Modeling of Growth Kinetics
259
v,
= min
r
i7, max
(5)
Here the maximum possible rate of respiration is scaled with the stoichiometric coefficient for oxygen in
eq. (1) to give the right comparison of the rates. Thus, at low glucose uptake rate, the rate of the
oxidative metabolism is determined by the glucose uptake rate, whereas at high glucose uptake rate, it is
determined by the maximum possible rate of respiration. If the glucose uptake rate is larger than
romaJQ-]2
the excess glucose will be metabolized by the fermentative metabolism given by eq. (2),
i.e.
v
fir
r
1
r
; |
-rs\
>
a \2
\
a n
(
6
)
Clearly reaction (2) acts as overflow reaction for excess glucose, and it is not active if rs<rümix/a ,i.
Biomass is formed by both (1) and (2), and the specific growth rate is:
V = / tvres
+y2v/a,
Hereby the yield coefficient for biomass on glucose becomes:
(7)
(8)
At low glucose uptake rate where the metabolism is purely respiratory the yield coefficient is Yh whereas
with mixed metabolism (high specific glucose uptake rates) the yield coefficient decreases. In Baker’s
yeast production where the yield of biomass on glucose has to be maximized it is obviously desirable to
reduce fermentative metabolism by controlling the glucose uptake rate below the critical value (given by
r
/a.,'i
With the rate of the two reactions specified it is also possible to find for the specific rate of carbon
dioxide production:
1
CU 2
ß\
I VWi +
ßl
1
V fer
(9)
and the specific rate of ethanol production:
r p = ß l 2 V fi r
(
10
)
The respiratory quotient (RQ) is often used to evaluate the metabolic state of baker’s yeast, and with the
Sonnleitner and Käppeli (1986) model we find:
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