Bistability and irreversible transitions in a simple substrate cycle

The dynamic properties of a simple substrate cycle involving two antagonist enzymes are investigated. One of these enzymes exhibits a non-linearity through inhibition by excess substrate. Depending either on the interconverted substrate pool concentration or the maximal activity of the non-inhibited enzyme, monostability, bistability and irreversible transitions may occur. A reversible bistable cycle is shown to present interesting features for regulatory purposes as it can respond to external (and/or internal) modulations in two different ways: A buffering effect by efficient stabilization of the steady-states, or, an increase in sensitivity by switching the system from one regime to the opposite one. The plausible biochemical and biological implications of irreversible transitions are discussed and emphasized in terms of "metabolic transitions".