Difference between revisions of "Team:KU Leuven/Modeling/Toulouse"

We cooperated with Toulouse on the modeling. Here we describe the Flux-Balance-Analysis the Toulouse team generously performed for us.
Flux balance analysis is a widely used approach for studying the flow trough metabolic networks. In our case we are interested in the Leucine and AHL production rates of the type A cells. To obtain these values toulouse ran a FB analysis. When a FBA is set up. The metabolic network of the organism in question is represented as a matrix $\mathbf{S}$ of size $m \times n$ is filled with the stoichiometric constants of each reaction. Each of the $m$ matrix rows represents a unique compound. Similarly each of the n columns represents one unique reaction. Next a vector $\mathbf{v}$ of length $n$ is defined which contains the flux trough each reaction. Finally the vector $\mathbf{x}$ is defined to contain the concentrations of each metabolite. The steady state solution in the insteresting one therefore: $$ \frac{dx}{dt} = \mathbf{Sv} = 0 $$ Which is the nullspace of $\mathbf{S}$. In this set of solutions a maximal or minimal value can be identified using numerical optimization. In order to run the optimization algorithm a cost function has to be defined. $$ f(x) = \mathbf{c}^{T}\mathbf{v} $$ The equation above shows such a cost function. Here the vector $\mathbf{c}$ represents a weight vector. In practice it is used to choose the metabolite of interested by setting the corresponding entry to one and all others to zero. From an optimization perspective the equation $\mathbf{Sv} = 0$ represents constraints, which guide the numerical solver to the right solution.
In our case the $\mathbf{S}$ matrix comes from the in silico E. Coli model K12MG1665. The model is contained in an XML file. We told the Toulouse modelers our two reaction of interest: $$ \text{glutamate} + \text{aKIC} \rightarrow \text{aKG} + \text{Leucine} $$ This reaction is interesting as Leucine serves as repellent in our scheme. The second reaction of interest is: $$ \text{acylACP} + \text{SAM} \rightarrow \text{ACP} + \text{MTA} + \text{AHL} $$ Given this information the Toulouse team was able to locate the reactions of interest in the XML model file, and simulate the cell metabolism. The results are:

Figure 1

AHL and Biomass production. Click to enlarge

Figure 2

AHL and Biomass production with maximal Leucine production rate.. Click to enlarge

Figure 3

Leucine and Biomass production. Click to enlarge

Figure 4

Leucine and Biomass production at AHL maximum. Click to enlarge

Colony level

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Hybrid model

Coming soon

Internal model

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Colony level

Our colony layer model relies on a Keller-Segel type system of differential equations. These equations are simulated using finite differences.

Hybrid model

Coming soon

Internal model

Coming soon