Figure 1.
The Flux-Force Efficacy and Minimum Optimized Driving-Force (MDF).
(A) A functional relationship between the reaction driving force (−ΔrG′) and its Flux-Force Efficacy, as described in detail in the Methods section. (B) Schematic comparison between two pathways. Each pathway starts and ends with the same compounds, employs five enzymes and carries the same net flux. The kinetic parameters of all enzymes in both pathways, as well as enzyme and metabolite concentrations, are assumed to be identical. (C) Energetic profile of Embden-Meyerhof-Parnas glycolysis. Dashed black line corresponds to ΔrG′o values (metabolite concentrations of 1 M) of pathway reactions at pH 7.5. Red line corresponds to ΔrG′ values of pathway reactions after an optimization procedure that maximizes the driving force of the reactions having the lowest driving forces, as described in the Methods section.
Figure 2.
MDF analysis of oxidative pathways.
(A) Structure of the TCA cycle. The reaction marked in red is the only one with a positive shadow price at pH 7.5. Non-cofactor metabolites shaded in green show positive shadow prices. (B) MDF as function of pH, as calculated for the TCA cycle and several of its similar variants. Solid cyan line: default metabolite concentration range used throughout this study (1 µM–10 mM). Dashed and dotted cyan lines: oxaloacetate concentration (marked as ‘OA’) is allowed to attain lower values, 100 nM and 10 nM, respectively. Solid magenta line: oxaloacetate is channeled (‘channeling’) between malate dehydrogenase and citrate synthase. Semi-dashed green line: quinone (‘MQO’) serves as the electron acceptor in malate oxidation, instead of NAD. The Flux-Force Efficacy axis, on the right, refers to the reactions that dissipate the smallest amount of Gibbs energy, and hence equal to the pathway MDF. The light grey line marks the values corresponding to pH 7.5, the pH used in (C). (C) The MDF and ATP yield per glucose of the different oxidative pathways. ‘PEP-GLX’ corresponds to the PEP-Glyoxylate pathway, which was found to operate in E. coli under glucose starvation [64]. ‘P. fluorescens’ corresponds to the pathway used by Pseudomonas fluorescens under conditions of aluminum toxicity [81]. ‘OxPP’ corresponds to the oxidative pentose phosphate cycle, which can be used to fully oxidize sugars into CO2, providing NADPH for cellular activity. Reducing power was assumed to be converted to ATP via oxidative phosphorylation, where NADH or a pair of reduced ferredoxins give rise to 1.5 ATP molecules and reduced ubiquinone produces one ATP molecule. The structures of all pathways are given in Figure S1.
Figure 3.
MDF analysis of fermentation pathways.
(A) Structure of EMP-glycolysis. (B) Structure of an EMP pathway variant in which substrate-level phosphorylation is bypassed. The reactions marked in red are those with positive shadow prices at pH 7.5. Non-cofactor metabolites shaded in green show positive shadow prices. (C) MDF as function of pH, as calculated for the EMP pathway (cyan) and for an EMP pathway variant in which substrate-level phosphorylation is bypassed (magenta). ‘SLP’ corresponds to substrate-level phosphorylation. The Flux-Force Efficacy axis, on the right, refers to the reactions that dissipate the smallest amount of Gibbs energy, and hence equal to the pathway MDF. The light grey line marks the values corresponding to pH 7.5, the pH used in (D). (D) The MDF and ATP yield per glucose of the different fermentation pathways. ‘ED’ corresponds to the Entner-Doudoroff pathway. ‘EDSP’ represents the semi-phosphorylative ED pathway, known to operate in several hyperthermophilic archaea lineages [84], [88], [89]. ‘EDNP’ represents the non-phosphorylative ED pathway, also known to operate in hyperthermophilic archaea [84], [88], [89]. ‘MGX’ corresponds to a variant of the EMP pathway in which dihydroxyacetone phosphate is converted into the toxic compound methylglyoxal when the concentration of inorganic phosphate becomes limiting [85], [86], [87]. ‘PKT’ represents a pathway, suggested long ago [103], that uses the pentose phosphate pathway in conjunction with the enzyme phosphoketolase that cleaves xylulose-phosphate to glyceraldehyde-phosphate and acetyl-phosphate [90], [91]. ‘EMP PFL’ corresponds to a variant of the EMP pathway that produces more ATP by using the enzyme pyruvate formate lyase and performing substrate-level phosphorylation on of acetyl-phosphate. The structures of all pathways are given in Figure S2.
Figure 4.
Schematic representation of the interplay between the net reaction flux and the internal and external (i.e., overall or net) energetic profiles.
ΔrG′ corresponds to the driving force of the net reaction (which depends on the concentrations of the substrates and products); ΔG‡fwd to the thermodynamic barrier of the forward reaction, associated with the binding of the substrates and with the different reaction intermediates formed during catalysis; and ΔG‡bwd corresponds to the thermodynamic barrier of the backward reaction, associated with the different reaction intermediates formed during catalysis and with the release of the products. All reactions are assumed to be catalyzed by the same amount of enzyme units. (A) High internal thermodynamic barrier and high thermodynamic driving force. (B) High internal thermodynamic barrier and low thermodynamic driving force. (C) Low internal thermodynamic barrier and low thermodynamic driving force. (D) Low internal thermodynamic barrier and high thermodynamic driving force.