Enzyme Inhibition with Time Delay

Consider the following consecutive enzyme reactions:

,

where is a substrate supply maintained at constant value, and are reaction rate constants, and molecules of inhibit the reaction step with . Assume the inhibitor molecules must travel to the position of the regulatory enzyme by diffusion or active transport causing a time delay ; the equations describing the system are

,

,

,

,

,

where and denote concentrations, is time, and isa positive constant. The system has an equilibrium when and .
This Demonstration investigates solutions of the system starting at a small perturbation away from the equilibrium.