Paris/Cell auto 2

From 2007.igem.org

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<br>
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We have 8 parameters and we can had noise for each of them.<br>
We have 8 parameters and we can had noise for each of them.<br>
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'''Mechanic'''<br>
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*DT time step<br>
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*K constant of the spring<br>
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*Mu variation of position<br>
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*R0_Gm minimal size of a BactG (after division)
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*R0_G maximal size of a BactG (before division)
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*R0_S maximal size of BactS
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<br>
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'''In Bact'''<br>
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*Diff diffusion constant<br>
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<br>
'''In BactS:'''<br>
'''In BactS:'''<br>
-
*Dap export<br>
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*Diffp probability of differentiation<br>
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*Dap import<br>
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*DEPOT production of DAP<br>
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*Dap production<br>
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*DeathSP probability of death <br>
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*CroitS probability of growth <br>
<br>
<br>
'''In BactG:'''<br>
'''In BactG:'''<br>
-
*Dap export<br>
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*CONS Dap consumed<br>
*Dap import<br>
*Dap import<br>
*Dap consummation<br>
*Dap consummation<br>
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*Maximal Dap needed for differentiation<br>
*Maximal Dap needed for differentiation<br>
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<br><br><br>
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=='''''Output'''''==
=='''''Output'''''==
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<br>

Revision as of 13:01, 22 October 2007




Contents

Spacial simulation

We try with this work to characterize the diffusion of the DAP and the effect on the cells. We have a growing culture with germinal cells and somatic cells.
We want to see if we can have different kinds of evolution for our cells

We make some hypothesis:

We work with a evolving population ( death for BactS and division BactG).

  • Case 1 : The differentiation is DAP dependent, it's append when the cell as enough DAP to evolve but not enough to divide.
  • Case 2 : The differentiation has a constant rate, it will be the same rate for each division cycle

The DAP is made in bacteria S, the production rate is the difference between the total production and self consummation
We consider a global variable DAP (no internal/external DAP)
The DAP is comsumme in bacteria G


All the cells grow

We have 3 entities in our model

Bact it has a concentration internal of DAP and a radius. It's a cell in our automaton
BactS is a Bact which produce DAP and can grow
BactG is a Bact which consume DAP and can divide or differentiate


Case 1

We produce this set of rules


Mecanic forces

  • We create a spring betwen the center of each Bac, then we compute the forces related to this spring and we update the position of the cells (adding noise to it)

For bactS

  • if random < Probability of death then
BactS=null
else
if random < probability to grow & size < max cell size then
BactS=BactS+{new size=size+delta}
else
nothing
  • Produce DAP


For BactG

  • DAP'=DAP - self consumed DAP - diffused DAP
  • if enough DAP then
if random< probability of differentiation then
BactG=BactS
else
BactG= BactG+{DAP'}
else
if size > max size then
if probability to divide > random & DAP'> minimal needed to divide then
BactG = 2 BactG with minimal size
else BactG= BactG +{DAP=DAP'}
else
if random < probability to grow then
BactG = BactG + {new size= size + delta}
else
nothing




Initial state


4 BactS and a BactG in the middle


Parameters


We have 8 parameters and we can had noise for each of them.
Mechanic

  • DT time step
  • K constant of the spring
  • Mu variation of position
  • R0_Gm minimal size of a BactG (after division)
  • R0_G maximal size of a BactG (before division)
  • R0_S maximal size of BactS


In Bact

  • Diff diffusion constant


In BactS:

  • Diffp probability of differentiation
  • DEPOT production of DAP
  • DeathSP probability of death
  • CroitS probability of growth


In BactG:

  • CONS Dap consumed
  • Dap import
  • Dap consummation
  • Minimal Dap needed for differentiation
  • Maximal Dap needed for differentiation




Output


The output is two animated pictures one showinf the differntiation 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 differention
Red BactG
Green BactS
The differentiation follow the wave front

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 systme to import or export DAP, so for each step there is a large amount of DAP lost.
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