134
Chapter 5
The reaction network (5.7) to (5.11) can be written in condensed form using the stoichiometric
matrix T, where the first “compound” is taken to be biomass, followed by glucose, oxygen and
carbon dioxide. The order of the intracellular metabolites is taken to be ATP, NADH and NADPH.
Thus,
( \
--0 + 0
0
_
v
1 xATP
Y
- Y
)
0
- l
0
1
0
0
2
0
- l
0
1
0.667
2
0
0
0
-0 .5
0
P/O
-1
0
,0
0
0
0
-1
0
0
,
We now introduce the reaction rate vector v for the five reactions:
(5.12)
V pp
VEMP
VOP
^ m ATPJ
(5.13)
The balances for the three cofactors ATP, NADH, and NADPH can then be derived directly from
Eqs. (5.2)-(5.4):
^ xatpM
+
0.667v£Ay/,
+
P/O
v0P
m ATP =
0
(5.14)
+
T-VEMP — V OF =
0
(5.15)
~
— 0
(5.16)
Using Eq. (5.1) we can also derive relationships for the four measurable rates: the specific
growth rate, the specific glucose and oxygen production rates, and the specific carbon dioxide
production rate, in terms of the five reaction rates:
V
f
rs
r
o
Jcj
V
1
0
- 0 + 0
- i
0
0
Y„
1
0
•1
0
CU
0
0
0
-0.5
0
1
0
0
f
p
\
■ 0
+ Yx c ) P ~ v rr
- V t.
- 0.5vo/,
Y„ +
vpn + v „ .
(5.17)
Clearly the top equation is trivial, but this is due to the simplified model applied. Often many
more reactions are considered for biomass synthesis and then P becomes a function of several of
the flux vector elements. Eliminating the three fluxes vEMP, vPP, and v0P from Eqs. (5.14)-(5.16),