Difference between revisions of "Team:Toulouse/Modeling"

One of the aim of our project is to create a biological system capable of producing two naturally occurring molecules: butyric acid and formic acid.
Before starting modelling, it can be helpful to get a panoramic view of both all known metabolic pathways and those specific of E. coli. The following metabolic network represents all known metabolites and metabolic pathways for E. coli K12 MG1655 (best known model) as of today. It was obtained from the KEGG database. Our first step was to identify the pathways from which our molecules will be derived, in order to have a clear understanding of their potential role and effects when produced or overproduced.

Formate is naturally produced by E. coli but at low levels. Our project requires that Apicoli produces quite high yields of formate. Hence in order to optimize formate biosynthesis we studied the genes coding for the enzymes involved in the pathway. We decided to focus our efforts on the Pyruvate Formate Lyase (PFL), the enzyme that causes degradation of pyruvate, thus yielding formate.

The subnetwork presented below was obtained from MetExplore platform and presents all reactions from the KEGG and ByoCyc databases involved in the production or consumption of formate. This map will help us predict the likely consequences of a PFL-induced formate overproduction in Apicoli. In fact, formate is harmful to our bacterium and is normally metabolized to other products to prevent toxicity effects and redox imbalance. We thus have to find the balance between producing enough formate to kill the varroa without killing Apicoli.

Contrary to formate, butyrate is not naturally produced by E. Coli. E. coli possesses an enzyme called (Butyryl-coA transferase (or Acetate-coA transferase) that yields butyrate, but this reaction cannot happen spontaneously in the organism due to the lack of butanoyl-coA, its substrate (Fig. 5). A careful analysis of the biosynthesis pathway shows that the enzymes responsible for Butanoyl-coA production (EC.2.1.3.19 phosphate butyryltransferase , EC.1.3.1.44 trans-2-enoyl-CoA reductase (NAD+) , etc.) cannot be found in our strain. Hence, in order to obtain butyrate, we chose to introduce a complete production pathway relying on genes originating from different organisms in Apicoli (see Attract).

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. EC_iJO1366 is a stoichiometric model defining all metabolic paths (as of today) in this particular strain. We modified this model to incorporate the various enzymes that we wanted to introduce in order to produce butyrate. The following link contains the newly built XML file.
Our model aims at determining the maximum butyrate and formate quantities that our strain could 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 set point for oxygen flux was chosen to simulate microaerobic conditions. The glucose flux set point was chosen according to the results of our tests with the Biosilta kit (see “Preliminary part”).
This kit was used to ensure a stable delivery of glucose over time (constant flux) for our bacteria. The medium contains enzymes capable of catabolizing starch, thus gradually releasing glucose into 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 0.4 mmol.gDW^-1.h^-1.

The model provides results for the metabolites flux in mmol.gDW^-1.h^-1 which we converted in mmol/L. To do this we chose a time period of 13 hours for the day and 7 hours for the night, since our solution will primarily be deployed during the summer. This means that butyric acid production time is estimated to be 13 hours and that formic acid production time is set 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: the acid/base balance. For each of our two acidic molecules, the bacteria will actually produce the associated base. However, it is the acid concentration that we are interested in. 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.

Under the described conditions, our first objective was to try to optimize butyrate production flux. As was said before, the support file of the stoichiometric model was modified to add the lacking butyrate biosynthesis enzymes.
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 ~0.02 mmol.L^-1, see Fig.1 (~ Flux value of 0.3 mmol.gDW^-1.h^-1).

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). 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 = 0.03).
As expected, the higher the initial glucose concentration, 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 0.4 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 modelling, 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 surprise, production of formic and butyric acids will be higher as the sugar given will contain more carbons. 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).