IGEM:IMPERIAL/2006/project/Oscillator/Theoretical Analyses/Results
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::*<b>[[IGEM:IMPERIAL/2006/project/Oscillator/Theoretical Analyses/2D Model3 Detail Analysis for Model with Bounded Growths]]</b>  ::*<b>[[IGEM:IMPERIAL/2006/project/Oscillator/Theoretical Analyses/2D Model3 Detail Analysis for Model with Bounded Growths]]</b>  
<br><br>  <br><br>  
  :<font size="4">  +  :<font size="4">'''2D Model 3bis: Bounded Prey Growth and Prey Killing '''</font size="4"> 
:::[[Image:Model3a.PNG]]  :::[[Image:Model3a.PNG]]  
  ::*We have studied this model in parallel with  +  ::*We have studied this model in parallel with Model 3. 
  ::*Instead of bounding the production of the predator, we bound the degradation of  +  ::*Instead of bounding the production of the predator, we bound the degradation of preys 
  ::*<b>[[IGEM:IMPERIAL/2006/project/Oscillator/Theoretical Analyses/2D Model3a Detail Analysis for Model  +  ::* In both cases the goal was to investigate whether the various terms of the model could balance each other and yield oscillations. 
  +  ::*<b>[[IGEM:IMPERIAL/2006/project/Oscillator/Theoretical Analyses/2D Model3a Detail Analysis for Model with bounded prey growth and degradation]]</b>  
  :  +  <br><br> 
+  :<font size="4"> '''2D Model 4: Bounded Predator and Prey Growth with Controlled Killing of Preys'''</font size="4">  
:::[[Image:Model4.PNG]]  :::[[Image:Model4.PNG]]  
  ::*  +  ::* Bounding growth and killing yielded oscillations; bounding prey and predator growths did not. 
  ::*  +  ::* We now combine both previous models and get one step closer to the final system 
::*<b>[[IGEM:IMPERIAL/2006/project/Oscillator/Theoretical Analyses/2D Model4 Detail Analysis for Model 4]]</b>  ::*<b>[[IGEM:IMPERIAL/2006/project/Oscillator/Theoretical Analyses/2D Model4 Detail Analysis for Model 4]]</b>  
  +  <br><br>  
:* '''Final 2D Model : 2D Model 5'''  :* '''Final 2D Model : 2D Model 5'''  
:::[[Image:Model5.PNG]]  :::[[Image:Model5.PNG]] 
Revision as of 10:07, 30 October 2006
Analysis of the Model of the Molecular Predation Oscillator
 Introduction
 Our Approach
 Model Simplication
 Our Results
 Conclusion
 Appendix
Our Results
 During the run of the summer 2006, we had time to study six 2dimensional Dynamical Systems. Unfortunately we lacked time to carry out a thorough analysis of the 3D model.In order of complexity, the 2D models are:
 2D Model 1: Lotka – Volterra
 2D Model 2: Bounded Prey Growth

 LotkaVolterra is far too simple to yield essential results on the complex 2D model.
 We start to investigate the influence of various components of the system by bounding the growth of the preys.
 Detail Analysis for Model with Bounded Prey Growth

 2D Model 3: Bounded Predator and Prey Growth

 Bounding the growth of the preys only stabilises the system to the extent we cannot make it oscillate anymore.
 We now seek ways to obtain oscillations by bounding the growth terms of both preys and predators.
 Detail Analysis for Model with Bounded Growths

 2D Model 3bis: Bounded Prey Growth and Prey Killing

 We have studied this model in parallel with Model 3.
 Instead of bounding the production of the predator, we bound the degradation of preys
 In both cases the goal was to investigate whether the various terms of the model could balance each other and yield oscillations.
 Detail Analysis for Model with bounded prey growth and degradation

 2D Model 4: Bounded Predator and Prey Growth with Controlled Killing of Preys

 Bounding growth and killing yielded oscillations; bounding prey and predator growths did not.
 We now combine both previous models and get one step closer to the final system
 Detail Analysis for Model 4

 Final 2D Model : 2D Model 5

 Model 4 can be made to oscillate but exhibit some very unrealistic properties. Fortunately experimental conditions lead us to introduce a final dissipative term –eU to the derivative of the prey population.
 We investigate the properties of this final 2D model and prove that the new dissipative term confers it some very interesting characteristics –among other things it prevents all the problems that may be encountered with Model 4.
 The "eU" term here is the "natural" decay rate of AHL. However, this is not mainly due to the halflife of the AHL since AHL is quite stable itself. The dominant contribution to this decay rate is the "washout" rate in the chemostat.
 AHL is small molecules that are free to move in the cells and medium. Hence it will be "washout" when we pump out the medium from the chemostat
 This will allow us to have a extra feature to change the magnitude of the parameter "e" and maybe give us a better control of the system
 Detail Analysis for Model 5