Metabolic oscillations in biochemical systems controlled by covalent enzyme modification

We analyze the conditions under which sustained oscillations develop in a biochemical system regulated autocatalytically by reversible, covalent enzyme modification. The analysis applies, for example, to the situation where adenylate cyclase (or guanylate cyclase) is activated through phosphorylation by a cAMP (or cGMP)-dependent protein kinase. The model then provides a non-allosteric mechanism for the periodic generation of cAMP or cGMP pulses. For certain parameter values close to those that produce oscillations, the system is excitable since it can amplify in a pulsatory manner suprathreshold perturbations. The results on excitable and oscillatory behavior are discussed in relation with the mechanism of cAMP relay and oscillation in the slime mold Dictyostelium discoideum.