Enzyme Kinetics and Metabolic Control Analysis
207
6.3 Metabolic Control Analysis
We have now seen how the kinetics of an enzyme reaction influences the rate of conversion of a
substrate to a product of the enzymatic reaction. But this is not really what we are interested in
when the objective is to design a pathway for optimal conversion of a substrate 5 to the final
product
P
of the pathway. It does not help much if a number of enzymes in the pathway operate
at high efficiency if just one single enzymatic reaction is slow. The steady state flux through the
pathway from
S
to
P
is determined by the bottleneck of the pathway, just as the flow of water by
gravity from one reservoir to another is determined by the piece of pipeline that offers the highest
resistance to the flow.
In the analysis of a sequence of chemical reactions one often talks about the “rate limiting” step.
The concepts of
Metabolic Control Analysis
(MCA) do, however, tell us that it is meaningless to
talk about “rate limiting” steps since flux control may well shift from one enzyme to another
enzyme depending on the environmental conditions. As will be illustrated in the following
description of MCA it is much more fruitful to look on the whole pathway rather than on the
individual enzymatic reactions, and that the task is to change the architecture of the pathway such
that the resistance to the flow through different steps is more or less the same when the pathway
is used to produce a valuable product at relevant environmental conditions. To quantify the
degree of flux control exerted by the different enzymes in a pathway and to compare different
pathway architectures the so called
Flux Control Coefficients
CJ, provide a good tool. Basically
C'j denotes how much the flux
J
through the pathway will change when the reaction rate of the
fth step of the pathway is increased by improving the catalytic activity of the f th enzyme.
Clearly Cj is a systemic property since we look at the change in the outcome of all / reactions in
the pathway when we change just one of the steps in the sequence of reactions.
To illustrate the concepts o f MCA it will be fruitful to consider a simple example that can be
treated analytically. In the example all the topics of MCA are discussed, but the heavy matrix
algebra that must necessarily be used to analyze a real pathway is avoided.
Consider therefore a two-step pathway:
5
- a - »
5,
—3 -»
P
(6.22)
For simplicity the reverse reactions are neglected. The concentrations ,v of
S
and
p
of
P
are fixed,
and we wish to calculate the steady state flux
J
of e.g. carbon from 5 to
P
via the intracellular
species 5, whose concentration will vary not only with s but also with the architecture of the
pathway, i.e. with the parameters of the two enzymatic reactions r, and
r ,.
Since the steady state is considered the two rates
r,
and
r2
must be equal and also equal to the
steady state flux
J
through the pathway.
We shall consider two different expressions for r ,:
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