Double Monod Model
It is more general to assume that the growth rate can be affected simultaneously by more than one substrate. A "Double Monod" model was initially proposed by McGee et.al., (1972).
Mathematically,
Bader's (1978, 1982) analysis of this model points out its narrow range of utility.
Graph of Double Monod Model
Experiments
- Move each slider to its far right position. Each nutrient is now near the same concentrations shown for the cases where the other is in excess. This is where the double-Monod model works fairly well.
- Move the slider bars to get roughly 0.5 on each. Now each is at half the concentration for the cases with excess. Note that at high concentrations, the red line approaches the other lines. However, at low concentrations the red line is far below the others. This is the range where the double-Monod model is poor.
- Try permutations of the slider bar settings. You will note that when either is set for a low concentrations the red line gets very close to the abscissa.
The Double-Monod model is widely used and is easy to use in computer programs.
However, it can be reduced to absurdity if extended to several potentially limiting nutrients.
The half-saturation coefficients were selected with slightly different values such that the blue and green lines were separated. You could observe what happens by changing them in the Maple program referenced below.
Bader, F.G.,(1978) "Analysis of Double Substrate Limited Growth", Biotechnol. Bioeng. 20:
183-202
Bader, F.G., (1982) "Kinetics of Double Substrate Limited Growth" in Microbial Population
Dynamics, ed. M.J. Bazin, CRC Press, 1-32
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