dx/dt = µ x
where x = microbial cell mass
µ = specific growth rate coefficient
This equation is acceptable for describing binary fission; the rate
of increase is proportional to the mass of organisms. However, this equation
lets the mass increase without limit. This must be false because no living
things can grow after their supply of food is exhausted. We can advance
our understanding of microbial growth by making the specific growth rate
a function of the concentration of some nutrient.
It is not simply mass that determines the growth-limiting nutrient, but rather the proportion. Something present at low concentrations can be growth-limiting if it is the first to be exhausted. Of several equations that relate specific growth rate coefficient to concentration of limiting nutrient, the Monod equation is most popular and usually fits actual data quite well:
The red curve is a plot of specific growth rate coefficient versus concentration of growth-limiting substrate when there is no inhibition (MonoD). The white line on the graph is one possibility for a substrate that inhibits growth).
Related material about diauxie
here to go to main menu
Go "with the flow to next section"