210
Chapter 6
1
Figure 6.8 Dimensionless flux
f
=
Jlk
2 through a two step pathway (6.22) as a function of the ratio
fmaxi/fmax: =
k]lk2
= x.
In both cases
r2
is given by (6.24), and the parameters of (6.25) are
a=
1,
b=c=
0.5.
a. r, given by (6.23a).
b. r, given by (6.23b).
We can conclude the following:
If both rate constants are multiplied with the same factor/the flux
J
through the pathway
also increases by a factor
f.
The shape of
f
does not change, since
f
is only a function of
x. For large values of
k,
the flux
J
becomes proportional to
k2
If 5 is doubled the value of all parameters a, b and c will decrease by a factor 2, and
v(x)
as determined from (6.28) will have a different shape.
T(x)
will increase faster with x,
but the initial slope
(b
+ 1 )1
will only increase by a factor 2 if
h
is much greater than 1.
Thus
f
does not react proportionally to a change in ,v.
These observations originate in the form of r,
In (6.23a) the parameters of
r2
have no influence
at all on the flux. With (6.23b) the control of the flux is distributed between the two reactions,
and it moves towards the second reaction when
k
, increases, since a larger value of
k{
leads to a
higher value o f
y
in (6.28), and this influences r, negatively through the denominator term with v.
The smaller the value of
c
the faster is step two of the sequence, and
S,
is removed fast enough to
avoid a build up of 5) waiting to be processed by step two.
It now appears that the question of flux control by either step 1 or 2 in the sequence depends on
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