Enzyme Kinetics and Metabolic Control Analysis
219
where
E =
1
s. k J k ;
l
k 2(\ + sJ k ;)
U2
s2
k J k ;
a2
^inhib + 53
0
1
0
k ^ i + sj/ k ;)
s ,
k J
k
;
k
j
\ - p k d
p O
' s + k ^ i + sJ k ; ) '
°2
si + K-2{\+s2! k 2)
a2
s2
+k 2(\ + sJ k ;)
y
j 2 +k ,(i +sJ
k ;)/
(5)
(
6
)
From Eq. (5) it is seen that the elasticity coefficients for the ith enzyme with respect to its substrate -i.e., the
(i-l)th intermediate - is positive, whereas its elasticity coefficient with respect to its product (i.e., the zth
intermediate) is negative.
If the kinetic parameters are known together with steady-state levels of the intermediates, the numerical
values of the elasticity coefficients can be calculated, but normally it is difficult to obtain
in vivo
experimental values for the parameters, and it is likely that the
in
vhro-determined parameters do not
represent the true situation. Here we will, however, assume that at a particular steady state [j,
p, (st, s2
rS3(j,p))] we have determined the elasticity coefficients to be given by
l
1
1
1
- 0.9
0.5
0
0
0
-0 .2
0.7
0
0
-1.0
-0.5
0.5
in which case the control coefficient matrix is obtained from Eqs. (6.41 and 6.44):
0.14
0.96
0.39
0.27
0.24
-0 .2 7
0.69
0.48
0.07
-0 .0 8
-1.23
0.14
v0.55
-0 .6 1
0.15
-0 .8 9
(8)
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