The signaling circuit

The signaling circuit 3 described in the Circuit Section has been modeled using Matlab Simbiology desktop. The following diagram shows the different parts of the model we have simulated:

For the level of detail considered, the main parts simulated are the following (the number correspond to the equations listed in the table in the next section):

Generation of L_aspartate induced by AAL
Diffusion of L_aspartate through the cell wall
Transcription of the aspA, promoted by FecI_a (active)
Translation of aspA
Activation of FecI, induced by the activation of FecR
Activation of FecR induced by FecA-PrhA
Plant cell wall lingand, FecA-PrhA binding

Reactions

The reaction equations for the previous parts, and the reactions rates associated, are summarized in the following table:

#	Reaction	ReactionRate	Active
1	ecoli.ammonia + ecoli.fumarate + ecoli.AAL <-> ecoli.L_aspartate + ecoli.AAL	k1ecoli.ammoniaecoli.fumarateecoli.AAL - k2ecoli.L_aspartate*ecoli.AAL	true
2	ecoli.L_aspartate <-> medium.L_aspartate	kWallDiffusionecoli.L_aspartate - kWallDiffusionBackmedium.L_aspartate	true
3	ecoli.DNAaspA + ecoli.FecI_a -> ecoli.ARNm_aspA + ecoli.DNAaspA + ecoli.FecI_a	kTranscriptecoli.DNAaspAecoli.FecI_a	true
4	ecoli.ARNm_aspA -> ecoli.AAL + ecoli.ARNm_aspA	kTranslation*ecoli.ARNm_aspA	true
5	ecoli.FecR_a + ecoli.FecI <-> ecoli.FecI_a + ecoli.FecR_a	kFecIActivationecoli.FecR_aecoli.FecI - kFecIDeactivationecoli.FecI_aecoli.FecR_a	true
6	ecoli.FecR + ecoli.[ligand:FecA-PrhA] <-> ecoli.FecR_a + ecoli.[ligand:FecA-PrhA]	kFecRActivationecoli.FecRecoli.[ligand:FecA-PrhA] - kFecRDeactivationecoli.FecR_aecoli.[ligand:FecA-PrhA]	true
7	plant_cell_wall.ligand + ecoli.[FecA-PrhA] <-> ecoli.[ligand:FecA-PrhA]	kCellBindingplant_cell_wall.ligandecoli.[FecA-PrhA] - kCellUnbinding*ecoli.[ligand:FecA-PrhA]	true

Simulations

The following figure shows the typical evolution of the output of the system (the generated chemoattractant) againts the inputs (the wall cells ligand and the FecA-PrhA components on the outer membrane)

Analysis

Sensibility

Simbiology allows to compute the sensibility of the system against the different parameters.

The following figure shows the sensibility of all state variables (molecules of the different species considered) with respecto to all the parameters.

What the analysis reveal is that the system is quite insensitive to changes in the parameters. This is due mainly to the nature of the transduction signals. The promoters act as a kind of "switch". This means that, provided these promoters reach certain levels, the other parts of the circuits are activated, even if the levels are not equal.

This analysis is referred to the steady-state of the system. Some parameters do not affect the final steady-state number of molecules, but on the other hand affects the velocity of the system in the transition. This can be seen in the following paragraphs.

Temporal evolution

If we perform a scan over several values of some parameters it can be seen the influence of these parameters on the output. For instance, in the following figure it can be seen how the parameter kCellBinding (the "force" of the binding with the cell wall) affects the final output of the system (medium.L_aspartate, the amount of chemoattractant), for several scales of magnitude.

This parameter affects the velocity of the system, but not in great deal. In the following, the same analysis is done for the four main steps in the generation of the chemoattractant (for quite different orders of magnitude):