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Team:Imperial College London/Modelling/Output/Detailed Description
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| Output Amplification Model | |||||||||||
Detailed DescriptionModel based on Law of Mass Action During a meeting with our advisors, it was noted that our initial models (which had assumed that our system obeyed Michaelis Menten kinetics) were wrong. This is due to the fact that Michaelis Menten kinetics does not apply to our system. In order to be able to use Michaelis Menten kinetics, there a lot of assumptions that have to be made. A few of these assumptions were not met by our system:
Since we are continuously producing enzyme, Vmax will change. Therefore the conservation E0 = E + ES does not hold for our system.
We are producing both substrate and enzyme, so we have approximately the same amount of substrate and enzyme.
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 involves writing down all of the biochemical equations and solving for these in Matlab). Change of output During our literature research, we came across a better output, so we abandoned the idea of using GFP as an output. Instead, we are using catechol. An enzyme, dioxygenase, will be acting on the catechol, which will then result in a coloured output. Catechol will be added to the bacteria manually (i.e. the bacteria will not produce catechol). Hence, in our models dioxygenase will be treated as an output as this enzyme is the only activator of catechol in our system. This means that the change of catechol into its colourful form is dependent on the dioxygenase concentration. Models Model preA: Simple production of dioxygenase
This model includes transcription and translation of the dioxygenase. It does not involve any amplification steps. It is our control model against which we will be comparing the results of other models. Model A: Activation of Dioxygenase by TEV enzyme |
This model consists of the basic enzymatic reaction: EQUATIONS 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: EQUATIONS These four equations were implemented in Matlab, using a built-in function (ode45) which solves ordinary differential equations. Implementation in TinkerCell Another approach to model the amplification module would be to implement it in a program such as TinkerCell (or CellDesigner). This would be useful to check whether the Matlab model works. |
Model B: Activation of Dioxygenase by TEV or activated split TEV enzyme |
This version includes the following features:
Model C: Further improvements This model has not been implemented because of the conclusions that we reached from Models A and B. It would include the following features:
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