Human liver - Hepatonet (ATP) SM rate law
(a) Metabolic fluxes (mM/s)
(b) Concentrations (mM)
1
Glucose [s]
2
Glucose [s]
Glucose [c]
Glucose [c]
Glucose−6P [c]
Glucose−6P [c]
Fructose−6P [c]
Fructose−6P [c]
Fructose−1,6PP [c]
Fructose−1,6PP [c]
ADP [c]
GDP [m] GDP [c]
ADP [c]
GDP [m] GDP [c]
1
DHAP [c] GAP [c]
GTP [m] GTP [c]
DHAP [c] GAP [c]
GTP [m] GTP [c]
ATP [c]
ATP [c]
1,3DPG [c]
Pi [c]
1,3DPG [c]
3PG [c]
2PG [c]
ATP [m] ADP [m]
H2O [s] H2O [c]
2PG [c]
ATP [m] ADP [m]
H2O [s] H2O [c]
PEP [c]
Pi [m]
PEP [c]
Pi [m]
Pyruvate [c]
H+(PG) [m] H+(PG) [c]
3PG [c]
Pi [c]
H+(PG) [m] H+(PG) [c]
Lactate [c]
H2O [m]
Lactate [c]
H2O [m]
Lactate [m]
Ferricytochrome C [m]
Ferrocytochrome C [m]
Acetyl−CoA [m]
OAA [m]
Citrate [m]
Malate [m]
Ubiquinone [m]
Ubiquinol [m]
Lactate [m]
Ferricytochrome C [m]
Ferrocytochrome C [m]
Pyruvate [m]
O2 [m]
0
Pyruvate [c]
Pyruvate [m]
Acetyl−CoA [m]
OAA [m]
Citrate [m]
Malate [m]
O2 [m]
Ubiquinone [m]
Ubiquinol [m]
Isocitrate [m]
O2 [c]
CO2 [m]
Succinate [m]
−1
Isocitrate [m]
O2 [c]
Fumarate [m] CoA [m]
CO2 [c]
Fumarate [m] CoA [m]
CO2 [m]
CO2 [s]
Succinate [m]
Oxalosuccinate [m]
O2 [s]
CO2 [c]
CO2 [s]
Oxalosuccinate [m]
O2 [s]
Succinyl−CoAAKG
[m] [m]
Succinyl−CoAAKG
[m] [m]
−1
−2
(c) Chemical potentials (kJ/mol)
(d) Thermodynamic forces (kJ/mol)
10.0793
317.237
Glucose [s]
Glucose [s]
Glucose [c]
Glucose [c]
Glucose−6P [c]
Glucose−6P [c]
Fructose−6P [c]
Fructose−6P [c]
Fructose−1,6PP [c]
Fructose−1,6PP [c]
GDP [m] GDP [c]
ADP [c]
GTP [m] GTP [c]
ATP [c]
GDP [m] GDP [c]
ADP [c]
GTP [m] GTP [c]
ATP [c]
DHAP [c] GAP [c]
DHAP [c] GAP [c]
1,3DPG [c]
1,3DPG [c]
Pi [c]
Pi [c]
3PG [c]
2PG [c]
ATP [m] ADP [m]
H2O [s] H2O [c]
H2O [s]H2O [c]
PEP [c]
Pi [m]
PEP [c]
Pi [m]
Pyruvate [c]
H+(PG) [m] H+(PG) [c]
Pyruvate [c]
H+(PG) [m] H+(PG) [c]
Lactate [c]
Lactate [c]
H2O [m]
Ferricytochrome C [m]
Ferrocytochrome C [m]
O2 [m]
Ubiquinone [m]
Ubiquinol [m]
H2O [m]
Lactate [m]
Ferricytochrome C [m]
Ferrocytochrome C [m]
Pyruvate [m]
Acetyl−CoA [m]
OAA [m]
Citrate [m]
Malate [m]
O2 [m]
Ubiquinone [m]
Ubiquinol [m]
O2 [c]
Fumarate [m] CoA [m]
CO2 [m]
Succinate [m]
CO2 [c]
Lactate [m]
Pyruvate [m]
Acetyl−CoA [m]
OAA [m]
Citrate [m]
Malate [m]
Isocitrate [m]
Isocitrate [m]
O2 [c]
3PG [c]
2PG [c]
ATP [m] ADP [m]
Fumarate [m] CoA [m]
CO2 [m]
CO2 [s]
Succinate [m]
Oxalosuccinate [m]
CO2 [c]
CO2 [s]
Oxalosuccinate [m]
O2 [s]
O2 [s]
Succinyl−CoAAKG
[m] [m]
Succinyl−CoAAKG
[m] [m]
1.00505
−2301.7
Figure 1: Model construction step by step. (a) Thermodynamically feasible flux distribution (grey arrows). (b) Metabolite
levels. (c) Chemical potentials. (d) Thermodynamic driving forces.
1
(e) Energy dissipation (kJ/(m3 s))
(f) Enzyme saturation
0.5
8.75482
Glucose [s]
Glucose [s]
Glucose [c]
Glucose−6P [c]
Glucose [c]
Fructose−6P [c]
Glucose−6P [c]
Fructose−1,6PP [c]
Fructose−6P [c]
GDP [m] GDP [c]
ADP [c]
GTP [m] GTP [c]
ATP [c]
Fructose−1,6PP [c]
GDP [m] GDP [c]
DHAP [c] GAP [c]
ADP [c]
DHAP [c] GAP [c]
GTP [m] GTP [c]
1,3DPG [c]
ATP [c]
1,3DPG [c]
Pi [c]
Pi [c]
3PG [c]
2PG [c]
ATP [m] ADP [m]
H2O [s]H2O [c]
H2O [s]H2O [c]
PEP [c]
PEP [c]
Pi [m]
0
Pyruvate [c]
H+(PG) [m] H+(PG) [c]
Pi [m]
3PG [c]
2PG [c]
ATP [m] ADP [m]
Pyruvate [c]
H+(PG) [m] H+(PG) [c]
Lactate [c]
H2O [m]
Lactate [c]
H2O [m]
Ferricytochrome C [m]
Ferrocytochrome C [m]
Lactate [m]
Ferricytochrome C [m]
Ferrocytochrome C [m]
O2 [m]
Acetyl−CoA [m]
OAA [m]
Citrate [m]
Malate [m]
O2 [m]
Ubiquinone [m]
Ubiquinol [m]
Ubiquinone [m]
Ubiquinol [m]
O2 [c]
Fumarate [m] CoA [m]
Fumarate [m] CoA [m]
CO2 [m]
CO2 [c]
Acetyl−CoA [m]
OAA [m]
Citrate [m]
Malate [m]
Isocitrate [m]
Isocitrate [m]
O2 [c]
Lactate [m]
Pyruvate [m]
Pyruvate [m]
CO2 [m]
CO2 [s]
Succinate [m]
Succinate [m]
Oxalosuccinate [m]
CO2 [c]
CO2 [s]
Oxalosuccinate [m]
O2 [s]
O2 [s]
Succinyl−CoAAKG
[m] [m]
Succinyl−CoAAKG
[m] [m]
−0.5
0.0430936
(g) Reaction elasticities
(h) Flux response
1
7.07505
Glucose [s]
Glucose [c]
Glucose−6P [c]
Glucose [s]
Glucose [c]
Fructose−6P [c]
Glucose−6P [c]
Fructose−1,6PP [c]
Fructose−6P [c]
GDP [m] GDP [c]
ADP [c]
GTP [m] GTP [c]
ATP [c]
Fructose−1,6PP [c]
GDP [m] GDP [c]
DHAP [c] GAP [c]
ADP [c]
1,3DPG [c]
DHAP [c] GAP [c]
GTP [m] GTP [c]
ATP [c]
1,3DPG [c]
Pi [c]
Pi [c]
3PG [c]
2PG [c]
ATP [m] ADP [m]
H2O [s]H2O [c]
H2O [s]H2O [c]
PEP [c]
Pi [m]
Lactate [c]
H2O [m]
Lactate [c]
H2O [m]
O2 [m]
Ubiquinone [m]
Ubiquinol [m]
Lactate [m]
Ferricytochrome C [m]
Ferrocytochrome C [m]
Pyruvate [m]
O2 [m]
Acetyl−CoA [m]
OAA [m]
Citrate [m]
Malate [m]
Ubiquinone [m]
Ubiquinol [m]
Lactate [m]
Pyruvate [m]
Acetyl−CoA [m]
OAA [m]
Citrate [m]
Malate [m]
Isocitrate [m]
O2 [c]
Isocitrate [m]
O2 [c]
0
Pyruvate [c]
H+(PG) [m] H+(PG) [c]
Pyruvate [c]
H+(PG) [m] H+(PG) [c]
Ferricytochrome C [m]
Ferrocytochrome C [m]
PEP [c]
Pi [m]
0
3PG [c]
2PG [c]
ATP [m] ADP [m]
Fumarate [m] CoA [m]
CO2 [m]
Succinate [m]
CO2 [c]
Fumarate [m] CoA [m]
CO2 [m]
CO2 [s]
Succinate [m]
Oxalosuccinate [m]
CO2 [c]
CO2 [s]
Oxalosuccinate [m]
O2 [s]
O2 [s]
Succinyl−CoAAKG
[m] [m]
Succinyl−CoAAKG
[m] [m]
−1
−7.07505
Figure 2: Model construction step by step (continued). (e) Local dissipation of Gibbs free energy (driving force multiplied
by flux). (f) Saturation values. (g) Scaled elasticities. (h) Scaled enzyme response coefficients, predicted by elasticity
sampling. Positive values are shown in blue, negative values in red, zero values in white.
2
Synergies (2nd order scaled control)
Synergy degrees
8
0.152804
Glucose [s]
Glucose [c]
Glucose−6P [c]
Glucose [s]
Glucose [c]
Fructose−6P [c]
Glucose−6P [c]
Fructose−1,6PP [c]
Fructose−6P [c]
GDP [m] GDP [c]
ADP [c]
GTP [m] GTP [c]
ATP [c]
DHAP [c] GAP [c]
Fructose−1,6PP [c]
GDP [m] GDP [c]
ADP [c]
1,3DPG [c]
DHAP [c] GAP [c]
GTP [m] GTP [c]
ATP [c]
1,3DPG [c]
Pi [c]
Pi [c]
3PG [c]
H2O [s]H2O [c]
2PG [c]
ATP [m] ADP [m]
H2O [s]H2O [c]
Pi [m]
Pyruvate [c]
Lactate [c]
H2O [m]
Lactate [c]
H2O [m]
Lactate [m]
Ferricytochrome C [m]
Ferrocytochrome C [m]
Pyruvate [m]
O2 [m]
O2 [m]
Ubiquinone [m]
Ubiquinol [m]
Acetyl−CoA [m]
OAA [m]
Citrate [m]
Malate [m]
Ubiquinone [m]
Ubiquinol [m]
Lactate [m]
Pyruvate [m]
Acetyl−CoA [m]
OAA [m]
Citrate [m]
Malate [m]
Isocitrate [m]
O2 [c]
Isocitrate [m]
O2 [c]
Pyruvate [c]
H+(PG) [m] H+(PG) [c]
H+(PG) [m] H+(PG) [c]
Ferricytochrome C [m]
Ferrocytochrome C [m]
PEP [c]
Pi [m]
PEP [c]
3PG [c]
2PG [c]
ATP [m] ADP [m]
Fumarate [m] CoA [m]
Fumarate [m] CoA [m]
CO2 [m]
Succinate [m]
CO2 [m]
CO2 [c]
CO2 [s]
Succinate [m]
Oxalosuccinate [m]
CO2 [c]
CO2 [s]
Oxalosuccinate [m]
O2 [s]
O2 [s]
Succinyl−CoAAKG
[m] [m]
Succinyl−CoAAKG
[m] [m]
−8
−0.152804
Synergy degree distribution
Fraction syn. deg. (positive) / syn. deg. (negative)
12
70
Positive, total: d
Negative, total: Q
60
10
Count number
Count number
50
40
30
8
6
4
20
2
10
0
−5
0
5
10
Synergy degree
15
0
20
Synergy degrees and scaled control
−5
−4
Synergy clusters
8
7
Synergy degree
6
5
4
3
2
1
0
0.02
−3 −2 −1
0
1
2
3
Synergy sign ratio (log2 scale)
0.04 0.06 0.08
0.1
0.12
First−order scaled control coefficient
0.14
Figure 3: Synergies: statistics
3
4
5
Synergies and Influences
Synergies
7
0.06
Count number (close−up)
Synergy (2nd order scaled control)
0.08
0.04
0.02
0
−0.02
−0.04
−0.06
−0.08
6
5
4
3
2
1
−0.1
0.02
0.04 0.06 0.08
0.1
0.12
Influence (1st order scaled control)
0
−0.15
0.14
Synergies and mean mutual flux control
−0.05
0
Synergy
0.05
0.1
Synergies, normalised by mean mutual flux control
7
0.06
6
Count number (close−up)
0.08
0.04
0.02
Synergy
−0.1
0
−0.02
−0.04
−0.06
−0.08
5
4
3
2
1
−0.1
0.02
0.04 0.06 0.08
0.1
0.12
Mean mutual flux control
0
−8
0.14
Synergy and influence product
2
Synergies normalised by influence product
0.1
Count number (close−up)
5
0.05
Synergy
−6
−4
−2
0
Synergy normalised by mean mutual flux control
0
−0.05
4
3
2
1
−0.1
0
0.005
0.01
0.015
Influence product
0
−60
0.02
−40
−20
0
20
Synergy normalised by influence product
Figure 4: Synergies: correlations to other quantities
4
40
5
# Cycles
10
Cycles from significant synergies
Randomized
# Cycles
P−value for cycles being positive
0
10
3
4
5
6
7
Cycle length
8
9
10
1
0
−1
3
4
5
6
7
Cycle length
8
9
10
2
10
Cycles from significant synergies <0
Randomized
0
10
3
4
5
6
7
Cycle length
8
9
Figure 5: Statistics of synergy cycles
5
10