Biochemical Reaction Networks
179
This structure may be represented by two elementary flux modes, pathway 1
and pathway 2, and the
mode of operation of the combined pathway (indicated by the fluxes) may be represented as the sum of
the two elementary modes.
The concept of elementary flux modes is similar to identification of the extreme pathways (Schilling
et
al.,
2000
), and clearly any flux vector (corresponding to a given operation of the network) can also be
specified as a linear combination of the extreme pathways. However, the elementary flux modes give a
more detailed representation of the network structure than the extreme pathways. Schuster and co-
workers recently released the software “Separator”, which enables a systematic division of metabolic
networks into subsystems, and investigated the metabolic network
of Mycoplasma pneumoniae
(Schuster
et
a/.,
2002
).
Elementary flux mode analysis has successfully been applied for the improvement of product yield in
aromatic amino acid production (Liao
et a l
1996). Furthermore, it may be used to analyze the function of
specific reactions in metabolic networks (Forster
et al.,
2002). However, a major problem with elementary
flux modes is that the number of modes increases drastically with the number of reactions in the model.
Thus, for a relatively simple metabolic network of
S. cerevisiae
consisting of 45 reactions (16 reversible
reactions and 29 irreversible reactions), 42 internal metabolites and 7 external metabolites, the number of
elementary flux modes was found to be 192 (Forster
et al.,
2002). If one additional isoenzyme is included in
the model the number of elementary flux modes increases to 307, and if one further reaction is included the
number of elementary flux modes increases to 1117. Clearly for genome-based metabolic models there will
be a very large number of elementary flux modes, and this limits the practical use of this approach for
analysis of such large networks.
PROBLEMS
Problem 5.1 Determination of stoichiometric coefficients in the biomass pathway reaction for
S. cerevisiae.
Assume that the metabolic pathway model corresponding to Example 3.8 can be approximated by the
following 3 pathway reactions:
v, : -(1+a)CH:0 + aCO; + pNADH + CHl(î,0052No,5-YATP = 0
v; : -1.5CH,0 + 0.5 CO; +CH;O05 + 0.5 ATP = 0
v3
- CH;0 + CH8;30 -
Уз
ATP - '/з NADH
= 0
Determine the value of a , (3 and у in the first reaction as functions of Fxs and F„.
(Answer:
a = (1/6)
Y,u
+
0.03 and у
=
(1/3)
Y„ -
(13/18)
- 0.343
)
Consider the set of experimentally obtained yield coefficients in eq (3.23). Determine numerical values
of
a
and у for this data set.
The yield coefficients of eq. (3.23) were obtained for a slightly different composition of the biomass.
Determine a and у with the biomass composition used in eq. (3.23) and discuss the sensitivity of the
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