# IGEM:IMPERIAL/2006/project/Oscillator/project browser/Full System/Modelling

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- | '''[http://openwetware.org/wiki/IGEM:IMPERIAL/2006/project/Oscillator/Modelling | + | '''[http://openwetware.org/wiki/IGEM:IMPERIAL/2006/project/Oscillator/Modelling Full derivation of the above equations.]''' |

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==Graphical representation of oscillator and simulation of oscillations== | ==Graphical representation of oscillator and simulation of oscillations== |

## Revision as of 10:10, 29 October 2006

Super Parts | Not applicable | |
---|---|---|

Actual Part | ||

Sub Parts | Prey Construct | Predator Construct |

- Specifications
- Design
**Modelling**- Implementation
- Testing/Validation

## Model assumptions and relevance

- General assumptions on gene expression modelling:
- Quasi-steady state hypothesis on mRNA expression.
- Gene activation can be approximated by Hill equations.

- Assumptions linked to the quorum sensing:
- As a first approximation, we assume that luxR and AHL molecules form a heterodimer (even if it has been found that the complex formed is more complicated)
- The concentration of the heterodimer is in equilibrium with the concentration of AHL
- LuxR is constitutively produced and reaches steady state before AHL production begins. [LuxR] in the prey can be considered constant
- The degradation rate of luxR and AHL-lactonase is due to the growth dilution which, in this case, is controlled by the chemostat
- AHL is diffusing freely throughout the system

## Model description of the oscillator

- mathematical description of the oscillator:

**Full derivation of the above equations.**

## Graphical representation of oscillator and simulation of oscillations

<showhide> __HIDER__ <hide> </hide></showhide>

- link to SBML file or matlab.

## Model variables and parameters for the growth of the prey

Variables
| ||||

Name | Description | Initial Value | Confidence | Reference |
---|---|---|---|---|

AHL | homoserine lactone acting as the prey-molecule | 0 | depends how good is the control of the prey positive feedback | links |

LuxR | LuxR is constitutively produced. It forms a complex with AHL to promote production of LuxI which produces AHL | constitutively produced, AHL assumed to be 'added' when LuxR production reaches steady state | ... | links |

Parameters
| ||||

Name | Description | Value | Confidence | Reference |
---|---|---|---|---|

a | Maximum rate of production of AHL | to be characterized | to be measured | links |

a0 | ... | to be characterized | to be measured | links |

gd | AHL wash-out | variable | to be measured/can be varied by chemostat | links |

## Model variables and parameters for the growth of the predator

Variables
| ||||

Name | Description | Initial Value | Confidence | Reference |
---|---|---|---|---|

AHL | homoserine lactone acting as the prey-molecule | 0 | depends how good is the control of the prey positive feedback | links |

luxR | molecule acting as the sensing module for the predator | 0 | to be measured as we might have to deal with some leakage of the promoter | links |

aiiA | molecule acting as the killing module of the prey for the predator | to be measured | to be measured as we might have to deal with some leakage of the promoter | links |

Parameters
| ||||

Name | Description | Value | Confidence | Reference |
---|---|---|---|---|

c | maximum synthesis rate of the pLux promoter | to be characterized | to be measured | links |

c0 | dissociation constant according to Hill eq | to be characterized | to be measured | links |

gd | growth dilution | variable | to be measured/can be varied by chemostat | links |

## Model description of the killing of the prey molecule by the predator

- mathematical description of the killing of the prey:

Variables
| ||||

Name | Description | Initial Value | Confidence | Reference |
---|---|---|---|---|

AHL | homoserine lactone acting as the prey-molecule | 0 | depends how good is the control of the prey positive feedback | links |

aiiA | molecule acting as the killing module of the prey for the predator | to be measured | to be measured as we might have to deal with some leakage of the promoter | links |

Parameters
| ||||

Name | Description | Value | Confidence | Reference |
---|---|---|---|---|

b | Maximum degradation rate catalyzed by aiiA | to be characterized | to be measured | links |

b0 | Michaelis-Menten constant of enzyme reaction | to be characterized | to be measured | links |

e | AHL wash-out | variable | to be measured/can be varied by chemostat | links |

## Dynamical and sensitivity analysis

Full system modelling and analysis

## Characterization

- Characterization of the parameters a, ao shall be done using the prey test contstruct
- Characterization of the parameters c, c0 shall be done using the predator sensing test construct
- Characterization of the parameters b, b0 shall be done using the predator killing test construct
- gd[luxR], gd[AHL] and gd[AiiA] can be controlled by the chemostat washout