Difference between revisions of "Team:TJU China/Model"

Modeling is a powerful tool in synthetic biology. It provides us with a necessary engineering approach to characterize our pathways quantitatively and predict their performance,thus help us test and modify our design.Through the dynamic model of heavy-metal detection biosensor,we hope to gain insights into the characteristics of our whole circuit's dynamics.

At the beginning, on the plasmid#1, the promoter $P_{arsR}$ isn't bound with ArsR,thus it is active.ArsR and smURFP are transcribed and translated under the control of the promoters $P_{arsR_{u}}$ and $P_{arsR_{d}}$,with subscript u and d representing upstream and downstream separately.The subscript l of smURFP in the equation means leaky expression without the expression of $As^{3+}$.As ArsR is expressed gradually,it will bind with the promoter $P_{arsR}$ and make it inactive.[1]

On the plasmid#2,the fusion protein of dCas9 and RNAP(RNA polymerase) are produced after transcription and translation,and sgRNA is produced after transcription.

dCas9(*RNAP) can bind with its target DNA sequence without cutting, which is at the upstream of the promoter $P_{arsR_{d}}$.Simulataneously,dCas9 can lead RNAP to bind with the promoter $P_{arsR_{d}}$ and enhance the transcription of smURFP.However,because the promoter $P_{arsR_{d}}$ has already bound with ArsR,as a result,RNAP can't bind with the promoter $P_{arsR_{d}}$. can’t bind with the promoter $P_{arsR_{d}}$.

However,at the presence of $As^{3+}$,it can bind with ArsR,then dissociate ArsR and $P_{arsR_{d}}$ , which makes the combination of RNAP and $P_{arsR_{d}}$ possible.

We then take degradation into account:

Applying mass action kinetic laws,we obtain the following set of differentiak equations.The several complexes involved:Ars$R^*$$P_{arsR}$,$As^{3+}$,${dCas9}^*$RNAP,${dCas9}^*$RNAP:sgRNA,${dCas9}^*$RNAP:${sgRNA}^*P_{arsR}$, are respectively abbreviated as $cplx_1$,$cplx_2$,$cplx_3$,$cplx_4$,$cplx_5$.

Our simulation is based on two softwares: MATLAB (SimBiology Toolbox) and COPASI.
SimBiology Toolbox provides functions for modeling,simulating and analyzing biochemical pathways by the powerful computing engine of MATLAB.

A good biosystem should have certain stability towards fluctuations in parameters.A good model should reflect this,and hence a test for robustness can be essential to the model.
Robustness analysis can also pinpoint which reactions/parameters that are important for obtaining a specific biological behavior.A simple measure for sensitivity is to measure the relative change of a system feaure due to a change in a parameter.As for our model,the feature can be the equilibrium concentration of the smURFP(C) for which the sensitivity(S) to a parameter k is:

After analysis, we found that the concentration of smURFP is relatively sensitive to parameters such as ktx3,ktl3,ktx4,kb4,kb6,kd2,kd5, kd6,kd7,kd8,kd11, etc. Among these parameters, except for the parameters that directly affect the production and degradation of smURFP,the rest of them are all related to dCas9-RNAP:sgRNA. It shows that our model reflects the critical role of dCas9-RNAP:sgRNA,which initially confirms our hypothesis:dCas0-RNAP can enhance transcription to increase the concentration of smURFP. However, due to the lack of previous modeling studies on dCas9-RNAP,some kinetic parameters may not be very accurate,and due to time limitation,we have not implemented experiments to measure related parameters,which may lead to some deviations in our model.
The sensitivity of each parameter is shown in the figures below.