Team:PKU Beijing/Modeling/Parameters

Parameters

Constructing ODEs is only the first step of simulating our design. The parameters, actually, play a bigger role in the modeling process. Here's two sets of parameters(T3 RNA polymerase and P2) we used.

We have done an systematic literature review to select parameters for our model. However, not every parameter can be found from existing works, which means we have to guess part of the parameters from trial and error. To check whether we have guessed correctly, we do the sensitivity test. The sensitivity test works like this: We first give both Sal(food) and AraC(bell) to make bistable turn to CI state(have memory). After a period of time, we give the E. coli AraC stimulus and GFP output will raise after a short while. We select the highest concentration point of GFP in the second procedure. The sensitivity of a parameter is calculated by using the following equations. The closer the sensitivity is to zero, the more reasonable the parameter is. <math>Sensitivity=\frac{c_{max}^{105%}-c_{max}^{95%)}{(105%-95%)*c_{max}^{100%}}</math>

Assumptions

Our model consists of 53 parameters, which makes the modeling process very difficult. To reduce the amount of work without losing quality, we proposed the following assumptions.

• Transcription

The average transcription speed in E.coli is 70nt/s. Assuming all the transcription in our circuit works in such speed, we can calculate the maximum transcription rate for each transcription equation by using this formula: Maximum Transcription Rate = Transcription Speed(nt/min)/Gene Length(bp)=4200/Gene Length (nM/min)

• Translation

The average translation speed in E.coli is 40Aa/s. Also assuming all the translation in our circuit works in the same speed, we can calculate the theoretical transcription rate. However, in wetlab, we can use different rbs to regulate the translation process, thus, the translation rate can be written as: Translation Rate = RBS * Translation Speed(Aa/min)/Protein Length(Aa) = 2400RBS/Protein Length (min^-1) This transformation does not change the degree of freedom of our system. However, this does limit the range of parameters since the concentration of RBS can not be too extreme.

Modeling - T3 RNA polymerase

We have construct two models, the difference of which is in the AND Gate 2 module. In this section, we'll demonstrate the parameters of our first model, in which T3 RNA polymerase mRNA with amber mutation and Aa-tRNA will be consumed to produce T3 RNA polymerase protein.

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