Microbial kinetics Monod model

Monod kinetics An unstructured model used to describe the correlation of substrate concentration with microbial growth kinetics. The model is based on enzymatic Michaelis-Menten kinetics ... 

A Langmuir-Hanes plot based on the Monod rate equation is presented in Figure 8.7. The Monod kinetic model can be used for microbial cell biocatalyst and is described as follows ... 

KiMM is given the subscript, MM, to remind us that it reflects Michaelis-Menten enzyme kinetics as distinguished from KiM used above to model microbial growth kinetics (see Monod cases above). Note, is the same as KE in Box 12.2 when it s value represents the reciprocal of the equilibrium constant for the binding step. 

Two continuous stirred-tank fermenters are connected in series, the first having an operational volume of 100 1 and that of the second being 50 1. The feed to the first fermenter is sterile and contains 5000 mg/1 of substrate, being delivered to the fermenter at 18 1/h. If the microbial growth can be described by the Monod kinetic model with /x, = 0.25 h l and Ks = 120 mg/l, calculate the steady-state substrate concentration in the second vessel. What would happen if the flow were from the 50 I fermenter to the 100 1 fermenter ... 

A second type of culture described by Monod kinetics is the continuous culture, in which a chemical is constantly fed into a vessel and both microbial cells and the chemical are constantly lost from the vessel at a given rate. This culture is often called a chemostat when operated under steady-state conditions. Like the batch culture, a continuous culture may be a useful model of certain environmental systems, such as lakes receiving continuous discharges of pollutants. Continuous cultures are common in industrial processes as... 

A number of publications have appeared on the dynamics of enzyme synthesis in a variety of situations. Most of the models are based on more or less sophisticated versions of the operon model of Jacob and Monod. The role of m-RNA and its stability were modeled by Terui (1972). Repressor and inducer control was treated by Knorre (1968), Imanaka et al. (1972 1973), van Dedem and Moo-Young (1973), and Suga et al. (1975). Allowance for dual control and catabolite repression was made by Toda (1976). [See also the kinetic treatment by Yagil and Yagil (1971), Imanaka and Aiba (1977), and Bajpai and Ghose (1978)]. A simple structured model was developed by Roels (1978) showing a combination of the features of the models published. More recently Toda (1981) reviewed the effects of induction and repression of enzymes in microbial cultures and their modeling. 

Other formal kinetic equations for the quantification of lag phases in microbial growth are found in the literature. A simple extension of Monod-type kinetics using the lag time as model parameter is given by Bergter and Knorre (1972) ... 

Figure 5.25. Representation of the influence of endogenous metabolism (as per Equ. 5.76 with kf) on obtaining model parameters for microbial growth with Monod kinetics using a double reciprocal plot. (From Moser and Steiner, 1975.)...

A systematic approach to unstructured modeling of microbial production has been presented by Ryu and Humphrey (1972) using a mechanism similar to that used for the derivation of Equ. 5.131. Here supplementary branching at a common intermediate was considered. Assuming that the conversion of li to both cells and product is limited by the rate of one single enzyme in the chain, and assuming that both processes follow Monod-type kinetics, the following relationship holds ... 

Figure 5.52. Conceptual representations of the interactive model, (a) is converted to Pi by an enzyme that requires S2 as a cofactor, (b) Substrates and S2 from two parallel pathways are combined by enzyme to produce a product P that is required for growth, (c) Plots of lines of constant dimensionless specific growth rate p/Prmx as a function of two dimensionless substrate concentrations for interactive models of the Megee type (cf. Equ. 5.169) with Monod kinetics (Reprinted with permission from In Microbial Population Dynamics, Bader, 1982. Copyright CRC Press, Inc., Boca Raton, FL.)...

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