There are many models of varying complexity that seek to relate specific growth rate to nutrition.  The Monod equation is one such expression.  It is particularly significant for this course because of its popularity, simplicity, and usefulness.  While an in-depth analysis would explore the implications of the mathematics, the equation's basic precepts should be recognized easily.

Microbial populations increase until nutrients are exhausted. Analysis is aided by focus on the limiting nutrient.  The Monod equation relates limiting nutrient concentration to a population's growth rate.

The expression is: 

Click for a repeat of this explanation in other words and a Java applet that lets you manipulate the coefficients.

Concepts of this expression:

• The Monod equation is empirical but fits actual data quite well.

• We can solve for continuous culture at steady state where µ = D to get: where D is the dilution rate defined as equal to the Flow/Volume. Click to see the algebra for this equation.
  

• Basically, this implies that the growth rate is primarily a function of S.  We have previously learned of different mechanisms that affect the operation and growth of a cell.
• The maximum growth rate itself is independent of S and K_s.

Further coverage:

• Prof. Bungay's material on growth  (presented in the previous week).
• Presentation on the kinetics of microbial growth courtesy of Robin L. Autenrieth at www-pipeline.tamu.edu