144
Chapter 5
As shown in Fig. 2.6 the formation of ethanol from pyruvate in
S. cerevisiae
proceeds via acetaldehyde,
which is a volatile compound, and small amounts of acetaldehyde may therefore be secreted from the
cell. In a simple model for anaerobic growth of
S. cerevisiae
we can therefore use the following reaction
network.
Glucose is distributed between three pathways with fluxes v1; v2 and v4. The branch point P is acetaldehyde,
which may either be excreted from the cell, v5 or be reduced by v3 to ethanol, which is immediately excreted
to the medium. Carbon dioxide (c) is also formed, but is not shown in the network. There are five
independent pathway reactions and 6 species with a net production rate different from zero (
5
,
x, g, e, c
and
a).
One constraint can be set up at the branch point
P:
The flux of carbon in v2 must be distributed between
excreted acetaldehyde and ethanol. This picture of the metabolism excludes the possibility of excretion of
any intermediate along the pathway v2,
i.e.
no pyruvate is excreted. Also it excludes the possibility of
formation of other metabolic products - e.g. HAc or consumption of intermediates from pathway v4 and v2
to cell components. It is assumed that the biomass formation can be correctly described by one single
pathway reaction v,, which in terms of carbon consumption is independent of the other pathways.
It is assumed that there are no other sources or sinks of NADH or ATP than those coupled to the five
pathway reactions,
i.e.
that rNADH
=0 and rATP = 0. Thus there are three constraints including the trivial v5 = v2
- v3. Since vs can be calculated directly from v2 and v3 we will only need four pathway stoichiometries.
v,
:
-1 A 2 C H 20 + CHluO06N 0A2 + 0A2CO 2 + 0A5NAD H -2 .4 2 A T P = 0
v2
:
-\.5 C H 2O + CH 2O0s +0.5CO2 +0.5NAD H + 0.5ATP = 0
v3
:
- C H 2O05 + C H }O05 -0.5N A D H
= 0
(1)
v„
:
- C H 2
O +
CHg/;O-0333NADH-0.333ATP =
0
The stoichiometry for the biomass formation reaction is given by
v,,
and the stoichiometry for the following
three reactions are taken from Table 3.4. We use a C-mole basis as in Chapter 3 for the black box models.
Note that any of the equations can be multiplied by an arbitrary constant without affecting the final result,
namely the distribution of carbon from glucose to different products. v2 specifies the rate at which one C-
mole of acetaldehyde is formed, whereas Table 3.4 gives the rate at which glucose is consumed to form
3 C-mole acetaldehyde.
The ATP coefficient in the first reaction is an empirical quantity used when nothing is specifically stated
concerning the fermentation conditions. It certainly varies significantly with the medium composition and
with operating conditions such as the dilution rate. In section 5.2 we have discussed how the ATP
requirement for growth can be determined from experiments (see Table 5.2 for experimental values), but in
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