Figures and data
Model and results of overflow metabolism in E. coli.
(A) The central metabolic network of carbon source utilization. The Group A carbon sources (Wang et al., 2019) are labeled with green squares. (B) Coarse-grained model for Group A carbon source utilization. (C) Model predictions (see Eqs. S47 and S160) and experimental results (Basan et al., 2015; Holms, 1996) of overflow metabolism, covering the data for all the Group A carbon sources shown in (A). (D) Growth rate dependence of respiration and fermentation fluxes (see Eqs. S47 and S160). (E) The proteome efficiencies for energy biogenesis in the respiration and fermentation pathways vary with growth rate as functions of the substrate quality of a Group A carbon source (see Eqs. S31 and S36). See Appendices 8 and 10 for model parameter settings and experimental data sources (Basan et al., 2015; Holms, 1996; Hui et al., 2015) for Figs. 1–4 of E. coli.
Influence of protein overexpression on overflow metabolism in E. coli.
(A) A 3D plot of the relations among fermentation flux, growth rate, and the expression level of useless proteins. In this plot, both the acetate excretion rate and growth rate vary as bivariate functions of the nutrient quality of a Group A carbon source (denoted as κA) and the useless protein expression encoded by lacZ gene (denoted as ϕZ perturbation; see Eqs. S57 and S160). (B) Growth rate dependence of the acetate excretion rate upon ϕZ perturbation for each fixed nutrient condition (see Eqs. S58 and S160). (C) Growth rate dependence of the acetate excretion rate as κA varies (see Eqs. S57 and S160), with each fixed expression level of LacZ.
Influence of energy dissipation, translation inhibition, and carbon source category alteration on overflow metabolism in E. coli.
(A) A 3D plot of the relations among fermentation flux, growth rate, and the energy dissipation coefficient (see Eqs. S70 and S160). (B) Growth rate dependence of the acetate excretion rate as the nutrient quality κA varies, with each fixed energy dissipation coefficient determined by or fitted from experimental data. (C) A 3D plot of the relations among fermentation flux, growth rate, and the translation efficiency (see Eqs. 85 and S160). Here, the translation efficiency is adjusted by the dose of chloramphenicol (Cm). (D) Growth rate dependence of the acetate excretion rate as κA varies, with each fixed dose of Cm. (E) Coarse-grained model for pyruvate utilization. (F) The growth rate dependence of fermentation flux in pyruvate (see Eqs. 105 and S160) significantly differs from that of the Group A carbon sources (see Eqs. 47 and S160).
Relative protein expression of central metabolic enzymes in E. coli under nutrient limitation and proteomic perturbation.
(A, C) Relative protein expression of representative genes from glycolysis. (B, D) Relative protein expression of representative genes from the TCA cycle. (A, B) Results of the perturbation through changes in nutrient quality κA (see Eq. S119). (C, D) Results of proteomic perturbation via varied levels of expression of the useless protein LacZ (i.e., ϕZ perturbation; see Eq. S121).
Model comparison with data on the Crabtree effect in yeast and the Warburg effect in tumors.
(A) A linear scale representation on the y-axis. (B) A log scale representation on the y-axis. In (A-B), 〈εr〉 and 〈εf〉 represent the population averages of εr and εf, while χεr and χεf are the coefficients of variation (CVs) of εr and εf · 〈εr〉/〈εf〉 represents the ratio of proteome efficiency between respiration and fermentation at the population-averaged level, while 
Molecular weight (MW) andinvivo/in vitrokcatdata forE. coli
Proteome and flux data (Basan et al., 2015) used to calculate the in vivo kcat of E. coli
Illustrations of symbols in this manuscript.
Central metabolic network and carbon utilization pathways of E. coli.
(A) Energy biogenesis details in the central metabolic network. In E. coli, NADPH and NADH are interconvertible (Sauer et al., 2004), and all energy carriers can be converted to ATP through ADP phosphorylation. The conversion factors are: NADH = 2ATP, NADPH = 2ATP, FADH2 = 1ATP (Neidhardt et al., 1990). (B) Relevant genes encoding enzymes in the central metabolic network of E. coli. (C-E) Three independent fates of glucose metabolism in E. coli. (C) For energy biogenesis through fermentation, a molecule of glucose generates 12 ATPs. (D) For energy biogenesis via respiration, a molecule of glucose generates 26 ATPs. (E) For biomass synthesis, glucose is converted into precursors of biomass. Note that biomass synthesis is accompanied by ATP production (see Appendix 2.1).
Model and results for experimental comparison of E. coli.
(A-C) Model analysis for carbon utilization in mixtures with amino acids. (A) Coarse-grained model for the case of a Group A carbon source mixed with extracellular amino acids. (B) Model predictions (Eqs. S157, S164–S165) and single-cell reference experimental results (Wallden et al., 2016) showing growth rate distributions for E. coli in three culturing conditions. (C) Comparison of the growth rate-fermentation flux relation for E. coli in Group A carbon sources between minimal media and enriched media (those with 7AA). (D-E) Influence of translation inhibition on overflow metabolism in E. coli. (D) A 3D plot illustrating the relations among fermentation flux, growth rate, and translation efficiency (Eqs. 79 and S160). (E) Growth rate dependence of acetate excretion rate as κA varies, with each fixed dose of Cm. Translation efficiency is tuned by the dose of Cm, and the maintenance energy coefficient is set to 0 (i.e., w0 = 0). (F) Coarsegrained model for Group A carbon source utilization, which includes more details to compare with experiments. (G) Comparison of in vivo and in vitro catalytic rates for enzymes of E. coli within glycolysis and the TCA cycle (see Appendix-table 1 for details). (H) The proteome efficiencies for energy biogenesis in the respiration and fermentation pathways vary with growth rate as functions of the substrate quality of pyruvate (Eqs. S93 and S96).
Relative protein expression of central metabolic enzymes in E. coli under various types of perturbations.
(A-D) Relative protein expression under κA perturbation. (A) Experimental data (Hui et al., 2015) for the catalytic enzymes at each step of glycolysis. (B) Experimental data (Hui et al., 2015) for the catalytic enzymes at each step of the TCA cycle. (C) Model predictions (Eq. S118, with w0 = 0) and experimental data (Hui et al., 2015) for representative glycolytic genes. (D) Model predictions (Eq. S118, with w0 = 0) and experimental data (Hui et al., 2015) for representative genes from the TCA cycle. (E-J) Relative protein expression under ϕZ perturbation. (E, F, I) Model predictions and experimental data (Basan et al., 2015) for representative glycolytic genes. (G, H, J) Model predictions and experimental data (Basan et al., 2015) for representative genes from the TCA cycle. (E–H) Results of ϕZ perturbation with w0= 0 (Eq. S120). (I–J) Results of ϕZ perturbation with w0 = 2.5 (h-1) (Eq. S121). (K-N) Relative protein expression upon energy dissipation. (K–L) Model fits (Eqs. S127 and S123) and experimental data (Basan et al., 2015) for representative glycolytic genes. (M–N) Model fits (Eqs. S127 and S123) and experimental data (Basan et al., 2015) for representative genes from the TCA cycle.
Asymptotic distributions of inverse Gaussian distribution and the inverse of Gaussian distribution.
(A) Comparison between the inverse of Gaussian distribution and the corresponding Gaussian distribution for various values of the coefficient of variation (CV) (Eqs. S140 and S145). (B) Comparison between the inverse Gaussian distribution and the corresponding Gaussian distribution for various values of CV (Eqs. S142 and S146). Both the inverse Gaussian distribution and the inverse of Gaussian distribution converge to Gaussian distributions when CV is small.
Carbon utilization in yeast and mammalian cells.
(A-D) Three independent fates of glucose metabolism in yeast and mammalian cells. (A-B) For energy biogenesis through fermentation, one molecule of glucose generates 2 ATPs. (C) For energy biogenesis through respiration, one molecule of glucose generates 32 ATPs. (D) For biomass synthesis, glucose is converted into biomass precursors, with ATP produced as a byproduct. In yeast and mammalian cells, the energy stored in NADH and FADH2 converts ADP into ATP in the mitochondria, with higher conversion factors than in E. coli: NADH = 2.5 ATP, FADH2 = 1.5 ATP (Nelson et al., 2008). (E) Coarse-grained model for Group A carbon source utilization in yeast. (F) Coarse-grained model for Group A carbon source utilization in mammalian cells.
