Enzyme Kinetics and Metabolic Control Analysis
227
b
----
y
a
M
\ + y
c
and
c + y
y(y
+
C)
1
+ -
s'+*| 1 +
a
(17)
Solving (3) for
5
' = 1 and x = 1 yields
y
= 0.6180 and CiJ„ ac,(l,l) = 0.7236. An approximate value for
C/( 1,1) is obtained by inserting into (17) an approximate value for y( 1,1) calculated as
y
=
y° + dy
from (14) or (15):
y (l,l)= / + 0.59175
dx
=0.22474 + 0.59175 - 0.5 = 0.52062
C/app,„x(l,l)= 0.7681.
This is a fair approximation of the true value C /esaM
(l,l) = 0.7236.
Another approximate method for calculation of C / is based on the shape of
J'(x).
If
J ’(x)
given by
J'(x)
X
x
+
K
Then for two different enzyme concentrations represented by
and
x:
08)
x(J'-J'(x0)) _ x
K (x-x °)
J '(x -x ° )
~ J' (x-x°)(x + K)(x° +K)
~
0
But
j
a / ’)
_
k
_ k j ’(x°)
' (X°} ~ d x '^ J 'i x 0) ” (x°+ K )2
J'(x°)~
(2
This means that an exact value for the control coefficient C/(x") can be found simply by measuring the
flux through the pathway for two known enzyme concentrations.
In our case and based on experimental determination of the flux at x = 0.5 and
x =
1 :
C,y(0.5)
1 (0.55278-0.31010)
0.878
0.55278-0.5
(
21
)