Biochemical Reaction Networks
159
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Notice the com plexity o f the solution,
i.e.,
the intracellular fluxes are functions o f alm ost all the
measured rates. In such cases, m anual solution o f the algebraic equations is forbidding, w hereas
computer solution using M athem atica, M able, or M atlab is trivial. O bviously v 12 = 0 and v, = v,0 w hen
the glyoxylate shunt is inactive. B y calcu latin g the unknow n rates (or fluxes) at different dilution rates in
a steady state chem ostat,
i.e.,
for differen t sets o f m easured rates, A iba and M atsuoka (1979) concluded
that m odel 1 gives reasonable values fo r the fluxes. F urtherm ore,
in vitro
m easurem ents o f the activity o f
four different enzym es (pyruvate carboxylase, citrate synthase, isocitrate dehydrogenase, and isocitrate
lyase) correlated fairly w ell w ith the calculated fluxes. W hen the tw o o ther m odels w ere tested, it was
found that som e o f the fluxes w ere negative,
e.g.,
m odel 2 predicts that 2-oxoglutarate is converted to
isocitrate. This is not im possible, but m ost o f the reactions are favored th erm odym ically in the direction
specified by the arrow s in Fig. 5.5. T hus,
&G°
for the conversion o f isocitrate to 2-oxoglutarate is -20.9
kJ (m ol)'1, and a large concentration ratio o f 2 -oxoglutarate to isocitrate w ould be required to allow this
reaction to run in the opposite direction. F urtherm ore, there is better agreem ent betw een the m easured
enzyme activities and flux p redictions by using m odel 1 than w ith the tw o other m odels. A iba and
M atsuoka (1979) therefore concluded that the glyoxylate shunt is inactive or operates at a very low rate
in C.
lipolvtica
un d er citric acid production conditions.____________________________________________________
Example 5.8 Analysis of the m etabolic netw ork in
S. cerevisiae
during anaerobic grow th
Nissen
et at.
(1997) constructed a netw ork m odel that can be used to describe anaerobic grow th o f
S.
cerevisiae.
The m odel was based on a com prehensive literature study to find w hich m etabolic pathw ays are
active in
S. cerevisiae.
The m odel contains 37 reactions and 27 intracellular m etabolites. Thus, the degrees
of freedom in the system are
F =
10. In chem ostat cultures operating a different dilution rates the rates o f
the follow ing 13 com pounds w ere m easured: glucose, am m onia, glycerol, pyruvate, carbon dioxide, acetate,
ethanol, succinate, carbohydrates, proteins, D N A , R N A and lipids. T he production rate o f ethanol and the
uptake rate o f am m onia w ere not used for the analysis, but these rates w ere used to validate the calculated
fluxes, which w ere calculated using the other 11 m easured rates together w ith eq. (5.27).
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