272
Chapter 7
As for the Williams model the first reaction represents conversion of glucose into small building blocks
in the A compartment and these are further converted into ribosomes. The stoichiometric coefficient Yu
can be considered as a yield coefficient since metabolic products {lactic acid, carbon dioxide etc.) are not
included in the stoichiometry. In the second reaction building blocks present in the A compartment are
converted into macromolecular components of the G compartment. In this process some by-products
may be formed and the stoichiometric coefficient Y22 is therefore slightly smaller than 1. It is assumed
that the formation of macromolecules is the rate-controlling process in the formation of both the A and G
compartments, and the kinetics of the two reactions therefore has the same form,
i.e.
v
,
=
*
,—
;
1=1,2
(3)
s + K -
vL
is taken both to be a function of the glucose concentration (the carbon and energy source) and of the
concentration of the active compartment (the catalyst for formation of biomass). From Eq. (7.11) the
specific growth rate for the biomass is found to be:
z o o 'l l
y 22
= rnv, - 0
- / n h
(4)
or with the kinetic expressions for v, and
v2
inserted:
ju
=
/
.A
s + K„
-{l-y22)k2
s+ K .
X ,
(5)
Thus the specific growth rate is proportional to the size of the active compartment. The substrate
concentration 5 influences the specific growth rate both directly and indirectly by also determining the
size of the active compartment. The influence of the substrate concentration on the synthesis of the active
compartment can be evaluated through the ratio v,/v2:
Z f _
S+Ks,2
v2
k 2 s + KiA
(
6
)
If
Ky]
is larger than
Ki2
the formation of
XA
is favored at high substrate concentration, and it is hereby
possible to explain the increase in the active compartment with the specific growth rate. Consequently,
when the substrate concentration increases rapidly there are two effects on the specific growth rate:
•
A fast increase in the specific growth rate, which results from an increase of
s/(s+Ky])
with
s.
The
time constant for increase of
s
in the medium is small compared to the time constant for the growth
process (see e.g. Fig. 7.13).
•
A slow increase in the specific growth rate, which is a result of a slow build up of the active part of
the cell,
i.e.
additional cellular synthesis machinery has to be formed in order for the cells to grow
faster.
This is illustrated in Fig. 7.14, which shows the biomass concentration in two independent wash out
experiments. In both cases the dilution rate was shifted to a value (0.99 h 1) above the critical dilution
rate (0.55 h'1), but in one experiment the dilution rate before the shift was low (0.1 h'1) and in the other
experiment it was high (0.5 h'1). The wash out profile is seen to be very different, with a much faster
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