## The Effect Of Growth Rate On Growth Stoichiometry

Maintenance Energy Concept

In his pioneering work, Monod (23) found that in exponential growth the amount of biomass formed increased in proportion to the amount of substrate consumed. This led to the definition of growth yield YDX [amount of biomass produced per amount of electron donor (substrate) consumed]. We have seen that YDX usually determines the complete growth stoichiometry. With the introduction of the che-mostat in the early 1950s, microbial growth could be studied at a range of growth rates, and it became clear that Ydx decreased at lower growth rates i, as shown in Figure 3 (24). This phenomenon was explained by two different concepts (24-26):

• Endogenous respiration or microbial decay, determined by the parameter kd

• Electron donor (substrate) requirements for maintenance, determined by the parameter mD

The basic idea is, however, similar in recognizing that a microorganism is a complex structure where the polymers (proteins, etc.) are subject to slow thermal denaturation

Microbial growth Biomass yield is function of growth rate ^

m ydx

m ydx

Maintenance concept mD Decay concept k kd - mn ydx

### Figure 3. Dependence of YDX on growth rate i.

and where there are numerous small leaks associated with the many transmembrane gradients (e.g., Na+ leaking into the microorganism). These leaking substances must be pumped out, and the degraded polymers must be rebuilt at the expense of Gibbs energy. This results in a small, but finite, need of Gibbs energy to maintain the biomass structure and the transmembrane gradients (maintenance Gibbs energy). In the concept of endogeneous respiration or microbial decay, this energy is produced by catabolism of biomass itself. In the concept of maintenance this energy is produced by catabolism of a part of the substrate (electron donor).

Mathematically, the dependence of YDX on growth rate l is described by equation 1a and shown in Figure 3.

This equation contains two model parameters, Y^X and mD, where mD is the rate of consumption of electron donor (substrate) that is catabolized to generate the necessary Gibbs energy flow for maintenance in C-mol electron donor per C-mol biomass per hour. Y^X is the maximal biomass yield. Figure 3 shows that YDX, using equation 1a, decreases with decreasing growth rate. Clearly, at higher growth rates YDX comes close to Y^X. Using typical values for mD it can be shown that only fori < 0.01 to 0.05 h~\ Ydx starts dropping significantly below YJ5X. This means that in exponential growth, as occurs in batch fermentation where i is high, the stoichiometry is properly covered by YSX. However, in many industrial-fed batch-production processes, maintenance is extremely important due to the low growth rates applied. For example, in penicillin fermentation i ^ 0.01 h_1 and about 70% of all consumed glucose is spent for maintenance (27). Similarly, in waste-water-treatment processes, where low growth rates are also applied, the maintenance effects are very relevant. However, in this area one often uses the biomass decay coefficient kd. This coefficient is however related to mD according to kd = mD YSX. In general, it can be shown that all biomass yields, YiX as defined in Figure 2a, decrease with decreasing growth rate i.

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