Paris/Cell auto


< Paris
Revision as of 08:13, 25 October 2007 by Vieira (Talk | contribs)


Spatial simulation

We try with this work to characterize the diffusion of the DAP and the effect on the cells. We have a lawn of bacterias with germinal cells and some somatic cells, we also introduce a spatial localisation for the cells.

We make some hypothesis:

We work with a constant population (no death and no division), we can imagine that we are a stationary phase or between to division cycle.
Without DAP a cell can't do anything, so it seems that DAP wake up bacteria but it's just an artifact.
The differentiation is DAP dependent, it's append when the cell as enough DAP to evolve but not enough to divide.
The DAP is made in bacteria S, the production rate is the difference between the total production and self consummation
The DAP can be under two types intra/extra cellular (DAPi/DAPe)
The DAP is consumed in bacteria G

We have 3 bags and 2 entities in our model

  • bag

Bact it has a concentration internal of DAP (DAPi) and external (DAPe). It's a cell in our automaton
BactS is a Bact which produce DAPi
BactG is a Bact which consume DAPi

  • entity

DAPi internal value of DAP
DAPe external value of DAP

We produce this set of rules

For bactS

*DAPe = DAPe + DAPe_diffused_in_neighborhood + DAPi_diffused_from_the_BactS
*DAPi= DAPi +DAPi_produced - DAPi_diffused_from_the_BactS

For BactG

*DAPe=DAPe + DAPe_diffused_in_neighborhood - DAPi_diffused_from_the_BactG
*DAPi= DAPi -DAPi_consummate + DAPi_diffused_from_the_BactG
*BactG = if minimal DAPi for differentiation < DAPi < maximal DAPi for differentiation BactS else stay BactG

Initial state

We use a 30x30 cells automaton. All cells are BactG excepted 4 BactS which are placed randomly on the automaton


We have 8 parameters and we can add noise for each of them.
In BactS:

  • Dap export
  • Dap import
  • Dap production

In BactG:

  • Dap export
  • Dap import
  • Dap consummation
  • Minimal Dap needed for differentiation
  • Maximal Dap needed for differentiation


We use gbview to generate those pictures

The output is two animated pictures one show the differentiation the other the diffusion of DAPe

Dap diffusionBact differentiation

  • The first picture show the diffusion of DAP
We can see a front wave in light blue after that there is a dark blue area in which the systeme is stable the concentration doesn't evolve.

  • The second picture show the differentiation
Red BactG
Green BactS
The differentiation follow the wave front

In reality this phenomenon does not exist, but this model show that the low concentration of DAP induces differentiation (dark blue) and with high concentration of DAP, the differentiation is inhibited.
We can also note that the population can be stabilized, and the level of DAP remains constant in these areas.

After playing with the parameters, we can deduct 2 important things:

  • The inhibition most be strong and effective (we play with the minimal and maximal value of DAP for differentiation)
if it isn't the case the system collapse all the bactG stay BactG if the inhibition is too strong or switch to BactS if the inhibition is not enough strong.
  • The production and diffusion of DAP will be a critical factor
The DAP has to be produce then he will be exported, it will diffuse in the medium and will be imported
There is no proof of a special system to import or export DAP, so for each step there is a large amount of DAP lost.