Cell-growth kinetics equation

Because this class of functions has been used extensively to model cell growth kinetics, these functions can be modified to describe subpopulations of cells. The equations below describe a Gompertz growth model that has been modified to allow cells to oscillate between a therapeutically sensitive state (Rs) and a resistant state (Rr). The same modification can also be made to the simple growth model (28). 

Another model for cell growth is that for situations of extremely low substrate concentrations, i.e., S < In this case, the growth kinetic equation reduced to ... 

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 kinetics of cell growth was discussed in Chapter 4. By combining Equations 4.2 and 4.6, we obtain ... 

Two possible explanations can be readily put forward as to why this form of equation should be suitable for describing the dependence of microbial growth rate on feed concentration. The first of these is that the equation has the same form as the theoretically based Michaelis-Menten equation used to describe enzyme kinetics. The chemical reactions occurring inside a microbial cell are generally mediated by enzymes, and it would be reasonable to suppose that one of these reactions is for some reason slower than the others. As a result the growth kinetics of the micro-organism would be expected to reflect the kinetics of this enzyme reaction, probably modified in some way, but in essence having the form of the Michaelis-Menten equation. 

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. 

Unfortunately, the cell growth rate is limited or inhibited by a number of factors. First is the limitation created by the substrate S or some other nutrient. The Monad kinetic model is typically used to represent the behavior of such biochemical systems according to the following equation ... 

To predict kinetic behavior it is necessary to know the change of the state variables over time. Thus, it is necessary to determine the characteristic rates of the system under transformation. The instantaneous cell growth rate, for example, is defined in Equation 1. 

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. 

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 ... 

Aiba, Moritz, Someya, and Haung (1969) also recognized that a favorable contact in the cultivation between cells and n-alkane droplets seemed indispensable to produce a normal pattern of yeast growth. They studied yeast growth kinetics in a fermenter, coupled with an empirical correlation between the interfadal area per unit volume of liquid and the operation condition, and obtained the following equation. 

The overall microbial growth rate rc can be quantified in terms of the specific growth rate p (1/s) and the cell concentration [C]. The specific growth rate itself can be predicted by the same form of kinetic equation as the Michaelis-Menten equation for enzyme-catalyzed reactions,... 

Strictly considered, the Walker plot applies to reactions in which only substrate is consumed the growth of cells is not anticipated and there is no other reaction. This linearization starts from the enzyme kinetic equation... 

Obviously, the growth rate constant will formally become dependent on biomass concentration in case of substrate limitation at high cell concentrations. This fact is of great significance in the area of population dynamics. Using Equ. 5.63 for the calculation of cell mass as a function of time, a kinetic equation can be derived... 

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