Growth relationship between substrate

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... 

It reflects a part with increasing growth, saturation, and inhibition similarly as the classical PI curve. The Monod equations are nowadays motivated by an enzymatic substrate uptake (Michaehs and Men ten, 1913 (2013)) step followed by a linear relationship between substrate uptake and growth (Pirt, 1965). In contrast, photosynthetic activity is typically understood as a sequence of a transport step, being light absorbance in the antennas, followed by a limiting bottleneck in the late enzymatic steps... 

Figure 2. Relationship between substrate utilization and growth...

The extent to which the yield of metabolite can be improved is indicated by the difference between the theoretical and observed yields. The latter must, of course, be corrected for substrates requirements of growth and maintenance. Clearly, the influence of the P/O quotient on the theoretical yield will depend on the relationship between energy and metabolite synthesis. Three classes of metabolite can be distinguished in this respect... 

From this perspective it would be interesting to discover if there is a relationship between the substrate used and the concentration of free CoA under conditions of unlimited growth. If there is, depending on the source of carbon and energy used and the K value of the 3-ketothiolase for CoASH, cell multiplication and poly(3HB) accumulation can occur simultaneously [60,61]. If this enzyme is not involved, poly(3HB) [29] and other polyesters [28,29] can also be synthesized during growth. 

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)] ... 

The relationship between i. and S as depicted in Figure 2.7 is relevant because it quantifies the importance of a substrate in terms of its concentration on the growth rate. As seen from Equation (2.16), X= 1/2 imax for S=Ks. For this reason, Ks is also named the half saturation constant. Equation (2.16) and the corresponding curves shown in Figure 2.7 are called the Monod expression and Monod curve, respectively. 

Wastewater in sewers includes different and varying species of heterotrophic microorganisms. A simple relationship between biomass growth and substrate utilization is needed. Several studies performed with different types of wastewater and sewer solids have shown that a simple description is possible and acceptable (Bjerre et al., 1995 Vollertsen and Hvitved-Jacobsen, 1999). 

Eq. (6.22) can be integrated if we know the relationship between Cs and Cx. It has been observed frequently that the amount of cell mass produced is proportional to the amount of a limiting substrate consumed. The growth yield (Yx/S) is defined as... 

Later, it was observed that substrate to cell yield factors (YX/s) could vary as a function of specific growth rate. Pirt (1966) described a linear relationship between growth and substrate consumption, as well as the statement of a term for cell maintenance (Equation 26). 

Gaertner and Dhurjati (1993) used the initial concentration of base medium (B) in an attempt to handle the absence of information concerning the limiting substrate (Equation 45). The base medium corresponded to a DMEM formulation without GLC, GLN, NaCl, and NaHCOj Different concentrations of this base were tested. The solution showed a hyperbolic relationship between the specific growth rate and the basal medium concentration, independently of the effective limiting component. 

Similar to what was shown for growth, some models establish a linear relationship between the specific death rate (kj) and an autoinhibitory product synthesis (Lee et al., 1995). This autoinhibitory product is represented by the expression Xv/D, where Xv is a viable cells concentration, measured in terms of cell number per volume, and D is the specific feed rate that plays the part of substrate supply to the culture. By setting kj/px as a function of Xt/D (where Xt is a total cell concentration) it is possible to build up a more robust model that can fit a larger amount of experimental data (Equation 56) (Zeng et al., 1998). 

To solve Equation 93 it is necessary to know the characteristic functions of the cellular physiology, that is, the growth rate r(m, S), the cellular division rate T(m, S), and the cell mass partition function p(m, m, S). Since these functions are substrate concentration- dependent, the substrate consumption rate must also be defined. These substrate concentration variations are calculated using the yield coefficient Yx/s, that establishes a relationship between the growth rates and the substrate consumption rate. The consumption rate is indicated by Equation 94. 

A similar material balance on the limiting substrate requires knowledge of the relationship between cell growth and substrate utilization. The simplest relationship would assume that a fixed amount of cells could be produced from a given amount of substrate, or the yield of biomass on substrate ... 

Figure 8.1 The relationship between bacterial growth efficiency and the C N ratio of the dissolved organic matter (DOM) substrate (C Ns).The curved indicate zero flux for a given bacterial C N (C Nb).Taken from Kirchman (2000).

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