Inhibition of Enzyme Reactions in Continuous Stirred-Tank Reactor and Batch Reactor

Inhibitors decrease the rates that enzymes bind to substrates and convert them to products. Three types of inhibition (competitive, uncompetitive, noncompetitive/mixed) and reaction with no inhibitor are compared for an enzyme reaction that obeys Michaelis–Menten kinetics. Substrate concentration is plotted versus time for a continuous stirred-tank reactor (CSTR) and for a batch reactor. Change the inhibitor concentration, which remains constant during reaction, with a slider. Set the substrate feed concentration with a slider. Select "inhibition type" to see the reaction steps, pathways, and a brief description of the type of inhibition. In competitive inhibition, the inhibitor attacks the enzyme to form an enzyme-inhibitor complex ; adding more substrate minimizes the inhibitor effect. In uncompetitive inhibition, the inhibitor attacks the enzyme-substrate complex ; adding more substrate does not overcome this type of inhibition since the inhibitor does not compete with the substrate for the enzyme sites. In noncompetitive inhibition, the inhibitor attacks the enzyme to form an enzyme-inhibitor complex or it attacks the enzyme-substrate complex to form an enzyme-substrate-inhibitor complex .
  • Contributed by: Rachael L. Baumann
  • Additional contributions by: John L. Falconer and Nick Bongiardina
  • (University of Colorado Boulder, Department of Chemical and Biological Engineering)


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


For a continuous-stirred tank reactor (CSTR) the material balance is written in the form of a differential equation:
for a batch reactor the material balance is:
where is substrate concentration (), is the feed substrate concentration (), is the rate of substrate consumption for various types of inhibition (), is residence time (min), and is time (min).
Rate laws are different for each type of inhibition:
competitive: ,
uncompetitive: ,
noncompetitive (mixed): ,
no inhibitor: ,
where is inhibitor concentration (), and are inhibitor and Michaelis constants (), and is the rate of reaction ().
[1] H. S. Fogler, Essentials of Chemical Reaction Engineering, Boston: Pearson Education, 2011 pp. 349–370.
    • 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.

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 © 2018 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+