Enzyme Kinetics and Metabolic Control Analysis
221
coefficients. The gene for this slightly different enzyme is cloned into the chosen production strain. Take
the elasticity coefficients for the second pathway reaction to be
'
1.0
'
f
|2
=
-
0.6
, -
0
-
3
,
(
10
)
i.e., the feedback inhibition by .v, is weaker and the ratio
K2/K 2
is slightly lower. With the slightly
different enzyme in the production strain instead of the native enzyme, the control matrix is found to be
0.25
0.83
0.72
0.50
0.23
-0 .2 5
0.65
0.45
0.19
-0 .2 2
-0 .8 8
0.39
0.33
-0 .3 6
-0 .4 9
-1.34
Thus with the new enzyme the flux control of the last enzyme has been reduced, and the control coefficients
are all close to 1 //= 0.25. Consequently, none of the enzymes dominate the flux control in the pathway.
MCA suggests a systematic way of improving the overall performance of a metabolic pathway and points to
specific experiments that may assist the protein engineering work. What has not been included in the above
discussion is the role of the operating conditions on the performance of the cell. All intracellular metabolite
concentrations are calculable once
s, p,
and the kinetics are given. The elasticity coefficients are complex
functions of
s{
and before any enzyme modification (i.e., changes of kinetic parameters) is attempted the
current reaction network must be optimized to give the maximum flux by simulations at different s and
p
values.
When flux control is lifted, all the control coefficients are of approximately the same size, but this does not
necessarily indicate that the flux through the pathway is significantly higher than in the native strain. This
has to be checked separately. However, if one obtains a modified strain in which all the control coefficients
have approximately the same value, the flux may be increased by amplifying the level of all the enzymes,
e.g., by inserting a stronger promotor upstream of the genes coding for the four enzymes.________________
We have until now considered only linear pathways, since these are much easier to analyze than
branched pathways. The MCA can, however, easily be extended to branched pathways. If the total
flux
J
branches into two fluxes./, and A, then [see, e.g., Westerhoff and Kell (1987)]:
Ji
Z C /- 7 ,
(6-45)
b ran ch !
branch 2
An attempt to increase the flux through the second branch by decreasing the control coefficients in
that branch relative to the rest of the control coefficients in the total pathway often fails because of
the interbranch interactions described by Stephanopoulos and Vallino (1991). With a branched
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