Difference between revisions of "Team:Toulouse/Modeling"

To go further in the development of our project, we decided to use a method called Flux Balance Analysis (FBA) and Flux Variability Analysis (FVA). It is based on the model EC_iJO1366 [1]. This is the most recent model concerning E. coli K12 MG1655. It is a stoichiometric model defining all metabolic ways known to this day in this particular strain. It has been modificated by introducing the following pathways. Here you will find the associated XML file. The modifications we made are such that the described strain is now capable of producing butyrate.
Our modeling aims at determining the maximum butyrate and formate quantities our strain would be able to produce, depending on two initial conditions: oxygen and glucose flux. We set them as follows:

It is interesting to note that FBA provides the produced and consumed metabolites in a quantitative way.
The setpoint for oxygen flux was choosen to simulate microaerobic conditions. The glucose flux setpoint was chosen according to the results of our tests with the Biosilta kit (see “Preliminary part”).
This kit was used to ensure a stable availability of glucose over time for our bacteria. Indeed the medium contains enzymes capable of catabolizing starch, thus gradually releasing glucose in the culture.
For known initial quantities of starch and enzymes, we are able to deduce the glucose release flux. Thus, we chose the appropriate enzyme concentration and polymer quantity in order to have a glucose rate of 0.3998 mmol.gDW^-1.h^-1.

The model provides results for the metabolites flux in mmol.gDW^-1.h^-1 but it is difficult to get an idea of the actual quantity this represents so we will convert it to mmol/L. To do this we chose a length of time of 13 hours for the day and 7 hours for the night, since our solution will primarily be deployed during summer. This means that butyric acid production time is estimated to 13 hours and formic acid production time to 7 hours.
Concerning biomass it is more complicated since the bacterium grows all the time. Thus in order to ensure a minimum production, biomass concentration (X) at the beginning is defined to X = 0.56 gDW.L^-1.

$$ \textrm{Real unit} (mmol.L^{-1})= \textrm{Model unit} (mmol.gDW^{-1}\cdot h^{-1})\times X \times time $$

Another parameter has to be taken into account, and this is the acid/base balance. Indeed, our bacteria will produce the base but we are actually interested in the acid concentration. The formula below is used:

$$pH = pKa + log\frac{C_b}{C_a}$$

Finally, it should not be forgotten that FBA methods rely on a stoichiometric model. This implies that some biological realities might be overlooked.
For example, it has been demonstrated that PFL (Pyruvate Formate Lyase), one of the enzymes involved in the production of formate, is inhibited in aerobic conditions [3], a fact that is not taken into account by the Flux Balance Analysis. This can result in the model predicting a higher formate production than what will actually be observed.

Thus under the described conditions, our first object was to try to optimize butyrate production flux. As was said before, the support file of the stoichiometric model was modified in such a way as to add the lacking butyrate biosynthesis enzymes. This was done to have a model as close to our in vivo system as possible.
As expected, when we optimize the objective function (butyrate production), it shows an optimum when all the carbon available is used for butyrate production, and none goes into biomass growth. So when there is no growth, butyrate production is equal to ~0.016 mmol.L^-1, see Fig.1 (~ Flux value of 0.352 mmol.gDW^-1.h^-1).

Thus under the described conditions, our first object was to try to optimize butyrate production flux. As was said before, the support file of the stoichiometric model was modified in such a way as to add the lacking butyrate biosynthesis enzymes. This was done to have a model as close to our in vivo system as possible.
If we set a minimal value for growth rate, butyrate production drops (Fig. 2), as it can be seen on the graph below obtained for different FBA simulations. We have tried different minimal growth rates up to 0.025 which is the maximal value obtained when the objective function under FBA simulation is biomass production.

Finally, to understand the effect of the initial glucose concentration on the maximum butyrate quantity we can expect, we tested different glucose concentrations between 0.4 and 15 mmol.gDW^-1.h^-1 using FVA method (Flux Variability Analysis). Indeed, 0.4 mmol.gDW^-1.h^-1 corresponds to the glucose flux obtained with the Biosilta Kit for a culture time of 14 days, while 15 mmol.gDW^-1.h^-1 is the flux needed to reach maximum growth rate (same rates are applicable to formate, Data not shown. FBA, objective function = biomass production, Result = 0.0268).
As expected, the higher the initial glucose concentration is, the higher the level of produced metabolites will be.

The maximal production implies no growth and is equal to ~ 0.006 mmol.L^-1, Fig. 4 (~ flux value of 2,917 mmol.gDW^-1.h^-1).

As with butyrate, formate biosynthesis is unfavorably altered when a high level of constraint is applied to the minimal growth rate (Fig. 5). And formate production will be more important when glucose availability is higher (Fig. 6).

The results presented above show that we won’t be able to obtain these concentrations without optimizing our system.
In particular, we can see that to optimize either butyrate or formate production, growth level should be as low as possible. Our first solution would thus be to exert a control on this growth rate by limiting the availability of the nitrogen source in our bacteria’s environment. To test the relevance of this method we used FVA (Fig 7.).

By combining this graph with the precedent results, we are able to define the nitrogen concentration required to get the wanted growth rate, which in its turn depends on the associated butyrate and formate quantities.

Another solution to optimize the metabolites production would be to change the initial carbon source. That’s why we tested different possible carbon sources and optimized either formate or butyrate production as the objective function, keeping initial glucose flux at 0.3998 mmol.gDW^-1.h^-1. Results (Fig. 8) thus show the maximal concentrations of either butyric or formic acid we can expect (let’s note that the method used suggests that there should be no cellular growth).

According to this modeling, the use of lactose, maltose or melto-triose/-pentose/-hexaose could enable us to obtain the required formic acid concentration. More generally and with no suprise, production of formic and butyric acids will be as higher as sugar is a high carbon source. As for butyric acid, even though the aforementioned sugars yield a higher final concentration, it is still not enough. To meet our expectations, it would be interesting to work on the parameters (size, volume…) of our device and/or our trap.

Finally, we also can adjust the pH value to increase final acids concentrations. Indeed, so far, pH has been set at 7. However, for example, if we set the pH value at 6, we can increase formic and butyric acids concentrations by a factor of 10 (Fig. 9).