Enzyme Kinetics and Metabolic Control Analysis
217
/
r J\
r 1
n
-1
fl)
_
1
f
£,2
CJ
VC2 J
^11
^12,
lo j
^12 ~ £'ll
\ ~ £U,
Obviously C\ + C1
, = 1, but more specifically
p j _
En
'■'l ~
^12 —
^11
1
1
1
+
y ( y + c)
1 + —
ac
________
acx
1 + £>| 1 + ^
(4)
Fig. 6.9 results by calculation of C1, as a function of
x
using (4) and eq. (6.28) to find
y
for a given value
of
x.
The use of elasticities to calculate C1, obviously bypasses a lot of the algebra associated with a
direct calculation of C1, from
J
by (6.31). The results are easily checked with values obtained by
numerical differentiation of
T(x)
in Fig. 6.8b since by (6.31)
,j _ SJ' x
'
dx J'
(5)
In general the enzymatic reaction rates are given as
. Consequently eq. (6) may be useful when
calculating elasticities, either manually or by a symbolic computer software program.
0.11
-
°0
0.5
Î
1.5
2
2.5
X
Figure 6.9 Flux coefficient
C'
calculated from elasticities.
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