Experimental verification of the kinetic model
To verify the appropriateness of the kinetic model, the simulated extracellular concentrations of fermentation products were compared with the experimental data obtained from batch cultures under micro-aerobic (DO level = 1%) and aerobic (DO level = 40%) conditions [41, 42], as shown in Fig. 2. The concentrations of acetate, lactate, formate, ethanol, and succinate in the batch culture of the WT strain were plotted at the time points at which 10 g/l (micro-aerobic) and 4 g/l (aerobic) of glucose were depleted. The model reproduced most of the experimental product concentration under both micro-aerobic and aerobic conditions (Fig. 2). In addition, the model almost reproduced the experimental time courses of the WT strain under micro-aerobic (DO level = 9%) and aerobic conditions [43, 44], as shown in Additional file 3: Figure S1. The correlation coefficient between the measured [41,42,43,44] and simulated metabolite concentrations was 0.98 (p < 0.05), as shown in Additional file 3: Figure S2.
Effect of DO level on the metabolic characteristics in the WT strain
Figure 3a shows the simulation result for a batch culture of the WT strain, in which the concentrations of acetate, lactate, formate, ethanol, and succinate were simulated at the time point at which 10 g/l of glucose was depleted. Acetate was the primary product at DO levels >15%. This acetate overflow was observed together with high CO2 production at a high growth rate in E. coli [45, 46], as shown in Additional file 3: Figure S3. The acetate concentration increased with decrease in the DO level (3–14%), as observed experimentally [24]. As the DO level decreased, the formate, ethanol, and succinate concentrations increased; the lactate concentration increased and then steeply decreased below 5% of DO level. At DO levels <2%, the lactate concentration was lower than that of the other products as experimentally observed [42, 47].
Changes in the metabolism of the WT strain with respect to DO level
As shown in Fig. 3b, the changes in the concentrations of intracellular metabolites and fluxes were simulated with respect to DO level in the WT strain. The metabolic characteristics were evaluated by classifying the DO level into four categories: (I) anaerobic condition (DO = 0%) in which both Fnr and ArcA are active; (II) micro-aerobic conditions (0% < DO < 7%) in which both Fnr and ArcA are active; (III) micro-aerobic conditions (7% ≤ DO < 20%) in which ArcA is primarily active and Fnr is inactive; and (IV) aerobic conditions (DO ≥ 20%) in which neither Fnr nor ArcA is active. TFFnr and TFArcA in Fig. 3b were calculated by Eqs. 8 and 9, respectively. The change in the typical carbon metabolism is illustrated for these categories in Additional file 3: Figure S4.
The specific oxygen uptake rate (qOUR), which indicates the rate of oxygen consumption via Cyo and Cyd reactions, was simulated to be high under condition IV, whereas it decreased under conditions III, II, and I (Fig. 3b). As the DO level decreased, the Cyd flux increased and then decreased at <7% DO. This up and down behavior can be attributed to the activation of Cyd synthesis by ArcA under condition III, whereas Cyd synthesis was repressed by Fnr under conditions I and II (Fig. 1). The Cyo flux was simulated to be higher than the Cyd flux under condition IV, whereas the Cyd flux was more dominant than the Cyo flux under condition II. These simulation results are supported by the experimental fact that the affinity of Cyd to oxygen is higher than that of Cyo [29]. Since quinone is produced by Cyo and Cyd, quinone decreases with a decrease in DO level. This phosphorylates ArcB and then ArcA, resulting in the increase in the ArcA activity under conditions I, II, and III.
Among the enzymes associated with consumption of pyruvate, Pfl, pyruvate dehydrogenase (PDH), and LDH, play critical roles in determining the metabolite formation pattern. As the DO level decreased, the Pfl flux was simulated to increase under condition III because ArcA activated the Pfl reaction (Fig. 1). The Pfl flux was further enhanced by Fnr and ArcA under conditions I and II. In contrast, as the DO level decreased, the PDH flux decreased under condition III because ArcA represses the aceE/F genes that encode PDH (Fig. 1). The Pfl and PDH fluxes were both active under condition III, which was consistent with the experimental data [48]. The LDH flux exhibited an up and down behavior with respect to DO level. As the DO level decreased, the LDH flux increased under condition III, whereas it declined steeply under condition II.
The NADH/NAD+ ratio increased steeply with decreasing DO level under conditions I and II because NADH is hard to be consumed by the NADH dehydrogenases in the respiratory chain. This simulation result was consistent with the experimental data [49]. A high NADH/NAD+ ratio promoted the ADH reaction, which resulted in enhanced ethanol production under conditions I and II. Since Fnr activates the Frd flux (Fig. 1), succinate production was enhanced under conditions I and II.
To obtain a better understanding of the mechanisms by which ATP and NADH are produced or consumed under the categorized DO conditions examined, the specific production/consumption rates of ATP and NADH were simulated, as illustrated in Fig. 3c, d. DO levels of 0, 3, 8, and 40% were selected as the representatives of conditions I, II, III, and IV, respectively. The specific ATP production rate decreased in the order of conditions IV, III, II, and I (Fig. 3c). Additional file 3: Figure S5 indicates the relationship between the specific ATP production rate and the specific growth rate. Once the specific ATP production rate was calculated by Eq. 1, the specific growth rate was estimated by Eq. 3. This linear relationship between the specific ATP production rate and the specific growth rate held not only under aerobic conditions but also under micro-aerobic and anaerobic conditions with a correlation coefficient of 0.92 (p < 0.05), as experimentally observed [25, 37, 38, 41, 42, 47].
The DO level affected the specific ATP production rate (Fig. 3c). ATP was primarily synthesized by respiration under condition IV. By contrast, substrate-level phosphorylation by glycolysis and acetate formation became dominant under conditions I and II. NADH was consumed by the NADH dehydrogenases (Nuo and Ndh) in the respiratory chain under condition IV, whereas NADH was primarily consumed by ethanol formation under conditions I and II (Fig. 3d). This simulation result demonstrates that the ADH flux increased under conditions I and II due to a high NADH/NAD+ ratio (Fig. 3b). In fact, it was experimentally shown that ethanol is produced under micro-aerobic and anaerobic conditions [42, 47, 50]. The reaction of reductive TCA arm via malate dehydrogenase (MDH) consumed NADH under conditions I and II (Fig. 3d). The resultant fumarate/malate were supplied as the substrates for the reaction of Fnr-activated Frd (Fig. 3b), producing succinate (Fig. 3a). This simulation result was consistent with the experimental observation [47, 50]. NADH was produced by glycolysis, the PDH reaction, and the TCA cycle under condition IV (Fig. 3d), whereas NADH production by the PDH flux and TCA cycle declined significantly under conditions I and II because ArcA represses the PDH flux and both ArcA and Fnr repress the TCA cycle.
Additional file 3: Figure S3A shows the carbon balances of the extracellular products, CO2, and biomass at different DO levels (conditions I, II, III, and IV) in the WT strain. The metabolic modes changed significantly depending on DO level. Most of glucose was converted to biomass, CO2, and acetate under condition IV. On the other hand, biomass and CO2 production were decreased under condition I.
Prediction of the metabolic characteristics of an fnr-knockout mutant
As Fnr and ArcA play critical roles in redox regulation at low DO levels, it is of interest to predict the effect of fnr or arcA gene knockout on the primary metabolism. Figure 4a shows the simulation results of an fnr-knockout mutant, in which the concentrations of acetate, lactate, formate, ethanol, and succinate were simulated at the time point at which 10 g/l of glucose was depleted. As compared to the WT strain (Fig. 3a), succinate was rarely produced at any DO level due to little activity of Frd caused by a lack of Fnr. As DO level decreased, lactate increased, peaking at 3% DO, and then slightly decreased. The lactate production in the fnr-knockout mutant was more enhanced than the WT strain at very low DO levels, which was supported by the experimental data [51].
Figure 4b shows the effect of DO level on the intracellular metabolic fluxes, redox status, and transcriptional activities. The Pfl flux was predicted to be lower in the fnr-knockout mutant than in the WT strain (Fig. 3b) under conditions I and II. The LDH flux increased under condition III and slightly decreased under conditions I and II in the fnr-knockout mutant, but it was higher than that of the WT strain (Fig. 3b). As the DO decreased, the NADH/NAD+ ratio increased under conditions III, II, and I, which resulted in the increased ADH flux, while the Frd flux was zero due to a lack of Fnr.
The simulated specific production/consumption rates of ATP and NADH are shown in Fig. 4c, d. The profiles of the specific ATP production rates of the fnr-knockout mutant were almost the same as those of the WT strain (Fig. 3c), whereas the specific NADH consumption rate in the lactate and ethanol formation through LDH and ADH and the respiratory pathway somewhat differed from that of the WT strain under condition I (Figs. 3d, 4d). The NADH consumption rate through LDH in the fnr-knockout mutant was higher than that of the WT strain (as discussed later), whereas the NADH consumption rate through ADH was lower than that of the WT strain. As compared with the WT strain, the NADH consumption rate by the NADH dehydrogenases in the respiratory chain increased under condition II because the lack of Fnr de-repressed the NADH dehydrogenase reactions.
Additional file 3: Figure S3B shows the carbon balances of the metabolic products including CO2 and biomass in the fnr-knockout mutant at different DO levels. The carbon balances differed between the WT strain and the fnr-knockout mutant under conditions I and II (Additional file 3: Figure S3A, B). More glucose carbon was converted into lactate in the fnr-knockout mutant than in the WT strain.
Prediction of the metabolic characteristics of an arcA-knockout mutant
As shown in Fig. 5a, the model predicted the changes in metabolic products with respect to DO level in an arcA-knockout mutant. Acetate production decreased slightly from 10 to 2% DO, as experimentally observed [52]. Ethanol production was predicted to be higher in the arcA-knockout mutant than in the WT strain and fnr-knockout mutant at DO <6%, which was consistent with the experimental data under micro-aerobic conditions [53, 54]. Under anaerobic condition, ethanol production was also predicted to be higher in the arcA-knockout mutant than in the other strains, while the ethanol production in the arcA-knockout mutant was reduced in the experiment [53]. This discrepancy will be discussed later. As the DO level decreased, lactate increased, peaking at 4% DO, and then decreased (Fig. 5a). The maximum concentration of lactate produced by the arcA-knockout mutant was higher than those of the WT strain and fnr-knockout mutant, as experimentally observed [53].
Figure 5b shows the effect of the DO level on the intracellular metabolic fluxes, redox status, and transcriptional activities. The Cyd flux was lower than that of the WT strain under conditions III and II (Figs. 3b, 5b), as experimentally observed [55]. As the DO level decreased under conditions III and II, the PDH flux slightly decreased. The decrease in the PDH flux was small compared to that of the WT strain and the fnr-knockout mutant (Figs. 3b, 4b, 5b) because the PDH flux is not repressed in the arcA-knockout mutant. The NADH/NAD+ ratio in the arcA-knockout mutant was higher than that of the WT strain and the fnr-knockout mutant under condition II (Figs. 3b, 4b, 5b), as experimentally observed [53]. As DO level decreased, the NADH/NAD+ ratio increased and then declined slightly as experimentally observed [53]. The simulated NADH/NAD+ ratio of the arcA-knockout mutant was higher than its experimental ratio, although the simulated NADH/NAD+ ratios of the WT strain and the fnr-knockout mutant were relatively consistent with their experimental ratios. While the activities of the PDH, citrate synthase (CS), and isocitrate dehydrogenase (ICDH) enzymes are allosterically inhibited by NADH to suppress an excess production of NADH [56, 57], the present model did not implement such allosteric inhibitions. The neglect of the allosteric inhibitions relatively reproduced the NADH/NAD+ ratios of the WT strain and the fnr-knockout mutant because their NADH level was not so high as that of the arcA-knockout mutant, but would overestimate the NADH/NAD+ ratio of the arcA-knockout mutant. As the DO level decreased, the Frd flux steeply increased and then declined (Fig. 5b). The simulation result of the Frd flux showed the similar trend as that of the NADH/NAD+ ratio due to the fact that NADH is oxidized at MDH with Frd.
The specific production/consumption rates of ATP and NADH were simulated as shown in Fig. 5c, d. The specific ATP production rate increased in the arcA-knockout mutant under condition III as compared with the WT strain (Figs. 3c, 5c) because Cyo is activated in the arcA-knockout mutant (Fig. 1). For this, the qOUR for the arcA-knockout mutant was higher than that of the WT strain under condition III (Figs. 3b, 5b), as experimentally observed [32]. The specific NADH production rate in the TCA cycle was slightly higher than that of the WT strain under condition III (Figs. 3d, 5d), as experimentally observed [32], because the TCA cycle is not repressed in this mutant. The specific NADH consumption rate through ethanol formation (by ALDH and ADH) was higher than that of the WT strain under conditions I and II (Figs. 3d, 5d).
Additional file 3: Figure S3C shows the carbon balances of the metabolic products including CO2 and biomass in the arcA-knockout mutant at different DO levels. More glucose carbon was converted to biomass, and more CO2 was produced in the arcA-knockout mutant than the WT strain due to de-repression of the PDH and TCA cycle under condition III (Additional file 3: Figure S3A, C).
Rational design of a method for lactate production by a pfl-knockout mutant
The present model was utilized for the rational design of microbial cellular factories and optimization of target metabolite production. While a pfl-knockout mutant was experimentally reported to exclusively produce lactate [44], the effect of the DO level on the energy generation, biomass formation, and productivity has been rarely investigated. Simulated time course data of a batch culture of the pfl-knockout mutant reasonably predicted the experimental data (Fig. 6a) [44]. Here, we considered operation strategies for the efficient production of lactate by the pfl-knockout mutant.
Dual-phase cultivation was designed to enhance the target metabolite production, starting with an aerobic cultivation to promote the cell growth, followed by an anaerobic or micro-aerobic condition to facilitate the target metabolite production. The switching time when the culture condition is changed from aerobic to micro-aerobic condition is generally a key parameter for enhanced productivity. The effect of the switching time on lactate yield (g of product/g of substrate consumed) and productivity (g/l of product concentration/h of cultivation time) was simulated for the pfl-knockout mutant when 10 g/l glucose was supplied as a carbon source (Fig. 6b). The DO levels of 40 and 1% were set to the aerobic and micro-aerobic conditions, respectively. The symbols in Fig. 6b represent the productivity of lactate obtained from the experiments [44, 58]. As expected, the yield was the highest when the cells were cultured consistently under the micro-aerobic condition, although the productivity was low. The productivity was improved to 0.81 g/l/h (at a switching time of 4.5 h) by the dual-phase cultivation, as compared to 0.38 g/l/h under the micro-aerobic condition throughout the cultivation (Fig. 6b).