Team:TU Delft-Leiden/Modeling/EET/FBA

Flux Balance Analysis of the EET Module

In the wet lab, we integrated the Extracellular Electron Transport (EET) module of S. oneidensis into E. coli , see the extracellular electron transport (EET) module. For the modeling of the EET module, we wanted at first to gain insight in the consequences of the integration of the EET module into E. coli. To achieve this, we had to find a way to simulate the cell metabolism of E. coli including the EET module. Flux Balance Analysis (FBA) is a method that calculates the fluxes of metabolites through a metabolic network [1], more about the theory of Flux Balance Analysis can be found in Flux Balance Analysis Method. Therefore, we decided to use the FBA method to gain insight in the resulting cell metabolism of E. coli. Our goal was to investigate the carbon metabolism providing the electrons for the EET module, as described in Carbon Metabolism and Electron Transport. Also, we want the EET pathway used by the cells in order to have a measurable electrical signal for our biosensor, see the gadget section of our wiki.

Extracellular Electron Transport in the E. Coli Core Model

To perform Flux Balance Analysis (FBA), we first had to find a model that represents the cell metabolism of E. coli. At first, we used the E. coli Core model [2], a simplified model of the metabolism of E. coli consisting of 95 reactions and 72 metabolites, as this model is not too big and complicated, so it is relatively easy to get an understanding of its dynamics. To include the EET pathway, we added the corresponding reactions from a FBA model describing S. oneidensis [3]. These reactions describe the transfer of electrons from quinol to cytochrome c molecules. The electrons are further transported through the Mtr pathway to the extracellular matrix. As this is not relevant for our goal of investigating the carbon metabolism, we modeled these reactions as an electron drain.

Now that the model was created, we performed the FBA method on our model of 99 reactions and 75 metabolites, which can be found in the code repository. We set the objective function equal to the reaction Biomass Objective Function with GAM, which can be seen as an equivalent of the growth rate of the cell. We performed our analysis using the COBRA Toolbox, which is a MATLAB toolbox [8]. Firstly, we maximized this objective function for a glucose uptake flux of 18.5 \(mmol \ (gDW)^{-1} \ hr^{-1}\) (per gram dry weight per hour) in aerobic conditions, as this is a realistic glucose uptake flux in an experimental setting [4]. The results from the FBA predicts a growth rate of 1.92 \(hr^{-1}\). Examination of the fluxes tells us that the EET pathway is not used in this case, implying that the reduction of oxygen is preferred over extracellular electron transport, as oxygen is a stronger oxidizing agent. The metabolism of the cell in this condition can be found here. The highlighted lines indicate reactions which have a non-negligible flux.
Secondly, under anaerobic conditions, we found a growth rate of 1.65 \(hr^{-1}\). The metabolism of the cell in this case can be found here. As can be seen from the figure, glycolysis and catabolism through the TCA cycle still occur. Fermentation does not occur. The production of quinol and NADH happens through glycolysis and the TCA cycle, and they subsequently react with the EET pathway to export the electrons out of the cell. We conclude that the EET pathway has the capability to replace oxygen as the oxidizing agent, as the cell uses the EET pathway to export the electrons out of the cell. Comparison with the metabolism of the cell for aerobic growth indicates that the pathways used are quite similar. However, for anaerobic growth the cell cannot import oxygen, and therefore, some additional pathways are used to make up for this disadvantage. Also, for anaerobic growth the final oxidizing agent is the EET pathway, where for aerobic growth the final oxidizing agent is oxygen.

Now we performed the FBA method with the E. coli Core model without the EET module added. Without the EET pathway, we predicted for growth under aerobic conditions a growth rate of 1.65 \(hr^{-1}\) and for anaerobic conditions 0.47 \(hr^{-1}\). From this we conclude that oxygen as an oxidizing agent in aerobic conditions is completely taken over by the EET pathway in anaerobic conditions, as we found the growth in anaerobic conditions with the EET pathway to be equal to growth in aerobic conditions without the EET pathway, namely 1.65 \(hr^{-1}\).

Thereafter, we set the objective function equal to the reaction Ex_Elec, which is a reaction we added to the E. coli Core model. The reaction represents the disappearance of extracellular electrons, which is exactly what happens in our experimental setting, as the extracellular electrons go to the cathode of our measurement setup. By maximizing this objective function, we can analyze the maximum EET flux of our system. Electrons are transported from the cytosol to the extracellular domain by the reactions we added from the S. oneidensis model to the E. coli Core model.
We maximized the objective function equal to the reaction Ex_Elec for a glucose uptake flux of 18.5 \(mmol \ (gDW)^{-1} \ hr^{-1}\) in anaerobic conditions. The resulting metabolism of the cell can be found here. As can be seen from the figure, the metabolism of the cell is nearly the same when optimizing for growth. However, not the whole TCA cycle is used in order to maximize EET flux.
In the E. coli Core model a lot of reactions that occur in E. coli are not present in order to keep the model relatively simple. However, all these reactions that are not included still cost energy, mainly in the usage of ATP. Therefore, there is a reaction called ATP maintenance requirement included in the core model to include the energy usage of these reactions in the model. Its flux is bounded to be at least 8.39 \(mmol \ (gDW)^{-1} \ hr^{-1}\), which is experimentally determined to be a realistic value [4]. In other words, if the ATP generated by the carbon metabolism is not high enough to fulfil the ATP maintenance requirement reaction, no growth and EET flux will be observed.
When optimizing the objective function for growth, the flux of the ATP maintenance requirement reaction is exactly equal to 8.39 \(mmol \ (gDW)^{-1} \ hr^{-1}\). However, when maximizing EET flux, we see a flux for the ATP maintenance requirement reaction equal to 271 \(mmol \ (gDW)^{-1} \ hr^{-1}\), exactly equal to the flux of the reaction that creates ATP, called ATP synthase (four protons for one ATP). Also, there is no growth when we optimize for EET flux, while there is plenty of ATP created. Even when we change the Biomass Objective Function with GAM reaction to only need 0.1 \(mmol \ (gDW)^{-1} \ hr^{-1}\) of ATP and release 0.1 \(mmol \ (gDW)^{-1} \ hr^{-1}\) of ADP (so it only needs the ATP metabolite), the growth rate is still equal to 0 \(hr^{-1}\). Because the growth rate is equal to 0 \(hr^{-1}\) and the ATP synthase (four protons for one ATP) reaction has a flux of 271 \(mmol \ (gDW)^{-1} \ hr^{-1}\) , the ATP maintenance requirement reaction also has a flux of 271 \(mmol \ (gDW)^{-1} \ hr^{-1}\) in order to recycle all the produced ATP back to ADP, as the FBA method solves for steady state solutions. Even when we bound the flux of the ATP maintenance requirement reaction to be exactly equal to 8.39 \(mmol \ (gDW)^{-1} \ hr^{-1}\), we still observe the growth rate to be equal to 0 \(hr^{-1}\).

As a next step, we changed the carbon source to D-lactate, as E. coli with the EET module implemented were fed L-lactate in [5] and [6]. However, L-lactate is not part of the E. coli Core model as a metabolite and therefore, we decided to use D-lactate as a carbon source, as D-lactate is present in the core model as a metabolite.
We used a D-lactate uptake flux of 30 \(mmol \ (gDW)^{-1} \ hr^{-1}\). For aerobic and anaerobic growth and maximizing the objective function for growth, the results of the metabolism of the cell are quite similar to the results with growth on glucose. Instead of glycolysis, D-lactate is oxidized to pyruvate, but the TCA cycle is still activated. Also, for the aerobic case oxygen is the final oxidizing agent and for the anaerobic case the EET pathway is the final oxidizing agent, which is the same for growth on glucose. However, the growth rate on D-lactate is lower than on glucose, because glycolysis will reduce NAD+ to NADH and it will also synthesize ATP from ADP, but the oxidation of D-lactate to pyruvate only reduces NAD+ to NADH.
Subsequently, we set the objective function equal to the Ex_Elec reaction and maximized this objective function for a D-lactate uptake flux of 30 \(mmol \ (gDW)^{-1} \ hr^{-1}\) in anaerobic conditions. The resulting metabolism of the cell can be found here. As can be seen from the figure, the TCA cycle is not activated in this case. Also, again, as in the case of growth on glucose, there is no growth and the flux of the ATP maintenance requirement reaction is 135 \(mmol \ (gDW)^{-1} \ hr^{-1}\). We consider the fact that no growth is possible when optimizing for EET flux for both growth on glucose and D-lactate a highly unrealistic scenario, as the function of the EET module is to enable growth in anaerobic conditions without using the fermentation pathway. So, we consider it highly unrealistic to have no growth. Even when it will cost the cell only 0.1 \(mmol \ (gDW)^{-1} \ hr^{-1}\) of ATP to grow, it will still prefer the ATP maintenance requirement reaction, or when that reaction is bounded to 8.39\(mmol \ (gDW)^{-1} \ hr^{-1}\) it will prefer other reactions, to recycle all produced ATP back to ADP. Therefore, we decided to not further pursue the method of setting the objective function equal to the Ex_Elec reaction and will only set the objective function equal to the Biomass Objective Function with GAM reaction. The FBA method yielded realistic results when setting the objective function equal to the Biomass Objective Function with GAM reaction and this reaction is specially made to be set equal to the objective function [9].

Robustness Analysis of the EET Pathway

We further examined the carbon metabolism of E. coli using the method robustness analysis. In order to perform a robustness analysis, the flux through one reaction is varied and the objective function is maximized or minimized as a function of this flux. By analyzing how much the objective function changes as a function of this flux , it can be revealed how sensitive the objective function is to a particular flux [4].

Using the core model with the EET pathway included, we investigated the growth rate and EET flux as a function of the amount of carbon source. We only did so under anaerobic conditions, as we found earlier that under aerobic conditions, oxygen is the preferred oxidizing agent, see Section Extracellular Electron Transport in the E. coli Core Model. The results of an robustness analysis are shown in figure 1. In these analysis’s, we used growth as the objective function, which we maximized. As carbon source, we considered glucose and D-lactate, as glucose is the most standard carbon source and D-lactate, because E. coli with the EET module implemented were fed L-lactate in [5] and [6].

From our robustness analysis’s, we found that a minimal amount of carbon source is needed to start growth. Moreover, there is no EET flux when there is no growth, and the EET flux starts at a non-zero level as soon as there is enough glucose or D-lactate to let the bacteria grow.

We speculate that the stepwise fluxes shown in figure 1, are a result of the ATP maintenance requirement reaction. If this is the case, setting the lower bound of the ATP maintenance requirement reaction to 0 \(mmol \ (gDW)^{-1} \ hr^{-1}\) instead of 8.39 \(mmol \ (gDW)^{-1} \ hr^{-1}\), the default lower bound value, would remove this stepwise behavior. Indeed this is what we find, as can be seen in figure 2, which displays the behavior for growth on glucose or D-lactate with the lower bound of the ATP maintenance requirement reaction set to 0 \(mmol \ (gDW)^{-1} \ hr^{-1}\).
For our subsequent simulations, we set the lower bound of the ATP maintenance requirement reaction to the default value of 8.39 \(mmol \ (gDW)^{-1} \ hr^{-1}\), which is experimentally determined to be a realistic value [4].

Phenotypic Phase Planes of the EET Pathway

For the robustness analysis performed in Section Robustness Analysis of the EET pathway, we only varied one parameter, namely carbon source uptake flux. It is also possible to vary two parameters simultaneously and plot the results in a phenotypic phase plane [4]. We varied the parameters carbon source uptake flux and maximum allowed EET flux, as we think it is unrealistic that the EET flux is unrestricted in reality. We did this by giving the reaction Ex_Elec an upper bound for its flux. The result of this analysis can be found in figure 3.

From figure 3 we conclude that the cell does not need the EET pathway to grow anaerobically with a rather low glucose uptake flux; we make the hypothesis that this is because the fermentation pathway is activated. Glycolysis will still occur without the EET pathway and will both reduce NAD+ to NADH and synthesize ATP from ADP. However, without a pathway to transport electrons out of the cell the NADH cannot be oxidized back to NAD+. By using the fermentation pathway the cell counters this problem, as the fermentation pathway oxidizes NADH back to NAD+. NAD+ and ATP are both needed for the biomass reaction, in this reaction NAD+ is reduced to NADH and ATP is reduced to ADP. Therefore, the fermentation pathway makes the growth reaction possible and anaerobic growth without the EET pathway is realized. The metabolism of the cell in anaerobic conditions without the EET pathway, when grown on glucose can be found here.
For growth on D-lactate, the EET pathway is necessary for anaerobic growth up to a very high D-lactate uptake flux. D-lactate is oxidized to pyruvate and NAD+ is reduced to NADH in this reaction, however no ATP is synthesized from ADP, which does happen in glycolysis. Therefore, without the EET pathway, the cell will only produce some ATP from ADP in the fermentation pathway. So, a very high D-lactate uptake flux is needed to give rise to some growth. In this fermentation pathway, NADH is also oxidized back to NAD+ and therefore, growth is possible. The metabolism of the cell in anaerobic conditions without the EET pathway, when grown on D-lactate can be found in here.
The fact that the oxidation of D-lactate to pyruvate only yields the reduction of NAD+ to NADH and no production of ATP from ADP, which does happen in glycolysis, also explains the fact that growth on D-lactate yields a lower growth rate in comparison to growth on glucose.
From the phenotypic phase planes of the EET flux, we can conclude that a minimum amount of carbon uptake flux is needed to turn on the EET pathway; this is in agreement with the data of figure 1. Also, we infer from the isolines of the EET flux in region III that the EET flux is limited (as soon as growth is possible) by the maximum EET flux and not by the carbon source uptake flux. So, in this region growth is hampered by maximum EET flux. This corresponds with the results of region III in the phenotypic phase planes representing growth, where it can be seen that growth will increase when the maximum EET flux is increased.
In region II of the phenotypic phase planes, the EET flux as well as the growth rate are limited by the carbon source uptake flux.

Flux Variability Analysis

As discussed in the introduction, the flux distribution calculated by FBA is often not unique. In many cases, alternative, phenotypically different, optimal solutions are possible, because biological systems can achieve the same objective value by using alternate pathways. A method that uses FBA to identify alternate optimal solutions is Flux Variability Analysis (FVA) [4]. FVA first performs the FBA method to optimize an objective function, for instance growth. Subsequently, it bounds the relevant reaction with this found value, in this case the growth. This can be done, because it is possible to give reactions a lower and upper bound flux. So, by setting the lower and upper bound flux equal to this found value, you can bound a reaction to a specific flux.
Then, the model is given a new objective function, for instance the reaction Ex_Elec, and FVA performs the FBA method again to optimize for the minimum and maximum value of this new objective function, here the reaction Ex_Elec.
In this way, one can study the different pathways that will lead to the same optimal solution, as the results of the second FBA will still have growth equal to the optimal value found in the first FBA. So, if the minimum and maximum value of the objective function found performing the second FBA are different from each other, there are multiple pathways possible to obtain the optimal value found in the first FBA. In our case, by setting the objective function equal to growth and maximizing this objective function in the first FBA and by setting it equal to the reaction Ex_Elec in the second FBA, we investigate the different EET fluxes that are possible in our system that give maximum growth. We did this while varying both the carbon source uptake flux and maximum EET flux, so a phenotypic phase plane could be made for both the minimum and maximum values of the EET flux. However, as the difference of the maximum and minimum values of the EET flux also gives the same information, namely if there are different EET fluxes possible in our system that give maximum growth, we made a phenotypic phase plane of the difference of the maximum and minimum values of the EET flux. The result can be found in figure 4.

The result show that in the whole phenotypic phase plane, the difference of the optimized maximum value and the optimized minimum value of the reaction Ex_Elec is zero. Therefore, it can be concluded that for maximum growth for each specific combination of carbon source uptake flux and maximum EET flux, only one possible EET flux is possible for both growth on glucose and growth on D-lactate, namely the EET flux shown in figure 3.

FVA can be used to study the different pathways that will lead to the same optimal solution. As performing the FBA method while optimizing for the reaction Ex_Elec, yielded no growth (as can be read in Section Extracellular Electron Transport in the E. coli Core Model), we wondered if there are pathways possible that would yield growth.
First, we had to make sure that each specific combination of carbon source uptake flux and maximum EET flux for both growth on glucose and growth on D-lactate yielded no growth. Therefore, we created phenotypic phase planes, where we show growth when optimizing for the reaction Ex_Elec for both growth on glucose and growth on D-lactate. They are shown in figure 5.

From figure 5, we conclude that each specific combination of carbon source uptake flux and maximum EET flux for both growth on glucose and growth on D-lactate yielded no growth. So, we performed FVA for each of these specific combinations of carbon source uptake flux and maximum EET flux for both growth on glucose and growth on D-lactate.
First, we set the objective function equal to the reaction Ex_Elec and maximized it. Then we bounded the reaction Ex_Elec with this found value and set the objective function equal to growth. We minimized and maximized this objective function, while varying both the carbon source uptake flux and maximum EET flux, so a phenotypic phase plane could be made for both the minimum and maximum values of growth. However, as the difference of the maximum and minimum values of growth also gives the same information, namely if there are different growth rates possible in our system that give maximum EET flux, we made a phenotypic phase plane of the difference of the maximum and minimum values of growth rate. The result can be found in figure 6. In this figure we also plotted the maximized EET flux.

From figure 6, we conclude that the maximized growth can be classified into three distinct regions, as the phenotypic phase planes show the difference between the optimized maximum value and the optimized minimum value of growth. However, as can be seen from figure 5, the optimized minimum value of growth is zero everywhere (growth rate cannot be lower than zero) and therefore, the difference between the optimized maximum value and the optimized minimum value of growth is equal to the optimized maximum value of growth. So, the phenotypic phase planes in figure 6 also show the optimized maximum value of growth.
The results show that in the phenotypic phase planes the optimized maximized growth can be classified into three distinct regions. In region III, growth will increase when maximum EET flux is increased and/or when carbon source uptake flux is increased. In region II, it can be seen that growth decreases when the maximum EET flux is increased. When the maximum EET flux becomes even higher, the cell will transition to region I where no growth is possible. Also, it can be seen that in region II, when the carbon source uptake flux is increased, growth will become higher. So, we conclude that when maximizing the flux of the reaction Ex_Elec there are pathways possible that yield growth, namely in the regions II and III.
For the maximized EET flux, we see the regions are exactly the same as for the EET flux when maximizing for growth. However, the EET flux is 2.8 times higher and 2 times higher in comparison, for glucose and D-lactate as a carbon source, respectively.

Extracellular Electron Transport in the iJO1366 Model

In the core model of E. coli, L-lactate is not present as a metabolite. Therefore, we decided to use D-lactate as a carbon source, as D-lactate is present as a metabolite in the core model. However, the EET pathway might only be used in E. coli when L-lactate is the only carbon source, as E. coli with the EET module implemented were fed L-lactate in [5] and [6] when measuring the generated current of E. coli in experiments. Therefore, we investigated an extended model of E. coli metabolism, the iJO1366 model [3][7]. The complete iJO1366 model consists of 2584 reactions and 1806 metabolites (excluding the relevant S. oneidensis reactions we added, see Section Extracellular Electron Transport in the E. coli Core Model). This iJO1366 model contains, in contrast to the previously used E. coli Core model, L-lactate as a metabolite.

Using the extended model, we found that for glucose and D-lactate as carbon sources, the maximized growth rate agreed quite well to the previous core model simulations.
Using L-lactate as a carbon source, which was previously not possible, the model was not capable of maximizing the growth rate under anaerobic conditions. This is an indication that the cell will not be viable when given L-lactate as a carbon source. Even when the lower bound of the ATP maintenance requirement reaction was set to zero, only a steady state growth rate of \(\sim 10^{-11} \ hr^{-1}\) was found; this resembles a cell which will not die but is also not capable of growth (or rather with such a small rate that it is not noticeable). Also, the EET flux was negligibly small. Using FVA, we conclude that for maximum growth for each specific combination of L-lactate uptake flux and maximum EET flux, only one possible EET flux is possible. This EET flux for each specific combination of L-lactate uptake flux and maximum EET flux is negligibly small. Therefore, we conclude that a steady state solution in which bacteria can grow on L-lactate and use the EET pathway is not possible.

Goldbeck et al. [5] indicated that E. coli cells fed with L-lactate might not reach a steady state growth phase; this observation is consistent with our modeling results. However, in the experiments the cells do have an EET flux. Because FBA can only model for a steady state solution, we did not obtain this result using FBA. A possible way to obtain information about the experimentally observed EET flux would be by the use of dynamic flux balance analysis (dFBA), which can also model the dynamics of a system before it reaches steady state [10].

Conclusions

Initially, we performed FBA with an unrestricted EET flux and glucose, and D-lactate uptake fluxes which were equal to 18,5 \(mmol \ (gDW)^{-1} \ hr^{-1}\) (per gram dry weight per hour) and 30 \(mmol \ (gDW)^{-1} \ hr^{-1}\), respectively. Subsequently, we investigated the resulting metabolisms of the cell. We conclude that in aerobic conditions the cell does not use the EET pathway, but oxygen gets reduced instead, as it is a stronger oxidizing agent. However, in anaerobic growth the cell does use the EET pathway to export electrons out of the cell and therefore, it activates the TCA cycle and does not need to use the fermentation pathway. When the cell is grown on glucose, the growth rate will be higher than when the cell is grown on D-lactate.
The FBA method yielded only realistic results when setting the objective function equal to the Biomass Objective Function with GAM reaction, which can be seen as an equivalent of the growth rate of the cell, this reaction is specially made to be set equal to the objective function [9]. Therefore, we decided to not further pursue the method of setting the objective function equal to the Ex_Elec reaction, which, by maximizing this reaction, we can use to analyze the maximum EET flux of our system, unless we explicitly state otherwise. As in aerobic conditions the cell does not use the EET pathway, we will also only investigate anaerobic conditions, as we want the EET pathway used by the cells in order to have a measurable electrical signal for our biosensor, see the gadget section and Carbon Metabolism and Electron Transport of our wiki. .

We performed a robustness analysis of the growth rate and EET flux as a function of the amount of carbon source. We found that there is no EET flux when there is no growth and that the EET flux starts at a non-zero level as soon as there is enough glucose or D-lactate to let the bacteria grow. This behavior is due to the ATP maintenance requirement reaction, as we concluded from figure 2, where we set the lower bound of the ATP maintenance requirement reaction equal to 0 \(mmol \ (gDW)^{-1} \ hr^{-1}\) instead of 8.39 \(mmol \ (gDW)^{-1} \ hr^{-1}\), the default lower bound value.

We also varied the maximum allowed EET flux and glucose or D-lactate uptake flux simultaneously and plotted the results as a phenotypic phase planes, see figure 3. From this analysis, we found that the cell does not need the EET pathway to grow anaerobically with a rather low glucose uptake flux, because the fermentation pathway is activated. However, for growth on D-lactate, the EET pathway is necessary for anaerobic growth up to a very high D-lactate uptake flux. Therefore, we propose it is better to let the cells grow on D-lactate instead of glucose, as in this case the EET pathway is really necessary in order for the cells to have growth and we want the EET pathway used by the cells in order to have a measurable electrical signal for our biosensor, see the gadget section of our wiki. In conclusion, we think that in an experimental setting the EET pathway has a higher chance of being used when the cells are grown on D-lactate as the EET pathway is necessary in order for the cells to grow, while when grown on glucose it is possible for the cells to also use the fermentation pathway.
We also conclude from figure 3 that there are different regions in which the cell can operate. In region I, there is no growth rate and EET flux. In region II, the EET flux as well as the growth rate are limited by the carbon source uptake flux. In region III, the EET flux is limited by the maximum EET flux and not by the carbon source uptake flux. In this region growth is hampered by maximum EET flux.
In an experimental setting, it can be investigated in which region the cell actually operates. From this, it can be deduced if the EET flux and growth rate are carbon source limited or limited by the maximum possible EET flux.

From Flux Variability Analysis, the results in figure 4 show that in the whole phenotypic phase plane, the difference of the optimized maximum value and the optimized minimum value of the reaction Ex_Elec is zero. Therefore, it can be concluded that for maximum growth for each specific combination of carbon source uptake flux and maximum EET flux, only one possible EET flux is possible for both growth on glucose and growth on D-lactate, namely the EET flux shown in figure 3.
As performing the FBA method while maximizing the flux of the reaction Ex_Elec yielded no growth (as can be read in Section Extracellular Electron Transport in the E. coli Core Model and seen in figure 5), we wondered if there are pathways possible that would yield growth. So, we performed FVA, the results can be found in figure 6.
From figure 6, we conclude that the maximized growth can be classified into three distinct regions. In region III, growth will increase when maximum EET flux is increased and/or when carbon source uptake flux is increased. In region II, it can be seen that growth decreases when the maximum EET flux is increased. When the maximum EET flux becomes even higher, the cell will transition to region I where no growth is possible. Also, it can be seen that in region II, when the carbon source uptake flux is increased, growth will become higher. So, we conclude that when maximizing the flux of the reaction Ex_Elec there are pathways possible that yield growth, namely in the regions II and III.
In an experimental setting, it can again be investigated in which region the cell actually operates and if it maximizes its growth rate or its EET flux. To be able to do this, the experimental observed pathway has to be compared to the possible pathways when maximizing the flux of the reaction Ex_Elec and to the pathway when maximizing the growth rate.

Finally, we investigated an extended model of E. coli metabolism, the iJO1366 model. This model contains, in contrast to the previously used E. coli Core model, L-lactate as a metabolite.
Using the extended model, we found that for glucose and D-lactate as carbon sources, the maximized growth rate agreed quite well to the previous core model simulations.
Using L-lactate as a carbon source the model was not capable of maximizing the growth rate under anaerobic conditions. We conclude that a steady state solution in which bacteria can grow on L-lactate and use the EET pathway is not possible. This agrees with experimental results obtained by Goldbeck et al. [5]. However, in the experiments the cells do have an EET flux when grown on L-lactate. We presume this is because they are not in steady state, which cannot be modeled by FBA. A possible way to obtain information about this EET flux would be by the use of dynamic flux balance analysis (dFBA), which can also model the dynamics of a system before it reaches steady state [10].

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