IGEM:Imperial/2010/Modelling
Have a look at this link: Synthetic Biology (Spring2008): Computer Modelling Practicals
Have a look at Cell Designer to easily generate images of the system.
Example on how Valencia 2006 team used SimulLink to simulate their project: Valencia 2006 PowerPoint presentation
Output amplification model
First attempt
Is it better to use TEV all the way or HIV1? Modelling should allows us to take decision which design is more efficient. If taken further, it will allow us to determine number of amplification steps that are most favourable.
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Second attempt
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Implementation in Matlab
The Matlab code for the different stages of amplification and diagrams can be found [here].
Kinetic constants
| Quality | GFP | TEV | split TEV | split GFP |
|---|---|---|---|---|
| Km and Kcat | Doesn't apply | TEV constants (Km and kcat) | 40% of whole TEV | Doesn't apply |
| half-life or degradation rate | Half-life of GFP in Bacillus = 1.5 hours - ref. Chris | ? | ? | Half-life shorter than GFP |
| production rate in B.sub | ? | ? | ? | ? |
Conclusions
We couldn't obtain all the necessary constants. Hence, we decided to make educated guesses about possible relative values between the constants as well as varying them and observing the change in output.
As the result, we concluded that the amplification happens at each amplification level proposed. It's magnitude varies depending on the constants. There doesn’t seem to be much difference in substitution of TEV with HIV1.
Modified version
We cannot use Michaelis-Menten kinetics because of its preliminary assumptions, which our system does not fulfil. These assumptions are:
- Vmax is proportional to the overall concentration of the enzyme.
But we are producing enzyme, so Vmax will change! Therefore, the conservation E0 = E + ES does not hold for our system.
- Substrate >> Enzyme.
Since we are producing both substrate and enzyme, we have roughly the same amount of substrate and enzyme.
- Enzyme affinity to substrate has to be high.
Therefore, the model above is not representative of the enzymatic reaction. As we cannot use the Michaelis-Menten model we will have to solve from first principle (which just means writing down all of the biochemical equations and solving for these in Matlab).
Prodction of Dioxygenase
The reaction can be rewritten as: TEV + split Dioxygenase <-> TEV-split Dioxygenase -> TEV + Dioxygenase. This is a simple enzymatic reaction, where TEV is the enzyme, Dioxygenase the product and split Dioxygenase the substrate. Choosing k1, k2, k3 as reaction constants, the reaction can be rewritten in these four sub-equations:
- [T'] = -k1[T][sD] + (k2+k3)[TsD] + sT - dT[T]
- [sD']= -k1[T][sD] + k2[TsD] + ssD - dsD[sD]
- [TsD'] = k1[T][sD] - (k2+k3)[TsD] - dTsD[TsD]
- [D'] = k3[TsD] - dD[D]
These four equations were implemented in Matlab, using a built-in function (ode45) which solves ordinary differential equations. The Matlab code for this module can be found here.
Implementation in TinkerCell
Another approach to model the amplification module would be to implement it in a program such as TinkerCell (or CellDesigner). It would also be useful to check whether the Matlab model works.
