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MCA |
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Back to the MCA homepage.
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In the previous sections both global (the control coefficients) and
local (the elasticity coefficients) properties of metabolic systems were
described. In this section of the MCA Web all is revealed about
using the elasticity coefficients to calculate the control
coefficients.
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A Metabolic Web |
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In each cell of a living organism there are hundreds of biochemical
reactions ocurring simultaneously. These reactions are interconnected
by the metabolites. Most metabolites are products of one reaction while
they are also substrates of another, this links the two reactions since
they are both sensitive to changes in the concentration of their common
metabolite. Figure 4 illustrates this web of
reactions, for a more detailed example see the
acyclic fatty acid synthesis pathways
or the
metabolic reactions and pathways database (INRA - France).
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The Connectivity Relations |
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A particularly useful and important feature of MCA is that
it can relate the kinetic properties of the individual reactions
(local properties) with (global) properties of the
whole intact pathway. This is done through the connectivity theorems
(Kacser and Burns 1973) that relate
the control coefficients and the elasticity coefficients of steps
with common intermediate metabolites.
The connectivity theorem for flux-control coefficients
(Kacser and Burns 1973) states that,
for a common metabolite S, the sum of the products of the
flux-control coefficient of all (i) steps affected by S
and its elasticity coefficients towards S, is zero:
 (6)
For the concentration-control coefficients, the following two
equations apply (Westerhoff and Chen
1984):
 (7)
 (8)
Equation 7 applies to the case in which the reference metabolite
(A) is different from the perturbed metabolite (S).
Equation 8 applies to the case in which the reference metabolite
is the same as the perturbed metabolite.
The connectivity theorems extend MCA to be able to describe
how perturbations on metabolites of a pathway propagate through the
chain of enzymes (the metabolic web). The local (kinetic)
properties of each enzyme effectively propagate the perturbation to and
from its immediate neighbours.
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From Enzyme Kinetics to Control Analysis |
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For linear metabolic pathways, i.e. those in which each
metabolite is never a substrate of more than one enzyme and/or a product
of more than an enzyme (see figure 5 for an
example), the set of connectivity relations together with the summation
theorem form a system of n equations in n unknows and
one can then calculate all control coefficients given all the enzyme
elasticities (Heinrich & Rapoport1974,
Fell & Sauro 1985). This can be done in a
systematic way using matrix methods and is indeed possible for
pathways with any structural complexity (see below).
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Group |
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