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 $cplx_1$,$cplx_2$,$cplx_3$,$cplx_4$,$cplx_5$.