Computational Modeling of Mitochondrial Energy Transduction (original) (raw)
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The advent of techniques with the ability to scan massive changes in cellular makeup (genomics, proteomics, etc.) has revealed the compelling need for analytical methods to interpret and make sense of those changes. Computational models built on sound physico-chemical mechanistic basis are unavoidable at the time of integrating, interpreting, and simulating high-throughput experimental data. Another powerful role of computational models is predicting new behavior provided they are adequately validated. Mitochondrial energy transduction has been traditionally studied with thermodynamic models. More recently, kinetic or thermo-kinetic models have been proposed, leading the path toward an understanding of the control and regulation of mitochondrial energy metabolism and its interaction with cytoplasmic and other compartments. In this work, we outline the methods, step-by-step, that should be followed to build a computational model of mitochondrial energetics in isolation or integrated to a network of cellular processes. Depending on the question addressed by the modeler, the methodology explained herein can be applied with different levels of detail, from the mitochondrial energy producing machinery in a network of cellular processes to the dynamics of a single enzyme during its catalytic cycle.
Quantitative analysis of mitochondrial ATP synthesis
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We present a computational framework for analyzing and simulating mitochondrial ATP synthesis using basic thermodynamic and kinetic principles. The framework invokes detailed descriptions of the thermodynamic driving forces associated with the processes of the electron transport chain, mitochondrial ATP synthetase, and phosphate and adenine nucleotide transporters. Assembling models of these discrete processes into an integrated model of mitochondrial ATP synthesis, we illustrate how to analyze and simulate in vitro respirometry experiments and how models identified from in vitro experimental data effectively explain cardiac respiratory control in vivo. Computer codes for these analyses are embedded as Python scripts in a Jupyter Book to facilitate easy adoption and modification of the concepts developed here. This accessible framework may also prove useful in supporting educational applications. All source codes are available on at https://beards-lab.github.io/QAMAS\_book/.
Modeling Mitochondrial Bioenergetics with Integrated Volume Dynamics
PLOS Computational Biology, 2010
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. PLoS Computational Biology | www.ploscompbiol.org 1 January 2010 | Volume 6 | Issue 1 | e1000632 Mitochondrial Reactions J PDH Pyruvate dehydrogenase PYR + CoASH + NAD + H 2 O « CO 2 + SCOA + NADH J CS Citrate synthase OAA + AcCoA + H 2 O « CoASH + CIT J ACH Aconitase CIT « ISOC J IDH Isocitrate dehydrogenase NAD + ISOC + H 2 O « aKG + NADH + CO 2 J aKGDH a-Ketoglutarate dehydrogenase aKG + CoASH + NAD + H 2 O « CO 2 + SCoA + NADH J SCoAS Succinyl CoA synthase SCoA + GDP + Pi « SUC + GTP + CoASH J SDH Succinate dehydrogenase SUC + UQ « UQH 2 + FUM J FH Fumarate hydratase FUM + H 2 O « MAL J MDH Malate dehydrogenase NAD + MAL « OAA + NADH J NDK Nucleoside diphosphokinase GTP + ADP « GDP + ATP J GOT Glutamate oxaloacetate transaminase ASP + aKG « OAA + GLU J CI Complex I NADH + UQ « NAD + UQH 2 J CIII Complex III UQH 2 + 2Cytc 3+ « UQ + 2Cytc 2+ J CIV Complex IV 2Cytc red + KO 2 « 2Cytc ox + H 2 O J F1FO F 1 F O ATP synthase ADP + Pi « ATP + H 2 O J AK Adenylate Kinase 2ADP « ATP + AMP Exchangers and Ion Channels J GAE Glutamate-aspartate exchanger GLU ims + H + ims + ASP mtx « GLU mtx + H + mtx + ASP ims J OME a-Ketoglutarate-malate exchanger aKG ims + MAL mtx « aKG mtx + MAL ims J PYRH Pyruvate-proton cotransporter PYR ims + H + ims « PYR mtx + H + mtx J GLUH Glutamate-proton cotransporter GLU ims + H + ims « GLU mtx + H + mtx J CITMAL Tricarboxylate carrier CIT ims + MAL mtx « CIT mtx + MAL ims J ISCOMAL Tricarboxylate carrier ISOC ims + MAL mtx « ISOC mtx + MAL ims J SUCPi Dicarboxylate carrier SUC mtx + Pi ims « SU C ims + Pi mtx J MALPi Dicarboxylate carrier MAL mtx + Pi ims « MAL ims + Pi mtx J ANT Adenine nucleotide transporter ATP mtx + ADP ims « ATP ims + ADP mtx J PIC Inorganic phosphate carrier Pi ims + H + ims « Pi mtx + H + mtx J mHleak Proton leak H + ims « H + mtx
Kinetic Mathematical Modeling of Oxidative Phosphorylation in Cardiomyocyte Mitochondria
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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.
A simplified model for mitochondrial ATP production
Journal of Theoretical Biology, 2006
Most of the adenosine triphosphate (ATP) synthesized during glucose metabolism is produced in the mitochondria through oxidative phosphorylation. This is a complex reaction powered by the proton gradient across the mitochondrial inner membrane, which is generated by mitochondrial respiration. A detailed model of this reaction, which includes dynamic equations for the key mitochondrial variables, was developed earlier by Magnus and Keizer. However, this model is extraordinarily complicated. We develop a simpler model that captures the behavior of the original model but is easier to use and to understand. We then use it to investigate the mitochondrial responses to glycolytic and calcium input. We use the model to explain experimental observations of the opposite effects of raising cytosolic Ca 2þ in low and high glucose, and to predict the effects of a mutation in the mitochondrial enzyme nicotinamide nucleotide transhydrogenase (Nnt) in pancreatic b-cells.
Journal of Biological Chemistry, 2007
A computational model of mitochondrial metabolism and electrophysiology is introduced and applied to analysis of data from isolated cardiac mitochondria and data on phosphate metabolites in striated muscle in vivo. This model is constructed based on detailed kinetics and thermodynamically balanced reaction mechanisms and a strict accounting of rapidly equilibrating biochemical species. Since building such a model requires introducing a large number of adjustable kinetic parameters, a correspondingly large amount of independent data from isolated mitochondria respiring on different substrates and subject to a variety of protocols is used to parameterize the model and ensure that it is challenged by a wide range of data corresponding to diverse conditions. The developed model is further validated by both in vitro data on isolated cardiac mitochondria and in vivo experimental measurements on human skeletal muscle. The validated model is used to predict the roles of NAD and ADP in regulating the tricarboxylic acid cycle dehydrogenase fluxes, demonstrating that NAD is the more important regulator. Further model predictions reveal that a decrease of cytosolic pH value results in decreases in mitochondrial membrane potential and a corresponding drop in the ability of the mitochondria to synthesize ATP at the hydrolysis potential required for cellular function.
Biophysical Journal, 2006
An intricate network of reactions is involved in matching energy supply with demand in the heart. This complexity arises because energy production both modulates and is modulated by the electrophysiological and contractile activity of the cardiac myocyte. Here, we present an integrated mathematical model of the cardiac cell that links excitation-contraction coupling with mitochondrial energy generation. The dynamics of the model are described by a system of 50 ordinary differential equations. The formulation explicitly incorporates cytoplasmic ATP-consuming processes associated with force generation and ion transport, as well as the creatine kinase reaction. Changes in the electrical and contractile activity of the myocyte are coupled to mitochondrial energetics through the ATP, Ca 21 , and Na 1 concentrations in the myoplasmic and mitochondrial matrix compartments. The pseudo steady-state relationship between force and oxygen consumption at various stimulus frequencies and external Ca 21 concentrations is reproduced in both model simulations and direct experiments in cardiac trabeculae under normoxic conditions, recapitulating the linearity between cardiac work and respiration in the heart. Importantly, the model can also reproduce the rapid time-dependent changes in mitochondrial NADH and Ca 21 in response to abrupt changes in workload. The steady-state and dynamic responses of the model were conferred by ADP-dependent stimulation of mitochondrial oxidative phosphorylation and Ca 21 -dependent regulation of Krebs cycle dehydrogenases, illustrating how the model can be used as a tool for investigating mechanisms underlying metabolic control in the heart.
Acta Biotheoretica, 2008
Hypoxia hampers ATP production and threatens cell survival. Since cellular energetics tightly controls cell responses and fate, ATP levels and dynamics are of utmost importance. An integrated mathematical model of ATP synthesis by the mitochondrial oxidative phosphorylation/electron transfer chain system has been recently published (Beard, PLoS Comput Biol 1(4):e36, 2005). This model was validated under static conditions. To evaluate its performance under dynamical situations, we implemented and simulated it (Simulink Ò , The Mathworks). Inner membrane potential (DW) and [NADH] (feeding the electron transfer chain) were used as indicators of mitochondrial function. Root mean squared error (rmse) was used to compare simulations and experiments (isolated cardiac mitochondria, Bose et al. J Biol Chem 278 : [39155][39156][39157][39158][39159][39160][39161][39162][39163][39164][39165] 2003). Steady-state experimental data were reproduced within 2-6%. Model dynamics were evaluated under: (i) baseline, (ii) activation of NADH production, (iii) addition of ADP, (iv) addition of inorganic phosphate, (v) oxygen exhaustion. In all phases, except the last one, DW and [NADH] as well as oxygen consumption, were reproduced (within 10, 7 and 12%, respectively). Under anoxia, simulated DW markedly depolarized (no change in experiments). In conclusion, the model reproduces dynamic data as long as oxygen is present. Anticipated improvement by the inclusion of ATP consumption and explicit Krebs cycle are under evaluation.
Control and Regulation of Mitochondrial Energetics in an Integrated Model of Cardiomyocyte Function
Biophysical Journal, 2009
Understanding the regulation and control of complex networks of reactions requires analytical tools that take into account the interactions between individual network components controlling global network function. Here, we apply a generalized matrix method of control analysis to calculate flux and concentration control coefficients, as well as response coefficients, in an integrated model of excitation-contraction (EC) coupling and mitochondrial energetics (ECME model) in the cardiac ventricular myocyte. Control and regulation of oxygen consumption (V O2) was first assessed in a mitochondrion model, and then in the integrated cardiac myocyte model under resting and working conditions. The results demonstrate that in the ECME model, control of respiration is distributed among cytoplasmic ATPases and mitochondrial processes. The magnitude of control by cytoplasmic ATPases increases under working conditions. The model prediction that the respiratory chain exerts strong positive control on V O2 (control coefficient 0.89) was corroborated experimentally in cardiac trabeculae utilizing the inhibitor titration method. In the model, mitochondrial respiration displayed the highest response coefficients with respect to the concentration of cytoplasmic ATP. This was due to the high elasticity of ANT flux toward ATP in the cytoplasm. The analysis reveals the complex interdependence of sarcolemmal, cytoplasmic, and mitochondrial processes that contribute to the control of energy supply and demand in the heart. Moreover, by visualizing the structure of control of the metabolic network of the myocyte, we provide support for the emerging concept of control by diffuse loops, in which action on the network (e.g., by a pharmacological agent) may bring about changes in processes without obvious direct mechanistic links between them.
PLoS ONE, 2011
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.