# Paris/Stochastic models

### From 2007.igem.org

## Contents |

## Why stochastic models?

We chose to make stochastic because of the lack of knowledge (No kinetic constant or association constant aviable) . With this kind of model we just have to infer rules and chose a probability of application for it. We just need an order of time for a rule to occur (Cell division time >> gene expression time), with this we can estimate the probability.

## What have we done

We work on two kinds of stochastic models, one at the part scale the other at the device scale. Why ? because we try to follow the spirit of iGEM : we build a model for a part A (promoter) with a lot of rules (association/dissociation of the inhibitor/activator and so on) and a second part B (reporter) with another set of rules. Now we want to make a model for the device promoter::reporter we can make a huge model with all the rules... Or as we known we have models for the parts that work we can put a black box on the device and just create a set of global rules and work at the device scale.

## Which tool

All the stochastic modeling have been made with **MGS**, it is a research project in the IBISC (Laboratory for Computer Science, Integrative Biology and Complex Systems) of the University of Evry, CNRS and Genopole. (http://mgs.ibisc.univ-evry.fr)
We use MGS to produce spatial model, with independent compartments.

MGS has the notion of bag, a bag can be see as a compartment and can contain entities or other compartment, let's see with an example it will be more easier to understand.

We have an environment and we want to model the evolution of a population of bacteria and the exchange of metabolites. We need a compartment by bacteria; so bacteria is a *bag* which can divide and we got two bacteria (*2 bags*) then 4 on so on...

In the environment there is also metabolites and it can be in the bacteria or outside if we give rules for export/import the MGS will know if a metabolite is inside or outside which bacteria, we don't have to make two variables one for the inside metabolites the other for the outside metabolites, so we work directly on the number of entities and not on an average of all metabolites inside (outside) bacteria.

An other advantage of MGS is the inheritance; if we have in our population two kinds of bacteria with specific and common rules, we can create a bag *Bacteria* with the common rules and two bag *bacteria1* and *bacteria2* with their proper rules and they inherit the rules of *Bacteria*.

MGS take count of all the bags individually (the same for the entities), consequently the computation time for a cycle of division will depend of the number of bags and entities

Thanks to that we can make *simple* spatial model.

## Simple automaton

A model focused on the diffusion of DAP and the differentiation between germinal and somatic cells

## Complex automaton

A model focused on the evolution of the bacteria putting black box on the process describe by the simple automaton