Histograms of Spearman correlation values between measured and predicted growth rates. The histograms show the accuracy of FBA (blue, dash-dot line) and MD-FBA growth rate predictions (red, solid line) for 81 gene deletion strains across 96 growth media. The median Spearman correlation for MD-FBA is significantly higher than that of FBA (Wilcoxon test P-value = 0.0145).

ROC curves of gene essentiality predictions. ROC curves of gene essentiality predictions under (a) glucose and (b) glycerol minimal media. Predictions were made by FBA, FBA-reduced biomass (FBA-r; utilizing the reduced biomass definition) and MD-FBA, where MD-FBA is shown to outperform both FBA and FBA-r under both growth media. FP, false positive; TP, true positive.

An example network featuring the difference in predicted flux distributions between FBA and MD-FBA. Thick arrows represent metabolic reactions and circular nodes represent metabolites. Narrow arrows represent the growth-associated dilution of their attached metabolites. Note that the stoichiometric coefficients for reaction v₂ are two molecules of A per one molecule of D. v₁ and v₆ represent the uptake for metabolites A and X, respectively. B is the sole metabolite within the biomass, and hence the flux through v₅ represents the growth rate. Blue (dash-dot) and red (solid) arrows represent reactions predicted to be active by MD-FBA and FBA, respectively, while black (dashed) arrows represent all other reactions. The figure illustrates growth on two media: (a) growth on a medium in which both A and X are present; (b) growth on a medium including only metabolite A. FBA predicts the same growth rate, which is equal to v₁ under both media, while MD-FBA predicts a growth rate equal to v₁ when both A and X are present in the medium and a growth rate equal to 0.5v1 when only A is included in the medium. The latter is due to the fact that when X is absent from the growth medium, MD-FBA cannot activate reactions v₄ and v₈, since the dilution of metabolites C and C* cannot be satisfied under this medium. The different flux distributions predicted by the two methods lead to different predictions of enzyme essentiality, as detailed in the main text.

Context-dependent activity of biosynthetic pathways for the co-factor ubiquinone-8 (q8h2). Edges represent reactions, circular nodes represent metabolites. Black (thin) edges represent reactions predicted to be active both by FBA and by MD-FBA and green (thick) edges represent reactions predicted to be inactive by FBA and active by MD-FBA. MD-FBA correctly predicts the pathway to be activated under succinate minimal medium (where q8h2 is used in aerobic respiration) and to be inactivated under other media. FBA falsely predicts the inactivity of the pathway (downstream to 2ohph), as it does not account for the dilution demand for the production of q8h2, which is not included in its biomass reaction (as it is used only under some environments). 2ohph, 2-octaprenyl-6-hydroxyphenol; 2ombzl, 2-octaprenyl-6-methoxy-1,4-benzoquinol; 2omhmbl, 2-octaprenyl-3-methyl-5-hydroxy-6-methoxy-1,4-benzoquinol; 2ommbl, 2-octaprenyl-3-methyl-6-methoxy-1,4-benzoquinol; 2omph, 2-octaprenyl-6-methoxyphenol; 2oph, 2-octaprenylphenol; 3ophb, 3-octaprenyl-4-hydroxybenzoate; ahcys, s-adenosyl-l-homocysteine; amet, s-adenosyl-l-methionine; atp, adenosine-3-phosphate; co2, carbon dioxide; h, hydrogen; h2o, water; nad, nicotinamide-adenine-dinucleotide; nadh, nicotinamide-adenine-dinucleotide-reduced; o2, oxygen; pi, phosphate; q8h2, ubiquinone-8-reduced.