A mathematical model of electron transfer within the mitochondrial respiratory cytochromes

A simple mathematical model of electron flow along the mitochondrial respiratory cytochrome assembly and the transfer of electrons to molecular oxygen is presented. First, an expression for the current-voltage relationship for a biological oxygen electrode is derived, and from this the relationship between oxygen consumption rate and oxygen partial pressure is determined. An independent relationship between mitochondrial oxygen partial pressure and oxygen supply rate is then derived. By eliminating oxygen partial pressure from these two expressions, we may obtain a relationship between oxygen supply rate and oxygen consumption rate. This model is then used to investigate the effects of tissue dysoxia, uncoupling of oxidative phosphorylation, increased cellular diffusional resistance and inhomogeneities in oxygen supply on oxygen consumption. It is concluded that each of the above contribute in varying degrees to the phenomenon of "pathological oxygen supply dependency".