220
Chapter 6
The desired flux-control coefficients
Cf
are in the first column of C*. The last enzyme in the pathway has a
flux-control coefficient significantly higher than
MI
= \
= 0.25, and it is therefore the rate controlling step.
The rate of conversion of .v, is too small. This in itself reduces the total flux through the sequence, and
furthermore a buildup of a high level of the metabolite
s3
impedes the second reaction, the conversion of
to
s2.
Thus an increase in the level of the enzyme
E2
that is under feedback control will not necessarily be
the best remedial action.
From Eq. (8), it is observed that the concentration-control coefficients for the i'th metabolite with respect to
the ith enzyme is positive, but with respect to the
(i
+ l)th enzyme it is negative. If the concentration of the
ith enzyme increases, the concentration of the ith intermediate (product of the reaction) increases, whereas
the concentration of the (i - l)th intermediate (the substrate) decreases. The last row of C* contains in its
last three columns the concentration-control coefficients pertinent to the last enzyme. When the activity of
this enzyme is increased, the level of the last intermediate
s3
and of the first intermediate x, sharply decrease
while the level of the second intermediate increases. This is easily understood; Both
s3
and
s,
are substrates
that are more rapidly consumed when the level of
E4
increases,
s3
directly and
s2
indirectly when the
inhibition control of
E2
is relieved. Notice that the last three columns of C* sum to zero, as they should
according to Eq. (6.36), and that the first row contains only positive control coefficients: The total flux as
well as the concentration level of all intermediates increases when the activity of the first enzyme is
increased.
The effect of the feedback inhibition can be illustrated by setting
e32
= 0 and calculating the control matrix
for this situation. The result is given in Eq. (9):
'0 .2 7
0 .8 2
0 .7 5
0 .5 2 '
0 .47
- 0 . 5 2
1.34
0 .9 4
0.13
- 0 . 1 5
- 1 .0 5
0 .2 7
v0.13
- 0 . 1 5
- 1 .0 4
- 1 .7 3 ;
By comparison of the control coefficients with those in Eq. (8), where feedback inhibition is present, it is
observed that the rate control is now at the second enzyme in the pathway. Thus this enzyme is a potential
rate-controlling enzyme for the true system with feedback inhibition, since if the inhibition is removed or
reduced in strength the second reaction is controlling the overall flux. When the feedback inhibition is
lifted, all three concentration-control coefficients in the last row become negative; Increasing the activity of
the last enzyme in a straight sequence lowers the level of all intermediates.
We now consider a microorganism in which the pathway described above (with feedback inhibition) is
active. The product of the pathway is a desired product, e.g., an antibiotic, and we want to design a new
strain - using MCA - in which an increased flux through the pathway is possible. Thus we want to decrease
the rate control, which can be done, e.g., by inserting a gene coding for an enzyme that also catalyzes the
conversion of
s,
to
but has different elasticity coefficients, i.e., kinetic parameters compared with the
native enzyme - e.g. a higher value of
K,^lh
(less inhibition) and/or a lower value of
K2IK 2
.
Assume that the search leads to a strain that has an enzyme similar to
E4
but with other elasticity
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