# IGEM:IMPERIAL/2006/project/Oscillator/project browser/Predator Construct/Modelling

Super Parts | Molecular Prey-Predator Oscillator | |
---|---|---|

Actual Part | ||

Sub Parts | Test Sensing Predator Construct | Test Killing Predator Construct |

## 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 degradation rate of luxR and aiiA is mainly due to the growth dilution.

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## Model description of the growth of the predator

- mathematical description of the predator growth and death:
- [math]\frac{d[luxR]}{dt} = \frac{c * [AHL] * [luxR]}{(c0 + [AHL] * [luxR])} - gd * [luxR][/math]
- [math]\frac{d[aiiA]}{dt} = \frac{c * [AHL] * [luxR]}{(c0 + [AHL] * [luxR])} - gd * [aiiA][/math]

- insert a graphical representation if possible (e.g. CellDesigner display)
- link to SBML file or matlab.

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

(list all the variables and parameters of the model in a table, specifying if their values are known, unknown, to be measured.)

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 | 0 | 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 | to be characterized | to be measured | links |

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

- mathematical description of the killing of the prey:
- [math]\frac{d[AHL]}{dt} = \frac{b * [aiiA] * [AHL]}{(b0 + [AHL])} - e * [AHL][/math]

## Model variables and parameters for the killing of the prey molecule by 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 |

aiiA | molecule acting as the killing module of the prey for the predator | 0 | 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 measured | links |

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

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

## Dynamical and sensitivity analysis

<showhide>

- Template__HIDER__

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- analyze model in order to show how the part could fulfill its specifications
- insert graph and charts

</hide></showhide> <showhide>

- We have decoupled the predator into sensing and killing parts
- For detail modelling, please refer to the modelling section in subparts.

## Characterization

- To characterize the part, we have to measure the production rate and aiiA enzyme activity seperately
- For details characterization, please refer to subparts