Monod model

Biomass Production. Biomass is usually measured by dry weight of viable cells per unit volume X. We bypass the sometimes tricky problems associated with this measurement except to say that it is the province of the microbiologist and usually involves plate cultures and filtration followed by drying. Suppose there is one limiting nutrient S, and that all other nutrients are available in excess. Then the Monod model for growth is... 

Fig. 6.10 The change of the concentrations of cells and substrate as a function of the residence time. Productivity is equal to the slope of the straight line OAB. The curve is drawn by using the Monod model with, jumax = 0.935 hr 1, Ks = 0.71 g/L, Yx/S= 0.6, and Cs.= 10 g/L.

Figure 6.20 shows the effect of bleeding ratio on the cell productivity for the Monod model. As j3 is reduced from 1 (no recycling) to 0.5, the cell productivity is doubled. 

As a result, this model can also predict the change of the average cell size with respect to time, which is not possible with the Monod model. Eqs. (6.73), (6.78), (6.79), and (6.80) can be expressed with the concentrations in terms of mass per unit culture volume as... 

Compare your simulation result with Figure 14 of the paper by Ramkrishna et al. (1967). If you showed the change of the cell concentrations in g dry weight/liter, the shape of the curves are quite different from those in the paper. What are the differences Explain. Do the parameter values predict realistic growth curves What new features can this model predict which the Monod model cannot ... 

The equations describing increase in cell density [Eqs. (8.3)-(8.8)] so far do not contain any information about the nature and concentration of any substrate such as the C-source. As the specific growth rate /i tends to depend on quality and amount of substrate, however, we require a growth model which provides the function /i = jU([S]). The most widely used growth model is the Monod model (Monod, 1950) which assumes that only one substrate limits cell growth and proliferation. The corresponding equation [Eq. (8.9), in which /imax is the maximum specific growth rate [h-1]] reads very similarly to the Michaelis-Menten equation. 

Figure 8.4 presents simulations of the Monod model with different sets of parameters. As a general rule, whenever the limiting substrate is in excess (S > > ks), specific cell growth takes the maximum value (Px,max)> and becomes independent of substrate. 

Sommer, U. (1991). A comparison of the Droop and Monod models of nutrient Hmited growth applied to natural populations of phytoplankton. Funct. Ecol. 5, 535—544. 

Analysis of the data for fundamental kinetic information was based on the Monod model. This model has been used by many successfully to describe the kinetics of biological waste treatment systems (26). The fundamental equation of this model is ... 

With fight metal cations it is valid to use the yield constant (Yo), maximum specific growth rate (km), specific decay rate (ka), and half maximum velocity constant (kg), as defined for the Monod model as the kinetic parameters to categorize toxicity data. It is suggested that this procedure be applied to all substances. 

From mass balances and the kinetics Monod model, the reactor model is given by. 

This type of rate expression is often used in models for water treatment, and many environmental factors can be included (the effect of, e.g., phosphate, ammonia, volatile fatty acids, etc.). The correlation between parameters in such complicated models is, however, severe, and very often a simple Monod model (7-92) with only one limiting substrate is sufficient. 

The relation between growth rate and substrate concentration can be represented by the Monod model ... 

For many of the drugs of interest, action occurs presumably only during some fraction of the cell mitotic cycle. Most often this is considered to be the DNA production or S-phase of the total Gi-S-G2-M cycle. A useful model, therefore, should at least be able to incorporate this type of information—e.g., the structured models of Tsuchiya, Fredrickson, and Aris (3). This means that simple gross descriptions, such as Michaelis-Menten-Monod models are not sufficient, and some attention must be paid to the cells during growth. We assume here for a first approximation that a single cell age or maturation variable is sufficient. 

Modifications to Model - The following three major modifications to the Jacob-Monod model occurred as the system was subjected to further analysis ... 

Table 3 lists the kinetic rate expressions for each of the hydrolysis and fermentation reaction rates shown in Fig. 5 and in the mass balance equations of Tables 1 and 2. Each of the reaction rates were found to fit the data through trial and error, starting with the simplest model. For the hydrolysis reaction rates (rs,arch and / maltose), the simplest form was the Michaelis-Menten model without inhibition. For all other reaction rates which described fermentation kinetics, the simplest form was the Monod model without inhibition. More descriptive models were found in the literature and tested one by one until the set of kinetic rate equations with the best fit to the experimental data were determined. This was completed with the hydrolysis datasets first, then the complete SSF datasets. 

The kinetics employed in the Monod model, however, lead to some interesting behavior. For low flow rate D —> 0, and one obtains the expected result that nearly... 

Figure 4.11 Dependence of S, C and (CD) on continuous culture dilution rate according to the Monod model for /im = 1 h , = 0.2 g/1, Y = 0.5. (From J.E. Bailey and D.F. Ollis,...

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