218
Chapter 6
l
9s j
J SjD
D1
N
1
d N
__1
dD
N dSj
D
^
(
6
)
Equation (6) is used in Example 6.4 to calculate elasticities.
Example 6.4. Illustration of metabolic control analysis
We now consider the linear pathway in Eq (6.32) for three intermediates. Consequently, there are four
enzymatic reactions, i.e., 7=4. Feedback inhibition of the second enzyme,
e:,
by the last intermediate,
s3,
is
included. All the reactions are taken to be reversible, and the feedback inhibition is taken to be non-
competitive. Thus we may write the net rates for the four enzymatic reactions as
r\ =
V i ■
■y
+ AM 1+ -L
K
,
(
1
)
i'l +
K2
(
2
)
l+5-‘
1V
3
K2
)
^jnhib
r, =
k3e,
-
s2+7f3(l+ ^
(3)
S
3
+ A4| 1
+
Ka
(4)
The rate of the reverse reaction is included in a somewhat unusual fashion, in the inhibition term in the
denominator, which increases with increasing conversion. Close to equilibrium, the rate expressions in Eqs.
(l)-(4) cannot possibly hold. For the purpose of illustrating the methodology the realism of the kinetic
expressions is, however, not of overriding importance.
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