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1.  Multistationary and Oscillatory Modes of Free Radicals Generation by the Mitochondrial Respiratory Chain Revealed by a Bifurcation Analysis 
PLoS Computational Biology  2012;8(9):e1002700.
The mitochondrial electron transport chain transforms energy satisfying cellular demand and generates reactive oxygen species (ROS) that act as metabolic signals or destructive factors. Therefore, knowledge of the possible modes and bifurcations of electron transport that affect ROS signaling provides insight into the interrelationship of mitochondrial respiration with cellular metabolism. Here, a bifurcation analysis of a sequence of the electron transport chain models of increasing complexity was used to analyze the contribution of individual components to the modes of respiratory chain behavior. Our algorithm constructed models as large systems of ordinary differential equations describing the time evolution of the distribution of redox states of the respiratory complexes. The most complete model of the respiratory chain and linked metabolic reactions predicted that condensed mitochondria produce more ROS at low succinate concentration and less ROS at high succinate levels than swelled mitochondria. This prediction was validated by measuring ROS production under various swelling conditions. A numerical bifurcation analysis revealed qualitatively different types of multistationary behavior and sustained oscillations in the parameter space near a region that was previously found to describe the behavior of isolated mitochondria. The oscillations in transmembrane potential and ROS generation, observed in living cells were reproduced in the model that includes interaction of respiratory complexes with the reactions of TCA cycle. Whereas multistationarity is an internal characteristic of the respiratory chain, the functional link of respiration with central metabolism creates oscillations, which can be understood as a means of auto-regulation of cell metabolism.
Author Summary
The mitochondrial respiratory chain shows a variety of modes of behavior. In living cells, flashes of ROS production and oscillations accompanied by a decrease of transmembrane potential can be registered. The mechanisms of such complex behavior are difficult to rationalize without a mathematical formalization of mitochondrial respiration. Our most complete model of mitochondrial respiration accounts for the details of electron transport, reproducing the observed types of behavior, which includes the existence of multiple steady states and periodic oscillations. This most detailed model contains hundreds of differential equations, and such complexity makes it difficult to grasp the main determinants of its behavior. Therefore the full model was reduced to a simplified description of complex III only, and numerical bifurcation analysis was used to study its behavior. Then the evolution of its behavior was traced in a sequence of models with increasing complexity leading back to the full model. This analysis revealed the mechanism of switching between the modes of behavior and the conditions for persistence in a given state, which defines ATP production, ROS signaling and destructive effects. This is important for understanding the biochemical basics of many systemic diseases.
doi:10.1371/journal.pcbi.1002700
PMCID: PMC3447950  PMID: 23028295
2.  Compartmentation of membrane processes and nucleotide dynamics in diffusion-restricted cardiac cell microenvironment 
Orchestrated excitation–contraction coupling in heart muscle requires adequate spatial arrangement of systems responsible for ion movement and metabolite turnover. Co-localization of regulatory and transporting proteins into macromolecular complexes within an environment of microanatomical cell components raises intracellular diffusion barriers that hamper the mobility of metabolites and signaling molecules. Compared to substrate diffusion in the cytosol, diffusional restrictions underneath the sarcolemma are much larger and could impede ion and nucleotide movement by a factor of 103–105. Diffusion barriers thus seclude metabolites within the submembrane space enabling rapid and vectorial effector targeting, yet hinder energy supply from the bulk cytosolic space implicating the necessity for a shunting transfer mechanism. Here, we address principles of membrane protein compartmentation, phosphotransfer enzyme-facilitated interdomain energy transfer, and nucleotide signal dynamics at the subsarcolemma–cytosol interface. This article is part of a Special Issue entitled ‘Local Signaling in Myocytes’.
doi:10.1016/j.yjmcc.2011.06.007
PMCID: PMC3264845  PMID: 21704043
ADP; ATP; ATP-sensitive K+ channel; Energy metabolism; Ion homeostasis; Macromolecular complex; Partitioning; Phosphotransfer; Submembrane
3.  Compartmentation of glycogen metabolism revealed from 13C isotopologue distributions 
BMC Systems Biology  2011;5:175.
Background
Stable isotope tracers are used to assess metabolic flux profiles in living cells. The existing methods of measurement average out the isotopic isomer distribution in metabolites throughout the cell, whereas the knowledge of compartmental organization of analyzed pathways is crucial for the evaluation of true fluxes. That is why we accepted a challenge to create a software tool that allows deciphering the compartmentation of metabolites based on the analysis of average isotopic isomer distribution.
Results
The software Isodyn, which simulates the dynamics of isotopic isomer distribution in central metabolic pathways, was supplemented by algorithms facilitating the transition between various analyzed metabolic schemes, and by the tools for model discrimination. It simulated 13C isotope distributions in glucose, lactate, glutamate and glycogen, measured by mass spectrometry after incubation of hepatocytes in the presence of only labeled glucose or glucose and lactate together (with label either in glucose or lactate). The simulations assumed either a single intracellular hexose phosphate pool, or also channeling of hexose phosphates resulting in a different isotopic composition of glycogen. Model discrimination test was applied to check the consistency of both models with experimental data. Metabolic flux profiles, evaluated with the accepted model that assumes channeling, revealed the range of changes in metabolic fluxes in liver cells.
Conclusions
The analysis of compartmentation of metabolic networks based on the measured 13C distribution was included in Isodyn as a routine procedure. The advantage of this implementation is that, being a part of evaluation of metabolic fluxes, it does not require additional experiments to study metabolic compartmentation. The analysis of experimental data revealed that the distribution of measured 13C-labeled glucose metabolites is inconsistent with the idea of perfect mixing of hexose phosphates in cytosol. In contrast, the observed distribution indicates the presence of a separate pool of hexose phosphates that is channeled towards glycogen synthesis.
doi:10.1186/1752-0509-5-175
PMCID: PMC3292525  PMID: 22034837
4.  Reactive Oxygen Species Production by Forward and Reverse Electron Fluxes in the Mitochondrial Respiratory Chain 
PLoS Computational Biology  2011;7(3):e1001115.
Reactive oxygen species (ROS) produced in the mitochondrial respiratory chain (RC) are primary signals that modulate cellular adaptation to environment, and are also destructive factors that damage cells under the conditions of hypoxia/reoxygenation relevant for various systemic diseases or transplantation. The important role of ROS in cell survival requires detailed investigation of mechanism and determinants of ROS production. To perform such an investigation we extended our rule-based model of complex III in order to account for electron transport in the whole RC coupled to proton translocation, transmembrane electrochemical potential generation, TCA cycle reactions, and substrate transport to mitochondria. It fits respiratory electron fluxes measured in rat brain mitochondria fueled by succinate or pyruvate and malate, and the dynamics of NAD+ reduction by reverse electron transport from succinate through complex I. The fitting of measured characteristics gave an insight into the mechanism of underlying processes governing the formation of free radicals that can transfer an unpaired electron to oxygen-producing superoxide and thus can initiate the generation of ROS. Our analysis revealed an association of ROS production with levels of specific radicals of individual electron transporters and their combinations in species of complexes I and III. It was found that the phenomenon of bistability, revealed previously as a property of complex III, remains valid for the whole RC. The conditions for switching to a state with a high content of free radicals in complex III were predicted based on theoretical analysis and were confirmed experimentally. These findings provide a new insight into the mechanisms of ROS production in RC.
Author Summary
Respiration at the level of mitochondria is considered as delivery of electrons and protons from NADH or succinate to oxygen through a set of transporters constituting the respiratory chain (RC). Mitochondrial respiration, dealing with transfer of unpaired electrons, may produce reactive oxygen species (ROS) such as O2− and subsequently H2O2 as side products. ROS are chemically very active and can cause oxidative damage to cellular components. The production of ROS, normally low, can increase under stress to the levels incompatible with cell survival; thus, understanding the ways of ROS production in the RC represents a vital task in research. We used mathematical modeling to analyze experiments with isolated brain mitochondria aimed to study relations between electron transport and ROS production. Elsewhere we reported that mitochondrial complex III can operate in two distinct steady states at the same microenvironmental conditions, producing either low or high levels of ROS. Here, this property of bistability was confirmed for the whole RC. The associations between measured ROS production and computed individual free radical levels in complexes I and III were established. The discovered phenomenon of bistability is important as a basis for new strategies in organ transplantation and therapy.
doi:10.1371/journal.pcbi.1001115
PMCID: PMC3068929  PMID: 21483483
5.  Edelfosine-induced metabolic changes in cancer cells that precede the overproduction of reactive oxygen species and apoptosis 
BMC Systems Biology  2010;4:135.
Background
Metabolic flux profiling based on the analysis of distribution of stable isotope tracer in metabolites is an important method widely used in cancer research to understand the regulation of cell metabolism and elaborate new therapeutic strategies. Recently, we developed software Isodyn, which extends the methodology of kinetic modeling to the analysis of isotopic isomer distribution for the evaluation of cellular metabolic flux profile under relevant conditions. This tool can be applied to reveal the metabolic effect of proapoptotic drug edelfosine in leukemia Jurkat cell line, uncovering the mechanisms of induction of apoptosis in cancer cells.
Results
The study of 13C distribution of Jukat cells exposed to low edelfosine concentration, which induces apoptosis in ≤5% of cells, revealed metabolic changes previous to the development of apoptotic program. Specifically, it was found that low dose of edelfosine stimulates the TCA cycle. These metabolic perturbations were coupled with an increase of nucleic acid synthesis de novo, which indicates acceleration of biosynthetic and reparative processes. The further increase of the TCA cycle fluxes, when higher doses of drug applied, eventually enhance reactive oxygen species (ROS) production and trigger apoptotic program.
Conclusion
The application of Isodyn to the analysis of mechanism of edelfosine-induced apoptosis revealed primary drug-induced metabolic changes, which are important for the subsequent initiation of apoptotic program. Initiation of such metabolic changes could be exploited in anticancer therapy.
doi:10.1186/1752-0509-4-135
PMCID: PMC2984393  PMID: 20925932
6.  Bistability of Mitochondrial Respiration Underlies Paradoxical Reactive Oxygen Species Generation Induced by Anoxia 
PLoS Computational Biology  2009;5(12):e1000619.
Increased production of reactive oxygen species (ROS) in mitochondria underlies major systemic diseases, and this clinical problem stimulates a great scientific interest in the mechanism of ROS generation. However, the mechanism of hypoxia-induced change in ROS production is not fully understood. To mathematically analyze this mechanism in details, taking into consideration all the possible redox states formed in the process of electron transport, even for respiratory complex III, a system of hundreds of differential equations must be constructed. Aimed to facilitate such tasks, we developed a new methodology of modeling, which resides in the automated construction of large sets of differential equations. The detailed modeling of electron transport in mitochondria allowed for the identification of two steady state modes of operation (bistability) of respiratory complex III at the same microenvironmental conditions. Various perturbations could induce the transition of respiratory chain from one steady state to another. While normally complex III is in a low ROS producing mode, temporal anoxia could switch it to a high ROS producing state, which persists after the return to normal oxygen supply. This prediction, which we qualitatively validated experimentally, explains the mechanism of anoxia-induced cell damage. Recognition of bistability of complex III operation may enable novel therapeutic strategies for oxidative stress and our method of modeling could be widely used in systems biology studies.
Author Summary
The levels of reactive oxygen species (ROS) that are generated as a side product of mitochondrial respiratory electron transport largely define the extent of oxidative stress in living cells. Free radicals formed in electron transport, such as ubisemiquinone, could pass their non-paired electron directly to oxygen, thus producing superoxide radical that gives rise to a variety of ROS. It is well known in clinical practice that upon recommencing oxygen supply after anoxia a tissue produces much more ROS than before the anoxia, and the state of high ROS production is stable. The mechanism of switching from low to high ROS production by temporal anoxia was unknown, in part because of the lack of detailed mathematical description of hundreds of redox states of respiratory complexes, which are formed in the process of electron transport. A new methodology of automated construction of large systems of differential equations allowed us to describe the system in detail and predicts that the mechanism of paradoxical effect of anoxia-reoxygenation could be defined by the properties of complex III of mitochondrial respiratory chain. Our experiments confirmed that the effect of hypoxia-reoxygenation is confined by intramitochondrial processes since it is observed in isolated mitochondria.
doi:10.1371/journal.pcbi.1000619
PMCID: PMC2789320  PMID: 20041200
7.  The Role of External and Matrix pH in Mitochondrial Reactive Oxygen Species Generation* 
The Journal of Biological Chemistry  2008;283(43):29292-29300.
Reactive oxygen species (ROS) generation in mitochondria as a side product of electron and proton transport through the inner membrane is important for normal cell operation as well as development of pathology. Matrix and cytosol alkalization stabilizes semiquinone radical, a potential superoxide producer, and we hypothesized that proton deficiency under the excess of electron donors enhances reactive oxygen species generation. We tested this hypothesis by measuring pH dependence of reactive oxygen species released by mitochondria. The experiments were performed in the media with pH varying from 6 to 8 in the presence of complex II substrate succinate or under more physiological conditions with complex I substrates glutamate and malate. Matrix pH was manipulated by inorganic phosphate, nigericine, and low concentrations of uncoupler or valinomycin. We found that high pH strongly increased the rate of free radical generation in all of the conditions studied, even when ΔpH = 0 in the presence of nigericin. In the absence of inorganic phosphate, when the matrix was the most alkaline, pH shift in the medium above 7 induced permeability transition accompanied by the decrease of ROS production. ROS production increase induced by the alkalization of medium was observed with intact respiring mitochondria as well as in the presence of complex I inhibitor rotenone, which enhanced reactive oxygen species release. The phenomena revealed in this report are important for understanding mechanisms governing mitochondrial production of reactive oxygen species, in particular that related with uncoupling proteins.
doi:10.1074/jbc.M801019200
PMCID: PMC2570889  PMID: 18687689
8.  Integration of enzyme kinetic models and isotopomer distribution analysis for studies of in situ cell operation 
BMC Neuroscience  2006;7(Suppl 1):S7.
A current trend in neuroscience research is the use of stable isotope tracers in order to address metabolic processes in vivo. The tracers produce a huge number of metabolite forms that differ according to the number and position of labeled isotopes in the carbon skeleton (isotopomers) and such a large variety makes the analysis of isotopomer data highly complex. On the other hand, this multiplicity of forms does provide sufficient information to address cell operation in vivo. By the end of last millennium, a number of tools have been developed for estimation of metabolic flux profile from any possible isotopomer distribution data. However, although well elaborated, these tools were limited to steady state analysis, and the obtained set of fluxes remained disconnected from their biochemical context. In this review we focus on a new numerical analytical approach that integrates kinetic and metabolic flux analysis. The related computational algorithm estimates the dynamic flux based on the time-dependent distribution of all possible isotopomers of metabolic pathway intermediates that are generated from a labeled substrate. The new algorithm connects specific tracer data with enzyme kinetic characteristics, thereby extending the amount of data available for analysis: it uses enzyme kinetic data to estimate the flux profile, and vice versa, for the kinetic analysis it uses in vivo tracer data to reveal the biochemical basis of the estimated metabolic fluxes.
doi:10.1186/1471-2202-7-S1-S7
PMCID: PMC1775047  PMID: 17118161

Results 1-8 (8)