Growth equations, cell

There is no cell removal from the batch vessel and the cell propagation rate is proportional to specific growth rate, /jl (h 1), using the differential growth equation the cell concentration with respect to the time is ... 

The growth of cells of mass m is indicated by function r(m, S), in Equation 93. It is a cell growth rate dependent on the cell mass and also on the limiting substrate concentration. If a cell increases its mass, as a consequence it leaves the class of the cells of mass m. 

Promotion action of additives on biological growth in considered kinetic theory is taken into account by introduction into equation (22) in an explicit form of dependence of coefficients of birth b and chain propagation p on promoter concentration. This dependence may be approximated by equation of Mono type for organisms or Michaelis-Menten for fermentative catalysis. Equation (22) for x1=x2= k wi= 0 and f=2 is solved in relation to Ci(t). Theoretical curves qualitatively correctly (Figure 6) reflects acceleration of growth of cells of mouse embryo Balb/c 3T3 [22] with increase of serum concentration containing stimulators. 

Equation 2.32 is often called a growth equation (to put this into the form generally found in the literature, L, should be replaced by LP, and by P — oil, changes based on irreversible thermodynamics that we will introduce in Chapter 3, Section 3.5). If water also evaporates from the cell, such as for certain cells in leaves, we should include such water movement in Equation 2.32. 

At the end of Chapter 1 (Section 1.5C) we indicated that cell enlargement requires yielding of the cell wall, an irreversible or plastic process that occurs when the internal hydrostatic pressure exceeds some critical or threshold value, />J,u.esh0id- This leads to another growth equation of the following form ... 

The growth rate for cells in a bioreactor can follow a variety of growth equations. Monod kinetics is represented by part (1) of Problem 8.3. A substrate-inhibition growth rate is given by (see Shuler, 1988) ... 

So that according to von Bertalanffy s equation, cell growth should follow the law... 

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... 

The consumption coefficient (f) can be numerically estimated from experimental data on growth, as shown in Fig. 5.19. The concept of a critical cell mass concentration is used, and it is determined by numerical methods from the plot of Fig. 5.19. The basic concept of the Kono approach is that reaction order changes at x nt following the general growth equation... 

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

ILLUSTRATIVE EXAMPLE 19.5 For an enzyme catalyzed reaction, calculate the time required to achieve a given conversion for a reactor operating at ambient temperature for a microbial reaction, calculate the time required to double the concentration of cells discuss the Michaelis-Menten equation, and the rate equation for growth of cells. Pertinent information is provided below. 

For cells in the stalionan phase, where there is no growth in cell concentration. ceil maintenance and product formation tire the only reactions to consume the secondary substrate. Under these conditions the substrate balance. Equation (9-76), reduces to... 

The following conditions should be noted for Equation (13) (a) molecular formulae are used to aid the subsequent material and energy balances (b) any target protein (e.g. IFN-y) is combined with the biomass which is expressed by a C-molar formula as customarily utilised for microbial biomass (see the Chapter by Duboc et al. in this Volume and also Reference [20]) and (c) the stoichiometric coefficient of the cell mass is set at unity and so the enthalpy change of the growth reaction now is based on unit number of C-molar biomass [105], It has been shown from experimentation (see Figure 27) that there is a one-to-one monotonic relationship between the metabolic flux (see Equation (7)) and the stoichiometry of the growth equation (Equation (13)). This can be expressed by ... 

It means that the metabolic activity of the cell determines the stoichiometry of the growth equation and a particular set of stoichiometric coefficients for this equation corresponds to a value of the metabolic activity for the same amount of viable cell mass. Thus, for Equation (13), the growth reaction is characterised by its set of stoichiometric coefficients [105], that is. 

A bacterium is grown aerobically with glucose as sole source of carbon and ammonium ions as nitrogen source. Experimental analysis shows that six moles of glucose are utilised for each mole of biomass produced. Write the reaction equation for growth if the elemental composition of the cells is CHi,666 CW Nojd. 

The requirement for oxygen and carbon source for cell biosynthesis are calculated using nitrogen-limited mass balance equations for growth during exopolysaccharide production 01 res (nitrogen-limited cultures). These balances are derived from experimentally determined values of ... 

Equation (3.14.2.9) contributes to the postulated model which is induced by an inhibition factor for the population growth rate. Assuming that the inhibition is second-order with respect to cell dry weight (x2), then the equation becomes 19... 

Growth-dependence of microbial cells on CO was proposed by equation of Andrew, that substrate inhibition was included as 26... 

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