Table 1.
Studies examining objective functions
| Ref | Objective Function(s) Examined | Modeling Approach | Metabolic Reconstruction and Model Used | Source of Experimental Data | Simple Statement |
|---|---|---|---|---|---|
| [11,12] 1992 | (1) Max. of growth rate, (2) Min. of ATP production, (3) Minimizing total nutrient uptake, and (4) Minimize redox metabolism through minimizing NADH production. | Linear Programming | Hybridoma cell line central metabolism (83 reactions, 42 metabolites) [11] | (1) aerobic batch bioreactor with growth, uptake, secretion, and protein production rates [20] | Optimization of biomass production can be used to examine growth characteristics and explain observed phenomena. |
| [13] 1997 | Max. or Min. of (1) growth rate, (2) ATP production rate, (3) substrate uptake, or (4) product formation | Linear Programming (iterative optimization) | E. coli central metabolsim model (300 reactions, 289 metabolites) [13] | Aerobic batch growth isotopomer based flux distribution on (1) acetate, and (2) glucose and acetate [38] | Optimization with a growth-rate dependent biomass objective function can accurately predict experimentally determined metabolic fluxes. |
| [14] 2003 | ObjFind Algorithm - Optimization-based framework to infer best objective function | Linear programming | E. coli core central metabolism model (62 reactions, 48 metabolites) (see [14]) | batch growth of (1) aerobic and (2) anaerobic growth isotopomer-based flux distributions [39] | Optimization of biomass production (growth) was identified as the most significant driving force in both cases examined. |
| [15] 2007 | (1) Max. of Growth rate, (2) Min. of the production rate of redox potential, (3) Min. of ATP production rate, (4) Max. of ATP production rate, and (5) Min. of nutrient uptake rate | Linear programming & Bayesian discrimination technique | E. coli genome-scale metabolic network iJR904 (1320 reactions, 625 metabolites) [40] | (1) batch aerobic growth, substrate, production rates [26] | Min. of the production rate of redox potential was determined to be the most probable objective function. |
| [16] 2007 | (1) Max. of biomass yield (production), (2) Max. of ATP yield (energy expenditure), (3) Min. of the overall intracellular yield, (4) Max. of ATP yield per unit flux, (5) Max. of biomass yield per unit flux, (6) Min. of glucose production, (7) Min. of reaction steps, (8) Max. of ATP yield per reaction step, (9) Min. of redox potential, (9) Min. of ATP producing reactions, (10) Max. of ATP producing fluxes | Linear programming & non-Linear programming | E. coli core central metabolism model (98 reactions, 60 metabolites) [16] | (1) Aerobic, (2) anaerobic, (3) anaerobic with nitrate growth in batch, and (4) carbon- and (5) nitrogen-limited limited growth in chemostat; Isotopomer-based flux distributions. [41-43] | No single objective describes the flux states under all conditions. Unlimited growth on glucose in oxygen or nitrate respiring batch cultures is best described by nonlinear Max. of the ATP yield per flux unit. Under nutrient scarcity in continuous cultures, in contrast, linear Max. of the overall ATP or biomass yields achieved the highest predictive accuracy. |
| [17] 2008 | Biological Objective Solution Search (BOSS) Algorithm - Optimization-based framework to infer best objective function | Linear programming | S. cerevisiae core central metabolism model (62 reactions, 60 metabolites) [44] | (1) Aerobic batch growth isotopomer-based flux distribution [44] | Growth is the best-fit objective function for the examined network and conditions. |
| [18] 2009 | GrowMatch Algorithm - Minimizes modifications (addition of reactions or activation of secretion of metabolites) in the metabolic model to match growth phenotype data | Linear programming (bi-level optimization) | E. coli genome-scale metabolic network iAF1260 (2077 reactions, 1039 metabolites) [8] | (1) growth phenotype data for wild type and mutant E. coli; (2) pathway content data; MetaCyc/KEGG [45-47] | GrowMatch is a useful model-refinement tool for curating/refining metabolic reconstructions and can be used to increase predictivity of phenotype data. |
| [19] 2009 | (1) Max. of biomass production (growth rate), (2) Max. of plasmid production rate (Max plasmid), and (3) maximizing maintenance energy expenditure (Max ATPm). | Linear programming | E. coli genome-scale metabolic network iJR904 (1320 reactions, 625 metabolites) with plasmid / protein product reactions [40] | Aerobic glucose-limited limited growth in chemostat of (1) wild-type and (2) plasmid-bearing cells with growth, substrate, and product rates and isotopomer-based flux | Wild-type can best be determined with the objective function of maximizing growth rate, and maximizing expenditure of ATP best predicts overall metabolism and phenotype of plasmid-bearing E. coli. |
Max. – maximization, Min. – minimization