Biochemical Reactions - A First Look
77
provide energy through respiration of some carbon to C 02) the maximum yield is obtained by setting
y,x
=
YsPl
= 0 in the redox balance.
y
=
4 - 4 | f
3
sp
|
= 1—2 y
(5)
from which
= 6 /7 C-mole lysine (C-mole glucose)'1
when
- 0. This result is higher than the
true theoretical maximum yield (0.75) which can only be found by analysis of individual pathways, but this
is due to the fact that the black box model is too crude.
In actual lysine production the biomass yield is far from zero - it is in fact higher than for most aerobic
processes. Consequently the theoretical limit for
YJP}
is not at all approached in practice - but carbon yields
of 0.30-0.35 are also economically acceptable. Furthermore, several essential amino acids must be supplied,
but the main lysine production comes from uptake of NH3 and conversion of the substrate to the amino acid.
Several recent reviews treat this important fermentation process (e.g. de Graaf, 2000). The global
production is several hundred thousand tons per year with a sales price in the range of 2.000 US $ per ton in
bulk quantities (see also Table 2.1).____________________________________________________________
3.6 Identification of Gross Measurement Errors
From the previous sections it has been established that four out of the
N + M
+ 1 rates can be
calculated based on C, H, O and N balances - or for simple systems from a carbon and redox
balance. It would, however, be catastrophic to use only the minimum number of rates when results
of a fermentation (at a given set of environmental conditions) are to be interpreted in terms of a
stoichiometric equation. First of all compounds may be missing from the stoichiometric equation as
was the case in Example 3.6 or their rates o f production or consumption may be misjudged due to
gross experimental errors as was the case for ethanol which was stripped away in Example 3.5.
But even small - and quite unavoidable - experimental inaccuracies will lead to substantial errors
in the calculated rates. The data of Duboc (1998), which were analyzed in Example 3.1, are very
accurate. The sum of yield coefficients o f products is 0,999 (Eq. 3.23) while the redox balance, Eq.
(1)
in Example 3.1 closes to within 0.008. Still, a calculation of two yield coefficients
and 7sg
based on
Y«.,
fse, and using the carbon - and the redox balances leads to significant errors due to the
ill-conditioned nature of the linear algebraic problem. Inserting
Ysc
and
Yx
from (3.22) one obtains
Carbon balance: 1 = 0.275 + 0.510 +
Ya
+
Ysg
Redox balance: 4 = 0.510 • 6 + 4.18yjjt + 4.667fJff
(YsA = _ J _ f 4.661
- i y 0 . 2 1 5 W 0 . 1 3 0 1!
[YsgJ
0.487 [-4 .1 8
1 J [
0.940
J
[o.0848j
(3.35)
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