From 2007.igem.org

Contents 1 Introduction 1.1 We make some hypothesis: 1.2 We have 3 bags and 1 entity in our model 2 Case 1 2.1 We produce this set of rules 2.2 Initial state 2.3 Parameters 2.4 Output 3 Case 2 3.1 We produce this set of rules 3.2 Initial state 3.3 Parameters 3.4 Output 4 Sources

Introduction

The cellular automaton develop to compare diffusion of DAP and differentiation is very restrictive and unrealistic due to the lake of natural behavior of cells like growth, division, death ... As a matter of fact, a cellular automaton point of view does not allow to deal with dynamical population:

• required automaton rules to push cells and to allow divisions, are hard to carry out;

• the rigid structure of the grid prevent any topological modification of the population organization;

• somatic cells that cannot divide keep on growing and become significantly bigger that germ bacteria, a missing notion in a cellular automaton.

With this second simulation we focus on this issue. We aim at studying the impact of the cells organization on the future of the population. In order to achieve this goal, we need a mechanistic model that will allow cell to divide and die. We propose to use a masses/springs model: such model allow

• division and death by adding or removing masses,

• cell growth by increasing springs rest length,

• to fill holes in the population (if there is some empty place in the population springs will push masses to fill it),

• to prevent a dispersion of cells (springs cannot infinitely extends).

This mechanistic model has to be coupled with the biological one we previously have developed.

We first stress out the hypothesis of this simulation, we then detail the mechanistic and biological models, and finally, we simulate the system considering either a DAP controlled differentiation or a DAP independent differentiation.

We make some hypothesis:

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 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.

Sources