IGEM:IMPERIAL/2006/project/Oscillator/Theoretical Analyses: Difference between revisions
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=='''Generalities on the Model'''== | =='''Generalities on the Model'''== | ||
<big>'''Introduction'''</big> | |||
The molecular predator-prey system can be modelled by the following 3D Dynamical System <br> | *The molecular predator-prey system can be modelled by the following 3D Dynamical System <br> | ||
Refer [http://openwetware.org/images/d/d8/ModellingOurOverallSystem2.pdf here] for detail derivation | *Refer [http://openwetware.org/images/d/d8/ModellingOurOverallSystem2.pdf here] for detail derivation | ||
:::[[Image:biological model.png]] | :::[[Image:biological model.png]] | ||
<big>'''Simplified Version of the Model'''</big> | |||
*In order to make the analysis of the dynamical system easier we formalise it as follows | |||
:::[[Image:3Dmodel.png]] | :::[[Image:3Dmodel.png]] | ||
*The coordinates U,V and W respectively stand for the concentrations of AHL, aiiA and LuxR. | |||
*Their time derivatives stand for their growth rates. | |||
*The bounded growth is due to gene expression. | |||
*Degradation of the prey (AHL) is partly due to an enzymatic reaction (as shows the second term of the first equation). | |||
*Finally The model comprises dissipative terms of the model (eU,dV,dW) that are due to the washout in the chemostat. | |||
<big>'''General Remarks on the Model of Interest'''</big> | |||
*In this part we only analyse the model presented above. We do not consider its possible (and natural) extensions with an exponent in the model and with leakage terms. | |||
*From an experimental point of view, restricting our analysis makes sense. We have built test constructs to measure the growth of AHL, aiiA and LuxR as well as the degradation of AHL by aiiA. Our experimental results generally showed that our model was valid. | |||
*However, we are very aware of the pitfalls of limiting our analysis, but due to the time constrain, we will not tackle them this year. | |||
Revision as of 02:32, 30 October 2006
Analysis of the Model of the Molecular Predation Oscillator
Generalities on the Model
Introduction
- The molecular predator-prey system can be modelled by the following 3D Dynamical System
- Refer here for detail derivation
Simplified Version of the Model
- In order to make the analysis of the dynamical system easier we formalise it as follows
- The coordinates U,V and W respectively stand for the concentrations of AHL, aiiA and LuxR.
- Their time derivatives stand for their growth rates.
- The bounded growth is due to gene expression.
- Degradation of the prey (AHL) is partly due to an enzymatic reaction (as shows the second term of the first equation).
- Finally The model comprises dissipative terms of the model (eU,dV,dW) that are due to the washout in the chemostat.
General Remarks on the Model of Interest
- In this part we only analyse the model presented above. We do not consider its possible (and natural) extensions with an exponent in the model and with leakage terms.
- From an experimental point of view, restricting our analysis makes sense. We have built test constructs to measure the growth of AHL, aiiA and LuxR as well as the degradation of AHL by aiiA. Our experimental results generally showed that our model was valid.
- However, we are very aware of the pitfalls of limiting our analysis, but due to the time constrain, we will not tackle them this year.
