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.

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Reference
[1] E. Hairer, S. P. Norsett, and G. Wanner, Solving Ordinary Differential Equations I: Nonstiff Problems, 2nd ed., New York: Springer–Verlag, 1993.
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