Monod equation, cell growth

Inhibition as a result of product formation (viz., ethanol production) is also handled by modifying the Monod-type cell growth equation ... 

The effect of substrate concentration on specific growth rate (/i) in a batch culture is related to the time and p,max the relation is known as the Monod rate equation. The cell density (pcell) increases linearly in the exponential phase. When substrate (S) is depleted, the specific growth rate (/a) decreases. The Monod equation is described in the following equation ... 

The parameters of the Monod cell growth model are needed i.e. the maximum specific growth rate and the Michaelis-Menten constant are required for a suitable rate equation. Based on the data presented in Tables 10.1 and 10.2, obtain kinetic parameters for... 

When microorganisms use an organic compound as a sole carbon source, their specific growth rate is a function of chemical concentration and can be described by the Monod kinetic equation. This equation includes a number of empirical constants that depend on the characteristics of the microbes, pH, temperature, and nutrients.54 Depending on the relationship between substrate concentration and rate of bacterial growth, the Monod equation can be reduced to forms in which the rate of degradation is zero order with substrate concentration and first order with cell concentration, or second order with concentration and cell concentration.144... 

The exponential and limiting regions of cell growth can be described by a single relation, in which /x is a function of substrate concentration, i.e., the Monod equation... 

For very high Cq the poison-free Monod equation just can t apply, for even if there is plenty enough food the cells will crowd out each other, and growth will slow down and will eventually stop. So, for very high cell concentration, we must go to product poison kinetics. 

The rate of cell growth is influenced by temperature, pH, composition of medium, rate of air supply, and other factors. In the case that all other conditions are kept constant, the specific growth rate may be affected by the concentration of a certain specific substrate (the limiting substrate). The simplest empirical expression for the effect ofthe substrate concentration on the specific growth rate is the following Monod equation, which is similar in form to the Michaelis-Menten equation for enzyme reactions ... 

In case the Monod equation holds for the rates of cell growth in the exponential growth, with decelerating and stationary phases in a uniformly mixed fermentor operated batchwise, a combination of Equations 4.2 and 4.6 gives... 

While the Monod equation is an oversimplification of the complicated mechanism of cell growth, it often adequately describes fermentation kinetics when the concentrations of those components which inhibit the cell growth are low. 

Product Concentration As cells grow they produce metabolic byproducts which can accumulate in the medium. The growth of microorganisms is usually inhibited by these products, whose effect can be added to the Monod equation as follows ... 

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. 

By analogy to Michaelis and Menten enzymatic kinetics, Monod (1949) proposed the formula shown in Equation 15 that represents the cell growth rate as a function of cell and substrate concentrations. 

Table 8.1 summarizes a set of mathematical expressions for the description of the specific growth rate during culture. Most of these formulations employ Monod-type structures for cell growth limitation by substrates (Monod, 1949), and structures for byproduct inhibition (Aiba and Shoda, 1969 see Equations 16 and 24). 

In addition to the Monod equation, two othei equations are also commonly used to describe the cell growth rate they are the Tessier equation. 

Because there is no growth during the stationary phase, it is clear that Equation (7-112) cannot be used to account for substrate consumption, nor can the rate of product formation be related to the growth rate [e.g., Equation (7-113)]. Many antibiatics, such as penicillin, are produced in the stationary phase. In this phase, the nutrient consumed for growth has become virtually exhausted and a different nutrient, called the secondary nutrients, is used for cell maintenance and to produce the desired product. Usually, the rate law for product formation during the stationary phase is similar in form to the Monod equation, that is,... 

Various models ranging from unstructured, nonse-gregated to structured, segregated are used to describe cell growth. The most common kinetic expression is the Monod equation ... 

---