# Paris/Cell auto 2

## Spatial simulation

We try with this work to characterize the effect on the cells, of the DAP diffusion in a free space where cells can divide or die.
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.
as we can see in the simple automaton the diffusion mechanism and the effect on differentiation can be describe more accurately, so for the moment we just ignore the diffusion putting a black box on it and just focused on the total number of DAP entities.

## 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 consumed in bacteria G

All the cells grow

## We have 3 bags and 1 entity in our model

• bag

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

• entity

DAP Value of DAP

# Case 1

## We produce this set of rules

Mechanic forces

• We create a spring between the center of each Bact, 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
• DivG probability of division
• CroitG probability of growth

## Output

We use imoview to generate those movies

The output is two videos showing the evolution of the organism

• The first video show a first comportment
Red : BactG
Green : BactS
dark<->light Bact : low<->high DAP
The number of bacteria (G or S) increase with the time
• The second video show a second comportment
Red BactG
Green BactS
dark<->light Bact : low<->high DAP
The number of cells is constant and maintains itself

After playing with the parameters we can isolate 4 kinds of comportment.
2 of them are not really interested the system doesn't evolve or collapse (all the bacteria become S type).
The other 2 comportment show that our system can lead to an evolving organism developing itself and colonizing the environment or it can stay stable like a tissue or an organ.

# Case 2

## We produce this set of rules

Mechanic forces

• We create a spring between the center of each Bact, 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 random< probability of differentiation then
BactG=BactS
else
if size > max size then
if probability to divide > random & DAP'> minimal needed to divide then
BactG = 2 BactG with minimal size
else
if random < probability to grow then
BactG = BactG + {new size= size + delta}
else
nothing
else
BactG = BactG + {DAP=DAP'}
```

## Initial state

6 BactS and a BactG in the middle for the first result 5 BactS and 2 BactG for the second result

## 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
• DivG probability of division
• CroitG probability of growth

## Output

We use imoview to generate those movies

The output is two videos showing the evolution of the organism

• The first video show a first comportment
Red : BactG
Green : BactS
dark<->light Bact : low<->high DAP
The number of bacteria (G or S) increase with the time
• The second video show a second comportment
Red BactG
Green BactS
dark<->light Bact : low<->high DAP
The number of cells is constant and maintains itself

After playing with the parameters we can isolate 4 kinds of comportment.
2 of them are not really interested the system doesn't evolve or collapse (all the bacteria become S type).
The other 2 comportment show that our system can lead to an evolving organism developing itself and colonizing the environment or it can stay stable like a tissue or an organ.