Enzyme Kinetics and Metabolic Control Analysis
213
e.
(
1
)
then the fractional change in all the reaction rates will also be
a
and the level of the intermediates is
therefore kept constant. Consequently, the fractional change in the overall flux is given by
dJ
— =
a
J
(
2
)
where J is a function of the level of all enzyme activities in the pathway and
dJ
is consequently the sum of
all the individual fractional changes in the flux when the level of each of the individual enzymes is changed.
Thus
cU
J
= 1 7
,_1
J
f dJ^
\ deU
>=1
de,
, / a n d
j*i
or when the definition of the control coefficients in Eq. (6.33) is introduced:
H
<
t
)
(3)
(4)
By inserting Eqs. (1) and (2), it is easily seen that the flux-control summation theorem in Eq. (6.34) is
derived.
Similar to the flux-control coefficients we define
Concentration-Control Coefficients
by
S] de,
i = \,.
..,I
and
j
= 1,
(6.35)
These coefficients specify the relative change in the level of the /th intermediate when the level of
the ith enzyme is changed. Since the level of the intermediates is not changed when all the enzyme
considerations are changed by the same factor
a
(see Note 6.3), we have
d
s
.
/
( i
f a y .
___
J_
s
,
= Z
H e . ,
J
\
i
de
> - • .
....1.
J»i
j
7
Tfsj oet
et
7
^
or
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