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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.  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
3.  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
4.  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
5.  Influence of Viable Cells on the Resuscitation of Dormant Cells in Micrococcus luteus Cultures Held in an Extended Stationary Phase: the Population Effect 
A high proportion of Micrococcus luteus cells in cultures which had been starved for 3 to 6 months lost the ability to grow and form colonies on agar plates but could be resuscitated from their dormancy by incubation in an appropriate liquid medium (A. S. Kaprelyants and D. B. Kell, Appl. Environ. Microbiol. 59:3187-3196, 1993). In the present work, such cultures were studied by both flow cytometry and conventional microbiological methods and were found to contain various numbers of viable cells. Pretreatment of such cultures with penicillin G, and subsequent dilution, was used to vary this number. When the initial number of colony-forming cells per 30-ml flask was approximately nine (±five) or more, resuscitation of 10 to 40% of the cells, and thus culture growth, was observed. The lag period before the appearance of a population of cells showing significant accumulation of the fluorescent dye rhodamine 123 (i.e., of cells with measurable membrane energization) decreased from 70 to 27 h when the number of viable cells was increased from 30 to 105 per flask, while the lag period before an observable increase in the number of colony-forming cells occurred was almost constant (at some 20 h). Provided there were more than nine (±five) initially viable cells per flask, the number of initially viable cells did not affect the final percentage of resuscitable cells in the culture. The lag period could be ascribed in part to the time taken to restore the membrane permeability barrier of starved cells during resuscitation, as revealed by flow cytometric assessment of the uptake of the normally membrane-impermeant fluorescent DNA stain PO-PRO-3 {4-[3-methyl-2, 3-dihydro-(benzo-1, 3-oxazole)-2-methylidene]-1-(3′-trimethylammonium propyl)-pyridinium diiodide}. Although cell populations which contained fewer than nine ±five viable cells per flask failed to grow, 4 to 20% of the cells (of 1.2 X 106) were able to accumulate rhodamine 123 after 80 to 100 h of incubation, showing the ability of a significant number of the cells in the population at least to display “metabolic resuscitation.” Resuscitation and cell growth under such conditions were favored by the use of a 1:1 mixture of fresh lactate medium and supernatant from late-logarithmic-phase M. luteus cultures as the resuscitation medium. We conclude that the presence of a small fraction of viable cells at the onset of resuscitation facilitates the recovery of the majority of the remaining (dormant) cells. The cell density dependence of the kinetics, or population effect, suggests that this recovery is due to the excretion of some factor(s) which promoted the transition of cells from a state in which they are incapable of growth and division to one in which they are capable of colony formation.
PMCID: PMC201800  PMID: 16349381

Results 1-5 (5)