IGEM:IMPERIAL/2006/project/Oscillator/Theoretical Analysis/Introduction

Generalities on the Model

 * Introduction

The molecular predator-prey system can be modelled by the following 3D Dynamical System
 * [[Image:biological model.png]]


 * Simplified Version of the Model


 * In order to make the analysis of the dynamical system easier we formalise it as follows
 * [[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 of 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. Another part of the Imperial College IGEM project involved building test-objects to measure the growth of AHL,aiiA and LuxR as well as the degradation of AHL by LuxR. Too few measurements were carried out this year to challenge the assumptions of our model.
 * However, we are very aware of the pitfalls of limiting our analysis and suggest extending in iGEM2007. For the sake of completeness, some preliminary results on these extensions (and their consequences) are discussed in [link]. Anyone who is interested in the finest aspects of the analysis of our model are strongly advised to consult the page.