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.

At each stage of amplification a distinct protease is being used

At each stage of amplification a distinct protease is being used

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TEV is used at both stages of amplification

TEV is used at both stages of amplification

Second attempt

Model improved to account for the enzymes (protease action)

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, we cannot use the Michaelis-Menten model and we 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:

1. [T'] = -k1[T][sD] + (k2+k3)[TsD] + sT - dT[T]
2. [sD']= -k1[T][sD] + k2[TsD] + ssD - dsD[sD]
3. [TsD'] = k1[T][sD] - (k2+k3)[TsD] - dTsD[TsD]
4. [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 enzymatic amplification above would be to implement it in a program such as TinkerCell (or CellDesigner).