258
Chapter 7
In the model of Sonnleitner and Kappeli (1986) the verbal model of Fig. 7.7 is applied with two reactions:
(1) oxidative glucose metabolism and (2) fermentative glucose metabolism. In the model two substrates,
glucose (5) and oxygen (02), and two metabolic products, ethanol (P) and carbon dioxide (C02) are
considered. In the original model formulation ethanol may also serve as a substrate when glucose is not
present, but here we will consider a simplified version of the model where ethanol uptake is not considered.
The stoichiometry for the two reactions considered in the model is:
X. Oxidative glucose metabolism:
y }X + 0 nCO2 - S - a n0 2
= 0
(0
2. Fermentative glucose metabolism:
y 2X + 0 2XCO2 + fi22P - S -
0
(2)
The nitrogen source (ammonia) and water are not included in the model.
When glucose is consumed solely by respiratory metabolism Eq. (1) is identical with the black box
description of the cell growth, and all stoichiometric coefficients can therefore be interpreted as the yield
coefficient F„. These stoichiometric coefficients can therefore easily be experimentally determined. At
anaerobic conditions the metabolism is exclusively fermentative, and Eq. (2) therefore represents a black
box description of cell growth at these conditions. The stoichiometric coefficients can therefore be found
as shown in Section 3.3. Fermentative metabolism has a much lower ATP yield than respiratory
metabolism, and the yield of biomass in the fermentative metabolism is therefore much lower than in the
respiratory metabolism.
In order to describe biomass growth when both (1) and (2) contribute to growth the rates of the two
reactions has to be specified. In order to do this Sonnleitner and Kappeli first specified the total glucose
uptake rate (equal to the breadth of the arrow in Fig. 7.7) as:
-r.= k.
s + K .
(3)
and the maximum possible rate of respiration - or the maximum specific oxygen uptake rate (equal to the
opening of the circle in Fig. 7.7) as:
= k.
s+K„
(4)
The maximum possible rate of respiration is a function of the dissolved oxygen concentration s0, but
normally
s0
is much larger than
K0
and the maximum rate of respiration becomes equal to
k0.
According
to the verbal model of Fig. 7.7 the rate of the respiratory metabolism is the minimum of either the
glucose uptake rate or the maximum possible rate of respiration,
i.e.
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