Biochemical Reaction Networks
135
the following linear relationships between measurable rates are obtained from (5.17):
- r s = (a + l + YIC
+
0.5
YxNADFH)h +b = Y™/u
+
ms
(5.18)
rc = (a + Yxc
+
0.5
YxSADPH
)M + b =
F'""> +
mc
(5.19)
-r0 =(a +
0.5
YxMDH )/J+b =
Y'™n
+
mo
(5.20)
The two common parameters
a
and
b
are obtained as a function of the energetic parameters FxATP
and
mAT
P and the P/O ratio, according to Eqs. (5.21) and (5.22):
Y
- Y
P/O
1 xATP
1xSADH
l'yj
a ~
0.667 + 2P/O
(5.21)
b
-
mATP
0.667 + 2P/0
(5.22)
Equation (5.18) is seen to be the same as the linear rate equation (5.5) with the difference that the
yields of that correlation are now obtained in terms of basic cellular energetic parameters. This is
true for all parameters in the preceding linear correlations since they are coupled via the ATP,
NADH, and NADPH balances. It is thus seen that the three true yield coefficients cannot have
arbitrary values since they are coupled through these balances. Furthermore, the maintenance
coefficients are the same. This is due to the choice of the unit C-moles per C-mole of biomass
per hour for the specific rates. If other units were used for the specific rates, the maintenance
coefficients would not have the same values, but they would still be simply related. This
coupling of the parameters shows that there are only two degrees o f freedom in the system
(equivalent to defining parameters
a
and
b
in Eqs. (5.21) and (5.22)).
Equation (5.18)-(5.20) contain three parameters TxNADH,
F
x n a d p h
and Fxc that are all related to the
redox balance for the cell. From Table 5.2 theoretical values of FxNADH
and FxNAIjI,h are obtained
and (5.7) can be used to calculate Fxc. Take
S. cerevisiae
and a standard biomass with Kx = 4.20.
The redox balance for reaction (5.7) is:
4.20 + 2'24.6 • 15.43 10‘3- 4 (1 + F J - 2 • 24.6 • 8.24 10'3 = 0
=> Fxc = 0.138 mole CO, (C-mole biom ass)1
(5.23)
It is now for a given strain seen that the three true yield coefficients in Eqs. (5.18)-(5.20), i.e.
Y
,
Y",'“’
and
Y'xr“e
; are fixed once the parameter
a
has been given a value,
b
is the same for all
three lines. Consequently (5.18)-(5.20) provides only two independent relations between the
three energetic parameters FxATP, P/O and mAIP. If we assume that these three parameters are
fundamental parameters for the strain then a similar model as derived above can be derived for
other substrates, e.g., for acetate, ethanol, glycerol or citrate, and in this model the yield
coefficients will be different functions of the three energetic parameters. If the yield coefficients
are experimentally determined for growth on different substrates this allows all three energetic
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