Modeling Mitochondrial Bioenergetics with Integrated Volume Dynamics

Mathematical models of mitochondrial bioenergetics provide powerful analytical tools to help interpret experimental data and facilitate experimental design for elucidating the supporting biochemical and physical processes. As a next step towards constructing a complete physiologically faithful mitochondrial bioenergetics model, a mathematical model was developed targeting the cardiac mitochondrial bioenergetic based upon previous efforts, and corroborated using both transient and steady state data. The model consists of several modified rate functions of mitochondrial bioenergetics, integrated calcium dynamics and a detailed description of the K+-cycle and its effect on mitochondrial bioenergetics and matrix volume regulation. Model simulations were used to fit 42 adjustable parameters to four independent experimental data sets consisting of 32 data curves. During the model development, a certain network topology had to be in place and some assumptions about uncertain or unobserved experimental factors and conditions were explicitly constrained in order to faithfully reproduce all the data sets. These realizations are discussed, and their necessity helps contribute to the collective understanding of the mitochondrial bioenergetics

Thermodynamically-Constrained Computational Modeling of Lung Tissue Bioenergetics and the Effect of Hyperoxia-Induced Acute Lung Injury

Altered lung tissue bioenergetics is an important and early step in the pathogenesis of acute lung injury (ALI), one of the most common causes of admission to medical ICUs. A wealth of information exists regarding the effect of ALI on specific mitochondrial and cytosolic processes in isolated mitochondria, cultured endothelial cell, and intact lungs. However, the interdependence of lung cellular processes makes it difficult to quantify the impact of a change in a single or multiple cellular process(es) on overall lung tissue bioenergetics. Integrating bioenergetics data from isolated mitochondria and intact lung is necessary for determining the functional significance of targeting a specific cellular process for prognostic and/or therapeutic purposes. Thus, the main objective of my dissertation was to develop and validate comprehensive, thermodynamically-constrained models of mitochondrial and lung tissue bioenergetics, and to use these models to predict the impact of ALI-induced changes in mitochondrial and cytosolic processes on lung tissue bioenergetics. For Aim 1, I developed an integrated model of the bioenergetics of mitochondria isolated from rat lungs, which incorporates the major biochemical reactions and transport processes in lung mitochondria. The model was validated by assessing its ability to predict experimental data not used for parameter estimation. The model provides important insights into the bioenergetics of lung mitochondria and how they differ from those of mitochondria from other organs. For Aim 2, I developed and validated an integrated computational model of lung tissue bioenergetics. The model expanded the computational model developed under Aim 1 by accounting for glucose uptake and phosphorylation, glycolysis, and the pentose phosphate pathway. The model was then used to gain novel insights into how lung tissue glycolytic rate is regulated by exogenous substrates, and assess differences in the bioenergetics of isolated mitochondria isolated from lung tissue and those of mitochondria in intact lungs. For Aim 3, the models developed under Aims 1 and 2 were used to quantify the impact of previously measured changes in specific mitochondrial processes in a rat model of clinical ALI on lung mitochondrial and tissue bioenergetics. To the best of our knowledge, the two computational models are the first for lung mitochondrial and tissue bioenergetics. These models provide a mechanistic and quantitative framework for integrating available lung tissue bioenergetics data, for testing novel hypotheses regarding the role of different cytosolic and mitochondrial processes in lung tissue bioenergetics and the pathogenesis of ALI, and for identifying potential therapeutic targets for ALI

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

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

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

Metabolic Compartmentation – A System Level Property of Muscle Cells: Real Problems of Diffusion in Living Cells

Problems of quantitative investigation of intracellular diffusion and compartmentation of metabolites are analyzed. Principal controversies in recently published analyses of these problems for the living cells are discussed. It is shown that the formal theoretical analysis of diffusion of metabolites based on Fick's equation and using fixed diffusion coefficients for diluted homogenous aqueous solutions, but applied for biological systems in vivo without any comparison with experimental results, may lead to misleading conclusions, which are contradictory to most biological observations. However, if the same theoretical methods are used for analysis of actual experimental data, the apparent diffusion constants obtained are orders of magnitude lower than those in diluted aqueous solutions. Thus, it can be concluded that local restrictions of diffusion of metabolites in a cell are a system-level properties caused by complex structural organization of the cells, macromolecular crowding, cytoskeletal networks and organization of metabolic pathways into multienzyme complexes and metabolons. This results in microcompartmentation of metabolites, their channeling between enzymes and in modular organization of cellular metabolic networks. The perspectives of further studies of these complex intracellular interactions in the framework of Systems Biology are discussed

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

Computational modeling of In vitro swelling of mitochondria: A biophysical approach

Swelling of mitochondria plays an important role in the pathogenesis of human diseases by stimulating mitochondria-mediated cell death through apoptosis, necrosis, and autophagy. Changes in the permeability of the inner mitochondrial membrane (IMM) of ions and other substances induce an increase in the colloid osmotic pressure, leading to matrix swelling. Modeling of mitochondrial swelling is important for simulation and prediction of in vivo events in the cell during oxidative and energy stress. In the present study, we developed a computational model that describes the mechanism of mitochondrial swelling based on osmosis, the rigidity of the IMM, and dynamics of ionic/neutral species. The model describes a new biophysical approach to swelling dynamics, where osmotic pressure created in the matrix is compensated for by the rigidity of the IMM, i.e., osmotic pressure induces membrane deformation, which compensates for the osmotic pressure effect. Thus, the effect is linear and reversible at small membrane deformations, allowing the membrane to restore its normal form. On the other hand, the membrane rigidity drops to zero at large deformations, and the swelling becomes irreversible. As a result, an increased number of dysfunctional mitochondria can activate mitophagy and initiate cell death. Numerical modeling analysis produced results that reasonably describe the experimental data reported earlier.National Institute of General Medical Sciences of the National Institutes of Health [SC1GM128210]; Puerto Rico Institute for Functional Nanomaterials (National Science Foundation Grant) [1002410]; National Aeronautics and Space Administration (NASA) Puerto Rico Established Program to Stimulate Competitive Research (EPSCoR) [NNX15AK43A

The microbiologist’s guide to membrane potential dynamics

All cellular membranes have the functionality of generating and maintaining the gradients of electrical and electrochemical potentials. Such potentials were generally thought to be an essential but homeostatic contributor to complex bacterial behaviors. Recent studies have revised this view, and we now know that bacterial membrane potential is dynamic and plays signaling roles in cell–cell interaction, adaptation to antibiotics, and sensation of cellular conditions and environments. These discoveries argue that bacterial membrane potential dynamics deserve more attention. Here, we review the recent studies revealing the signaling roles of bacterial membrane potential dynamics. We also introduce basic biophysical theories of the membrane potential to the microbiology community and discuss the needs to revise these theories for applications in bacterial electrophysiology

Glucose metabolism determines resistance of cancer cells to bioenergetic crisis after cytochrome-c release

How can cancer cells survive the consequences of cyt-c release? Huber et al provide a quantitative analysis of the protective role of enhanced glucose utilization in cancer cells and investigate the impact of cell-to-cell heterogeneity in mitochondrial bioenergetics