Multistationary and Oscillatory Modes of Free Radicals Generation by the Mitochondrial Respiratory Chain Revealed by a Bifurcation Analysis

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.

1. equations describing electron transport between the redox states (Ci, Cj), with the rate constants kij and kji, that do not require binding/dissociation. They represent the main part of the reactions of the model. In a general form, they can be written as: 2. equations describing transitions between the configurations by binding/dissociation of quinones: 3. reduction/oxidation of quinones: Here ki is the rate constant of the combined reaction of QH2 dissociation and Q binding at the Qi site; ko is the rate constant of the combined reaction of Q dissociation and QH2 binding at the Qo site; ke is the rate constant of electron transport reactions from Qo to Qi; x0 is the sum of forms with both the Qo and the Qi sites oxidized; Qx is the sum of the forms with the Qi sites reduced and Qo oxidized; xQ is the sum of the forms with the Qi sites oxidized and the Qo reduced; QxQ is the sum of the forms with both Qo and Qi sites reduced. The factor of 2 in equation 2b takes into account that two molecules of QH2 must be oxidized at the Qo site in order to reduce one Q at the Qi site.
Electron transport (1) proceeds much faster than binding/dissociation and can be considered to be in a quasi steady state. Each variable of the system (2) in fact represents the sum of a number of various redox states of the complex combined in accordance with the redox state of the Qi and Qo sites that determine the possibility of binding/dissociation. Thus, assuming the apparent difference in time scales between the electron transport and binding/dissociation, we consider the reduced systems (2) and (3), which implicitly include steady state solution of equations (1).
After the transition to unitless concentrations and time, for the sake of simplicity of description, we preserve the notation ke, ko, and vSDH for the unitless quantities (since they have the same meanings as the ones initially presented in equations (2) and (3).
The concentration q0 is about an order of magnitude higher than the one c0. Thus, strictly speaking, c0/q0 cannot be considered as a small parameter, however it indicates that the relative changes of the forms of the complex III are faster and it sooner reaches a quasi-equilibrium than the ubiquinone does.
In a quasi-equilibrium, equations (4) take the form: Solving the equations (6) for z0, qz, zq, and qzq, gives: Thus, eq. (7) represents a simplification of the whole system to a single equation.
The steady state solution of the system reduced to one equation (7) corresponds to the derivative equal to zero: The graph of the steady state equation (8) (taking into account eq (5b)) in two variables: concentration of the free ubiquinone q and vSDH that represents the succinate concentration, is given in Figure 1. This curve has a typical shape of a fold bifurcation. Thus, the analysis indicates that the oxidation/reduction of the ubiquinone, coupled with binding/dissociation at the Qo and Qi sites, can be considered as the main process determining fold bifurcation.