Model and results of overflow metabolism.

(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 (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 (Eqs. S47 and S160). (E) The energy efficiencies of respiration and fermentation pathways vary with the growth rate as functions of the substrate quality of a Group A carbon source (Eqs. S31 and S36). See Appendix 8 for model parameter settings and experimental data sources (Basan et al., 2015; Holms, 1996; Hui et al., 2015) of Figs. 1–4.

Influence of protein overexpression on overflow metabolism.

(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 substrate quality of a Group A carbon source (denoted as κA) and the useless protein expression encoded by LacZ (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 (Eq. S58 and S160). (C) Growth rate dependence of the acetate excretion rate as κA varies (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.

(A) A 3D plot of the relations among fermentation flux, growth rate, and the energy dissipation coefficient (Eqs. S70 and S160). (B) Growth rate dependence of the acetate excretion rate as κA varies, with each fixed energy dissipation coefficient determined by/fitted from experimental data. (C) A 3D plot of the relations among fermentation flux, growth rate, and the translation efficiency (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 (Eqs. 105 and S160) significantly differs from that of the Group A carbon sources (Eqs. 47 and S160).

Relative protein expression of central metabolic enzymes under κA and ϕZ perturbations.

(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 κA perturbation (Eq. S119). (C, D) Results of ϕZ perturbation (Eq. S121).

Molecular weight (MW) andinvivo/in vitrokcatdata forE. coli

Proteome and flux data(Basan et al., 2015)used to calculate the in vivo kcat

Central metabolic network and carbon utilization pathways

(A) Energy production details of 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 with ADP. The conversion factors are: NADH=2ATP, NADPH=2ATP, FADH2=1ATP(Neidhardt et al., 1990). (B) Relevant genes for enzymes in the central metabolic network.(C-E) Three destinies of glucose metabolism.(C) Fermentation pathway, where a molecule of glucose generates 12 ATPs in E. coli. (D) Respiration pathway, where a molecule of glucose generates 26 ATPs. (E) Biomass pathway, where glucose turns into precursors of biomass. Note that the process of biomass generation is accompanied by ATPs production (see Appendix 2.1).

Model and results for experimental comparison

(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) of the growth rate distributions forE. coli in three culturing conditions. (C) Comparison of thegrowth rate-fermentation flux relationfor E. coli in Group A carbon sources between minimum media and enriched media (those with 7AA).(D-E)Influence of translation inhibition on overflow metabolism.(D) A 3D plot of the relations among the fermentation flux, growth rate, and the translation efficiency (Eqs. 79 and S160). (E) Growth rate dependence of acetate excretion rate as κA varies, with each fixed dose of Cm.The translation efficiency is tuned by the dose of Cm, and the maintenance energy coefficient is set to be 0 (i.e., w0 = 0).(F) The coarse-grained model for Group A carbon source utilization. This model includes more details to compare with experiments. (G) Comparison of the in vivo and in vitro catalytic rates for enzymes within glycolysis and the TCA cycle (see Appendix-table1 for details). (H) The energy efficiencies of 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 under various types of perturbations

(A-D) Relative protein expression under κA perturbation.(A) Experimental data(Hui et al., 2015)of the catalytic enzymes for each step of glycolysis.(B) Experimental data(Hui et al., 2015)of the catalytic enzymes for each step of the TCA cycle. (C) Model predictions (Eq. S118, with w0 = 0) and experimental data(Hui et al., 2015) of representative genes from glycolysis. (D) Model predictions (Eq. S118,with w0 = 0) and experimental data(Hui et al., 2015) of 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) of representative genes from glycolysis. (G, H, J) Model predictions and experimental data(Basan et al., 2015) of 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 (Eq. S121).(K-N)Relative protein expressionuponenergy dissipation.(K-L) Model fits (Eqs. S127 and S123) and experimental data(Basan et al., 2015) of representative genes from glycolysis. (M-N) Model fits(Eqs. S127 and S123) and experimental data(Basan et al., 2015) of representative genes from the TCA cycle.

Asymptotic distributions ofinverse Gaussian distribution and the inverse of Gaussian distribution

(A) Comparison between the inverse of Gaussian distribution and the corresponding Gaussian distribution for each value of coefficient of variation (CV) (Eqs. S140 and S145). (B)Comparison between the inverse Gaussian distribution and the corresponding Gaussian distribution for each value of CV (Eqs. S142 and S146). Both inverse Gaussian distribution and the inverse of Gaussian distribution converge to Gaussian distributions when CV is small.