Model Using Weighting Factors

Our group searched for a better model but wanted to avoid adding any new coefficients. Our relationship uses exactly the same coefficients as the double Monod model and is not at all difficult to program on a computer. Growth rates under dual substrate limitation may be expressed by weighting the contributions of individual nutrient limitations:

where W(i) is the weight ascribed to nutrient i.

Weight coefficients were assigned based on the relative half-saturation values ( Ks in the Monod equation ) of the nutrients of interest in the form:

where

It is reasonable that µ is a function of how far the concentrations are removed from the relative half-saturation values. As the substrate concentrations S1 and S2 are increased, the growth rate approaches its maximum value asymptotically. This model fits actual data better than do other proposed methods of handling multiple limitations (Mankad and Bungay, 1988). This growth model is suitable for simulations of batch or of continuous culture, but changes in growth limitation are particularly interesting for continuous culture with variations in the feed stream. Be sure that you understand the graphing of the double-Monod equation before comparing it with the weighted model with the next applet.

Graph Comparing Double Monod Model with Weighted Model

The weighted model always gives a line above the corresponding line for the double -Monod model. Pay particular attention to the region near the origin where the double-Monod model fails badly while the weighted model makes sense. When one substrate reaches high concentration and poses no appreciable limitation, you should not use either the DM model or the weighted model.

You can experiment by using the Maple program twosub.ms. You can download it and try permutations of its coefficients.

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

Mankad, T.and H.R. Bungay, (1988) "Model for Microbial Growth with More than One Limiting Nutrient",Jour. Biotechnol. 7 161-166

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