Acetate Metabolism and the Inhibition of Bacterial Growth by Acetate

In order to dissect the mechanism of growth inhibition by acetate, we adapted a standardized, well-controlled experimental setup from reference 4. We use the Escherichia coli BW25113 strain. E. coli bacteria from an overnight preculture in minimal medium supplemented with glucose were diluted into the same medium and grown in a shake flask batch culture. The growth characteristics of our strain are identical to those measured for similar strains of E. coli (31). As shown in Fig. S1 in the supplemental material, after about 7 h of growth, the bacteria reach a final optical density at 600 nm (OD₆₀₀) of 3.5. pH and oxygen pressure decrease continuously during the exponential growth phase due to the increasing number of bacteria consuming oxygen and secreting acidic by-products. During the entire growth of the culture, the partial oxygen pressure, pO₂, never falls below 40%, meaning that the bacteria grow aerobically (31). The pH remains close to neutral (pH 7) at the beginning of the experiment but drops to a value of 6.4 at the end of exponential phase (Fig. S1).

In order to quantify the effect of acetate on the growth of the culture, identical starting cultures were split at the beginning of the experiment and grown in separate shake flasks. After about 3 h of growth, a solution with a defined concentration of acetate was added to the medium in one flask and a solution without acetate to the medium in another flask (Fig. 2). Growth of both the acetate-treated and the control culture were monitored until the end of exponential phase, and the OD₆₀₀ and extracellular metabolites were measured at regular time intervals (see below). From these measurements we computed the growth rate, as described in Materials and Methods. The growth rate was determined from optical densities below 1, since above this value the oxygen pressure decreases to a point that it no longer allows growth at the maximum rate supported by the medium. Moreover, in the fast-growing control culture, acidification of the medium due to overflow metabolism sets in at higher optical densities (Fig. S1), confounding the effect from external acetate addition.

Growth inhibition by acetate is quantified using a so-called inhibition index (i) (4), defined aswhere μ_control denotes the growth rate in the culture without added acetate and μ_acetate the growth rate in the culture with added acetate. Note that the value of the inhibition index varies between 0 and 1. An inhibition index of 0 means no growth inhibition by acetate, whereas an inhibition index of 1 corresponds to full growth inhibition.

Figure 3 shows the measured growth rate of the wild-type strain after the addition of different concentrations of acetate to a culture growing under the reference conditions at pH 7.4, close to the intracellular pH value enabling maximal growth (14). As can be seen, the growth rate drops from 0.75 h⁻¹ to 0.4 h⁻¹ when the acetate concentration increases from 0 to 128 mM. This change in growth rate corresponds to an inhibition index of 0.47. A previous report (4) had suggested an exponential decrease of growth rate as a function of the concentration of added acetate. When allowing for an offset of the exponential function, we obtain the best exponential fit with a baseline at 0.3 h⁻¹. This baseline value corresponds to the growth rate of E. coli in the same medium with 128 mM acetate as the sole carbon source (0.27 h⁻¹) (Fig. 3).

Given that growth inhibition is a monotonic function of the acetate concentration and that industrially relevant concentrations of acetate are on the order of 100 mM (32), we decided to carry out all subsequent experiments at 128 mM acetate. The qualitative effect of acetate is probably the same at all concentrations, but quantitative estimates are much more easily obtained for larger effects. While most measurements were carried out at pH 7.4, we also quantified growth inhibition by acetate at pH 6.4 and found an even stronger effect of acetate: the growth rate drops from 0.74 h⁻¹ to 0.084 h⁻¹ when adding 128 mM acetate, corresponding to an inhibition index of 0.89 (Fig. 3).

Previous results have shown that the addition of methionine to the medium can alleviate the inhibitory effect of acetate (18). Further work indicated that acetate inhibits methionine biosynthesis and, more particularly, the activity of the MetE enzyme (20, 33). As a further control, we therefore tested whether supplementing the growth medium with methionine could offset the inhibition effect. We added 128 mM acetate during growth in minimal medium with glucose at pH 7.4, in the absence of methionine and in the presence of 3.3 mM methionine (comparable to the concentration of 2 mM used in reference 18). We found only a small, nonsignificant effect of methionine under our conditions, consisting of an increase of the growth rate from 0.38 h⁻¹ to 0.43 h⁻¹ and a corresponding decrease of the inhibition index from 0.52 to 0.45 (Fig. S2). Roe et al. observed a much stronger effect, where supplementing methionine could restore 75 to 80% of the growth rate diminution due to acetate (18). More recent data also demonstrate a relief of growth inhibition by methionine, but the magnitude is closer to what we observed (reduction of inhibition index from 0.71 to 0.53) (33). Note that these experiments were carried out at pH 6, which may account for the difference in strength of the relief of growth inhibition by methionine observed under our conditions. For our purpose, however, the most important conclusion is that methionine is not a major contributor to growth inhibition at physiological pH levels. Therefore, in the remainder of the paper, we will investigate another hypothesis.

While growing at a high rate under aerobic conditions, E. coli redirects some of the glycolytic flux toward the production of acetate, since limited respiration capabilities do not allow all carbon intermediates to enter the tricarboxylic acid (TCA) cycle (2). This physiological response optimizes the balance between demands for energy production and biomass synthesis (3). Conversion of acetyl coenzyme A (acetyl-CoA) into acetate involves the phosphotransacetylase Pta and the acetate kinase AckA. Acetate can also be produced from pyruvate, the metabolite just before acetyl-CoA in glycolysis, by pyruvate oxidase, PoxB (Fig. 1). When E. coli cells are growing on acetate, the Pta-AckA pathway operates in the reverse direction, converting acetate into acetyl-coenzyme A (AcCoA). For low concentrations of acetate in the medium, on the order of a few millimolars, the main route for acetate assimilation involves the acetyl-CoA synthetase Acs (23).

Recent work has shown that, during growth of E. coli on glucose, acetate metabolism not only produces but also consumes acetate, and acetate uptake or secretion corresponds to the net flux through the Pta-AckA pathway (22; see also reference 21). At high external concentrations, the net flux of acetate was observed to change direction and flow into the cells. This suggests that excess acetate flows into central metabolism and possibly perturbs fluxes necessary for sustaining maximal growth. Moreover, excess acetate may change the concentration of acetyl-phosphate (Ac∼P), the intermediate of the Pta-AckA pathway. Ac∼P plays an important role in the regulation of various cellular processes, as mentioned in the Introduction (see references 23 and 24 for reviews).

Valgepea et al. found that in continuous culture experiments at low dilution rates, even in the absence of acetate secretion, the Pta-AckA and Acs pathways are actively recycling acetate (34), possibly to maintain an appropriate level of Ac∼P. Under our conditions, Acs is not significantly expressed at the reduced growth rate following acetate addition (Fig. S3). However, the more general point, that perturbing the concentration of Ac∼P may have consequences on growth, remains valid.

The above-described considerations motivate the main question of the present work: do the perturbations of acetate metabolism, due to the inflow of excess acetate from the medium, play a role in growth inhibition by acetate, either by perturbing the distribution of fluxes in central carbon metabolism or by affecting the regulatory role of Ac∼P? In order to answer this question, we constructed mutants that cut different parts of the acetate utilization and synthesis pathways and modify the concentration of Ac∼P. All these mutants are derived from the wild-type strain, BW25113, and their genotypes are listed in Table 1. We measured the growth rate of all strains under our reference conditions (growth on minimal medium with glucose at pH 7.4). As can be seen in Fig. 4a, none of the mutants significantly reduces the growth rate on glucose, in agreement with previous observations for the BW25113 strain under comparable growth conditions (35).

We next measured the effect of acetate on the growth rate of the mutant strains by experiments analogous to the one shown in Fig. 2. The results are shown in Fig. 4b. The wild-type and all mutant strains are strongly inhibited by the addition of 128 mM acetate to the growth medium. Even though all strains are strongly affected, we observe two distinct groups: strains that carry the ackA deletion grow faster than strains that carry a wild-type copy of the gene. The inhibition indices of ΔackA strains are around 0.4, compared to the values of around 0.5 for all other strains (Fig. 4c). The observed differences in growth rates and inhibition indices, between the wild-type strain on the one hand and the ackA mutants on the other, are statistically significant (see Materials and Methods).

To preclude the possibility of unmapped, secondary mutations being responsible for the differential effect in ΔackA strains, we constructed a revertant of the phenotype of the ackA deletion. In the Δacs pta ackA::ackA_wt strain, the wild-type allele of ackA was restored. The slight growth advantage of the ΔackA strains in acetate, reflected by the smaller inhibition indices (0.4 versus 0.5), disappears in the complemented strain. The inhibition index increases to about 0.47 and reaches the same level as that for the equivalent Δacs pta strain (Fig. 4c). We conclude that even though the construction of the triple mutant has involved many growth and selection steps, the observed phenotypes of the mutants are not due to secondary mutations elsewhere on the chromosome.

The differential effect of the ackA deletion is not caused by a decreased flux of acetate into central carbon metabolism (and a corresponding decrease in ATP consumption), since the pta deletion, which interrupts the same pathway (Fig. 1), does not reduce growth inhibition by acetate. However, the ackA deletion is expected to modify the intracellular concentration of Ac∼P. During growth on glucose without excess acetate, Ac∼P is produced by Pta from acetyl-CoA (23, 36), but in the presence of high concentrations of acetate in the medium, we expect Ac∼P to be mostly generated by phosphorylation of acetate. The latter reaction no longer takes place in a ΔackA strain, so the concentration of Ac∼P will be lower than that in a strain with a functional AckA. In the extreme, deletion of both ackA and pta, like the Δpta ackA, Δacs pta ackA, and Δacs pta ackA poxB strains shown in Fig. 4, eliminating all reactions that can produce Ac∼P, results in a strain that is completely devoid of Ac∼P (36).

Thus, the 20% decrease of the inhibition index in the ΔackA strains can be explained by (partial) compensation for the increase in Ac∼P expected in the presence of excess acetate in the medium. The growth-inhibitory effect of an increase of the concentration of Ac∼P is consistent with the observation that deleting one of the known deacetylases in E. coli, CobB, reduces the growth rate of E. coli on acetate by almost 2-fold (37). Moreover, in the presence of 160 mM acetate, wild-type cells that are in a growth-arrested state (because of a lack of a nitrogen source in the medium) have a much higher degree of lysine acetylation than the ΔackA derivative (28), suggesting an increased Ac∼P concentration.

So far, we have focused on the reactions producing and consuming acetate inside the cell, ignoring questions about acetate uptake. This is motivated by the fact that, as mentioned in the Introduction, the protonated form of acetate acid, HAc, can freely diffuse into the cell. Nevertheless, two specific transporters of acetate, SatP and ActP, have been identified previously (38). We therefore wanted to ascertain that active acetate uptake or secretion is not necessary for the growth-inhibitory effect of acetate in the medium. Using satP and actP mutants of the wild-type strain (39), we tested under the same conditions as those described above the effect of adding acetate on the growth rate of the mutant strains compared to that of the wild-type strain. We found no significant difference in the growth inhibition index between the wild type and the mutants (Fig. S4), showing that under our conditions active acetate uptake is not required for growth inhibition.

As explained above, the results reported in Fig. 4 do not support the hypothesis that the influx of excess acetate into central carbon metabolism plays a significant role in growth inhibition. While no such influx can occur in the Δacs pta mutant, in which both the Acs and the Pta-AckA pathways have been eliminated, the growth rate in the presence of acetate and the inhibition index are the same as those for the wild-type strain. In order to further characterize central carbon metabolism on a coarse-grained level (40), we measured the extracellular concentration of glucose and the major fermentation products known to accumulate during aerobic growth of E. coli on glucose in the wild-type strain, in the Δacs pta double mutant, and in the Δacs pta ackA triple mutant. In particular, we quantified acetate, ethanol, formate, lactate, and pyruvate during growth experiments, as described for Fig. 2 (35, 41–43).

The results shown in Fig. 5 (left column) confirm the expected overflow metabolism during growth of the wild-type strain on glucose, namely, the secretion of acetate (31). This overflow metabolism is almost completely abolished in the mutants, confirming that the major pathway of acetate production is interrupted. In order to dissipate the extra reducing equivalents, other metabolites, in particular lactate and pyruvate, are secreted during growth of the mutants on glucose. When 128 mM acetate is added to the growth medium (Fig. 5, right column), the growth rate slows and the glucose uptake rate diminishes accordingly. Because of the lower growth rate, there is no longer any detectable overflow metabolism, except for a small amount of pyruvate in the wild type and triple mutant. Notice that changes in acetate concentration are undetectable, since there is a large excess of acetate in the growth medium under this condition. Diminished pyruvate excretion in the Δacs pta mutant may be an unknown regulatory effect mediated by Ac∼P and affected by the additional deletion of ackA in the triple mutant. The slight relief of growth inhibition by acetate in the triple mutant is consistent with the somewhat higher glucose uptake rate in this strain (Fig. 5, right column, blue curve).

Despite some small differences between strains, the data shown in Fig. 5 reveal that the pattern of uptake and secretion of carbon compounds by the cell is not significantly perturbed by the addition of large concentrations of acetate to the growth medium. A similar observation can be made for the changes in extracellular pH. None of the three strains shows a noticeable difference in extracellular pH at a given OD in strains growing in medium with and without added acetate (Fig. S5). Moreover, the extracellular pH curves are quite similar for the wild-type and mutant strains. Using the uptake and secretion patterns as proxies for the functioning of central metabolic pathways, this suggests that addition of acetate indeed does not entail a profound reorganization of metabolism, apart from a global rescaling of fluxes due to the reduced growth rate.

In order to further probe this conclusion, we used a genome-scale reconstruction of E. coli metabolism (29). From the data shown in Fig. 5 we computed the glucose uptake rate and the secretion rates of acetate, ethanol, formate, lactate, and pyruvate, which were integrated into the model to constrain the exchange fluxes. Moreover, the biomass reaction in the model was set equal to the measured growth rate. We also formulated a limited number of additional uptake and reversibility constraints that are directly motivated by the composition of the growth medium and the utilization of glucose as the sole carbon source (see Materials and Methods and File S1).

Using this model, we performed a metabolic flux analysis (44, 45) to obtain the flux distribution minimizing the difference between the predicted and measured fluxes, including the biomass production rate (46, 47). We used a Monte Carlo sampling approach to characterize the space of possible solutions, focusing on the reactions in central carbon metabolism (see Materials and Methods). As shown in Fig. 6, when scaling the fluxes under each condition by the growth rate, the distribution of internal metabolic fluxes is the same in the absence or presence of acetate. The results of this computational analysis are in agreement with the conclusions drawn from inspection of Fig. 5 that the inhibitory effect of acetate does not profoundly change the global functioning of metabolism.

As explained above, when 128 mM acetate is added to the medium, quantification of the acetate uptake or secretion rates is unreliable. Therefore, in this case, we did not constrain the corresponding reaction in the metabolic flux analysis. Interestingly, the exchange fluxes predicted by the approach correspond well with the ¹³C flux measurements carried out by Enjalbert et al. (22). In the case of the wild-type strain, the direction of the acetate exchange flux inverts upon the supply of acetate (secretion of 3.5 mmol gDW⁻¹ h⁻¹ for 0 mM acetate and uptake of 2.7 mmol gDW⁻¹ h⁻¹ for 128 mM acetate). The deletion of the Pta-AckA pathway, however, prevents this inversion (secretion of 0.7 mmol gDW⁻¹ h⁻¹ for 0 mM acetate and secretion of 3.8 mmol gDW⁻¹ h⁻¹ for 128 mM acetate).

The bacteria used in this study were E. coli K-12, strain BW25113 (39), that we designated the wild type (rrnB_T14 ΔlacZ_WJ16 hsdR514 ΔaraBAD_AH33 ΔrhaBAD_LD78). The following deletion mutants were constructed by removing the entire open reading frames of the corresponding genes: the Δacs, ΔackA, Δpta, Δpta ackA, Δacs pta, Δacs pta ackA, and Δacs pta ackA poxB strains. Δpta ackA is the shorthand notation for the Δpta ΔackA double mutant (an analogous abbreviation is used for the other strains). We also constructed a Δacs pta ackA::ackA_wt reversion mutant. In this mutant, a wild-type copy of the ackA gene was reintroduced into the mutant strain in order to verify the strain constructions. The phenotype of the resulting complemented strain should be identical to that of the Δacs pta strain.

The standard minimal medium contained 11.1 mg/liter CaCl₂, 240.73 mg/liter MgSO₄, 5 mg/liter thiamine, 1 g/liter NH₄Cl, 0.5 g/liter NaCl, 3 g/liter KH₂PO₄, 8.5 g/liter Na₂HPO₄·2H₂O, 3 mg/liter FeSO₄·7H₂O, 15 mg/liter Na₂EDTA·2H₂O, 4.5 mg/liter ZnSO₄·7H₂O, 0.3 mg/liter CoCl₂·6 H₂O, 1 mg/liter MnCl₂·4H₂O, 1 mg/liter H₃BO₃, 0.4 mg/liter Na₂MoO₄·2H₂O, and 0.3 mg/liter CuSO₄·5H₂O. In order to obtain a growth medium at pH 7.4 or 6.4, the relative concentrations of KH₂PO₄ and Na₂HPO₄·2H₂O were adjusted appropriately without changing the total (molar) phosphate concentration. As a carbon source, 3 g/liter glucose was used. The growth medium was supplemented with methionine to a final concentration of 3.3 mM when appropriate. Acetate was added to the growth medium as a concentrated solution of sodium acetate equilibrated to pH 7.4 or pH 6.4 in order to obtain the desired final concentration of acetate (128 mM in most experiments).

All of our mutants were derived from strains in the Keio collection (39). The kanamycin resistance cassette replacing the coding sequence of the genes was removed such that none of our mutants carries an antibiotic resistance cassette. The kanamycin resistance cassette is flanked by recognition sites of the Flp recombinase, and the cassette can therefore be excised using a plasmid expressing the Flp recombinase (plasmid 705-FLP) (51). This excision creates an in-frame scar sequence (102 bp), reducing polar effects on downstream gene expression. The first mutants to be constructed, by simply removing the kanamycin resistance cassette from the corresponding Keio clone, were the ΔackA and Δpta mutants.

We constructed the Δacs and the Δpta ackA mutants by replacing the gene acs and the operon pta-ackA with an FLP recombination target-flanked kanamycin resistance gene generated by PCR (52). Primers have 20-nucleotide (nt) 3′ ends homologous to the kanamycin resistance cassette used in the Keio collection and 50-nt 5′ ends of homology targeting the chromosomal region of interest. PCR products were transformed into a BW25113 strain expressing the λ Red recombinase (plasmid pSIM5) (53). Antibiotic-resistant recombinants were then selected and the kanamycin resistance cassette removed.

We constructed the Δacs pta, Δacs pta ackA, and Δacs pta ackA poxB mutants by P1 transduction (54). The P1 lysate was grown on our Δpta ackA::kan mutant and the Δpta::kan mutant from the Keio collection. These lysates were then used to infect the Δacs strain in order to obtain Δacs pta ackA::kan and Δacs pta::kan transductants. The kanamycin resistance cassette was removed as described above. The same procedure was used for moving the ΔpoxB::kan mutation from the ΔpoxB Keio mutant to our Δacs pta ackA strain.

We reintroduced the gene ackA into the Δacs pta ackA mutant precisely into the original locus by following a previously described approach (55), thereby effectively restoring a Δacs pta mutant. Primers pta-CCDB1 and ackA-KN1 were used to amplify a kan:p_BAD:ccdB cassette. The PCR product was transformed into a Δacs pta ackA mutant expressing the λ Red recombinase (plasmid pSIM5). Antibiotic-resistant recombinants were selected. Primers Y2-ACKA and ackA_pta_left_PCR_verif were used to amplify the sequence between the initiation codon of ackA and the initiation codon of pta of the Δacs pta mutant. The PCR product was recombined into the chromosome in place of the cassette. Recombinants were selected on medium containing arabinose for activation of the suicide gene ccdB, which kills cells that have not recombined the ackA gene.

All mutants were verified by PCR and DNA sequencing. The list of primers used in this study can be found in Table 2.

For each strain, a seed flask (50-ml capacity), containing 10 ml of filtered minimal medium with glucose, was inoculated from a glycerol stock. The culture in the seed flask was grown overnight at 37°C with orbital agitation of 200 rpm. At the same time, 50 ml of filtered minimal medium with glucose (and methionine when appropriate) was pipetted into different 250-ml flasks (as many as there were experimental conditions and replicates) and stored overnight at 37°C without shaking. The following day, each 250-ml flask was inoculated to an OD₆₀₀ of 0.02 from the seed flask. For each strain, two 250-ml flasks were used: one for the addition of 2 ml of filtered minimal medium with acetate and the other for the addition of 2 ml of filtered minimal medium without any carbon source (control). Cultures were grown at 37°C with orbital shaking at 200 rpm. Growth of the strains was monitored every 30 min by removing a sample of 1 ml. Samples were used to measure the optical density. The remaining volume was centrifuged at 14,000 × g for 3 min at 4°C. The supernatant was frozen at −20°C for the quantification of metabolites. Acetate stock solution was prepared in concentrated form such that 2 ml of the stock solution, added to the culture, would give a final concentration of 128 mM acetate. Minimal medium with acetate and minimal medium without any carbon source were stored at 37°C before addition to the growing culture. Acetate was added when the OD₆₀₀ reached about 0.2.

Cell growth was monitored by measuring the OD₆₀₀ with a spectrophotometer (Eppendorf BioPhotometer). Dilutions were done when appropriate in order to stay in the range of linearity of the instrument. The partial oxygen pressure, pO₂, and the pH were measured with a Clark electrode (LAMBDA fermentor) and a pH (micro)probe (Mettler Toledo or Thermo Scientific Orion), respectively.

d-Glucose, acetic acid, formic acid, pyruvic acid, d-lactate, and ethanol were assayed by enzymatic assay kits according to the manufacturer’s recommendations: R-Biophar no. 10 716 251 035 (Boehringer Mannheim), K-ACETRM (Megazyme), K-FORM (Megazyme), K-PYRUV (Megazyme), K-LATE (Megazyme), and K-ETOH (Megazyme), respectively. All of the above-mentioned measurement procedures are based on coupled enzyme assays.

Quantifications were done in 96-well microplates (clear, flat bottomed, plastic). Depending on the metabolite we wanted to quantify, different enzymatic reactions led to the consumption or the production of NADH. The concentration change of NADH was quantified by measuring the difference in absorbance at 340 nm (ΔA_metabolite) with a microplate reader (Perkin Elmer Fusion Alpha). The concentration of the sample, C_metabolite (diluted in order to remain within the linearity region of the assay) is then calculated aswhere ΔA_standard and C_standard are the measured absorbance difference and the concentration of the metabolite standard. The metabolite standard solution was provided with each kit. In order to compute ΔA_metabolite and ΔA_standard, the absorbance before starting the reactions (A₁) and the absorbance at the end of the reactions (A₂) were read ten times at regular time intervals in order to ensure that the reaction had reached equilibrium. In order to compensate for drift in the measurements, we fitted a straight line to the repeated measurements of A₁ and A₂. Using this straight-line extrapolation, the absorbance difference, ΔA = A₂ – A₁, was calculated at the time of addition of the last enzyme that starts the reactions. Metabolite concentrations were corrected to take into account the dilution due to the addition of 2 ml of medium with or without acetate. Concentrations are given as the means from at least three independent experiments. Error bars are set equal to twice the standard errors of the means.

In order to compute growth rates for the different strains, cultured in the presence or absence of acetate, we used the exponential growth modelwith B(t) and B₀ being the time-varying and initial biomass in OD₆₀₀ units, respectively, and μ the growth rate (per hour). This model has the explicit solution

This equation was fitted to each individual time series of optical density measurements. We checked that within the chosen time interval, the underlying assumption of exponential growth at a constant rate is satisfied. The reported growth rate values are the means from at least three independent experiments. Error estimates are reported as twice the standard errors of the means.

In order to compute the glucose uptake rate, we combined the growth model with the glucose consumption modelwhich has the explicit solutionwhere G(t) and G₀ are the time-varying and initial glucose concentrations (in millimolars), respectively, and Y (OD₆₀₀ per millimolar) is the biomass yield, defined as the ratio of the growth rate and the glucose uptake rate, r_glc (in millimolars per OD₆₀₀ unit per hour). We simultaneously fitted equations 4 and 6 to each individual time series data set of glucose concentrations and optical densities, obtained in a single growth experiment. For each of the six conditions considered (wild-type, Δacs pta, and Δacs pta ackA strains under the two growth conditions, 0 or 128 mM acetate added to the glucose minimal medium), estimates of μ and Y were obtained. The glucose uptake rate can be directly obtained from these estimates, bearing in mind that Y = μ/r_glc. The reported values are the means from four independent replicate experiments. Error estimates are reported as twice the standard errors of the means.

In order to obtain the secretion rate of the fermentation by-products, used in the flux balance model, we again fitted equation 6 to the data but replaced the glucose uptake rate with the appropriate secretion rate and used the values of μ and B₀ obtained as described above. All uptake and secretion rates are computed from four independent replicate experiments with error estimates given by twice the standard errors of the means.

All computational analyses were performed with a slightly modified version of the genome-scale reconstruction iAF1260-flux1 of Escherichia coli metabolism (29), to which we added a reaction accounting for transport of acetate anions by ActP (38). The lower bound of exchange fluxes was set to zero, except for components of the in silico growth medium (water, vitamin, salts, traces, and glucose), which were left unconstrained, and for the oxygen uptake rate, which was limited to 20 mmol gDW⁻¹ h⁻¹. The upper bound of the exchange fluxes was set to zero for secreted products, except for those detected in the external medium in our experiments, namely, acetate, formate, lactate, pyruvate, and ethanol. These fluxes were set to their measured values ± two standard errors of the means, except for acetate when excess acetate is supplied to the medium. A theoretical exchange flux of carbon dioxide was determined based on the carbon mass balance. Eighteen additional reactions were constrained by literature data to allow normal functioning of the glycolysis and the pentose phosphate pathway (File S1). Reactions allowing glycogen consumption and transport of d-glucose through alternative pathways were blocked, as were fluxes through reactions catalyzed by putative sugar phosphatase and aldehyde dehydrogenase. The maintenance fluxes were set to their default values (59.81 mmol gDW⁻¹ h⁻¹ and 8.39 mmol gDW⁻¹ h⁻¹ for the growth- and non-growth-associated maintenance fluxes, respectively). We checked that this allows flux balance analysis to reproduce the measured growth rate of the wild-type strain cultured in minimal medium with glucose in the absence of acetate, when the objective function is the maximization of biomass. The biomass function used is Ec_biomass_iAF1260_core_59p81M (29).

In order to test the consistency of the metabolite measurements with the network stoichiometry, we performed a metabolic flux analysis (44), where the objective is to minimize the differences between the measured and predicted exchange fluxes and growth rate. Let v denote the vector of fluxes at steady state, N the stoichiometry matrix, v^l and v^u the vectors of upper and lower bounds on fluxes, respectively, and $\widehat{v}$ the vector of p measurements of exchange fluxes. We assume that the first p elements of v correspond to the measured exchange fluxes. Moreover, we define u⁺ and u^– as nonnegative dummy variables. Following the formulation of reference 46 (see also references 45 and 47), metabolic flux analysis can be formulated as the following linear programming problem:

This minimization problem was solved for each of the strains considered, both in the absence and presence of acetate, using the COBRA v3.0 Toolbox (56) with Gurobi 7.5.2 as the linear programming solver (Gurobi Optimization, Inc., Houston, TX).

In order to further characterize the solution space of the above-described metabolic flux analysis problem, we used a Monte Carlo sampling approach to estimate for each reaction in the network a distribution of possible flux values (57). In particular, we performed uniform random sampling by means of the coordinate hit-and-run with rounding (CHRR) algorithm implemented in the COBRA Toolbox (58). We computed the distribution of reaction fluxes consistent with the measured growth rate and exchange fluxes for each condition, focusing on reactions in central carbon metabolism. These reactions were determined by their annotation in the iAF1260-flux1 model: pentose phosphate pathway, anaplerotic reactions, glycolysis gluconeogenesis, pyruvate metabolism, and citric acid cycle. The maximum of the resulting distributions, one for each reaction, was used for comparing reaction fluxes in the presence or absence of acetate in the growth medium. To this end, the reaction fluxes were rescaled by dividing them by the measured growth rate.

In order to quantify Acs expression, we used a fluorescent reporter gene system based on a transcriptional fusion of the acs promoter with a stable green fluorescent protein, GFPmut2, carried on the low-copy-number plasmid pUA66 (59). The wild-type strain was transformed with this plasmid, and experiments were carried out under the reference conditions described above. In addition to being used for measuring the optical density, samples taken were transferred to a 96-well plate to quantify the fluorescence emitted by the cultures in a microplate reader (Tecan Infinite 200 PRO). The excitation wavelength was set to 480 nm, and the emitted fluorescence was measured at 520 nm.

The data were corrected for background fluorescence levels using the wild-type strain as described previously (60). An estimate of the reporter protein concentration, in arbitrary units, was obtained by dividing, at each time point, the background-corrected fluorescence level by the optical density. Assuming that Acs is a stable protein, like the GFP variant used in this study, the reporter concentration can be assumed to be proportional to the Acs concentration (61).

In order to test the hypothesis that the growth rates or biomass yields of two strains in a given condition are equal, we used Welch’s t test, a t test for normally distributed variables with possibly unequal variances and an unequal number of independent samples (experiments) (62). A pair of strains failing the test, for significance thresholds of 0.06 or 0.01, are concluded to have significantly different growth rates.

No off-the-shelf statistical method is available for testing the hypothesis that two inhibition indices are equal, as inhibition indices, which quantify the effect of acetate on the growth rate, are defined as ratios of normally distributed variables with nonzero means (equation 1). We therefore followed a bootstrap procedure by randomly resampling with replacement the experimentally determined distributions of the growth rates and computing the corresponding inhibition indices, thereby obtaining estimates of the mean and confidence interval of the inhibition indices (63). These bootstrap distributions were used to test the null hypothesis that the inhibition indices of two strains under a given condition are equal by computing the P value corresponding to the probability that the difference between the inhibition indices estimated from the data would occur if the two indices were equal. The inhibition indices were concluded to be different for P values below 0.03 or 0.005, corresponding to significance thresholds of 0.06 or 0.01, respectively, because of the two-sidedness of the distribution.