# IGEM:IMPERIAL/2006/project/Oscillator/Theoretical Analyses/Conclusion

Analysis of the Model of the Molecular Predation Oscillator

**Conclusion**

**Overview of our Results on the Molecular Predation System**

- We haven't carried out the full study of the 3D model of Molecular Predation System
- Instead we have used some biologically justifiable hypotheses to simplify the model to a 2D model
- We have also carried out a complete theoretical study of the 2D system and are now able to predict for every combination of parameters how the
**Molecular Predation System**will behave. - In particular we have proved that the Molecular Predation System can operate in two modes:

- - It can work as an oscillator (oscillating around unique limit cycle)
- - It can work in stable regime (both prey and predator populations converge to limit value)

**What was learnt from modifying the model**

- Oscillations are the results of a subtle balance between the growth terms and degradation terms of the system.
- Oscillations appeared to be mainly due to balancing the growth and degradation terms of the preys
- The washout terms in the model were crucial to control the system

** Examples of Oscillations with the Molecular Predation System**

**Control of the Oscillations of the Molecular Predation Oscillator**

Control of the oscillations is not as simple as with Lotka-Volterra, but simulations show that we have **good control over the amplitude** and **total control over the frequency** as shown below.

**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

- These assumptions are reasonable a first sight. However, some preliminary results (available in

**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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