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 F(0)F(1)-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

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

Philosophical Basis and Some Historical Aspects of Systems Biology: From Hegel to Noble - Applications for Bioenergetic Research

We live in times of paradigmatic changes for the biological sciences. Reductionism, that for the last six decades has been the philosophical basis of biochemistry and molecular biology, is being displaced by Systems Biology, which favors the study of integrated systems. Historically, Systems Biology - defined as the higher level analysis of complex biological systems - was pioneered by Claude Bernard in physiology, Norbert Wiener with the development of cybernetics, and Erwin Schrödinger in his thermodynamic approach to the living. Systems Biology applies methods inspired by cybernetics, network analysis, and non-equilibrium dynamics of open systems. These developments follow very precisely the dialectical principles of development from thesis to antithesis to synthesis discovered by Hegel. Systems Biology opens new perspectives for studies of the integrated processes of energy metabolism in different cells. These integrated systems acquire new, system-level properties due to interaction of cellular components, such as metabolic compartmentation, channeling and functional coupling mechanisms, which are central for regulation of the energy fluxes. State of the art of these studies in the new area of Molecular System Bioenergetics is analyzed

Roles of the creatine kinase system and myoglobin in maintaining energetic state in the working heart

<p>Abstract</p> <p>Background</p> <p>The heart is capable of maintaining contractile function despite a transient decrease in blood flow and increase in cardiac ATP demand during systole. This study analyzes a previously developed model of cardiac energetics and oxygen transport to understand the roles of the creatine kinase system and myoglobin in maintaining the ATP hydrolysis potential during beat-to-beat transient changes in blood flow and ATP hydrolysis rate.</p> <p>Results</p> <p>The theoretical investigation demonstrates that elimination of myoglobin only slightly increases the predicted range of oscillation of cardiac oxygenation level during beat-to-beat transients in blood flow and ATP utilization. In silico elimination of myoglobin has almost no impact on the cytoplasmic ATP hydrolysis potential (Δ<it>G</it>_ATPase). In contrast, disabling the creatine kinase system results in considerable oscillations of cytoplasmic ADP and ATP levels and seriously deteriorates the stability of Δ<it>G</it>_ATPasein the beating heart.</p> <p>Conclusion</p> <p>The CK system stabilizes Δ<it>G</it>_ATPaseby both buffering ATP and ADP concentrations and enhancing the feedback signal of inorganic phosphate in regulating mitochondrial oxidative phosphorylation.</p

Molecular System Bioenergics of the Heart: Experimental Studies of Metabolic Compartmentation and Energy Fluxes versus Computer Modeling †

In this review we analyze the recent important and remarkable advancements in studies of compartmentation of adenine nucleotides in muscle cells due to their binding to macromolecular complexes and cellular structures, which results in non-equilibrium steady state of the creatine kinase reaction. We discuss the problems of measuring the energy fluxes between different cellular compartments and their simulation by using different computer models. Energy flux determinations by 18O transfer method have shown that in heart about 80% of energy is carried out of mitochondrial intermembrane space into cytoplasm by phosphocreatine fluxes generated by mitochondrial creatine kinase from adenosine triphosphate (ATP), produced by ATP Synthasome. We have applied the mathematical model of compartmentalized energy transfer for analysis of experimental data on the dependence of oxygen consumption rate on heart workload in isolated working heart reported by Williamson et al. The analysis of these data show that even at the maximal workloads and respiration rates, equal to 174 μmol O2 per min per g dry weight, phosphocreatine flux, and not ATP, carries about 80–85% percent of energy needed out of mitochondria into the cytosol. We analyze also the reasons of failures of several computer models published in the literature to correctly describe the experimental data

Metabolic Dynamics in Skeletal Muscle during Acute Reduction in Blood Flow and Oxygen Supply to Mitochondria: In-Silico Studies Using a Multi-Scale, Top-Down Integrated Model

Control mechanisms of cellular metabolism and energetics in skeletal muscle that may become evident in response to physiological stresses such as reduction in blood flow and oxygen supply to mitochondria can be quantitatively understood using a multi-scale computational model. The analysis of dynamic responses from such a model can provide insights into mechanisms of metabolic regulation that may not be evident from experimental studies. For the purpose, a physiologically-based, multi-scale computational model of skeletal muscle cellular metabolism and energetics was developed to describe dynamic responses of key chemical species and reaction fluxes to muscle ischemia. The model, which incorporates key transport and metabolic processes and subcellular compartmentalization, is based on dynamic mass balances of 30 chemical species in both capillary blood and tissue cells (cytosol and mitochondria) domains. The reaction fluxes in cytosol and mitochondria are expressed in terms of a general phenomenological Michaelis-Menten equation involving the compartmentalized energy controller ratios ATP/ADP and NADH/NAD+. The unknown transport and reaction parameters in the model are estimated simultaneously by minimizing the differences between available in vivo experimental data on muscle ischemia and corresponding model outputs in coupled with the resting linear flux balance constraints using a robust, nonlinear, constrained-based, reduced gradient optimization algorithm. With the optimal parameter values, the model is able to simulate dynamic responses to reduced blood flow and oxygen supply to mitochondria associated with muscle ischemia of several key metabolite concentrations and metabolic fluxes in the subcellular cytosolic and mitochondrial compartments, some that can be measured and others that can not be measured with the current experimental techniques. The model can be applied to test complex hypotheses involving dynamic regulation of cellular metabolism and energetics in skeletal muscle during physiological stresses such as ischemia, hypoxia, and exercise

Analyzing the Functional Properties of the Creatine Kinase System with Multiscale 'Sloppy' Modeling

In this study the function of the two isoforms of creatine kinase (CK; EC 2.7.3.2) in myocardium is investigated. The ‘phosphocreatine shuttle’ hypothesis states that mitochondrial and cytosolic CK plays a pivotal role in the transport of high-energy phosphate (HEP) groups from mitochondria to myofibrils in contracting muscle. Temporal buffering of changes in ATP and ADP is another potential role of CK. With a mathematical model, we analyzed energy transport and damping of high peaks of ATP hydrolysis during the cardiac cycle. The analysis was based on multiscale data measured at the level of isolated enzymes, isolated mitochondria and on dynamic response times of oxidative phosphorylation measured at the whole heart level. Using ‘sloppy modeling’ ensemble simulations, we derived confidence intervals for predictions of the contributions by phosphocreatine (PCr) and ATP to the transfer of HEP from mitochondria to sites of ATP hydrolysis. Our calculations indicate that only 15±8% (mean±SD) of transcytosolic energy transport is carried by PCr, contradicting the PCr shuttle hypothesis. We also predicted temporal buffering capabilities of the CK isoforms protecting against high peaks of ATP hydrolysis (3750 µM*s(−1)) in myofibrils. CK inhibition by 98% in silico leads to an increase in amplitude of mitochondrial ATP synthesis pulsation from 215±23 to 566±31 µM*s(−1), while amplitudes of oscillations in cytosolic ADP concentration double from 77±11 to 146±1 µM. Our findings indicate that CK acts as a large bandwidth high-capacity temporal energy buffer maintaining cellular ATP homeostasis and reducing oscillations in mitochondrial metabolism. However, the contribution of CK to the transport of high-energy phosphate groups appears limited. Mitochondrial CK activity lowers cytosolic inorganic phosphate levels while cytosolic CK has the opposite effect

Mitochondrial function at extreme high altitude.

At high altitude, barometric pressure falls and with it inspired P(O2), potentially compromising O2 delivery to the tissues. With sufficient acclimatisation, the erythropoietic response increases red cell mass such that arterial O2 content (C(aO2)) is restored; however arterial P(O2)(P(aO2)) remains low, and the diffusion of O2 from capillary to mitochondrion is impaired. Mitochondrial respiration and aerobic capacity are thus limited, whilst reactive oxygen species (ROS) production increases. Restoration of P(aO2) with supplementary O2 does not fully restore aerobic capacity in acclimatised individuals, possibly indicating a peripheral impairment. With prolonged exposure to extreme high altitude (>5500 m), muscle mitochondrial volume density falls, with a particular loss of the subsarcolemmal population. It is not clear whether this represents acclimatisation or deterioration, but it does appear to be regulated, with levels of the mitochondrial biogenesis factor PGC-1α falling, and shows similarities to adapted Tibetan highlanders. Qualitative changes in mitochondrial function also occur, and do so at more moderate high altitudes with shorter periods of exposure. Electron transport chain complexes are downregulated, possibly mitigating the increase in ROS production. Fatty acid oxidation capacity is decreased and there may be improvements in biochemical coupling at the mitochondrial inner membrane that enhance O2 efficiency. Creatine kinase expression falls, possibly impairing high-energy phosphate transfer from the mitochondria to myofibrils. In climbers returning from the summit of Everest, cardiac energetic reserve (phosphocreatine/ATP) falls, but skeletal muscle energetics are well preserved, possibly supporting the notion that mitochondrial remodelling is a core feature of acclimatisation to extreme high altitude.Dr Murray thanks the Research Councils UK for supporting his Academic Fellowship, and the British Heart Foundation, BBSRC, Action Medical Research, Isaac Newton Trust and Oroboros Instruments for supporting research in his laboratory. Mr Horscroft thanks the BBSRC for funding his PhD Studentship.This is the author accepted manuscript. The final version is available from Wiley via http://dx.doi.org/10.1113/JP27007

Systems biology of energy metabolism in skeletal muscle

The primary function of skeletal muscle tissue is to produce force or cause motion. To perform this task chemical energy stored in nutrients (glucose and fatty acids) has to be converted into an energy currency that can drive muscle contraction (adenosine-tri-phosphate, ATP). This process is known as the energy metabolism of skeletal muscle and consists of a large number of chemical reactions that are organized in metabolic pathways. Unraveling this complex network is important from a fundamental biological perspective, but also essential to understand how a disturbance of muscle bioenergetics can cause metabolic disorders. ?? 31P magnetic resonance spectroscopy (MRS) has emerged as one of the premier methods to study skeletal muscle energy metabolism in vivo. It, however, remains challenging to relate the observed metabolite dynamics to an understanding of the underlying processes at the level of the metabolic pathways. A possible solution for bridging this gap between macroscopic measurements and mechanistic understanding at pathway level is the application of mechanistic computational modeling. This dissertation describes a series of studies in which a mechanistic model of ATP metabolism was developed and applied in the analysis of skeletal muscle bioenergetics. Skeletal muscle cells contain two primary processes that are responsible for the conversion of glucose and fatty acids into ATP. These processes are known as glycolysis and oxidative phosphorylation in mitochondria. The initial mathematical models of these processes were obtained by integration of known enzyme kinetics and thermodynamics. Testing of these models, however, showed that they failed to reproduce many of the in vivo observed metabolite dynamics, as has been described in chapter 1 and 2. These results indicated that the models might be missing essential regulatory mechanisms or that the model parameterization required changes. First, the physiological implications of necessary model adaptations were investigated in a series of studies described in chapters 2 – 5. ?? Numerical analysis of the initial glycolysis model revealed that the experimentally observed slow turnover rate of phosphorylated sugars post exercise could only be explained by rapid deactivation of phosphofructokinase (PFK) and pyruvate kinase (PK) in non-contracting muscle. In particular the deactivation of PFK was crucial for adequate control of pathway flux. Therefore, in a follow-up study, it was tested if the missing regulation at the level of PFK could be explained by calcium – calmodulin mediated activation of this enzyme. To this end, pathway behavior, represented by phosphocreatine (PCr) and pH dynamics, was measured in ischemic skeletal muscle for a wide variety of muscle excitation frequencies (0 – 80 Hz). Next, it was shown that addition of the calcium – calmodulin mediated activation of PFK was necessary to accurately reproduce these data. These results provided important new quantitative support for the hypothesis that this particular mechanism has a key role in the regulation of glycolytic flux in skeletal muscle.?? The initial model of oxidative phosphorylation was first tested against empirically determined mitochondrial input – output relations, i.e., [ADP] – mitochondrial ATP synthesis flux (Jp) and phosphate potential (¿Gp) – Jp. These empirically determined relations were derived from 31P MRS measurements of metabolite dynamics post-exercise. They capture key features of the regulation of oxidative phosphorylation in vivo and are therefore considered relevant for testing the quality of the mathematical model. Numerical model analysis (i.e., parameter sensitivity analysis) was applied to investigate which components significantly influenced predictions of these input – output relations. Based on these results it was concluded that the adenine nucleotide transporter (which facilitates the exchange of ATP and ADP across the inner mitochondrial membrane) has a dominant role in controlling the ADP sensitivity of mitochondria. Furthermore, we identified that Pi feedback control of respiratory chain activity was essential to explain measurements of ¿Gp at low metabolic rates. These insights were used to improve the predictive power of the model, as described in chapters 4 and 5. ?? In the studies described in chapters 2 - 5 the glycolytic and mitochondrial model components were tested for conditions in which only one of the two processes was active (ischemia and post exercise recovery, respectively). It remained therefore unknown if the control mechanisms included in these models could also explain the contribution of mitochondrial versus glycolytic ATP synthesis for conditions in which both processes are active (aerobic exercise). In an attempt to answer this question, dynamics of ATP metabolism were recorded during a full rest – exercise – recovery protocol under aerobic conditions and subsequently used for testing of the integrated mitochondrial + glycolytic model. The results presented in chapter 8 showed that the integrated model could accurately reproduce the observed metabolite and pH dynamics for varying exercise intensities. The main physiological implications of these results were that, substrate feedback control (ADP + Pi) of oxidative phosphorylation combined with substrate feedback control (ADP + AMP + Pi) and control by parallel activation (calcium – calmodulin mediated activation of PFK) of glycolysis, provides a set of key control mechanisms that can explain the regulation of ATP metabolism in skeletal muscle in vivo for a wide range of physiological conditions. By application of several cycles of model development it was possible to improve the models performance to the point it was consistent with 31P MRS measurements of muscle bioenergetics in both healthy humans and animals. As described in chapters 6 and 7, it is was investigated if the model could be applied to analyze the adaptations of muscle physiology that underlie changes in mitochondrial capacity that occur in for instance type 2 diabetes patients or with aging. A decrease of mitochondrial capacity in these subjects can be diagnosed accurately by determining the rate of PCr recovery post exercise. However, the changes in muscle physiology responsible for any observed difference in oxidative capacity cannot be deduced from these measurements. Therefore additional muscle biopsy samples are collected and analyzed for in vitro markers of oxidative capacity. State-of-the-art analyses of these data are typically limited to statistical or intuitive approaches. We investigated if the insight obtained from the combined in vivo + in vitro data sets could be increased by application of our mathematical model. To this end, first, the model was extended from a single uniform cell type model to a three types cell model (type I, IIA, and IIX), capturing the microscopic heterogeneity of muscle tissue. In addition, several key validation tests were conducted, as described in chapter 6. Subsequently, we demonstrated that the model could explain the prolongation of PCr recovery period observed in type 2 diabetes patients by integrating available literature data of in vitro markers of mitochondrial function. Although this result was already very promising, it was also concluded that the approach could be tested more rigorously by obtaining all data (in vivo + in vitro) in a single study. Therefore, the method was further tested in an animal model of decreased mitochondrial function: 8 versus 25 week old Wistar rats. The first main result of this study was that the mathematical model could accurately reproduce the delayed PCr recovery kinetics in 25 week old animals based on in vitro determined changes in muscle physiology. In addition, model predictions provided quantitative insight in the individual contribution of the different factors responsible for the decreased oxidative capacity. This type of information is considered very relevant for the design of (pharmaceutical) therapies aimed at improving mitochondrial function. For example, model predictions of the physiological changes that contribute the most to the decrease in oxidative capacity provide potentially promising targets for therapy design. Based on these considerations it was concluded that application of the mathematical model provides new promising opportunities for future studies of mitochondrial (dys)function in skeletal muscle. ?? In conclusion, through application of a series of iterative cycles of model development combined with multiple new experimental studies it was possible to develop a detailed mechanistic model of ATP metabolism that was consistent with in vivo observations of skeletal muscle bioenergetics for a wide range of physiological conditions. This process provided new insight in the key control mechanisms embedded in the metabolic pathways that have a dominant role in regulating ATP metabolism in skeletal muscle in vivo. In addition, we successfully demonstrated the feasibility and added value of application of the model for integration of in vivo and in vitro measurements of oxidative capacity in future studies of mitochondrial (dys)function in, for example, type 2 diabetes, aging or mitochondrial myopathy