Monod’s model

A kinetic model originally derived by Nyholm is distinguished from Monod s model by the fate of a hmiting substrate. Instead of immediate metabolism, the substrate in Nyholm s model is sequestered. The governing equations are ... 

General kinetic model have involved Monod s model. 

Steady-state B) is the interesting one, of course, since steady-state (A) corresponds to complete washout of cells. Stability analysis has shown that the two cannot coexist at the same holding time either (A) is stable and (B) is unstable, or (S) is stable and (A) is unstable. Moreover, since (B) is a node if it is stable, we see that Monod s model will not predict oscillations— even damped ones—about a steady state of nonzero cell concentration. Hence, in this sense, there has been no improvement over the Verhulst-Pearl model. 

Moser (Ml4) applied extensions of Monod s model to growth of mixed... 

Consider Monod s model of growth. It is often possible to arrange experimental conditions so that a single substrate does in fact limit growth. One can then proceed to test the more quantitative aspects of the model. Monod s model has been applied to two cases batch growth and continuous propagation. To fulfill the first requirement for a valid model, it should predict the results of (say) continuous propagation from batch data, if the model is to be accepted. 

Figure 15, in terms of dimensionless quantities, shows expected results of Monod s model for continuous propagation productivity P is the amount of biomass formed per unit time per unit volume of culture ... 

Fig. 15. Continuous propagation—predictions of Monod s model for steady-state values of various quantities as functions of holding time.

Fig. 16. Comparison of Monod s model with data of Herbert et al. (HIO) on growth of Aerobacter cloacae. Solid line calculated from Monod s model with /a = 0.85 hr , K = 0.0123 g/liter, C,f = 2.5 g/liter, and a = 1.89 g/g. Replotted from J. Gen. Microbiol. 14, 601-622 (1956), by permission of Cambridge University Press.

Experimental results of Herbert et al. are compared with predictions of Monod s model in Fig. 16. At long holding times, agreement of the model with experiment is good this is not the case at holding times near the critical, where there is a definite trend not predicted by the model. Thus, it appears that the maximum specific growth rate (//) is faster than that determined from batch experiments also the stoichiometric coefficient a changes as 6 approaches the critical. 

Herbert attributes part of the discrepancy to the occurrence of endogenous metabolism, not accounted for in Monod s model. In other words, cells not only convert substrate into protoplasm, but they also carry on reactions... 

The growth rate and the stoichiometric coefficients Oi used in Monod s model represent averages over the distribution of cell ages. Thus, from Eq. (131) and the definition of / , we find... 

In continuous, steady-state culture, and a,- will in general depend on the holding time, since U z) varies with holding time. Hence the model is able to account for dependence of stoichiometric coefficients and growth rates on the steady-state holding time in Monod s model, there is no dependence of these quantities on holding time. It is possible, then, for the newer model to rationalize data such as those shown in Fig. 16. 

It is of interest to note that Eqs. (170-172) reduce to Monod s model [Eqs. (41-42)] under certain conditions. These can be established by multiplying Eq. (170) by m and integrating the resulting equation over all w. One finds that Monod s equations are obtained if ... 

Waltman of the University of Iowa recently pointed out to me in a personal communication that even when Lotka-Volterra concepts are discarded entirely and Monod s model is used for all growth rates, the resulting competition equations for two predators and one prey seem to have limit cycle solutions for certain conditions of operation. Mr. Basil Baltzls has found that use of a so-called multiple saturation model for the predators, which seems to be more appropriate than Monod s model for protozoans at any rate... 

If there is Indeed a threshold density of bacteria below which protozoans like Tetrahymena do not feed, then it follows that growth and feeding of such organisms cannot be described by Monod s model of growth (69) A model that suggests itself for situations like this is... 

As pointed out above, Tetrahymena pyrlformls consistently falls to clear batches of water of bacteria, and the explanation for this may be that some of the bacteria are too small or too large to be captured by the protozoans. If this Is the case, then there is no threshold density of the bacteria, of course, so there would be little justification for using models like Equations (1) or (2). In this circumstance, what one needs to do is to divide the bacteria into sub-populations, one which is eaten by the protozoans and one or more which is (are) not eaten by them. Monod s model might be assumed for feeding of the protozoans on the subpopulation of bacteria that they can eat, and models for transfer of bacteria from one sub-population to another would be needed, also. 

For the net cell growth rate, we use Monod s model for growth and a first order rate of loss of viability ... 

Another deviation often observed is the so-called wall growth, which results in plots similar to Fig. 3.12. Topiwala and Hamer (1971) analyzed this effect of the adherence of microorganisms to glass or metal surfaces. When the part of adhered biomass that cannot wash out is denoted by x, the following modification of Monod s model results ... 

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