9846

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.

SNAPSHOTS

  • [Snapshot]
  • [Snapshot]
  • [Snapshot]

DETAILS

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

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.









 
RELATED RESOURCES
Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2014 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+