Team:Evry/Metabolism model

Introduction

In this part of our modeling work we focus on genome scale analysis of the enterobactin production pathway. A major concern about our system is its non-orthogonality with the natural metabolic network of the cells : E. coli already possesses the genes for producing enterobactins. Therefore we wanted to assess the possible interactions between our system and the bacterial metabolism.

Observations

This model stems from the following observations :

• Enterobactin production pathway is a metabolic process;
• Any of the involved metabolites may limit the rate of the reactions.

The Figure 1 presents the biochemical pathway for producing the enterobactin compound in E. coli.

As can be seen in the Figure 1 the pathway is 4 steps long and composed of six different enzymes. Hence there exists 4 possible metabolites which concentration may be limiting :

• Chorismate
• Isochorismate
• 2,3-dihydroxy-2,3-dihydrobenzoate
• 2,3-dihydroxybenzoat

Goals

We highlighted two main kind of interactions between the bacterial and our system :

1. The synthetic system interacts with the bacterial metabolism. Leading to a depletion of the metabolites involved in the pathway for the other (possibly essential) metabolic reactions of the cell.
2. The other way round, the metabolic reactions could prevent our synthetic system to work as expected by limiting the quantity of the involved metabolites available.

From these assumptions we formulated the following questions :

• Is the metabolic model of E. coli able to provide any information about the possible interactions between our system and the metabolism?
• Is the concentration of any metabolite limiting ?
• In the latter case, what is the quantity of precursor to should be added in the medium?

Materials and Methods

Model

We used the metabolic model E. coli iJR904 downloaded from the BiGG model database[1]. We chose this model because it contains all the metabolites involved in the enterobactin production pathway.

This model contains 4037 reactions and 625 metabolites but lacks the enterobactin syntase (the last reaction of the enterobactin production pathway). Thus we extended it, adding this reactions and an enterobactin output reaction to be able to consider enterobactin as a component of the model. The inserted reactions are the following:

Name	Formula
ENTSYNTH	6 ATP + 3 2,3-Dihydroxybenzoate + 3 L-Serine <=> Enterobactin + 6 AMP + 6 Diphosphate
ENTOUT	=> -1 Enterobactin

The modified E. coli iJR904 model containing these two new reactions can be found in the download section at the bottom of the page.

Network Reduction

As an analysis of the whole network is too complex, we focused our analysis on the subnetwork presented in Figure 2. We considered the CHORISMIC ACID (hereafter called CHORISMATE) as the first step of the anterobactin production pathway. This is justified by the fact that chorismate can be bought from any compound supplier (for example sigma).

We also found that it would also be possible to by the 2-3-DIHYDROXYBENZOATE compound from the same provider. This compound may be very interesting to test our constructions later as the last precursor of the pathway. For the same reason, and because it does participate in any other reaction in the used model, this compound has no interest in our metabolic modeling.

Figure 2:

The considered subnetwork of metabolic reactions of E. coli. Red arrows are reaction consuming compounds used in the ENTEROBACTIN production pathway. Arrows : reactions, circles : enzymes.

Flux Balance Analysis

The metabolic model of E. Coli is represented as a stoichiometry matrix S representing the metabolic network. Our modified version has the size 4039 (reactions) * 625 (compounds). The unknown is the flux distribution vector v, a 4039-vector representing the flow of matter (mmol/gDW/h) going through each reactions.

The Flux Balance Analysis method is about finding this flux repartition vector v given an objective function to optimize (usually the growth rate) and a set of constraints of fluxes.

Assumptions of the model

The Two assumptions at the heart of the method are the following :

1. steady state: The fluxes are considered to have attained a static equilibrium value and do not change through time.
2. No enzyme saturation: The enzymes are supposed to be not saturated, the number of enzymes is always greater than the number of the corresponding reactions happening.

Formalism

The FBA method use a representation of the metabolic reaction network in the form of a stoichiometry matrix S where :

• Each row corresponds to a reaction R_i
• Each column corresponds to a metabolite C_j

The definition of S is :

The FBA problem is then formulated as a maximisation problem under some constraints :

where :

• v is the vector of unknown reaction fluxes
• c is a vector of constants defining the objective function
• S is the stoichiometry matrix
• lowerbound and upperbound are vector of constraints (minimal and maximal flux values for each reactions)

The values for the lower and upper bounds on the flux of each reactions are either deduced from experiments or put to a very high value when unknown (most of the time) :

Tunning these boundaries allows to represent different experimental conditions, for example reducing an upper bound to a low value may represent a loss of reaction flux due to the scarcity of a certain compound.

Such optimization is then realized through a linear programming algorithm finding an approximated solution of the real optimal flux distribution (the distribution maximizing the objective function).

Software used

To perform the simulations we decided to use the cobrapy software[2] in conjunction with the GLPK (GNU Linear Progamming Kit) linear programming solver.

All the simulations of model modifications were made through python scripts, available at the end of the document.

Results

Question 1: Interractions between the artifitial system and the metabolism of E. coli

Model : E. coli iJR904 with addition of ENTSYNTH and ENTOUT reactions.

In order to test whether the system interacts with the metabolism of the bacteria we applied the FBA with a modification to the objective function:

By varying i between 0 and 1 we can vary the contributions of enterobacting production and biomass growth.

Simulation

The Figure 3 presents the results of the simulation following the previous settings.

Figure 3:

Fluxes as function of the i coefficient of the modified objective function. Dotted lines : Important fluxes; Solid lines : Reactions belonging to the ENTEROBACTIN biosynthesis pathway; Dashed lines : Other reactions consuming important metabolites.

• Setup : i varied from 0 to 1 with a step of 0.01.
• The code for this model can be found at the bottom of the page

Interpretation

The graph is divided in two parts :

i < 0.303

In this part, no ENTOUT flux is present, hence there is no production of enterobactin. In the other hand there are two non-zero constant fluxes, the CHORISMATE MUTASE (at 0.28 mmol/gDW/h) and DEOXYCHORISMATE SYNTHASE (at 0.04 mmol/gDW/h). The objective function is linearly decreasing with i meaning that the system does not change in this part.

i = 0.303

For this value of i there is a brutal change in the different fluxes :

• CHORMISMATE MUTASE flux goes to 0 mmol/gDW/h
• DEOXYCHORISMATE SYNTHASE flux goes to 0 mmol/gDW/h
• ISOCHORISMATE SYNTHASE, ISOCHORISMATASE, ENTOUT fluxes goes to their maximal values 2.1 mmol/gDW/h

The objective function f stops decreasing.

i > 0.303

After this value of i the system stays the same as proved by the linear increase of the objective function with i.

Conclusion

The production of enterobactin modifies the flux distribution for only two reactions out of 5 (the others have a nul flux) : CHORMISMATE MUTASE and DEOXYCHORISMATE SYNTHASE.
Thus there is an interaction between the enterobactin production system and the E. coli metabolism that happen at the level of these reactions.

Studying the perturbation

model: E. coli iJR904 wild type

In order to understand the type of perturbation happening two new simulations were created in which the upper bound of the fluxes going through those reactions are progressively reduced until attaining 0. The response of the system (the biomass function) is plotted against these changes in upper bound flux value.

Upper bound modification for the CHORMISMATE MUTASE reaction

Simulation

The results of the simulation are presented in

References:

1. Schellenberger, J., Park, J. O., Conrad, T. C., and Palsson, B. Ø., "BiGG: a Biochemical Genetic and Genomic knowledgebase of large scale metabolic reconstructions", BMC Bioinformatics, 11:213, (2010).
2. Ebrahim A, Lerman JA, Palsson BO, Hyduke DR. 2013 COBRApy: COnstraints-Based Reconstruction and Analysis for Python. BMC Syst Bio 7:74.

Contact: igemevry@gmail.com