MODEL 1. provides additional information about the performance of the CeSS algorithm.

Transcription

1 MODEL 1 Sections 1 to 4 describe Model 1, a metabolic model of E. coli s Central Carbon Metabolism. Section 5 provides additional information about the performance of the CeSS algorithm. 1 Model structure: metabolites and reactions 1.1 Metabolite list Last column: 1 for external metabolites, 0 for internal. # Metabolite Name KEGG ID Ext. / Int. 1 Pyruvate C Thiamin diphosphat C (alpha-Hydroxyethyl)thiamine diphosphat C CO2 C ATP C H2O C AMP C Phosphoenolpyruvat C Orthophosphat C ADP C Acetyl-CoA C Formate C CoA C (S)-Malate C NAD+ C NADH C H+ C NADP+ C NADPH C Acetaldehyd C Acetyl phosphat C Acetate C Diphosphat C L-Glutamat C Oxoglutarat C NH3 C Oxalosuccinat C Oxaloacetat C Citrate C Succinate C Succinyl-Co C Acceptor C Fumarate C Reduced accepto C Glyoxylate C Isocitrate C Carboxy-1-hydroxypropyl-ThP C Phospho-D-glycerat C

2 39 (S)-Lactat C Ethanol C D-Glyceraldehyde 3-phosphat C Glycerone phosphat C D-Ribose 5-phosphat C Phospho-alpha-D-ribose 1-diphosphat C D-Ribulose 5-phosphat C Phospho-D-glyceroyl phosphat C beta-d-fructose 1,6-bisphosphat C cis-aconitat C Phospho-D-glycerat C Phospho-D-gluconat C D-Xylulose 5-phosphat C beta-d-glucose C beta-d-glucose 6-phosphat C Sedoheptulose 7-phosphat C Dihydrolipoamid C Lipoamide C D-Erythrose 4-phosphat C beta-d-fructose 6-phosphat C D-Glucono-1,5-lactone 6-phosphat C Dehydro-3-deoxy-6-phospho-D-gluconat C Enzyme N6-(dihydrolipoyl)lysin C (Dihydrolipoyllysine-residue acetyltransferase)-sacetyldihydrolipoyllysin C (Dihydrolipoyllysine-residue succinyltransferase)- C S-succinyldihydrolipoyllysin 64 Ferricytochrome b C Ferrocytochrome b C Enzyme N6-(lipoyl)lysin C sn-glycerol 3-phosphat C Glycerol C GlycerolEx 1 70 beta-d-glucoseex 1 71 GTP C GDP C O2 C Biomass Reaction list # Formula KEGG ID 1 Pyruvate + Thiamin diphosphate 2-(alpha-Hydroxyethyl)thiamine diphosphate + CO2 R Pyruvate + ATP + H2O AMP + Phosphoenolpyruvate + Orthophosphate R Pyruvate + ATP Phosphoenolpyruvate + ADP R Acetyl-CoA + Formate Pyruvate + CoA R (S)-Malate + NAD+ Pyruvate + CO2 + NADH + H+ R (S)-Malate + NADP+ Pyruvate + CO2 + H+ + NADPH R CoA + NAD+ + Acetaldehyde Acetyl-CoA + NADH + H+ R Orthophosphate + Acetyl-CoA CoA + Acetyl phosphate R

3 9 ATP + CoA + Acetate AMP + Acetyl-CoA + Diphosphate R H2O + NAD+ + L-Glutamate NADH + H+ + 2-Oxoglutarate + NH3 R Oxalosuccinate CO2 + 2-Oxoglutarate R ATP + Acetate ADP + Acetyl phosphate R ATP + Oxaloacetate CO2 + Phosphoenolpyruvate + ADP R (S)-Malate + NAD+ NADH + H+ + Oxaloacetate R CoA + Citrate H2O + Acetyl-CoA + Oxaloacetate R Citrate Acetate + Oxaloacetate R ATP + CoA + Succinate Orthophosphate + ADP + Succinyl-CoA R Succinate + Acceptor Fumarate + Reduced acceptor R CoA + (S)-Malate H2O + Acetyl-CoA + Glyoxylate R Isocitrate Succinate + Glyoxylate R Thiamin diphosphate + 2-Oxoglutarate CO2 + 3-Carboxy-1-hydroxypropyl-ThPP R Phospho-D-glycerate H2O + Phosphoenolpyruvate R NAD+ + (S)-Lactate Pyruvate + NADH + H+ R NAD+ + Ethanol NADH + H+ + Acetaldehyde R D-Glyceraldehyde 3-phosphate Glycerone phosphate R ATP + D-Ribose 5-phosphate AMP + 5-Phospho-alpha-D-ribose 1-diphosphate R D-Ribose 5-phosphate D-Ribulose 5-phosphate R Orthophosphate + NAD+ + D-Glyceraldehyde 3-phosphate NADH + H+ + 3-Phospho- R01061 D-glyceroyl phosphate 29 beta-d-fructose 1,6-bisphosphate D-Glyceraldehyde 3-phosphate + Glycerone phosphate R (S)-Malate H2O + Fumarate R Citrate Isocitrate R Citrate H2O + cis-aconitate R ATP + 3-Phospho-D-glycerate ADP + 3-Phospho-D-glyceroyl phosphate R Phospho-D-glycerate 3-Phospho-D-glycerate R NADP+ + 6-Phospho-D-gluconate CO2 + H+ + NADPH + D-Ribulose 5-phosphate R D-Ribulose 5-phosphate D-Xylulose 5-phosphate R ATP + beta-d-glucose ADP + beta-d-glucose 6-phosphate R D-Glyceraldehyde 3-phosphate + Sedoheptulose 7-phosphate D-Ribose 5-phosphate + R01641 D-Xylulose 5-phosphate 39 NAD+ + Dihydrolipoamide NADH + H+ + Lipoamide R D-Glyceraldehyde 3-phosphate + Sedoheptulose 7-phosphate D-Erythrose 4-phosphate R beta-d-fructose 6-phosphate 41 D-Glyceraldehyde 3-phosphate + beta-d-fructose 6-phosphate D-Xylulose 5-phosphate R D-Erythrose 4-phosphate 42 NADP+ + Isocitrate H+ + NADPH + Oxalosuccinate R Isocitrate H2O + cis-aconitate R H2O + D-Glucono-1,5-lactone 6-phosphate 6-Phospho-D-gluconate R Phospho-D-gluconate H2O + 2-Dehydro-3-deoxy-6-phospho-D-gluconate R Acetyl-CoA + Enzyme N6-(dihydrolipoyl)lysine CoA + [Dihydrolipoyllysine-residue R02569 acetyltransferase]s-acetyldihydrolipoyllysine 47 Succinyl-CoA + Enzyme N6-(dihydrolipoyl)lysine CoA + [Dihydrolipoyllysine-residue R02570 succinyltransferase]s-succinyldihydrolipoyllysine 48 NADP+ + beta-d-glucose 6-phosphate H+ + NADPH + D-Glucono-1,5-lactone 6- R02736 phosphate 49 Pyruvate + H2O + Ferricytochrome b1 CO2 + Acetate + Ferrocytochrome b1 R (alpha-Hydroxyethyl)thiamine diphosphate + Enzyme N6-(lipoyl)lysine Thiamin diphosphate + [Dihydrolipoyllysine-residue acetyltransferase]s-acetyldihydrolipoyllysine R

4 51 3-Carboxy-1-hydroxypropyl-ThPP + Enzyme N6-(lipoyl)lysine Thiamin diphosphate + R03316 [Dihydrolipoyllysine-residue succinyltransferase]s-succinyldihydrolipoyllysine 52 beta-d-glucose 6-phosphate beta-d-fructose 6-phosphate R ATP + beta-d-fructose 6-phosphate ADP + beta-d-fructose 1,6-bisphosphate R H2O + beta-d-fructose 1,6-bisphosphate Orthophosphate + beta-d-fructose 6- R04780 phosphate 55 2-Dehydro-3-deoxy-6-phospho-D-gluconate Pyruvate + D-Glyceraldehyde 3-phosphate R ATP + AMP 2ADP R H2O + sn-glycerol 3-phosphate Orthophosphate + Glycerol R NAD+ + sn-glycerol 3-phosphate NADH + H+ + Glycerone phosphate R GlycerolExt Glycerol 60 beta-d-glucoseext beta-d-glucose 61 NADPH NADP+ 62 ADP + GTP ATP + GDP ADP + Reduced acceptor O ATP + H2O + Acceptor ADP + NADH O ATP + H2O + NAD+ 65 ATP ADP Pyruvate CO ATP Phosphoenolpyruvate Oxoglutarate Oxaloacetate NAD Acetyl-CoA D-Glyceraldehyde-3- phosphate D-Ribose-5-phosphate beta-d-fructose-6-phosphate D- Erythrose-4-phosphate NADPH beta-d-glucose-6-phosphate O ADP NADH NADP CoA + Biomass 2 Simulated experiments The following tables describe the settings used to generate the simulated experimental data. Tables show the concentrations of enzymes and external metabolites. The initial concentrations of the internal metabolites are considered as model parameters and as such they are shown in subsection Enzyme concentrations Enzyme concentrations of the 66 reactions (rows 1 66) for 10 different simulations (columns A J). A B C D E F G H I J

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6 2.2 External metabolites Initial concentrations of the 25 external metabolites (rows 1 25) for 10 different simulations (columns A J). A B C D E F G H I J Model parameters The following tables show the nominal values of the model parameters, p. The upper and lower bounds used in the optimizations are p L =0.1 p; p U =10 p. 3.1 Model parameters (1 490) Initial concentrations of the 49 internal metabolites (rows 1 49) for 10 different simulations (columns A J). A B C D E F G H I J

7 Model parameters ( ) Activation (k A ), Inhibition (k I ), and Michaelis-Menten (k M ) constants. The third column shows the corresponding reaction and metabolite number. Param. Type (Reaction, Param. number Metabolite) value 7

8 491 k A (3,7) k A (53,7) k A (53,10) k A (53,72) k I (54,5) k I (54,7) k I (53,8) k I (54,8) k I (54,9) k I (54,10) k I (15,16) k I (48,16) k I (15,25) k M (1,1) k M (2,1) k M (3,1) k M (4,1) k M (5,1) k M (6,1) k M (23,1) k M (49,1) k M (55,1) k M (66,1) k M (1,2) k M (21,2) k M (50,2) k M (51,2) k M (1,3) k M (50,3) k M (1,4) k M (5,4) k M (6,4) k M (11,4) k M (13,4) k M (21,4) k M (35,4) k M (49,4) k M (66,4) k M (2,5) k M (3,5) k M (9,5) k M (12,5) k M (13,5) k M (17,5) k M (26,5) k M (33,5) k M (37,5) k M (53,5) k M (56,5) k M (62,5)

9 541 k M (63,5) k M (64,5) k M (65,5) k M (66,5) k M (2,6) k M (10,6) k M (15,6) k M (19,6) k M (22,6) k M (30,6) k M (32,6) k M (43,6) k M (44,6) k M (45,6) k M (49,6) k M (54,6) k M (57,6) k M (63,6) k M (64,6) k M (2,7) k M (9,7) k M (26,7) k M (56,7) k M (2,8) k M (3,8) k M (13,8) k M (22,8) k M (66,8) k M (2,9) k M (8,9) k M (17,9) k M (28,9) k M (54,9) k M (57,9) k M (3,10) k M (12,10) k M (13,10) k M (17,10) k M (33,10) k M (37,10) k M (53,10) k M (56,10) k M (62,10) k M (63,10) k M (64,10) k M (65,10) k M (66,10) k M (4,11) k M (7,11) k M (8,11) k M (9,11)

10 592 k M (15,11) k M (19,11) k M (46,11) k M (66,11) k M (4,12) k M (4,13) k M (7,13) k M (8,13) k M (9,13) k M (15,13) k M (17,13) k M (19,13) k M (46,13) k M (47,13) k M (66,13) k M (5,14) k M (6,14) k M (14,14) k M (19,14) k M (30,14) k M (5,15) k M (7,15) k M (10,15) k M (14,15) k M (23,15) k M (24,15) k M (28,15) k M (39,15) k M (58,15) k M (64,15) k M (66,15) k M (5,16) k M (7,16) k M (10,16) k M (14,16) k M (23,16) k M (24,16) k M (28,16) k M (39,16) k M (58,16) k M (64,16) k M (66,16) k M (5,17) k M (6,17) k M (7,17) k M (10,17) k M (14,17) k M (23,17) k M (24,17) k M (28,17) k M (35,17)

11 643 k M (39,17) k M (42,17) k M (48,17) k M (58,17) k M (6,18) k M (35,18) k M (42,18) k M (48,18) k M (61,18) k M (66,18) k M (6,19) k M (35,19) k M (42,19) k M (48,19) k M (61,19) k M (66,19) k M (7,20) k M (24,20) k M (8,21) k M (12,21) k M (9,22) k M (12,22) k M (16,22) k M (49,22) k M (9,23) k M (10,24) k M (10,25) k M (11,25) k M (21,25) k M (66,25) k M (10,26) k M (11,27) k M (42,27) k M (13,28) k M (14,28) k M (15,28) k M (16,28) k M (66,28) k M (15,29) k M (16,29) k M (31,29) k M (32,29) k M (17,30) k M (18,30) k M (20,30) k M (17,31) k M (47,31) k M (18,32) k M (63,32) k M (18,33) k M (30,33)

12 694 k M (18,34) k M (63,34) k M (19,35) k M (20,35) k M (20,36) k M (31,36) k M (42,36) k M (43,36) k M (21,37) k M (51,37) k M (22,38) k M (34,38) k M (23,39) k M (24,40) k M (25,41) k M (28,41) k M (29,41) k M (38,41) k M (40,41) k M (41,41) k M (55,41) k M (66,41) k M (25,42) k M (29,42) k M (58,42) k M (26,43) k M (27,43) k M (38,43) k M (66,43) k M (26,44) k M (27,45) k M (35,45) k M (36,45) k M (28,46) k M (33,46) k M (29,47) k M (53,47) k M (54,47) k M (32,48) k M (43,48) k M (33,49) k M (34,49) k M (35,50) k M (44,50) k M (45,50) k M (36,51) k M (38,51) k M (41,51) k M (37,52) k M (60,52) k M (37,53)

13 745 k M (48,53) k M (52,53) k M (66,53) k M (38,54) k M (40,54) k M (39,55) k M (39,56) k M (40,57) k M (41,57) k M (66,57) k M (40,58) k M (41,58) k M (52,58) k M (53,58) k M (54,58) k M (66,58) k M (44,59) k M (48,59) k M (45,60) k M (55,60) k M (46,61) k M (47,61) k M (46,62) k M (50,62) k M (47,63) k M (51,63) k M (49,64) k M (49,65) k M (50,66) k M (51,66) k M (57,67) k M (58,67) k M (57,68) k M (59,68) k M (59,69) k M (60,70) k M (62,71) k M (62,72) k M (63,73) k M (64,73) k M (66,73) k M (66,74) Model parameters ( ) Velocity (k v ) and equilibrium (k eq ) constants of the reactions. React. Param. k v Param. k eq # number number

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15 Model outputs The 115 model outputs are: Outputs 1 49: concentrations of the 49 internal metabolites listed in table 1. Outputs : concentrations of the 66 reaction fluxes listed in table 2. 5 Influence of the tuning parameters in the performance of CeSS First we test what happens when the threads exchange information at different time intervals (τ). Figure 1 (top) shows the convergence curves, which plot the logarithm of the objective function value against the computation time. The performance of 10 individual, non cooperative threads is shown in black. It is compared to the performance of 10 cooperative threads which exchange information with different values of τ: 2.53 (approximately 12 hours in the hardware used, red curve), 2.70 (18 hours, green), 2.83 (24 hours, blue), 3.13 (48 hours, magenta), and 3.30 (72 hours, cyan). For this system, the performance of the cooperative algorithm is not significantly influenced by the choice of the time between information sharing: τ can range between 2.53 and 3.13 without affecting significantly the outcome of the optimization. Next we test the influence of the other cooperative optimization parameter, the number of threads η. We fix τ = 12 hours and compare the algorithm s performance for η = 5, 10, 20, and 30 threads. Results are shown in Fig. 1 (bottom); as expected, convergence improves when the number of threads increases. However, the improvement is not linear: the objective function value is very much reduced when changing from 5 to 10 threads, but it is only slightly reduced with 20 or 30 threads. 15

16 Objective Function (logarithmic) τ = 2.53 τ = 2.70 τ = 2.83 τ = 3.13 τ = 3.30 no coop Computation Time (hours) Objective function (logarithmic) threads 7 threads 10 threads 20 threads 30 threads Computation time (hours) Figure 1: Convergence curves, Model 1. TOP: different τ, η = 10. BOTTOM: different η, τ =