1 2 0
Chapter 5
about the
in vivo
flux. Furthermore, in enzyme assays the maximum enzyme activity is typically
measured and in order to identify the actual rate of an enzyme catalyzed reaction it is necessary
to know the substrate concentration (as well as the concentrations of all other metabolites that
affect the enzyme reaction rate). Through material balances around intracellular metabolites it is,
however, possible to calculate the
in vivo
fluxes through different branches of the metabolic
network as will be illustrated in the following. This concept is referred to as
metabolite
balancing.
Consider a network in which we have identified
J
fluxes (or rates of pathways reactions) v,,.
... v,
which we desire to calculate. The calculation relies on measurement of specific rates of substrate
uptake and product secretion, and in the network we consider
N
substrates and
M
metabolic
products (see Fig. 5.1). Since we can also measure the specific growth rate of the biomass there
are therefore r,,.
. w
MH measurable rates. In addition to the measurable rates there are a set of
constraints imposed by mass balances around the individual metabolites, each of which express
that the concentration of a certain metabolite is constant, i.e., that the net rate of production of the
metabolite is zero. Formulation of the constraint is done rigorously in the following way (see
also Fig. 5.2):
For all intracellular metabolites the fluxes leading to a given metabolite are
balanced with the fluxes leading away from the metabolite. Hereby there is no net
accumulation o f the metabolite.
As a corollary to this definition we again emphasize that metabolites in un-branched pathways do
not provide a constraint of much use, as illustrated in Fig. 5.2. Clearly the two first reactions
could have been lumped into a single overall conversion of the substrate to the metabolite B. To
illustrate with a real example consider the EMP pathway in Fig. 2.4. In this pathway 3-
phosphoglycerate (3PG) is produced and consumed at the same rate, but it is not involved in any
other reaction, and the constraint r3PG=0 is of no use. Conclusions based on only part of the
metabolic network of an organism can, however, prove to be wrong. Actually 3PG is also used as
precursor for synthesis of the amino acid serine, and if the flux towards this amino acid is
significant compared with the flux through the EMP pathway the balance around 3PG may
suddenly be important in the analysis. As long as only parts of the metabolic network are
analyzed simplified pathway diagrams can, however, be used with confidence.
Similar to balancing of pathway intermediates redox equivalents formed in one pathway (see
Table 3.4) as a result of a net oxidation of a substrate to a product will have to be consumed in
other pathways. As long as only one type of redox carrying co-factor, e.g., NADH, is involved
the constraint
r
NADH~0 is immediately applicable, but some reactions in the cell may apply
different co-factors, e.g., both NADH and NADPH may be used as co-factor in the conversion of
acetaldehyde to acetate in 5.
cerevisiae
(see Fig. 2.6). Compartmentation of the cell also leads to
difficulties, since e.g. NADH in the cytosol of yeast is not interchangeable with NADH in the
mitochondria. Thus, the finer details of redox balancing require a sophisticated treatment, but in
simple approximate calculations, especially in calculations of the distribution of metabolic
products in fermentative pathways it is sufficient to work with only one redox carrier as
illustrated in Section 5.3.
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