IGEM:IMPERIAL/2006/project/Oscillator/Theoretical Analyses/Conclusion
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Analysis of the Model of the Molecular Predation Oscillator
Conclusion
- General Conclusion of our Studies
- Existence limit cycles
- Influence of parameters
- What was learnt from modifying the model
Future Works
Future Works on the 2D Model
- The normalised 2D model of the molecular predation oscillator has been extensively studied.
- Some more work on the oscillator still needs doing however
- The most important work remaining on the normalised 2D model concerns the characterisation of the output of the oscillator with regards to the model parameters
- - Amplitude
- - Frequency
- - Profile (measures of shape in phase diagrams or time diagrams)
- To be complete the characterisation should also be dome with the experimental constraints in mind (e.g: washout cannot be infinitely small)
Extensions to the 2D Model
- The model of the molecular predation oscillator overlooks the leakage terms and does not comprise any exponent in the growth terms.
- With these new terms the dimensionless model would look like
- These assumptions are reasonable a first sight. However, some preliminary results (available in Future Works on the 2D Model) suggest that the oscillator is very sensitive to the assumption on the exponent.
- We therefore suggest carrying out a thorough analysis of the extended model next year
Future Works on the 3D Model
- We only studied the case when d1=d2 and thus simplified the 3D model into 2D
- At the very least the study should be extended to the vicinity of d1=d2
- Ideally the whole 3D system would be studied
- NB: the complexity of the study will increase dramatically
- - Making sure steady points are unstable is not enough
- - We need a solid criterion on how to get a cycle
Stochastic Analysis
- What is the influence of the distributions of gene-expression parameters such as ao,bo,co?
- We may in practice need to drop the Dynamical System approach and go fully stochastic
- An entirely new level of complexity!!!!!
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