Modeling of oscillatory dynamics of a simple enzyme-diffusion system with hysteresis. The case of lumped permeabilities

We study the oscillatory dynamics of an enzyme-diffusion system with produc t inhibition of substrate flux. A lumped model is considered in which the d iffusion medium is a thin membrane whose permeabilities to substrate and pr oduct undergo discrete transitions in response to product concentration, wi th hysteresis. Assuming piecewise constant permeabilities and linear reacti on kinetics, we derive analytical criteria for single steady state, double steady state, and oscillatory behavior as a function of system parameters. System behavior is pulsatile in the oscillatory regime. Analytical equation s for pulse widths and interpulse intervals are presented, along with numer ical calculations that confirm the validity of these equations. This system is similar but not completely analogous to chemical oscillators based on b istability/feedback mechanisms. (C) 1999 American Institute of Physics. [S0 021-9606(99)50704-6].