A mathematical model to study short-term regulation of mitochondrial energy transduction.

A mathematical model is presented which includes the following elementary process of mitochondrial energy transduction: hydrogen supply, proton translocation by the respiratory chain, proton-driven ATP synthesis by the F0F1-ATPase, passive back-flow of protons (leak) and carrier-mediated exchange of adenine nucleotides and phosphate. For these processes empirical rate laws are used. The model is applied to calculate time-dependent states of energy transduction in isolated rat liver mitochondria. From the general agreement of the computational results with experimental data (Ogawa, S. and Lee, T.M. (1984) J. Biol. Chem. 259, 10004-10011) the following conclusions can be drawn. (1) The length of the time interval during which mitochondria are able to maintain a relatively high and constant delta pH in the absence of oxygen (anaerobiosis) is limited by the availability of intramitochondrial ATP. (2) The overshoot kinetics of delta pH which appear when reoxigenating mitochondria after a preceeding anaerobiosis might be due to a lag phase kinetics of the F0F1-ATPase. (3) In phosphorylating mitochondria the homeostasis of delta pH is brought about by a high sensitivity of the respiration rate and the rate of the F0F1-ATPase as to changes of delta pH. (4) Analysis of the mean transient times shows that the rate of ATP synthesis in State 3 is controlled to almost the same extent by the hydrogen supply, the respiratory chain, the adenine nucleotide translocator and the proton leak.