Biochemical Reaction Networks
175
catabolism and the biochemical production capabilities of this organism.
The model consisted of 107
metabolites (including substrates and metabolic products) and 95 reversible reactions, and because each
reaction has to be included in both a forward and backward direction this gives a stoichiometric matrix of
107 x 190,
i.e.,
there are 83 degrees of freedom. None of the fluxes were measured, but one flux (the
specific glucose uptake rate) was used to scale the fluxes. The only experimental data used for the flux
calculations were the following:
Metabolic demands for growth were used to calculate the drain of precursor metabolites for biomass
synthesis. In practice, the drain of precursor metabolites is included as stoichiometric coefficients in
a reaction leading to biomass synthesis.
ATP requirements for maintenance. By fitting the specific glucose uptake rate at different specific
growth rates to experimental data, a requirement of 23 mmoles ATP (g DW
) 1
for growth-associated
maintenance and 5.87 mmoles ATP (g DW h)
1
for non-growth-associated maintenance was
estimated, and these values are used in the calculations.
The specific oxygen uptake rate was given an upper bound of 20 mmoles (g DW h)'1.
The objective function was the specific growth rate, which in all cases was maximized. Thus, if a
specific glucose uptake rate is given, the model determines the corresponding maximum specific growth
rate along with all the fluxes in the network.
To evaluate the model the production rates of metabolites formed by
E. coli
were plotted as functions of
the specific growth rate, and the results are shown in Fig. 5.14. It is observed that at low specific glucose
uptake rates (corresponding to low specific growth rates), no byproducts are formed,
i.e.,
growth is by
pure respiration. As a result, in this regime the specific oxygen uptake rate increases linearly with the
specific growth rate. When the specific glucose uptake rate approaches
8
mmol (g DW h
) 1
(corresponding to a specific growth rate of about 0.9 h'1) the oxygen requirement for complete oxidation
of glucose to carbon dioxide exceeds the specified maximum of 20 mmol (g DW h )'. The cells therefore
shift to a mixed metabolism with both respiration and fermentation. The first fermentative metabolite
that is excreted is acetate, and at higher glycolytic flux (or higher specific growth rate) formate is also
excreted. Finally, at very high glycolytic flux ethanol is excreted. It is interesting that the model predicts
the right sequence of excretion of metabolites,
i.e.
.
first acetate, then formate, and finally ethanol, which
is consistent with experimental findings. This could indicate that when respiration operates at its
maximum rate the cells are constrained by the supply of ATP (notice that more ATP is gained by the
formation of acetate than by formation of formate and ethanol, see Fig. 2.6). When the glycolytic flux
increases further oxidation of NADH starts to become a problem for the cell, and it will therefore first try
to reduce the formation of NADF1 in connection with acetyl-CoA synthesis, namely by by-passing the
pyruvate dehydrogenase complex (see Fig. 2.6) through the use of pyruvate-formate lyase, and when this
is not sufficient start to convert acetyl-CoA to ethanol which is accompanied by a net consumption of
NADH.
An advantage of linear programming is that additional information can be obtained by calculating the
sensitivity
X
of the objective function Z with respect to the system variables. These sensitivities are
sometimes called
shadow prices.
For the
E. coli
metabolic model discussed above (maximization of ,u)
c r
previous page 199 Bioreaction Engineering Principles, Second Edition  read online next page 201 Bioreaction Engineering Principles, Second Edition  read online Home Toggle text on/off