Steady-state properties of a model ternary substrate cycle: theoretical predictions

Numerous ternary substrate cycles are metabolically operative in vivo. The relative concentrations of the interconverted substrates are generally correlated with different physiological states. These cycles often include reversible and/or substrate-inhibited enzymic steps. The switch between one steady state (metabolic state) and another may be the consequence of either the effect of an exogeneous metabolite or signal, or the alteration of a cycle internal parameter. The interpretation of results obtained with currently designed experiments on substrate cycles seldom take into account the very dynamic and regulatory properties inherent in the cyclic and often autocatalytic nature of the pathway. In the present report, the various dynamic properties of a model ternary substrate cycle, bounded by moiety conservation, are investigated. Three situations with increasing complexity are considered: (i) the three enzymes are michaelian and catalyse irreversible steps; (ii) one of the enzymic steps is reversible; and (iii) one step is subjected to a destabilizing factor, i.e. inhibition by excess of substrate. The behavior(s) of the whole cycle is mainly controlled by four parameters, that is, ST, the total concentration of the substrate pool, and the three enzyme maximal velocities, VMi (i = 1,2,3). As ST (= S1 + S2 + S3) is constant, the Si steady-state concentrations (stable or not) can be represented in barycentric coordinates in a triangle (simplex). This convenient representation allows us to predict the different states of the system when one enzyme maximal activity is varied. The steady-state concentration dependencies as a function of one or several parameters may be either monostable (possibility of zero-order ultrasensitivity) or bistable (with or without reversible transitions). The physiological and experimental relevances of these observations are emphasized.