A Thermodynamically‐Constrained Mechanistic Mathematical Model for the Catalytic Action of Mitochondrial Cytochrome c Oxidase

Cytochrome c oxidase (CcO) is the terminal electron acceptor in the mitochondrial electron transport chain. It catalyzes the exothermic reduction of O 2 to H 2 O by utilizing electrons from cytochrome c, and hence plays a crucial role in ATP production. Although details on the enzyme structure and redox centers, which participate in O 2 reduction, are known over past several decades, there still remains a considerable ambiguity on its mechanism of action. Several anomalies such as the number of sequential electrons donated to O 2 in each catalytic step, the sites of proton pumping, protonation and H 2 O releasing steps in the catalytic scheme are not clearly understood. Although some mathematical models exist on the catalytic action of CcO, they are phenomenological and cannot accurately describe the recently available kinetic data on the enzyme's catalytic action. These kinetic data characterize the CcO catalytic action in isolated liver mitochondria as a function of the electrical and proton gradients (i.e. proton motive force; energy state) across the inner mitochondrial membrane (IMM), cytochrome c redox fraction, O 2 , and pH. In this work, we developed a thermodynamically‐constrained mechanistic mathematical model for the catalytic action of CcO based on these recent kinetic data. The model considers a minimal number of redox centers on the CcO and suitably couples electron transfer and proton pumping driven by the IMM proton motive force. Some of the model parameters (i.e. reaction rate constants) of the derived steady‐state flux expression are fixed based on thermodynamic constraints utilizing equilibrium constants of the individual redox reaction steps, and some of the rate constants are fixed based on existing knowledge from the literature. The remaining unknown model parameters are estimated based on fittings of the model to the recent kinetic data on the CcO catalytic action described above. This minimal model is able to fit very well all the available data on the CcO kinetics under diverse experimental conditions. The model predictions show that (1) the apparent K m of O 2 varies considerably and increases from fully reduced cytochrome c to fully oxidized cytochrome c depending on pH and the energy state of the mitochondria; (2) the intermediate enzyme states depend on pH and cytochrome c redox fraction, and play a central role in coupling the mitochondrial respiration to the energy state; and (3) the enzyme resides mainly in the O 2 bound form under uncoupled mitochondria conditions, which is altered as the mitochondria become hyperpolarized leading to accumulation of other intermediate enzyme states that lead to decreased turnover number under alkaline conditions. The developed model is mechanistic and suitable to be integrated into the mitochondrial bioenergetics models to understand its role in controlling oxidative phosphorylation in normal and disease conditions such as ischemia‐reperfusion injury. Support or Funding Information P01‐GM066730