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Home , Erythrose, Sedoheptulose

Saccharomyces cerevisiae

(a)Metabolicfluxes(mM/s) (b)Concentrations(mM) 1 2

β β− β β−Glucose −GlucoseExt Glucono−1,5−lactone 6−phosphate −GlucoseExt Glucono−1,5−lactone 6−phosphate 6−Phospho−gluconate 6−Phospho−gluconate

α−Glucose 6−phosphate β−Glucose 6−phosphate α−Glucose 6−phosphate β−Glucose 6−phosphate Glucose 1−phosphate Glucose 1−phosphate

Erythrose 4−phosphateRibulose 5−phosphate 4−phosphateRibulose 5−phosphate β− 6−phosphate β−Fructose 6−phosphate

UDP−glucose 5−phosphate UDP−glucose Xylulose 5−phosphate 1 β−Fructose 1,6−bisphosphate β−Fructose 1,6−bisphosphate

α,α’− 6−phosphate 7−phosphate α,α’−Trehalose 6−phosphate Sedoheptulose 7−phosphate

Glycerone phosphateGlyceraldehyde 3−phosphate 5−phosphate Glycerone phosphateGlyceraldehyde 3−phosphate Ribose 5−phosphate

3−Phospho−glyceroyl phosphate 3−Phospho−glyceroyl phosphate α,α−Trehalose α,α−Trehalose

sn−Glycerol 3−phosphate sn−Glycerol 3−phosphate 3−Phospho−glycerate 3−Phospho−glycerate

2−Phospho−glycerate 2−Phospho−glycerate 0 Ethanol EthanolExt Ethanol EthanolExt Glycerol Glycerol Phosphoenolpyruvate Phosphoenolpyruvate

Pyruvate Acetaldehyde Pyruvate Acetaldehyde GlycerolExt GlycerolExt

Acetyl−CoA Acetate Acetyl−CoA Acetate

Oxaloacetate Citrate Oxaloacetate Citrate

Alanine AlanineExt Alanine AlanineExt Malate Isocitrate Malate Isocitrate −1 Glyoxylate Glyoxylate O2 O2 Glutamate Glutamate Acceptor Acceptor Fumarate Fumarate 2−Oxoglutarate 2−Oxoglutarate Reduced acceptor Reduced acceptor Glutamine Glutamine Succinate Succinyl−CoA Succinate Succinyl−CoA

−1 −2

(c)Chemicalpotentials(kJ/mol) (d)Thermodynamicforces (kJ/mol)

394.252 49.9049

β−GlucoseExt β−Glucose β−GlucoseExt β−Glucose Glucono−1,5−lactone 6−phosphate Glucono−1,5−lactone 6−phosphate 6−Phospho−gluconate 6−Phospho−gluconate

α−Glucose 6−phosphate β−Glucose 6−phosphate α−Glucose 6−phosphate β−Glucose 6−phosphate Glucose 1−phosphate Glucose 1−phosphate Erythrose 4−phosphate Erythrose 4−phosphate 5−phosphate Ribulose 5−phosphate β−Fructose 6−phosphate β−Fructose 6−phosphate UDP−glucose Xylulose 5−phosphate UDP−glucose Xylulose 5−phosphate β−Fructose 1,6−bisphosphate β−Fructose 1,6−bisphosphate α α Sedoheptulose 7−phosphate α,α’−Trehalose 6−phosphate Sedoheptulose 7−phosphate , ’−Trehalose 6−phosphate

Glycerone phosphateGlyceraldehyde 3−phosphate Ribose 5−phosphate Glycerone phosphateGlyceraldehyde 3−phosphate Ribose 5−phosphate

3−Phospho−glyceroyl phosphate 3−Phospho−glyceroyl phosphate α α α,α−Trehalose , −Trehalose

sn−Glycerol 3−phosphate sn−Glycerol 3−phosphate 3−Phospho−glycerate 3−Phospho−glycerate

2−Phospho−glycerate 2−Phospho−glycerate Ethanol EthanolExt Ethanol EthanolExt Glycerol Glycerol Phosphoenolpyruvate Phosphoenolpyruvate

Pyruvate Acetaldehyde Pyruvate Acetaldehyde GlycerolExt GlycerolExt

Acetyl−CoA Acetate Acetyl−CoA Acetate

Citrate Oxaloacetate Citrate Oxaloacetate

Alanine AlanineExt Alanine AlanineExt Malate Isocitrate Malate Isocitrate Glyoxylate Glyoxylate O2 O2 Glutamate Glutamate Acceptor Acceptor Fumarate Fumarate 2−Oxoglutarate 2−Oxoglutarate Reduced acceptor Reduced acceptor Glutamine Glutamine Succinate Succinyl−CoA Succinate Succinyl−CoA

−1895.05 2.7742

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)Enzymesaturation 1

30.3277 β−GlucoseExt β−Glucose Glucono−1,5−lactone 6−phosphate 6−Phospho−gluconate

β−GlucoseExt β−Glucose Glucono−1,5−lactone 6−phosphate α−Glucose 6−phosphate β−Glucose 6−phosphate 6−Phospho−gluconate Glucose 1−phosphate

α−Glucose 6−phosphate β−Glucose 6−phosphate Erythrose 4−phosphateRibulose 5−phosphate Glucose 1−phosphate β−Fructose 6−phosphate

Erythrose 4−phosphateRibulose 5−phosphate UDP−glucose Xylulose 5−phosphate β −Fructose 6−phosphate β−Fructose 1,6−bisphosphate UDP−glucose Xylulose 5−phosphate α,α’−Trehalose 6−phosphate Sedoheptulose 7−phosphate β−Fructose 1,6−bisphosphate

α,α’−Trehalose 6−phosphate Sedoheptulose 7−phosphate Glycerone phosphateGlyceraldehyde 3−phosphate Ribose 5−phosphate

Glycerone phosphateGlyceraldehyde 3−phosphate Ribose 5−phosphate 3−Phospho−glyceroyl phosphate α,α−Trehalose 3−Phospho−glyceroyl phosphate α α sn−Glycerol 3−phosphate , −Trehalose 3−Phospho−glycerate sn−Glycerol 3−phosphate 3−Phospho−glycerate 2−Phospho−glycerate 0 Ethanol EthanolExt 2−Phospho−glycerate Glycerol Ethanol EthanolExt Phosphoenolpyruvate Glycerol Phosphoenolpyruvate Pyruvate Acetaldehyde GlycerolExt Pyruvate Acetaldehyde GlycerolExt Acetyl−CoA Acetate Acetyl−CoA Acetate Oxaloacetate Citrate Oxaloacetate Citrate Alanine AlanineExt Alanine AlanineExt Malate Isocitrate Malate Isocitrate Glyoxylate Glyoxylate O2 O2 Glutamate Glutamate Acceptor Acceptor Fumarate Fumarate 2−Oxoglutarate 2−Oxoglutarate Reduced acceptor Reduced acceptor Glutamine Glutamine Succinate Succinyl−CoA Succinate Succinyl−CoA

5.98389e−15 −1

(g)Reactionelasticities (h)Fluxresponse 1

1.77653

β β−Glucose −GlucoseExt Glucono−1,5−lactone 6−phosphate 6−Phospho−gluconate β−GlucoseExt β−Glucose Glucono−1,5−lactone 6−phosphate α β 6−Phospho−gluconate −Glucose 6−phosphate −Glucose 6−phosphate Glucose 1−phosphate

α β −Glucose 6−phosphate −Glucose 6−phosphate Erythrose 4−phosphateRibulose 5−phosphate Glucose 1−phosphate β−Fructose 6−phosphate Erythrose 4−phosphate Ribulose 5−phosphate UDP−glucose Xylulose 5−phosphate β−Fructose 6−phosphate β−Fructose 1,6−bisphosphate UDP−glucose Xylulose 5−phosphate β−Fructose 1,6−bisphosphate α,α’−Trehalose 6−phosphate Sedoheptulose 7−phosphate

α,α’−Trehalose 6−phosphate Sedoheptulose 7−phosphate Glycerone phosphateGlyceraldehyde 3−phosphate Ribose 5−phosphate

Glycerone phosphateGlyceraldehyde 3−phosphate Ribose 5−phosphate 3−Phospho−glyceroyl phosphate α,α−Trehalose 3−Phospho−glyceroyl phosphate α,α−Trehalose sn−Glycerol 3−phosphate 3−Phospho−glycerate sn−Glycerol 3−phosphate 3−Phospho−glycerate 2−Phospho−glycerate 0 Ethanol EthanolExt 2−Phospho−glycerate 0 Glycerol Ethanol EthanolExt Glycerol Phosphoenolpyruvate Phosphoenolpyruvate Pyruvate Acetaldehyde GlycerolExt Pyruvate Acetaldehyde GlycerolExt Acetyl−CoA Acetate Acetyl−CoA Acetate Oxaloacetate Citrate Oxaloacetate Citrate Alanine AlanineExt Alanine AlanineExt Malate Isocitrate Malate Isocitrate Glyoxylate Glyoxylate O2 O2 Glutamate Glutamate Acceptor Acceptor Fumarate Fumarate 2−Oxoglutarate 2−Oxoglutarate Reduced acceptor Reduced acceptor Glutamine Glutamine Succinate Succinyl−CoA Succinate Succinyl−CoA

−1.77653 −1

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(2ndorderscaledcontrol) Synergydegrees 17 1.29968

β β−Glucose −GlucoseExt Glucono−1,5−lactone 6−phosphate 6−Phospho−gluconate β−GlucoseExt β−Glucose Glucono−1,5−lactone 6−phosphate 6−Phospho−gluconate α−Glucose 6−phosphate β−Glucose 6−phosphate Glucose 1−phosphate α−Glucose 6−phosphate β−Glucose 6−phosphate Glucose 1−phosphate Erythrose 4−phosphateRibulose 5−phosphate β−Fructose 6−phosphate Erythrose 4−phosphateRibulose 5−phosphate β−Fructose 6−phosphate UDP−glucose Xylulose 5−phosphate β−Fructose 1,6−bisphosphate UDP−glucose Xylulose 5−phosphate β−Fructose 1,6−bisphosphate α,α’−Trehalose 6−phosphate Sedoheptulose 7−phosphate

α α Sedoheptulose 7−phosphate , ’−Trehalose 6−phosphate Glycerone phosphateGlyceraldehyde 3−phosphate Ribose 5−phosphate Glycerone phosphateGlyceraldehyde 3−phosphate Ribose 5−phosphate 3−Phospho−glyceroyl phosphate α,α−Trehalose 3−Phospho−glyceroyl phosphate α α , −Trehalose sn−Glycerol 3−phosphate 3−Phospho−glycerate sn−Glycerol 3−phosphate 3−Phospho−glycerate 2−Phospho−glycerate Ethanol EthanolExt 2−Phospho−glycerate Ethanol EthanolExt Glycerol Glycerol Phosphoenolpyruvate Phosphoenolpyruvate Pyruvate Acetaldehyde Pyruvate Acetaldehyde GlycerolExt GlycerolExt Acetyl−CoA Acetate Acetyl−CoA Acetate

Oxaloacetate Citrate Oxaloacetate Citrate Alanine AlanineExt Alanine AlanineExt Malate Isocitrate Malate Isocitrate Glyoxylate Glyoxylate O2 O2 Glutamate Glutamate Acceptor Acceptor Fumarate Fumarate 2−Oxoglutarate 2−Oxoglutarate Reduced acceptor Reduced acceptor Glutamine Glutamine Succinate Succinyl−CoA Succinate Succinyl−CoA

−1.29968 −17

Synergydegreedistribution Fractionsyn.deg.(positive) / syn. deg. (negative) 90 Positive, total: Ã˙ 80 Negative, total: ¿ 25

70 20 60

50 15 40 Count number Count number 30 10

20 5 10

0 0 −5 0 5 10 15 20 −5 −4 −3 −2 −1 0 1 2 3 4 5 Synergy degree Synergy sign ratio (log2 scale)

Synergydegreesandscaledcontrol Synergyclusters

16

14

12

10

8

6 Synergy degree

4

2

0 −1 −0.5 0 0.5 1 First−order scaled control coefficient

Figure 3: Synergies: statistics

3 SynergiesandInfluences Synergies

5 25

20

15 0

10 Count number (close−up) 5 Synergy (2nd order scaled control)

−5 0 −1 −0.5 0 0.5 1 −10 −5 0 5 10 15 Influence (1st order scaled control) Synergy

Synergiesandmeanmutualfluxcontrol Synergies,normalised by mean mutual flux control

12

10 35

8 30 6 25 4 20 2 Synergy 15 0

−2 10 Count number (close−up)

−4 5 −6 0 −1 −0.5 0 0.5 1 −2000 0 2000 4000 6000 8000 Mean mutual flux control Synergy normalised by mean mutual flux control

Synergyandinfluenceproduct Synergiesnormalisedbyinfluence product

12 30 10 8 25 6 20 4 2 15 Synergy 0 10 −2 Count number (close−up) −4 5 −6 0 −1.5 −1 −0.5 0 0.5 1 1.5 −5000 0 5000 10000 Influence product Synergy normalised by influence product

Figure 4: Synergies: correlations to other quantities

4 5 10 Cycles from significant synergies Randomized # Cycles

0 10 3 4 5 6 7 8 9 10 Cycle length 0.1

0.05

0 3 4 5 6 7 8 9 10 Cycle length

P−value for cycles being positive

2 10 Cycles from significant synergies <0 Randomized # Cycles

0 10 3 4 5 6 7 8 9 10 Cycle length

Figure 5: Statistics of synergy cycles

5