit phosphocreatine recovery kinetics, and the time constant of ESA decay was slower following severe (180 s) than moderate (90 s) exercise. Additionally, a strong inhibition of (anaerobic) glycolysis by protons (glycolytic rate inversely proportional to the cube of proton concentration) provided the best fit to the experimental pH kinetics, and may contribute to the progressive increase in oxidative ATP supply during acidifying contractions. During severe-intensity exercise, an 'additional' ATP usage (a 27% increase at 8 min, above the initial ATP supply) was necessary to explain the observed V̇O2 slow component. Thus, parallel activation of ATP usage and ATP supply (ESA), and a strong inhibition of ATP supply by anaerobic glycolysis, were necessary to simulate the kinetics of muscle bioenergetics observed in humans.

Coronary and muscle blood flow during physical exercise in humans; heterogenic alliance

In this review, we present the relation between power generation capabilities and pulmonary oxygen uptake during incremental cycling exercise in humans and the effect of exercise intensity on the oxygen cost of work. We also discuss the importance of oxygen delivery to the working muscles as a factor determining maximal oxygen uptake in humans. Subsequently, we outline the importance of coronary blood flow, myocardial oxygen uptake and myocardial metabolic stability for exercise tolerance. Finally, we describe mechanisms of endothelium-dependent regulation of coronary and skeletal muscle blood flow, dysregulation of which may impair exercise capacity and increase the cardiovascular risk of exercise.

Integrative methods for studying cardiac energetics

The more recent studies of human pathologies have essentially revealed the complexity of the interactions involved at the different levels of integration in organ physiology. Integrated organ thus reveals functional properties not predictable by underlying molecular events. It is therefore obvious that current fine molecular analyses of pathologies should be fruitfully combined with integrative approaches of whole organ function. It follows an important issue in the comprehension of the link between molecular events in pathologies, and whole organ function/dysfunction is the development of new experimental strategies aimed at the study of the integrated organ physiology. Cardiovascular diseases are a good example as heart submitted to ischemic conditions has to cope both with a decreased supply of nutrients and oxygen, and the necessary increased activity required to sustain whole body-including the heart itself-oxygenation.By combining the principles of control analysis with noninvasive (31)P NMR measurement of the energetic intermediates and simultaneous measurement of heart contractile activity, we developed MoCA (for Modular Control and Regulation Analysis), an integrative approach designed to study in situ control and regulation of cardiac energetics during contraction in intact beating perfused isolated heart (Diolez et al., Am J Physiol Regul Integr Comp Physiol 293(1):R13-R19, 2007). Because it gives real access to integrated organ function, MoCA brings out a new type of information-the "elasticities," referring to internal responses to metabolic changes-that may be a key to the understanding of the processes involved in pathologies. MoCA can potentially be used not only to detect the origin of the defects associated with the pathology, but also to provide the quantitative description of the routes by which these defects-or also drugs-modulate global heart function, therefore opening therapeutic perspectives. This review presents selected examples of the applications to isolated intact beating heart and a wider application to cardiac energetics under clinical conditions with the direct study of heart pathologies.

Regulation of oxidative phosphorylation during work transitions results from its kinetic properties

The regulation of oxidative phosphorylation (OXPHOS) during work transitions in skeletal muscle and heart is still not well understood. Different computer models of this process have been developed that are characterized by various kinetic properties. In the present research-polemic theoretical study it is argued that models belonging to one group (Model A), which predict that among OXPHOS complexes complex III keeps almost all of the metabolic control over oxygen consumption (Vo2) and involve a strong complex III activation by inorganic phosphate (Pi), lead to the conclusion that an increase in Pi is the main mechanism responsible for OXPHOS activation (feedback-activation mechanism). Models belonging to another group (Model B), which were developed to take into account an approximately uniform distribution of metabolic control over Vo2 among particular OXPHOS complexes (complex I, complex III, complex IV, ATP synthase, ATP/ADP carrier, phosphate carrier) encountered in experimental studies in isolated mitochondria, predict that all OXPHOS complexes are directly activated in parallel with ATP usage and NADH supply by some external cytosolic factor/mechanism during rest-to-work or low-to-high work transitions in skeletal muscle and heart ("each-step-activation" mechanism). Model B demonstrates that different intensities of each-step activation can account for the very different (slopes of) phenomenological Vo2-ADP relationships observed in various skeletal muscles and heart. Thus they are able to explain the differences in the regulation of OXPHOS during work transitions between skeletal muscle (where moderate changes in ADP take place) and intact heart in vivo (where ADP is essentially constant).

Systemic modelling of human bioenergetics and blood circulation

This work reviews the main aspects of human bioenergetics and the dynamics of the cardiovascular system, with emphasis on modelling their physiological characteristics. The methods used to study human bioenergetics and circulation dynamics, including the use of mathematical models, are summarised. The main characteristics of human bioenergetics, including mitochondrial metabolism and global energy balance, are first described, and the systemic aspects of blood circulation and related physiological issues are introduced. The authors also discuss the present status of studies of human bioenergetics and blood circulation. Then, the limitations of the existing studies are described in an effort to identify directions for future research towards integrated and comprehensive modelling. This review emphasises that a multi-scale and multi-physical approach to bioenergetics and blood circulation that considers multiple scales and physiological factors are necessary for the appropriate clinical application of computational models.

Non-invasive integrative analysis of contraction energetics in intact beating heart

The comprehensive study of human pathologies has revealed the complexity of the interactions involved in cardiovascular physiology. The recent validation of system's biology approaches - like our Modular Control and Regulation Analysis (MoCA) - motivates the current interest for new integrative and non-invasive analyses that could be used for medical study of human heart contraction energetics. By considering heart energetics as a supply-demand system, MoCA gives access to integrated organ function and brings out a new type of information, the "elasticities", which describe in situ the regulation of both energy demand and supply by cellular energetic status. These regulations determine the internal control of contraction energetics and may therefore be a key to the understanding of the links between molecular events in pathologies and whole organ function/dysfunction. A wider application to the effects of cardiac drugs in conjunction with the direct study of heart pathologies may be considered in the near future. MoCA can potentially be used not only to detect the origin of the defects associated with the pathology (elasticity analyses), but also to provide a quantitative description of how these defects influence global heart function (regulation analysis) and therefore open new therapeutic perspectives. Several key examples of current applications to intact isolated beating heart are presented in this paper. The future application to human pathologies will require the use of non-invasive NMR techniques for the simultaneous measurement of energy status ((31)P NMR) and heart contractile activity (3D MRI). This article is part of a Directed Issue entitled: Bioenergetic dysfunction, adaptation and therapy.

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.

In silico studies on the sensitivity of myocardial PCr/ATP to changes in mitochondrial enzyme activity and oxygen concentration

The ratio of myocardial phosphocreatine (PCr)/ATP reflects the balance of energy consumption and energy supply in the heart. It is reduced in a range of important physiological conditions including during and after acute hypoxia, after a prolonged visit to high-altitude, and in those suffering from both type 2 diabetes mellitus and various forms of heart failure. Yet despite its significance, the factors underlying the reduced PCr/ATP ratio seen in heart failure remain poorly understood. Given that oxidative phosphorylation is the only viable steady-state provider of ATP in the heart, the argument has been put forward that the observed reduction in myocardial PCr/ATP in all these conditions can be accounted for by some form of mitochondrial insufficiency. Thus we used a computer model of oxidative phosphorylation, coupled with creatine kinase, to study the effects of hypoxia and mitochondrial dysfunction on myocardial PCr/ATP. In physiological normoxia, all oxidative phosphorylation complexes, NADH supply and proton leak exerted comparable (of the same order of magnitude) control over PCr/ATP, as defined within Metabolic Control Analysis (MCA). Under hypoxia, the control increased considerably for all components of the system, especially for cytochrome oxidase and mitochondrial proton leak. Hypoxia alone, without any changes in other factors, exerted a pronounced effect on PCr/ATP. Our simulations support three important ideas: First, that mitochondrial abnormalities can contribute considerably to a blunted PCr/ATP; second, that hypoxia and mitochondrial dysfunction can interact in important ways to determine the energy status of the failing heart; and third, that hypoxia alone can account for significant decreases in cardiac PCr/ATP.

Modeling of mitochondria bioenergetics using a composable chemiosmotic energy transduction rate law: theory and experimental validation

Mitochondrial bioenergetic processes are central to the production of cellular energy, and a decrease in the expression or activity of enzyme complexes responsible for these processes can result in energetic deficit that correlates with many metabolic diseases and aging. Unfortunately, existing computational models of mitochondrial bioenergetics either lack relevant kinetic descriptions of the enzyme complexes, or incorporate mechanisms too specific to a particular mitochondrial system and are thus incapable of capturing the heterogeneity associated with these complexes across different systems and system states. Here we introduce a new composable rate equation, the chemiosmotic rate law, that expresses the flux of a prototypical energy transduction complex as a function of: the saturation kinetics of the electron donor and acceptor substrates; the redox transfer potential between the complex and the substrates; and the steady-state thermodynamic force-to-flux relationship of the overall electro-chemical reaction. Modeling of bioenergetics with this rate law has several advantages: (1) it minimizes the use of arbitrary free parameters while featuring biochemically relevant parameters that can be obtained through progress curves of common enzyme kinetics protocols; (2) it is modular and can adapt to various enzyme complex arrangements for both in vivo and in vitro systems via transformation of its rate and equilibrium constants; (3) it provides a clear association between the sensitivity of the parameters of the individual complexes and the sensitivity of the system's steady-state. To validate our approach, we conduct in vitro measurements of ETC complex I, III, and IV activities using rat heart homogenates, and construct an estimation procedure for the parameter values directly from these measurements. In addition, we show the theoretical connections of our approach to the existing models, and compare the predictive accuracy of the rate law with our experimentally fitted parameters to those of existing models. Finally, we present a complete perturbation study of these parameters to reveal how they can significantly and differentially influence global flux and operational thresholds, suggesting that this modeling approach could help enable the comparative analysis of mitochondria from different systems and pathological states. The procedures and results are available in Mathematica notebooks at http://www.igb.uci.edu/tools/sb/mitochondria-modeling.html.

Computer-aided analysis of biochemical mechanisms that increase metabolite and proton stability in the heart during severe hypoxia and generate post-ischemic PCr overshoot

During severe hypoxia in the heart, impaired supply of ATP by oxidative phosphorylation could lead to a great drop in ATP turnover and heart work. Anaerobic glycolysis enables unchanged ATP turnover to be maintained, but leads to huge changes in metabolite (PCr, ATP, ADP, P (i)) concentrations and to cytosol acidification. A computer model of heart energetics developed previously is used to analyze semi-quantitatively the effect of different processes/mechanisms that can partly counteract these effects. Down-regulation of ATP usage compromises cardiac output, but reduces changes in cytosolic pH and metabolite concentrations. AMP decomposition delays cytosol acidification but reduces metabolite homeostasis (concentration stability). An increase in the parallel activation of oxidative phosphorylation (OXPHOS) (a hypothetical mechanism involving direct activation of all OXPHOS complexes by a cytosolic factor, postulated to take place also during work increase) reduces cytosol acidification and elevates metabolite homeostasis. All these mechanisms can generate the post-ischemic PCr overshoot.

Mitochondrial approaches to protect against cardiac ischemia and reperfusion injury

The mitochondrion is a vital component in cellular energy metabolism and intracellular signaling processes. Mitochondria are involved in a myriad of complex signaling cascades regulating cell death vs. survival. Importantly, mitochondrial dysfunction and the resulting oxidative and nitrosative stress are central in the pathogenesis of numerous human maladies including cardiovascular diseases, neurodegenerative diseases, diabetes, and retinal diseases, many of which are related. This review will examine the emerging understanding of the role of mitochondria in the etiology and progression of cardiovascular diseases and will explore potential therapeutic benefits of targeting the organelle in attenuating the disease process. Indeed, recent advances in mitochondrial biology have led to selective targeting of drugs designed to modulate or manipulate mitochondrial function, to the use of light therapy directed to the mitochondrial function, and to modification of the mitochondrial genome for potential therapeutic benefit. The approach to rationally treat mitochondrial dysfunction could lead to more effective interventions in cardiovascular diseases that to date have remained elusive. The central premise of this review is that if mitochondrial abnormalities contribute to the etiology of cardiovascular diseases (e.g., ischemic heart disease), alleviating the mitochondrial dysfunction will contribute to mitigating the severity or progression of the disease. To this end, this review will provide an overview of our current understanding of mitochondria function in cardiovascular diseases as well as the potential role for targeting mitochondria with potential drugs or other interventions that lead to protection against cell injury.

System analysis of the effect of various drugs on cardiac contraction energetics

We used MoCA (Modular Control and Regulation Analysis) to demonstrate in intact beating rat heart that physiological activation of contraction by adrenaline involves the almost perfect parallel activation of both mitochondria and myofibrils by intracellular Ca(2+). This explains the perfect homoeostasis of the energetic intermediate PCr (phosphocreatine) in heart. When using drugs specifically stimulating either supply or demand activities, MoCA helped reveal the very specific mode of regulation of heart contraction energetics. Only activation of myofibrils activity (demand), either by increasing intracellular Ca(2+) concentration or myofibrils sensitivity to Ca(2+), triggers activation of contractile activity. In contrast, the activation of mitochondrial activity (supply) has strictly no effect on contraction, either directly or through PCr changes (intermediate).

Absence of mitochondrial activation during levosimendan inotropic action in perfused paced guinea pig hearts as demonstrated by modular control analysis

Levosimendan is a calcium sensitizer developed for the treatment of heart failure. It increases contractile force by enhancing the sensitivity of myofilaments to calcium. Besides this sensitizing effect, the drug has also been reported to show some inhibitory action on phosphodiesterase 3 (PDE3). The inotropic effects of levosimendan have been studied on guinea pig paced perfused hearts by using modular control analysis (MoCA) (Diolez P, Deschodt-Arsac V, Raffard G, Simon C, Santos PD, Thiaudiere E, Arsac L, Franconi JM. Am J Physiol Regul Integr Comp Physiol 293: R13-R19, 2007.), an integrative approach of heart energetics using noninvasive (31)P NMR. The aim was to evaluate quantitatively the respective effects of this drug on energy supply and demand modules. Under our experimental conditions, 0.7 muM levosimendan induced a 45% increase in paced heart output associated with a 7% decrease in phosphocreatine and a negligible increase in oxygen consumption. Because MoCA allows in situ study of the internal regulations in intact beating heart energetics, it was applied to describe quantitatively by which routes levosimendan exerts its inotropic action. MoCA demonstrated the absence of any significant effect of the drug on the supply module, which is responsible for the lower increase in oxygen consumption, compared with epinephrine, which increases the ratio between myocardial oxygen consumption and cardiac contraction. This result evidences that, under our conditions, a possible effect of levosimendan on PDE3 activity and/or intracellular calcium remains very low on mitochondrial activity and insignificant on integrated cardiac energetics. Thus, levosimendan inotropic effect on guinea pig heart depends almost entirely on the calcium-sensitizing properties leading to myofilament activation and the concomitant activation of energy supply by the decrease in PCr, therefore improving energetic efficiency of contraction.

Imaging and modeling of myocardial metabolism

Current imaging methods have focused on evaluation of myocardial anatomy and function. However, since myocardial metabolism and function are interrelated, metabolic myocardial imaging techniques, such as positron emission tomography, single photon emission tomography, and magnetic resonance spectroscopy present novel opportunities for probing myocardial pathology and developing new therapeutic approaches. Potential clinical applications of metabolic imaging include hypertensive and ischemic heart disease, heart failure, cardiac transplantation, as well as cardiomyopathies. Furthermore, response to therapeutic intervention can be monitored using metabolic imaging. Analysis of metabolic data in the past has been limited, focusing primarily on isolated metabolites. Models of myocardial metabolism, however, such as the oxygen transport and cellular energetics model and constraint-based metabolic network modeling, offer opportunities for evaluation interactions between greater numbers of metabolites in the heart. In this review, the roles of metabolic myocardial imaging and analysis of metabolic data using modeling methods for expanding our understanding of cardiac pathology are discussed.

Evaluation of cardiac oxygen consumption under hypoxia with tissue model integrating microcirculation model and cell model

Analyzing the microscopic energy balance of cardiac tissue is very important for understanding heart diseases. However, such analysis is difficult with animal experiments. Therefore, the accurate simulation model is expected to be an important tool for such research. We propose a cardiac tissue model which can reproduce accurate distribution of oxygen consumption under hypoxia. The model includes blood tissue exchange model of capillary and oxygen consumption model of cells. The capillary model is based on the model proposed by Dash et al. 2006, and the cell model is based on the model proposed by Kuzumoto et al. 2007. By analyzing the oxygen consumption of the proposed model, the relation between the oxygen consumption and the arterial oxygen concentration was found to be largely different from that of single cell model. This implies that the animal experimental data should be carefully used for constructing a biological simulation model, depending on whether the experiment is performed within a cell or a tissue.

Effect of pyruvate, lactate and insulin on ATP supply and demand in unpaced perfused rat heart

Mitochondrial respiration/oxidative phosphorylation is the main source of energy, in the form of ATP, in the heart under physiological conditions. Different respiratory substrates were used in various experiments during heart perfusion: glucose, pyruvate, lactate, glucose+pyruvate, glucose+lactate, glucose+insulin etc. Also under physiological conditions, the concentration of respiratory substrates/hormones in blood can vary significantly. In the present study, we tested the effect of pyruvate, lactate and insulin (all in the presence of glucose) and glucose (in the presence of pyruvate) on the ATP-producing and -consuming blocks in perfused rat heart, in a system where HR (heart rate) was allowed to vary (no pacing). Changes in RPP (rate-pressure product) and PCr (phosphocreatine) concentration were measured. PAA (Proportional Activation Approach) was used to visualize and quantitatively analyse the data. It was demonstrated that addition of glucose (in the presence of pyruvate) exerted essentially no effect on the system. Insulin (in the presence of glucose) activated only the ATP producer. The most interesting finding is that, in our system, pyruvate and lactate (added in the presence or instead of glucose) activated ATP producer, but significantly inhibited ATP consumer (their effect was quantitatively identical).

Mitochondrial reactive oxygen species production in excitable cells: modulators of mitochondrial and cell function

The mitochondrion is a major source of reactive oxygen species (ROS). Superoxide (O(2)(*-)) is generated under specific bioenergetic conditions at several sites within the electron-transport system; most is converted to H(2)O(2) inside and outside the mitochondrial matrix by superoxide dismutases. H(2)O(2) is a major chemical messenger that, in low amounts and with its products, physiologically modulates cell function. The redox state and ROS scavengers largely control the emission (generation scavenging) of O(2)(*-). Cell ischemia, hypoxia, or toxins can result in excess O(2)(*-) production when the redox state is altered and the ROS scavenger systems are overwhelmed. Too much H(2)O(2) can combine with Fe(2+) complexes to form reactive ferryl species (e.g., Fe(IV) = O(*)). In the presence of nitric oxide (NO(*)), O(2)(*-) forms the reactant peroxynitrite (ONOO(-)), and ONOOH-induced nitrosylation of proteins, DNA, and lipids can modify their structure and function. An initial increase in ROS can cause an even greater increase in ROS and allow excess mitochondrial Ca(2+) entry, both of which are factors that induce cell apoptosis and necrosis. Approaches to reduce excess O(2)(*-) emission include selectively boosting the antioxidant capacity, uncoupling of oxidative phosphorylation to reduce generation of O(2)(*-) by inducing proton leak, and reversibly inhibiting electron transport. Mitochondrial cation channels and exchangers function to maintain matrix homeostasis and likely play a role in modulating mitochondrial function, in part by regulating O(2)(*-) generation. Cell-signaling pathways induced physiologically by ROS include effects on thiol groups and disulfide linkages to modify posttranslationally protein structure to activate/inactivate specific kinase/phosphatase pathways. Hypoxia-inducible factors that stimulate a cascade of gene transcription may be mediated physiologically by ROS. Our knowledge of the role played by ROS and their scavenging systems in modulation of cell function and cell death has grown exponentially over the past few years, but we are still limited in how to apply this knowledge to develop its full therapeutic potential.

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.

Physiological heart activation by adrenaline involves parallel activation of ATP usage and supply

During low-to-high work transition in adult mammalian heart in vivo the concentrations of free ADP, ATP, PCr (phosphocreatine), P(i) and NADH are essentially constant, in striking contrast with skeletal muscle. The direct activation by calcium ions of ATP usage and feedback activation of ATP production by ADP (and P(i)) alone cannot explain this perfect homoeostasis. A comparison of the response to adrenaline (increase in rate-pressure product and [PCr]) of the intact beating perfused rat heart with the elasticities of the PCr producer and consumer to PCr concentration demonstrated that both the ATP/PCr-producing block and ATP/PCr-consuming block are directly activated to a similar extent during physiological heart activation. Our finding constitutes a direct evidence for the parallel-activation mechanism of the regulation of oxidative phosphorylation in heart postulated previously in a theoretical way.

Adenine nucleotide-creatine-phosphate module in myocardial metabolic system explains fast phase of dynamic regulation of oxidative phosphorylation

Computational models of a large metabolic system can be assembled from modules that represent a biological function emerging from interaction of a small subset of molecules. A "skeleton model" is tested here for a module that regulates the first phase of dynamic adaptation of oxidative phosphorylation (OxPhos) to demand in heart muscle cells. The model contains only diffusion, mitochondrial outer membrane (MOM) permeation, and two isoforms of creatine kinase (CK), in cytosol and mitochondrial intermembrane space (IMS), respectively. The communication with two neighboring modules occurs via stimulation of mitochondrial ATP production by ADP and P(i) from the IMS and via time-varying cytosolic ATP hydrolysis during contraction. Assuming normal cytosolic diffusion and high MOM permeability for ADP, the response time of OxPhos (t(mito); generalized time constant) to steps in cardiac pacing rate is predicted to be 2.4 s. In contrast, with low MOM permeability, t(mito) is predicted to be 15 s. An optimized MOM permeability of 21 mum/s gives t(mito) = 3.7 s, in agreement with experiments on rabbit heart with blocked glycolytic ATP synthesis. The model correctly predicts a lower t(mito) if CK activity is reduced by 98%. Among others, the following predictions result from the model analysis: 1) CK activity buffers large ADP oscillations; 2) ATP production is pulsatile in beating heart, although it adapts slowly to demand with "time constant" approximately 14 heartbeats; 3) if the muscle isoform of CK is overexpressed, OxPhos reacts slower to changing workload; and 4) if mitochondrial CK is overexpressed, OxPhos reacts faster.

Regulation of oxidative phosphorylation through parallel activation

When the mechanical work intensity in muscle increases, the elevated ATP consumption rate must be matched by the rate of ATP production by oxidative phosphorylation in order to avoid a quick exhaustion of ATP. The traditional mechanism of the regulation of oxidative phosphorylation, namely the negative feedback involving [ADP] and [Pi] as regulatory signals, is not sufficient to account for various kinetic properties of the system in intact skeletal muscle and heart in vivo. Theoretical studies conducted using a dynamic computer model of oxidative phosphorylation developed previously strongly suggest the so-called each-step-activation (or parallel activation) mechanism, due to which all oxidative phosphorylation complexes are directly activated by some cytosolic factor/mechanism related to muscle contraction in parallel with the activation of ATP usage and substrate dehydrogenation by calcium ions. The present polemic article reviews and discusses the growing evidence supporting this mechanism and compares it with alternative mechanisms proposed in the literature. It is concluded that only the each-step-activation mechanism is able to explain the rich set of various experimental results used as a reference for estimating the validity and applicability of particular mechanisms.

Parallel activation of mitochondrial oxidative metabolism with increased cardiac energy expenditure is not dependent on fatty acid oxidation in pigs

Steady state concentrations of ATP and ADP in vivo are similar at low and high cardiac workloads; however, the mechanisms that regulate the activation of substrate metabolism and oxidative phosphorylation that supports this stability are poorly understood. We tested the hypotheses that (1) there is parallel activation of mitochondrial and cytosolic dehydrogenases in the transition from low to high workload, which increases NADH/NAD+ ratio in both compartments, and (2) this response does not require an increase in fatty acid oxidation (FAO). Anaesthetized pigs were subjected to either sham treatment, or an abrupt increase in cardiac workload for 5 min with dobutamine infusion and aortic constriction. Myocardial oxygen consumption and FAO were increased 3- and 2-fold, respectively, but ATP and ADP concentrations did not change. NADH-generating pathways were rapidly activated in both the cytosol and mitochondria, as seen in a 40% depletion in glycogen stores, a 3.6-fold activation of pyruvate dehydrogenase, and a 50% increase in tissue NADH/NAD+. Simulations from a multicompartmental computational model of cardiac energy metabolism predicted that parallel activation of glycolysis and mitochondrial metabolism results in an increase in the NADH/NAD+ ratio in both cytosol and mitochondria. FAO was blocked by 75% in a third group of pigs, and a similar increase in and the NAHD/NAD+ ratio was observed. In conclusion, in the transition to a high cardiac workload there is rapid parallel activation of substrate oxidation that results in an increase in the NADH/NAD+ ratio.

Role of Cellular Compartmentation in the Metabolic Response to Stress: Mechanistic Insights from Computational Models

The mechanisms controlling ATP generation in the transition from normal resting conditions to either high work states or ischemia are poorly understood. ATP generation depends upon compartmentation between the mitochondria and cytosol of metabolic pathways and key energy transfer species that cannot be easily assessed experimentally. We developed a multicompartment mathematical model of cardiac metabolism to simulate the metabolic responses to ischemia and increased workload. The model is based on mass balances, transport, and metabolic processes in cardiac tissue, and has three distinct compartments (blood, cytosol, and mitochondria). In addition to distinguishing between cytosol and mitochondria, the model includes a cytosolic subcompartment for glycolytic metabolic channeling. The model simulations predict the rapid activation of glycogenolysis and lactate production at the onset of ischemia, and support the concept of localization of glycolysis to a cytosolic subcompartment. In addition, simulations show that mitochondrial NADH/NAD(+) is primarily determined by oxygen consumption during ischemia, while cytosolic NADH/NAD(+) and lactate production are largely a function of glycolytic flux during the initial phase, and is controlled by mitochondrial NADH/NAD(+) and the malate-aspartate shuttle during the steady state. Finally, the model predicts that metabolic activation with an abrupt increase in workload requires parallel activation of ATP hydrolysis, glycolysis, mitochondrial dehydrogenases, the electron transport chain, and ADP phosphorylation. Taken together, these studies demonstrate the importance of metabolic compartmentation in the regulation of cardiac energetics in response to acute stress, and they highlight the usefulness of computational models in this line of investigation.

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.

Biochemical background of the VO2 on-kinetics in skeletal muscles

This review discusses the present knowledge on the oxygen uptake kinetics at the onset of exercise in skeletal muscle and the contribution of a previously developed computer model of oxidative phosphorylation in intact skeletal muscle to the understanding of the factors determining this kinetics on the biochemical level. It has been demonstrated recently that an increase in the total creatine pool [PCr + Cr] and in glycolytic ATP supply lengthen the half-transition time of the VO2 on-kinetics, while an increase in mitochondria content, in parallel activation of ATP supply and ATP usage, in muscle oxygen concentration, in proton leak, in resting energy demand, in resting cytosolic pH, and in initial alkalization diminish this parameter. It has also been shown that the half-transition time is near-linearly proportional to the absolute difference between the phosphocreatine concentration during work and at rest (deltaPCr). The present review discusses whether the V/O2 on-kinetics on the muscle level is strictly or only approximately exponential. Finally, it is postulated that a short transition time of the VO2 on-kinetics in itself does not need be profitable for the skeletal muscle functioning during exercise, but usually a short transition time is correlated with factors that improve exercise capacity. The transition time is a phenomenological parameter resulting from the biochemical properties of the system and not a physical factor that can cause anything in the system.

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.

Modular regulation analysis of heart contraction: application to in situ demonstration of a direct mitochondrial activation by calcium in beating heart

Heart contraction is characterized by the absence of changes in energetic intermediates in response to a large increase of activity. Until now no experimental approach could address this question concerning the intact beating heart. Ca(2+) plays a crucial role in the excitation-contraction coupling, and in vitro studies have evidenced that Ca(2+) may also directly activate mitochondrial oxidative phosphorylation. We applied our new in situ modular control and regulation analysis on isolated beating rat heart perfused under two different calcium concentrations with pyruvate or glucose as the substrate. Modular control analysis demonstrated experimentally that, although control by energy production was slightly higher under glucose conditions compared with pyruvate, most of the control of heart contraction resides in energy utilization. This behavior is the direct consequence of the high sensitivity (elasticity) of the energy producer processes to ATP utilization. Interestingly, the increase in heart metabolic rate by Ca(2+) did not significantly change the pattern of control distribution. The regulation analysis performed under the two calcium conditions demonstrated a balanced activation of myofibrils ATPases, and mitochondrial ATP synthesis in response to Ca(2+) increase. This first study demonstrates in situ the hypothesis that the energetic adequation in heart contraction is mediated by a parallel activation of both processes of energy production and utilization by Ca(2+). The results presented here show that modular control and regulation analyses allow in situ study of internal regulations in intact beating heart energetics and function and may now be applied to heart dysfunctions and therapeutic effects.

Oxygen consumption and metabolite concentrations during transitions between different work intensities in heart

Steady-state metabolite (ADP, ATP, P(i), PCr, and NADH) concentrations usually differ little between different workloads with significantly different oxygen consumption rates in the heart. However, during transitions between steady states, metabolite concentrations may in some cases change transiently, exhibiting a significant overshoot or undershoot, whereas in other cases they approach near-exponentially new steady-state values. Oxygen consumption rate usually reaches the new steady-state value very quickly (within a few seconds). The present in silico studies, performed using a previously developed computer model of oxidative phosphorylation in the heart, demonstrate that such a behavior of the oxidative phosphorylation system can be reproduced only under the assumption that ATP usage, substrate dehydrogenation, and (particular steps of) oxidative phosphorylation are directly activated to a similar extend by some cytosolic factor/mechanism during transition from low work to high work (the so-called parallel-activation mechanism). Computer simulations show that some differences observed between different experimental systems can be explained by a slightly different balance of the activation of particular components of the system and/or by a delay in time of the activation/inactivation of substrate dehydrogenation and oxidative phosphorylation during low-to-high and high-to-low work transitions. Thus the presented theoretical approach offers a general idea that is able to unify, at least semiquantitatively, different experimental data available in the literature.

Regulation of myocardial substrate metabolism during increased energy expenditure: insights from computational studies

In response to exercise, the heart increases its metabolic rate severalfold while maintaining energy species (e.g., ATP, ADP, and Pi) concentrations constant; however, the mechanisms that regulate this response are unclear. Limited experimental studies show that the classic regulatory species NADH and NAD+ are also maintained nearly constant with increased cardiac power generation, but current measurements lump the cytosol and mitochondria and do not provide dynamic information during the early phase of the transition from low to high work states. In the present study, we modified our previously published computational model of cardiac metabolism by incorporating parallel activation of ATP hydrolysis, glycolysis, mitochondrial dehydrogenases, the electron transport chain, and oxidative phosphorylation, and simulated the metabolic responses of the heart to an abrupt increase in energy expenditure. Model simulations showed that myocardial oxygen consumption, pyruvate oxidation, fatty acids oxidation, and ATP generation were all increased with increased energy expenditure, whereas ATP and ADP remained constant. Both cytosolic and mitochondrial NADH/NAD+ increased during the first minutes (by 40% and 20%, respectively) and returned to the resting values by 10-15 min. Furthermore, model simulations showed that an altered substrate selection, induced by either elevated arterial lactate or diabetic conditions, affected cytosolic NADH/NAD+ but had minimal effects on the mitochondrial NADH/NAD+, myocardial oxygen consumption, or ATP production. In conclusion, these results support the concept of parallel activation of metabolic processes generating reducing equivalents during an abrupt increase in cardiac energy expenditure and suggest there is a transient increase in the mitochondrial NADH/NAD+ ratio that is independent of substrate supply.

Calcium-mediated coupling between mitochondrial substrate dehydrogenation and cardiac workload in single guinea-pig ventricular myocytes

We measured mitochondrial NADH autofluorescence or Ca(2+) using Rhod-2, simultaneously with cell shortening in isolated guinea-pig ventricular myocytes. When both frequency and amplitude of twitch shortening (work intensity) were increased by raising stimulus frequency in incremental steps from 0.1 to 3.3 Hz, the steady level of NADH signal increased in a frequency-dependent manner. Mitochondrial Ca(2+) also increased with increasing work intensity. Applying Ru360, an inhibitor of mitochondrial Ca(2+) uniporter, largely attenuated the response of both NADH fluorescence and mitochondrial Ca(2+). The increase in mitochondrial Ca(2+) was slow with t(1/2)=~12 s and no obvious cyclic changes were observed in the NADH signal. When a step change from 0.1 to 3.3 Hz stimulation was applied, the NADH signal first decreased to 83% and then increased to 155% of the control level. Upon returning to 0.1 Hz, the NADH signal showed an overshoot before declining to the control level. The biphasic onset time course was well explained by the delayed Ca(2+) activation of the substrate dehydrogenation superimposed on the feedback control of the ATP synthesis, while the offset time course with a delayed deactivation of dehydrogenation. A computer simulation using an oxidative phosphorylation linked to the cardiac excitation contraction model well reconstructed the response of NADH. This model simulation predicts that the activation of substrate dehydrogenation provides ~23% of driving force of the ATP synthesis to meet the increased workload induced by the jump of stimulus from 0.1 to 3.3 Hz, and remaining ~77% is supplied by the feedback control.

Regulation of lactate production at the onset of ischaemia is independent of mitochondrial NADH/NAD+: insights from in silico studies

Ischaemia decreases mitochondrial NADH oxidation, activates glycolysis, increases the NADH/NAD+ ratio, and causes lactate production. The mechanisms that regulate anaerobic glycolysis and the NADH/NAD+ ratio during ischaemia are unclear. Although continuous measurements of metabolic fluxes and NADH/NAD+ in cytosol and mitochondria are not possible in vivo with current experimental techniques, computational models can be used to predict these variables by simulations with in silico experiments. Such predictions were obtained using a mathematical model of cellular metabolism in perfused myocardium. This model, which distinguishes cytosolic and mitochondrial domains, incorporates key metabolic species and processes associated with energy transfer. Simulation of metabolic responses to mild, moderate and severe ischaemia in large animals showed that mitochondrial NADH/NAD+ was rapidly reset to higher values in proportion to the reduced O2 delivery and myocardial oxygen consumption . Cytosolic NADH/NAD+, however, showed a biphasic response, with a sharp initial increase that was due to activation of glycogen breakdown and glycolysis, and corresponded with lactate production. Whereas the rate of glycolysis and the malate-aspartate shuttle had a significant effect on the cytosolic NADH/NAD+, their effects on the mitochondrial NADH/NAD+ were minimal. In summary, model simulations of the metabolic response to ischaemia showed that mitochondrial NADH/NAD+ is primarily determined by O2 consumption, while cytosolic NADH/NAD+ is largely a function of glycolytic flux during the initial phase, and is determined by mitochondrial NADH/NAD+ and the malate-aspartate shuttle during the steady state.