# Team:Paris/Modeling/hill approach

### From 2008.igem.org

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As a first approach, we had decided to take into account the binding to the promoters steps. Moreover, the transcription rates were expected to be Hill functions. Obvisouly, this modeling requires a huge number of parameters. To obtain them, we had planed to devise specific experiments (described below). | As a first approach, we had decided to take into account the binding to the promoters steps. Moreover, the transcription rates were expected to be Hill functions. Obvisouly, this modeling requires a huge number of parameters. To obtain them, we had planed to devise specific experiments (described below). | ||

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This part describes in detail the first approach and the codes that have been produced. | This part describes in detail the first approach and the codes that have been produced. | ||

- | + | == First Approach == | |

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As a first approximation, we have proposed a set of 5 ordinary differential equations, without taking into account the translation step. Besides, we have had not introduced yet a synchronizaton module. Therefore, the repression of FlhDC is directly modeled by the presence of the 'Z3' gene (that is the last that is turned on). | As a first approximation, we have proposed a set of 5 ordinary differential equations, without taking into account the translation step. Besides, we have had not introduced yet a synchronizaton module. Therefore, the repression of FlhDC is directly modeled by the presence of the 'Z3' gene (that is the last that is turned on). | ||

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The methods employed are described there : [[Team:Paris/Modeling/first approach| First Approach]]. | The methods employed are described there : [[Team:Paris/Modeling/first approach| First Approach]]. | ||

- | + | == More precise Bio-Mathematical Description == | |

After trying to obtain oscillations from a simple model, we have tried to described more precisely the studied system. Therefore, we have obtained the following formalism : [[Team:Paris/Modeling/description|Bio-Mathematical Description]]. | After trying to obtain oscillations from a simple model, we have tried to described more precisely the studied system. Therefore, we have obtained the following formalism : [[Team:Paris/Modeling/description|Bio-Mathematical Description]]. | ||

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## Revision as of 14:03, 12 August 2008

## Contents |

# Hill functions approach

## Introduction

As a first approach, we had decided to take into account the binding to the promoters steps. Moreover, the transcription rates were expected to be Hill functions. Obvisouly, this modeling requires a huge number of parameters. To obtain them, we had planed to devise specific experiments (described below).

Nonetheless, after reading some more articles, we have decided to change several assumptions of the modeling choice. Therefore, we have devised a perhaps more biologically relevant framework (see above).

This part describes in detail the first approach and the codes that have been produced.

## First Approach

As a first approximation, we have proposed a set of 5 ordinary differential equations, without taking into account the translation step. Besides, we have had not introduced yet a synchronizaton module. Therefore, the repression of FlhDC is directly modeled by the presence of the 'Z3' gene (that is the last that is turned on).

In this framework, we have found parameters that have provided oscillations as well as a function that automatically detects whether the output of the ode system is oscillating. This has allowed to screen a little the parameters used, in order to evaluate the robustness of the system.

The methods employed are described there : First Approach.

## More precise Bio-Mathematical Description

After trying to obtain oscillations from a simple model, we have tried to described more precisely the studied system. Therefore, we have obtained the following formalism : Bio-Mathematical Description.