# Paris/Cell auto 2

### From 2007.igem.org

## Contents |

## 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 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**

**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**

**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**

**Initial state**

4 BactS and a BactG in the middle

## **Parameters**

**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**

**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**

**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**

**Initial state**

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

## **Parameters**

**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**

**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.