Simulation of oxidative phosphorylation in hepatocytes

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.

Modeling the detailed kinetics of mitochondrial cytochrome c oxidase: Catalytic mechanism and nitric oxide inhibition

Cytochrome c oxidase (CcO) catalyzes the exothermic reduction of O₂ to H₂O by using electrons from cytochrome c, and hence plays a crucial role in ATP production. Although details on the enzyme structure and redox centers involved in O₂ reduction have been known, there still remains a considerable ambiguity on its mechanism of action, e.g., the number of sequential electrons donated to O₂ in each catalytic step, the sites of protonation and proton pumping, and nitric oxide (NO) inhibition mechanism. In this work, we developed a thermodynamically constrained mechanistic mathematical model for the catalytic action of CcO based on available kinetic data. The model considers a minimal number of redox centers on CcO and couples electron transfer and proton pumping driven by proton motive force (PMF), and accounts for the inhibitory effects of NO on the reaction kinetics. The model is able to fit well all the available kinetic data under diverse experimental conditions with a physiologically realistic unique parameter set. The model predictions show that: 1) the apparent K_m of O₂ varies considerably and increases from fully reduced to fully oxidized cytochrome c depending on pH and the energy state of mitochondria, and 2) the intermediate enzyme states depend on pH and cytochrome c redox fraction and play a central role in coupling mitochondrial respiration to PMF. The developed CcO model can easily be integrated into existing mitochondrial bioenergetics models to understand the role of the enzyme in controlling oxidative phosphorylation in normal and disease conditions.

Explaining the enigmatic K(M) for oxygen in cytochrome c oxidase: a kinetic model

We present a mathematical model for the functioning of proton-pumping cytochrome c oxidase, consisting of cyclic conversions between 26 enzyme states. The model is based on the mechanism of oxygen reduction and linked proton translocation postulated by Wikström and Verkhovsky (2007). It enables the calculation of the steady-state turnover rates and enzyme-state populations as functions of the cytochrome c reduction state, oxygen concentration, membrane potential, and pH on either side of the inner mitochondrial membrane. We use the model to explain the enigmatic decrease in oxygen affinity of the enzyme that has been observed in mitochondria when the proton-motive force is increased. The importance of the 26 transitions in the mechanism of cytochrome oxidase for the functional properties of cytochrome oxidase is compared through Metabolic Control Analysis. The control of the K(M) value is distributed mainly between the steps in the mechanism that involve electrogenic proton movements, with both positive and negative contributions. Positive contributions derive from the same steps that control enzyme turnover rate in the model. Limitations and possible further applications of the model are discussed.

Magnitude and control of mitochondrial sensitivity to ADP

The transduction function for ADP stimulation of mitochondrial ATP synthesis in skeletal muscle was reconstructed in vivo and in silico to investigate the magnitude and origin of mitochondrial sensitivity to cytoplasmic ADP concentration changes. Dynamic in vivo measurements of human leg muscle phosphocreatine (PCr) content during metabolic recovery from contractions were performed by (31)P-NMR spectroscopy. The cytoplasmic ADP concentration ([ADP]) and rate of oxidative ATP synthesis (Jp) at each time point were calculated from creatine kinase equilibrium and the derivative of a monoexponential fit to the PCr recovery data, respectively. Reconstructed [ADP]-Jp relations for individual muscles containing more than 100 data points were kinetically characterized by nonlinear curve fitting yielding an apparent kinetic order and ADP affinity of 1.9 +/- 0.2 and 0.022 +/- 0.003 mM, respectively (means +/- SD; n = 6). Next, in silico [ADP]-Jp relations for skeletal muscle were generated using a computational model of muscle oxidative ATP metabolism whereby model parameters corresponding to mitochondrial enzymes were randomly changed by 50-150% to determine control of mitochondrial ADP sensitivity. The multiparametric sensitivity analysis showed that mitochondrial ADP ultrasensitivity is an emergent property of the integrated mitochondrial enzyme network controlled primarily by kinetic properties of the adenine nucleotide translocator.

Modeling the electron transport chain of purple non-sulfur bacteria

Purple non-sulfur bacteria (Rhodospirillaceae) have been extensively employed for studying principles of photosynthetic and respiratory electron transport phosphorylation and for investigating the regulation of gene expression in response to redox signals. Here, we use mathematical modeling to evaluate the steady-state behavior of the electron transport chain (ETC) in these bacteria under different environmental conditions. Elementary-modes analysis of a stoichiometric ETC model reveals nine operational modes. Most of them represent well-known functional states, however, two modes constitute reverse electron flow under respiratory conditions, which has been barely considered so far. We further present and analyze a kinetic model of the ETC in which rate laws of electron transfer steps are based on redox potential differences. Our model reproduces well-known phenomena of respiratory and photosynthetic operation of the ETC and also provides non-intuitive predictions. As one key result, model simulations demonstrate a stronger reduction of ubiquinone when switching from high-light to low-light conditions. This result is parameter insensitive and supports the hypothesis that the redox state of ubiquinone is a suitable signal for controlling photosynthetic gene expression.

A generic model of electron transport in mitochondria

In this paper, a simplified, generic model of mitochondrial metabolism is explored. In particular the following question is addressed: To what extent are phenomena observed in experiments and simulations of mitochondrial metabolism generic, in the sense that they must occur in all models with this basic structure? Of particular interest are the electron transport chain and oxidative phosphorylation, and how flux through the system and the redox states of intermediates respond to physiologically important stimuli. These stimuli include changes in substrate supply (NADH/FADH(2)), in oxygenation, and in membrane proton gradient/ATP demand. Analytical techniques are used to show that certain experimentally observed effects must occur in the generic model. These include the responses of both flux and redox states to changed substrate and oxygen concentrations. At the same time other effects, such as the responses of redox states to changes in proton gradient, are dependent on the details of the model, and are not common to every model with the same basic structure. The phenomenon of saturation in response to large inputs is also discussed.

Virtual mitochondria: metabolic modelling and control

Inside the eukaryotic cell, mitochondria are internal organelles of prokaryotic origin, responsible for energy supply in the cell. The control of the mitochondrial ATP production is a complex problem with different patterns according to different tissues and organs. Our aim is to continue to develop the modelling of oxidative phosphorylation in different tissues, to model other parts of mitochondrial metabolism and to include this virtual mitochondria in a virtual cell. In constructing the complete metabolic map of mitochondria, we will take advantage of the sequenced genomes of eukaryotic organism (10-15% of the yeast genome concerns mitochondria).

An integrated model of cardiac mitochondrial energy metabolism and calcium dynamics

We present an integrated thermokinetic model describing control of cardiac mitochondrial bioenergetics. The model describes the tricarboxylic acid (TCA) cycle, oxidative phosphorylation, and mitochondrial Ca(2+) handling. The kinetic component of the model includes effectors of the TCA cycle enzymes regulating production of NADH and FADH(2), which in turn are used by the electron transport chain to establish a proton motive force (Delta mu(H)), driving the F(1)F(0)-ATPase. In addition, mitochondrial matrix Ca(2+), determined by Ca(2+) uniporter and Na(+)/Ca(2+) exchanger activities, regulates activity of the TCA cycle enzymes isocitrate dehydrogenase and alpha-ketoglutarate dehydrogenase. The model is described by twelve ordinary differential equations for the time rate of change of mitochondrial membrane potential (Delta Psi(m)), and matrix concentrations of Ca(2+), NADH, ADP, and TCA cycle intermediates. The model is used to predict the response of mitochondria to changes in substrate delivery, metabolic inhibition, the rate of adenine nucleotide exchange, and Ca(2+). The model is able to reproduce, qualitatively and semiquantitatively, experimental data concerning mitochondrial bioenergetics, Ca(2+) dynamics, and respiratory control. Significant increases in oxygen consumption (V(O(2))), proton efflux, NADH, and ATP synthesis, in response to an increase in cytoplasmic Ca(2+), are obtained when the Ca(2+)-sensitive dehydrogenases are the main rate-controlling steps of respiratory flux. These responses diminished when control is shifted downstream (e.g., the respiratory chain or adenine nucleotide translocator). The time-dependent behavior of the model, under conditions simulating an increase in workload, closely reproduces experimentally observed mitochondrial NADH dynamics in heart trabeculae subjected to changes in pacing frequency. The steady-state and time-dependent behavior of the model support the hypothesis that mitochondrial matrix Ca(2+) plays an important role in matching energy supply with demand in cardiac myocytes.

Cardiac energy metabolism: models of cellular respiration

The heart requires a large amount of energy to sustain both ionic homeostasis and contraction. Under normal conditions, adenosine triphosphate (ATP) production meets this demand. Hence, there is a complex regulatory system that adjusts energy production to meet this demand. However, the mechanisms for this control are a topic of active debate. Energy metabolism can be divided into three main stages: substrate delivery to the tricarboxylic acid (TCA) cycle, the TCA cycle, and oxidative phosphorylation. Each of these processes has multiple control points and exerts control over the other stages. This review discusses the basic stages of energy metabolism, mechanisms of control, and the mathematical and computational models that have been used to study these mechanisms.

Theoretical studies on the regulation of oxidative phosphorylation in intact tissues

The theoretical studies on the regulation of oxidative phosphorylation that were performed with the aid of kinetic models of this process are overviewed. A definition of the regulation of the flux through a metabolic pathway is proposed and opposed to the control exerted by particular enzymes over this flux. Different kinetic models of oxidative phosphorylation proposed in the literature are presented, of which only the model proposed by myself and co-workers was extensively used in theoretical studies on the regulation and compensation in the oxidative phosphorylation system. These theoretical studies have led to the following conclusions: (1) in isolated mitochondria, an increase in the activity of an artificial ATP-using system stimulates mitochondria mainly via changes in [ADP], while changes in [ATP] and [P(i)] play only a minor role; (2) in non-excitable tissues (e.g. liver), hormones (acting via some cytosolic factor(s)) activate directly both ATP usage and at least some enzymes of the ATP-producing block; (3) in excitable tissues (e.g. skeletal muscle), neural signals stimulate (via some cytosolic factor(s)) in parallel all the steps of oxidative phosphorylation together with ATP usage and substrate dehydrogenation; (4) the decrease in the flux through cytochrome oxidase caused by a decrease in oxygen concentration is, at least partially, compensated by a decrease in Delta p and increase in the reduction level of cytochrome c. A theoretical prediction is formulated that there should exist and be observable a universal cytosolic factor/regulatory mechanism which directly activates (at least in excitable tissues) all complexes of oxidative phosphorylation during an increased energy demand.

Internal regulation of ATP turnover, glycolysis and oxidative phosphorylation in rat hepatocytes

Previously [Ainscow, E.K. & Brand, M.D. (1999) Eur. J. Biochem. 263, 671-685], top-down control analysis was used to describe the control pattern of energy metabolism in rat hepatocytes. The system was divided into nine reaction blocks (glycogen breakdown, glucose release, glycolysis, lactate production, NADH oxidation, pyruvate oxidation, mitochondrial proton leak, mitochondrial phosphorylation and ATP consumption) linked by five intermediates (intracellular glucose 6-phosphate, pyruvate and ATP levels, cytoplasmic NADH/NAD ratio and mitochondrial membrane potential). The kinetic responses (elasticities) of reaction blocks to intermediates were determined and used to calculate control coefficients. In the present paper, these elasticities and control coefficients are used to quantify the internal regulatory pathways within the cell. Flux control coefficients were partitioned to give partial flux control coefficients. These describe how strongly one block of reactions controls the flux through another via its effects on the concentration of a particular intermediate. Most flux control coefficients were the sum of positive and negative partial effects acting through different intermediates; these partial effects could be large compared to the final control strength. An important result was the breakdown of the way ATP consumption controlled respiration: changes in ATP level were more important than changes in mitochondrial membrane potential in stimulating oxygen consumption when ATP consumption increased. The partial internal response coefficients to changes in each intermediate were also calculated; they describe how steady state concentrations of intermediates are maintained. Increases in mitochondrial membrane potential were opposed mostly by decreased supply, whereas increases in glucose-6-phosphate, NADH/NAD and pyruvate were opposed mostly by increased consumption. Increases in ATP were opposed significantly by both decreased supply and increased consumption.

Theoretical studies on the control of oxidative phosphorylation in muscle mitochondria: application to mitochondrial deficiencies

1. The dynamic model of oxidative phosphorylation developed previously for rat liver mitochondria incubated with succinate was adapted for muscle mitochondria respiring on pyruvate. We introduced the following changes considering: (1) a higher external ATP/ADP ratio and an ATP/ADP carrier less displaced from equilibrium; (2) a substrate dehydrogenation more sensitive to the NADH/NAD+ ratio; and (3) the respiratory chain, ATP synthase and phosphate carrier being more displaced from equilibrium. The experimental flux control coefficients already determined in state 3 for respiratory rate and ATP synthesis were used to adjust some parameters. This new oxidative phosphorylation model enabled us to simulate the whole titration curves obtained experimentally in state 3. These curves, which mimic the effect of mitochondrial complex deficiencies on oxidative phosphorylation, show a threshold effect, which is reproduced by the model. 2. the model was also used to simulate other physiological conditions such as (i) state 3.5, conditions in-between state 4 and state 3; and (ii) hypoxic conditions. In both cases a profound change in the pattern of the control coefficients was shown. 3. This model was thus found useful in investigating a variety of new conditions, the most interesting of which can then be experimentally studied.