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

Objectives

Week 6

• Get results for the output amplification models (hopefully, we can find constants; if not, we can say for which range of values our model will work)
• August 12th: Find constants
• August 13th:

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)

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).

Production 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.

Results of the Matlab simulation, setting all constants to 1

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.

LHS: Network implemented in TinkerCell, RHS: constants and results

Improved model

This version includes the following features:

• 2 amplification steps (TEV and split TEV)
• Split TEV is specified to have a and b parts
• TEVa is forbidden to interact TEVa (though in reality there could be some affinity between the two). Same for interaction between Tevb and Tevb
• Both TEV and TEVs are allowed to activate dioxugenase molecule
• Dioxugenase is assumed to be active as a monomer
• Activate split TEV (TEVs) is not allowed to activate sTEVa or sTEVb (this kind of interaction is accounted for in the next model version)
• There is no specific terms for time delays included

The MatLab code canbe found here. Note that no final conclusions should be drawn before realistic estimates for kinetic constants are included. It wasn’t done so far.

All chemical species appearing in the model	Network of the improved model
Resulting graphs part 1. Compare the production graphs of TEV (transcribed and translated from scratch and the Dioxugenase which is the final species in the whole cascade	Resulting graphs part 2.

Further improvement

This model is not implemented yet.

This version adds the following features:

• activated split TEV (TEVs) is allowed to activate not only sD but sTEVa and sTEVb

Network of the further improved model

Network of the further improved model (continued)