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Supplemental material 1 – Example network
The reaction scheme in Figure C1 includes the tricarboxylic acid (TCA) cycle, glyoxylate
shunt and adjacent amino acid metabolism. In this example, all cofactors, such as ATP and
NAD+ were considered as external, as are 2-phospho-glycerate (PG), NH3 and CO2. A
detailed description of the enzymes and metabolites is given in the legend of figure C1.
The metabolic network for the demonstration of the proposed method was derived from
Schuster et al. [1].
PG
Pps
Eno
Pyk
PEP
AceEF
Pyr
AcCoA
Ppc
GltA
OAA
Pck
Cit
Acn
Mdh
AlaCon
Icl
Mal
Glu
AspC
Gly
Mas
IsoCit
Fum
Ala
IivE/AvtA
Icd
Pyr
OG
Asp
AspCon
AspA
Fum
OG
Sdh
Succ
SucCD
SucCoA
Gdh
GluCon
Glu
SucAB
SucCoACon
Figure C1: Reaction scheme consisting of the tricarboxylic acid cycle, glyoxylate shunt and some adjacent
reactions of amino acid metabolism in Escherichia coli. Abbreviations of metabolites: AcCoA, acetyl-CoA;
Ala, alanine; Asp, aspartate; Cit, citrate; Fum, fumarate; Glu, glutamate; Gly, glyoxylate; IsoCit,
isocitrate; Mal, malate; OAA, oxaloacetate; OG, 2-oxoglutarate; PEP, phosphoenolpyruvate; PG, 2phosphoglycerate; Pyr, pyruvate; Succ, succinate; SucCoA, succinyl-CoA. Abbreviations of enzymes:
AceEF, pyruvate dehydrogenase; Acn, aconitase; AspA, aspartase; AspC, aspartate aminotransferase;
Eno, enolase; Fum, fumarase; Gdh, glutamate dehydrogenase; GltA, citrate synthase; Icd, isocitrate
dehydrogenase (in E. coli with cofactors NADP/NADPH); Icl, isocitrate lyase; Mas, malate synthase;
IlvE/AvtA, branched-chain amino acid aminotransferase/valine-pyruvate aminotransferase; Mdh, malate
dehydrogenase; Pck, PEP carboxykinase (in E. coli with cofactors ADP/ATP); Ppc, PEP carboxylase; Pps,
PEP synthetase; Pyk, pyruvate kinase; Sdh, succinate dehydrogenase; SucAB, 2-oxoglutarate
dehydrogenase; SucCD, succinyl-CoA synthetase (in E. coli with cofactors ADP/ATP); AlaCon, AspCon,
GluCon and SucCoACon, consumption of alanine, aspartate, glutamate and succinyl-CoA, respectively.
Reversible reactions are indicated by double arrow-heads.
9
10
11
12
13
14
15
16
0
0
0
0
0
1 0 0 0 0 1 0 0 0 0 0 1 0 0 0
0
0
0
0
0 0 1 0 0 0 0 1 0 0 0 0 0 0 0
0
0
0
0
0 0 0 0 1 1 0 0 0 0 0 0 0 0 0
1
1
0
0
0 0 0 0 0 1 0 2 2 1 1 0 1 1 1
2
1
1
0
1 0 0 0 0 0 0 2 2 1 0 0 1 1 1
2
1
1
0
0 1 0 0 1 0 0 0 0 0 0 1 0 0 0
0
0
1 1
0 1 0 0 0 0 0 2 2 1 0 0 1 1 1
1
0
0
1
0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1
0 2 0 0 0 0 0 2 2 1 0 1 1 1 1
0
1 1  2
0 0 0 1 0 0 0 1 1 1 0 1 1 0 0
0
0
0
0
0 1 0 0 0 0 0 1 1 1 0 1 1 0 0
0
0
0
0
0 0 0 1 0 0 0 3 3 2 0 0 2 1 1
2
1
1
0
0 0 0 0 0 0 0 1 1 1 0 0 1 0 0
1
1
1
1
0 1 0 0 0 0 0 3 3 2 0 0 2 1 1
2
1
1
0
SucAB
Icd
0
0
GltA
Pck
Ppc
Acn
0
0 0 0 0 0 0 1 1 0 0 0 0 0 0 0
AceEF
0 0 0 0 0 0 0 0 0 0 1 1 0 0 0
Gdh
IlvE/AvtA
AlaCon
GluCon
AspA
AspC
Pps
Pyk
SucCD
8
Sdh
6
7
Fum
5
Mdh
3
4
Icl
Mas
0

0
1

1
0

1

2
1

2
1

3
2

2

3
1

3
1
2
AspCon
SucCoCon
Eno
No. Emodes
All 16 elementary modes (for detail see [1]) were transformed in matrix notation:
0 0 0 0

0 0 0 0
1 0 0 0

1 1 0 0
1 0 0 0 
0 0 0 0

1 0 0 0
1 0 0 0

0 0 0 0
0 0 0 0

0 0 0 0
1 0 0 1

0 0 1 1

1 0 0 1
0 0 1 1

0 0 1 1
The reactions (enzymes) are presented in the columns, the elementary modes in the rows.
For the calculation of target validity for succinyl-CoA production (SucCoACon), only
elementary flux modes with succinyl-CoA production were considered, which means that all
rows with a zero entry in column SucCoACon were deleted. Hence, the matrix dimension
decreased from a dimension 16 x 24 matrix (16 elementary modes; 24 reactions) to a 6 x 24
matrix, whereas only the elementary modes {8, 9, 10, 11, 13, 16} were further used for the
calculation.
The coefficients si,j of reactions i of each elementary mode j are normalized to the substrate
coefficients sC,j (Eno) leading to the yield coefficients i,j. The modes have been arranged with
increasing size of the succinyl-CoA yields SucCoACon (reaction: SucCoACon) as shown in
0
0
0 12 0 0 0 0 0 12 12 12 0 12 12
0
0
0
0
0 0 13 13
1 2 0 0
0
0
Icd
0
SucAB
13
0
Gdh
IlvE/AvtA
Sdh
13
12 12 12 12
SucCD
Fum
23 13 13 23
0
Mas
0
12 0
Icl
23 0
1
Acn
1
1
Ppc
1
0 12 0 0 0 0 0
Pck
0 13 0 0 0 0 0
GltA
Mdh
AlaCon
GluCon
AspA
AspC
Pps
SucCoCon
AceEF
1

1
1

1
1

1

Pyk
16
9
13
11
8
10
Eno
AspCon
No. Emodes
following matrix.
0
0 0 12 12
1 3 1 3  2 3 0 0
0 23 0 0 0 0 0 23 23 13 0 13 13 13 13
0
0
0
0
1
0 0 1 1 0
0
0
0
0
1
0
0
0
0
0
1
1
1 0
0
0
0
1
0 0 0 0 0
0
0
0
0
1
0
0
0
1
1
1
1
0 0
0
0
SucCoACon
i










The formation of interesting substances from succinyl-CoA can occur via the six different
modes {8, 9, 10, 11, 13, 16}, whereas no co-production of glutamate, alanine and aspartate
were observed. The modes {8, 10} offered the highest maximal theoretical yields for
succinyl-CoA.
Each of i were correlated as function of SucCoACon resulting in statistical evident correlations
or not (Table C2).
Statistical evaluation
Table C2: Statistical analysis of simulation data for succinyl-CoA production with E. coli. R²: regression
coefficient, alpha: slope-correlation coefficient, NOSTAT: no statistical evaluation. The values correspond to
Figure 2a. The entries of ‘#DIV/0’ regarded to constant values (or complete zeros) of stoichiometric coefficients
for the corresponding enzyme.
Enzymes
AspCon
SucCoACon
AlaCon
GluCon
AspA
AspC
Pps
Pyk
AceEF
GltA
Pck
Ppc
Acn
Icl
Mas
Mdh
Fum
Sdh
SucCD
Gdh
IIvE/AvtA
SucAB
Icd
R²
#DIV/0!
1
#DIV/0!
#DIV/0!
0.3428571
0.3428571
#DIV/0!
0.8552036
0.8552036
1
#DIV/0!
0.8552036
1
0.3962264
0.3962264
0.621135
0.481203
1
0.8552036
0.3428571
#DIV/0!
0.3962264
0.3962264
alpha
0
1
0
0
0.8571429
0.8571429
0
-1.5
-1.5
-1
0
1.5
-1
-0.5
-0.5
-1.642857
-1.142857
-2
-1.5
0.8571429
0
-0.5
-0.5
evaluation correlation
#DIV/0!
#DIV/0!
#DIV/0!
#DIV/0!
NOSTAT
NOSTAT
#DIV/0!
-1.5
-1.5
-1
#DIV/0!
1.5
-1
NOSTAT
NOSTAT
NOSTAT
NOSTAT
#DIV/0!
-1.5
NOSTAT
#DIV/0!
NOSTAT
NOSTAT
Reference
1.
Schuster S, Dandekar T, Fell DA: Detection of elementary flux modes in
biochemical networks: a promising tool for pathway analysis and metabolic
engineering. Trends Biotechnol 1999, 17(2):53-60.