Biochemical Reaction Networks
139
These data will now be analyzed using a sim ple m odel w here three reactions are considered:
B iom ass + 0.10 C 0
2
+ 0.10 N A D H - 1 .1 0 CH 20 - a A TP = 0
;
v,
(1)
C O : + 2 N A D H + P A T P - C H 20 = 0
;
v;
(2)
C H
3 0 „ . 5
+ 0.50 CO : + 0.5 A TP - 1.5 C H 20 = 0
;
v;
(3)
In the first reaction glucose is converted to biom ass. The second reaction is com plete oxidation o f glucose
to carbon dioxide via the EM P pathw ay, T C A cycle and regeneration o f N A D ' by respiration. The last
reaction is the ferm entative pathw ay o f glucose to ethanol. T he biom ass form ula is taken to be
CH
1
.g
3
O
0
.
5
eN
0.17
(Kx = 4.20) as in Exam ple 3.5. The stoichiom etry o f pathw ay reaction v, requires a few
comments. Som e carbon is lost to C O :, and this carbon loss varies betw een
8
% and 16% depending on the
environmental conditions. T he form ation o f C O : in connection with biom ass form ation is due to
requirements o f specific precursor m etabolites, w hich w hen they are derived from glucose leads to a net
formation o f CO :,
e.g.
ribose-5-phosphate that serves as a precursor m etabolite for nucleotide biosynthesis.
The stoichiom etric coefficient for N A D H is derived from a redox balance: (4 • 1.10 - 4.20)/2 = 0.10.
The ATP requirem ent a for production o f biom ass will be calculated (note that a is identical to T ^ tp). The
ATP production P per C -m ole glucose converted to CO: via the EM P pathw ay and the TC A cyclus is
probably not independent o f
D.
W hen no ethanol is form ed one m ight assum e that the pyruvate shunt
via
acetaldehyde to acetate (in the cytosol) and to acetate incorporated as A cC oA in the m itochondna is not
operative. C onsequently p = 2/3 since 1/3 A TP is generated on the w ay to pyruvate and 1/3 GTP
(energetically equivalent to A TP) is generated in the TCA cycle. Since in
S. cerevisiae
FA D H ; and N A D H
enter at the sam e place in the respiratory chain they will both have a theoretical P/O ratio o f 2 in the
production o f A TP from oxidation o f the reduced cofactor. C onsequently reaction (2) is exact with respect
to an NADH coefficient o f 2 and P = 2/3 in the case o f pure respiration. W ith increasing ethanol production
rate it is conceivable that a substantial part o f the pyruvate flux passes via acetate and back into the
mitochondria w here 1/3 A TP per glucose carbon is consum ed to convert acetate to A cCoA . In the follow ing
calculations P is taken to be 0.5 at
D
= 0.3h
1
and 0.36 at
D =
0.4h '. The low est possible value o f P is 1 3 -
and we shall exam ine the sensitivity o f the result with respect to p.
Case A: D = 0.15 If' , v, = 0
In this case w e find:
where
-
ro
=
2 v 2 + 0. lv ,
- r s
= 1 . 1 0 v , + v 2
V,
= 0.952(1
- Y sJ - r s)
v
2
= (1 -1 .0 4 8 (1 - T j X - c )
Y
=
r
_____
o_
r
y„
= —
= 0.952(1
- Y j
- r .
(5)
and
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