Diauxic Growth of Bacteria on Two Substrates

This Demonstration shows the effect of initial substrate concentrations and initial key enzyme concentrations on the cell growth dynamics in batch cultures. Vary the initial concentrations of the two substrates and to see if and how the cell growth and substrate consumption dynamics respond. More subtly, vary the initial concentrations (gram per gram cell mass dry weight) of two hypothetical key enzymes and to simulate the effects of preculturing the inoculum in one or the other of two available substrates.
A more interesting activity on this interactive simulation is to vary the maximum specific growth rates and on the two individual substrates and observe how these values affect the order in which these substrates are consumed sequentially. Varying the Monod constants and (also known as saturation constants) has a more subtle effect on the sharpness of the transition to diauxic lag phase or the stationary phase.


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


Vast numbers of experimental reports show a sequential utilization of two available substrates by many different species of bacteria in a typical "diauxic" growth phenomenon. The substrate utilized first is the one that supports a faster growth rate ). These typical experimental observations have been predicted in this numerical simulation by using the cybernetic model equations developed by Kompala et al. (1984) and modified in Kompala et al. (1986) (see below for complete citation).
The cybernetic modeling approach approximates the unknown details of genetic regulatory mechanisms of enzyme repression/induction and enzyme inhibition/activation by two simple "cybernetic" variables, which are determined by optimization of instantaneous cell growth rate. More details on this modeling philosophy and its experimental validation may be found in
[1] D. S. Kompala, D. Ramkrishna, N.B. Jansen, and G. T. Tsao, "Investigation of Bacterial Growth on Mixed Substrates. Experimental Evaluation of Cybernetic Models," Biotechnology and Bioengineering, 28, 1986 pp. 1044–1055.
[2] D. S. Kompala, D. Ramkrishna, and G. T. Tsao, "Cybernetic Modeling of Microbial Growth on Multiple Substrates," Biotechnology and Bioengineering, 26, 1984 pp. 1272–1281.
    • 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+