Theoretical study of oscillatory and resonance phenomena in an open system with induction of enzyme by substrate

A simple mathematical model of an open metabolic system is constructed in which the metabolism of a substrate is enhanced by induction of the catalyzing enzyme. It is demonstrated that the steady-state in such a system may be approached by damped oscillations of substrate and enzyme levels. If the input rate of substrate into the system has periodic fluctuations, the phenomenon of resonance is observed. Numerical analysis reveals the non-linear character of the resonance.