Control of energy transformation of mitochondria. Analysis by a quantitative model

A mathematical model of control of energy transformation in mitochondria is presented. The considered processes are: the proton translocation by the respiratory chain, the production of ATP by ATPase, the translocation of adenine nucleotides and of phosphate by their translocators, and a passive backflow of protons through the mitochondrial membrane. The mathematical equations expressing the steady-state kinetics of these processes and the relations between them were derived on the basis of current experimental data. The model predicts fairly well the values of the proton electrochemical gradient, of the ATP/ADP ratios within and outside mitochondria and of the distribution of phosphate between both compartments in different metabolic states of mitochondria. From the general agreement of model computations with experimental data, it is suggested that the electron flux through the respiratory chain is immediately controlled by the energy back-pressure of the proton electrochemical gradient, that the ATPase reaction is near equilibrium in phosphorylating mitochondria but that the adenine nucleotide exchange across the mitochondrial membrane requires some loss of energy. The latter is caused by an inhibition of the translocator by ATP from the outer side or by ADP from the inner side depending on the actual ATP/ADP in both compartments. It explains that no fixed relation exists between the rate of respiration and the phosphorylation state of extramitochondrial adenine nucleotides. The relation is modified by the concentration of phosphate and by intramitochondrial energy utilization.