Computational Analysis of Hysteresis and Bistability in the Mitochondrial Respiratory Chain

Quantitative analysis of bistability in operation of the respiratory chain was performed with the help a computational mechanistic model developed by us earlier. This study included numerical solving of a system of algebraic equations according to steady states in a system of differential equations comprising the computational model and analysis of a wide spectrum of steady-state solutions in the model. Detailed quantitative analysis of the mechanisms of appearance of hysteresis in steady-state characteristics that accords with bistability and conditions of availability of bistability in the entire respiratory chain during oxidation of NADH, succinate and NADH+succinate was carried out. It was shown that although hysteresis and bistability in respiratory chain operation during oxidation of NADH and succinate has the same kinetic mechanism, namely an apparent substrate inhibition of $\mathrm{QH}_2$ oxidation at the $\mathrm{Qo}$-site of Complex III, conditions of bistability arising in respiratory chain fueled by succinate alone differ from those during oxidation of NADH or NADH + succinate because of a different $\mathrm{QH}_2$-dependence of the $\mathrm{QH}_2$ generation rate by Complex II and Complex I. The most important factors which affect occurrence of bistability in the respiratory chain during oxidation of NADH and NADH + succinate are the rates of NADH reduction in the matrix and the total concentration of Complex I $\mathrm{[CI]}$ and ubiquinone $\mathrm{[Q]}_{tot}$ in the inner membrane. A high rate of NADH reduction and a high ratio $\mathrm{[Cl]}/\mathrm{[Q]}_{tot}$ are condition that would favorable for hysteresis and bistability. The mechanism of a drastic increase in ROS production due to bistable switches in the respiratory chain during hypoxia-reoxygenation suggested earlier by Selivanov and colleagues was analyzed. A computational simulation of hypoxia-reoxygentaion under condition of existence of bistability shows a considerable increase in the rate of ROS production if hypoxia induces a switch of the respiratory chain to the reduced steady state. However, no changes occur in the ROS production rate during reoxygenation following hypoxia compared to the initial state if the membrane potential drops during hypoxia keeping a high rate of respiration and oxidized steady state of the respiratory chain. This implies that additional mechanisms of a considerable increase in ROS production during hypoxia-reoxygentaion which initiate ROS-related cellular hypoxia-reoxygenation injury should be.