Aim: To predict the amount of GFP translated by several experimental groups.
Step:
  1.Establish ODE equations based on Mass-action law;
  2.Investigate reasonable parameter sets from the database online;
  3.Simulation;
  4.Compare the experimental data and the predicted data to find some incorrect things.

We focused on the Experimental group 4: RBS0 + CDS + RBS1 to make our first step to find how our RNA guardian will protect our RNA from 3 common kinds of exonuclease :PNPase,RNaseII,Oligoribonucle(Figure 2).We put an sketch map easy to understand according to our aim. And based on it, we establish our ordinary differential equations. Each reaction showing in the map means two objects linked to it will react, especially if only one object j linked to reaction i,that means the reaction i will happen only in object j.

Fig.1 A brief ideograph to our expectation of RNA guardian in 3’-UTR (BBa_K1059004).


Figure2. A sketch map of reactions for experimental Group 4

The reaction 1 to 7 are indicated below:



We get some useful parameters from the BRENDA database online, but some parameters are not available, so we finally choose the Turnover Numer and Km for each enzymes.


Table1. Physical & Chemical property of some enzymes related to RNA turnover.

Accroding our pre-experiment result, we adjust our parameters to fit our experiment well,and show them below:



Fig.3 The parameters we use in this turn

We put the parameters in the Simbiology in Matlab to run our Model,and we get the simulated result (Figure 3 and Figure 4)


Figure 4. Simulated result for control group


Figure 5. Simulated result for experimental Group 4

From the two figures above, we can see that the control group without the RBS1 's protection achieves RNA balance at in around 406 molecules ,and the experimental group 4 achieves the RNA balance state at around 690 molecules, more than 69% as much as the Control Group .In fact ,only two of our experimental data showing below is approximate to 69%.Others are around 20%.What we have supposed is that the ribosome argue with 3 kinds of exonuclease on RBS1 strictly, but in fact, we don't pay attention to the mechanism behind them, we just simplify it ,and may overdo. So there are some drawbacks in our model we can't overcome.NO.5 and NO.6 are measured in other situation, but we just focus on their relative increasing.


Table2.Comparison of Control Group and Experimental Group 3

Next,we try to predict the experimental group 2:


Fig.6 A brief ideograph to our expectation of RNA guardian in 5’-UTR(BBa_K1059003).


Fig.7 A sketch map of reactions for experimental Group 4



Fig.8 The parameters we use in this turn

We establish our ODE as follow:

Just to see the number of RNA better,we only plot the RNA in Figure 4 and Figure5.


Just to see the number of RNA better,we only plot the RNA in Figure 4 and Figure5.


Figure 9. Simulated result for The Experimental Group 3 (only plot the RNA).

Judging from our simulation, we can see the Control Group without RBS1 in front of RBS0 will drop down sooner than the Experimental Group 4,but the RNA balanced state is the same in aound 900 molecules.


Table3. Comparison of Control Group and Experiment Group2

From the chart we learn about the number of molecules in Experimental Group 2 is a little higher than the control group,comparing with what we have done in model 1 and model 2,we will know that is within our prediction.In mode 2, we don't take the RBS0's effciency into consideration ,but conclude that the experiment group 2 's RNA will have more risk and degrates sooner,and in Model 1,we know the RBS0 in Control Group is more effective than Experiment Group 2 though it is not obvious,so at least we can make a qualitative prediction.


Fig.10 A brief ideograph to our expectation of RNA guardian in 5’-UTR(BBa_K1059005).

It is amazing that the experimental data about experimental group 4 is much lower comparing the control group,in model 1, we guess the RBS1 may influence RBS0 so that lower the translation rate .The effect is so stong so that it may pull down the RBS1's protective effect near the 5' end.But we could not make sure our assumption correct. We shoud try once again in our futher work to confirm our RNA Guardian.


Table.4 Comparison of Control Group and Experimental Group 4