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can be exerted on a metabolic flux. Further interpretation depends on ancillary
assumptions that cannot be rigorously claimed to be necessary and invariant
properties of all metabolic pathways. For example, if all flux control coefficients
are constrained to be zero or positive (as would be the case in a linear sequence
of enzymes all of which had rates accelerated by their substrates and inhibited
by their products), then no flux control coefficient could be greater than one, and
could be equal to one only if all the other flux control coefficients were zero. A
flux control coefficient of one would mean that the enzyme is a linear controller
of the metabolic flux, in other words, a rate-limiting step. However, Kacser
& Burns (1973) showed that there was no particular reason to expect such a
situation, because their algebraic analysis made it apparent that the flux control
coefficient of any enzyme contained terms relating to the kinetic properties of
all the other enzymes. Furthermore, they showed that many of the traditional
identifying characteristics of the supposed rate-limiting enzymes could not in
fact reliably indicate the value of the enzyme's flux control coefficient. Rather,
they claimed it was more likely that the total available flux control of one
would be shared, though not equally, between all the enzymes of the system. In
large metabolic systems with many enzymes, this implied that the average flux
control coefficient would be small, and there was no
a priori
reason to expect
any enzyme to have a large flux control coefficient. This conclusion cannot be
claimed to be an invariant principle, though, and has often been contested. In
branched metabolic pathways (which are usual in metabolic networks), some of
the flux control coefficients are naturally negative, which relaxes the limitation
on the magnitude of the positive flux control coefficients. Indeed, it is possible
to think of scenarios where the summation total is different from one, though
many of these discrepancies can be avoided by ensuring consistency between
the precise definition of the flux control coefficient and the experimental system
and its mathematical representation (e.g. Kholodenko et al., 1995). However,
30 years of measuring flux control coefficients have turned up relatively few
instances of exceptions to the generalisations of a summation total of one and
have been consistent with a tendency for control to be shared between enzymes
(e.g. Fell, 1997). Furthermore, the generalisations can be used as a basis for
explaining how the genetic phenomenon of dominance of wild type over mutant
phenotypes arises (Kacser & Burns, 1981; Porteous, 2004). Another phenomenon
that can be explained in similar terms is that of the threshold for the onset of
disease symptoms in mitochondrial cytopathies (Letellier et al., 1994). Therefore
an argument in favour of metabolic control analysis indeed being a theory is
that it not only furnishes explanations in its own domain of metabolism, but it
is compatible with observations in other fields of biology such as genetics.
Views of the role of feedback inhibition in metabolic pathways have also been
affected by metabolic control analysis and the other forms of sensitivity analysis
of metabolic systems. Kacser & Burns (1973) analysed the role of feedback
