Team:PKU Beijing/Modeling/Parameters

Modeling > Parameters

Parameters
Constructing ODEs is only the first step of simulating our design. The parameters, actually, play a significant role in the modeling process. Here are 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 data, 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 salicylate(food) and arabinose(bell) to make bistable turn to CI state(have memory). After a period of time, we give the E. coli arabinose 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.

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.

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) Ref: http://gchelpdesk.ualberta.ca/CCDB/cgi-bin/STAT_NEW.cgi, NTU-Singapore iGEM2008 Team
 * Transcription

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 strength of RBS can not be too extreme. Ref: http://gchelpdesk.ualberta.ca/CCDB/cgi-bin/STAT_NEW.cgi, NTU-Singapore iGEM2008 Team
 * Translation

We have assume the period of cell division is 30 mins, which means the "degradation rate" in our model is actually the sum of degradation rate of the substance(1/half life) and cell division rate(1/30 mins).
 * Cell Division Rate

From Ref1(Belasco 1993) and Ref2(Genome Biology 2006, 7:R99), we have decided that all the mRNA in our system have a half life of 4.4 mins.
 * Degradation of mRNA

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 cooperate to produce T3 RNA polymerase protein.

Overall, the sensitivity of parameters from trial and error is generally low. The bi-stable-related parameters' sensitivity indicates that the bi-stable model, which is the core in the circuit, is very stable. With all of these facts, we have concluded that this model is reasonable.

Modeling - P2
Here's our second model, the one with P2 instead of T3 RNA polymerase

Overall, the sensitivity of parameters from trial and error is also low. The bi-stable is also shows great stability. However, we consider the value in AND Gate 2 is too extreme. Although this fact doesn't indicate that the circuit design is wrong or we can't finish the weblab project theoretically, we decided that it's very necessary to construct the circuit with T3 RNA polymerase.

With all necessities prepared, it's time to see the result!