Abstract
In this work, the stoichiometric metabolic network ofEscherichia coli has been formulated as a comprehensive mathematical programming model, with a view to identifying the optimal redirection of metabolic fluxes so that the yield of particular metabolites is maximized. Computation and analysis has shown that the over-production of a given metabolite at various cell growth rates is only possible for a finite ordered set of metabolic structures which, in addition, are metabolite-specific. Each regime has distinct topological features, although the actual flux values differ. Application of the model to the production of 20 amino acids on four carbon sources (glucose, glycerol, lactate, and citrate) has also indicated that, for fixed cell composition, the maximum amino acid yield decreases linearly with increasing cell growth rate. However, when the cell composition varies with cell growth rate, the amino-acid yield varies in a nonlinear manner. Medium optimization studies have also demonstrated that, of the above substrates, glucose and glycerol are the most efficient from the energetic viewpoint. Finally, model predictions are analyzed in the light of experimental data.
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Abbreviations
- b :
-
vector of net conversion rates, T-1
- C :
-
time required to replicate the chromosome, T
- Cp :
-
peptide elongation rate, LT-1
- D :
-
time period between termination of a round of replication and the following cell division, T
- Di :
-
drain factor of metabolite,i,T -1
- (Ds/rx)gr :
-
growth related dissipation of Gibbs energy, L2T-2
- fai :
-
amount of amino acid,ai, needed for biomass formation, M
- Ji :
-
reaction flux, T-1
- me :
-
maintenance related dissipation of Gibbs energy, L2T-2
- P :
-
total protein in cell, M
- Po :
-
protein per origin, M
- S :
-
stoichiometric matrix
- t :
-
time, T
- X :
-
metabolite concentration, ML-3
- YATP/X :
-
biomass yield coefficient; Z, objective function, T-1
- αi :
-
maximum flux allowable through reaction flux,υ i,T-1
- βr :
-
ribosome activity;μ, specific growth rate, T-1
- τ:
-
doubling time, T
- ν :
-
vector of net conversion rates, T-1
- νi :
-
flux of reactioni, T-1
- γs :
-
degree of reduction
- γai :
-
amount of amino acid over the total amino acid in cell
- Ac :
-
Acetate
- AcCoA :
-
Acetyl coenzyme A
- ADPGlc :
-
ADP-Glucose
- ADPHep :
-
ADP-D-Glycerol-D-mannoheptose
- ASPSA :
-
Aspartate semihaldehyde
- C14:0 :
-
Myristic acid (n-Tetradecanoic)
- C14:1 :
-
β-Hydroxymyristic acid
- C16:0 :
-
Palmitic acid (n-Hexadecanoic)
- C16:1 :
-
Palmitoleic acid (hexa-9-decanoic)
- C18:1 :
-
Oleic Acid
- CaP :
-
Carbamoyl-phosphate
- CDP :
-
Cytidine-5′-diphosphate
- CDPDG :
-
CDP-Diacylglycerol
- CDPEtN :
-
CDP-Ethanolamine
- Chor :
-
Chorismate
- Cit :
-
Citrate
- Citr :
-
Citrulline
- CL :
-
Diphosphatidylglycerol
- CMP :
-
Cytidine-5′-monophosphate
- CMPKDO :
-
CMP-3-Deoxy-D-manno-octulosonic acidCO 2 Carbon dioxide
- dADP :
-
2′-Deoxy-adenosine-5′-diphosphate
- dATP :
-
2′-Deoxy-adenosine-5′-triphosphate
- dCDP :
-
2′-Deoxy-cytidine-5′ -diphosphate
- dCTP :
-
2′ -Deoxy-cytidine-5′ -triphosphate
- dGDP :
-
2′-Deoxy-guanosine-5′-diphosphate
- dGTP :
-
2′-Deoxy-guanosine-5′-triphosphate
- DHF :
-
7,8-Dihydrofolate
- dTTP :
-
2′-Deoxy-thymidine-5′-triphosphate
- dUDP :
-
2′-Deoxy-uridine-5′ -diphosphate
- d UTP :
-
2′ -Deoxy-uridine-5′ -triphosphate
- E4P :
-
Erythrose-4-phosphate
- Eth :
-
Ethanol
- F6P :
-
Fructose-6-phosphate
- FADH :
-
Flavine adenine dinucleotide (reduced)
- Form :
-
Formate
- FTHF :
-
N5-Formimino-tetrahydrofolate
- FNTHF :
-
N10-Formyl-tetrahydrofolate
- Fum :
-
Fumarate
- G1P :
-
Glucose-1-phosphate
- G6P :
-
Glucose-6-phosphate
- GDP :
-
Guanosine-5′-diphosphate
- GL :
-
Glycerol
- GL3P :
-
Glycerol-3-phosphate
- Glc :
-
Glucose
- H2S :
-
Hydrogen sulfide
- Hexp :
-
Protons exported
- HSer :
-
Homoserine
- ICit :
-
Isocitrate
- IGP :
-
Indoleglycerolphosphate
- IMP :
-
Inosinemonophosphate
- Lac :
-
Lactate
- LPS :
-
Lipopolysaccharide
- αKG :
-
α-Ketoglutarate
- Kval :
-
Ketoisovalerate
- Mal :
-
Malate
- MalACP :
-
Malonyl-ACP
- mDAP :
-
meso-Diaminopimelate
- MeTHF :
-
N5, N10-Methenyl-tetrahydrofolate
- MetTHF :
-
N5, N10-Methylene-tetrahydrofolate
- MTHF :
-
N5-Methyl-tetrahydrofolate
- NH3 :
-
Ammonia
- OA :
-
Oxaloacetate
- Orn :
-
Ornithine
- PA :
-
Phosphatidic acid
- PE :
-
Phosphatidyl-ethanolamine
- PEP :
-
Phosphoenolpyruvate
- PG :
-
Phosphatidyl-glycerol
- 3PG :
-
Glycerate-3-phosphate
- Pi :
-
Inorganic orthophosphate
- PPi :
-
Inorganic pyrophosphate
- PRAIC :
-
5′ -Phosphoribosyl-4-carboxamide-5-aminoimidazole
- ProCoA :
-
Propionyl-CoA
- PRPP :
-
Phosphoribosylpyrophosphate
- PS :
-
Phosphatidyl-serine
- PTRSC :
-
Putrescine
- Pyr :
-
Pyruvate
- Pyrroline :
-
Δ1Pyrroline-5-carboxylate
- QH2 :
-
Hydroquinone
- R5P :
-
Ribulose-5-phosphate
- Rib5P :
-
Ribose-5-phosphate
- S7P :
-
Sedoheptulose-7-phosphate
- SPRMD :
-
Spermidine
- Succ :
-
Succinate
- SuccCoA :
-
Succinyl coenzyme A
- T3P :
-
Triose-3-phosphate (for glyceraldehyde-3-P and dihydroxyacetone-P)
- TREDH :
-
Thioredoxin (reduced)
- UDPNAG :
-
UDP-N-Acetyl-glucosamine
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See, S.M., Dean, J.P. & Dervakos, G. On the topological features of optimal metabolic pathway regimes. Appl Biochem Biotechnol 60, 251–301 (1996). https://doi.org/10.1007/BF02783588
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DOI: https://doi.org/10.1007/BF02783588