# Paris/Cell auto

### From 2007.igem.org

## Contents |

## 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 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**

**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**

**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**

**Initial state**

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

## **Parameters**

**Parameters**

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

## **Output**

**Output**

*We use gbview to generate those pictures*

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

- 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 (cells become green)(dark blue),then with high concentration of DAP, the differentiation is inhibited. That why some cells stay in red

We can also note that the population can be stabilized, and the level of DAP remains constant in these areas, the color of the cells doesn't change anymore and the concentration of DAP doesn't change too.

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.

## **Sources**

**Sources**