# Team:Paris/Modeling/hill approach

### From 2008.igem.org

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- | + | ==What kind of Mathematical Simulation ?== | |

We decided to use mostly Ordinary Differential Equation approach, at least for the study of the Oscillations and of the FIFO. For the Synchronisation module, we will probably use Probabilistic Differential Equations, in order to introduce the differences between the cells. | We decided to use mostly Ordinary Differential Equation approach, at least for the study of the Oscillations and of the FIFO. For the Synchronisation module, we will probably use Probabilistic Differential Equations, in order to introduce the differences between the cells. | ||

- | + | ==Bio-Chemical General Assumptions== | |

We know that the following equations do not describe properly what ''really'' happens in the cells. For exemple, we know that the transcription factor flhD-flhC is actually an ''hexamere'' flhD<sub>4</sub>C<sub>2</sub>. But, as we will surely not get access to the ''dissociation constant'' of the ''hexamerisation'', we just treat it as an ''abstract'' inducer protein ''flhDC'', with an order in its ''Hill function'' probably between 3 and 6 (but perhaps completly different; the estimation of the error by the [[Team:Paris/Modeling/Programs|'findparam']] program will tell us if we are right to do so). | We know that the following equations do not describe properly what ''really'' happens in the cells. For exemple, we know that the transcription factor flhD-flhC is actually an ''hexamere'' flhD<sub>4</sub>C<sub>2</sub>. But, as we will surely not get access to the ''dissociation constant'' of the ''hexamerisation'', we just treat it as an ''abstract'' inducer protein ''flhDC'', with an order in its ''Hill function'' probably between 3 and 6 (but perhaps completly different; the estimation of the error by the [[Team:Paris/Modeling/Programs|'findparam']] program will tell us if we are right to do so). | ||

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To see more details about the modelisation and the values of the involved constants, see [[Team:Paris/Modeling/Bibliography|the bibliography]]. | To see more details about the modelisation and the values of the involved constants, see [[Team:Paris/Modeling/Bibliography|the bibliography]]. | ||

- | + | ==Separated and detailed Parts of our Project== | |

* [[Team:Paris/Modeling/Oscillations|Oscillations]] | * [[Team:Paris/Modeling/Oscillations|Oscillations]] | ||

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* [[Team:Paris/Modeling/Synchronisation|Synchronisation]] | * [[Team:Paris/Modeling/Synchronisation|Synchronisation]] | ||

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## Revision as of 12:17, 13 August 2008

## Contents |

# Hill functions approach

## What kind of Mathematical Simulation ?

We decided to use mostly Ordinary Differential Equation approach, at least for the study of the Oscillations and of the FIFO. For the Synchronisation module, we will probably use Probabilistic Differential Equations, in order to introduce the differences between the cells.

## Bio-Chemical General Assumptions

We know that the following equations do not describe properly what *really* happens in the cells. For exemple, we know that the transcription factor flhD-flhC is actually an *hexamere* flhD_{4}C_{2}. But, as we will surely not get access to the *dissociation constant* of the *hexamerisation*, we just treat it as an *abstract* inducer protein *flhDC*, with an order in its *Hill function* probably between 3 and 6 (but perhaps completly different; the estimation of the error by the 'findparam' program will tell us if we are right to do so).

For the moment, at each part of our modelisation, we reduce the expression of a gene at its **transcription**. The **translation** process is not taken into acount.

To see more details about the modelisation and the values of the involved constants, see the bibliography.

## Separated and detailed Parts of our Project