Steady-State Metabolite Concentrations Reflect a Balance between Maximizing Enzyme Efficiency and Minimizing Total Metabolite Load

Steady-state metabolite concentrations in a microorganism typically span several orders of magnitude. The underlying principles governing these concentrations remain poorly understood. Here, we hypothesize that observed variation can be explained in terms of a compromise between factors that favor minimizing metabolite pool sizes (e.g. limited solvent capacity) and the need to effectively utilize existing enzymes. The latter requires adequate thermodynamic driving force in metabolic reactions so that forward flux substantially exceeds reverse flux. To test this hypothesis, we developed a method, metabolic tug-of-war (mTOW), which computes steady-state metabolite concentrations in microorganisms on a genome-scale. mTOW is shown to explain up to 55% of the observed variation in measured metabolite concentrations in E. coli and C. acetobutylicum across various growth media. Our approach, based strictly on first thermodynamic principles, is the first method that successfully predicts high-throughput metabolite concentration data in bacteria across conditions

mTOW predictions of metabolite concentrations in glycolysis and pentose phosphate pathway are in accordance with experimental data.

<p>Reactions with high adjusted Gibbs energies (above 5.7 kJ/mol) are marked in red, and measured metabolites are marked with an asterisk. (a) On glucose media mTOW predicts a gradual decrease in metabolite concentrations across a distributed thermodynamic bottleneck from FBP to BPG (as supported by the measurements of FBP and DHAP) in both aerobic and anaerobic conditions. In aerobic acetate medium, the reversal of the glycolytic flux direction eliminates the thermodynamic bottleneck and leads to the prediction of markedly lower concentrations for FBP and DHAP in accordance with experimental data. (b) mTOW correctly predicts a marked decrease in concentration of 6PG in glucose media under anaerobic versus aerobic glucose conditions, due to thermodynamic considerations involving the decrease in flux through phosphogluconate dehydrogenase (that metabolite 6PG to Ru5P) in anaerobic conditions. Metabolite abbreviations presented in the figure: FBP-D-fructose 1,6-bisphosphate, DHAP - dihydroxyacetone phosphate, GAP-D-glyceraldehyde 3-phosphate, BPG-D-glycerate 1,3-bisphosphate, PPP - Pentose Phosphate Pathway, G6P - D-glucose 6-phosphate, X5P - D-xylulose 5-phosphate, 6PG - D-gluconate 6-phosphate, Ru5P - D-ribulose 5-phosphate, R5P - D-ribose 5-phosphate.</p

Measured metabolite concentration for aerobic glucose-fed <i>E. coli</i> versus predictions made by integrating mTOW with chemical properties-based concentration prediction.

<p>Measured metabolite concentration for aerobic glucose-fed <i>E. coli</i> versus predictions made by integrating mTOW with chemical properties-based concentration prediction.</p

The contribution of the two optimization factors, minimization of metabolite load and maximization of enzyme efficiency, to the successful prediction of metabolite concentrations.

<p>(a) Pareto-optimal solutions predicted by mTOW for <i>E. coli</i> grown under glucose, acetate and glycerol media. Axes values are normalized to minimal values, where 1 represents the minimum, and the rest of the values represent the deviations (in fold change) from those minimal values. (b) The correlation between mTOW’s predicted and measured metabolite concentrations when considering either one of the optimization factors or both of them together.</p

Using CCM to evaluate a reaction Gibbs energy.

<p>(a) The reaction catalyzed by phosphoribosyl formyl glycinamidine synthase (I) involves mostly compounds from TECRDB and two others: N2-Formyl-N1-(5-phospho-D-ribosyl) glycinamide (FGAM) and 2-(Formamido)-N1-(5-phospho-D-ribosyl) acetamidine (FPRAM). In this case, CCM divides the reaction into two parts: one which can be completely evaluated using directly observed reaction data (II) and another which can only be resolved using group contributions (III). The five groups that change throughout this reaction are highlighted in red. The final <i>ΔG</i>'⁰ estimation is simply the sum of these two half-reactions: -164.0 + 204.9 = 40.9 kJ/mol. The last stage in the algorithm is to apply the Legendre transform [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0075370#B59" target="_blank">59</a>] (using pKa data from ChemAxon; see Supp. Material). The result in this case is <i>ΔG</i>'⁰= -39.8 kJ/mol. The previous GCM prediction for the same reaction is <i>ΔG</i>'⁰= -90.8 kJ/mol (as appears in iAF1260). Note that the values appearing in iAF1260 are also Legendre transformed. (b) The cumulative distribution functions of the absolute errors for CCM and versus that of GCM taken from the iAF1260 model. The error was calculated by comparing the prediction to the median value for that reaction taken from TECRDB. Only reactions that appear in all three datasets are shown (113 in total). The intersections with the dashed lines indicate the fraction of reactions whose predicted value are in the range of ±RT (2.5 kJ/mol) of the value in TECRDB. One can see that for CCM, 70% of these reactions are in this category, compared to only about 30% in iAF1260.</p