Quantification of the relative contribution of parallel pathways to signal transfer: application to cellular energy transduction.

A simple mathematical formalism designed to quantify the relative contribution of parallel pathways to signal transduction is presented and applied to the regulation of the respiration rate by ATP, ADP and Pi concentrations in response to an increase of energy demand in isolated mitochondria. Theoretical studies were performed by means of the computer model of oxidative phosphorylation developed previously. Many earlier experimental studies have shown that externally-manipulated concentrations of all three metabolites can influence the respiration rate significantly. However, the effect of changes in [ATP], [ADP] and [Pi] that actually take place during an increased energy demand have not been determined in a quantitative way. It was shown in the present paper that [ADP] is the main regulatory factor which stimulates respiration during transition from state 4 to state 3 imposed by an addition of increasing amounts of an artificial ADP-regenerating system. Changes in [ATP] and [Pi] contribute to the respiration rate increase very weakly, and only in the nearest neighbourhood of state 3. Generally, changes in [ADP] are responsible for approx. 90% of the respiration rate increase during the state 4-->state 3 transition, while the remaining approx. 10% is due to changes in [Pi] and [ATP].