Supplementary file
List of Contents
1. Modified Control Effective Flux (mCEF) algorithm
2. Metabolic networks models

1 Modified Control Effective Flux (mCEF) algorithm
mCEF predicts the gene expression profile of genetically modified mutants where an enzyme
coding gene is over-expressed (the relative enzyme activity ratio of a mutant versus wild type is >1) or under-expressed (0 < enzyme activity ratio of mutant versus wild type < 1). Details ofmCEF algorithm are described using a small metabolic network model.
The metabolic network model is shown in Figure S1. R6 is reversible reaction and the others areirreversible reactions. Ax, F and G are the external metabolites and the others are the internalmetabolites.

Figure S1. A small metabolic network map. The formation of F (R8: EÆF) is the cellularfunction. Ax, F and G are the external metabolites.
The formation of F from E is regarded as a biological function. In a mutant the gene responsible
for the reaction A --> C is 2-fold over-expressed, i.e., the relative enzyme activity parameter EAPof reaction 5 is set to 2.
There are four elementary modes (EMs) for the example network model. The fluxes could bedecomposed onto EMs as follows:

1
0
0
0v = P•λ = 1
01
1636311020-20060603
00   λ1   1   λ2 •
3   λ3   1   λ4 0
0 where v is the flux; P is the EM matrix; λ is the EM coefficient (EMC) vector.

The elements in an EM are normalized by the element of the substrate uptake reaction in eachEM.
Table S1 EMs normalized by the substrate uptake reaction
Reaction, iAbsolute element in the j-th EM pi , j
130422060010

1301

AÆC3CÆ2D0131000

CÆEEÆF111100

1R22AÆB

12R3

3BÆ4D

13R42DÆG

45R5R6

67R7R811300

The efficiency of each EM for the mutant is calculated by:ε mj,CELLOBJ =pCELLOBJ , j ⋅ EA j∑( pi, j⋅ηii) EAPi (if reaction i is modified)1 (if reaction i is not modified)ηi = Table S2 Parameter ηi for each reaction

ηiReaction, i
1
234
5
67R2R3R4R5R6R7R82AÆB
3BÆ4D2DÆGAÆC3CÆ2DCÆEEÆF1112111nEAj = ∏ gei , ji =1

 EAPi (if the i -th reaction is involved in the j -th EM)
gei , j = 1 (if the i -th reaction is not involved in the j -th EM)
Table S3 Parameter EAj for each EM
The j-th EMEAj
1122
32
41

1263

mCEFi (mut ) =∑ p

CELLOBJ

1∑ (εjmax
CELLOBJmj ,CELLOBJ∑ε⋅ pi , j ⋅ηi)

mj ,CELLOBJ

j1× 1
1=132 × 1 + 6 × 1 + 0 × 1 + 0 × 2 + 3 × 1 + 1 × 1 + 1× 10× 2=0
ε 2,7 =0 × 1 + 0 × 1 + 1 3 × 1 + 1 × 2 + 13 × 1 + 0 × 1 + 0 × 1
1× 2
1
ε 3,7 =
=0 × 1 + 0 × 1 + 0 × 1 + 1 × 2 + 0 × 1 + 1 × 1 + 1× 1 20 ×1
ε 4,7 = 1=0112 ×1 + 6 ×1 + 3 ×1 + 0 × 2 + 0 ×1 + 0 × 1 + 0 ×1

ε1,7 = 11

The mCEF for each reaction is calculated.

1 13 ⋅ ( 12 ×1) + 0 ⋅ ( 0 × 1) + 12 ⋅ ( 0 × 1) + 0 ⋅ ( 12 × 1) 1
mCEF1 ( mut ) = ⋅=15( 13 + 0 + 1 2 + 0 )1 13 ⋅ ( 16 ×1) + 0 ⋅ ( 0 ×1) + 1 2 ⋅ ( 0 × 1) + 0 ⋅ ( 16 × 1) 1
mCEF2 ( mut ) = ⋅=115( 13 + 0 + 1 2 + 0 )1 13 ⋅ ( 0 ×1) + 0 ⋅ ( 13 ×1) + 12 ⋅ ( 0 ×1) + 0 ⋅ ( 13 × 1)
mCEF3 ( mut ) = ⋅=01( 13 + 0 + 1 2 + 0 )1 13 ⋅ ( 0 × 2 ) + 0 ⋅ (1× 2 ) + 1 2 ⋅ (1× 2 ) + 0 ⋅ ( 0 × 2 ) 6mCEF4 ( mut ) = ⋅=15( 13 + 0 + 1 2 + 0 )1 13 ⋅ ( 13 × 1) + 0 ⋅ ( 13 × 1) + 1 2 ⋅ ( 0 × 1) + 0 ⋅ ( 0 × 1) 2
mCEF5 ( mut ) = ⋅=115( 13 + 0 + 1 2 + 0 )1 13 ⋅ (1× 1) + 0 ⋅ ( 0 × 1) + 12 ⋅ (1× 1) + 0 ⋅ ( 0 × 1)
mCEF6 ( mut ) = ⋅=11( 13 + 0 + 1 2 + 0 )1 13 ⋅ (1× 1) + 0 ⋅ ( 0 × 1) + 12 ⋅ (1×1) + 0 ⋅ ( 0 × 1)
mCEF7 ( mut ) = ⋅=11( 13 + 0 + 1 2 + 0 )The mCEFs of an over-expressing mutant are calculated below.

Θi ( w, mut ) =mCEFi (mut )mCEFi ( w)Table S4 Values of mCEFs of an over-expressing mutant
mCEFi(mut)Reaction i
mCEFi(w)
1R2

2AÆB

2

R3

3BÆ4D

3
4R4R52DÆ3F
AÆC

5R63CÆ2D

6
7R7R8CÆE
EÆFΘ i(w, m ut)

1411215115454500112166521512565111111

2. Metabolic networks models
Table S5 Metabolic network model of Escherichia coli

GeneACEAACEB
ACKACNACXT
ADKATP
ATPDRAINCO2XT
CYOEDAGAPGLCUP
GLTGND
GPM

Gene description
Isocitrate lyase
Malase synthase A
Acetate kinase
Aconitase
Acetate transport
Adenylate kinase
F0F1-ATPase
ATP drain
CO2 transport
Cytochrome oxidase bo36-phosphogluconate dehydratase2-keto-3-deoxy-6-phosphogluconate
aldolase
EnolaseFructose-1,6-bisphosphatase aldolase
Fructose-1,6-bisphosphatase
Fumarate reductase
Fumarase
Glyceraldehyde-3-phosphatedehydrogenase
uptake of glucose
Citrate synthase
6-phosphoglycononate dehydrogenase
Phosphoglycerate mutase

GROWTH

GrowthICD
LPD
MAEB

Isocitrate dehydrogenaselipoamide dehydrogenase
Malic enzyme (NADP)

EDD
ENO
FBA
FBP
FRD
FUM

Reaction
ICIT ==> SUCC + GLXACCOA + GLX ==> MAL + COA
ACTP + ADP <==> ATP + AC
CIT <==> ICIT
AC ==> ACXT
ATP + AMP <==> 2 ADP
PI + 4 HEXT + ADP <==> ATP
ATP ==> PI + ADP
CO2 <==> CO2XT
2 QH2 + O2 ==> 2 Q + 4 HEXT
KetoPGluc ==> T3P1 + PYR
D6PGC ==> KetoPGluc
P2G <==> PEP
FDP <==> T3P1 + T3P2
FDP ==> F6P + PI
FADH + FUM ==> FAD + SUCC
FUM <==> MAL
PI + T3P1 + NAD <==> P13DG + NADH
GLCXT ==> GLC
ACCOA + OA ==> COA + CIT
D6PGC + NADP ==> RL5P + CO2 + NADPH
P3G <==> P2G
0.1 F6P + 1.5 P3G + 3.7 ACCOA + 0.2 G6P + 41.3 ATP + 0.5 PEP + 1.1 AKG +0.4 E4P + 18.2 NADPH + 1.8 OA + 0.9 R5P + 0.1 T3P1 + 3.5 NAD + 2.8 PYR==> 41.3 PI + 3.7 COA + 41.3 ADP + 3.5 NADH + 18.2 NADP + BIOMASSICIT + NADP <==> AKG + CO2 + NADPH
COA + NAD + PYR ==> ACCOA + CO2 + NADH
MAL + NADP ==> CO2 + NADPH + PYR

Table S5 (continued)
Gene
Gene description
MDH
Malase dehydrogenase
NUO
NADH dehydrogenase
O2XT
Oxygen transport
PCK
Phosphoenolpyruvate carboxykinase
PFK
Phosphofructokinase
PGI
Phosphoglucoisomerase
PGK
Phosphoglycerate kinase
PGL
6-phosphoglyconolactonase
PIXT
Inorganic phosphate transportPNTA
Pyridine nucleotide transhydrogenase A
PNTB
Pyridine nucleotide transhydrogenase B
PPC
Phosphoenolpyruvate carboxylase
PPS
Phosphoenolpyruvate synthase
PTA
Phosphotransacetylase
PTS
Glucose transport
PYK
Pyruvate kinase
RPE
Ribulose phosphate 3-epimerase
RPI
Ribose-5-phosphate isomerase
SDH
Succinate dehydrogenase
SDH2
Succinate dehydrogenase complex
SUCAB
2-Ketoglutarase dehydragenase
SUCCD
Succinyl-CoA synthetase
TALB
Transaldolase B
TKTA
Transketolase I
TKTB
Transketolase II
TPI
Triosphosphate isomerase
ZWF
Glucose-6-phosphate 1-dehydrogenase

Reaction
MAL + NAD <==> OA + NADH
Q + NADH ==> QH2 + 2 HEXT + NAD
O2 <==> O2XTATP + OA ==> PEP + CO2 + ADP
F6P + ATP ==> ADP + FDP
G6P <==> F6P
ADP + P13DG <==> P3G + ATP
D6PGL ==> D6PGC
PI <==> PIXT
NADPH + NAD ==> NADH + NADP
2 HEXT + NADH + NADP ==> NADPH + NAD
PEP + CO2 ==> PI + OA
ATP + PYR ==> PI + PEP + AMPACCOA + PI <==> ACTP + COA
PEP + GLC ==> G6P + PYR
PEP + ADP ==> ATP + PYR
RL5P <==> X5P
RL5P <==> R5PFAD + SUCC ==> FADH + FUM
FADH + Q <==> FAD + QH2
AKG + COA + NAD ==> CO2 + SUCCOA + NADH
PI + ADP + SUCCOA <==> ATP + SUCC + COA
S7P + T3P1 <==> F6P + E4P
X5P + R5P <==> S7P + T3P1
X5P + E4P <==> F6P + T3P1
T3P1 <==> T3P2
G6P + NADP <==> NADPH + D6PGLTable S6 Metabolites in metabolic network model of Escherichia coli

Abbreviations

Full name

Abbreviations

AC
ACCOA

AcetateAcetyl coenzyme A

KetoPGluc
MAL

ACTP

Acetyl phosphateNAD

ACXT

external acetate

NADH

ADP

Adenosine diphosphate

NADP

AKG

alpha-Ketoglutarate
Adenosine5'-monophosphate
Adenosine triphosphate
Biomass

NADPH

AMP
ATP
BIOMASS
CIT
CO2
CO2XT
COA
D6PGC
D6PGL
E4P
F6P
FAD
FADH
FDP
FUM
G6P
GLC
GLCXT
GLX
HEXT
ICIT

CitrateCarbon dioxide
external carbon dioxide
Coenzyme A
6-Phospho-D-gluconate
D-Glucono-1,5-lactone
6-phosphate
Erythrose-4-phosphate
Fructose-6-phosphate
Flavin adenine dinucleotide
Flavin adenine
dinucleotide-reduced
D-Fructose
2,6-bisphosphate
Fumarate
Glucose-6-phosphate
GlucoseExternal glucose
Glyoxylateexternal hydrogenisocitrate

O2O2XT
OA

Full name2-Keto-3-desoxy-6-phospho
gluconatemalateNicotinamide adenine
dinucleotide
Nicotinamide adenine
dinucleotide - reduced
Nicotinamide adenine
dinucleotide phosphate
Nicotinamide adenine
dinucleotide
phosphate-reduced

P13DG
P2G
P3G
PEP
PI

OxygenExternal oxygen
oxaloacetate
3-Phospho-D-glyceroyl
phosphate
2-Phosphoglycerate
3-Phosphoglycerate
Phosphoenolpyruvate
Phosphate

PIXT
PYR
Q
QH2

external phosphate
Pyurvate
Ubiquinone-8
Ubiquinol-8

R5P

ribose-5-phosphate

RL5P
S7P
SUCC
SUCCOA
T3P1T3P2X5P

ribulose-5-phosphatesedoheptulose-7-phosphate
succinatesuccinyl-coenzyme A
glyceraldehyde-3-phosphate
dihydroxyacetate phosphate
xylulose-5-phosphateFigure S2 Central network model of E. coli. Grey ones are external metabolites.

Table S7 Metabolic network model for Corynebacterium glutamicum

Gene
asp
glt, acn,icd
tkt IIsucCD

Gene description
Asparagine transaminase
Citrate synthase, Aconitase, isocitrate dehydrogenase

ilvBCDE

Transketolase II
SUCCCoA synthase
Glyceraldehyde-3-phosphate dehydrogenase,
Phosphoglycerate kinase
Transaldolase
Glutamate dehydrogenase
trehalose-6-phosphate synthase
Phosphoglucoisomerase
Ribose-5-phosphate isomerase
Ribulose phosphate 3-epimerase
Phosphoglycerate mutase, Enolase
Oxygen uptake
Transketolase I
SUCC-CoA synthase
Lysine transport
Pyruvate dehydrogenase
Trehalose transport
2-Ketoglutarase dehydragenase
Phosphoenolpyruvate synthase, Pyruvate kinase
Acetolactate synthase I, Acetohydroxy acidisomeroreductase, Dihydroxy acid dehydratase,
Branched chain amino acid aminotransferase

GrowthBiomass formation

ATPATP synthase

gap, pgk
talglutDH
ots
pgi
rpi
rpe
gpm, enoO2ext
tkt IsucCD
LysextpdhTreext
sucAB
pps, pykReaction
OAA + GLUT <==> ASP + AKG
OAA + ACCOA + H2O + NADP <==> AKG + CO2 + NADPH + COA
E4P + XYL5P <==> GAP + FRU6P
ADP + SUCCOA <==> ATP + COA + SUC
GAP + ADP + NAD <==> ATP + G3P + NADH
SED7P + GAP <==> E4P + FRU6P
AKG + NH3 + NADPH <==> H2O + NADP + GLUT
ATP + 2 GLC6P <==> TREHAL + ADP
GLC6P <==> FRU6P
RIBU5P <==> RIB5P
RIBU5P <==> XYL5P
G3P <==> PEP + H2O
O2 <==> O2XTRIB5P + XYL5P <==> SED7P + GAP
FAD + H2O + NAD + SUC <==> OAA + FADH + NADH
LYSI ==> LYSIXTCOA + NAD + PYR ==> ACCOA + CO2 + NADH
TREHAL ==> TREHALXT
AKG + COA + NAD ==> CO2 + SUCCOA + NADH
PEP + ADP ==> ATP + PYR
NADPH + GLUT + 2 PYR ==> VAL + AKG + CO2 + H2O + NADP
332 ACCOA + 40 VAL + 3000 ATP + 80 ASP + 126 RIB5P + 33 LYSI+ 150 G3P + 52 PEP + 13 GAP + 100 NADPH + 54 ALA + 25 GLUM+ 7 FRU6P + 21 GLC6P + 446 GLUT + 30 PYR ==> 364 AKG + 143
CO2 + 332 COA + 3000 ADP + 100 NADP + 1000 BIOMASS
4 ADP + 2 NADH + O2 ==> 4 ATP + 2 H2O + 2 NADTable S7 (continued)
Gene description
Gene
alaTr
Alanine transaminase
ATPdrain ATP drain
Lys
Diaminopimelate decarboxylase
FADHDH FADH dehydrogenase
Succinyl diaminopimelate aminotransferase,
Tetrahydrodipicolinate succinylase, Succinyl
diaminopimelate desuccinylase
dapCEFfbp
Fructose-1,6-bisphosphatasepts
Phosphotransferase system
Fructosebisphophaphate aldolase,Triosphosphatefba, tpiisomerase
CO2 transport
CO2extppc
Phosphoenolpyruvate carboxylase
H2OextWater transport
Thr, asd
Aspartate kinase, Aspartate semialdehyde
GLCupGlucose uptake
Glutamine synthase
Glumpfk
Phosphofructokinase
Ammonia transport
NH3extZwf, pgl, Glucose-6-phosphate 1-dehydrogenase,gnd
6-phosphoglyconolactonase, 6-phosphoglycononate
dehydrogenase

Reaction
GLUT + PYR ==> AKG + ALA
ATP ==> ADP
MDAP ==> LYSI + CO2
2 FADH + 2 ADP + O2 ==> 2 ATP + 2 FAD + 2 H2O
AKP + SUCCOA + H2O + GLUT ==> MDAP + AKG + COA + SUC
H2O + FDP ==> FRU6P
PEP + GLC ==> GLC6P + PYR
FDP ==> 2 GAP
CO2 ==> CO2XT
PEP + CO2 ==> OAA
H2O ==> H2OXT
ATP + ASP + 2 NADPH + PYR ==> AKP + ADP + H2O + 2 NADPGLCXT ==> GLC
ATP + NH3 + GLUT ==> ADP + GLUM
ATP + FRU6P ==> ADP + FDP
NH3XT ==> NH3
H2O + 2 NADP + GLC6P ==> CO2 + 2 NADPH + RIBU5P

Table S8 Metabolites in metabolic network models for Corynebacterium glutamicum

Abbreviations Full name

Abbreviations Full name

OAA

Oxaloacetic acid

SUCCOA

Succinyl -coenzyme A

FADH

Flavin adenine dinucleotide

H2O

Water

NADH

Nicotinamide adenine(reduced)
ACCOA

Acetyl-coenzyme A

dinucleotide (reduced)
VAL

ValineO2OxygenATP

Adenosine triphosphate

ALA

AlanineASP

Aspartate

NAD

Nicotinamide adenine
dinucleotide (oxidized)

SED7P

Sedoheptulose-7-phosphate

GLUM

Glutamine

RIB5P

Ribose-5-phosphate

GLC

Glucose

LYSI

LysineNADP

Nicotinamide adenine
dinucleotide phosphate(oxidized)

G3P

3-phosphoglycerate

FRU6P

Fructose-6-phosphate

AKP

2-Amino-6-ketopimelate

XYL5P

Xylulose-5-phosphate

PEP

Phosphoenolpyruvate

GLC6PGlucose-6-phosphateMDAPmeso-diaminopimelate

FDP

Fructose 2,6-bisphosphate

GAP

Glyceraldehyde-3-phosphate

GLUT

Glutamate

AKG

alpha-ketoglutarate

SUC

Succinate

E4P

Erythrose-4-phosphate

PYR

Pyruvate

TREHAL

Trehalose

LYSIXT

External lysine

NH3Ammonia

O2XTExternal oxygen

FAD

Flavin adenine dinucleotide

CO2XT

External carbon dioxide(oxidized)
CO2

Carbon dioxide

TREHALXT

External trehalose

NADPH

Nicotinamide adenine

BIOMASS

Biomass

dinucleotide phosphate(reduced)
COA

Coenzyme A

H2OXT

External Water

RIBU5P

Ribulose-5-phosphate

GLCXT

External glucose

ADPAdenosine diphosphate

NH3XT

External ammonia

Figure S3 Central network model of C. glutamicum. Grey ones are external metabolites.

Table S9 Prediction errors for nine mutants of E. coli by FBA, MOMA and GMF
Mutant

FBAa

FBAb

MOMA

GMF

fbp

38.19

23.69

19.65

20.00

pps

35.31

20.66

10.78

9.97

rpe

32.65

34.84

11.64

9.20

tktA

38.44

40.82

15.17

14.12

tktB

21.01

23.25

4.78

4.68

fba

26.93

28.85

20.20

19.43

pgi

26.97

24.80

19.94

24.56

pgl

21.97

23.68

21.04

21.97

gnd

28.61

32.30

17.22

14.39

a: the objective function in FBA is the maximum biomass formation;b: the objective function in FBA is the maximum ATP per flux unit (Schuetz et al, 2007);
The metabolic fluxes for mutants were cited from the reference (Ishii,N. et al., 2007)
FBA is performed by linprog in Matlab.

min ∑ ci v ii

subject toS⋅v = 0vi ,min ≤ vi ≤ vi ,max ( i = 1,..., n )In the metabolic network models of E. coli and C. glutamicum, the reaction for biomass
formation was presented. The coefficients of the objective function, ci, are -1 for this biomass
formation reaction while they are zero for other reactions.