DM vs Weighted Model for Inhibitory Substrate
The double-Monod model does not match actual data as well as does our weighted model, but there may be complications when one of the substrates becomes inhibitory at higher concentrations.
When using the DM approach, the Monod equation for
the non-inhibitory nutrient is multiplied by the Andrews equation for the inhibitory nutrient. This is the red line in the next figure. When using the weighting concept, each term is weighted by the ratio of its concentration to Ks. The weighted model is shown by the while line in the figure. As before, our equation always gives a value of µ
greater than that from the DM model. However, our equation becomes hopelessly inaccurate at high
concentrations of the toxic nutrient. The weighting is based on the ratio to Ks, but this is
incorrect for toxic concentrations.
The figure was drawn by the Maple program twosub.ms
You can experiment with the coefficients Ks, Ki, and mumax by downloading the Maple file
twosub.ms. Remember to position the cursor at the top when in Maple and
keep hitting "Enter" (return) to process each line. Repeat after you have changed a
coefficient.
Our weighting according to Ks makes the effect of the toxic ingredient drop out at high
concentrations while, in fact, it should dominate. The problem becomes that of retaining the
superiority of our model at low concentrations while correcting for high concentrations of the
toxic nutrient. We have no interest in equations that introduce new coefficients.