Growth rate, specific kinetics

As linear relationships have been found for both glucose and glutamine uptake rate as a function of the specific growth rate, the kinetic expressions proposed in Equations 4.3.3 and 4.3.5 can be considered applicable ... 

Table 3.1 shows the kinetic parameters for cell growth, rate models with or without inhibition and mass transfer coefficient calculation at various acetate concentrations in the culture media. The Monod constant value, KM, in the liquid phase depends on some parameters such as temperature, initial concentration of the carbon source, presence of trace metals, vitamin B solution, light intensity and agitation speeds. The initial acetate concentrations in the liquid phase reflected the value of the Monod constants, Kp and Kp. The average value for maximum specific growth rate (/xm) was 0.01 h. The value... 

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... 

Microbial Biotransformation. Microbial population growth and substrate utilization can be described via Monod s (35) analogy with Michaelis-Menten enzyme kinetics (36). The growth of a microbial population in an unlimiting environment is described by dN/dt = u N, where u is called the "specific growth rate and N is microbial biomass or population size. The Monod equation modifies this by recognizing that consumption of resources in a finite environment must at some point curtail the rate of increase (dN/dt) of the population ... 

Substrate-limited growth in terms of reduced availability of both the electron donor and the electron acceptor is common in wastewater of sewer systems. Based on the concept of Michaelis-Menten s kinetics for enzymatic processes, Monod (1949) formulated, in operational terms, the relationship between the actual and the maximal specific growth rate constants and the concentration of a limiting substrate [cf. Equation (2.14)] ... 

In this example, it is easy to see that, the dynamics of C is quite independent of the kinetics p, which gives a specific solution to the well known problem of the biomass growth rate ignorance in the bioprocess [66]. It is also verified that the convergence rate cannot be tuned because it depends exclusively on the value of the dilution rate. Indeed, Bastin and Dochain [6] have shown that a condition to guarantee the convergence of the observer is that the dilution rate D must be a persisting input, i.e., that there are two positive constants Cl and C2 such as, at every time t ... 

Three methods to derive a state space model for a crystallizer were discussed. The choice of a method in a specific situation depends on the crystallizer configuration, the growth rate kinetics and the variables to be controlled. 

The Kq saturation coefficient of oxygen in the Monod-type kinetic equation is an important parameter, too. Its value strongly influences the specific growth rate, especially when the value of oxygen concentration is of the same order of magnitude as or lower than the Kq value. Its effect is illustrated in Fig. 10 in the presence of a dispersed organic phase, e = 0.2. The increasing value of Kq (Kq was chosen to be equal to 0.64 x 10 0.16 x 10 and 0.016 x 10 kg m ) has a... 

The graphical significance of the constants in the Monod equation are identical to the corresponding constants in the Michaelis-Menten relationship for enzyme kinetics (see Section 5.4.4). The specific growth rate initially increases with increas-... 

It should be noted that this result is independent of the type of growth kinetics which the micro-organisms follow. If the dependence of specific growth rate on substrate concentration is described by the Monod equation, then substitution from equation 5.62 will give for the steady-state condition ... 

The shape of the performance curve for a continuous stirred-tank fermenter is dependent on the kinetic behaviour of the micro-organism used. In the case where the specific growth rate is described by the Monod kinetic equation, then the productivity versus dilution rate curve is given by equation 5.137 and has the general shape shown by the curve in Fig. 5.58. However, if the specific growth rate follows substrate inhibition kinetics and equation 5.65 is applicable then, at steady state, equation 5.131 becomes ... 

Contois, D. E. J. Gen. Microbiol. 21 (1959) 40. Kinetics of microbial growth. Relationship between population density and specific growth rate of continuous culture. 

The equality of the specific growth rate and the dilution rate of the steady-state CSTF shown in Eq. (6.30) is helpful in studying the effects of various components of the medium on the specific growth rate. By measuring the steady-state substrate concentration at various flow rates, various kinetic models can be tested and the value of the kinetic parameters can be estimated. By rearranging Eq. (6.30), a linear relationship can be obtained as follows ... 

The data from batch runs can be used to determine the kinetic parameters, even though this is not a highly recommended procedure. The specific growth rate during a batch run can be estimated by measuring the slope of the cell concentration versus time curve at the various points. The substrate concentration needs to be measured at the same points where the slope is read. Then, the plots according to Eqs. (6.35), (6.36), (6.37) can be constructed to determine the kinetic parameters. However, the parameter values obtained in this method need to be checked carefully whether they are in the reasonable range for the cells tested. 

There are two other kinetic parameters that are used in the model. The specific production rate of ethanol R,> (grams of ethanol produced per hour per gram of cells in the fermentor) depends on the specific growth rate /a. The most simple relationship is a linear one ... 

The effects of elevated lactic acid concentration on the cell cycle kinetics of hybridoma cell growth and antibody production in batch culture were studied by Kromenaker and Srienc (1994). When 33 mM lactic acid was initially present, the specific growth rate was reduced by 37% and the cell-specific antibody production rate increased by a factor of 2.6 relative to a control culture with no additional lactic acid. 

Typical kinetic profiles (hybridoma). (A) Cell concentration and viability (B) glucose consumption (GLC) and lactate production (LAC) (C) monoclonal antibody production (mAb) (D) glutamine consumption (GLN) and ammonium production (NH4+) (E) specific growth rate (px) (F) alanine (ALA) and glycine (GLY) production. Adapted from Lee (2003). Symbols correspond to the experimental data and the lines to the manual curve fitting. Vertical lines indicate the instant at which exponential growth phase ended (gx < Px.max)-... 

Table 8.1 Kinetic equations for specific hybridoma growth rates...

Andrew s kinetic model (Equation 21) (Andrews, 1968), for example, relates the specific growth rate (px) with the substrate concentration S, applying three parameters (p max, ks and k s). 

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